List of Tables

2 Illustration of confined TBA (red)/TOL(cyan) mixture into the cylindrical nanopore obtained from the force field developed by Brodka and Zerda [42]. For clarity, silica framework is removed. This Figure shows that TBA (red colour) and TOL (cyan colour) molecules sample as well the surface as centre of pore. . . . . . . . 4.3 a) Profiles of radial density of centre of mass of TOL and TBA confined into the silica nanopore with a TBA/TOL molar fraction composition 56/44% such as the silica framework is described with the model of Brodka and Zerda [42]. Introduction "The discovery of the Hydrogen Bond could have won someone the noble prize, but it didn't." [1] 1.1 Literature review Nanotechnologies and nanosciences have been accompanied by new challenge requiring the revision of condensed matter physics [2][3][4][5][6]. There are enormous scale differences in our universe, and at different scales, different forces dominate and different mechanisms better explain phenomena.

At the nanometric scale, the physical properties of confined liquids such as the dielectric permittivity [7,8], the surface tension [9,10], and the melting point [11] drastically differ from the bulk counterpart. These behavioral changes occur when the length scale of the confined liquid is similar to the range of their molecular interactions. As a result, these systems appeared to have a strong surface-to-volume ratio. That is an important point because it influences how well a components will interact with other materials around it. Under confinement, the interactions of liquid with the confining walls clearly begin to have important effects and can impact the structure, dynamics, and thermodynamics of the liquids in comparison with the bulk state [12][13][14].

Among the so-studied fluids, the hydrophilic liquids (water, alcohol, amine, etc) are important

given their manipulation at the nanoscale such as nanofluidic [15]. Additionally, the impact of the confinement on the behavior of fluids is important in diverse phenomena, from the creation of micro-emulsions to drug delivery [16][17][18], to the assembly of proteins into the functional complexes, and to engineering processes [19][20][21].

Recently, a series of studies have been conducted to clarify the properties of fluids in nanometric confinement [22][23][24][25][26][27][28]. Gubbins et al. have essentially focused on study the adsorption of different gas [29,30], water [31][32][33] and other mixtures [34,35] systems confined to different nanopores using molecular dynamics. Other studies have also been conducted to understand the behaviour of confined fluids by characterizing the fluid-fluid and fluid-wall interaction [27,[36][37][38].

Interestingly, they were able to demonstrate that the change in interaction in a given system can induce several significant changes in the behaviour of confined fluids. This is explained in particular by the fact that alcohol molecules composed of a hydrophobic part (non-polar part and otherwise it is the alkyl carbon chain) and a hydrophilic part (polar part or hydroxyl group) can make fluid-fluid and fluid-wall interactions increasingly anisotropic in a confined medium. While

Zhang et al [39]., by studying the transport of water with methanol in hydrophilic and hydrophobic nanopores, using molecular dynamics, have shown that methanol diffuses more rapidly than water in hydrophobic nanopores, from which a phase separation has been proposed for this type of mixture (alcohol/water). Kaneko and his group are interested in studying the structure of the different alcohols included (ethanol, methanol and 1-propanol) confined in carbon nanopores by X-ray diffraction [40][41][42], they have shown that all alcohol molecules can form ordered structures in the nanopore, except ethanol which has a preferential orientation in this nanopore. In addition to these studies, Kumar et al. highlighted that water can freeze at 105-151 °C and 87-117 °C when confined in 1.05 nm and 1.06 nm single-walled nanotubes, respectively [11]. Morineau et al.

also studied alcohol molecules confined in silica nanopores by X-ray diffraction [43], their results

