Chapter 1 Introduction 1.1 The self-assemblies of surfactants

Surfactants are amphiphilic molecules composed of a hydrophilic head group and a hydrophobic tail chain. The hydrophilic head group is usually a polar group, and the hydrophobic tail chain is usually a non-polar hydrophobic hydrocarbon chain. They can be orientated and arranged at interfaces, reducing surface tension.

Surfactants adsorb at air/liquid interfaces. At low concentrations, surfactants exist as monomers in aqueous solution. When the concentration increases to a certain concentration, the surfactant molecules will start to self-assemble into various aggregates in solution. This critical concentration is called CMC (critical micelle concentration). There are many types of surfactant self-assembly. As shown in Fig. 1.1, common ones include spherical micelles, wormlike micelles, vesicles and so on.

Critical packing parameter of surfactants

The molecular structure of surfactants and solvent environment have a significant effect on the shape and size of micelles. According to the concept of critical packing parameter proposed by Israelachivili [2] , the geometric shape of the aggregate can be predicted by the formula: P = v/a0l, where v is the volume of the hydrophobic chain of the surfactant; l is the maximum effective length of the hydrophobic chain, and a0 is the effective area of the hydrophilic head group in the cross section. P characterizes the molecular interface packing parameter, and different packing patterns present different aggregate morphologies. As shown in Fig. 1.2, when P ≤ 1/3, the morphology of surfactant is expected to self-assemble into spherical micelles; when 1/3 ≤ P < 1/2, it is rod-like or wormlike micelles; when 1/2 ≤ P <1, the aggregates are tubular or vesicles; when P = 1, they usually form lamellar structures.

However, P is also affected by the external environment, such as surfactant concentration, temperature, pH, and ionic strength as this changes the interactions between the surfactants. predicted by Israelachivili [2][3] 1.1.2 Spherical micelles Spherical micelles are the most common type of micelle structure. For most surfactants, when the concentration is above CMC, the surfactant will self-assemble to form spherical micelles in the aqueous solution. In the process of self-assembly, a permanently charged surfactant (positively or negatively) in an aqueous solution faces at least two opposite forces:

(1) the associative force due to the hydrophobic effect; (2) The repulsive force due to the same charge of the polar head group [4] . The interaction between surfactant molecules allows them to spontaneously form micelles in aqueous solution.

Rod-like or wormlike micelles

After increasing the surfactant concentration or adding other additives to the surfactant system, due to the adjustment of the molecular arrangement, the morphology of the aggregates will change from small spherical micelles to larger micelles accordingly. In most cases, spherical micelles grow in one-dimension, forming cylindrical or rod-like micelles. As the concentration of surfactants or the amount of added additives continues to increase, short rodlike micelles will grow in length to form elongated wormlike micelles (WLMs) [5] .

Vesicle

In water, surfactants with lower spontaneous curvate arrange in bilayers, formed of two layers of surfactants with hydrophobic groups facing inwards and hydrophilic groups facing outwards. When the bilayer is closed on itself, vesicles are formed. The structure of vesicles is similar to the structure of primitive biological cells and their size distribution is usually from 50nm to 200nm. Vesicles are of great significance in many fields, such as controlled drug release, bioseparation, and sensor [6] . The existence of surfactant vesicles greatly facilitates the study of bilayers, and play a significant role in the study of simulating biofilms and expanding the application of surfactants in biomedicine.

Other self-assemblies

In addition to spherical micelles, wormlike micelles and vesicles, Surfactants can aggregate into a whole variety of structures such as a gels [START_REF] Loos | Design and Application of Self-Assembled Low Molecular Weight Hydrogels[END_REF] , lyotropic liquid crystalline phases [8-9] , and aqueous multi-phase systems which are organized at macroscopic length-scales [START_REF] Shang | Aqueous Two-Phase System (ATPS) Containing Gemini (12-3-12•2Br -) and SDS: Phase Diagram and Properties of ATPS[END_REF][11][START_REF] Shang | Phase behavior and microstructures of the Gemini (12-3-12•2Br -)/SDS/H2O ternary[END_REF][START_REF] Shang | Effect of salts on the aqueous two-phase system in mixed solutions of Gemini (12-3-12•2Br -) and sodium dodecyl sulfate[END_REF] .

These surfactant self-assembly strucutres have a wide range of applications in gene therapy, drug carriers, chemical reactions, daily chemicals, nanomaterials, etc.

Rheological properties of surfactant solutions

Surfactant solutions exhibit complex rheological behavior. The rheological properties of surfactant solutions depend on the self-assembly structures formed, which in turn is affected by the concentrations of the surfactant and counter ion, temperature, and the presence of added salts. Understanding the relationships between the self-assembly morphology and rheological behavior of surfactant solution are of great importance to numerous applications.

Spherical and short rod-like micelles

Spherical micelles at low concentrations are Newtonian fluids at a low shear rates. At high shear rates, the solution exhibits shear thickening behavior due to the shear-induced structures [14] . With the increase of surfactant concentration, the spherical micelles grow in one direction and become short rod-like micelles. The solution still maintains the same properties as the spherical micelles except for an increased viscosity.

Wormlike micelles

When the concentration of surfactant exceeds the critical overlapping concentration of wormlike micelles (C*), the wormlike micelles begin to entangle with each other to form a dynamically reversible three-dimensional network structure. This structure remains in a dynamic equilibrium and can be continuously broken and reorganized, endowing the system with significant viscoelasticity, similar to "living" polymers [START_REF] Cates | Statics and dynamics of wormlikesurfactant micelles[END_REF] . At low shear rate, the threedimensional network structure of wormlike micelles is stable and the viscosity of them is considerable and nearly unchanged with the increase of the shear rate. The wormlike micelles undergo a shear-induced transition from a state of entangled, weakly oriented micelles to a state of highly aligned micelles above a certain critical shear rate after which shear thinning behavior is observed [START_REF] Ballesta | Superposition rheology of shear-banding wormlike micelles[END_REF] . Once the degree of cross-linking and branching of the wormlike micelles is high enough, an elastic gel is formed. For the gel structure formed by surfactants, the shear thinning behavior also occurs due to the breakage of the network structure [START_REF] Montalvo | Rheological properties of a surfactant-induced gel for the lysozymesodium dodecyl sulfate-water system[END_REF] .

The widely accepted model used to describe the viscoelastic behavior of wormlike micelles was proposed by Cates and his colleagues [START_REF] Cates | Reptation of living polymers: dynamics of entangled polymers in the presence of reversible chain-scission reactions[END_REF] . This model is mainly composed of two characteristic relaxation times: one is the breaking time τb, which is used to characterize the time for the micelle to break into two parts; the other is the reptation time τrep, which is to characterize the micelle destruction and reptation time. The dynamic viscoelastic behavior of wormlike micelles attracts interest for both basic research and technical applications. When τb >> τrep, the dissociation and repacking of micelles is a slow process. At this time, the dominant stress relaxation mechanism is reptation. The wormlike micelles behave similarly to polydisperse, non-fractured polymers and have a certain non-exponential relaxation time τR = τrep. When τrep >> τb, the micelles are in a process of continuously rapid fracture and reorganization. The wormlike micelles formed by surfactants usually have this characteristic behavior which follows the Maxwell model [START_REF] Rogers | Rheology of branched wormlike micelles[END_REF] . The long-term behavior of stress relaxation can be described by a single exponential decay, and the corresponding relaxation time calculation formula is

τ R = (τ rep τ b) 1/2 (1-1)
This single exponential viscoelastic system has simple linear rheological behavior. For this Maxwell-compliant fluid, its viscoelasticity can be characterized by the following formula [20] :

G ' (ω)=G 0 ω 2 τ R 2 1+ω 2 τ R 2
(1-2)

G '' (ω)=G 0 ωτ R 1+ω 2 τ R 2 (1-3)
G0 is the elastic plateau modulus obtained by the extrapolation method; τR is the relaxation time; G' is the elastic modulus; G" is the viscous modulus; when G" > G', the system mainly shows viscosity. When G' > G", the system mainly shows elasticity.

The Cole-Cole rule [21] is an effective method to check whether a fluid conforms to the Maxwell fluid model. The corresponding formula is as follows:

G '' +(G ' - G 0 2 ) 2 =( G 0 2 )
2 (1-4) For fluids conforming to the Maxwell model, the G'-G" curve should be a semicircle, and the diameter of the semicircle should be G0. However, due to the Rouse relaxation modes, the sample curve may deviate from the standard semicircular curve at high frequency.

Obviously, the viscoelastic behavior of the wormlike micelles can be studied by rheological methods. The characteristic parameters of the wormlike micelles can be estimated and characterized by the rheological properties of the system. The wormlike micelles formed by surfactants have been widely used in the industry due to their dynamic viscoelasticity. For example, in the process of oil recovery, the traditional polymer drilling mud will leave many holes of uneven size in the wellbore after the drilling process, reducing the efficiency of oil recovery. However, the surfactant-type drilling mud can be completely restored after the drilling process and it does not cause any damage to the system [START_REF] He | Evaluation of surfactant performance in fracturing fluids for enhanced well productivity in unconventional reservoirs using Rock-on-a-Chip approach[END_REF] . Therefore, more in-depth research on wormlike emicelles can help them better apply in various fields.

Other self-assembly structures

For the self-assembled vesicle structure of surfactant, when the vesicle concentration is low, the vesicle is a double-layer structure and the solution exhibits a Newtonian fluid behavior [23] . When the vesicle concentration is high enough, multilamellar vesicles were formed. The viscosity of the solution increases and the solution shows a shear thinning behavor without the zero-shear viscosity [START_REF] Dong | Self-assembly of onion-like vesicles induced by charge and rheological properties in anionic-nonionic surfactant solutions[END_REF] .

Gemini surfactant

Oligomeric surfactants are a type of surfactant developed in recent years. Such molecules are composed of two or more amphiphilic chains, and the amphiphilic chains are connected together by linking groups. Gemini surfactants are typical oligomeric surfactants, consisting of two hydrophobic tails and two hydrophilic head groups connected by a spacer. Bunton et al.

first reported the synthesis of this type of a surfactant, which was named "Gemini" by Menger and Littau [START_REF] Menger | Gemini-surfactants: synthesis and properties[END_REF] . Compared with traditional single-chain surfactants, Gemini surfactants have the advantages of extremely low critical micelle concentration (CMC), low interfacial tension, good solubilization ability and strong self-assembly ability and richer aggregate morphologies, etc. Because of these unique properties, Gemini surfactants are considered to be the "next generation" high-quality surfactants and are widely used in various research fields [START_REF] Menger | Gemini surfacants[END_REF][START_REF] Shukla | Cationic gemini surfactants: a review[END_REF][START_REF] Kumar | Industrial Applications of Dimeric Surfactants: A Review[END_REF] .

The structure of Gemini surfactant

Gemini surfactants are composed of two hydrophobic tails, two hydrophilic head groups, and a spacer group which links the two head groups, as shown in Fig. 1.3. The molecular structure of most Gemini surfactants is symmetric: two identical polar head groups and two hydrophobic tail chains with the same chain length. However, there are also some studies on the synthesis and self-assembly behavior of asymmetric Gemini surfactants [START_REF] Xu | Synthesis and properties of dissymmetric gemini surfactants[END_REF][30][START_REF] Oda | Aggregation Properties and Mixing Behavior of Hydrocarbon, Fluorocarbon, and Hybrid Hydrocarbon-Fluorocarbon Cationic Dimeric Surfactants[END_REF][START_REF] Huc | Gemini surfactants: studying micellisation by 1 H and 19 F NMR spectroscopy[END_REF] .

Gemini surfactants can be divided into different subcategories according to the length and composition of the hydrophobic chain, the flexibility (rigid/flexible) and structure (length and polarity) of the spacer group, and the chemical structure of the polar head group (cationic/anionic/nonionic). The hydrophobic tails of Gemini surfactants are usually composed of alkyl chains with adjustable length. The types of polar head groups and spacer groups are also rich. The polar ion head groups can be cationic quaternary ammonium salts, amine ions or anionic phosphoric acid groups, sulfate ester groups, carboxylic acid groups, and sulfonic acid groups. The polar nonionic head group can be polyether or sugar. The spacer group can be a rigid chain (short chain composed of methylene, stilbene, etc.) or a flexible chain (long hydrocarbon chain), and it can also be a polar group (polyether) or non-polar group (aliphatic, aromatic, etc.). By changing the structure or length of the hydrophobic tail chains, polar head groups and the spacer group, we can adjust the hydrophilicity, the charge and other properties of Gemini surfactants, thereby enabling Gemini surfactants to have a rich variety, unique physical and chemical properties and adaption to a variety of specific applications [START_REF] Kumar | Industrial Applications of Dimeric Surfactants: A Review[END_REF] . Gemini surfactants are classified according to their charge in aqueous solution. They can be classified into four types: cationic, anionic, zwitterionic and nonionic Gemini surfactants.

Among them, cationic surfactants play an important role in the field of self-assembly and quaternary ammonium salt Gemini surfactants are main cationic surfactants. This Gemini surfactant has a simple structure which is easy to synthesize and has excellent performance.

And because of the special structure of its head group, it presents many unique properties, such as sterilization, anti-corrosion, antistatic, etc., which cannot be replaced by other types of Gemini surfactants. Quaternary ammonium salt cationic Gemini surfactants are composed of a quaternary ammonium salt ion head group and a linear hydrocarbon tail chain, which can be expressed as m-s-m, where m and s respectively represent the number of carbon atoms in the alkyl tail chain and the number of carbon atoms of the spacer. Their molecular structure is shown in Fig. 1.4. Quaternary ammonium salt cationic Gemini surfactants have greater flexibility than the corresponding single-chain surfactants. For example, the quaternary ammonium Gemini surfactant C12-s-C12⋅2Br -(s = 2, 4, 6...20), as the methylene chain(s) grows, aggregates with different morphologies such as wormlike micelles, spherical micelles and vesicles can appear in the solution [START_REF] Lu | Effect of Hydrotropic Salt on the Assembly Transitions and Rheological Responses of Cationic Gemini Surfactant Solutions[END_REF] . Zana's group has carried out a lot of research work on the synthesis and properties of quaternary ammonium cationic Gemini surfactants, which has promoted the development of Gemini surfactants [START_REF] Zana | Dimeric and oligomeric surfactants. Behavior at interfaces and in aqueous solution: a review[END_REF] .

Fig. 1.4 Schematic structure of quaternary ammonium cationic Gemini surfactants m-s-m [START_REF] Zana | Dimeric and oligomeric surfactants. Behavior at interfaces and in aqueous solution: a review[END_REF] 1.

Properties of Gemini surfactants

Traditional surfactants have to maintain a certain distance between the molecules due to the electrostatic repulsion between their polar head groups. For Gemini surfactants, two polar head groups are connected by chemical bonds, thereby the two head groups are very tightly connected together. On the one hand, this connection greatly weakens the electrostatic repulsion between the two polar head groups. On the other hand, due to the proximity of the two alkyl chains, a strong interaction is generated between the hydrophobic tails, thereby greatly enhancing the hydrophobic binding force, which promotes the adsorption on the interface and the self-polymerization in the solution. Therefore, Gemini surfactants have many advantages over traditional surfactants [START_REF] Shukla | Cationic gemini surfactants: a review[END_REF][START_REF] Kumar | Industrial Applications of Dimeric Surfactants: A Review[END_REF][START_REF] Zana | Dimeric and oligomeric surfactants. Behavior at interfaces and in aqueous solution: a review[END_REF] .

Excellent interfacial activity

Owing to the existence of the spacer group, Gemini surfactants can overcome the separation tendency of traditional surfactants due to the electrostatic repulsion between polar ion head groups. The CMC of Gemini surfactants is usually one to two orders of magnitude lower than the corresponding single-chain surfactants. In addition, there are more efficient in reducing the surface tension at gas/water and oil/water interfaces than traditional single-chain surfactants [START_REF] Zana | Gemini surfactants: synthesis, interfacial and solution-phase behavior, and applications[END_REF][START_REF] Ao | Comparison of aggregation behaviors between ionic liquid-type imidazolium gemini surfactant [C12-4-C12im]Br2 and its monomer [C12mim[END_REF] .

Stronger self-assembly ability and richer aggregation behavior

Compared with traditional surfactants, Gemini surfactants have a stronger tendency to aggregate and more readily form self-assemblies with low curvature in solution. In addition, Gemini surfactants have a rich aggregation morphology due to the packing pattern affected by their special molecular structure. The micelles in some Gemini surfactant solutions even selfassemble into unusual shapes, such as hollow cylinders (tube), ring, disk etc. [37][START_REF] Bernheim | Microstructures in Aqueous Solutions of Mixed Dimeric Surfactants: Vesicle Transformation into Networks of Thread-Like Micelles[END_REF] . The aggregate morphology of Gemini surfactant micelles depends not only on the molecular structure of the surfactant, but as all surfactants, also on external conditions, including the concentration of the solution, temperature, ionic strength, etc.

Chen [START_REF] Chen | Temperature-induced micelle transition of gemini surfactant in aqueous solution[END_REF] observed the microstructure of the aggregates of Gemini surfactant m-3-m (m = 16, 18) at different temperatures using a transmission electron microscope, and found that the aggregation morphology of 18-3-18 in aqueous solution changes from spherical micelles to rodlike micelles and to wormlike micelles with the increase of temperature. The micelle morphology can be restored to the original structure when the temperature is lowered. However, traditional surfactants hardly exhibit such complex microstructure changes with temperature changes.

Rheological properties

The aggregate structure of surfactant molecules in aqueous solution has a direct impact on the rheological properties of the system. The self-assembly of Gemini surfactant is special and arrives at lower concentrations, therefore the rheology follows. Compared with traditional surfactants, Gemini surfactants have higher viscosity when the concentration is lower, and the viscosity and concentration are positively correlated within a certain concentration range. Zana [40] studied the rheological properties of Gemini surfactant 12-s-12 (s = 2, 3, 4) and found that when the concentration of the 12-2-12 solution exceeds 2%, an entangled wormlike micelles form is produced. The solution exhibits viscoelasticity, endowing the surfactant solution rheological properties similar to the polymer solution. However, compared with polymer solutions, the wormlike micelles formed by surfactant molecules are in a dynamic equilibrium process, so they have better shear resistance. In addition, due to their special structure, the position and properties of the spacer group of Gemini surfactants is easy to adjust, so as to control the micelle type and the rheological properties of the system.

Other advantages

In addition, compared with single chain surfactants, Gemini surfactants also have better synergistic effect, water solubility and wettability, foaming ability, more complex phase behavior with polymers and other surfactants, stronger solubilization and emulsification capabilities, and lower Krafft points. These excellent properties of Gemini surfactants make it have broad application prospects in the fields of chemical flooding, skin care, material synthesis, biomedicine, etc [START_REF] Hait | Gemini surfactants: a distinct class of self-assembling molecules[END_REF] .

Responsive self-assembly system constructed by surfactants

In the previous sections we saw that surfactants can self-assemble in aqueous solutions to form a wide variety of ordered aggregates. In some fields such as, material synthesis from surfactant templates, drug delivery and release systems in pharmaceutics, and gene transfer in biological sciences, the conversion of aggregates between different structures would be interesting [START_REF] Drummond | Surfactant self-assembly objects as novel drug delivery vehicles[END_REF] . For example, when a vesicle formed by surfactants is used as a drug delivery carrier, in order to improve the release efficiency of the drug at the target site the structure and morphology of the vesicle needs to be adjusted appropriately [43] . Small changes in external environmental conditions (such as pH, CO2, temperature, light, electric field and magnetic field, etc.) can stimulate changes in the molecular structure of the surfactant system, thereby affecting the interfacial properties of the system and the structure of the self-assembled aggregates.

Stimulation can also be used to make the system transition between different microstructures Such changes are accompanied by changes in the physical and chemical properties of the system on the macro scale, such as viscosity [START_REF] Brown | Stimuli-responsive surfactants[END_REF] . The research and application of stimulus-responsive materials constructed by surfactants has become a topic of increasing interest to scientists [45- 47] .

These stimuli can be divided into physical and chemical, as shown in Fig. 1.5. Chemical stimuli require that the responders are directly added to the system to adjust the interaction between the surfactant and the solvent molecules on the molecular scale, including redox, pH and CO2 response. The physical signal response is to adjust the self-assembly morphology of the system from outside the system by changing the kinetics and thermodynamics of the system or the interaction between molecules at specific positions, by using physical signals such as temperature, light, and electromagnetic fields [START_REF] Dai | Thermo-and photo-responsive polymeric systems[END_REF][START_REF] Stuart | Emerging applications of stimuli-responsive polymer materials[END_REF] . Therefore, we can control and adjust physical and chemical properties by changing the environmental conditions in the responsive self-assembly system (pH value, ionic strength, etc.) or applying external stimuli (temperature, light, magnetic field, electric field, etc.), so as to expand application of this system in the functional material preparation, printing and dyeing, catalysis, biomedicine, micro-control sensing [START_REF] Fameau | Responsive self-assemblies based on fatty acids[END_REF][START_REF] Xue | Soluble Main-Chain Azobenzene Polymers via Thermal 1,3-Dipolar Cycloaddition: Preparation and Photoresponsive Behavior[END_REF][START_REF] Peng | Azobenzene moiety variation directing self-assembly and photoresponsive behavior of azo-surfactants[END_REF] . There are two main ways for surfactants to participate in the construction of intelligent responsive self-assembly systems: one is to introduce stimulus-responsive functional groups into the molecular structure of surfactants, that is, to synthesize new functional surfactants; the other is to introduce environmentally responsive components into the surfactant system, and construct an environmentally responsive system by the synergistic effect between the responsive components and surfactant molecules. The pros and consof the former are obvious.

The system contains only one single component and no other additives are needed. The operation is simple and convenient. However, such surfactants often require complex synthesis, which is time-consuming and labor-intensive, and cannot effectively form ordered aggregates.

Surfactants in the latter type of system are easy to synthesize and inexpensive. Based on the non-covalent interactions between surfactants and the response molecules, including van der Waals forces, hydrogen bonds, hydrophobic/hydrophilic interactions, electrostatic forces, π-π stacking and metal-ligand coordination complexes, the self-assembly in such system is easy to adjust and control [START_REF] Zhao | CO2-controllable smart nanostructured fluids in a pseudo-Gemini surfactant system[END_REF][START_REF] Lu | Spherical-to-wormlike micelle transition in a pseudogemini surfactant system with two types of effective pH-responsive groups[END_REF][START_REF] Lin | Hydrotropic salt promotes anionic surfactant self-assembly into vesicles and ultralong fibers[END_REF] . In this dissertation, we are interested in the stimulus responsive system constructed through the synergy between surfactants and additives, which is why I will concentrate on describing such systems in the following.

Chemical signal responsive self-assembly system

Chemical signal responsive self-assembly refers to the surfactant self-assembly systems that respond to changes in chemical components or chemical properties of the system through adding extra substance into the system. The stimulus depends on a certain chemical reaction, and the responsive behavior of the system is adjusted by controlling the direction and degree of the reaction. Common chemical signal responsive self-assembly system includes the pHresponsive, CO2-responsive, redox-responsive self-assembly and so on.

pH-responsive

pH-responsive self-assembly refers to adjusting the morphology and physicochemical properties of aggregates in the system by changing the pH value in the solution. Surfactant molecules in such systems or their additives contain pH-responsive groups (such as -COOH, -NH2, -ArOH, -OPO3H2, and -PO3H2, etc.). They can change the molecular structure and the driving force for the formation of aggregates by interacting with H + or OH -and further affect the physical and chemical properties of the solution on the macroscopic level [START_REF] Lin | A facile route to design pH-responsive viscoelastic wormlike micelles: Smart use of hydrotropes[END_REF] .

A pH responsive system can be constructed by adding pH-sensitive molecules to the surfactant system. As shown in Fig. 1.6, Feng's research group [START_REF] Chu | pH-switchable wormlike micelles[END_REF] prepared a pH-responsive wormlike micelle system by simply mixing the amphiphilic molecule N-erucamidopropyl-N, N-dimethylamine with the pH-responsive molecule maleic acid (UC22AMPM). It was found that when the pH of the system increased from 6.20 to 7.29, the zero-shear viscosity of the wormlike micelles decreased by five orders of magnitude.

Fig. 1.6 pH-responsive self-assemblies constructed by surfactants [START_REF] Chu | pH-switchable wormlike micelles[END_REF] 1.4.1.2 CO2-responsive Another chemical stimulus is CO2, which has excellent biocompatibility and reproducibility, and does not contaminate products. When the absorbed CO2 is replaced by an inert gas, there is also no accumulation in the system. The CO2 response shows more advantages than the pH response [START_REF] Jessop | CO2-triggered switchable solvents, surfactants, and other materials[END_REF] . For mixed systems, the additives or surfactants containing tertiary amine groups are usually used to construct a CO2-responsive self-assembly system. Feng [START_REF] Zhang | CO2-switchable viscoelastic fluids based on a pseudogemini surfactant[END_REF] developed a CO2-responsive wormlike micelle system based on the anionic surfactant sodium dodecyl sulfate (SDS) and N, N, N', N'-tetramethyl-1,3-propanediamine (TMPDA) in a ratio of 2:1. As shown in Fig. 1.7, when CO2 is introduced into the mixed solution, the TMPDA molecule is protonated into a quaternary ammonium salt. Every two SDS molecules and a protonated TMPDA molecule are bridged together by non-covalent electrostatic attraction, forming a "pseudo" Gemini surfactant. At this time, a wormlike micelle with viscoelasticity is constructed in the system. After N2 is introduced into the system to remove CO2, the quaternized molecules are deprotonated into tertiary amines, which destroys the bridge of "pseudo" Gemini surfactant. They return to the traditional SDS molecules and reassemble into low-viscosity spherical micelles. This reversible spherical-wormlike micelle conversion can still have good CO2 responsiveness after several repeated cycles.

Fig. 1.7 CO2-responsive self-assemblies constructed by surfactants [START_REF] Zhang | CO2-switchable viscoelastic fluids based on a pseudogemini surfactant[END_REF] 1.4.1.1 Redox-responsive

In the physiological environment redox processes are widespread, which is why the redox self-assembly system has important research value. Usually, self-assembled systems with redox response contain ferrocene, sulfur atoms and other groups in their surfactants or additives. By controlling and changing the molecular redox state, the microstructure of the self-assembled body and the macroscopic properties of the system can be adjusted. Abe's group [START_REF] Tsuchiya | Control of viscoelasticity using redox reaction[END_REF] developed a redox fluid based on cationic ferrocene-based surfactant (11-ferrocenylundecyl) trimethylammonium bromide (FTMA) and sodium salicylate (NaSal). As shown in Fig. 1.8, initially, FTMA and NaSal self-assemble to form wormlike micelles. The redox active ferrocene group at the end of alkyl tail chain of FTMA can control of its chemical structure by switching between the reduced and oxidized states: the reduced ferrocene group is hydrophobic, and the oxidized ferricinium cation is hydrophilic. Therefore, the wormlike micelles are transformed into rod-like micelles after oxidization, resulting in a sharp decrease in the viscosity of the system and the loss of elasticity. Based on the control of the hydrophilic-lipophilic balance of FTMA through redox stimulation, a smart material that can switch between wormlike micelles and short rod-like micelles can be constructed.

Fig. 1.8 Redox-responsive self-assemblies constructed by surfactants [START_REF] Tsuchiya | Control of viscoelasticity using redox reaction[END_REF] 1.4.2 Physical signal responsive self-assembly system Physical stimuli can be simple, convenient, environmentally friendly and effective methods to regulate the formation and performance of aggregates. We start with a short section on temperature-responsive systems, before describing photo-responsive systems in more detail.

Temperature-responsive

The most widely used temperature-responsive surfactant system is that of temperatureresponsive fluids, i.e., systems whose flow properties change with temperature. People divide the fluids formed into two types: thermal thinning (the viscosity of the system decreases with temperature) and thermal thickening (the viscosity of the system increases with temperature).

Following the Arrhenius law, the length of the micelle decays exponentially with the increase of temperature, which leads to an exponential drop in the zero-shear viscosity of the system.

Since the thermal thinning of wormlike micelles is a very common phenomenon, surfactant self-assemblies with thermal thickening have been the focus of many researchers [START_REF] Kern | Rheological properties of semidilute and concentrated aqueous solutions of cetyltrimethylammonium chloride in the presence of sodium salicylate and sodium chloride[END_REF] . The thermal thickening behavior is mainly caused by the transformation of low-viscosity spherical micelles or vesicles into wormlike micelles with high viscosity, and the transformation of viscoelastic wormlike micelles into elastic gels. Raghavan [START_REF] Kalur | Viscosity increases with temperature in cationic surfactant solutions due to the growth of wormlike micelles[END_REF][START_REF] Davies | Self-Assembly of Surfactant Vesicles that Transform into Viscoelastic Wormlike Micelles upon Heating[END_REF] developed a thermal thickening micelle system (Fig. 1.9) by simply mixing cetyl trimethylammonium bromide (CTAB) and 5methyl salicylic acid (5MS). As the temperature increases, the self-assembly system transforms from vesicles to wormlike micelles, and the zero-shear viscosity increases by more than 1000 times. When they are heated, some anions at the aggregate/water interface are transferred to the bulk phase because heating hinders the weak physical adsorption. This desorption changes the geometry of the molecules, thereby reducing the interfacial curvature of the aggregates, resulting in a transformation of the aggregate structure.

Fig. 1.9 Temperature-responsive self-assemblies constructed by surfactants [START_REF] Davies | Self-Assembly of Surfactant Vesicles that Transform into Viscoelastic Wormlike Micelles upon Heating[END_REF] 1.4.2.2 Photo-responsive self-assembly system Photo-responsive self-assembly of surfactants requires that a component involved in the self-assembly will undergo photo-isomerization, photo-polymerization, or photo-degradation under stimulation of a specific wavelength of light, which causes a change of the structure or polarity of the photo-sensitive group. This change will affect the interaction between molecules, which will regulate their self-assembly behavior (the microstructure of the self-assembly, the phase behavior and rheology of the macroscopic system) [START_REF] Eastoe | Self-assembly of light-sensitive surfactants[END_REF] .

Compared to the stimuli introduced in the previous section, photo stimulus has many advantages. First, light is a non-invasive trigger which avoids direct contact with the sample, thereby avoiding changes in system components and in temperature. Second, light provides a wide range of adjustable parameters (such as wavelength, intensity, and duration) to manipulate the self-assembly behavior of the photo-responsive system. Third, compared with redox reagents, pH changes, salinity, etc., light is a mild, inexpensive and easily available energy source. Compared with electricity and ultrasound, light can be finely positioned in time and space. This is especially valuable in nanoscience and nanotechnology: such as sensor systems, nano-electronics, microfluidics, information storage and MEMS devices [START_REF] Fameau | Photoresponsive self-assemblies based on fatty acids[END_REF] . In Fig. 1.10, common photo-responsive additives are shown, these include azobenzene molecules, cinnamic acid molecules, and spiropyran molecules. They all have in common, that under irradiation of ultraviolet light, they absorb the energy of the excited photon, and then undergo electronic transitions and the transformation of molecular structure. These changes affect the packing pattern of the surfactant molecules in the aggregates, thereby regulating the self-assembly behavior of the system. In the next section the different types of systems will be described in more detail. [START_REF] Chu | Smart wormlike micelles[END_REF] Photo-responsive self-assemblies constructed by azobenzene

The azophenyl group is one of the typical photo-induced isomerization groups. The trans to cis isomerization of the azophenyl group in ultraviolet-visible light can be repeated many times without decomposition [START_REF] Wang | Photocontrolled Reversible Supramolecular Assemblies of an Azobenzene-Containing Surfactant with α-Cyclodextrin[END_REF] . As shown in Figure 1.11, Raghavan [START_REF] Oh | A simple route to fluids with photo-switchable viscosities based on a reversible transition between vesicles and wormlike micelles[END_REF] Fig. 1.11 Photo-responsive behavior of the EHAC-ACA system [START_REF] Oh | A simple route to fluids with photo-switchable viscosities based on a reversible transition between vesicles and wormlike micelles[END_REF] Besides the photo-thickening behavior, a large number of photo-thinning fluids that transform from relatively viscous wormlike micelles into aggregates with relatively low viscosity after exposure to ultraviolet light have also been reported. Huang's group [START_REF] Lin | Creation of photo-modulated multi-state and multi-scale molecular assemblies via binary-state molecular switch[END_REF] established a photo-controllable and adjustable polymorphic multi-scale binary self-assembly system by adding azobenzene sodium (AzoNa) to the traditional surfactant CTAB (Fig. 1.12).

With the extension of ultraviolet light irradiation time, the isomerization state of azobenzene can regulate the self-assembly from long flexible wormlike micelles to vesicles, lamellae, rodlike micelles and small spherical micelles. Therefore, the properties of the solution change significantly on a macroscopic scale. The photo-induced changes in the dipole moment and geometric configuration of the azophenyl cause the transition of the self-assembly in multi-state multi-scale. This kind of photo-regulated multi-state and multi-scale self-assembly system expands the industrial applications of photo-responsive self-assembly system, such as molecular devices, logic gates and sensors.

Fig. 1.12 Photo-responsive behavior of the AzoNa/CTAB system [START_REF] Lin | Creation of photo-modulated multi-state and multi-scale molecular assemblies via binary-state molecular switch[END_REF] Photo-responsive self-assemblies constructed by spiropyran isomers [START_REF] Minkin | Thermo-, Solvato-, and Electrochromic Spiroheterocyclic Compounds[END_REF][START_REF] Khairutdinov | Photocontrol of Ion Permeation through Bilayer Membranes Using an Amphiphilic Spiropyran[END_REF] . In Fig. 1.13, Raghavan [START_REF] Lee | Reversible photorheological fluids based on spiropyrandoped reverse micelles[END_REF] incorporated the SP into lecithin/sodium deoxycholate (SDC) reverse micelles to obtain a photo-responsive rheological fluid. Under ultraviolet light, SP is isomerized to MC, reducing the fluid viscosity by 10 times. Furthermore, Sakai [START_REF] Sakai | Adsorption Characteristics of Spiropyran-Modified Cationic Surfactants at the Silica/Aqueous Solution Interface[END_REF] studied the adsorption behavior of spiropyran-modified cationic surfactants on the silica/water solution interface and the photo-responsive properties of the assembled molecules on the interface after adsorption. Hanley [START_REF] Tangso | Novel Spiropyran Amphiphiles and Their Application as Light-Responsive Liquid Crystalline Components[END_REF] synthesized a series of surfactants with SP as the head group, and discussed the influence of the length of the hydrophobic tail chain on its physical and chemical properties and the behavior of the liquid crystal matrix, which paves the way for a stimulus response element for ultraviolet light. micelles and SP [START_REF] Lee | Reversible photorheological fluids based on spiropyrandoped reverse micelles[END_REF] Photo-responsive self-assemblies constructed by cinnamic acid Cinnamic acid molecules are also a common photo-responsive additive. In the absence of ultraviolet light irradiation, the cinnamic acid group exists stably in trans structure. When the cinnamic acid group is irradiated with ultraviolet light (wavelength around 365nm), the cinnamic acid is isomerized from the trans structure to the cis structure. This structure change can lead to an increase or decrease in solubility, as will be discussed in Chapter 3. The small changes in the photo-responsive molecular structure lead to changes in the microstructure of the aggregates of the system and the macroscopic physical and chemical properties. Compared with azobenzene molecules, cinnamic acid molecular additives have better solubility, so they can be directly compounded with surfactants, and do not need to be improved by further synthesis like azobenzene additives. It is simpler and more convenient. Compared with azobenzene additives, cinnamic acid additives have lower cost, better biocompatibility, and rich morphologies. And they are relatively stable under visible light, and are colorless and transparent. Therefore, cinnamic acid additives are an excellent choice for studying the photoresponsive self-assembly system constructed by surfactants although their response is irreversible.

(1) Photo-responsive wormlike micelles constructed by cinnamic acid Raghavan's group has done a lot of work on the photo-responsive wormlike micelles constructed by the cinnamic acid additive/surfactant mixture system [START_REF] Lee | Reversible photorheological fluids based on spiropyrandoped reverse micelles[END_REF][START_REF] Ketner | A simple class of photorheological fluids: surfactant solutions with viscosity tunable by light[END_REF][START_REF] Kumar | Photogelling fluids based on light-activated growth of zwitterionic wormlike micelles[END_REF] . As shown in Fig.

1.14, they [START_REF] Ketner | A simple class of photorheological fluids: surfactant solutions with viscosity tunable by light[END_REF] constructed wormlike micelles through the cationic surfactant CTAB and transo-methoxycinnamic acid (trans-OMCA) in alkaline solution, Under UV light, OMCA is isomerized from trans-OMCA to cis-OMCA, which changes the packing patterns of molecules at the micelle interface, resulting in the transformation of long wormlike micelles into shorter wormlike micelles or rod-like micelles. The rheological results show that the viscosity of the solution can be reduced by more than 4 orders of magnitude with the extension of the UV irradiation time. The performance of the fluid can be adjusted by changing the composition of the system and the duration of ultraviolet light irradiation, thereby expanding its potential applications in sensors and microfluidic devices.

In addition to the aqueous system, Raghavan [START_REF] Kumar | Nonaqueous photorheological fluids based on lightresponsive reverse wormlike micelles[END_REF] also reported a photo-responsive system based on reverse micelles in non-polar solutions. Dai's research group has also done a lot of research in this area [START_REF] Du | Investigation on the aggregation behavior of photo-responsive system composed of 1-hexadecyl-3-methylimidazolium bromide and 2-methoxycinnamic acid[END_REF][START_REF] Zhao | Investigation of Novel Triple-Responsive Wormlike Micelles[END_REF] . The photo-thinning fluid formed by wormlike micelles constructed 14 Photo-responsive behavior of the CTAB/trans-OMCA wormlike micelle system [START_REF] Ketner | A simple class of photorheological fluids: surfactant solutions with viscosity tunable by light[END_REF] (2) Photo-responsive vesicle constructed by cinnamic acid

Besides the reports of the photo-responsive wormlike micelles constructed by cinnamic acid salts, the photo-responsive behavior of vesicles has also been extensively studied. As shown in Fig. 1.15, Hao's group [21] studied the phase behavior and photo-responsiveness of the mixed system of tetradecyldimethylamine oxide (C14DMAO) and para-coumaric acid (trans-PCA). Their study found that when the concentration of C14DMAO in the mixed system was fixed, with the increase of PCA concentration, L1 phase (micelle), two-phase L1/La, La phase (vesicle) and La/precipitation appeared in sequence. By irradiating the area of the vesicles with ultraviolet light, the vesicles will be transformed into wormlike micelles.

Fig. 1.15 Photo-responsive behavior of the C14DMAO/trans-PCA vesicle-to-wormlike micelle system [21] Li's group [START_REF] Jia | Light-responsive multillamellar vesicles in coumaric acid/alkyldimethylamine oxide binary systems: Effects of surfactant and hydrotrope structures[END_REF] studied the photo-responsive behavior of vesicles constructed by (3) Photo-responsive lyotropic liquid crystal constructed by cinnamic acid Apart from the nano-scale wormlike micelles and vesicles in the photo response research, the meso-scale lyotropic liquid crystals constructed by cinnamic acid derivatives also have important research value. Yu's group [START_REF] Bi | Aggregation Behavior of Imidazolium-Based Surface-Active Ionic Liquids with Photoresponsive Cinnamate Counterions in the Aqueous Solution[END_REF] [PCA]/H2O binary systems [START_REF] Bi | Aggregation Behavior of Imidazolium-Based Surface-Active Ionic Liquids with Photoresponsive Cinnamate Counterions in the Aqueous Solution[END_REF] 1.4.2.3 Applications of the photo-responsive self-assembly

As shown in Fig. 1.17, photo-responsive self-assemblies have a wide range of applications in the fields of smart fluids, material synthesis, drug delivery systems, and gene transfer in biological sciences. Tian [START_REF] Long | Synergistic solubilization of polycyclic aromatic hydrocarbons by mixed micelles composed of a photoresponsive surfactant and a conventional non-ionic surfactant[END_REF] constructed a reversible solubilization system through the micelles formed by the photo-responsive surfactant AZTMA and the commercial non-ionic surfactant Tween 80 to solubilize the organic pollutants in the soil, thereby purifying the soil. This system overcomes some shortcomings of traditional surfactants in strengthening soil restoration, such as high cost and secondary pollution caused by washing agents and increases the commercial application value of photo-responsive self-assembly.

Surfactant wormlike micelle systems used for fluid drag reduction (DR) have poor heat transfer capabilities. Therefore, these fluids are only used in some circulation systems where heat exchange is not important. Based on this, Jacques [START_REF] Shi H F | Light-responsive threadlike micelles as drag reducing fluids with enhanced heat-transfer capabilities[END_REF] constructed a photo-responsive wormlike micelle system through the cationic surfactant oleyl bis(2-hydroxyethyl)methyl ammonium chloride (EO12) and trans-OMCA, which provided a potential solution for the above problems. Initially, these strong viscoelastic wormlike micellar fluids have a good drag reduction efficiency (DR efficiency up to 75%). After UV irradiation, OMCA undergoes photoisomerization from trans to cis. The liquid shows lower viscoelasticity and lower DR performance. However, its heat transfer performance is far better than the original fluid. This study highlights the possibility of cutting off DR (and thus enhancing heat transfer) at the inlet of the heat exchanger in the circulation system.

Huang [START_REF] Zhao | Smart nanocarrier: self-assembly of bacteria-like vesicles with photoswitchable cilia[END_REF] reported a bacterial-like vesicle system (C4AG@2β-CD). The ultraviolet light will trigger the development of hair on the surface of the vesicle (similar to cilia extending from the surface of bacteria). The formation of cilia causes the encapsulated drug to be released from the vesicles. This bioinspired vesicle creates a novel type of photo-responsive nano-carrier which releases active ingredients through deformation rather than complete destruction.

The hydrated structure of hydrogel makes it attractive as a bio-friendly material. Therefore, hydrogels have various potential applications in the biomedical field, such as drug delivery and tissue engineering scaffolds. Alexander [START_REF] Tomatsu | Photoresponsive hydrogels for biomedical applications[END_REF] reviewed the latest research progress of photoresponsive hydrogel systems. The transition from gel to sol under light irradiation makes photoresponsive hydrogel systems have a good application prospect in emerging biomaterials. Ehud [START_REF] Aleandri | Design of Light-Triggered Lyotropic Liquid Crystal Mesophases and Their Application as Molecular Switches in "On Demand" Release[END_REF] reported a new photo-responsive lyotropic liquid crystal system designed by the host-guest method. The system consists of monoolein (MO) and oleic acid (OA) as the host lipids and the active unit of azobenzene as the guest. The isomerization of the guest molecule is controlled by light, so as to achieve the precise control of the time, space and dosage of drug release. When a continuous release may be toxic, using this lipid biomaterial is a good alternative as an effective matrix in therapy.

Fig. 1.17 Applications of photo-response self-assembly [START_REF] Shi H F | Light-responsive threadlike micelles as drag reducing fluids with enhanced heat-transfer capabilities[END_REF][START_REF] Zhao | Smart nanocarrier: self-assembly of bacteria-like vesicles with photoswitchable cilia[END_REF][START_REF] Tomatsu | Photoresponsive hydrogels for biomedical applications[END_REF][START_REF] Aleandri | Design of Light-Triggered Lyotropic Liquid Crystal Mesophases and Their Application as Molecular Switches in "On Demand" Release[END_REF]

Bubble rise in wormlike micelles

Gas-liquid two-phase flow is widely present in chemical processes and when the gas phase dispersed in the continuous phase is in the form of bubbles it is an ideal contact method for heat and mass transfer. In typical gas-liquid contact equipment such as bubble columns, fluidized beds, and biochemical reactors, coalescence and collision of bubbles have an important impact on the internal fluid mechanics, heat transfer, mass transfer, and reaction of the equipment [START_REF] Howard | Bubbles, drops and particles in non-Newtonian fluids[END_REF] .

A comprehensive understanding of bubble rising helps to optimize equipment structure and improve process efficiency

Bubbly liquid

As shown in Fig. 1.18, gas-liquid mixtures can be divided into different regions depending on the volume fraction of gas (φgas) single bubble (φgas ≈ 0), bubbly liquid (φgas < 64%), wet foam (64% < φgas < 85%) and dry foam (φgas > 95%). When the gas fraction is below 64%, the bubbles can remain spherical, and such suspensions are called bubbly liquids. Bubbly liquids are unstable dispersions, as the bubbles rise rapidly because of gravity and turn it into a wet foam. Since the gas phase and the liquid phase are immiscible, the surface tension σ must be considered. For the bubble, ηd and ρd are practically zero. it is generally believed that when ignoring the wall effect, the shape of freely rising bubbles in the fluid mainly depends on the following dimensionless parameters:

Re = ρ c v s d e 2 η c
(1-6)

Eo = ρ c gd e 2 σ
(1-7)

Mo = gη c 4 ρ c σ 3 (1-8)
where, Re is the Reynolds number; Mo is the Morton number; Eo is the Eötvös number; ρ is the density; η is the viscosity; de is the bubble equivalent diameter; g is the acceleration of gravity;

σ is the surface tension; the subscripts c and d represent the continuous phase and the dispersed phase, respectively; dv and dh are the diameter of the bubble in the vertical and horizontal directions.

Grace and Weber [START_REF] Clift | Bubbles, Drops and Particles[END_REF][START_REF] Bhaga | Bubbles in viscous liquids: shapes, wakes and velocities[END_REF][START_REF] Grace | Shapes and velocities of single drops and bubbles moving freely through immiscible liquids[END_REF][START_REF] Grace | Hydrodynamics of Liquid Drops in Immiscible Liquids[END_REF] summarized a large number of experimental data on bubble shape and velocity, and drew the bubble shape diagram in Newtonian fluids based on dimensionless parameters. Generally, the shapes of freely rising bubbles are divided into three categories: spherical, ellipsoidal, and spherical cap or ellipsoidal cap. When the aspect ratio of the bubble is within the range of 0.9-1.1 or the system is at low Re, Eo and Mo numbers, interfacial tension and viscous force dominate the bubble shape instead of inertial force, and the bubble shape basically maintains a spherical shape with little change (Fig. 1.20 (a)) [START_REF] Clift | Bubbles, Drops and Particles[END_REF] . The ellipsoidal bubbles appear in the range of high Re number and medium Mo number, with small aspect ratio and convex surface (Fig. 1.20 (b)). In the actual rising process, the viscosity of the liquid phase may cause the bubble to stretch in the horizontal direction, and the bubble shape may be an asymmetric ellipsoid. At the same time, the ellipsoidal bubble is usually accompanied by oscillation or swing when it rises, which also causes the bubble shape to change continuously.

When the Re and Mo are high, the bottom of the larger bubble is usually flat or jagged, which looks like a part cut from the upper part of the sphere. This shape is called a spherical cap shape or an ellipsoidal cap shape (Fig. 1.20 (c)). In addition to the three typical bubble shapes, other shapes such as bubbles with depressions at the bottom, skirt-like bubbles, and wobbling bubbles are also reported. These shapes can be seen as deformations of the three basic shapes mentioned above [START_REF] Clift | Bubbles, Drops and Particles[END_REF][START_REF] Chen | The development of a bubble rising in a viscous liquid[END_REF] . If the bubble is deformed, any shape change will affect its rise velocity. For correcting this, the drag coefficient CD is used as a dimensionless parameter that characterizes the resistance of the fluid. Hadamard [START_REF] Hadamard | Mouvement permanent lent d'une sphere liquide et visqueuse dans un liquide visqueux[END_REF] was the first to theoretically derive the drag coefficient under low Reynolds number. For creeping flow in Newtonian liquids with the low Reynolds number, Hadamard ignored the inertial force and obtained the expression of drag coefficient with respect to Reynolds number:

C D = 24 Re ( 2+3(η d /η c ) 3+3(η d /η c ) ) (1-9)
For the gas-fluid system, because of the ηd is much smaller than ηc, CD is close to 16/Re, whereas for the case of solid-liquid system, CD ≈ 24/Re. And the bubble rise velocity after correction can be given by:

v HR = ρ c gd e 2 18η c 3η d +3η c 3η d +2η c (1-10)
which is called Hadamard-Rybczynski equation [START_REF] Rybczynski | Ueber die fortschreitende bewegung einer fluessigen kugel in einem zachen medium[END_REF] . It can be seen from this equation that for a single bubble (ηd ≈ 0), the vHR will be close to 3/2 of the predicted value by the Stokes law velocity. Although formula (1-10) has strict theoretical significance, it is only applicable to the creeping flow state when the Reynolds number is very small (Re ≤ 1). In the actual process, the Reynolds number is usually larger than 1, even hundreds or thousands, which is often accompanied by the deformation of the bubble. This causes the formula (1-10) to deviate greatly from the actual situation. For this reason, many researchers have made many amendments to the drag coefficient. Here, no more detailed will be discussed.

Single bubble rise velocity in non-Newtonian fluid

In non-Newtonian fluids, due to the complexity of rheological properties, bubbles show more diverse shapes [START_REF] Rybczynski | Ueber die fortschreitende bewegung einer fluessigen kugel in einem zachen medium[END_REF][START_REF] Calderbank | Gas absorption from bubbles[END_REF][START_REF] Miyahara | Mechanics of motion and deformation of a single bubble rising through quiescent highly viscous Newtonian and non-Newtonian Media[END_REF] . As shown in Fig. 1.21, the shape of the bubble generally evolves with increasing bubble volume with the increasing volume from a spherical shape to an elongated teardrop shape, a flat teardrop shape and a pointed ellipsoid at the bottom, and finally becomes a spherical cap shape. The shape of the bubble generally evolves from a spherical shape to ellipsoidal shape and finally to spherical cap shape in shear-thinning inelastic fluid.

And the unique shape of the bubble shape in the non-Newtonian fluid is the pointed tail, which usually exists in the non-Newtonian fluid with strong viscoelasticity [START_REF] Kee | A photographic study of shapes of bubbles and coalescence in non-Newtonian polymer solutions[END_REF][START_REF] Kee | Bubble velocity and coalescence in viscoelastic liquids[END_REF][START_REF] Astarita | Motion of gas bubbles in non-Newtonian liquids[END_REF][START_REF] Calderbank | Mechanics and mass transfer of single bubbles in free rise through some Newtonian and non-Newtonian liquids[END_REF][START_REF] Rodrigue | A simple correlation for gas bubbles rising in power-law fluids[END_REF] . Compared with Newtonian fluids, large-volume bubbles in non-Newtonian fluids are easier to maintain a spherical shape. However, due to the complexity of the rheological properties of different non-Newtonian fluids, it is currently difficult to accurately predict the shape of bubbles in non-Newtonian fluids. When a bubble in a viscoelastic fluid rises, due to the shearing effect of the bubble and the shear thinning effect of the fluid, the viscosity around the bubble decreases, causing the bubble to rise faster than in Newtonian fluid under the same conditions. As we know, according to the Stokes' law, the bubble rise velocity increases with the bubble size continuously in a Newtonian fluid. However, there is a peculiar phenomenon when a bubble rises in a non-Newtonian fluid, that is, as the size of the bubble increases, the rising velocity of the bubble is discontinuous, and the velocity jumps at a certain critical size. The bubble diameter range of velocity jump is usually 3-6 mm, and the maximum velocity jump value can reach 6-10 times of the free ascent velocity [START_REF] Herrera-Velarde | The flow of non-Newtonian fluids around bubbles and its connection to the jump discontinuity[END_REF] . There are many factors that may cause the bubble rise velocity jump, including bubble shape change, the reduction of the viscosity and the change of boundary condition. There is no unified theoretical explanation so far.

In the past few decades, researchers have conducted a lot of research on the free rise of bubbles in non-Newtonian fluids. For a single bubble in non-Newtonian fluid, Dewsbury [START_REF] Dewsbury | Wall Effects for the Free Rise of Solid Spheres in Moderately Viscous Liquids[END_REF] proposed the bubble drag coefficient. In a weakly shear thinning fluid, the correlation formula for the drag coefficient of a single (deformable) bubble is: (1-11)

C D =

Bubble rise in Newtonian fluid

In industrial problems the bubbles are often encountered as multiple bubbles or bubble groups. The descriptions obtained from the study of single bubbles cannot be directly extrapolated to the case of bubble liquids as the interactions between the rising bubbles are far from trivial.

In a very dilute bubbly liquid (gas fraction less than 10 -4 ), bubbles can be evenly distributed in a static Newtonian fluid. At these concentrations the distance between the bubbles is very large. The separation of bubbles is larger enough to ignore the liquid velocity field induced by each bubble which decays as (de/2) -1 and they can be assumed to not interact with each other at all. At this time, Stokes' Law can be used to describe the motion of bubbles.

However, for more concentrated bubbly liquids, if the separation of bubbles is not so large, the flow caused by one bubble will affect the motion of other bubbles, and vice versa, resulting in effective hydrodynamic interaction between the bubbles. Within a fixed volume, the liquid moves downwards on average to compensate for the rise of the bubbles. This fluid backflow hinders the rising of the bubbles and causes the average rise velocity to be less than that of an isolated bubble. As the gas fraction increases, the hindering effect becomes more obvious. In order to include this hindering effect, Richardson and Zaki (1954) proposed an empirical correlation [START_REF] Richardson | The sedimentation of a suspension of uniform spheres under conditions of viscous ow[END_REF] :

v RZ = v s (1-φ gas ) n (1-12)
where φgas is the gas fraction of the bubbly liquid and n is an experimentally determined constant varying with the Reynolds number. For low Re it is usually between 4.65 and 6.55 [106] .

The Richardson-Zaki law has been proved to be a good agreement with experimental data of various gas fractions [START_REF] Drenckhan | Structure and energy of liquid foams[END_REF] . However, when the gas approach to the jamming transition 0.60, the bubbles will interact with each other and the rise velocity starts to deviate from this correlation [108] .

Bubbles rise in non-Newtonian fluid

The current research on the rise of multiple bubbles is mainly focused on the interaction between bubbles in certain non-Newtonian fluids, such as Boger fluids and shear-thinning inelastic fluids.

For shear-thinning inelastic fluids (Fig. 1.22 (b)), the bubbles tend to form vertical doublets and large aggregations. Clustering is assumed to be triggered by the shear-thinning wake behind each bubble: the bubbles rising in the low-viscosity wake are unlikely to disperse from the side to the high-viscosity area [START_REF] Vélez-Cordero | Hydrodynamic interaction between a pair of bubbles ascending in shear-thinning inelastic fluids[END_REF] . Once formed, this vertical doublet and triplet rises faster than a single bubble and traps more bubbles. As the cluster grows, its rising speed and inertia also increase. Eventually, the cluster became a large aggregate of bubbles, showing an elliptical shape and almost horizontal orientation. However, excessive inertia combined with the ability of small bubbles to deform (that is, under conditions of large Re and low Eo) tends to hinder bubble aggregation and promote dispersion.)

Boger fluids are a kind of viscoelastic fluid with constant (or nearly constant) viscosity [110] . Vé lez investigated the the properties of bubbly flows in Boger fluids [START_REF] Velez-Cordero | Study of the properties of bubbly flows in Bogertype fluids[END_REF] . In their research, they did not change the gas volume fraction of a given bubble size, but experimented with two different bubble sizes at a fixed volume fraction. Interestingly, they found that small bubbles tend to aggregate and form vertical bubble chains as shown in Fig. 1.22 (c), while larger bubbles rise in a dispersed manner as shown in Fig. 1.22 (d). This change in behavior is consistent with bubble velocity discontinuity: in the specific fluid used in this study, these two dimensions cross the critical value of bubble velocity discontinuity.

Research on bubble rise in non-Newtonian fluids is mainly focused on low gas fractions below 1%. For higher gas fraction, the interaction between bubbles is more complex. The viscosity of viscoelastic shear-thinning fluids will decrease with the velocity of bubble rise; however, the detailed mechanisms are still unknown. [START_REF] Zenit | Hydrodynamic Interactions Among Bubbles, Drops, and Particles in Non-Newtonian Liquids[END_REF] 1

.6 Molecular dynamics simulation

Experimental methods, computer simulations and theoretical calculations have become three most important methods in modern chemical and physical research. In recent years, with the crossover and communication between research fields and the development of computer performance, computer simulation and theoretical calculation have been increasingly applied to various branches of the chemical and physical field. MD simulation is the most widely used method for computing materials, biological and other complex systems. MD simulation samples and detects the phase space composed of the coordinates and velocities of all particles in the system by integrating the Newtonian equation of motion, and calculates the position and velocity of next time step based on the current position and velocity of the particle. Various properties of the system can be inferred by the statistical analysis results of the movement of each particle, such as the conformation and dynamic properties of the molecule, the thermodynamic properties of the system, and various equilibrium/non-equilibrium properties, etc. The advantage of MD simulation is that the trajectory of particles in the system has a precise physical basis. The dynamic change information and thermodynamic statistical information of the system can also be obtained at the same time. Therefore, it is widely used in the research of various microscopic systems.

Basic principles of molecular dynamics simulation

According to the Born-Oppenheimer approximation, MD simulation uses classical mechanics to describe the movement of atoms over time. The various properties of the system can be calculated through the following basic processes:

1. Input the initial configuration of the system, the potential energy function V(ri) as a function of atom position, the position ri and initial velocity v0i of all atoms in the system. The initial velocity distribution satisfies the Maxwell-Boltzmann velocity distribution at the set temperature.

2. Calculate the force of each atom.

Update the configuration and simulate the motion of atoms by numerically solving

Newton's equation of motion.

4. Repeat steps 2 and 3 according to the number of steps to be calculated to obtain the trajectory of the system evolution.

In the above process, the trajectory of a system containing N interacting atoms with time t is obtained by solving the Newtonian equation of motion of N atoms as

2 2 , 1,... i ii m iN t  ==  r F (1-13)
where mi is the mass of the atom i, and the force Fi experienced by the atom is the negative value of the derivative of the potential energy function V(ri):

() i i i V  =-  F r r (1-14)
Commonly used integration methods for solving Newtonian equations of motion in MD simulation include Verlet algorithm [START_REF] Verlet | Experiments" on classical fluids. I. thermodynamical properties of Lennard-Jones molecules[END_REF] , Velocity-Verlet algorithm [START_REF] Swope | A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters[END_REF] and Leap-frog algorithm [START_REF] Hockney | Quiet high-resolution computer models of a plasma[END_REF] . Among them, the Leap-frog algorithm is simple, efficient and stable. Therefore, the Leap-frog algorithm has become the most mainstream integration method at present. The Leap-frog algorithm uses the position r at time t and the speed v at time t-

1 2
Δt to calculate the force F(t), and update the speed and position using the following method:

11 ( ) ( ) ( ) 22 t t t t t t m  +  = - + v v F (1-15) 1 ( ) ( ) ( ) 2 t t t t t t +  = +  +  r r v (1-16)
The speed at time t can be calculated by the following formula,

1 1 1 ( ) [ ( ) ( )] 2 2 2 t t t t t = - + +  v v v (1-17)
The information of each frame in the trajectory of the system can be obtained by completing the integral solution of the above equation. According to the ergodicity assumption in statistical mechanics, the average value of various physical quantities Q of the system can be obtained by statistics:

1 ( , ) , ( 1, 2,. li .) m ., m m i i t M t Q r v m M M Q → = =  (1-18)
1.6.2 Molecular forcefields MD simulation uses a molecular forcefield to describe the potential energy function V(ri)

between atoms, and can further calculate the forces experienced by the atoms at various moments. The forcefield information is composed of the equations and the parameters of the equations that can generate the potential energy and its derivatives. It mainly describes the nonbonding interaction composed of electrostatic interaction and van der Waals interaction and the bonding interaction composed of information such as bond length and bond angle:

U = Uelec + Uvdw (non-bonding interaction) +Ubond + Uangle + Uoutp + Utorsion (bonding interaction) (1-19)
The electrostatic interaction Uelec in non-bonding interaction is expressed as: elec ()

ij ij r ij U qq rf r  = (1-20) Among them, f = 1 4πε 0
, ε is the dielectric constant. qi and qj are the charges of atom i and atom j, and rij is the distance between atom i and atom j.

Van der Waals interaction Uvdw is usually described by Lennard-Jones (LJ) 12-6 potential energy function, as shown in Equation 1-21:

12 vdw 6 ( 4 ) ij ij ij ij ij ij r r U r         =-              (1-21)
εij and σij are usually calculated using the Lorentz-Berthelot hybrid rule:

2 ij i j ij ij       =   + =   (1-22)
εi and σi are the depth and diameter of the potential well of atom i, respectively.

The bonding effect of most forcefields is composed of the bond expansion term Ubond, the bond angle bending term Uangle, the off-plane potential energy Uoutp, and the dihedral torsion term Utorsion. The form most commonly used to describe Ubond, Uangle, and Uoutp, is the resonance potential,

2 bond 1 ( ) ( ) 2 b ij ij ij ij r k b U r =- (1-23)
Ubond describes the potential energy curve of bond length stretching vibration, where bij is the balance bond length between atoms i and j, and k ij b is the resonance potential energy parameter.

2 angle 0 1 ( ) ( ) 2 a ijk ijk ijk k U    =- (1-24)
Uangle describes the potential energy curve of the flexural vibration of the bond angle,

where θijk is the bond angle between atoms i, j, and k, θ0 is the equilibrium angle of the bond angle, and k ijk b is the resonance potential energy parameter.

2 outp 0 ( ) ( ) k U     =- (1-25)
Uoutp is used to describe the potential energy curve of the atom deviating from the plane formed by the other three adjacent atoms, where χ is the angle away from the plane, χ0 is the equilibrium angle, and kχ is the resonance potential energy parameter.

The dihedral angle formed by three adjacent bonds in the same molecule relates to the spatial configuration of the molecule. The torsional potential energy curve of the dihedral angle is periodic, which is usually described by multiple sets of cosine functions:

torsion 0, 1 ( ) [1 cos( )] 2 N i ii i V U n    = = + -  (1-26)
Where φ is the dihedral angle; n corresponds to the nth minimum point of the potential energy curve in the angle range of 0~360°, φ0, i is used to adjust the phase, and Vi is the barrier height corresponding to each extreme value. For more complex dihedral torsion potential energy curves, multiple items are often needed to fit properly.

According to the degree of fineness when modeling molecules, molecular forcefields are usually divided into all-atom forcefield (AA), united atom forcefield (UA), and coarse-gained forcefield (CG). The all-atom forcefield clearly defines each atom as a particle, which has high accuracy and relatively expensive calculation cost. It is usually used for nano-scale simulations.

After years of development, there are many kinds of all-atom forcefields available, and the parameterization methods of different forcefields are slightly different, and the applicable molecular types are also different. The most commonly used all-atom forcefields to describe small organic molecules and protein molecules are AMBER forcefield [START_REF] Cornell | A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules[END_REF][START_REF] Wang | How well does a restrained electrostatic potential (RESP) model perform in calculating conformational energies of organic and biological molecules?[END_REF][START_REF] Weiner | An all-atom force field for simulations of proteins and nucleic acids[END_REF] , CHARMM forcefield [START_REF] Brooks | CHARMM: A program for macromolecular energy, minimization, and dynamics calculations[END_REF][START_REF] Foloppe | All-atom empirical force field for nucleic acids: I. Parameter optimization based on small molecule and condensed phase macromolecular target data[END_REF][START_REF] Hart | Optimization of the CHARMM Additive Force Field for DNA: Improved Treatment of the BI/BII Conformational Equilibrium[END_REF] , OPLS-AA forcefield [START_REF] Damm | OPLS all-atom force field for carbohydrates[END_REF][START_REF] Jorgensen | Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids[END_REF][START_REF] Robertson | Improved Peptide and Protein Torsional Energetics with the OPLS-AA Force Field[END_REF] , etc. The united atom forcefield considers part of the hydrocarbyl group as a single particle located at the center of mass of the group, and the mass and charge of the joint atom are the sum of all atoms in the group. The united atom forcefield reduces the amount of calculation to a certain extent, but the description of the molecular structure is not complete. The more commonly used united atom forcefield includes the OPLS-UA forcefield [START_REF] Jorgensen | The OPLS [optimized potentials for liquid simulations] potential functions for proteins, energy minimizations for crystals of cyclic peptides and crambin[END_REF] and the GROMOS forcefield [START_REF] Daura | Parametrization of aliphatic CHn united atoms of GROMOS96 force field[END_REF][START_REF] Oostenbrink | A biomolecular force field based on the free enthalpy of hydration and solvation: The GROMOS force-field parameter sets 53A5 and 53A6[END_REF] .

The coarse-grained forcefield treats 3-4 heavy atoms and their connected hydrogen atoms as a bead, and describes the MD simulation process by calculating the interaction between the beads. It further reduces the degree of freedom of the system, greatly reduces the computational cost, and can simulate large-scale proteins, DNA molecules and biofilm systems on a mesoscopic scale. The coarse-grained forcefield retains the most basic molecular information.