show that the creation of a hydrogen bonding interaction between the methanol and the confined surface affects the local structure of the methanol at the interface. While Ghoufi et al. were able to show a super-permittivity of the water confined in carbon nanotubes, they also highlighted remarkable dielectric properties of the confined electrolyte solutions [7,8]. Muthulakshmi and coworkers reported an experimental evidence of a partial phase separation of an ethanol-water mixture confined in mesoporous silica using positron annihilation lifetime spectroscopy. They showed that a small fraction of the ethanol molecules seemed to be anchored at the silica surface [44]. A similar results was also established by Guo et al. who have studied confinement of Chapter 1 Ilham Essafri 13 Microstructure of binary mixtures in bulk and nanoconfined phases an ethanol-water mixture between two planar silica walls [45]. A partial and local separation between water and ethanol close to the silica surface were thus evidenced [45]. In the same time Schmitz et al. have exhibited that the glycol-water mixture could undergo an interfacial separation [46]. This phenomenon was also numerically observed by You et al. who exhibited a local demixing of binary hard-core Yukawa mixtures in a slitlike pore [47]. More recently, Krycka et al. displayed a separation between two confined apolar liquids [48]. Whereas these works only suggest a partial separation of two hydrogen bonds forming liquids or two apolar liquids near the solid surface, More recently, Hamid et al. have provided a direct experimental structural evidence of the microphase separation of macroscopically miscible liquids consisting of hydrogen bonds forming liquid and an apolar one. Indeed, the structure of a mixture comprising toluene (TOL) and tertbutanol (TBA) molecules confined in a cylindrical silica nanopore (MCM-41) of radius 24 Å was explored by neutron scattering and compared with the miscible bulk one [49]. Using a core-shell (CS) model, the authors established, for the first time, a molecular-scale phase-separated tubular structure with the TBA molecules forming a layer at the pore surface (shell), surrounding a TOLrich phase at the center of the pore (core). This observation was later extended down to low temperature in the glassy states and to the larger pores sizes of SBA-15 [50,51]. A consistent picture, showing the highly selective segregation of polar molecules at the pore surface, was deduced from binary gas adsorption experiments [52]. Up to now, the physical mechanism ruling this phase separation at the nanometric scale stays unknown. In this context, we suggest that this peculiar structure is due to the hydrogen bond network. In order to better understand this behavior at the nanoscale. It is essential to provide a good description of the hydrogen bond network under these conditions. This work aims characterizing the connection between the hydrogen bonding (HB) network and phase separations at the nanoscale. On the other hand, these properties imply especially to study how the HB network evolves under nanoconfinement, its interaction with the confining surface and its impact on the physical properties.

14 Chapter 1 Ilham Essafri

Motivation and aim

The objective of this thesis is to capture and understand the structural behavior of the HB network at the nanoscale. We would also attempt to examine whether the hydrogen bonding network initially observed in bulk phase will survive in nanometric confinement or will change. Among HB forming liquids, alcohols are considered as good models to investigate the characteristics of the HB structure. Indeed, alcohols are capable of forming 1D, 2D, and 3D networks according to their hydrophobicity (alcohol tertiary, secondary and primary). In this work, Alcohols such as methanol, ethanol, propanol, butanol, and pentanol will be considered as well as their mixtures with other molecules toluene, and cyclohexane. The objective here is to investigate the dilution of HB network by using a non HB former liquid and the relation between two hydrogen bonding networks. For the cluster type structure, the tert-butanol will be considered. Finally, our goal will be to investigate the confinement through hydrophilic (silica nanopore [53,54] and water nanotube) and hydrophobic nanopore as (carbon nanotube [55]). For that, molecular dynamics simulations of alcohols are performed to include linear, branched and tertiary alcohols within cylindrical nanopores (hydrophilic and hydrophobic pores) with the purpose of understanding how the surface effect can impact the hydrogen-bonding network.

As stated previously, in this work molecular dynamics simulation is used. This choice is based on the issue addressed in this work. This involves studying the dynamics and structure of binary liquids confined to the nanoscale. Since our study on confined binary liquids involves the use of models that can contain several thousand of atoms with dynamics that must be monitored for several hundred picoseconds (or even several nanoseconds), we chose an approach using classical mechanics. The selection of the numerical simulation method is based on both temporal and spatial scales. The quantum computation methods (ab initio, semi-empirical, DFT) concern both the atomic radius length-scales and the femtosecond time scale. These quantum techniques take an official interest in the field of chemistry such as modeling the making and/or breaking of chemical bonds. However, molecular dynamic methods handling interactions at molecular level combine space scales in the range of nanometers with time scales ranging from picoseconds to nanoseconds. Indeed, molecular dynamics refers to the physical motion of a collection of atoms or molecules interacting with each other. So depending on the physical problem, the length-scale

Chapter 1 Ilham Essafri

Microstructure of binary mixtures in bulk and nanoconfined phases and the time scale we could choose our suitable simulation tool.

Structure of the thesis

Our work will be presented in this manuscript by five chapters, the first chapter discuss the state of the art of the confined liquids and our objectives related to that. The second chapter focuses on the methods used. The third chapter aims to study binary liquids in the bulk phase. Chapter four focused on the study of liquids in confined phases. As a final conclusion, the thesis presents the scope of the results obtained and their consequences in the scientific field of nanopores, and, more generally, materials at the nanometric scale.