The most commonly used coarse-grained forcefields at this stage are the Martini forcefield [128- 129] and the PLUM forcefield [START_REF] Dawson | Coarse-grained modeling of RNA 3D structure[END_REF] .

Temperature coupling

Temperature is one of the most critical properties in the simulation process. The temperature of the system needs to be adjusted in different statistical ensembles such as NVT and NPT. The temperature T in the MD simulation is defined by the particle velocity vi:

2 B 11 22 ii m v k T = (1-27)
In the formula, kB is Boltzmann's constant and means the average of ensemble.

The temperature coupling ensures that the temperature of the simulation system is maintained near the expected value by continuously correcting the velocity of the particles.

Commonly used temperature coupling methods include Berendsen coupling algorithm [START_REF] Berendsen | Molecular dynamics with coupling to an external bath[END_REF] ,

Nose-Hoover coupling algorithm [START_REF] Nosé | A molecular dynamics method for simulations in the canonical ensemble[END_REF][START_REF] Hoover | Canonical dynamics: Equilibrium phase-space distributions[END_REF] and Velocity-rescaling coupling algorithm [START_REF] Bussi | Canonical sampling through velocity rescaling[END_REF] .

The Berendsen algorithm realizes the connection to an external thermal bath with a given reference temperature T0, and has a weak coupling with first-order kinetic characteristics. The deviation of the system temperature to T0 is slowly corrected by the following formula:

0 d d T TT T t  - = (1-28)
τT is the time constant. The smaller the value, the more accurate the temperature control.

However, the Berendsen coupling will cause the particle velocity in the system to deviate from the Maxwell-Boltzmann velocity distribution, failing to produce a correct canonical ensemble.

The Nose-Hoover coupling algorithm directly adds a thermal bath to the equation of motion, and assigns virtual parameters to it to obtain a new equation of motion as the system evolves:

2 2 dd dd i i i i p t m Q t  =- r F r (1-29) 2 2 4 T ref T Q   = (1-30)
Q is the virtual mass of the hot bath and pξ is the momentum of the hot bath, which is calculated by the following equation of motion:

0 d () d p TT t  =- (1-31)
The Nose-Hoover thermal bath produces particle velocities that satisfy the Maxwell-Boltzmann distribution, but exhibits oscillating characteristics during the relaxation process to the reference temperature, which is usually used in the pre-equilibration process.

The Velocity-rescaling coupling algorithm adds a random term to the Berendsen coupling algorithm to ensure that the correct velocity distribution of the particles in the system can be given. The kinetic energy is corrected according to the following formula:

0 0 ) d ( 2 d d T f T KK tW N K K K   = + - (1-32)
In the formula, K is the kinetic energy of the system. Nf is the degree of freedom, and dW represents the Brownian motion process. The velocity-rescaling algorithm has first-order dynamics characteristics with no relaxation oscillations. Velocity-rescaling algorithm is currently a better temperature coupling algorithm.

Pressure coupling

Except temperature, many simulation processes also need to control the pressure of the system. In MD, the pressure of the system is closely related to the coordinates of the particles.

The pressure coupling algorithm can be used to scale the coordinates of the particles to make the average pressure of the system constant at the desired value. Currently commonly used pressure coupling algorithms are Berendsen pressure coupling algorithm [START_REF] Berendsen | Molecular dynamics with coupling to an external bath[END_REF] and Parrinello-Rahman pressure coupling algorithm [START_REF] Parrinello | Polymorphic transitions in single crystals: A new molecular dynamics method[END_REF] .

Similar to the Berendsen temperature coupling algorithm, the Berendsen pressure coupling algorithm also conforms to the first-order dynamics characteristics. The coupling parameter τp controls the speed of the system pressure changing to the reference pressure P0:

0 d d p t  - = PP P (1-33)
Similarly, the Berendsen pressure coupling algorithm is a weak coupling algorithm, and it is impossible to define an accurate ensemble.

The Parrinello-Rahman pressure coupling algorithm uses an algorithm similar to the Nose-Hoover temperature coupling, which realizes the true NPT ensemble by changing the motion equation of the particles, and finally causes the motion equation to be updated to:

2 2 dd dd i i i i t m t =- r F r M (1-34)
M is the virtual mass matrix of the pressure bath, which is adjusted by setting the compressibility and coupling parameter τp. The Parrinello-Rahman pressure coupling algorithm is usually used in conjunction with the Nose-Hoover temperature coupling algorithm or the Velocity-rescaling temperature coupling algorithm to jointly control the pressure and temperature of the system during the simulation of the finished product.

Quantum chemistry calculations

Overview of quantum chemistry calculations

As a branch of theoretical chemistry and an interdisciplinary subject of chemistry and physics, quantum chemistry is a basic science that applies the basic principles and methods of quantum mechanics to study chemical problems. The structure and chemical properties of a molecule are closely related to the atomic composition of the molecule and its electronic arrangement or state of motion. Quantum chemistry starts from the basic laws of electronic motion to describe the relative spatial positions of all electrons and atoms in the system, so as to achieve to study the reactivity and structure of the system. Quantum chemistry calculations are very powerful and can be applied in many different systems, such as studying the structure and performance of stable and unstable molecules, the relationship between structure and performance, the interactions between molecules; the mutual collision and mutual reaction between molecules, which provides important theoretical tools for current chemical research.

The calculation methods of quantum chemistry mainly include: ab initio calculation method, semi-empirical method and density functional theory (DFT).

The ab initio calculation method is based on the Schrodinger equation. In the process of solving Schrodinger's equation, only a few basic physical constants are used, including the speed of light, Planck's constant, and the mass of electrons and nucleus. In the process of solving Schrödinger's equation, a series of mathematical approximations are used. Different approximations lead to different methods. The most classic mehod is the Hartree-Fock (HF) equation. The electronic structure and properties of the system can be obtained using selfconsistent field method to solve this equation. The HF method can obtain good results for the stable molecules and some transition metals. It is a good basic theoretical method and the basis of other ab initio calculation methods. However, the HF method does not consider electron in theory, so it is insufficient in the application of some special systems.

The ab initio calculation method has a huge amount of calculation. The main difficulty is the calculation of the repulsive integrals between electrons in the HF equation. The number of these repulsive integrals is large and the calculation is cumbersome. Therefore, there are some schemes for simplifying the calculation of repulsive integrals, which are called approximate calculation methods. The approximate HF equation generally yields poor results. Taking some empirical parameters instead of some integrals in the approximate HF equation, while ignoring some integrals, satisfactory results can be obtained. This method is called the semi-empirical approximate calculation method. Common semi-empirical methods include AM1, MINDO/3, PM3, etc.

Density functional theory

In the Thomas-Fermi model developed independently by Thomas and Fermi in 1927, they used electron density instead of wave function to describe the multi-electron system. Although this model was not very successful in describing the entire molecule, this idea laid the foundation for the later well-known density functional theory (DFT).

The classical methods of electronic structure theory, especially the Hatree-Fock method and the self-consistent field method, are based on complex multi-electron wave functions.

Density functional theory further considers exchange-correlation energy on the basis of Hatree-Fock approximation, which can describe the multi-electron system more accurately. Unlike the Hartree-Fock method, density functional theory uses electron density instead of wave function as the basic quantity for research, which makes the calculation easier, because the n electron wave function is a function of 3n variables, and the electron density is only a function of 3 variables. Therefore, density functional theory guarantees the accuracy of calculation when dealing with polyatomic systems or even macromolecular systems, and saves computational costs more than the self-consistent field method. It is currently one of the most commonly used methods in computational chemistry.

Although the concept of density functional theory originated from the Thomas-Fermi model in 1927, it did not have a theoretical basis until the Hohenberg-Kohn theorem was proposed in 1964 [START_REF] Hohenberg | Inhomogeneous Electron Gas[END_REF] . Hobenberg-Kohn first theorem states that for a given nucleus coordinate, the energy and properties of the ground state of the system are only determined by the electron density. Hobenberg-Kohn second theorem shows that the ground state energy is obtained after the system energy is minimized with the ground state density as a variable. Designing an accurate functional is the key to the DFT method.

The total energy in the DFT method can be expressed as a function of ρ:

E(ρ) = E T (ρ) + E V (ρ) + E J (ρ) + E XC (ρ) (1-35)
Among them, E T is electron kinetic energy; E V is the attraction potential energy of electron and atomic nucleus; E J is the Coulomb repulsion energy between electrons; E XC is the exchange-correlation energy. Among them, E V and E J are direct because they represent the classical Coulomb action, while E J and E XC are not direct. Finding high-precision exchangecorrelation approximations is the main problem of density functional theory.

In 1965, Kohn and Sham [START_REF] Kohn | Self-Consistent Equations Including Exchange and Correlation Effects[END_REF] proposed the Kohn-Sham equation, which made it possible to accurately calculate the electron density of the system and the total energy of the system, thus opening the way for density functional theory to be used in practical calculations. In the framework of Kohn-Sham DFT, the most difficult many-body problem (due to the interaction of electrons in an external electrostatic potential) is simplified to the problem of the sports of an electron with no interaction in the effective potential field. This effective potential field includes the effects of external potential fields and coulomb interactions between electrons, such as exchange and correlation effects. Dealing with exchange and correlation effects is the difficulty in Kohn-Sham DFT. At present, there is no accurate method to solve the exchangecorrelation energy E XC . The simplest approximate solution method is Local Density Approximation (LDA). LDA approximately uses homogeneous electron gas to calculate the exchange energy of the system (the exchange energy of homogeneous electron gas can be accurately solved), and the correlation energy part uses the free electron gas fitting method to process.

Since the definition of the exchange-correlation energy functional includes a part of the contribution of kinetic energy, many researchers consider that the kinetic energy density should be included as a variable in the exchange-correlation functionals [START_REF] Parr | Density-functional theory of atoms and molecules[END_REF] . This is the meta-GGA functional. In order to improve the accuracy of the calculation results of various approximate functionals, in1988, Becke [START_REF] Becke | Density-functional exchange-energy approximation with correct asymptotic behavior[END_REF] proposed the idea of adding part of the exchange energy calculated according to the Hartree-Fock method to the energy density functional, thereby constructing a series of hybrids exchange-correlation functionals. The mixed exchangecorrelation energy expression form has achieved great success in the calculation of density functional theory. The commonly used exchange-correlation energy functional is to mix the Hartee-Fock exchange energy with the approximate exchange-correlation energy density functional in a fixed proportion. For example, "half to half" functional, its expression can be written as:

E XC HH = 1 2 E XC HH + 1 2 E XC HH (1-36)
Because the theoretical basis of this type of hybrid density functional method is the adiabatic correlation formula, it is called the adiabatic correlation method. The methods including B3P, B3LYP, B1B95, PBEO, B97, B98, etc. Among them, the famous B3LYP functional which is the hybrid density functional composed of the Becke three-parameter hybrid exchange functional and Lee-Yang-Parr related functionals can be expressed as:

E XC B3LYP = aE X LDA + (1-a)E X HF + bE X Becke + cE C LYP + (1-c)E C VWN (1-37)
In the formula, a, b, and c are parameters.

Due to the relatively small amount of calculation of density functional theory, it can be applied to larger molecular structures [START_REF] Holthausen | A chemist's guide to density functional theory[END_REF] . To a certain extent, the electronic correlation effect is considered, and satisfactory results can be obtained in predicting molecular structure and energy. Therefore, it is currently the most popular quantitative calculation method.

Proposal for the thesis

The photo-responsive wormlike micelle constructed by Gemini surfactants and cinnamic acid photo-responsive molecules has excellent photorheological properties and potential value in petrochemical, skin care, photosensitive devices, drug release and other fields. However, due to the limited experimental conditions and material resources, the photo-responsive mechanism and the influence of the molecular structure of cinnamate derivatives on its photo-sensitive ability have not been fully investigated. Wormlike micelles exhibit complex viscoelasticity.

The rising behavior of bubbles has great industrial application value, and the current research on the rising behavior of bubbles in viscoelastic fluids is also very scarce. Based on this:

(1) We chose Gemini surfactant N, N'-bis(dodecyldimethyl)-1,2-ethane diammonium dibromide (12-2-12• 2Br -) and photo-sensitive small molecule trans-o-methoxycinnamic acid (trans-OMCA) to construct a photo-responsive self-assembly system. The photo-responsive behavior of the system and the microscopic mechanism of self-assembly morphology transformation were studied through the combination of rheology, MD and quantitative calculation.

(2) Based on our understanding of the transformation mechanism of photo-responsive wormlike micelle, we selected three ortho-substituent cinnamates, trans-o-methoxy cinnamate MD simulation and quantitative calculation were used to study the influence of different substituent positions on photo-responsive behavior of wormlike micelle. In addition, we also calculated the structural properties of dozens of cinnamates, which provided theoretical guidance for experimentally constructing a wormlike micelle system with stronger photoresponsiveness.

(4) We chose a classic viscoelastic shear-thinning fluid (CTAB/NaSal wormlike micelle system) as bubbly liquid to study the rising of bubbles at relatively high gas fractions (5%-30%).

Our experimental results deepen and enrich the research of bubble rising in non-Newtonian fluids, and also provide theoretical guidance for its industrial applications such as froth flotation.

Chapter 2 Molecular Dynamics Simulations and Quantitative

Calculations on Unraveling Photo-responsive Behavior of

Wormlike Micelles Constructed by 12-2-12• 2Br -and trans-o-

Methoxy-cinnamate

The results of this chapter have been published in Langmuir (Langmuir 2020 36 (32), 9499-9509).

Introduction

A great scientific challenge over the past years on soft matter field has been transferred to design adaptable materials in response to the triggers aroused by environmental changes, which can significantly alter their configuration and functionality [3] . Those smart self-assembly materials can dynamically respond to external environmental changes including electrical- [START_REF] Dylla-Spears | Charged micelle halo mechanism for agglomeration reduction in metal oxide particle based polishing slurries[END_REF] ,

photo- [START_REF] Tu | A gemini surfactant-containing system with abundant self-assembly morphology and rheological behaviors tunable by photoinduction[END_REF] , thermal- [START_REF] Yang | Thermal-Responsive Polymers for Enhancing Safety of Electrochemical Storage Devices[END_REF] , pH- [START_REF] Tu | Shape-Changing and Amphiphilicity-Reversing Janus Particles with pH-Responsive Surfactant Properties[END_REF] , magnetic- [START_REF] Yang | Probing of the magnetic responsive behavior of magnetorheological organogel under step field perturbation[END_REF] , CO2-stimulus even multiple stimuli [START_REF] Zhou | Polymerization-Induced Self-Assembly under Compressed CO2: Control of Morphology Using a CO2-Responsive MacroRAFT Agent[END_REF][START_REF] Lin | Highly ordered and multiple-responsive graphene oxide/azoimidazolium surfactant intercalation hybrids: a versatile control platform[END_REF][START_REF] Yang | Systems of mechanized and reactive droplets powered by multi-responsive surfactants[END_REF] .

Among those stimuli, light stands out owing to its outstanding characteristics including responding non-invasively, operating simply, accessing easily and aiming at a precise spatial location [START_REF] Sakai | Adsolubilization by a photoresponsive surfactant[END_REF][START_REF] Huang | Light-controlled synthesis of gold nanoparticles using a rigid, photoresponsive surfactant[END_REF] . The photo-responsive viscoelastic fluids composed of wormlike micelles are of particular interest because these viscoelastic fluids with tunable aggregate morphologies and rheological properties have played an increasingly important role in many fields such as microfluidics, drug delivery, sensors, drag reduction agent and so on [START_REF] Long | Reversible solubilization of typical polycyclic aromatic hydrocarbons by a photoresponsive surfactant[END_REF][START_REF] Kim | Highly stable and reduction responsive micelles from a novel polymeric surfactant with a repeating disulfide-based gemini structure for efficient drug delivery[END_REF] . As is well known, owing to special amphiphilic properties, surfactants can form different kinds of self-assembly aggregates such as spherical micelles [START_REF] Jayaraman | Counterion-Dependent Access to Low-Symmetry Lyotropic Sphere Packings of Ionic Surfactant Micelles[END_REF] , wormlike micelles [START_REF] Kwiatkowski | Growth of wormlike micelles of surfactant induced by embedded polymer: role of polymer chain length[END_REF] , vesicles or gels [START_REF] Mondal | Ionic liquid mediated micelle to vesicle transition of a cationic gemini surfactant: a spectroscopic investigation[END_REF][START_REF] Owoseni | Microstructural characteristics of surfactant assembly into a gel-like mesophase for application as an oil spill dispersant[END_REF] , and liquid crystals (LCs) [START_REF] Li | Phase behaviours of a cationic surfactant in deep eutectic solvents: from micelles to lyotropic liquid crystals[END_REF] . Without a doubt, smart self-assembly materials constructed by surfactants have become one of the hotspots that researchers pay much attention to recent years.

Adding certain photosensitive molecules directly to a surfactant solution is the most effective and simplest method to obtain a photo-responsive wormlike system [START_REF] Zhao | Investigation of Novel Triple-Responsive Wormlike Micelles[END_REF] . For example, Raghavan proposed a simple photo-rheological fluid system based on the cationic surfactant cetyltrimethylammonium bromide (CTAB) and the photo-responsive organic derivative transortho-methoxycinnamic acid (trans-OMCA) in aqueous solution [START_REF] Kumar | Photogelling fluids based on light-activated growth of zwitterionic wormlike micelles[END_REF] . The mixture of trans-OMCA and CTAB generated elongated and entangled wormlike micelles. After irradiation of UV-light, trans-OMCA transformed into cis-OMCA isomer. The alteration in molecular structure of OMCA aroused the long wormlike micelles to transform to short rod-like micelles with the solution viscosity degrading over 4 orders of magnitude. Following this paper, several studies were carried out revealing analogous effects in different surfactant solution containing OMCA and its derivatives [START_REF] Ali | Photoresponsive Functionalized Vinyl Cinnamate Polymers: Synthesis and Characterization[END_REF][START_REF] Baglioni | Surfactant-based photorheological fluids: effect of the surfactant structure[END_REF] . It is generally known that Gemini surfactants are a type of surfactant consisting of two amphiphilic chains linked by a spacer at or near the hydrophilic head groups. Unlike conventional surfactants, Gemini surfactants possess not only richer aggregation morphologies but also excellent physicochemical properties such as lower critical micelle concentration and stronger self-assembly ability. Based on Gemini surfactants and photo-sensitive molecules, a photo-responsive system with multiple photo-responsive behaviors can be constructed by employing photo-isomerization of trans-OMCA isomers into Gemini surfactant solution [START_REF] Tu | UV-Responsive Behavior of Multistate and Multiscale Self-Assemblies Constructed by Gemini Surfactant 12-3-12•2Brand trans-o-Methoxy-cinnamate[END_REF][START_REF] Tu | Photoresponsive Behavior of Wormlike Micelles Constructed by Gemini Surfactant 12-3-12•2Br-and Different Cinnamate Derivatives[END_REF] . Therefore, extensive investigations on the photo-responsive wormlike micelle systems containing Gemini surfactants have a great value in soft matter fields.

However, a great challenge about explaining the different properties between trans/cis-OMCA and microscopic mechanisms of micelle transformation after UV irradiation still exists.

Atomistic MD simulations and quantitative calculations provide us with a new solution to obtain specific self-assembly process of micelles, the details of packing patterns of certain molecule on the micelle surface, and energy changes on atom and molecular scale respectively [162-163] . In the past few years, the self-assembly process of surfactant has been well investigated using simulation method [START_REF] Tang | Molecular Dynamics Simulations of the Oil-Detachment from the Hydroxylated Silica Surface: Effects of Surfactants, Electrostatic Interactions, and Water Flows on the Water Molecular Channel Formation[END_REF][START_REF] Zhang | Effect of organic salt on the self-assembly of ammonium gemini surfactant: An experiment and simulation study[END_REF][START_REF] Sangwai | Coarse-grained molecular dynamics simulations of the sphere to rod transition in surfactant micelles[END_REF][START_REF] Wang | Molecular dynamics simulations of threadlike cetyltrimethylammonium chloride micelles: effects of sodium chloride and sodium salicylate salts[END_REF] . For example, Heerdt employed time-dependent DFT calculations and atomistic MD simulation to study photo-isomerization of trans/cis-OMCA isomers and the self-assembly of CTAB micelles with trans/cis-OMCA in water solution [START_REF] Heerdt | Photoisomerization induced scission of rod-like micelles unravelled with multiscale modeling[END_REF] .

In order to save the simulation time, pre-assembled rod-like micelles in water solution were chosen as initial configuration in his simulation. The results showed that under low OMCA concentration, CTAB micelles and cis-OMCA formed several spherical micelles while trans-OMCA and CTAB micelles fused into long rod-like micelles, which agreed well with experiments. However, this study did not involve the infinite wormlike micelles and Gemini surfactant which has richer morphologies with different states and scales.

In this section, N, N'-bis(dodecyldimethyl)-1,2-ethane diammonium dibromide (12-2-12• 2Br -) was selected to construct the photo-responsive wormlike micelles because of the rich self-assembly morphologies and strong self-assembly capacity of 12-2-12• 2Br -. We utilized rheology and transmission electron microscopy (TEM) to study the micelle morphologies before and after UV illumination. Atomistic MD simulations with united-atom forcefield were employed to investigate the morphology transformation process of micelles after UV illumination at constant 12-2-12• 2Br -concentration and various trans/cis-OMCA concentrations. Owing to the large size of micelles, most of studies tend to use coarse-grained molecular dynamics (CG-MD) or united-atom forcefield with initial pre-assembled cylindrical micelles to simulate the self-assembly behavior [START_REF] Wang | Molecular dynamics simulations of threadlike cetyltrimethylammonium chloride micelles: effects of sodium chloride and sodium salicylate salts[END_REF][START_REF] Heerdt | Photoisomerization induced scission of rod-like micelles unravelled with multiscale modeling[END_REF][START_REF] Wang | Coarse-grained molecular dynamics study on the self-assembly of Gemini surfactants: the effect of spacer length[END_REF] . However, in order to simulate the spontaneous self-assembly process of Gemini surfactants in solution, we employed a random distribution of 12-2-12• 2Br -surfactants in water solution as initial configuration. Density functional theory (DFT) calculations with B3LYP and M052X functionals were conducted to investigate the distinctions of energy and hydrophobicity properties between trans/cis-OMCA isomers. The present experimental and simulations studies on the photo-responsive behavior of surfactant micelles allow us to strengthen the comprehension towards the mechanism of photoresponsive behavior and to extend for further applications of photo-responsive systems.

Materials and Methods

Sample Preparation and UV-Light Irradiation

N, N-Bis(dodecyldimethyl)-1,2-ethane diammonium dibromide (12-2-12• 2Br -) was prepared according to our previous study [START_REF] Yue | Effect of ionic liquid C2mimBr on rheological behavior of Gemini surfactant 12-2-12 aqueous solution[END_REF] . Trans--methoxycinnamic acid (99%) was purchased from TCI Chemical Industry Development Co., Ltd without further purification.

Furthermore, trans-ortho-methoxy cinnamate (trans-OMCA) used in this thesis was prepared by mixing trans-ortho-methoxy cinnamate with a slight excess of sodium hydroxide (NaOH) in solution. The mixed solution (17 mM 12-2-12• 2Br -/7 mM trans-OMCA) was prepared by quantitatively adding trans-OMCA to the 12-2-12• 2Br -solutions, followed by standing in an incubator (25 ± 0.1°C) for 48 h to ensure equilibrium.

An ultra-high pressure short arc mercury lamp (CHF-XM35-500W) with a 365 nm optical filter was used to illuminate OMCA from trans to cis. Samples were put in a 10 ml quartz crucible and stirred constantly at 25°C ± 0.1 in a jacketed beaker connected to a lowtemperature thermostat bath. The distance between the samples and the light source was fixed at 8 cm.

Rheology Measurements

Rheological properties were investigated using the double gap measurement system (C-DG26.7/T200, 23.831 mm ID, 27.597 mm diameter) of the Physical MCR 302 rheometer produced by Austrian Anton Paar Co., Ltd. A sample of about 8 ml was poured into the double gap and kept stable for at least 5 min before measurements. Steady shear rheology was measured by the shear rates changing from 0.01 s -1 to 1000 s -1 . The dynamic shear rheology was examined in the range of 0.05-100 Hz, with a fixed strain value (γ = 1%). The experimental temperature was controlled at 25.0 ± 0.1°C.

Transmission Electron Microscopy

The microstructures of aggregates were observed via transmission electron microscope (Jeol JEM-1400, Japan). Firstly, an appropriate amount of solution was slowly dropped on the margin of the copper mesh containing the carbon support film; subsequently the sample was adsorbed on the copper mesh after a couple of minutes. Then the excess solution was removed by filter paper. After that, the samples were dyed with phosphotungstate for 10-20s, and finally the excess solution was cleaned with filter paper for observation as well.

Force-field parameters

Gaussian 09 quantum chemistry packages were used to optimize trans/cis-OMCA molecule structures as initial structures of atomistic MD simulations [START_REF] Frisch | Gaussian 09, Revision A.1[END_REF] . Solvation free energy and molar volume of OMCA isomers were also calculated by Gaussian 09 at the M052X/6-31G* level [START_REF] Ho | Comment on the correct use of continuum solvent models[END_REF] . The interaction energies of typical 12-2-12 2+ /OMCA packing patterns were obtained using 6-311g** basis set with B3LYP functional in SMD solvationmodel.

GROMOS96 45a3 forcefield was employed for all our simulations because of its good agreement with simulation research and experimental data [START_REF] Schuler | An improved GROMOS96 force field for aliphatic hydrocarbons in the condensed phase[END_REF][START_REF] Jia | Molecular dynamics simulation of shape and structure evolution of preassembled cylindrical cetyltrimethylammonium bromide micelles induced by octanol[END_REF] . The initial coordinates of 12-2-12 2+ (Scheme 2.1 (a)) and trans/cis-OMCA -(Scheme 2.1 (b)) molecules were generated using Gaussian 09. We utilized the ATB server to generate the forcefield parameters for the 12-2-12 2+ [START_REF] Malde | An automated force field topology builder (ATB) and repository: version 1.0[END_REF] . The charge distribution and forcefield parameters on trans/cis-OMCA were obtained from the data of DFT calculations of Heerdt [START_REF] Heerdt | Photoisomerization induced scission of rod-like micelles unravelled with multiscale modeling[END_REF] . The charges assignments for 12-2-12 2+ are showed in Table 2.1. . For convenience, we define r n as the ratio of the number of OMCA molecules to the number of 12-2-12• 2Br -molecules when the number of 12-2-12• 2Br -is constant at 216 in our simulations.

r n = N OMCA N Surfactant (2-1)
Periodic boundary conditions were employed in all three dimensions to obtain the effectively infinite part of wormlike micelle. Corresponding number of counter ions Na+ were distributed in the box randomly as well. The 12-2-12• 2Br -concentrations were approximately 0.35 mol/L in small box and 0.25 mol/L in big box, which were far above the CMC (8.09 mmol/L) of 12-2-12• 2Br -in water solution [START_REF] Alimohammadi | Aggregation behavior and intermicellar interactions of cationic Gemini surfactants: Effects of alkyl chain, spacer lengths and temperature[END_REF] . The OMCA concentrations range from 0.07 to 0.33 mol/L. The details of box are shown in Table 2.

All the simulations were carried out by GROMACS 2018 packages [START_REF] Abraham | GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers[END_REF] . Berendsen bath coupling scheme was used to maintain a constant temperature of 300 K and a constant pressure of 1 bar [START_REF] Berendsen | Molecular dynamics with coupling to an external bath[END_REF] . Semi-isotropic pressure coupling was applied owing to the convenience of simulating rod-like and wormlike micelles [START_REF] Heerdt | Photoisomerization induced scission of rod-like micelles unravelled with multiscale modeling[END_REF][START_REF] Wang | Coarse-grained molecular dynamics study on the self-assembly of Gemini surfactants: the effect of spacer length[END_REF] . The simulation box was rescaled independently in z-direction but isotopically in x-and y-directions. The SPC water model was employed in all simulations [START_REF] Berendsen | Interaction Models for Water in Relation to Protein Hydration[END_REF] . The trajectories were saved every 2ps with a time-step of 2 fs.

Interactions were subjected to a cutoff distance of 1 nm, and the long-range electrostatic interactions were handled with a grid size of 0.12 nm using the Particle Mesh Ewald technique [180] . Bonds containing hydrogen atoms were constrained using the Linear Constraint Solver (LINCS) [START_REF] Hess | LINCS: a linear constraint solver for molecular simulations[END_REF] . The trajectories and configurations were visualized using VMD 1.9.2 [START_REF] Humphrey | VMD: visual molecular dynamics[END_REF] .

Potential of mean force calculation

Two separate pre-assembly spherical micelles were constructed by Packmol software, then dissolved in water with the SPC water model in the box with size of 6nm × 6nm × 12nm, respectively. The solutions contained approximately 13000 water molecules, 32 cis or trans OMCA and corresponding counter ions. The steepest descent of energy minimization was employed. These two systems were carried out in NPT ensemble at 300 K and 1 atm for 50 ns with the time step of 2 fs. Periodic boundary conditions were applied in three dimensions. The temperature and pressure were controlled by the Berendsen bath coupling scheme [START_REF] Berendsen | Molecular dynamics with coupling to an external bath[END_REF] .

Interactions were subjected to a cutoff distance of 1 nm where the long-range electrostatic interactions were set to 0.12 nm using the Particle Mesh Ewald technique. In the pulling process, the motion of micelles was restricted to maintain their initial configuration. A harmonic umbrella potential with a force constant of 1000 Kcal• mol -1 • nm -2 was applied between the COM of the micelle and a 12-2-12 2+ ion or an OMCA -ion using pull code. Umbrella sampling simulations were carried out in 25 different windows ranging from 1.5nm to 6.5nm with a sequential stepwise reduction by 0.2 nm. The MD simulation time for each window was 10 ns.

The potential of mean force was calculated from the sample windows using the Weighted

Histogram Analysis Method which are implemented by g_wham command in GROMACS.

Interface simulation

The double layers of 12-2-

Snapshots of micelles

In general, 12-2-12• 2Br -can form aggregates with different morphologies in aqueous solution depend on its concentration [START_REF] Bernheim-Groswasser | Sphere-to-cylinder transition in aqueous micellar solution of a dimeric (gemini) surfactant[END_REF] . At very low concentration, 12-2-12• 2Br -molecules tend to aggregate into a multitude of spherical micelles. Fig. 2.3 provides the snapshot of the species formed in 12-2-12• 2Br -aqueous solution after 100ns MD simulation. Obviously, the spherical micelles are formed. The average aggregation number of the formed micelles is 22.5, which is very close to the experimental aggregation number of 21.2 [START_REF] Alargova | Micelle aggregation numbers of surfactants in aqueous solutions: a comparison between the results from steady-state and time-resolved fluorescence quenching[END_REF] . The simulation result is in good agreement with that obtained by experiments.

51

In order to obtain the detailed aggregation information after introducing OMCA and the influence of isomerization of OMCA, simulations of 12-2-12• 2Br -with trans-OMCA and cis-OMCA were carried out respectively. Fig. 2.4 presents the snapshots of simulation results. With the addition of trans-OMCA, a rod-like micelle appears firstly (r n = 0.75). After that, a rodlike micelle similar with r n = 0.75 was formed with denser bulk density when more trans-OMCA molecules were introduced to the 12-2-12• 2Br -system (r n = 1). When r n reaches 1.25, rod-like micelles further merged into a long wormlike micelle with several ellipsoidal micelles.

Finally, at the highest OMCA concentration (r n = 1.5), the micelle with trans-OMCA molecules grew into the elongated and intertwined network structure. The main reason for morphologies changes is that OMCA molecule is amphiphilic. After being added to 12-2-12• 2Br -system, OMCA will participate in the micelle formation with 12-2-12• 2Br -. Meanwhile, owing to the strong electrostatic interaction between the head groups of cationic 12-2-12• 2Br -and anionic OMCA as well as π-cation interaction between the benzene ring of OMCA and the charged head group of 12-2-12• 2Br -, the bulk density of micelles increases, inducing the formation of rod-like micelles even wormlike micelles [START_REF] Drechsler | Role of the surfactant headgroup on the counterion specificity in the micelle-to-vesicle transition through salt addition[END_REF][START_REF] Janiak | Soluble aggregates in aqueous solutions of polyion-surfactant ion complex salts and a nonionic surfactant[END_REF] .

After being irradiated under UV light, trans-OMCA isomerizes into cis-configuration.

Rod-like micelles formed by trans-OMCA split into small, spherical micelles when r n = 0.75.

After that, surfactant micelles started to split to an ellipsoidal micelle and a rod-like micelle (r n = 1). Subsequently, with the increase of cis-OMCA molecules to r n = 1.25, a whole rod-like micelle appeared. Finally, at the highest cis-OMCA concentration (r n = 1.5), the network micelles ruptured into a long wormlike micelle. Morphology changes because of the increase of the steric hindrance of OMCA after the photoisomerization, which disturbs the internal structure of the micelles. This steric effect and the electrostatic interaction as well as π-cation interaction will compete and finally affect the micellar morphology together. When the cis-OMCA concentration is lower, the steric hindrance effect is dominant, so that long micelles are split into smaller micelles. When the cis-OMCA concentration is higher, the electrostatic interaction as well as π-cation interaction start to be stronger than steric hindrance effect. At this time, the micelles begin to lengthen, while they are still smaller than that formed in trans-OMCA system. To testify the formation of micelles with special morphologies, the specific density information of ions in these systems are calculated and provided in Fig. 2.5. As shown in Fig. From the result above, the 12-2-12• 2Br -and trans-OMCA micelle perform obvious photoresponsive behavior, which is corresponding to the phenomenon that the long wormlike micelles gradually break into shorter units after UV light in our TEM results. The specific morphologies during micelle transformation in Fig. 2.1 are all captured in our simulation in Fig. can be defining as:

g AB (r)= 〈ρ B (r)〉 〈ρ B 〉 local = 1 〈ρ B 〉 local 1 N A ∑ ∑ δ(r ij -r) 4πr 2 N B j∈B N A i∈A (2-2)
where 〈ρ B (r)〉 is the density of particle B at a distance r around A particles, and 〈ρ B 〉 local is the average density of particle B at a radius of rmax over all spheres around A particles. Usually, the value of rmax is half length of the box. The averaging is also carried out in time.

As is shown in the Fig. 2.6 (a), the g(r) curve between N1-N1 atoms in 12-2-12• 2Br -system has two peaks located on 0.91 and 1.2nm. With the addition of trans-OMCA molecules, the two peaks shift left. The first peak of trans-OMCA moves to 0.64nm and the peak height has a considerable increase. The second peak moves to 0.86 nm. After isomerization, the first peak does not move while the second peak locates at 0.81 nm. The left shifting and height increase of the peaks suggest that the addition of OMCA promotes a closer packing between head groups of 12-2-12• 2Br -. This is because that the strong electrostatic association between OMCA and 12-2-12 2+ ions decreases the surface charges of micelles, thereby reducing the effective area of charged head groups. And it is noticeable that the height of first peak for system containing trans-OMCA is significantly higher than that of the system containing cis-OMCA, suggesting that 12-2-12• 2Br -surfactants in trans-OMCA system have a closer and more ordering packing than in cis-OMCA system.

C3 in benzene ring, C7 in methoxy, and C10 in carboxyl of OMCA are the key atoms to calibrate the main position of OMCA. The g(r) between them and the N1 atoms in 12-2-12• 2Br - was also calculated. As can be seen in Fig. 2.6 (b), the two isomers pack in very different patterns. The gN1-C3(r) function curves have a peak at 0.85 nm for system containing trans-OMCA and a peak at 0.48 nm for system containing cis-OMCA. The gN1-C7(r) witnesses a similar distribution with a peak at 0.52 nm for systems containing both cis-and trans-OMCA.

A sharp N1-C10 peak was observed at 0.43 nm for trans-OMCA system in gN1-C10(r) curve and at 0.46 nm for cis-OMCA system. The proximity of C3 to N1 of cis-OMCA system implies that its emergence on the micelle surface while the C3 of trans-OMCA is embedded into the micelle.

For both isomers, C7 is inserted inside the micelle (but not as deep as C3 for trans-OMCA) and C10 is distributed on the surface of micelle. The sharp N1-C10 peak reveals a highly orderly arrangement between these two atoms. The approaching of C10 to N1 for trans-OMCA system discloses a stronger electrostatic interaction between the charge centers of trans-OMCA and 12-2-12• 2Br -. The distinctions of cis/trans-isomer on the micelle surface can also be characterized by the solvent accessible surface area (SASA) between micelles and water. The SASA means the surface area of the micelle that is accessible to the solvent. In Gromacs, a 1.4Å spherical solvent probe is used to scan the surface of the micelle by default. The part with a charge between -0.2 and 0.2 is regarded as hydrophobic area, and the other part is the hydrophilic area. The SASA of surfactant micelles under different concentrations are displayed in Fig. 2.8. With the increase of the OMCA concentration, the total area, the hydrophilic area, and the hydrophobic area decrease. This indicates that the micelle become denser and the contact area with solution decreases because of the stronger electrostatic interaction. OMCA on micelles. The trend of spherical or rod-like micelles formation can also be explained by another important parameter, the critical packing parameter [START_REF] Dong | Self-assembly of onion-like vesicles induced by charge and rheological properties in anionic-nonionic surfactant solutions[END_REF] . In our simulation, l is calculated by the distance between C15 and C26. As is shown in Table 2.3, the P values for micelles with cis/trans-OMCA are 0.19 and 0.33, respectively. These values suggest that the most stable and favorable morphologies for cis/trans-OMCA at r n = 0.75 are spherical shape and rod-like shape. In other words, when the trans-isomers photo-isomerize into cis-isomers after UV irradiation, the originally stable rod-like micelle will become unstable. To reacquire a stable structure, rod-like micelles will gradually break up and transform into several spherical micelles.

Micelle transition

From above, we can see that the packing patterns of OMCA and 12-2-12• 2Br -affect the morphology of micelles. In order to further explore the mechanism of micelle transition after the UV irradiation, the quantitative calculations and other MD methods are adopted to further analyze the detailed information including geometric structure of OMCA, hydrophilicity of OMCA and the interaction energy between OMCA and 12-2-12• 2Br -at the molecular scale.

Geometry

Firstly, the optimized structures of OMCA molecules are shown in the Fig. 2.9. The value is the angle between the plane of benzene ring and carboxyl in OMCA. We can find that almost all atoms of a trans-OMCA molecule are oriented at a same plane with an angle 180° while the angle (140°) and shorter distance (6.46 Å) between C10 and H3 of cis-OMCA molecule show its three-dimensional configuration and higher bending degree. Moreover, as can be seen in Furthermore, we calculated the PMF by sampling method. The potential of mean force is the potential energy obtained by integrating the average force of the configuration ensemble, which can be calculated by:

PMF(r) = -kBTlng(r) (2-3)
where kB is the Boltzmann constant and g(r) is the radial distribution function.

The PMF in Fig. 2.13 represents the change of potential under a given pull force which pulls out a molecule from a pre-assembled spherical micelle to different distances. From Fig.

2.13 (a), we can see that it is much easier to pull out a cis-OMCA -ion from the stable spherical micelle than pull out a trans-OMCA -ion. The results once again approved that cis-OMCA molecules are more likely to escape from micelles to the solution. In Fig. 2.13 (b), the PMF of pulling out a trans-OMCA -is much larger than pulling out a cis-OMCA -from spherical micelle formed by OMCA and 12-2-12• 2Br -. This indicates that the spherical micelle containing trans-OMCA have a more stable configuration than that containing cis-OMCA. After UV irradiation, the steric hindrance of cis-OMCA molecule becomes larger and the electrostatic interaction and π-cation interaction become weaker leading to the disintegration of original micelle.

Secondly, a lower solubility in water has been proved to be related to a stronger association with micelles. [START_REF] Dong | Self-assembly of onion-like vesicles induced by charge and rheological properties in anionic-nonionic surfactant solutions[END_REF] Through comparing the solvation free energy, it is demonstrated that trans-OMCA is more hydrophobic than cis-OMCA. The stronger hydrophobicity of trans-OMCA indicates that the trans-OMCA remains associated with micelles to a larger degree. [START_REF] Dong | Self-assembly of onion-like vesicles induced by charge and rheological properties in anionic-nonionic surfactant solutions[END_REF] On the contrary, the stronger hydrophilicity of cis-OMCA endows it the chance to move towards the outer layer of micelles and even escape from the 12-2-12• 2Br -micelle layers, and finally induce the split of the micelle.

Finally, by calculating interaction energy, the micelles containing cis-OMCA are proved to be less stable. After the photoisomerization of trans-OMCA, to obtain a stable packing pattern with a lowest energy, cis-OMCA will change its packing pattern from embedding the aromatic ring into micelle to orienting that on the surface of micelle. Therefore, the long rodlike micelles will split into several spherical micelles.

Conclusions

In this chapter, we investigated photo-responsive behavior of Gemini surfactant 12-2- Moreover, the cis-OMCA has a weaker interaction with the 12-2-12• 2Br -than trans-OMCA.

All these factors induce the breakage and repacking of wormlike micelles.

Regarding the experimental research on photo-responsive wormlike micelles systems, 12-2-12• 2Br -and OMCA in water solution emerged as a photo-responsive system with different morphologies. At high concentration, 12-2-12• 2Br -surfactant will form vesicles even liquid crystals with large aggregation number. After UV light, the vesicle firstly transforms into long and elongated wormlike micelles and with the UV irrational time prolonged, the wormlike micelles will continue to break up and finally split into spherical micelles. Because of the multiple transformation process from vesicle to wormlike micelle and finally to spherical micelle, multiple control of the viscosity of the system can be achieved via UV light. We have studied several morphologies such as spherical, ellipsoidal, rod-like, wormlike and network micelles. However, owing to the scale limitation of simulation box, we cannot simulate the vesicles with micron size through united atom forcefield. From experiments after the trans/cis-OMCA photoisomerization, the complete transformation process from wormlike micelles to spherical micelles costs 60 minutes whereas the initial alteration in morphology takes place at the first few seconds. Moreover, several papers which depict the self-assembly aggregates of surfactant confirm that the micelle breakage and coalescing processes happen at the millisecond to second timescale under standard conditions [START_REF] Kubo | Photocurrent-determining processes in quasi-solidstate dye-sensitized solar cells using ionic gel electrolytes[END_REF][START_REF] Oelschlaeger | Structural, Kinetics, and Rheological Properties of Low Ionic Strength Dilute Solutions of a Dimeric (Gemini) Surfactant[END_REF][START_REF] Oda | Elongated aggregates formed by cationic gemini surfactants[END_REF] . However, the timescale of atomistic MD simulations is within microsecond. These scales could not entirely satisfy the time in micellar transformation and size of vesicle. Coarse-Grained (CG) model has an extended timescale which might accomplish the simulation of vesicle, but the subtle alterations of packing patterns between OMCA and 12-2-12• 2Br -will be hard to capture. To the best of our knowledge, rare articles report different aggregate self-assembly process and those aggregate transition process using atomistic MD simulation for 100ns from a random arrangement of surfactant solution.

We achieve this simulation successfully. Various micelle morphologies and specific packing patterns during micellar transformation were displayed. The causes of those different packing were elucidated comprehensively and systematically. Our simulation morphologies are in good agreement with our TEM results and others' experimental as well as calculation results. The present molecular-level details of the micellar repacking process and mechanism of aggregate transformation can be utilized to design novel photo-rheological systems with tunable rheological properties. Such photo-responsive system will widen the application prospect in microscale engineering fields such as drug delivery, soft materials, smart fluids and purification and separation.

The influence of the substituents at the benzene ring on the kinetic of photo-isomerization reaction is quite complicated. In addition, the insufficient investigation of micellar transition mechanism and the variation of viscoelastic properties of photo-responsive wormlike micelle of Gemini surfactants and cinnamates mixed system under UV irradiation have severely

Materials and methods

Materials

In this chapter, timethylene-1,3-bis (dodecyldimethylammonium bromide); 12-3-12•2Br -) was synthesized according to our previous work [START_REF] Chen | Effect of the spacer group of cationic gemini surfactant on microemulsion phase behavior[END_REF] . Three cinnamate derivatives, trans-o-

methoxy

UV irradiation

The ultra-high pressure short-arc mercury lamp (CHF-XM35-500W) with a 365 nm optical filter was applied to illuminate the solution to make cinnamate derivatives to photoisomerize from trans-form to cis-form. About 3.0g Samples were placed in a 10 ml quartz crucible and stirred continuously at 25 ± 0.1°C in a jacketed beaker connected to a lowtemperature thermostat bath. The distance between the samples and the light source was fixed at 20 cm.

High performance liquid chromatography details

High performance liquid chromatography (HPLC) was used to obtain the conversion fraction of the system under UV irradiation. The chromatographic separation was carried out by using ultra performance liquid chromatograph with an C18 column (250 × 4.6 mm, 5 μm, Agilent Germany). The temperature of the column was maintained at 25 ± 0.1°C during the analyzing process. 20 μl sample was injected and eluted with the mobile phase 0.1% phosphoric acid solution /acetonitrile = 60/40 in 15 min. The conversion fraction is defined as f, which can be calculated by

f = ci -ce ci (3-1)
where ci is the initial concentration of trans-isomer and ce is the equilibrium concentration of trans-isomer.

Rheological property measurement

Anton Paar MCR 302 rheometer (Anton Paar, Graz, Austria) was used to measure the steady and dynamic rheological properties of the studied WLM solutions with a cone plate system (CP50-1) with a radius of 50 mm and a taper angle of 1°. Flow curves were measured at a range of shear rate from 0.01 s -1 to 1000 s -1 and the dynamic frequency sweep was measured with a fixed strain value (γ = 1%) and a frequency of 0.1-100 Hz at 25.0 ± 0.1°C.

Microstructure observation of the micelles by TEM

The microstructure of surfactant aggregates was observed by TEM (Jeol JEM-1400, Japan).

Firstly, about 10µL sample was dripped onto the margin of the copper and adsorbed on the copper mesh after a few minutes; the excessive solution was eliminated with filter paper.

Subsequently, the sample was negatively stained with phosphotungstate for 5-10s, and the excessive solution was absorbed by filter paper.

Quantitative calculations and force-field parameters

The structures of six trans/cis-cinnamate derivatives ions were optimized by Gaussian 09 quantum chemistry packages through a hybrid functional B3LYP at the 6-311+g (d, p) level.

The optimized structures will be used as initial structures of MD simulations and to calculate the molar volume of six trans/cis-cinnamate molecules. The electrostatic potential distribution of cinnamate ions were calculated using Multiwfn software packages [START_REF] Tian | Multiwfn: A multifunctional wavefunction analyzer[END_REF] . The solvation free energy of cinnamate ions were calculated Gaussian 09 at the M052X/6-31G* level. The interaction energies of the packing pattern between 12-3-12 2+ and trans/cis-cinnamates were obtained using 6-311g+** basis set with B3LYP functional in SMD solvation model.

Since the force field GROMOS96 45a3 [START_REF] Schuler | An improved GROMOS96 force field for aliphatic hydrocarbons in the condensed phase[END_REF] has been proved to be in good agreement with the experimental data in many surfactant micellar systems [START_REF] Chen | Molecular Dynamics Simulations and Density Functional Theory on Unraveling Photoresponsive Behavior of Wormlike Micelles Constructed by 12-2-12•2Brand trans-ortho-Methoxy Cinnamate[END_REF] , we adopted GROMOS96 45a3 forcefield in all our molecular simulations. We optimized the initial structure and generated the coordinates of 12-3-12 2+ (Fig. 2.1(a)) and trans/cis-cinnamate ions using Gaussian 09. The force field parameters for 12-3-12 2+ , trans/cis-CA, trans/cis-OHCA were generated by the ATB server. The dihedral angle information of trans/cis-cinnamate ions were obtained from Heerdt's literature [START_REF] Heerdt | Photoisomerization induced scission of rod-like micelles unravelled with multiscale modeling[END_REF] which had been well estimated by DFT calculations. As to trans/cis-OMCA, the corresponding parameters can be found in our previous work [START_REF] Chen | Molecular Dynamics Simulations and Density Functional Theory on Unraveling Photoresponsive Behavior of Wormlike Micelles Constructed by 12-2-12•2Brand trans-ortho-Methoxy Cinnamate[END_REF] .

Simulation details

The box size of the pure 12-3-12• 2Br -surfactant molecule was set to 7.5×7.5×12 nm 3 . For the cinnamates and 12-3-12• 2Br -surfactant system, the cuboid box size in MD simulations was set to 7.5×7.5×24 nm 3 in order to fully show the wormlike micelle. Periodic boundary conditions were set in all three dimensions. In all our simulation systems, the concentration of 12-3-12• 2Br -was approximately 0.23 mol/L, which is far above the CMC (0.91 mM) of 12-3-12• 2Br -in aqueous solution [START_REF] Li | The self-assembly properties of a series of polymerizable cationic gemini surfactants: Effect of the acryloxyl group[END_REF] . For the pure 12-3-12• 2Br -system, 90 12-3-12• 2Br -surfactant molecules were dissolved in 19834 water molecules. For the cinnamates and 12-3-12• 2Br - surfactant mixed system, the number of 12-3-12• 2Br -molecules was fixed at 180 and the number of trans/cis-cinnamate ions was defined according to their conversion fractions that obtained by experiment (HPLC). All the surfactants and cinnamates were arranged randomly with approximately 37000 water molecules using Packmol. Corresponding number of counter ions of Br -and Na + were added in the box in a random assignment as well to maintain the charge equilibrium of the system. The simulation details of our systems are displayed in Table 3.1. The MD simulations were preformed using GROMACS 2018 software packages. The constant temperature of 298.15 K and the constant pressure of 1 bar were kept by Berendsen bath coupling scheme. Semi-isotropic pressure coupling was conducted in order to simulate rod-like and wormlike micelles. The simulation box was independently scaled in z-direction but was isotopically scaled in x-and y-directions. The time step was 2 fs in all simulations.

The SPC water model was employed. The trajectories were saved every 2ps. For all the system, the simulation time is 100ns. The short-range electrostatic cutoff and short-range Van der Waals cutoff were set to 1.0 nm, and the long-range electrostatic interactions were set to 0.12 nm by PME (Particle Mesh Ewald) method. Bonds were constrained using LINCS (Linear Constraint Solver) algorithm. VMD 1.9.2 was employed to visualize and display the trajectories and configurations of simulated system.

PMF calculation details

Six pre-assembly spherical micelles containing 32 12-3-12•2Br -and 32 cinnamates at K and 1 atm for 50 ns with the time step of 2 fs for six systems. Periodic boundary conditions were applied in three dimensions. The temperature and pressure were controlled by the Berendsen bath coupling scheme. Interactions were subjected to a cutoff distance of 1 nm where the long-range electrostatic interactions were set to 0.12 nm using the Particle Mesh Ewald technique. In the pulling process, the motion of micelles was restricted to maintain their initial configuration. A harmonic umbrella potential with a force constant of 1000 Kcal• mol -1 •nm -2 was applied between the COM of the spherical micelle and a 12-3-12 2+ ion using pull code.

Umbrella sampling simulations were carried out in 25 different windows ranging from 1.5nm to 6.5nm with a sequential stepwise reduction by 0.2nm. The MD simulation time for each window was 10 ns. The PMF was calculated from the sample windows using the Weighted

Histogram Analysis Method which are implemented by g_wham command in GROMACS. fluids shows a plateau at lower shear rates while exhibits a shear-thinning phenomenon in the higher shear rate region before UV illumination, which prove that the studied system is composed by typical wormlike micelles [START_REF] Lin | Spherical-to-Wormlike Micelle Transition in CTAB Solutions[END_REF] . As for the dynamic frequency sweep measurement, the viscoelastic modulus of these wormlike micellar solutions exhibits a typical Maxwell behavior [START_REF] Clausen | Viscoelastic micellar solutions: microscopy and rheology[END_REF] , which can be depicted by following equations.

Results and Discussions

G ' (ω) = G 0 ω 2 τ R 2 1+ω 2 τ R 2 (3-2) G " (ω) = G 0 ωτ R 1+ω 2 τ R 2 (3-3) G0 = 2G* (3-4)
Here G′ is the elastic modulus, G″ is the viscous modulus. ω is the angular frequency. The relaxation time τR is calculated by 1/ωc, where ωc is the angular frequency at the intersection of G′ and G″. G0 is the elastic plateau modulus value at higher ω. If G′ does not reach an apparent plateau value at higher frequency, the estimation of G0 can be calculated from equation (3-4),

where G* is the G′ at ωc.

For the 12-3-12•2Br -/trans-CA system, the zero-shear viscosity (η0, the viscosity at plateau) decreases from 1.1 Pa•s to 0.74 Pa•s after 160 minutes UV irradiation. In addition, the elastic modulus (G′) and viscous modulus (G″) curves of 12-3-12•2Br -/trans-CA (Fig. 3.2(d))

show an inconspicuous change before and after 160 min UV irradiation, suggesting the imperceptible changes of the viscoelasticity and further the morphology of the wormlike micelles after UV irradiation. These rheological results suggest that the photo-responsiveness of wormlike micelles formed in 12-3-12•2Br -/trans-CA system is almost negligible. However, for the system containing trans-OHCA, the phenomenon of shear-thinning still exists while the η0 is significantly reduced from 19.7 Pa•s to 2.63 Pa•s after undergoing 160 min UV irradiation.

Regarding the dynamic viscoelastic behavior, it can be seen that the frequency at intersection of curves for the variation of G′ and G″ with frequency increase gradually with the prolonging of UV irradiation time. Obviously, the relaxation time of the wormlike micelles decrease, indicating the weakening of the network structure [START_REF] Acharya | Wormlike micelles in mixed surfactant solutions[END_REF] . In terms of the wormlike micelles containing trans-OMCA, the shearing-thinning phenomenon becomes more and more subtle and tends to disappear with UV irradiation and the intersection of G′ and G″disappears gradually (at 80 minutes). This may be due to the transition of wormlike micelles to shorter rodlike micelles and even spherical micelles after UV irradiation. For providing the more intuitive changes of wormlike micelles, some structural parameters of wormlike micelles were calculated according to the following equations [START_REF] Koehler | Microstructure and Dynamics of Wormlike Micellar Solutions Formed by Mixing Cationic and Anionic Surfactants[END_REF] .

G 0 G min " = L L e (3-5) L e = ξ M 5/3 L P 2/3 (3-6) ξ=( k B T G 0 ' ) 1/3 (3-7)
L is the average extension length. Le is the entanglement length between two entanglements. G min ″ represents the minimum value of G″ at higher frequency; ξ refers to hydraulic correlation length (representing the mesh size of micelle network); Lp is the persistence length of micelles, Lp ≈ 15-20 nm [START_REF] Liu | Effect of the Substituent Position on the Phase Behavior and Photoresponsive Dynamic Behavior of Mixed Systems of a Gemini Surfactant and trans-Methoxy Sodium Cinnamates[END_REF] ; kB is Boltzmann constant (kB = 1.3806 × 10 - 23 J/K); T is Kelvin temperature. According to these equations, the L and Le values of wormlike micelles with different UV irradiation time were obtained and showed in Table 3.2. Obviously, after 160 min of UV irradiation, the length of the wormlike micelles containing trans-CA was slightly reduced from 289-350 nm to 213-258 nm, while the wormlike micelles containing trans-OHCA witness a sharp drop in length from 548-663 nm to 347-420 nm after 160 min UV illumination. The reduction in length of wormlike micelles containing trans-OMCA is the most significant (from 355-430 nm to 167-202 nm). the wormlike micelles almost fission within 40 min UV irradiation, which is confirmed by the disappearance of the intersection of G′ and G″.

Obviously, the sensitivity of the wormlike micelles to UV irradiation is trans-OMCA > trans-OHCA > trans-CA. The rheological results are in good agreement with the TEM images.

The photo-isomerization kinetics of the cinnamates

In order to explore the intrinsic reason for the difference of the photo-responsive behaviors of the studied three cinnamates, the photo-isomerization reaction kinetics of these cinnamates were studied firstly. To ensure that the trans-isomers are converted to cis-isomers as much as possible, the solution for constructing worm like micelles originally was diluted 1000 times (40 After we know the equilibrium conversion fraction of the cinnamates, the variation of conversion fraction with time can be plotted. Fig. 3.4 provides the variation of conversion fraction for different cinnamates with UV irradiation time and the corresponding kinetic curves.

From our previous work [START_REF] Cates | Rheology of giant micelles[END_REF] , the photo-isomerization reaction of cinnamates usually follows the law of the first order opposite reaction. Therefore, we plotted the variation of ln ci-ce ci-ce-c with time and found that these points are perfectly comply with the law of the first order opposite reaction. Then a linear fit was used to fit these kinetic curves to obtain the slopes (k1+k-1) so that the reaction equilibrium constant (Kc), forward rate constant (k1) and reverse rate constant (k-1) can be calculated by the following equations.

Kc = ce ci -ce (3-8) Kc = k1 k-1 (3-9)
These kinetic parameters are provided in Table 3.3. As shown in Table 3. For the kinetics of the three photo-isomerization reactions, the order of k1 is trans-OMCA (1.09) > trans-OHCA (0.12) > trans-CA (0.006), indicating that at same concentration of transcinnamate, the forward photo-isomerization reaction rate of trans-OMCA is the fastest. This is consistent with the experiment results of the highest morphological transition rate and micellar shortening rate of trans-OMCA.

It is reported that among the many factors of affecting the kinetic of photo-isomerization reaction of the cinnamates, the existence of the lone-pair electrons should have a positive effect in lowering the energy barrier of the double bond rotation, thereby accelerating the photoisomerization reaction rate [START_REF] Cates | Rheology of giant micelles[END_REF] . That is why the conversion velocity of the trans-OMCA and trans-OHCA with lone-pair electrons on the oxygen atom of the methoxy group and hydroxyl group next to the aromatic ring are higher. Besides, the methoxy group in benzene ring may benefit to lower the energy barrier of the rotation potential of the double bond more than hydroxyl group. Obviously, the photo-responsive behavior of the system not only related to the photochemical reaction rate directly but also depends on the change of the molecular geometry before and after UV irradiation. To further explain the mechanism of the photo-responsive behavior of the micelles at a microscopic level, the MD simulations and quantitative calculations are needed. 3-12•2Br -surfactant will form aggregates with different morphologies [START_REF] Kostrzewa | Particle settling in micellar solutions of varying concentration and salt content[END_REF] . As the concentration of 12-3-12•2Br -increases, morphologies with larger scale and much more aggregation number can be found. Fig. 3.5 shows the snapshots of the initial and final configuration of single 12-3-12•2Br -simulation box. From Fig. 3.5, it can be found that the randomly assignment 90 12-3-12•2Br -molecules finally form three spherical micelles after 100 ns MD simulation. The average aggregate number is 30, which is in good agreement with the experimental value 32 [START_REF] Danino | Alkanediyl-alpha, omega-Bis(Dimethylalkylammonium Bromide) Surfactants (Dimeric Surfactants). 5. Aggregation and Microstructure in Aqueous Solutions[END_REF] . This confirmed that GROMOS96 45a3 forcefield and our simulation parameters are feasible. Due to the electrostatic interaction between polar head of surfactants and counter ions in solution, 12-3-12•2Br -micelles will display a more complex morphology in the presence of counter ions with hydrophobic structure [START_REF] Lin | Spherical-to-Wormlike Micelle Transition in CTAB Solutions[END_REF][START_REF] Clausen | Viscoelastic micellar solutions: microscopy and rheology[END_REF] . Fig. This result means the mixed micelles containing trans-CA will still maintain the morphology of worm micelles and will never be transformed into rod-like or spherical micelles after being exposed to infinite ultraviolet light. For system containing trans-OHCA, when f = 0.24, the wormlike micelle starts to rupture and finally appears the coexistence of short rod-like and spherical micelle at f = 0.65 (equilibrium conversion of trans-OHCA). This phenomenon suggests that the long and twined wormlike micelles constructed by 12-3-12•2Br -and trans-OHCA have the potency to transform into rod-like and spherical micelles after being exposed to enough ultraviolet light. For trans-OMCA system, the shape of wormlike micelle remains when f = 0.24. The wormlike micelle splits into rod-like micelles once f reaches to 0.65. After long enough UV irradiation (equilibrium conversion of trans-OMCA f = 0.88), the micelles will eventually transform into spherical micelles. In order to confirm these special morphologies, the density profiles along z axis of these micelles were calculated and shown in Fig. 3.7. Obviously, before UV irradiation the wormlike micelle is formed represented by the corona-shape curves of 12-3-12 2+ . After UV irradiation, the variation of density distributions of 12-3-12 2+ in three systems are the same as the micelle transition tend. The density distribution curve of CA system maintains the corona-shape at f = 0.24. The corona-shape of density distribution curve for OHCA fission into a small coronashape peak and a sharp peak at f = 0.65. The sharp peak and the small corona-shape peak of 12-3-12 2+ in curves reconfirms the morphology of short rod-like micelle and spherical micelle.

Three sharp peaks appear at f = 0.88 for OMCA, implying the formation of three spherical micelles. Obviously, the photo-responsive behavior of three trans-cinnamate is successfully simulated. These special morphologies in our simulation are in good agreement with our TEM experiments that wormlike micelles containing trans-OMCA and trans-OHCA will gradually break into smaller aggregates, while wormlike micelles containing trans-CA can still maintain initial shape at equilibrium even undergoing long enough UV irradiation.

Based on all the above experimental results, it can be preliminarily concluded that the photo-responsiveness of the system containing cinnamates is derived from the photoisomerization rate and the equilibrium conversion fraction of trans-CA. In order to study the photo-responsive behavior more systematically, further simulation and calculation such as critical packing parameter, packing patterns, potentials of mean force, potential distribution and so forth were performed and discussed in the following sections

Critical packing parameter of the micelles

The systems undergo different UV irradiation time present different morphologies. To explore the difference of micelles containing trans/cis-cinnamates, some important parameters of the micelles were calculated and shown in Table 3.4. The critical packing parameter [2] is a significant parameter of determining the micelle morphology. As shown in Table 3.4, the P values of the micelles containing CA at f = 0 and 0.24 (0.48 and 0.40) imply that the wormlike micelles are the relatively stable and favorable morphology at f = 0 and 0.24. For the micelles containing trans-OHCA, with the increase of f, the P values decrease though still locate in the region of 0.33~0.5. This maybe the reason for the length of wormlike micelles containing trans-OHCA are shorten under the UV irradiation. The wormlike micelles containing trans-OMCA witness the same tendency as wormlike micelles containing trans-OHCA, while at f = 0.88, the P is reduced to 0.29 (P ≤ 0.33), correspondingly that the wormlike micelles transformed into spherical micelles. In our simulation, the P values are very consistent with TEM images in Fig.

3.1.

Table 3.4 Geometric information of micelles and interaction energy between 12-3-12 2+ and cis/transisomers after system equilibrium in MD simulations: V, volume (nm 3 ) of the last frame; apho, hydrophobic (nm 2 ), aphi, hydrophilic (nm 2 ) and atot, total (nm 2 ) surface areas of the last frame; l, the length of alkyl chain (nm); P; Ecoul, coulomb interaction energy (kJ/mol); ELJ Lennard-Jones interaction energy (kJ/mol); Etol, total interaction energy.

The energy difference in micelles transition

The relative energy and its variation can estimate the stability of the micelles and illustrate the mechanism of the micelle transformation. The interaction energies among 12-3-12 2+ and cinnamate derivatives in system at different f are calculated by g_energy in Gromacs. The curves of the interaction energy with simulation time are displayed in Fig. 3.8. It can be seen from Table 3.4 that the absolute values of the coulomb interaction energy, Lennard-Jones interaction energy as well as total interaction energy all decrease with the increases of f, indicating that the electrostatic interaction energy and van der Waals interaction between 12-3-12 2+ and cinnamate derivatives become weaker after UV irradiation, which cause the fission of the micelles. Furthermore, the packing pattern can also be deduced from the solvent-accessible surface area of micelles. Table 3.4 and Fig. 3.13 provide the information of hydrophobic, hydrophilic and total surface areas of aggregates with the variation of f. The hydrophobic area increases with f, which reconfirmed the hydrophobic aromatic ring of trans-isomer is oriented inside the micelles while that of cis-isomers is exposed on the surface of micelle. So far, the different numbers of trans/cis-cinnamates have been used to represent the different conversion fractions to simulate the system after UV irradiation. The morphological transition process of micelles containing three different cinnamates under UV irradiation was 85 successfully simulated. P and density distributions demonstrate these special micelle morphologies, the interaction energy and the PMFs prove that the micelles containing more trans-isomers has higher stability. The aromatic ring of trans-cinnamate tends to insert into the hydrophobic region of micelle while that of cis-cinnamate apt to orient on the micelle surface.

The calculated g(r) and solvent-accessible surface area further provide the packing pattern information of different micelles. However, a more in-depth understanding of these difference quantitatively at atom level is still needed.