16

Chapter 1 Ilham Essafri

Introduction

The Molecular Dynamics (MD) simulation is a powerful tool for the understanding of physical phenomena at the microscopic level. It allows us the study of the interactions between two molecules and to an ensemble of molecules representing a liquid in terms of microscopic (or molecular) details. This computational method is among the strongest tool existing for exploring structural and dynamical properties of complex systems and condensed phases. The concept of MD method is to simulate the motion of a set of particles, atoms or molecules over time by numerically integrating classical equation of motion. Although, we might ask why do we use classical mechanics rather than quantum mechanics to describe the motion of the atoms? The Schrödinger equation is so complex that it can only be solved analytically for a few simple cases. Indeed, a direct numerical solution on computers is limited to systems that have small numbers of atoms due to the large size of the space in which the Schrödinger equation is placed. Fortunately, Born-Oppenheimer approximation are used to simplify the problem. This approximation are based on the fact that the mass of electrons is much smaller than the mass of nuclei. The effect of electrons on the interaction between nuclei is then described by an effective potential.

As another simplification, the nuclei are moved according to Newton's classical equations using either effective potentials resulting from quantum mechanics calculations, which include electron effects, known as ab-initio molecular dynamics simulation or empirical potentials that have been adjusted to the results of quantum mechanics calculations or experimental results defined as classical molecular dynamics simulations.

These numerical simulation methods for studying physical properties were developed in the Almost at the same period, Alder and Wainwright conducted the first technique that could provided the dynamic properties, referred as MD simulations in 1957 [4], they discussed the collision of an assembly of hard spheres. Interestingly, they highlighted a solid-phase transition that was not observed by the so-called MC simulations. MD simulation method is based on a fundamental dynamic equation (Newton's Law) to simulate the temporal evolution of a molecular system. It was in 1964 that Rahman and al. solved the equation of motion for a set of Lennard Jones particles [5]. A series of research presented in Figure 2.1 followed these numerical studies, using numerical and computational methods to comprehend distinct phenomena related to microscopic scale [6][7][8][9][10][11][12][13][14][15][16][17].

Statistical Mechanics

As molecular dynamics are used mainly for simulating behaviors at molecular or atomic level, the macroscopic physical property needs statistical mechanics to be used. Thermodynamics and statistical mechanics enable us to create a connection between the experimental macroscopic observations and the microscopic behavior of the simulated system. Both of these are strongly connected and we have to rely on both in order to perform and obtain informations from MD Chapter 2 Ilham Essafri simulations. MD requires, as an input, a description of the interparticle interactions to provide a picture of a system's microscopic behavior from the laws of classical mechanics. In order to well introduce MD simulation, we need to detail some concepts that are essential to understand the statistical physics that provides a basis for associating the microscopic properties of molecules with the macroscopic ones. Thus, it describes physical properties as the result of the statistical approach at the microscopic level. Herein we focus on classical liquids, meaning that the behavior of a liquid state can be described using laws of classical mechanics.

Classical description of liquids

In Classical mechanics the dynamical state of a system composed of N atoms at any particular time is determined completely by the 3N coordinates r N = {r 1 ,...,r N }, where r N represents the 3N Cartesian components of position, and 3N momenta of the atoms p N = {p 1 ,...,p N } at the same time, with p N = mv N and v N represents the 3N Cartesian components of atomic velocity.

These 6N coordinates (3N positions and 3N momenta) constitute the phase space and each phase space is connected to a microstate. We define a state of a system by a set of positions and momenta of N atoms by (r 3N ,p 3N ), which is called a phase space denoted as = (r 3N , p 3N ).

So, the time evolution of a system in classical description is governed by Newton's equations expressed as :

N X i=1 F i = m i a i = dp i dt (2.1)
with F i is the force acting on atom i, m i and a i is the mass and the acceleration of atom i respectively and t is the time. The equation (2.1) can be rewritten in cartesian coordinates as:

N X i=1 F ix (x, y, z) = m i d 2 x i (t) dt 2 ; N X i=1 F iy (x, y, z) = m i d 2 y i (t) dt 2 ; N X i=1 F iz (x, y, z) = m i d 2 z i (t) dt 2 (2.2)
where (F ix , F iy , F iz ) are the three component of the force F (x, y, z) acting on atom i. From Equation (2.2), the x i (t), y i (t) and z i (t) can be derived. The atom's trajectory is calculated by this three-dimensional path.

Ergodic hypothesis: time average and ensemble average

By using Newton's equations coupled with the forces involved, we can deduce the whole history and predict the future behavior of the atoms. Then, a trajectory obtained by molecular dynamics provides such a set of configurations. Each configuration is defined by phase space trajectory as [r N (t), p N (t)]. Therefore, a measurement of a physical quantity A by simulation is simply obtained as an arithmetic average of the various instantaneous values assumed by that quantity during the MD run. For each point of this trajectory, it is possible to calculate the value of A(t) as well as the experimentally measurable quantity A obs that can be regarded as the time average of A(t) expressed as:

A obs =< A(t) >= lim ⌧ !1 1 ⌧ Z ⌧ 0 A( (t))dt (2.3)
with ⌧ is the observation time of the measurement and the brackets indicate an average value.