The difference in geometry structure of cinnamate derivative molecules

The photo-responsiveness difference of the wormlike micelle containing the cinnamates with different substituents should be attributed to the difference of the molecular properties such as molecule volume, solvation free energy, bond angle, and electrostatic potential distributions before and after UV irradiation. To further explore the distinction between theses cinnamates and how the ortho-substituents affect the photo-isomerization ability, the Gaussian 09 quantum chemistry packages are used on different basis set. Firstly, the structures of trans/cis-cinnamates are optimized at b3lyp/6-311+g (d, p) level and shown in Fig. 3.14. From Fig. 3.14, it can be seen that trans-cinnamates have a planar structure while the cis-cinnamates have a three-dimensional structure. This means that the trans-cinnamate is easier to insert into the micelle and the carboxyl of the trans-cinnamate is closer to the head group of 12-3-12•2Br -, thereby forming a denser morphology compared with that of system containing cis-cinnamates.

The angle α (defined as the dihedral angle between the aromatic ring plane and carbonyl plane) was calculated further. The α values of trans-isomers are all 180°, indicating a planar structure.

For the cis-isomers, the α values are 57.8° (cis-CA), 66.1° (cis-OHCA) and 66.1° (cis-OMCA) respectively. Obviously, the α of cis-CA is smaller, implying that the cinnamates ion is more like a plane while the cis-OHCA and cis-OMCA ions show a significant curvature, indicating that cis-OHCA and cis-OMCA occupy more space in micelles than cis-CA. This can also be proved by the calculated molar volumes. This suggests that the space steric of OMCA and OHCA is strengthen after UV irradiation, causing the micelles to become looser and looser until break. All these geometric parameters indicate that after UV irradiation, the arrangement of surfactant in micelle become loose and some cis-OHCA and cis-OMCA ions can escape from 12-3-12 2+ layers owing to the increase of steric hindrance after UV irradiation, which maybe the main reason for the higher sensitivity to UV of micelles containing trans-OHCA and trans-OMCA. The lower sensitivity of system containing CA ions should be attributed to the decrease of its steric hindrance after UV irradiation and the cis-CA ions remain embedded in the 12-3-12 2+ layers. Obviously, the existence of ortho-substituents enhances the difference of the molecular steric hindrance before and after UV irradiation and strengthen the photo-responsive ability correspondingly. The cinnamate with ortho-methoxy group has better photo-responsive ability than that with orthohydroxyl.

Electrostatic potential distribution of trans/cis-cinnamates

The electrostatic potential distributions of these three cinnamate ions have been calculated

and shown in Fig. 3.15. It can be seen that the maximum of negative charge is concentrated on the carboxyl group and the minimum of negative charge is concentrated on the aromatic ring.

The order of the maximum value of the electrostatic potential is trans-OMCA (-7.37 eV) > trans-OHCA (-7.36 eV) > trans-CA (-7.19 eV), while the electrostatic potential distributions in solvation free energy represents the hydrophilicity of the molecule. The solvation free energies of cis-isomers are all higher than trans-isomers, revealing that the cis-isomers are easier to escape from the micelles and linger in the solution owing to higher hydrophilicity. ΔE is the difference of solvation free energy between trans / cis-isomers. As can be seen, the order of ΔE is ΔE (OMCA) >ΔE (OHCA) > ΔE (CA). This implies that the cis-OMCA ions are more likely to flee away from the micelles than OHCA and CA ions after photo-isomerization. In addition, compare with CA, the existence of hydrophilic ortho-substituents (hydroxyl and methoxy)

enhances not only the hydrophilicity of the molecule but also the hydrophilic difference of cinnamate before and after UV irradiation. Reasonably, the system composed by cinnamate with different ortho-substituents show different photo-responsive behaviors.

Interaction energy of representative packing patterns

To further study the photo-responsive mechanism at an atom level in detail, two typical packing patterns of trans/cis-isomers in micelle in MD simulations were intercepted for calculating the interaction energy between trans/cis-isomers and 12-3-12 2+ at special packing patterns by using Gaussian at 6-311+g** basis set with B3LYP functional in SMD solvation The interaction energy among cis-cinnamate and surfactants is lower when aromatic ring oriented near the head group of 12-3-12•2Br -. While for trans-cinnamate packing patterns, the energy of the trans packing with aromatic rings embedded into micelle is relatively lower.

Obviously, the lower interaction energy keeps the micelle more stable. For CA, although the cis packing (a) and trans packing (d) have similar packing patterns (aromatic rings embedded into micelle), the interaction energy of cis packing is higher than that of trans packing. This means that when the stable trans packing (d) transforms into cis packing (a) after UV irradiation, to obtain a new stable state, the cis-CA will change its previously packing pattern from embedding into micelle (a) to orienting on the surface of micelle (b). It is the same for OHCA and OMCA.

Furthermore, the differences of interaction energy between two cis packing patterns for CA, OHCA and OMCA are calculated. They are 15.84, 22.81 and 31.68 kJ/mol for CA, OHCA and OMCA, respectively. These energy differences also provide some information about the ability of micelle transformation after UV irradiation in some degree (OMCA > OHCA > CA), which is very consistent with the experiment results. Simultaneously, this energy difference implies that the introduction of ortho-subsistent can promote the transformation of micelle morphology by UV irradiation.

Reaction equilibrium constant

The reaction equilibrium constant is an important parameter to determine the conversion fraction of the photo-isomerization reaction of cinnamates. We calculated the Gibbs free energy by Gaussian at b3lyp/6-311+g (d, p) level and then obtained the reaction equilibrium constant (K) at 25°C by:

K = exp (- ∆G RT ) (3-10)
where R is the molar gas constant (R = 8.3145 J/(mol•K)) and T is the Kelvin temperature. The calculation results are shown in Table 3

Mechanism of photo-responsive transition of wormlike micelles

Considering all the above experimental, simulation and calculation results comprehensively and systematically, the underlying mechanisms of the photo-responsive transition of wormlike micelles containing trans-CA, trans-OHCA and trans-OMCA were speculated and shown in Fig. 3.17. The planar structure and lower steric hindrance and hydrophilicity of trans-cinnamates as well as the higher electrostatic potential in carboxyl endow them with a denser packing pattern (trans-cinnamates vertically insert into the surfactant hydrophobic layers.) with surfactants, thereby forming wormlike micelles. After UV irradiation, the trans-cinnamates photo-isomerize into cis-cinnamates. The higher steric hindrance and hydrophilicity as well as the lower electrostatic potential in carboxyl and evener electrostatic distribution of cis-cinnamates lead to a loose packing pattern (cis-cinnamates orient at the micelle surface.) which weakens the interaction between surfactants and finally causes the fission of micelles.

Among three cinnamate, the presence of ortho-substituents in cinnamate enlarges the difference between the steric hindrance, electrostatic distribution and hydrophilicity of trans/cis-cinnamates. These larger differences before and after UV irradiation allows the cis-OMCA and cis-OHCA to escape away from the micelle and linger in solution more easily than cis-CA and lead to the micelle transformation. Besides, the conversion fraction of the photoisomerization reaction is the most important factor determining the degree of morphological transition of wormlike micelle. The existence of the ortho-substituents increases the equilibrium constant of the photo-isomerization reaction (OMCA increases most.). Therefore, trans-OMCA is endowed with the best photo-responsive capability.

Conclusions

In this chapter, we used experimental methods such as rheology, TEM, UV-Vis absorption spectroscopy and HPLC, combined with MD simulation and quantitative calculations to study the photo-responsive behavior of wormlike micelles constructed by Gemini surfactant 12-3-12•2Br -and three cinnamates. In experiment, the three systems show varying degrees of photoresponse capabilities. The wormlike micelle system containing trans-OMCA has the strongest photo-responsive ability, with a morphology transition from wormlike to spherical after long enough UV irradiation. The wormlike length of trans-OHCA system is shortened while for trans-CA, the wormlike micelle maintains its shape. The kinetics results show that trans-OMCA has the highest equilibrium conversion fraction and the fastest reaction rate, followed by trans-OHCA and trans-CA.

In simulation, different numbers of trans/cis-isomers represents the conversion fraction.

The micellar morphologies corresponding to our experimental results were successfully captured and verified by the density distribution and the Ps. The different packing patterns between 12-3-12•2Br -and trans/cis-isomers (trans-isomers are embedded into the hydrophobic layers of surfactants and cis-isomers orient at the micelle surface.) were visualized and characterized by g(r) and SASA. ΔPMFs and the interaction energy of certain packing patterns confirm that the micelle containing trans-isomers is more stable.

In quantitative calculations, the higher steric hindrance and hydrophilicity as well as the lower electrostatic potential of cis-isomers allow cis-isomer to flee away from the micelles and stay at solution, thereby causing the breakage of the micelles. In addition, the presence of ortho-substituent in cinnamate promotes the difference of the steric hindrance, electrostatic distribution and hydrophilicity of trans/cis-isomers and further influences the packing pattern of them with 12-3-12 2+ in micelles. The higher difference in electrostatic potential distributions and the highest difference in solvation free energy, molecule volume as well as the highest reaction equilibrium constant indicates the best photo-responsive ability of trans-OMCA.

However, the limit of the time scale and box scale of MD simulation prevent us from simulating longer, more entangled wormlike micelles at a longer timescale. And the transition state and the mechanism of the kinetic of these photo-isomerization reaction will be the focus of our further research.

Our systematical study of the photo-responsive wormlike micelles constructed by Gemini surfactant and cinnamates will expand its application prospects in microscale engineering fields such as the drug delivery, optoelectronic materials, smart fluids and purification and separation.

software packages. The solvation free energy of trans/cis-cinnamate derivatives were calculated at the M052X/6-31G* level in SMD solvation model.

The force field GROMOS96 45a3 is used in our MD simulations owing to its good consistency with the experimental data which has been confirmed in our previous studies. We optimized the initial structure and generated and the coordinates of 12-3-12 2+ and trans/cis-OMCA, trans/cis-MMCA and trans/cis-PMCA using Gaussian 09. The structures of Gemini

Simulation Details

The cuboid box size in MD simulations was scaled to 7.5 × 7.5 × 24 nm 3 . Periodic boundary conditions were set in all three dimensions. In our simulation system, the number of 12-3-12•2Br -molecules was fixed at 180. Correspondingly, the concentration of 12-3-12•2Br - was approximately 0.23 mol/L, which is far above the CMC (0.91 mM) of 12-3-12•2Br -in aqueous solution. The number of trans/cis-cinnamates in simulation system depends on the experimental conversion fraction which has been published (0.88 for tran-OMCA, 0.91 for trans-MMCA and 0.82 for trans-PMCA) [START_REF] Cates | Rheology of giant micelles[END_REF] . Here, we define f as the conversion fraction. The surfactant and cinnamate ions as well as corresponding number of counter ions of Br -and Na + were distributed randomly in approximately 37000 water molecules using Packmol. The system details are exhibited in Table 4.1. The simulation box was independently scaled in z-direction but was isotopically scaled in xand y-directions by semi-isotropic pressure coupling in order to simulate rod-like and wormlike micelles. Simulation time was set to 100 ns with a 2 fs time step and the trajectories were saved every 2ps. The SPC water model was employed. The short-range electrostatic cutoff and shortrange Van der Waals cutoff were set to 1.0 nm, and the long-range electrostatic interactions were set to 0.12 nm by PME (Particle Mesh Ewald) method. LINCS (Linear Constraint Solver) algorithm were used to constrain bonds. VMD 1.9.2 was employed to visualize and display the trajectories and configurations. with the experiment [START_REF] Cates | Rheology of giant micelles[END_REF] . and trans-PMCA (f) ruptures into two corona-shape peaks, suggesting the formation of two short rod-like micelles. For (f), the trough between two peaks do not reach zero, which is attribute the overlapping of micelles in z direction. The wormlike micelles with different position of substituent group exhibits different photo-responsive ability under the UV irradiation. The critical packing parameter is a significant parameter which can be used to explain the micelle morphology. The Ps of these systems and corresponding parameters were calculated and shown in Table 4.2. As shown in Table 4.2, although the P value of micelles containing trans-OMCA remains in the wormlike micelle region (0.33 < P < 0.5), they still decrease from 0.44 to 0.35 (at f = 0 and 0.94), which implies that the length of wormlike micelle is shortened and tend to transform into spherical micelle. For the micelles containing trans-MMCA, the P values are 0.46 and 0.42 (at f = 0 and 0.91). This may explain that the wormlike micelle containing trans-MMCA is transformed to two short rod-like micelle after UV irradiation. For trans-PMCA system, the same trend as trans-MMCA can be found. When at f = 0.82, the P is reduced to 0.38 from 0.53 (f = 0.82),

Results and Discussions

indicating that the wormlike micelle tends to shorten. The P values are very consistent with the micelle morphology in Fig. 4.2 and in experiments [START_REF] Cates | Rheology of giant micelles[END_REF] , which can give a good prediction on the micelle morphologies and a good explanation of micelle transition.

The energy difference in micelles transition

The interaction energy and its variation can estimate the stability of the micelles and illustrate the mechanism of the micelle transformation. The variation of interaction energy (Coulombic, LJ and total interaction energy) with time between 12-3-12 2+ and cinnamates (including cis and trans) ions is shown in Fig. 4.4 and the equilibrium interaction energies of systems are calculated and shown in the Table 4.2. It can be seen from Fig. 4.4 that the six systems reach to the equilibrium at approximately 10 ns. The Coulombic, LJ and total interaction energy all decrease after UV irradiation, causing the wormlike micelle to become unstable and eventually fission. This indicates the interaction between 12-3-12 2+ and cisisomers is weaker than that of trans-isomers. Based on the interaction energy and the Ps result, we can draw a conclusion that wormlike micelle composed by 12-3-12•2Br -and transcinnamates is relatively more stable than that of cis-cinnamates. After the UV irradiation, transcinnamates start to photo-isomerize into their cis-form, and the difference in interaction energies of sysyem is tha main drive force that causes the wormlike micelle to fission.

Packing patterns between MCAs and 12-3-12 2+

From above, we have studied the difference of the photo-responsive behavior of the systems containing trans-cinnamates with different methoxy-substituent position. In order to further understand the mechanism of micelle transformation, it is very important to understand how trans/cis-cinnamates arrange in micelles. Firstly, we calculated g(r) of certain atoms to characterize the packing pattern between 12-3-12 2+ ions and cinnamates. Fig. 4.5 displays the radial distribution functions (gN1-N1(r)) between the N1 atoms of different 12-3-12 2+ in system.

It can be seen from Fig. 4.5 that before and after UV irradiation, all curves show three continuous peaks, indicating that an orderly repeating hexagonal crystal structure 12-3-12 2+ is formed. The first peak positions of gN1-N1(r) of the system containing trans-OMCA and trans-PMCA appears at 0.64 nm, and the height of the peaks decreases, indicating a less orderly arrangement of 12-3-12 2+ after UV irradiation. While for trans-MMCA, after the UV irradiation, the increase of the first peak height indicates the formation of a more orderly arrangement Fig. 4.6 (c) (f) (i), all the gN1-C10(r) exhibits the same distribution with a sharp peak near 0.44nm, which indicates that a strong electrostatic interaction between cinnamates and surfactants. For OMCA, the peak moved slightly from 0.43 nm to 0.45 nm after UV irradiation with no change in the peak height, indicating that electrostatic interaction between 12-3-12•2Br -and OMCA becomes weaker. For MMCA, the peak position and height of gN1-C10(r) are nearly unchanged.

Furthermore, the peak height of PMCA decreases after the UV, indicating the weaker electrostatic interaction after UV irradiation. It is worth noting that the Coulombic interaction energies of trans-OMCA and trans-PMCA at f = 0 are much higher than the Coulombic interaction energies at equilibrium, while trans-MMCA is almost the same. This is consistent with g(r) results. deeply, in the order of ortho-, meta-and para-. The carboxyls of trans-cinnamates are close to center of the head group of 12-3-12 2+ owing to the strong electrostatic interaction. On the contrary, cis-cinnamates are located horizontally on micelle surface. Their aromatic ring and carboxyl groups are close to the head group of 12-3-12 2+ , and the methoxy of them inserted into the interior of the micelles except for the cis-PMCA whose methoxy are oriented on the micellar surface. Thus, when trans-cinnamates photo-isomerize into cis form after UV irradiation, the aromatic rings will detach from the interior of micelles and rearrange on the surface of the micelles. This rearrangement loosens the packing pattern and weakens the interaction between cinnamates and 12-3-12 2+ , leading to wormlike micelles to fission into short rod-like even spherical micelles. The packing pattern can also be deduced from the solvent-accessible surface area of micelles. To further study the difference in packing pattern of cinnamates and surfactant in micelle The solvent accessible surface including hydrophobic (apho), hydrophilic (aphi) and total surface area of the micelle containg three cinnamates at iniatial and equilibrium are calculated and shown in Fig. 4.8 and Table 4.2. It can be seen from Fig. 4.8 that the surface areas of three systems all decrease before 10 ns and keep stable after 10 ns, implying the surfactant molecules self-assemble into a certain morphology and maintain this morphology till the end of simulation.

The hydrophobic surface area all incrase after UV irradiation, which reconfirm that the beneze ring of trans-cinnamate is inserted into the micelle layer while that of cis-cinnamate is oriented on the micelle surface. In addition, the hydrophilic surface areas of micelles containg trans-OMCA and trans-MMCA decrease after UV irradiation while that of trans-PMCA increases, proving that the methoxy of cis-OMCA and cis-MMCA are embedded into micelle while that of cis-PMCA is oriented on micelle surfacr after UV irradiation.

Table 4.2 Geometric information of micelles and interaction energy between 12-3-12 2+ and cis/trans-MCAs after system equilibrium in MD simulations: V, volume (nm 3 ) of the last frame; apho, hydrophobic (nm 2 ), aphi, hydrophilic (nm 2 ) and atot, total (nm 2 ) surface areas of the last frame; l, the length of alkyl chain (nm); P; Ecoul, coulomb interaction energy (kJ/mol); ELJ Lennard-Jones interaction energy (kJ/mol); Etol, total interaction energy; the average hydrogen bond number. In addition, the packing pattern can also be reflected from the hydrogen bond. The number of the hydrogen bond between the cinnamate ions and the water were calculated and shown it in Fig. 4.9. With the methoxy shifting from the ortho to meta and para position, the methoxy of trans-cinnamate is inserted more and more deeply into the interior of micelles. Thereby the number of the hydrogen bond between trans-cinnamate and the water decreases. After the UV irradiation, because the methoxy of cis-OMCA and cis-MMCA (more inner) is plugged into the interior of the micelle, the number of the hydrogen bond of the systems containing OMCA and MMCA decreases while for trans-MMCA, the number of hydrogen bond drop more sharply.

On the contrary, because the packing pattern for cis-PMCA and surfactant has been changed

into the methoxy group lying on the micelle surface instead of being inserted into the micelle like trans-PMCA after UV irradiation, there is a converse trend that the number of hydrogen bond between trans-PMCA and the water increases. In order to further explore the geometrical differences between OMCA, MMCA and PMCA and how the position of methoxy substituent affects the photo-response behavior of wormlike micelles, the Gaussian 09 quantum chemistry packages were used. Firstly, the structures of trans/cis-cinnamates were optimized using b3lyp/6-311+g (d, p) basis set and shown in Fig. 4.10. It can be seen from Figure 4.10 that trans-cinnamates have a planar structure, while cis-cinnamates has a three-dimensional structure. This indicates that when 12-3-12 2+ and cinnamates form micelles in the solution, trans-MCA is more likely to insert vertically into the micelles, thus forming a dense morphology. For the trans-cinnamates ions, α values (the dihedral angle between the aromatic ring plane and carbonyl plane) are 180°, which confirms their planar structure. For the cis-cinnamates ions, α values are 66.1° (cis-OMCA), 60.9° (cis-MMCA), and 46.9° (cis-PMCA). It indicates that when the methoxy group moves from the ortho position to the meta position and the para position, the structure of cis-cinnamates is closer and closer to a plane structure.

The molar volume directly reflects the steric hindrance of the molecule. Table 4.4 lists the calculated molar volumes of cinnamates ions. Obviously, before UV irradiation, the molar volume of trans-cinnamates ions increases as the methoxy group moves from the ortho position to the meta position to the para position. After UV irradiation, except for the sharp increase in the molar volume of cis-OMCA ion, the molar volume of cis-MMCA and cis-PMCA ions decreased significantly. The increase in the degree of bending and molar volume of OMCA ions after UV irradiation promotes its steric hindrance, which leads to the loosening and rupture of micelles. For MMCA and PMCA ions, the molar volume decreases after UV illumination, which is not conducive to the transformation of wormlike micelles. This confirms our experimental results that trans-OMCA wormlike micelles break up into spherical and rod-like distribution in carboxyl group decreases, and more potential is transferred to the benzene ring.

The weaker electrostatic interaction between cis-cinnamates and surfactants lead to the rupture of micelle. Among the three types of cis-cinnamates, the electrostatic potential distribution in carboxyl group of cis-OMCA decreases the most (0.33), indicating the strongest photo-response ability of wormlike micelle containing trans-OMCA. Owing to the presence of methoxy at meta and para position, the difference in maximum of electrostatic potential in carboxyl group decreases, leading to a drop in photo-responsive ability of wormlike micelle.

Hydrophilicity

The molecular structure also has an important impact on the hydrophilicity of the molecules. To explore the difference of hydrophilicity for these trans/cis-cinnamate molecules, we calculated the solvation free energies of them at the M052X/6-31G* level in SMD solvation model and summarized the results in Table 4.3. The solvation free energy represents the strength of the hydrophilicity of the molecule. The higher the absolute value of solvation free energies, the stronger the hydrophilicity of the molecule. As shown in Table 4.3, before the UV irradiation, the order of the solvation free energy is trans-PMCA > trans-MMCA > trans-OMCA. This order indicates that the trans-OMCA has the strongest hydrophobicity, which may be the reason for the strongest binding with the 12-3-12 2+ . After UV irradiation, the solvation free energy of linger in the solution due to its higher hydrophilicity. On the contrary, the MMCA and PMCA witness a slight and sharp drop in the solvation free energy. The decrease of the hydrophilicity tends to drive the cis-MMCA and cis-PMCA to stay in the micellar layer instead of heading to the solution, thereby reducing the photo-responsive ability of corresponding wormlike micelle.

The farther distance between the methoxy group and the double bond for trans-MMCA and trans-PMCA reverses the difference in molar volume and hydrophilicity of them before and after the UV irradiation, thereby reducing micellar transition velocity and degree of wormlike micelle. Furthermore, to obtain the energy information more accurately, we intercepted two typical packing patterns between trans/cis-cinnamates and 12-3-12 2+ in micelles from MD simulation to calculate their interaction energies and show the results in Fig. 4.12. One is that the benzene ring is embedded in the surfactant hydrophobic layer ((b), (c), (f), (g), (j), (k)), and the another one is that the benzene ring is oriented near the head group of 12-3-12•2Br -((a), (

). For convenience, the relative lower interaction energies for packing pattern (b) (f) (j) are set to 0 kJ/mol. As shown in Fig. 4.12, for the trans-isomers, the packing pattern that the benzene ring is embedded in the micelle has relatively low energy, imply that the micelle with this packing pattern is more stable. While for the cis-isomer, the packing pattern of the benzene ring on the surface of the micelle is relatively stable. This means that when the stable trans packing pattern is converted to the cis packing pattern after UV irradiation, in order to reobtain a stable packing pattern, the cis-isomer will change its packing pattern (the benzene ring are moved from the micelle interior to the micelle surface). This change of the packing pattern will cause the loosening and rupture of the micelles. In addition, the difference in the interaction energy between the two cis packing patterns of OMCA, MMCA and PMCA is 96.8, 1.0 and 17.2 kJ/mol, respectively. These differences reflect the ability to change their packing pattern after UV irradiation is OMCA > PMCA > MMCA. This sequence is very consistent with our experimental results. For clarity, hydrogen atoms on 12-3-12 2+ and methoxy group are not shown. For convenience, the interaction energy of packing pattern which the aromatic ring is embedded into micelle for trans-isomer is set to 0 kJ/mol.)

The prediction of photo-sensitivity for different cinnamic acid

In addition, to screen out the cinnamic acid with the best photosensitive ability, we selected several cinnamic acids with different electron donating substituents at ortho-, meta-and parapositions and calculated a series of parameters including molar volume and solvation free

Conclusion

In this chapter, we have combined MD simulations with quantitative calculations to study the photo-responsive behavior of the wormlike micelle systems containing Gemini surfactant 12-3-12•2Br -and three trans-methoxy-cinnimates with methoxy group in ortho-, meta-and para-position. In MD simulations, we have simulated the wormlike micelles, rod-like and spherical micelles corresponding to the experimens and the transition between them successfully before and after UV irradiation. These micelle morphologies were recomfirmed by the density distribution and the Ps. The different packing patterns between 12-3-12•2Br -and trans/cis-isomers were visualized and then confirmed by g(r) and SASA. The interaction energy between 12-3-12•2Br -and trans/cis-isomers illustrates that the micelle containing transisomers is more stable.

Quantitative calculations including the electrostatic potential distributions, solvation free energy, molecule volume, angle α and interaction energy of typical packing patterns help us to explore the difference in structure and property between trans/cis-isomers. These results indicate that the presence of ortho-substituent in cinnamate has a more significant impact on strengthening the difference of the steric hindrance, electrostatic distribution and hydrophilicity of the trans/cis-cinnamates before and after UV irradiation and further promotes the photoresponsive ability of corresponding wormlike micelle.

We further used the quantitative calculations to predict the photo-sensitivity of several cinnamic acids. Considering the molar volume, hydrophilicity, electrostatic distribution, reaction equilibrium constant comprehensively, the photo-sensitivity of OMCA is the best.

Chapter 5 The rise of bubbles in shear thinning fluid

Introduction

Bubbly liquids have many practical applications, for instance in flotation of minerals, water purification, two-phase reactors, and fizzy drinks. The role of the bubbles can be active to fix impurities or passive to change the fluid texture. However, due to the large density difference between the liquid and the gas, the bubbles will rise in most of the cases. In flotation or purification this allows to concentrate the material to be separated from the solution in the foam at the top. In many applications, the fluids are non-Newtonian which brings changes the bubble dynamics in ways that are not fully understood yet [START_REF] Clift | Bubbles, drops, and particles[END_REF] .

The motion of single bubbles in Newtonian liquids under the action of gravity has been extensively investigated [START_REF] Legendre | On the deformation of gas bubbles in liquids[END_REF] . The problem is more complex than for solid particles because bubbles usually deform and may even shrink under the action of capillary pressure. Bubbles can deform if viscous or inertial forces are able to overcome the capillary forces. The degree to which bubbles are deformed can be predicted using the capillary and Weber numbers [START_REF] Palaparthi | Theory and experiments on the stagnant cap regime in the motion of spherical surfactant-laden bubbles[END_REF] . Their motion also depends on the surface boundary condition: the surface is usually immobile due to residual contaminants but may become mobile in the presence of surfactants [START_REF] Vélez-Cordero | Bubble cluster formation in shear-thinning inelastic bubbly columns[END_REF] . Bubbles may also shrink or grow due to capillary pressure differences (Ostwald ripening) and coalesce.

Bubble rise is non-Newtonian fluids has been recently reviewed by Zenit and Feng [START_REF] Clift | Bubbles, drops, and particles[END_REF] .

When bubbles rise in a non-Newtonian fluid new feature can be observed: instead of flattening, the bubbles can take the form of a tear drop with a sharp tip. In shear-thinning fluids, increased velocity of the bubble leads to increased shear, which results in a decreased drag. The combination of shape change and decreased drag has been shown to result in a velocity jump, where the rise velocity of single bubbles increases sharply above a critical radius.

Once several bubbles are rising together, they interact. While the pair-wise interaction in non-Newtonian fluids is still not fully understood [START_REF] Clift | Bubbles, drops, and particles[END_REF] , it is known that the interaction depends on the rheology of the suspending fluid, and in shear thinning fluids (of interest in the current thesis), the bubbles tend to approach each other. This is because the leading bubble will leave the fluid in its wake in a state of lower viscosity, thus allowing the following bubbles to rise faster and to catch up. Indeed, bubbles organising in columns or into clusters are frequently observed. Clustered bubbles rise faster than those that remain separated.

In Newtonian fluids an increase of bubble volume fraction leads to a decrease in the rise velocity [START_REF] Legendre | On the deformation of gas bubbles in liquids[END_REF] . However, in shear thinning fluids a maximum has been observed as a function of bubble volume fraction [START_REF] Rothstein | Complex flows of viscoelastic wormlike micelle solutions[END_REF] , the studies have explored volume fractions of bubbles up to 10 %.

The increase can occur, both because of higher shear rates around the concentrated bubbles, which leads to lower viscosities, and because of clustering.

In order to explore the influence of the fluid rheology of bubble rise, we chosed a model shear thinning fluid composed of wormlike micelles of CTAB (cetytrimethyl ammonium bromide) NaSal (sodium salicylate). Moderate concentrations of NaSal result in Newtonian solutions of increasing viscosity before becoming shear thinning and viscoelastic at higher concentrations. This system has been widely used in many studies involving flow of shear thinning fluids [START_REF] Kostrzewa | Particle settling in micellar solutions of varying concentration and salt content[END_REF] . Recently Kostrezwa [START_REF] Gaillard | Controlled foam generation using cyclic diphasic flows through a constriction[END_REF] explored single particle sedimentation in CTAB/NaSal mixtures (4 mm stainless steel sphere), where they found a decrease of the sedimentation velocity with decreasing micellar length in agreement with lower viscosities.

In this thesis, we will address the case of small bubbles in solutions of micelles of varying viscosity. We measured the bubble rise velocity at different gas volume fractions in the different solutions. We are interested in bubble rise in concentrated dispersions of bubbles, volume fractions up to 30 %, as these high volume fractions are encountered in applications such as flotation. The difference between bubble rise in Newtonian and shear thinning fluids were systemically studied. We show that bubble rise in the shear thinning fluids is faster than predicted from the viscosity of the solutions if the shear is sufficient for the bubbles to experience the shear thinning of the fluids. If the bubble rise is sufficiently slow and the bubbles experience a constant viscosity, the bubbles rise as in Newtonian fluids. We also discuss the implications of the particular dependence on bubble volume fraction to flotation design.

Materials and Methods

Materials

The surfactant cetyltrimethylammonium bromide (CTAB) was purchased from Sigma-Aldrich with 99 % purity. Sodium salicylate (NaSal) was purchased from VWR with 100 % purity. They were used without further purification. Ultrapure water with a resistivity of 18.2 M.cm produced using a Veolia water purification system was used to prepare all samples.

Sample preparation

Series of solutions were prepared with 20 mM of CTAB and increasing concentrations of NaSal (0-13 mM) by adding ultrapure water into the weighed compounds. The solutions were sonicated in a Branson 3510 Ultrasonic Cleaner for 1 h to homogenise the solution. The solutions were stored at room temperature (22 ℃) for at least 24 h to ensure equilibration.

Rheology

The viscosity of the samples was measured using an MCR302 rheometer (Anton Paar, Graz, Austria). A cone plate system (CP50-2) with a radius of 50 mm and a taper angle of 2 ° was used. The temperature is controlled with a Peltier plate and set to 22 °C. The samples were inserted in the rheometer about 5 min before the measurement. Flow curves were measured at increasing shear rates from 0.01 s -1 to 1000 s -1 . The shear moduli were measured with a constant strain of γ = 1 %.

Generation of bubbly liquids

Bubbly liquids were prepared using the double syringe method, which has been characterised by Gaillard [START_REF] Lam | Structural properties of the evolution of CTAB/NaSal micelles investigated by SANS and rheometry[END_REF] Two 10 mL syringes from Fisher scientific were used with a tube connector with an inner radius of 2 mm. The CTAB/NaSal mixed solutions were poured into the syringe directly. The gas fraction of air was measured using the syringe indicators, and is known to ± 2 %. The syringe pistons were pushed back and forth 30 times for each sample to obtain bubbles of well-defined radius (typically between 15 and 40 µm). The gas fraction φgas was varied between 5 % and 30 % in the samples.

Bubble size

A Malvern Mastersizer laser granulometer (Malvern Instruments, France) was employed to measure the surface weighted mean radius of the bubbles (R32, Sauter radius). The sample dispersion unit was filled with 10 mM CTAB solution, this concentration was sufficient to ensure that the bubbles were stable during measurement but less wasteful of CTAB as each measurement requires two litres of solution. After generation of the bubbles, the samples were transferred into the sample dispersion unit of Mastersizer with the stirring speed 1000 r/min.

The bubble size was measured 10 times with a 3 s measurement time and an average taken.

Bubble rise velocity

After preparation, the bubbly liquids were immediately transferred into glass vials. A Ueye camera was used to observe the bubble rise. The time interval between images was 30 seconds for most experiments, but for the samples with very fast bubble rise the interval was decreased to 5 seconds.

The Image J software was used to analyse the photographs, monitoring the grey scale I of pixels. In order to locate the front accurately, we determined the front position corresponding to different grey values. The details on how to obtain the average grey value of a certain area and the corresponding front position can be found in Figure 5.6.

Surface tension

The surface tension experiments were performed with a Tracker instrument (Teclis, France) at 20°C in the rising bubble configuration A bubble was created and the surface tension was measured during 10 minutes at which point it had reached its equilibrium value for all of the samples and no longer changed. These values are shown in Table 5.1. The surface tension decreases when the NaSal concentration increases, a common effect for salts (they screen the electrostatic repulsion between surfactant polar heads, the surface layer becoming more compact).

Results and Discussion

Rheology of micellar solutions

In order to interpret the rise of bubbles in micellar solutions, we need to determine the viscoelastic properties of the solutions, which depend on the concentration of NaSal. The increase in the concentration of NaSal causes the micelles to gradually change from small elliptical ones to long tangled worm-like micelles, and the solutions become viscoelastic [START_REF] Clausen | Viscoelastic micellar solutions: Microscopy and rheology[END_REF] .

We have measured the flow curves of mixed solutions for 20 mM CTAB and different NaSal concentrations, as shown in Fig. 5.1. These solutions exhibit two types of behaviour, at low shear rates viscosity is independent of shear rate, however above a critical shear rate they become shear thickening (empty symbols) or shear thinning (filled symbols).

For pure CTAB solution and CTAB solutions with low NaSal concentrations (0, 2, 4, 8, 9 mM empty symbols) at low shear rates the viscosity is independent of shear rate, and they behave as Newtonian fluids. As the concentration of NaSal increases to 8 and 9 mM, the viscosity of the solution increases to several times that of pure CTAB solution. At high shear rates (30-100 s -1 ) a shear thickening is observed. As will be seen later, the shear rates experienced by the bubbles are smaller and we will call these solutions "Newtonian" in the following.

In the solutions at higher concentrations (NaSal concentration = 10, 11, 11.5, 12, 12.5, 13 mM, filled symbols) a viscosity plateau at low shear rates is observed, which is followed by a shear thinning behaviour. Shear thinning starts at lower shear rates as the concentration of NaSal frequencies of the order of 1 Hz. Even for the largest salt concentration, the storage modulus is very small (G' less than about 1 Pa).

Bubble size

The generation of bubbles in viscous fluids is not easy. We made the bubbles using the double syringe method with bubble volume fractions ranging from 5 to 30 %. In this gas fraction range, all the gas is incorporated into the solution. We did not use higher gas volume fractions as all the gas can no longer be incorporated into the most viscous samples. Once the bubbles are formed, we measure their size using a Mastersizer 3000. The Sauter radius R32 is shown in The bubble size is the smallest for the samples with the lowest concentrations of NaSal and remains almost constant until 8 and 9 mM NaSal when a transition to larger bubbles is observed. These two samples are still Newtonian but have higher viscosities than the other samples.

For small NaSal concentrations, the average bubble radii are between 12 and 22 µm (still larger with 8 and 9 mM NaSal). The bubble size increases weakly, but systematically, with gas volume fraction φgas. The bubble size distributions are shown in Fig. 5.4. As φgas increases, the bubble size distributions become wider. In the shear thinning solutions, the bubble sizes are larger, between 25 to 35 μm. There is no dependence of the bubble size on the gas fraction, but as with the Newtonian solutions, the bubble sizes have wider distributions at higher gas fractions.

The bubble size is in principle affected by surface tension: the lower the tension, the easier it should be to make bubbles and hence the smaller the radius. Table 5.1 shows that surface tension decreases with NaSal concentration. This should lead to a smaller bubble size, but this

is not what we observe. This suggests that other factors control bubble size. In the two syringe method Gaillard et al. found that bubble size increases with φgas and decreases with viscosity [209] . The trend observed with φgas with the Newtonian solutions in Fig. 5.3 is consistent with this work, but here the more viscous samples have larger bubbles. In the work of Gaillard et al the solutions used were Newtonian, whereas our solutions are shear-thinning or shearthickening at high shear rates. In the two-syringe method, as the bubbly liquid passes through the constriction, it experiences very high shear rates. We estimated the shear rate from the piston velocity  10 cm/s and the constriction radius of 2 mm as around 50 s -1 . This is close to the shear-thinning transition, which makes prediction of the viscosity. In any case, a full understanding of the bubble generation in shear thinning fluids is beyond the scope of this thesis. Fig. 5.4 shows the size distributions of bubbles made with the two-syringe technique using solutions containing 20mM CTAB and various amounts of NaSal (0-13mM) at 22°C. In Newtonian fluids, the bubble size distributions become wider with increase of φgas, and the peak position moves to higher values. In the non-Newtonian solutions, no obvious dependence of bubble size on gas fraction can be found. ). The differences are due to the broadening of the rise front, which in turn is caused by the polydispersity in bubble size. As the smallest bubbles rise more slowly, the lowest intensity will be sensitive to the smallest bubbles. In the following we will use the measurements with I = 80, which is the average intensity in the images to define the position of the bubble rise front.

(c).

There is a lot of noise for the gray value curve at long time, indicating the high polydispersity of the bubble size for non-Newtonian fluids. We can observe an initial "fast" rise of the bubbles during a few 100 seconds (as seen in the inset of Fig. 5.8 (c). After this the bubbles slow down dramatically and the creaming process takes more than 15 hours. The final photograph of Fig. 5.8 (a) is taken after 63 000 s so 17.5 hours after the start, and still some small bubbles remain in solution. We will now discuss the expected bubble rise regimes, before comparing the bubble rise velocities to the predictions.

Bubble rise regime

Bubble rise is known to depend on several factors: Reynolds number; bubble surface boundary condition and; whether the bubbles can deform or not. We studied relatively small bubbles (R < 35µm), for which the Reynolds number Re is small

Re = 2ρvR η (5-1)
where ρ and η are respectively the fluid density and viscosity, 𝑣 the velocity, and 𝑅 the bubble radius. For pure CTAB solutions, using ρ = 10 3 Kg/m 3 , η = 1 mPa/s, v = 0.3 mm/s, R = 20 µm, we find Re ~10 -2 . For the shear thinning solutions, v decreases and η increases and 𝑅𝑒 decreases. Therefore, the experiments are all carried out in a region of small Re.

Bubbles remain spherical if both the inertial and viscous forces are small compared to 123 surface tension forces [START_REF] Taylor | Ostwald ripening in emulsions[END_REF] . This happens when the Weber number We and the capillary number Ca are small:

We = ρv 2 R γ (5-2) Ca = ηv γ (5-3)
Here, with γ = 35 mN/m, We ~ 10 -7 and Ca ~ 10 -5 are both very small for pure CTAB solutions. For the solutions with NaSal, the viscosity increases but the velocity decreases, so both numbers remain small, and we can safely assume that our bubbles are not deformed during the rise process.

A further question concerns the boundary condition at the bubble surface, which would change the bubble rise velocity. In dilute surfactant solutions and small Reynolds numbers, the surfaces of rising bubbles are immobilized by surface tension gradients and Marangoni forces created by the liquid flow: surfactant is depleted from the bubbles' apex and it accumulates at their rear. The bubbles behave as solid particles [START_REF] Legendre | On the deformation of gas bubbles in liquids[END_REF] . When surfactant concentration is higher, the depleted surfaces can be replenished by surfactant adsorbing from the bulk. The problem was discussed in detail by Maldarelli and co-workers [START_REF] Vélez-Cordero | Bubble cluster formation in shear-thinning inelastic bubbly columns[END_REF] who predicted that the Marangoni force is larger for smaller bubbles. Above the critical micellar concentration, the adsorption kinetics is also controlled by the micelle lifetime, which is very long (minutes) in the presence of salt. It is therefore likely that in our experiments, the bubble surfaces can be considered as immobile.

In this case the bubble rise velocity for a single bubble in a Newtonian fluid would be given by the Stokes expression:

v s = 2∆ρgR 2 9η
(5-4) Δρ is the difference between the gas and the fluid densities.

The Stokes expression is valid for a single particle and corrections have been proposed to account for the influence of particle concentration. When the particles behave as hard spheres, the phenomenological expression of Richardson and Zaki [START_REF] Sankaranarayanan | Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice Boltzmann method[END_REF] is accurate up to large volume fractions:

v = v s (1-φ gas ) n (5-5)
Here φgas is the particle volume fraction. The exponent n varies with the Reynolds number Re. In the current flow regimes, we expect the n = 4.5 [START_REF] Blazejewski | Apparent viscosity and settling velocity of suspensions of rigid monosized spheres in Stokes flow[END_REF] , very close to what describes data with solid particles at the Re encountered here [START_REF] Nicolai | Particle velocity fluctuations and hydrodynamic self-diffusion of sedimenting non-Brownian spheres[END_REF][START_REF] Taylor | Ostwald ripening in emulsions[END_REF] .

Bubble rise in Newtonian solutions 124

In the following we will use the measurements with I = 80, which is the average grey value in the rising front. Fig. 5.9 shows the variation of the bubble rise velocity normalised by the Stokes velocity, v/v s as a function of gas fraction for the Newtonian solutions measured with I = 80. The different velocities collapse onto a single mastercurve, as expected for Newtonian fluids. We calculate vs using equation 3 with the experimentally measured viscosities and Sauter radii. We use the radii measured just after generation, as we do not expect the bubble size to change during their rise. This is because Ostwald ripening is too slow to change it during the rise process and we do not observe any coalescence. We can estimate the rate of Oswald ripening which does not change much with bubble volume fraction [START_REF] Loisy | Buoyancy-driven bubbly flows: Ordered and free rise at small and intermediate volume fraction[END_REF] and is given for small φgas by where Dm is the gas diffusion coefficient in water, He* the Henry constant expressed as the volume fraction of gas in water and P the atmospheric pressure. For bubbles with R = 20 μm in water, Dm = 2.6×10 -9 m 2 /s, He*= 0.013, which results in  ~ 10 -17 m 3 /s, and increase in radius of about 2 µm in 100s.

We cannot follow the individual bubbles as they rise to see if they coalesce or not. However, once all the bubbles have reached the top of the solution and form a froth, its height remains constant, suggesting the absence of coalescence. Therefore, we do not expect to have any coalescence during the bubble rise process either, as the volume fraction of bubbles is much smaller.

Small bubbles rise sufficiently slowly and the shear rate is small enough, so that the solution viscosity remains Newtonian throughout the process. For the sample at 20mM CTAB/4 mM NaSal at φgas= 5% the velocity is the highest at v ~ 0.25 mm/s. At this velocity we have the maximum shear on the bubbles, which we can estimate as γ̇ = v/R ~ 20 s -1 . This shear rate is lower than the shear rate at the onset of shear-thickening and the liquids remain Newtonian during the front motion.

The Richardson and Zaki prediction calculated using Equation (5-5) is shown in Fig. 5.10 with a black line. We can see that within error bars, the data is in good agreement with the model. The extrapolation to φgas = 0 coincides with the Stokes velocity calculated with the average Sauter radius, confirming that the bubbles behave as solid particles, as the velocity would have been higher if the bubble surfaces were mobile. Note that the Richardson and Zaki prediction does not work when larger bubbles are used [START_REF] Gheissary | Unexpected phenomena observed in particle settling in non-Newtonian media[END_REF] .

In The decrease of the rise velocity with gas fraction is much weaker than predicted by Equation (5-5) and almost vanishes at large NaSal concentration (see Fig. 5.11 (b)). Therefore, the Richardson and Zaki prediction does not seem to apply here. For the most viscous samples, the velocity can even be higher at higher φgas as seen with the samples with 12.5 and 13 mM of NaSal, we will come back to this a little later. The evolution of the rise velocity with φgas is different than with Newtonian solutions, however this might be because the viscosity experienced by the bubbles depends on their velocity. We can compare the bubble rise velocities to those found in Newtonian solutions if we can estimate the viscosity experienced by the bubbles as they rise (as done for single particles sedimenting in viscoelastic solutions by Gheissary et al for example [START_REF] Prakash | Flotation technique: Its mechanisms and design parameters[END_REF] ). We use the velocity at φgas = 0.05 and and the average bubble radius 〈𝑅〉 of 30 µm to estimate the shear rate as γ̇ ~v (φ gas = 0.05) R

. We can then calculate v s (η) using equation (5-4) with η(γ) and 〈R〉. The front velocities normalised by v s (η) are shown in Fig. 5.12.

For the sample at NaSal = 10 mM (black points) the normalised velocities with the estimated v s (η) are close to 1 (between 0.7 and 1.2). This can be explained by the low shear rate experienced by the bubbles at 1.6 s -1 , which lies on the Newtonian plateau. However, for all of the other samples the situation is very different, and the measured velocities are around 127 10 times higher (for NaSal = 13 mM they are almost 20 times higher). Either our estimation of the shear rate and hence the velocity is poor, or then we are in a different bubble rise regime.

Vélez-Cordero and Zenit showed that at small Re and large Bo bubbles cluster while they rise [START_REF] Finch | Gas dispersion properties: bubble surface area flux and gas holdup[END_REF] . The prediction for the free bubble to clustering could be predicted from studies on pairs of bubbles and is due to attractive hydrodynamic interactions acting via the bubbles wake.

The studies were done with lower φgas and larger monodisperse bubbles. Comparing to their predictions, the bubbles in our systems could be expected to be in the clustering regime, however due to the high volume fractions and small bubble sizes we do not observe clustering in the videos. Clustering could therefore explain the faster than expected bubble rise of Fig. 5.12. It could also explain the weak (or non-monotonous) rise velocities of Fig. 5.11 (b), as it has been shown to cause both higher rise velocities and a non-monotonous velocity dependence on φgas [START_REF] Clift | Bubbles, drops, and particles[END_REF] . Another peculiarity of bubbles' motion observed for the most viscous liquid (13 mM Na Sal) is the fact that it slows down considerably after some tens of minutes, as seen in Fig. 5.7.

The second bubble rise velocity is also quite constant in time; it is shown with the initial velocity in Fig. 5.13. The second velocity is around 10 -7 m/s, which is 100 times slower than the initial velocity.

If we look at the photographs in Fig. 5.7 (a) corresponding to the slow rise regime, we can see that the volume fraction of bubbles left is relatively small, with most of the bubbles having risen during the first stage. The samples are polydisperse and we know that the smallest bubbles lag behind. If we use the bubble rise velocity to again estimate the shear rate, we find γ̇ ≈ 10 - 2 , which is on the Newtonian plateau with η (γ̇ = 10 -2 ) = 10.7 Pa•s. We have seen that on the Newtonian plateau, the Stokes velocity compares well with the rise velocity, therefore we can estimate the size of bubbles rising at such slow velocities. We find R= 22 µm, which is in the tail of the bubble size distribution (around 10% of the bubbles). This suggests that how the bubbles rise could be different depending on their size within the polydisperse samples. The larger bubbles rise fast enough to experience shear rates within the shear thinning regime, while the smaller bubbles rise so slowly that they experience shear rates on the Newtonian plateau and hence maximal fluid viscosity. It might also be that the smaller bubbles cluster less than the larger ones, which would lead to a significant decrease in the rise velocity.

We do not see such a slow rising population of bubbles at the lower concentrations of NaSal. This is because even for the next sample with 12.5 mM NaSal the plateau viscosity is 3.9 Pa•s, which means that only bubbles with R < 13 µm would reach the second creaming regime. The tail of the bubble size distribution is very close to this value and there are hardly any bubbles of this size in the samples, and explains why we do not observe the slower bubble rise in the other samples.

Flotation in a shear thinning fluid

Foam flotation is used to purify and separate materials from fluids: the material attaches onto the bubble surfaces, which rise up for separation. An important parameter to quantify foam flotation is the bubble surface area flux 𝑆 , which tells how much surface area is swept up per second and is directly linked to how efficiently the process works [222][223] . In a bubble column 𝑆 ̇ is given by product of the average bubble rise velocity v(φgas) and the number density of bubbles:

Conclusion

We have explored bubble rise in micellar solutions of varying viscosity, with both Newtonian and shear thinning properties. We made the bubbles using two connected syringes, and observe two plateaus of bubble size: smaller bubbles at the lowest concentrations of NaSal where the bubbles are Newtonian until a viscosity jump at high shear rates, and larger bubbles in the shear thinning fluids.

The rise of the concentrated suspensions of bubbles in the Newtonian fluids is well described using the Richardson and Zaki description. However, in the shear thinning fluids different phenomena can be observed depending on the shear rate around the bubbles, which in turn changes with bubble size and rise velocity. If the bubbles rise sufficiently slowly (smaller bubbles) such that the shear rate is on the Newtonian plateau, the bubble rise velocity is close to that expected from the Stokes velocity. However, once the shear rate around the bubbles is high enough to reach the shear thinning regime, the bubbles will rise faster and prediction using local shear rates lead to an underestimation of the bubble rise velocity, probably because of the onset of bubble clustering.

The variation of the bubble rise velocity as a function of volume fraction of bubbles is much weaker than in Newtonian fluids. Indeed, an exponent of n = 1 instead of around 4.5 in the Richardson and Zaki expression describes the data reasonably well. This can have important implications to the flotation process in shear thinning fluids, as we show that the maximum area flux occurs at higher gas volume fractions than found in Newtonian fluids.

Our results give insight into bubble rise of concentrations solutions of bubbles in shear thinning fluids, which have been little studied so far, despite their importance in applications.

The interaction through the shear thinning fluid leads to changes in the bubble rise velocity, the exact origin of which requires further experimental and theoretical works.

calculation results show that the presence of ortho-methoxy and ortho-hydroxyl in cinnamate has a significant impact on increasing the equilibrium constant of photo-isomeriaztion reaction and enhancing the difference of the steric hindrance, electrostatic distribution and hydrophilicity of the trans/cis-cinnamates, thereby improving the photo-responsive ability of wormlike micelle. And ortho-methoxy has better effects.

( In MD simulations, the micelle morphologies corresponding to the experimental results initially and at equilibrium were successfully captured and reconfirmed by density distributions and Ps. Three systems show different packing patterns. With the increasing distance between methoxy and carbon-carbon double bond, the methoxy inserts more and more deeply into the micelle. In addition, the benzene rings of trans-isomers are embedded into the hydrophobic layers of surfactants while those of cis-isomers orient at the micelle surface. After UV irradiation, the motion of benzene ring in cinnamates cause the rupture of wormlike micelle.

Quantitative calculations reveal that when the methoxy is oriented in meta-, and paraposition, the molar volume and hydrophilicity of cinnamates decrease after UV irradiation, which hinders the escape of cis-isomers, thereby weakening the photo-responsive ability of wormlike micelles. For OMCA, the ortho-methoxy is closest to the carbon-carbon double bond so that they have the largest difference in steric hindrance, electrostatic distribution and hydrophilicity before and after UV irradiation. Furthermore, the photo-sensitivity of 24 cinnamic acid ions are predicted according to their molar volume, hydrophilicity, electrostatic distribution, reaction equilibrium constant. Base on the information comprehensively, among 24 cinnamates, the photo-sensitivity of OMCA is the best.

In summary, the micellar transition mechanism of the wormlike micelles constructed by Gemini surfactant and cinnamate has been well studied. We also screened out the cinnamic acid with the best photo-responsiveness (trans-OMCA) among the 24 cinnamic acids. However, we still haven't found a cinnamic acid with photosensitivity that exceeds trans-OMCA. We will try to search more cinnamic acids and the transition state and kinetic mechanism of these cinnamic acids photoisomerization reactions will be the focus of our further research. The limitation of the time scale of the united-atom force field and the size of the box prevents us from simulating larger-sized and more complex self-assemblies, such as vesicles and gels. We will focus on the coarse-grained force field to simulate large-scale self-assemblies. In addition, the irreversible transformation of wormlike micelles containing cinnamates hinders their industrial application.

We will try to use some reversible photosensitive molecules to build a photo-responsive system in further research.

(4) We investigate the bubble rise behavior in shear thinning solutions made of cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal) (a common wormlike system). The results show when the NaSal concentration is low, the solutions are Newtonian fluids and the rise of the concentrated suspensions of bubbles in these fluids is well described using the Richardson and Zaki description. For the shear thinning solutions, the Richardson-Zaki relation no longer applies. Bubble clustering leads to faster rise velocities and a weaker dependence on the bubble volume fraction. At the largest concentrations two rise regimes are observed, the smaller bubbles have lower shear rates around them and they experience higher viscosities. If they rise sufficiently slowly, the shear rate reaches the plateau region, and their rise is comparable to the Stokes expectations. However, when the shear rates are in the shear thinning regimes, the bubble rise is faster than expected.

Our results also show that maximum area flux in the shear thinning solutions occurs at higher gas volume fractions than found in Newtonian fluids, and this peculiar dependence of the rise velocity with volume fraction of bubbles in the shear thinning solutions can have important implications in flotation. And in the future, we will probe more finely the different rise regimes of the bubbles in higher viscosity solutions, and study the variation of fluid structure around the bubble. In addition, it would be interesting to control the rise velocity of bubbles with external stimuli such as light or electricity.

Titre:水相等1

  photosensibles peuvent non seulement être faciles à concevoir, propres et sans pollution, mais il est également possible d'ajuster et de contrôler avec précision le temps de réponse et la localisation du stimulus. C'est pourquoi de tels systèmes présentent des perspectives d'application prometteuses dans la libération de médicaments, l'industrie pétrochimique, la catalyse commutable, la modification de surface, la bio-ingénierie, les matériaux photosensibles intelligents et le domaine de l'optique. L'un de ces systèmes est composé de molécules photosensibles à base de cinnamate et de tensioactifs Gemini. Il montre une riche zoologie de morphologies d'auto-assemblage, y compris des micelles sphériques, des micelles vermiformes, des vésicules, des cristaux liquides, un système aqueux à deux phases, etc. Ces autoassemblages présentent tous un excellent comportement photosensible. Cependant, en raison de l'échelle microscopique des auto-assemblages, la question de savoir comment ils s'assemblent et ce qui entraî ne le changement de morphologie sous irradiation UV est encore ouverte. Les méthodes de simulation informatique à l'échelle atomique et moléculaire suscitent notre intérêt en raison du succès de la modélisation du comportement d'auto-assemblage. Avec l'amélioration rapide des performances des ordinateurs et les progrès des méthodes théoriques, les méthodes de simulation et de calcul sur ordinateur sont devenues une méthode indispensable dans la recherche théorique. Dans cette thèse, pour construire les micelles wormlike photosensibles, les cinnamates, représentés par l'o-méthoxycinnamate (OMCA), avec différents ortho-substituants en position méta-, para ont été sélectionnés comme molécules photosensiblesà introduire dans la solution de tensioactif Gemini.

Fig. 1 . 1

 11 Fig. 1.1 The morphologies of the self-assembly formed by surfactant

Fig. 1 . 2

 12 Fig. 1.2 Relationship between the critical packing parameter P and the morphology of self-assemblies

Fig. 1 . 3

 13 Fig. 1.3 Schematic structure of Gemini surfactant

Fig. 1 . 5

 15 Fig. 1.5 Responsive self-assembly system constructed by surfactants

Fig. 1 .

 1 Fig. 1.10 Common photo-sensitive molecules (a) Azobenzene (b) Spiropyran (c) Cinnamic acid[START_REF] Chu | Smart wormlike micelles[END_REF]

  used 4-azobenzene carboxylic acid (ACA) and a cationic surfactant bis(2-hydroxyethyl)methyl ammonium chloride (EHAC) to prepare a new type of photo-responsive fluid. It was found that initially ACA and EHAC self-assembled to form unilamellar vesicles. These vesicles are well dispersed in the solution, so the sample has a lower viscosity. After being exposed to ultraviolet light, the vesicles transform into wormlike micelles. The flexible chains of long wormlike micelles entangle with each other in the aqueous solution, so the sample exhibits an extremely high viscosity, which is nearly 1 million times higher than that of the vesicle solution. The selfassembly constructed by the azobenzene molecules can be switched back and forth between ultraviolet light and visible light, so that the sample can reversibly cycle between the lowviscosity state and the high-viscosity state.

  Spiropyran (SP) is a well-known photochromic compound that can undergo photoisomerization between the colorless SP form and the open merocyanine (MC) under different wavelengths of light irradiation. The closed SP is a non-ionic hydrophobic molecule, while the open MC form is an ionic hydrophilic molecule. The different properties before and after the light cause the difference in the interaction between the surfactant molecules and two photo-

Fig. 1 .

 1 Fig. 1.13 Photo-responsive behavior of photorheological fluids constructed by the lecithin/SDC reverse

  by trans-OMCA and C16mimBr in aqueous solution was systematically studied. They used Ncetyl-N-methylmorpholinium bromide (CMMB) and trans-cinnamic acid (trans-CA) to construct a new type of triple responsive (photo, pH and temperature responsive) wormlike micelles, which can be used as a good model of wormlike micelles with multiple responses to light stimulation. Their studies help to understand the mechanism of multiple responses and broaden its application range.

Fig. 1 .

 1 Fig.1.14 Photo-responsive behavior of the CTAB/trans-OMCA wormlike micelle system[START_REF] Ketner | A simple class of photorheological fluids: surfactant solutions with viscosity tunable by light[END_REF]

  alkyldimethylamine oxide (CmDMAO, m = 10, 12, 14) and trans-coumaric acid isomerides, including trans-ortho-coumaric acid (trans-OCA), trans-meta-coumaric acid (trans-MCA) and trans-para-coumaric acid (trans-PCA). The results show that multi-lamellar vesicles (MLV) appeared in certain areas in trans-PCA/C12DMAO and trans-OCA/CmDMAO systems. The molecular structures of CmDMAO and trans-coumaric acid isomers significantly affects the region of MLV. The larger the m, the larger the MLV area. For the trans-OCA/CmDMAO system, depending on the chain length of CmDMAO and the ratio of trans-OCA to CmDMAO, multi-lamellar vesicles can be transformed into a homogeneous and transparent micellar phase or two-phase system by ultraviolet light irradiation. This research is of great significance for the systematical understanding of the ratio and structure of surfactants on the photo-responsive behavior of self-assemblies in the system. Furthermore, the research on photo-responsive selfassembly constructed by surfactants of different chain lengths and photo-sensitive molecules of different structures provides basic data and theoretical guidance for expanding the application of smart materials.

  combined two imidazole-based surface active ionic liquids (SAIL) with photo-responsive molecules (trans-CA; trans-PCA) to synthesize 1hydroxy-cinnamate ([C12mim][PCA]), and studied their selfassembly behavior in aqueous solution. As shown in Fig. 1.16, hexagonal liquid crystal phase (H1) and cubic liquid crystal phase (V2) are constructed in [C12mim][CA] aqueous solution. In contrast, the [C12mim][PCA] / H2O system displays a single hexagonal liquid crystal phase (H1) in a wide concentration region. Under ultraviolet light, the photo-isomerization of cinnamate molecules causes the decrease of surface activity of the SAIL and the lattice parameters of the formed liquid crystal phase. This work enriches the research on photo-responsive lyotropic liquid crystals, and expands the potential applications of smart-responsive liquid crystal materials in drug delivery, biochemistry, materials science, etc.

Fig. 1 .

 1 Fig. 1.16 Photo-responsive behavior of [C12mim][CA]/H2O and [C12mim][PCA]/H2O binary systems[START_REF] Bi | Aggregation Behavior of Imidazolium-Based Surface-Active Ionic Liquids with Photoresponsive Cinnamate Counterions in the Aqueous Solution[END_REF]

Fig. 1 .Fig. 1 .

 11 Fig. 1.18 Classification of bubbles in liquid

Fig. 1 .

 1 Fig. 1.20 Three representative shapes of the single bubble in Newtonian fluid (a) spherical, (b) ellipsoidal, (c) spherical cap

Fig. 1 .

 1 Fig. 1.21 Representative shapes of the single bubble in Newtonian fluid (a) spherical, (b) ellipsoidal, (c) teardrop shape, (d) flat teardrop shape with a pointed ellipsoid, (e) spherical cap.

Fig. 1 .

 1 Fig. 1.22 Bubbles rise in Newtonian fluid (a), shear-thinning inelastic fluid (b) and Boger fluid (c), (d)[START_REF] Zenit | Hydrodynamic Interactions Among Bubbles, Drops, and Particles in Non-Newtonian Liquids[END_REF]

(

  trans-OMCA), trans-o-hydroxy cinnamate (trans-OHCA), and trans-cinnamate (trans-CA), to construct photo-responsive wormlike micelle systems with Gemini surfactant trimethylene-1,3-bis (dodecyldimethylammonium bromide) (12-2-12• 2Br -). We investigated the photoresponsive behavior and photoisomerization reaction kinetics of wormlike micelle, combined with MD simulation and quantitative calculations to study the effects of different orthosubstituents in cinnamates on the photo-isomerization reaction rate and the photo-responsive behavior of wormlike micelles.(3) Based on the previous two parts of the research, we further studied the photoresponsive wormlike micelle system composed of Gemini surfactant 12-3-12• 2Br -abd cinnamates with ortho-, meta-and para-methoxy (trans-o-methoxy cinnamate (trans-OMCA), trans-m-methoxy cinnamate (trans-MMCA) and trans-p-methoxy cinnamate (trans-PMCA)).

  Scheme 2.1 Model structures and numberings of: (a) N, N'-bis(dodecyldimethyl)-1, 2-ethane diammonium ion (12-2-12 2+ ); (b) trans-ortho-methoxycinnamic acid ion (trans-OMCA -); (c) cis-ortho-methoxycinnamic ion (cis-OMCA -).

Fig. 2 . 1 ,

 21 the system initially performed an entangled and dense network structure, indicating the generation of wormlike micelles. The network structure started to branch into rod-like micelle after 40 min UV irradiation. Further prolonging the UV irradiation time, the micelles continued to split into spherical micelles subsequently, and the rod-like micelles were entirely transformed into spherical micelles when the UV irradiation time is 60 min. Obviously, the wormlike micelles formed by the Gemini surfactant 12-2-12• 2Br -and trans-OMCA have excellent photo-responsiveness and the system changes from wormlike micelles to rod-like micelles and until spherical micelles after UV irradiation.

Fig. 2 .

 2 Fig. 2.1 TEM images for the sample of 17 mM 12-2-12• 2Br -/7 mM trans-OMCA system at 25°C with the prolongation of UV irradiation time [(a) 0 min; (b) 40 min; (c) 60 min].

Fig. 2 .

 2 Fig. 2.2 provides the rheological properties of 17 mM 12-2-12• 2Br -/7 mM trans-OMCA mixed solution under different UV irradiation time. It can be seen from Fig. 2.2 (a) that the high viscosity and the appearance of the shear-thinning phenomenon and zero-shear viscosity of 17 mM 12-2-12• 2Br -/7 mM trans-OMCA indicates the formation of wormlike micelles before UVirradiation. The wormlike micelles entangle with each other to form a network structure. The network structure is difficult to be destroyed when the shear rate is lower and therefore the platform appears (zero-shear viscosity, η0). However, when the shear rate is relatively higher, the network structure will firstly disentangle, then be destroyed and transform into short rodlike micelles. Therefore, the shearing-thinning behavior occurs. With the prolongation of UV irradiation time, the shear-thinning behavior of the system gradually disappears accompanied by a decrease of the viscosity of the system. It reconfirms that the longer wormlike micelles can be destroyed after a period of UV irradiation and be transformed into smaller micelles; the results are coincided with the previous TEM observation. The zero-shear viscosity (Fig. 2.2 (b)) of the present system drops rapidly within 40 min and almost keeps constant over 60 min. The viscosity of the system decreases by about 3 orders of magnitude (from 2.7 ± 0.1Pa• s to 7.3± 0.1mPa• s) within 60 min. The viscoelasticity curves (Fig. 2.2 (c)) and the Cole-Cole plots (Fig. 2.2 (d)) of samples undergo different UV irradiation time once again prove the fact that the transformation from wormlike micelle to spherical micelles after UV irradiation.

Fig. 2 . 2

 22 Fig. 2.2 Effect of UV irradiation time on rheological properties for the system of 17 mM 12-2-12• 2Br -/7 mM trans-OMCA at 25°C (a) steady shear viscosity, (b) zero-shear viscosity, (c) dynamic frequency sweep, and (d) Cole-Cole plots.

Fig. 2 . 3

 23 Fig. 2.3 Snapshots for the initial simulation box and final micelle morphology of pure 90 12-2-12• 2Br - surfactants. (The cyan molecules are 12-2-12 2+ ; for clarity, water, and Br -ions are not shown.)

Fig. 2 . 4

 24 Fig. 2.4 Snapshots for the initial simulation box and final micelle morphologies of r n = 0.75 [(a) and (b)]; r n = 1 [(c) and (d)]; r n = 1.25 [(e) and (f)]; r n = 1.5 [(g) and (h)]. The left is aggregates containing 12-2-12• 2Br -and trans-OMCA. The right is aggregates containing 12-2-12• 2Br -and cis-OMCA. (a), (b), (c), (d), (f) have one period. (The cyan molecules are 12-2-12 2+ ; the red molecules are OMCA; for clarity, water and ions are not shown. Specially, to show the long wormlike and network morphologies, (e), (h) have three periods and (g) have nine periods.)

2. 5 ,

 5 12-2-12 2+ molecules mixed with cis-OMCA at r n = 0.75 integrate into four spherical micelles, therefore four peaks are found in (b) along z axis. The long and finite rod-like micelle has a corona-shape peak such as (a), (c), (f), (g1). (d) and (e1) represent that spherical micelle and rod-like micelle coexist. When the long and infinite wormlike micelles appear, the density curve along x axis is infinite and successive like (e2), (g2) and (h2). The network micelles have infinite and successive curve in both x and y axis but they are not successive in z axis, as shown in (g1), (g2) and (g3).

2. 4 .

 4 Nevertheless, to understand how the cis/trans-OMCA isomers impact differently on the surfactant micelle morphology, the deeper discussion of mechanisms of micelle transformation is of great value.

Fig. 2 . 5

 25 Fig. 2.5 The average density distributions of 12-2-12 (black line), OMCA (blue line), Na + (red line), Br - (green line) along x (e2, g2, h2), y (g3), z (a, b, c, d, e1, f, g1, h1) at last 100 frames. The graph numbers are corresponding to the numbers of morphologies in Fig. 2.4.

Fig. 2 . 6

 26 Fig. 2.6 Radial distribution functions (a) between nitrogen atoms gN1-N1(r) and (b) between nitrogen N1 atoms from 12-2-12• 2Br -and specific carbon atoms from OMCA isomers, gN1-C(r) at r n = 0.75.

Fig. 2 .

 2 Fig. 2.7 shows the representative packing intercepted from micelles at r n = 0.75. Combining the results of g(r) with Fig. 2.6, we can easily capture the difference in packing patterns of cis/trans-OMCA: the aromatic ring of cis-OMCA is situated on the surface of micelles while that of trans-OMCA is inserted into the hydrophobic alkyl chain of 12-2-12• 2Br -; the carboxyl groups of both cis/trans-OMCA are oriented on the surface of micelles and the methoxy groups of them are embedded into the micelles. Meanwhile, on the micelle surface, it is noticeable that there are more red parts (oxygen atoms in OMCA) on 12-2-12• 2Br -/trans-OMCA micelle surface than in 12-2-12• 2Br -/cis-OMCA micelle surface. And we can hardly observe the white parts (hydrogen atoms in OMCA) on 12-2-12• 2Br -/trans-OMCA micelle surface. These atoms distribution confirms that the aromatic ring of trans-OMCA is embedded entirely into the 12-2-12• 2Br -micelle and that of cis-OMCA lies on the surface of micelles.

Fig. 2 . 7

 27 Fig. 2.7 The arrangements of 12-2-12• 2Br -and OMCA molecules on micelles at r n = 0.75. (The cyan parts are 12-2-12 2+ ; the red parts are OMCA -; the red beads and white beads are oxygen atoms and hydrogen atoms in OMCA.)

  12• 2Br -/cis-OMCA mixed micelles while the hydrophilic area of 12-2-12• 2Br -/trans-OMCA micelles witnesses a contrary result. Obviously, the trans-OMCA molecules expose their carboxyl group to the water whereas cis-OMCA molecules expose their benzene ring to the water. The difference in SASA reconfirms the different packing patterns of cis-and transisomers on micelle surface.

Fig. 2 . 8 33 57

 2833 Fig. 2.8 The hydrophobic(apho), hydrophilic(aphi) and total(atot) surface areas of 12-2-12• 2Br -/OMCA micelles with the OMCA concentration change.

Fig. 2 . 9

 29 Fig. 2.9 The structures of OMCA molecules after being optimized at the M052X/6-31G* level. (a), (c) cis-OMCA top and front view; (b), (d) trans-OMCA top and front view.

Fig. 2 .

 2 10 provides the snapshots of 12-2-12• 2Br -on air-water interface before and after MD simulations with 12-2-12• 2Br -/OMCA proportion of 26/52. According to Fig.2.10, after 30ns MD simulation, several OMCA molecules are observed to escape from the surfactant layer and move toward the water solution. Obviously, the number of escaping cis-OMCA molecule is much more than that of trans-OMCA. The stronger hydrophilicity of cis-OMCA drives it to run from the hydrophobic interior of 12-2-12• 2Br -to the water. Once the cis-OMCA escape from its position, the original wormlike micelles break into rod-like micelles even spherical micelles correspondingly.

Fig. 2 .

 2 Fig. 2.10 Snapshots of 12-2-12• 2Br -on air-water interface before and after MD simulations with 12-2-12• 2Br -/OMCA proportion of 26/52. (Red parts are OMCA molecules escaping from micelles; yellow parts are OMCA molecules embedded into micelles; cyan parts are 12-2-12• 2Br -layers. The middle transparent part is water.)

Fig. 2 .Fig. 2 .

 22 Fig. 2.11 Relative interaction energies (kJ/mol) of specific packing patterns between 12-2-12 2+ and OMCA - on micelles. The benzene rings of (a) and (d) are embedded into the micelles and the benzene rings of (b) and (c) appear on the micelle surface. (a) and (b) are cis-OMCA. (c) and (d) are trans-OMCA. (For clarity, hydrogen atoms are not shown.)

Fig. 2 .

 2 Fig. 2.13 Potentials of mean force (PMF) of pulling out an OMCA or 12-2-12 2+ ion from a spherical micelle formed by 32 12-2-12• 2Br -and 32 OMCA to different distances.

Fig. 2 .

 2 Fig. 2.14 The mechanism of photo-responsive 12-2-12• 2Br -/trans-OMCA micelle morphology transition.

  photoisomerizes into cis-OMCA. The wormlike micelles crack to rod-like micelle and finally to spherical micelles. Three primary factors (geometry, hydrophilicity and energy) affecting those micelle transitions are unraveled systematically. The larger steric hindrance of cis-OMCA weakens π-cation interaction and electrostatic interaction. The stronger hydrophilicity of cis-OMCA leads to the moving of cis-OMCA from the interval of micelles to the solution.

  photo-sensitive molecules to adjust the morphology of surfactant assemblies in the photoresponsive system. The Gemini surfactant timethylene-1, 3-bis (dodecyldimethylammonium bromide) (12-3-12•2Br -) was specified as the elementary entity of surfactant assemblies. The photo responsive wormlike micelles were then constructed by aromatic cinnamates and 12-3-12•2Br -. The corresponding morphologies during the photo-responsive process of the studied wormlike micelles were observed by transmission electron microscopy (TEM) and the kinetics of photo-isomerization of three trans-isomers were studied by UV-Vis absorption spectrum and high performance liquid chromatography (HPLC). MD simulations and quantitative calculations were employed to simulate the morphological transformation of micelles under UV irradiation and to investigate the differences of structure and properties between cinnamates with various ortho-substituent groups. Especially, we constructed simulation systems using different numbers of trans/cis-isomers to simulate the UV irradiation time. Our simulations and calculations display the detailed information about how photo-sensitive molecules participate in the construction and fission of wormlike micelles composed of cinnamates and 12-3-12•2Br - before and after UV irradiation and elucidate the impacts of different ortho-substituents on the photo-behavior of these photo-responsive systems. This study allows us to optimize the photoresponsive self-assembly system containing Gemini surfactants and cinnamates, which is of great importance for the design of smart responsive systems and expansion of their applications in soft material and other fields.

  Scheme. 3.1 Structures of Gemini surfactant 12-3-12•2Br -and cinnamate derivatives (trans/cis-CA, trans/cis-OHCA and trans/cis-OMCA)

  initial and equilibrium states (32 trans-CA for f = 0, 24 trans-CA and 8 cis-CA for f = 0.24, 32 trans-OHCA for f = 0, 11 trans-OHCA and 21 cis-OHCA for f = 0.65, 32 trans-OMCA for f = 0, 4 trans-OMCA and 28 cis-OMCA for f = 0.88, respectively) were constructed by Packmol software and put in the box with the size of 6nm × 6nm × 12nm. Approximately 13000 water molecules by the SPC water model were added into boxes. The steepest descent of energy minimization was used. Then the MD simulation were carried out in NPT ensemble at 298.15

3. 3 . 1

 31 Photo-responsive behavior of the 12-3-12• 2Br -/cinnamates mixed systems In order to investigate the effect of the ortho substituents of the photosensitive molecules on the photo-responsive behavior of the photo-responsive fluids, three different wormlike micelles were constructed (40 mM 12-3-12•2Br -/24 mM cinnamates), and the photoresponsiveness of the studied wormlike micelles were investigated by observing the structure transition induced by UV irradiation. The microstructures of the aggregates that undergone different UV irradiation time were obtained through TEM. As shown in Fig. 3.1, the system containing 40 mM 12-3-12•2Br -/24 mM trans-CA initially performs an entangled and dense network structure of wormlike micelles. After 160 min UV irradiation, the structure of micelles does not change significantly. As for the system of 40 mM 12-3-12•2Br -/24 mM trans-OHCA, the wormlike micelles entangle with each other and form a denser and flexible network structure before UV irradiation. However, the intertwined network structures begin to unravel and become loose after 160 min UV irradiation. For 40 mM 12-3-12•2Br -/24 mM trans-OMCA, the surfactant molecules firstly form long and entangled wormlike micelles, while after the 160 min UV irradiation, the wormlike micelles transform into the short rod-like micelles and even spherical micelles.

Fig. 3 .

 3 Fig. 3.1 TEM images of the sample of 40 mM 12-2-12•2Br -/24 mM trans-cinnamates at 25°C under different UV irradiation time [(a) trans-CA, 0 min; (b) trans-CA, 160 min; (c) trans-OHCA, 0 min; (d) trans-OHCA, 160 min; (e) trans-OMCA, 0 min; (f) trans-OMCA, 160 min].

Fig. 3 . 2

 32 Fig. 3.2 Steady shear viscosity curves (trans-CA (a), trans-OHCA (b), trans-OMCA (c)) and the dynamic viscoelastic modulus (trans-CA (d), trans-OHCA (e), trans-OMCA (f)) of the systems of 40 mM 12-3-12•2Br -/24 mM cinnamates with different UV irradiation time at 25°C

μM 12 - 3 -

 123 12•2Br -/24 μM trans-isomer) The UV-Vis absorption spectrum and high performance liquid chromatography (HPLC) were applied to obtain the conversion fraction. The HPLC results are shown in Fig. 3.3. From the ratio of peak height before and after UV irradiation, we can obtain the equilibrium conversion fractions f of trans-CA, trans-OHCA and trans-OMCA are 0.24, 0.65 and 0.88.

Fig. 3 . 3

 33 Fig. 3.3 High performance liquid chromatography spectra of three cinnamate derivatives before UVirradiation and in equilibrium state after UV irradiation.

  3 and Fig.3.4, it can be seen that the order of f and Kc is trans-OMCA (f = 0.88, Kc = 7.33) > trans-OHCA (f = 0.65, Kc = 1.88) > trans-CA (f = 0.24, Kc = 0.31). This confirms our experimental results that trans-OMCA experience a dramatic morphology transition from wormlike micelle to rod-like micelle even spherical micelle whereas the micelle length of trans-OHCA and trans-CA is just shortened under long enough UV irradiation.

Fig. 3 . 4

 34 Fig. 3.4 Conversion fraction curves with UV irradiation time ((a), (b), (c)) and kinetic curves ((d), (e), (f)) of 40 μM 12-3-12•2Br -/24 μM trans-cinnamates ((a), (d) trans-CA, (b), (e) trans-OHCA, (c), (f) trans-OMCA)) at 25°C.

Fig. 3 . 5

 35 Fig. 3.5 Snapshots of the initial and final configuration of pure 12-3-12•2Br -surfactants. (The cyan molecules are 12-3-12 2+ ; the transparent parts are water; for clarity, Br -ions are not shown.)

3 . 6

 36 displays snapshots of the initial simulation box and final micelle morphologies (12-3-12 2+ / cinnamate derivatives = 180:135) at different conversion fraction after 100ns simulation at 298.15K. It can be seen from Fig. 3.6, after 100 ns MD simulation, the 12-3-12 2+ ions with trans-cinnamates all form a wormlike morphology from a random arrangement. After enough UV light, the photo-isomerization of trans-CA reaches equilibrium at f = 0.24 (equilibrium conversion of trans-CA). The micelle containing trans-CA hardly changes and maintains the wormlike shape after 100 ns simulation.

Fig. 3 . 6

 36 Fig. 3.6 Snapshots Snapshots of the initial simulation box and corresponding micelle morphologies of 12-3-12 2+ / cinnamate derivatives = 180:135 at different conversion fraction after 100 ns simulation at 298.15 K. (The cyan parts are 12-3-12 2+ ; the orange parts are trans-isomers; the red parts are cis-isomers. For clarity, water, Br -and Na + are not shown.)

Fig. 3 . 7

 37 Fig. 3.7 The density distributions of 12-3-12 2+ , cinnamate derivatives, Na + , Br -along z axis in systems at different f.

Fig. 3 . 8

 38 Fig. 3.8 The interaction energy (Coulombic, LJ and total interaction energy) between 12-3-12 2+ and cinnamate (cis-isomers and trans-isomers) in the system calculated by g_energy at different f with simulation time (a) trans-CA; (b) trans-OHCA; (c) trans-OMCA.

Fig. 3 .

 3 Fig. 3.10 Radial distribution functions gN1-N1(r) of N1-N1 atoms ((a) trans-CA (b) trans-OHCA (c) trans-OMCA) for the system 12-3-12 2+ /trans-cinnamates = 180:135 at different conversion fraction.

Fig. 3 .

 3 Fig. 3.11 Radial distribution functions gN1-C3(r) of N1-C3 ((a) trans-CA (b) trans-OHCA (c) trans-OMCA) for the system 12-3-12 2+ /trans-cinnamates = 180:135 at different conversion fraction.

Fig. 3 .

 3 Fig. 3.12 displays the representative packing patterns between the cinnamate and 12-3-12 2+ ions intercepted from micelle. It is obvious that the cis-isomer is orient on the surface of the micelles horizontally and its aromatic ring and carboxyl are located close with the head group of 12-3-12 2+ . The hydroxyl of cis-OHCA and the methoxy of cis-OMCA insert into the interior of the micelles. While the trans-isomer is plugged into the micelle vertically. The aromatic ring of trans-cinnamates is embedded into the hydrophobic region formed by surfactant alkyl chains. The carboxyl of trans-cinnamates is close to center of the head group

Fig. 3 .

 3 Fig. 3.12 The representative packing patterns between 12-3-12 2+ and trans/cis-cinnamates intercepted from micelles of last frame in MD simulations.

Fig. 3 .

 3 Fig. 3.13 The hydrophobic (apho), hydrophilic (aphi) and total (atot) surface areas of aggregates containing 12-3-12 2+ and cinnamate derivatives at different f with simulation time. (a) trans-CA; (b) trans-OHCA; (c) trans-OMCA.

Fig. 3 .

 3 Fig. 3.14 The top view and side view of optimized structures of trans/cis-cinnamate ions after being optimized at the b3lyp/6-311+g (d, p) level.

  model. One packing pattern is the aromatic ring embedded into the 12-3-12 2+ alkyl chain layer ((a), (d), (e), (h), (i), (l)) and the other is the aromatic ring oriented near the head group of 12-3-12•2Br -((b), (c), (f), (g), (j), (k)). For convenience, the relative lower interaction energies for packing pattern (d) (h) (l) are set as 0 kJ/mol. The calculation results are shown in Fig.3.16.

Fig. 3 .

 3 Fig. 3.16 The different packing patterns and corresponding relative interaction energies (kJ/mol) of 12-3-12•2Br -and trans/cis-cinnamate derivatives on micelles. (In (a), (d), (e), (h), (i), (l), aromatic rings are embedded into micelle. In (b), (c), (f), (g), (j), (k), aromatic rings are oriented on the surface of micelle. For clarity and convenience, hydrogen atoms on 12-3-12 2+ are not shown and the relative lower interaction energies for packing pattern (d) (h) (l) are set as 0 kJ/mol.)

Fig. 3 .

 3 Fig. 3.17 Mechanism of 12-3-12•2Br -and cinnimate derivatives micelle morphology transition under UV irradiation.

surfactant 12 - 3 -

 123 12•2Br -and trans/cis-OMCA, trans/cis-MMCA and trans/cis-PMCA are shown in Fig. 4.1. The force field parameters for trans/cis-MMCA and trans/cis-PMCA were generated by the ATB server and the force field parameters for trans/cis-OMCA and12-3-12•2Br -can be obtain from last chapter.

Fig. 4 . 1

 41 Fig. 4.1 Structures of Gemini surfactant 12-3-12•2Br -and trans/cis-OMCA, trans/cis-MMCA and trans/cis-PMCA.

  carried out by GROMACS 2018 software packages. Berendsen bath coupling scheme was used to maintain a constant temperature at 298.15 K and pressure at 1 bar.

4. 3 . 1

 31 Self-assembly behavior of 12-3-12• 2Br -and trans-cinnamates in water We have proved in previous chapter that the pure 12-3-12•2Br -can self-assemble into several spherical micelles with the aggregation number 30, which confirm the feasibility of GROMOS96 45a3 forcefield. Subsequently, we simulated the system containing 180 12-3-12•2Br -and 135 cinnamates with different cis/trans ratio to represent the initial and equilibrium conversion fraction from an entirely random arrangement state. The snapshots of the simulation box and initial as well as the final micelle morphologies after 100 ns simulation at 298.15K are shown in Fig. 4.2. Obviouly, without UV irradiation, 12-3-12•2Br -/ trans-cinnamates system self-assemble into a wormlike micelle after 100 ns MD simulation owing to the strong electrostatic attraction between polar head of surfactants and counter ions in solution. After enough UV irradiation, the wormlike micelle containing trans-OMCA transforms into spherical micelles. At equilibrium conversion fraction, wormlike micelles containing trans-MMCA and trans-PMCA fission into short rod-like micelles. The simulation results are in good agreement

Fig. 4 . 2 Fig. 4 .

 424 Fig. 4.2 Snapshots of the initial simulation box and corresponding micelle morphologies of 12-3-12 2+ / trans-cinnamates = 180:135 at equilibrium conversion fraction after 100ns simulation at 298.15K. (The cyan parts are 12-3-12 2+ ; the orange parts are trans-isomers; the purple parts are cis-isomers. For clarity, water, Br -and Na + are not shown.)

Fig. 4 . 3

 43 Fig. 4.3 The density distributions of 12-3-12 2+ , trans/cis-cinnamate ions, Na + , Br -along z axis at different f.((a) trans-OMCA f = 0; (b) trans-MMCA f = 0; (c) trans-MMCA f = 0; (d) trans-OMCA f = 0.88; (e) trans-OMCA f = 0.91; (f) trans-PMCA f = 0.82)

Fig. 4 . 4

 44 Fig. 4.4 The interaction energy (Coulombic, LJ and total interaction energy) between 12-3-12 2+ and MCA (cis-isomers and trans-isomers) at different f with simulation time (a) trans-OMCA; (b) trans-MMCA; (c) trans-PMCA.

Fig. 4 . 6 Fig. 4 .

 464 Fig. 4.6 Radial distribution functions gN1-C(r) between N1 atom of 12-3-12 2+ and C3, C7, C10 atoms of cinnamates at initial and equilibrium conversion fraction. ((a) (d) (g) N1-C3; (b) (e) (h)N1-C7; (c) (f) (i) N1-C10; (a) (b) (c) trans-OMCA; (d) (e) (f) trans-MMCA; (g) (h) (i) trans-PMCA)

Fig. 4 . 7

 47 Fig. 4.7 The representative packing patterns between 12-3-12 2+ and trans/cis-cinnamates with different methoxy-substituent positions intercepted from micelles of last frame in MD simulations.

Fig. 4 . 8

 48 Fig. 4.8 The hydrophobic (apho), hydrophilic (aphi) and total (atot) surface areas of aggregates containing 12-3-12 2+ and methoxy sodium cinnamates at different f with simulation time. (a) trans-OMCA; (b) trans-MMCA; (c) trans-PMCA.

Fig. 4 . 9

 49 Fig.4.9 The hydrogen bond numbers between cinnamate ions and water in simulation system before and after UV irradiation

Fig. 4 .

 4 Fig. 4.11 The electrostatic potential distributions (eV) of trans/cis-cinnamate ions after being optimized at the b3lyp/6-311+g (d, p) level. The blue dots represent the minimum of potential in near area. The red dots represent the maximum of potential in near area.

Fig. 4 .

 4 Fig. 4.12 The different packing patterns and corresponding relative interaction energies (kJ/mol) of 12-3-12 2+ and OMCA, MMCA, PMCA. (In (a), (d), (e), (h), (i), (l), the aromatic rings are oriented on the surface of micelle. In (b), (c), (f), (g), (j), (k), the aromatic rings are embedded into the alkyl chain of the 12-3-12 2+ .

  energy and their difference (ΔV ΔE), and photo-isomerization reaction equilibrium at singlet state (Kg-s) and triplet state (Kg-t), the maximum of negative electrostatic potensial (cis-max, trans-max), and their difference (Δmax) of trans/ciscinnamic acid under UV irraidaition. The calcaulted results are shown in Fig.4.14. Those cinnamic acid are meta-hydroxylcinnamic acid (MHCA), para-hydroxylcinnamic acid (PHCA), ortho-sulfhydrylcinnamic acid (OSCA), metasulfhydrylcinnamic acid(MSCA), para-sulfhydrylcinnamic acid (PSCA), orthomethylthiocinnamic acid (OMTCA), meta-methylthiocinnamic acid (MMTCA), paramethylthiocinnamic acid (PMTCA), ortho-aminocinnamic acid (OACA), meta-aminocinnamic acid (MACA), para-aminocinnamic acid (PACA), ortho-methylaminocinnamic acid (OMACA), meta-methylaminocinnamic acid (MMACA), para-methylaminocinnamic acid (PMACA), ortho-dimethylaminocinnamic acid (ODACA), meta-dimethylaminocinnamic acid (MDACA), para-dimethylaminocinnamic acid (PDACA), ortho-nitrocinnamic acid (ONCA), metanitrocinnamic acid (ONCA), para-nitrocinnamic acid (ONCA), respectively. And their chemical structures are shown in Fig.4.13.

Fig. 4 .

 4 Fig. 4.13 The structures of cinnamic acids for calculations to screen out the photosensitive molecule with the best photosensitive ability

Fig. 5 . 2

 52 Fig. 5.2 The The storage modulus G' and loss modulus G'' with frequency for the 20mM CTAB and NaSal (0-13mM) samples at 22°C. (a) Newtonian solution; (b) shear-thinning solutions.

Fig. 5 .

 5 Fig. 5.3 for all the samples studied. The error bars denote the standard deviation between ten subsequent measurements. The bubbles made in the Newtonian solutions are shown with empty symbols and the bubbles in the shear thinning solutions with filled symbols.

Fig. 5 . 3

 53 Fig. 5.3 Sauter radius of bubbles produced in solutions with CTAB (20 mM) and NaSal (0-13mM) at 22 °C.The corresponding bubble size distributions can be found in Fig.5.4.

Fig. 5 . 4

 54 Fig. 5.4 Bubble size distribution of 20 mM CTAB and various amounts of NaSal (0-13 mM) for bubbles made with the two-syringe method at 22 °C. The volume fraction represents the gas fraction.

Fig. 5 .

 5 Fig. 5.5 shows the width of the bubble size distribution at half height and the width normalized by the bubble size. The width exhibits the same trends as the bubble size with the increase of the viscosity and gas fraction,

Fig. 5 . 5

 55 Fig. 5.5 Width of the size distribution at half height for bubbles (a) and width of the distribution at half height normalized by bubble size (b) in solutions of 20 mM CTAB and NaSal (0-13 mM) at 22 °C

Fig. 5 .

 5 Fig. 5.6 (a) Images of the bottles containing bubbly liquids at different times, showing the front evolution. The three horizontal lines (green, red and blue) indicate the position of the front for the three different grey levels I = 40, 80 and 120 respectively. (b) Grey value curves at different times (The overlapped curves at heights below 8 mm are the top black part, which represents the foams.) (c) Height of bubbly liquid versus time for different grey levels. Solution with 20 mM CTAB and 4 mM NaSal and φgas= 5%

Fig. 5 .

 5 Fig. 5.7 (a) The gray value curve and (b) The bubble rise curve area of 20mM CTAB and 11.5 mM NaSal at φgas= 5%.

Fig. 5 .

 5 Fig. 5.8 (a) Images of the bottles containing bubbly liquids at different times, showing the front evolution at the different intensity levels I = 40 (green), 80 (red) and 120 (blue). The white line indicates the level of the bubbly liquid at the beginning of the experiment. (b) The gray value with the height of the front (c) Height of bubbly liquid versus time for different grey levels. The inset is a semi-logarithmic plot. The system shown in the image is a solution with 20mM CTAB and 13 mM NaSal at φgas= 5%.

Fig. 5 .Fig. 5 . 9 Fig. 5 .

 5595 Fig. 5.9 The bubble rise velocity v normalised using the Stokes velocity vs, as a function of gas fraction for the Newtonian solutions. The velocity is measured using the intensity I = 80. The solid line is the Richardson and Zaki prediction of equation (5-5) with n = 4.5.

Fig. 5 .

 5 Fig. 5.11 (a) Front rise velocity, v as a function of φgas for the non-Newtonian solutions, i.e., CTAB 20 mM with NaSal 10-13 mM indicated in the legend. The velocities are measured using I = 80. (b) Front velocity normalised by the velocity at φgas = 0.05, the dashed line shows the prediction of Richardson and Zaki equation. The weak variation of the velocity as a function of φ can be described using v v(φ gas =0.05) =1.1(1-φgas) the dotted (colour) line.

Fig. 5 .

 5 Fig. 5.12 Bubble front rise velocity v of the non-Newtonian samples normalised by the Stokes velocity calculated using η estimated at the shear rate around the bubbles v/R.

Fig. 5 .

 5 Fig. 5.13 The front rise velocity v of the initial bubble rise, and the velocity at long times, once it has considerably slowed down. Both were measured using I = 80. Solution with 20mM CTAB and 13 mM NaSal at φgas= 5%.

As 1 ( 5 - 9 )

 159 𝑣 varies very differently in the Newtonian and the non-Newtonian fluids, we can expect S ̇ to also change.In Newtonian fluids the Richardson Zaki expression works well, as given by equation(5- 5). For the non-Newtonian fluids, we saw that the velocity depends weaklier on φgas (for example in Fig. 5.11 (a)). The velocity varies with volume fraction as v Non-Newt ∝(1-φgas) which has been shown by the dotted line in Fig. 5.11 (b). We can therefore use the two expressions for velocity to estimate S ̇ in Newtonian and shear thinning fluids. This results in very distinctive bubble surface area variations with φgas , as shown in Fig. 5.14. Indeed, if maximisation of the bubble surface area flux is an objective, in Newtonian fluids the optimum is at φgas = 0.16, while in non-Newtonian fluids higher φgas would improve the area flux. Our experiments are limited to gas fractions less than 0.3, and we cannot speculate about what happens at higher φgas. However, our results suggest that the parameters for optimum flotation when non-Newtonian fluids are present can be very different from those with Newtonian fluids.

Fig. 5 .

 5 Fig. 5.14 Bubble surface area flux as a function of bubble volume fraction for Newtonian and non-Newtonian fluids. The dependence is very different, and the maximum in non-Newtonian fluids occurs at a much higher φgas.

)

  Based on the previous research, to comprehensively study the effects of cinnamate structure on the photo-responsive behavior of corresponding wormlike micelles, MD simulations and quantitative calculations were used to investigate the influence of ortho-, metaand para-methoxy on the photo-responsive behavior of the wormlike micelle systems containing Gemini surfactant 12-3-12•2Br -and three trans-methoxy-cinnimates trans-OMCA, trans-MMCA and trans-PMCA.

2

  photosensible. Le comportement photosensible du système et le mécanisme microscopique de transformation de la morphologie de l'auto-assemblage ont été étudiés en combinant rhéologie, dynamique moléculaire et calcul quantitatif. Le mécanisme de comportement photosensible pour la micelle 12-2-12•2Br -/trans-OMCA est proposé (Fig. 2.14). De toute évidence, le motif de tassement entre 12-2-12•2Br -et OMCA détermine directement la morphologie existante de la micelle et les trois principaux facteurs affectent le motif de tassement entre 12-2-12•2Br -et OMCA : structure géométrique de l'OMCA, hydrophilie de l'OMCA et de l'énergie d'interaction entre l'OMCA et le 12-2-12•2Br-. Tout d'abord, il convient de noter que la structure relativement plane du trans-OMCA et le degré de flexion inférieur rendent le trans-OMCA plus facile à insérer dans l'intervalle des tensioactifs. Il est démontré par g(r) et SASA que la géométrie moléculaire différente du trans/cis-OMCA influence leurs modes de tassement : le cycle aromatique du trans-OMCA est complètement noyé dans la chaîne alkyle hydrophobe de 12-2-12•2Br -et celle de cis-OMCA est exposé à la surface de la micelle. De ce fait, il y a un arrangement plus étroit entre le centre chargé de trans-OMCA et 12-2-12.2Br -, provoquant une interaction électrostatique et une interaction -cation plus fortes. Après irradiation UV, l'encombrement stérique de la molécule cis-OMCA devient plus grand et l'interaction électrostatique et l'interaction cation-cation s'affaiblissent, conduisant à la désintégration de la micelle d'origine. Deuxièmement, il a été prouvé qu'une solubilité plus faible dans l'eau était liée à une

Fig. 2 . 1 3Fig. 3 . 1 .

 2131 Fig. 2.1 Le mé canisme de la transition morphologique des micelles photosensibles 12-2-12.2Br -/trans-OMCA.

Fig. 3 . 1 157 4 158 5Fig. 5 . 1

 3115715851 Fig. 3.1 Mécanisme de transition de la morphologie des micelles du 12-3-12•2Br -et des dérivés cinnimates sous irradiation UV.

Fig. 5 . 1 摘要(的 14 图 3 . 3 ) 1 ) 3 . 5

 511433135 Fig. 5.2 (a) Vitesse de montée du front, v en fonction de gaz pour les solutions non newtoniennes, c'est-àdire CTAB 20 mM avec NaSal 10-13 mM indiqué dans la légende. Les vitesses sont mesurées en utilisant I = 80. (b) Vitesse frontale normalisée par la vitesse à gas = 0,05, la ligne pointillée montre la prédiction de l'équation de Richardson et Zaki. La faible variation de la vitesse en fonction de peut être décrite en utilisant

图 5 . 2 22°C

 52 此外,我们截取了 MD 模拟中蠕虫状胶束上 trans/cis-MCA 与 12-3-12 2+ 的两种典型 的排布方式,并计算了它们之间的相互作用能。其中一种是苯环嵌入到 12-3-12 2+ 烷基链 中,另一种是苯环位于 12-3-12•2Br -的头基附近。我们将(d) (h) (l)这三种的排布方式的 相对相互作用能定义为 0 kJ/mol。如图 4.6 所示,对于 trans-MCA,苯环嵌入到胶束内 部的排布方式相对作用能较低,较为稳定,而对于 cis-MCA,苯环位于胶束表面的排布 方式相互作用能更低,较为稳定。这意味着当稳定的反式排布方式在紫外线照射后转变 为顺式排布方式后,为了获得新的稳定排布方式,cis-MCA 将改变其排布方式将嵌入胶 束的苯环移动到胶束表面上。这个排布方式变化的过程会导致胶束的松散和破裂。 图 4.6 12-3-12 2+ 和 OMCA、MMCA、PMCA 在胶束上不同排布方式和相应的相互作用能 (kJ/mol) 。在(a)、(d)、(e)、(h)、(i)、(l)中,苯环分布在胶束表面。在(b)、(c)、(f)中, (g)、(j)、 (k)中,苯环嵌入 12-3-12 2+ 的烷基链中。为清楚起见,未显示和甲氧基和 12-3-12 2+ 上的氢原子。为 方便起见,将苯环嵌入胶束中的反式异构体排布方式的相互作用能设为 0 kJ/mol。) 为了筛选出光敏效果最好的肉桂酸衍生物,我们选择了二十四种在邻位、间位和对 位具有不同供电子取代基的肉桂酸衍生物,并计算了摩尔体积(V)、溶剂化自由能(E)下 20 mM CTAB 和 0-13 mM NaSal 溶液中产生的气泡的 Sauter 半径 5.3. 气泡上升速度的测量 为了研究 CTAB/NaSal 溶液中气泡是如何上升的,我们拍摄了不同浓度和气体分 数下气泡上升的照片。图 5.3 (a) 显示了 20 mM CTAB/4 mM NaSal 在 φ = 5%时气泡上 升过程的照片。当样品瓶内填充满气泡液时,瓶身呈现黑色。气泡随着上升,气泡液和 透明液之间的分界线变得清晰可见。分界线随着时间向上移动。我们使用 Image J 软件 来处理图片并通过计算分界线的移动速度来计算气泡上升速度,并绘制了不同时间下, 灰度随分界线高度变化的曲线图 5.3 (b)。 从图 5.3 (b)中,可以看出图像灰度在 0 到 160 之间变化,于是我们选择了三个灰度 值 I = 40、80 和 120(较小的 I 表示较暗的区域)并从中截取出不同时间下的相同灰度 对应的分界线高度,并绘制了图 5.3(c)。如图 5.3(c)所示,分界线高度随时间线性变化, 且每个灰度值的分界线上升速度不同,分别为 0.31mm/s (I = 40)、0.23mm/s (I = 80)、 0.18mm/s (I = 120)。这些气泡上升速度差异是由于气泡尺寸的多分散性引起的。在下文 中,我们使用 I = 80(图像中的平均灰度)的高度值来定义气泡上升分界的位置。

Table 2 .

 2 1 The charge assignments for 12-2-12 2+ used in the MD simulations.

	12-2-12 2+

Scheme 2.1 Model structures and numberings of:

Table 2 .

 2 2 Number of 12-2-12 2+ , Br -, OMCA -, Na + ions and water molecules in simulation box.

	System	12-2-12 2+	Br -	OMCA -([mol/L])	Na +	H2O
				12-2-12 2+
	1	90	180	-	-	11960
			12-2-12 2+ + trans-OMCA
	2	216	432	324 (0.40)	324	36626
	3	216	432	270 (0.33)	270	36993
	4	216	432	252 (0.31)	252	37218
	5	216	432	216 (0.27)	216	37463
	6	216	432	162 (0.20)	162	38057
	7	216	432	108 (0.13)	108	38546
	8	216	432	54 (0.07)	54	39037
				12-2-12 2+ + cis-OMCA
	9	216	432	324 (0.40)	324	36630
	10	216	432	270 (0.33)	270	37066
	11	216	432	252 (0.31)	252	37203
	12	216	432	216 (0.27)	216	37510
	13	216	432	162 (0.20)	162	38070
	14	216	432	108 (0.13)	108	38663
	15	216	432	54 (0.07)	54	38972
	2.3 Results and Discussion
	2.3.1 Photo-responsive behaviors of the wormlike micelle system
	2.3.1.1 Microstructure.
	The wormlike micelles formed in 17mM 12-2-12• 2Br

-/7mM trans-OMCA aqueous solution were singled out to study the responsive behavior after UV irradiation. The microstructures of the aggregates after different UV irradiation times are obtained by TEM combined with a negative staining technique. As can be seen from

Table 2 .

 2 3 presents some geometrical properties for the micelles at r n = 0.75 in our simulation. From Table2.3, we can find that there is a larger hydrophobic area for 12-2-

Table 2 .

 2 4, trans-OMCA molecule has a smaller molar volume. Therefore, when inserted into the 12-2-12• 2Br -layers, trans-OMCA molecule is easier to embedded into hydrophobic interior of 12-2-12• 2Br -and shows a more ordering arrangement. After UV irradiation, owing to higher bending degree and larger volume, cis-OMCA molecules occupy more space and has a farther distance to the charged head group of 12-2-12• 2Br -, which has been testified via g(r) of N1-C10

	in Fig. 2.6. Therefore, the arrangement between OMCA and 12-2-12• 2Br -becomes looser and
	the interactions between OMCA and 12-2-12• 2Br -become weaker, giving rise to the break of
	micelles.

Table 2 .

 2

		Solvation free	C10-H3 Distance	Molecular volume
		energy (kJ/mol)	(Å)	(cm 3 /mol)
	cis-OMCA	-40.56	6.46	125.16
	trans-OMCA	-37.68	9.02	122.23
	2.3.4.2 Hydrophilicity

4 Solvation Free Energy of cis/trans-OMCA, distance between H3 and C10 and molar volume calculated by Gaussian 09 at M052X/6-31G* level in SMD solvation model. Subsequently, we explore the hydrophobicity of cis/trans-OMCA by calculating the solvation free energy using Gaussian 09 at M052X/6-31G* level in SMD solvation model. Solvation free energy represents the intensity of hydrophilic capacity of a molecule. The free energy of solvation refers to the change in free energy that moves a solute molecule in a gas phase state of 1 atm into a solvent to become a solvation state of 1 mol. As is shown in

Table 2 .

 2 4, the solvation free energies of cis-OMCA and trans-OMCA are -40.56 kJ/mol and -37.68 kJ/mol. Obviously, cis-OMCA is more hydrophilic, and it should have a stronger trend to move to the water rather than stay in the micelle than trans-OMCA. In order to verify this inference,

	we constructed an air/water interface with well-arranged surfactant layers consisting of 26 12-
	2-12• 2Br -(CMC concentration) and 52 OMCA are oriented randomly between the 12-2-
	12• 2Br -. 47 Excessive OMCA molecules ensure that OMCA molecules are able to escape from
	surfactant layers.

Table 2 .

 2 5 Interaction energies between OMCA -and 12-2-12 2+ ions at r n = 0.75 after equilibrium in MD Fig.2.12 Interaction energies (kJ/mol) between 12-2-12 2+ and OMCA -during MD simulations at r

		simulations:
		Coulombic	LJ	Total Interaction
	System
		(kJ / mol)	(kJ / mol)	(kJ / mol)
	cis-OMCA	-16807.90	-13316.07	-30123.97
	trans-OMCA	-17402.15	-14632.52	-32034.68

n = 0.75.

Table 3 .

 3 1 Number of 12-3-12 2+ , Br -, cinnamate derivatives, Na + ions and water molecules in simulation box.

	System	12-3-12 2+	Br -	cis/trans-isomers	Na +	H2O
				12-3-12 2+
	1	90	180	0/0	0	19834
				12-3-12 2+ + OMCA
	2	180	360	0/135	135	38233
	3	180	360	32/103	135	38295
	4	180	360	88/47	135	38230
	5	180	360	118/17	135	38227
				12-3-12 2+ + OHCA
	6	180	360	0/135	135	38253
	7	180	360	32/103	135	38290
	8	180	360	88/47	135	38330
				12-3-12 2+ + CA
	9	180	360	0/135	135	38397
	10	180	360	32/103	135	38327

Table 3 .

 3 2 Variation of rheological parameters of the wormlike micelle constructed by 40 mM 12-3-12•2Brˉ/24 mM trans-cinnamates with the prolongation of UV irradiation time at 25 °C.

		UV time	G *	G 0 '	″ G min	ωc	τ	ξ	Le(nm)	L(nm)
		(min)	(Pa)	(Pa)	(Pa)	(rad/s)	(s)
	CA	0	12.2 23.8	9.1	25.1	0.040	5.6×10 -8	110-133	289-350
		160	38.1 27.4	13.1	15.5	0.064	5.4×10 -8	102-124	213-258
	OHCA	0	28.9 64.7	7.5	3.3	0.31	4.0×10 -8	63-77	548-663
		160	33.8 65.6	11.9	10.6	0.094	4.0×10 -8	63-76	347-420
	OMCA	0	15.2 31.4	8.4	17.5	0.057	5.1×10 -8	95-115	355-430
		40	18.0 25.5	16.2	48.4	0.021	5.5×10 -8	106-129	167-202

Table 3 .

 3

		CA	OHCA	OMCA
	f	0.24	0.65	0.88
	k1+k-1	0.026	0.19	1.24
	Kc	0.31	1.88	7.33
	k1	0.006	0.12	1.09
	k-1	0.020	0.07	0.15
	3.3.3 Micelles of pure 12-3-12• 2Br -in water
	To better understanding the complex photo-responsive behaviors of the assemblies
	containing 12-3-12•2Br -and different cinnamates, it is necessary to study the self-assembly
	behavior of single 12-3-12•2Br -in water. It is well known that different concentrations of 12-

3

The conversion fraction f, the slope (k1+k-1) of the kinetic curve, reaction equilibrium constant (Kc), forward rate constant (k1) and reverse rate constant (k-1) of the photo-isomerization reaction of trans-CA, trans-OHCA and trans-OMCA at 25°C.

Table 3 .

 3 5 summarizes the corresponding parameters calculated by Gaussian 09. The smallest molar volume of trans-OHCA means the smallest steric hindrance, which can explain the tightest arrangement of trans-OHCA ions in micelle. The molar volumes of trans-isomer for OMCA and OHCA are smaller than that of the cis-isomer.

Table 3 .

 3 5 The solvation free energy and the difference of them between trans/cis-cinnamate molecules, molar volume of cinnamate ions, Gibbs free energy (ΔGg-s and ΔGg-t) and reaction equilibrium constant (Kg-s and Kg-t) at singlet and triplet at 25°C calculating by Gaussian 09.

		trans-	cis-	trans-	cis-	trans-	cis-
	System
		CA	CA	OHCA	OHCA	OMCA	OMCA
	Solvation free energy
		-35.28	-37.16	-53.97	-56.39	-37.68	-40.56
	(kJ/mol)
	Molar volume (cm 3 /mol)	116.16 104.50	107.35	110.60	122.23	125.16
	ΔE (kJ/mol)	-1.88	-2.42		-2.88
	ΔGg-s (kJ/mol)	19.33	16.21		14.36
	ΔGg-t (kJ/mol)	-24.63	-31.20	-33.26
	Kg-s	4.10×10 -4	1.45×10 -3	3.05×10 -3
	Kg-t	2.06×10 4	2.92×10 4	6.72×10 4

Table 4 .

 4 3 The solvation free energy and the molecule volume of trans/cis-cinnamate ions calculating by

			Gaussian 09.
		trans-	cis-	trans-	cis-	trans-	cis-
	System
		OMCA	OMCA	MMCA	MMCA	PMCA	PMCA
	Solvation free energy
		-37.68	-40.56	-29.66	-27.72	-30.44	-27.44
	(kJ/mol)
	Molar volume (cm 3 /mol)	113.7	146.5	129	99.3	152.3	136.4
	4.3.4.4 Interaction energy of representative packing patterns

Table 5

 5

	.1 Surface tension of mixed CTAB/NaSal solutions. CTAB concentration: 20 mM
	NaSal concentration (mM)	0	4	10	13
	Surface tension (mN/m)	35.1	31.5	27.4	27.0

  à son tour provoque des changements dans la configuration macroscopique des micelles et des changements dans les propriétés macrophysiques et chimiques, et parce que les molécules d'acide cinnamique elles-mêmes ont une certaine activité de surface, faible coût, excellente photosensibilité. Par conséquent, les micelles ressemblant à des vers sensibles à la lumière composées de petites molécules photosensibles à base d'acide cinnamique et de tensioactifs Gemini sont devenues un objet de recherche brûlant à l'heure actuelle. La structure moléculaire détermine la nature de la molécule.Les différents substituants sur les petites molécules photosensibles à base d'acide cinnamique et les différentes positions de ces substituants auront un grand impact sur la capacité de photoisomérisation de la petite molécule d'acide cinnamique et la capacité de photoréponse du grand impact. En raison de la limitation des conditions expérimentales, la recherche sur le mécanisme microscopique du comportement sensible à la lumière des micelles ressemblant à des vers sensibles à la lumière est insuffisante.En même temps, en raison de la complexité et de la difficulté de la synthèse et de la main-d'oeuvre et du matériel limités. ressources, il nous est difficile de photosensibiliser une

	1 Introduction
	Au cours des dernières décennies, les matériaux intelligents auto-assemblés capables de
	répondre de manière dynamique aux stimuli environnementaux externes (y compris l'électricité,
	la lumière, le magnétisme, la chaleur, le pH, le CO2, etc.) ont été un point névralgique de la
	recherche pour les chercheurs. Parmi eux, l'auto-assemblage sensible à la lumière construit par
	des tensioactifs a attiré l'attention des scientifiques. Ce système d'auto-assemblage sensible au
	stimulus a non seulement des morphologies d'auto-assemblage abondantes et différentes
	échelles d'auto-assemblage, y compris des micelles sphériques, des micelles vermiformes, des
	vésicules, des gels, des cristaux liquides cristallins lyotropes (LC) et aqueux à deux phases
	celle des tensioactifs conventionnels. L'excellente capacité d'auto-assemblage et le
	comportement d'agrégation riche des tensioactifs Gemini font que le système sensible à la
	lumière composé de petites molécules sensibles à la lumière joue un rôle plus important dans
	les applications industrielles.
	La capacité de réponse à la lumière des micelles ressemblant à des vers sensibles à la
	lumière dépend non seulement de la capacité d'auto-assemblage des tensioactifs du système,
	mais aussi de la photosensibilité des petites molécules sensibles à la lumière dans le système.

(ATPS), etc., et son positionnement est propre, précis, sans interférence et facile à utiliser. Ces avantages le distinguent dans les domaines de la libération de médicaments, de l'industrie pétrochimique, de la catalyse commutable, de la modification de surface, de la bio-ingénierie, des matériaux photosensibles intelligents et des systèmes optiques, présentant une grande valeur d'application. Parmi ces auto-assemblages réactifs, les micelles de type ver sensibles à la lumière ont une variété de morphologies de micelles contrôlables et une large gamme de propriétés rhéologiques réglables, ce qui en fait des applications pratiques dans les fluides rhéologiques optiques, les dispositifs photosensibles, les réducteurs de traînée, etc. CUHK brille. L'introduction de petites molécules photosensibles dans le système tensioactif est le moyen le plus simple d'obtenir un système micellaire ressemblant à un ver sensible à la lumière. La capacité de réponse à la lumière du système dépend de la capacité d'auto-assemblage du tensioactif d'une part. Par rapport aux tensioactifs monocaténaires traditionnels, la capacité d'auto-assemblage des tensioactifs Gemini à la même concentration est beaucoup plus forte que La double liaison carbone-carbone dans la structure moléculaire de l'acide cinnamique est tordue de trans à cis à une longueur d'onde ultraviolette de 365 nm. Cette réaction de photoisomérisation conduit à un changement dans l'agencement de l'auto-assemblage du système, qui

  中列举了顺反肉桂酸酯的溶剂化自由能。UV 照射前后,OMCA 和 PMCA 的溶剂化自由能增加,说明 cis-OMCA 和 cis-

	分子结构对分子的亲疏水性也有重要影响。表 4.1 PMCA 相比反式构型更加亲水,更容易从胶束中逃逸出进入溶液。相反,MMCA 的溶
	剂化自由能略有下降,这说明 cis-MMCA 更有可能留在胶束层中而不是移动到溶液中,
	从而降低蠕虫状胶束光响应能力。
	表 4.1 通过 Gaussian 09 计算得到的 trans/cis-MCA 分子的溶剂化自由能与 trans/cis-MCA 的离子
					体积
		trans-	cis-	trans-	cis-	trans-	cis-
		OMCA	OMCA	MMCA	MMCA	PMCA	PMCA
	溶剂化自由能
		-37.68	-40.56	-29.7	-27.7	-27.4	-30.4
	(kJ/mol)
	离子体积 (cm 3 /mol)	113.7	146.5	129	99.3	152.3	136.4
		35.28		-37.16	-53.97	-56.39	-37.68	-40.56
	α (°)	180		57.8	180	66.1	180	66.1
	摩尔体积
	(cm 3 /mol)	116.16	104.50	107.35	110.60	122.23	125.16
	ΔE (kJ/mol)		-1.88		-2.42	-2.88
	3.6.2 静电势
	三种肉桂酸衍生物离子的静电势分布如图 2.10 所示。我们可以发现负电荷均集中
	在羧基上,而负电荷则集中在苯环上。由于羟基的存在,trans-OHCA 静电势分布最不均
	匀。trans-OHCA 具有最高的负电荷极值 (-7.36 eV) 和最不均匀的电荷分布。这表明
	trans-OHCA 与 12-3-12 2+ 之间的静电相互作用最强,这也印证了含有 trans-OHCA 的蠕
	虫状胶束具有最致密的形态和最高的粘度。此外,在紫外线照射后,OHCA 和 OMCA 的
	静电势的极值下降得更显著,表明它们具有比 CA 更强的光响应能力。这也说明了在邻
	位引入羟基和甲氧基会增加肉桂酸衍生物中羧基的静电势,增强紫外线照射前后羧基上
	的静电势差,从而提高体系的光响应性。

Table 4.1 Number of 12-3-12 2+ , Br -, cinnamate derivatives, Na + ions and water molecules in simulation box.

Acknowledgements ............................................................................................................... Resumé substantiel de la thè se ............................................................................................ Acknowledgements I will show my sincere thanks to Prof. Anniina Salonen, Prof. Dominique Langevin and Prof. Frédéric Restagno and Prof. Yazhuo Shang for their enduring support and patience throughout my thesis. This thesis was completed with their constructive suggestions and inspiring encouragement. Their deep understanding of interface physics and chemistry has greatly helped me design and conduct experiments scientifically. Their desire for scientific research and considerate care always encourages me to use appropriate methods to analyze problems and overcome difficulties. Thank Prof. Yazhuo Shang for giving me the opportunity to study abroad. Thank Prof. Anniina Salonen for offering me the impressive experience of conducting the research in Laboratoire de Physique des Solides. Thanks for the financial support of China Scholarship Council. I feel lucky that I am surrounded by intelligent and helpful member of MMOI group: Emmanuelle Rio, Liliane Léger, François Boulogne, Christophe Poulard, Sandrine Mariot, Anna Kharlamova, Laura Wallon, Chiara Guidolin, Marina Pasquet, Marie Corpart, Aymeric Duigou Majumdar, Julian Wailliez, Raphaelle Taub, Suzanne Lafon, Elina Gilbert, Manon Marchand, Jonas Miguet, Marion Grzelka and Ning Jiang. Thank you for your meticulous help and company in my daily life and in research when I was in Orsay. Sincere gratitude should also go to my group mates in China: Yi Guo, Meng Li, Hengjiang Liu, Meng Zhou, Mengge Gao, Yan Tu, Ruijin Wang, Zhicheng Ye, Xiangrong Huang, Jie Shuai, Wenxiu Liu, Jiajie Hu, Xinrui Li, Hanglin Li, Zilong Li, Xinyue Sun, Zheng Wu, Xin Bai, Jingwen Wang, Xin Li, Hao Feng, Yawen Lv, Zhuoyao Ni, Yuchen Cong, Lin Ding, Ning Di, Zhicheng Liu, Shiqiang Cheng and Tianyi Gao. Thanks for your assistance and companionship during my five-year PhD study at ECUST. I am extremely grateful to my friends Guanfei Shen, Zehua Song, Weishu and Guohui Gao and in France. Your basketball skills, cooking skills and game time made my life no longer monotonous in France. You are really talkative and funny guys, which made me so much joy in the journey. I can remember every scene as if it happened yesterday.

Especially this thesis owes a debt to my friends Bin Lei, Yapeng Niu, Xiaohui Gao, Tony Yang, Young Weng (Se Jiong), He Li, Mengqi Wu, Manyu Chen, Shiqun Wu. Your company and support are the most significant motivation for me to finish my PhD for five years.

Finally, I would like to give my heartfelt thanks to my parents, for their endless love and care for me. You always tell me that the world is a more beautiful place than you can suppose, and then you release me into future, the black row of cedars under the dawn in the distance.

Though the chilling winter wind shakes me with solitude and frustration, when you look at me with love, the color of snowy mountains and moonlight paint on me. I love you forever.

Chapter 3 Molecular Dynamics Simulations and Quantitative

Calculation of Photo-responsive Behavior of Wormlike Micelles

Constructed by Gemini Surfactant 12-3-12• 2Br -and Cinnamate Derivatives with different ortho-substituents

Introduction

In last chapter, we studied the photo-responsive behavior of wormlike micelles constructed by Gemini surfactant 12-2-12•2Br -and photo-sensitive molecule trans-OMCA. To further promote the photo-responsive ability of photo-responsive wormlike micelles, it is important to study the wormlike micelles constructed with different photo-sensitive cinnamate molecules.

As we know, the subtle difference in the substituents at the phenyl ring of cinnamates has a significant impact on the velocity of photo-isomerization reaction of cinnamate derivatives and the interaction between cinnamate derivatives and surfactant, which further influence the photoresponsive behavior of the photo-responsive wormlike micelles. Promkatkaew's group [190] used B3LYP geometric optimization and SAC/SAC-CI calculations to study the effects of hydroxyl, nitro, and fluorine substitutions at ortho-, meta-, and para-position of cinnamate derivatives on the velocity photo-isomerization reaction. The results indicated that ortho-and metasubstituted derivatives have longer emission lifetimes than those at the para derivatives.

Although the quantitative calculation method can accurately capture the differences between molecules, the microscopic changes in the morphology of micelles cannot be observed. MD simulations provide a way to visualize these interesting photo-responsive phenomena, to capture how substituents on the phenyl ring affect the packing pattern between photo-sensitive molecule and surfactant and to elucidate the mechanism of morphology transition of surfactant self-assembly. However, most studies on the surfactant self-assembly use coarse-grained (CG) forcefield in order to save simulation time. As a result, the subtle changes of molecular structure before and after UV irradiation have not been well observed and understood. For example, Zheng's group [START_REF] Chen | Multiscale modeling and simulations of responsive polymers[END_REF] used a coarse-grained model to investigate the photo-responsive selfassembly and disassembly process of cis-, trans-AzoC10/alpha-CD mixture at a timescale of ten microseconds. Their results indicate that there is a significant correlation between the size and shape of aggregates and the molecular structure and concentrations of trans-AzoC10. As for the slight change in structure of AzoC10 and the effects of it before and after UV irradiation were not fully investigated. Subsequently, we used umbrella sampling method to calculate potentials of mean force (PMF) versus pulling distance during the process of pulling out a 12-3-12 2+ ion from a preassembled spherical micelle composed of 32 12-3-12 2+ ions and corresponding number of three cinnamates at initial and equilibrium f. ΔPMF represents the energy of pulling a 12-3-12 2+ ion from the initial position to the infinity. Fig. 3.9 displays the variation of PMF for pulling out a 12-3-12 2+ ion from a pre-assembled spherical micelle at initial state (f = 0) and equilibrium state.

As shown in Fig. 3.9, the ΔPMFs decrease for all the cinnamates when the systems are at equilibrium conversion fraction under UV irradiation, implying that it is easier to pull out a 12-3-12 2+ from the spherical micelle after UV irradiation. This can be attributed to the weaker association between 12-3-12 2+ ions in micelle with the photo-isomerization of trans-isomer.

Packing patterns between cinnamate derivatives and 12-3-12 2+

The photo-responsive behavior and the corresponding difference of three wormlike micelle systems has been revealed to a certain extent during our simulation process. However, to fully understand how these trans/cis-isomers affect the stability and the morphology of micelle, the radial distribution functions between the N1 atoms of different 12-3-12 2+ in system (gN1-N1(r) in Fig. 3.10) as well as that between the N1 atom of 12-3-12 2+ and the C3 atom of the cinnamates (gN1-C3(r) in Fig. 3.11) were calculated to explore the packing pattern of species in micelles. As shown in Fig. 3.10, the gN1-N1(r) function curves of containing three cinnamate derivative systems all show three peaks at approximately 0.62, 0.82 and 1.4 nm, indicating the formation of a hexagonal crystalline-like structure [START_REF] Abraham | GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers[END_REF] . With the increase of f, the height of the first peaks (gN1-N1(r)) for the systems decreases gradually, indicating the interaction between surfactants become weaker and weaker and leading to a less orderly arrangement of surfactants after the photo-isomerization of cinnamate. Reasonably, the micelles will rupture when the interaction is weak enough. trans-OHCA is most uneven owing to the presence of hydroxyl. This indicates that trans-OHCA has the strongest electrostatic association with 12-3-12 2+ which can explain why the wormlike micelles containing trans-OHCA have the denser arrangement and the solution has higher viscosity. For cis-isomers, the maximum of the electrostatic potential of cis-isomers is lower (cis-CA (-6.94 eV) < cis-OHCA (-7.02 eV) < cis-OMCA (-7.04 eV)) and more evenly distributed than trans-isomers. Therefore, the weaker electrostatic potential leads to the weaker electrostatic interaction with surfactant and finally causes the formation of loosen micelles.

Then the evener electrostatic distribution allows the aromatic ring to stay on the micelle surface other than insert into the surfactant layer. The significant decrease of the electrostatic potential maximum for OHCA and OMCA after UV irradiation endows the system with a better photoresponsive ability. The introduction of hydroxyl and methoxy groups in the adjacent position of cinnamate enlarge the differences of both electrostatic potential of carboxyl group and the uneven distribution of electrostatic potential before and after the UV irradiation, resulting in the higher sensitivity of the system to UV irradiation.

Hydrophilicity of trans/cis-cinnamates

Subsequently, we explored the solvation free energies of these cinnamate molecules at the M052X/6-31G* level in SMD solvation model and the results are showed in Table 3.5. The

Chapter 4 Molecular Dynamics Simulations and Quantitative

Calculation of Photo-responsive Behavior of Wormlike Micelles

Constructed by Gemini Surfactant 12-3-12• 2Br -and Cinnamte

Derivatives with Different Methoxy Position

Introduction

In the previous chapter, we discussed the influence of different ortho-substituents of cinnamates on the photo-responsive behavior of 12-3-12•2Br -wormlike micelles. The results show that the existence of orth-substituents affects the molar volume, hydrophilicity, electrostatic potential distributions, reaction equilibrium constant of the cis/trans-cinnamates and further affects the photo-responsive behavior of the wormlike micelles. In this chapter, we will further study the effects of the methoxy position (ortho-, meta, para-) in cinnamates on photo-responsive behavior of the wormlike micelle composed of Gemini surfactant 12-3-12•2Br -and trans-methoxycinnamic acid (trans-MCA). MD simulations are used to reproduce the micelle transition after UV irradiation and to characterize the micelle properties.

Quantitative calculations are also used to optimize the molecular structure and obtain the hydrophilicity, molar volume and electrostatic potential distributions of trans/cis-cinnamates.

Furthermore, we select 24 cinnamates with different substituents in ortho-, meta, para-position and compare the photo-sensitive of them.

Materials and methods

Quantitative calculation details and force-field parameters

We optimized the structures of 24 kinds of trans/cis-cinnamates by Gaussian 09 quantum chemistry packages through a hybrid functional B3LYP at the 6-311+g (d, p) level. Among them, the optimized structures of trans/cis-ortho-methoxycinnamic acid (trans/cis-OMCA), trans/cis-meta-methoxycinnamic acid (trans/cis-MMCA) and trans/cis-para-methoxycinnamic acid (trans/cis-PMCA) were used as initial structures in MD simulations. The molar volume, the Gibbs free energy of trans/cis-cinnamate ions, photo-isomerization reaction equilibrium constants and the interaction energies of the representative packing pattern of 12-3- The C7 in the methoxy is the most representative atom characterizing the difference of the packing pattern between three MCA and 12-3-12 2+ . From Fig. 4.6 (b) (e) (h), the gN1-C7(r) curves of three systems are quite different. For trans-OMCA, the gN1-C7(r) curve exhibits a high peak at 0.51 nm before and after the UV irradiation. The lower height of the peak suggests that the C7 in cis-OMCA have a less orderly arrangement with the head group of 12-3-12 2+ after UV irradiation. For trans-MMCA, the peaks of the gN1-C7(r) appear at 0.51 nm and 1.1 nm and the peak at 1.1 nm is higher than that at 0.51 nm, indicating that more C7 atoms are arranged at 1.1 nm away from N1. After UV irradiation, the height of the first peak of the gN1-C7(r) at 0.51 increases sharply, implying that more C7 atoms were transferred to the position 1.1 nm away from N1 in a more orderly arrangement. For trans-PMCA, before the UV irradiation, the first peak is located at a quite far position (1.12 nm) owing to the presence of para-methoxy. After UV irradiation, the peak shifts to left (0.68 nm), indicating a rearrangement of the C7 close to the head group of surfactants.

The gN1-C10(r) of the MCA reflects the strength of the electrostatic interaction because N1 and C10 are the charge center of surfactant and cinnamates, respectively. It can be seen from micelles after UV illumination, while trans-MMCA and trans-PMCA are converted into shorter wormlike micelles. We can also conclude that the presence of meta-and para-methoxy groups will reverse the difference in the molar volume of cinnamate derivatives before and after UV irradiation, leading to a decrease in photo-responsive ability of wormlike micelle.

Electrostatic potential distributions of three cinnamates

To obtain more microscopic and precise molecular information, the electrostatic potential distributions (eV) were calculated and shown in Fig. 4.11. It can be seen from Fig. 4.11, the negative electrostatic potential of trans/cis-cinnamate ions are mainly concentrated on the carboxy group. The maximums of negative electrostatic potential of trans-cinnamates are larger than those of cis-cinnamates and the electrostatic potential distributions of cis-cinnamates are evener. These evidences indicate that trans-cinnamates have a stronger electrostatic interaction with surfactants when forming micelle. After UV irradiation, the electrostatic potential increases. These samples will be referred to as "shear thinning".

The response of the solutions to shear can be explained by the structure of the micelles. In pure CTAB solution and at low low NaSal concentrations, the surfactants self-assemble into small cylindrical micelles [START_REF] Clausen | Viscoelastic micellar solutions: Microscopy and rheology[END_REF][START_REF] Cates | Rheology of giant micelles[END_REF] . As the concentration of NaSal increases to 8 and 9 mM, the viscosity of the solution increases, as the length of the micelles increases. This is because as the concentration of NaSal increases, the Sal -ions incorporate into the surfactant layer. The observed shear-thickening phenomenon is induced by the formation of shear-induced structures, the origin of which is not yet fully understood [START_REF] Padding | Review of multi-scale particulate simulation of the rheology of wormlike micellar fluids[END_REF] .

When the concentration of NaSal reaches 10 mM, the length of the wormlike micelles is large, they begin to entangle. As the shear rate increases, above a critical value the solutions become shear thinning and the viscosity starts to decay as 𝛾̇- 1 This behaviour has been attributed to shear banding [START_REF] Padding | Review of multi-scale particulate simulation of the rheology of wormlike micellar fluids[END_REF][START_REF] Richardson | The sedimentation of a suspension of uniform spheres under conditions of viscous flow[END_REF] .

The frequency dependence of the shear moduli G′ and G″ are shown in Fig. 5.2. The storage modulus G′ remains smaller than the loss modulus G″ up to 10 mM NaSal, meaning that the solutions are predominantly viscous. At larger salt concentration, G′ become slightly larger than G″ above frequencies of the order of 1 Hz. Even for the largest salt concentration, the storage modulus is very small (G′ less than about 1 Pa).

Chapter 6 Conclusions

This thesis is focused on the photo-responsive behavior of a series of wormlike micelles constructed by Gemini surfactant and different cinnamates and on the applications (bubble rise) of wormlike micelles.

(1) The photo-responsive behavior of wormlike micelles constructed by 12-2-12• 2Br -and trans-OMCA and the mechanism of its photo-responsiveness are investigated. Owing to the electrostatic interaction, trans-OMCA associates strongly with 12-2-12• 2Br -, leading to the formation of wormlike micelles. After UV irradiation, trans-OMCA photoisomerizes into cis-OMCA and then wormlike micelles break to rod-like micelles and finally to spherical micelles.

Three primary factors (geometry, hydrophilicity and energy) affecting the micelle transition are unraveled systematically. The larger steric hindrance of cis-OMCA weakens π-cation interaction and electrostatic interaction after UV irradiation. The stronger hydrophilicity of cis-OMCA leads to the moving of cis-OMCA from micelle interior to solution. Moreover, cis-OMCA has a weaker interaction with the 12-2-12• 2Br -than trans-OMCA after UV irradiation.

All these factors induce the breakage and repacking of wormlike micelles.

( (5-1)