The idea here is that MD simulation methods provide microscopic information in terms of 3N positions and 3N momenta of atoms as a function of time. While the statistical mechanics translate these 6N coordinates into macroscopic properties by using ergodic hypothesis and laws of thermodynamics. Interestingly, statistical mechanics calculate all macroscopic observable as averages over phase trajectories or as averages over an ensemble of systems. As a result, a macroscopic quantity A can be determined by averaging its values over a set of micro-state characteristics.

Statistical mechanics makes it possible to replace a system that evolves over time with a representative set of simultaneous replicas of this system prepared in the same microscopic state.

If these replicas show different values from the quantity to be measured A obs at a given time t, their average is called ensemble average denoted as < A > ensemble " and given by:

< A > ensemble = 1 Z Z A(r, p) exp( E(r, p))drdp (2.4)
with Z is the partition function which is a measure of the volume occupied by the system in the phase space. Basically, it gave us an information on how many microstates are accessible to our system in a given ensemble. This concept will be details later. = 1/kT is the inverse temperature (k is the Boltzmann constant) and (r,p) represents the coordinates and the momenta of Chapter 2 Ilham Essafri atoms in the microstate. E is the energy of the microstate. Recall that a microscopic state is a point in the phase space. The equation (2.5) leads to the average value measured over time for a good number of replicas. This is the ergodic hypothesis, one of the fundamental axioms of statistical mechanics, which translates into the relationship (2.5) by considering an infinite number of configurations and an infinite sampling time [18,19].

A obs =< A(t) >=< A > ensemble (2.5)

Thermodynamic ensembles

In molecular dynamics simulation, various thermodynamic ensembles can be used. These ensembles are characterized by the thermodynamic parameters that are imposed: the number of particles (N), the volume (V), the total energy of the system (E), the temperature (T), the pressure (P), etc. In this section, we present the two NVT and NpT ensembles explored in this thesis.

Canonical ensemble: NVT

The canonical ensemble is the statistical ensemble where the number of particles N, the volume V and the temperature T are fixed. NVT ensemble represents a closed system with no exchange of matter or work with the external medium and in thermal contact with an energy reservoir.

The partition function of the canonical ensemble is expressed:

Q(N, V, T ) = X i: exp( E i ) (2.6)
where the sum is expressed on all possible states i of the system, = 1/kT is the inverse temperature (k is the Boltzmann constant) and E i is the eneregy of state i.

Within the classical limit of statistical mechanics, any discrete summation on the accessible states is replaced by an integral on the phase space:

X i ) 1 h 3 Z d (2.7) 28 Chapter 2 Ilham Essafri
Microstructure of binary mixtures in bulk and nanoconfined phases with d = dxdydzdp x dp y dp z is the infinitesimal volume in the phase space.

In the classical limit this partition function for indistinguishable particles is:

Q(N, V, T ) ⌘ 1 N !h 3N Z Z dr 3N dp 3N exp[ H (r 3N , p 3N )] (2.8)
with H (r 3N ,p 3N ) represents the Hamiltonian that characterizes these N particles, which is expressed in terms of the total potential energy U and the total kinetic energy K (H (r, p) =

K(p) + U (r)).
Following the definition of the ensemble average, a physical quantity A(r 3N ,p 3N ) is determined according to the following Eq. (2.9) given by:

< A > NV T ⌘ R R dr 3N dp 3N exp[ H (r 3N , p 3N )]A(r 3N , p 3N ) R R dr 3N dp 3N exp[ H (r 3N , p 3N )]
(2.9)

Isothermal-isobaric ensemble: NpT

This ensemble is well suited for experimental observations based on normal laboratory conditions.

In the NpT ensemble, the quantities N, P and T are conserved during the simulation. The volume varies isotropically (same variation in all directions of space) or anisotropically, and in this case, it is possible to choose the direction on which to apply the volume variation. The volume is therefore fluctuating. The volume should instead add to the list of phase-space microscopic quantities. In other words, the phase space of this system in this ensemble is specified by < V, r 3N , p 3N >. Thus, the isothermal-isobaric partition function in the semi-classical form is :

Q NP T = 1 N !h 3N V 0 Z dV Z dr 3N dp 3N exp( [H(r 3N , p 3N ; V ) + P V ]) (2.10)
while V 0 is the unit volume.

Chapter 2 Ilham Essafri

Molecular dynamics simulation method

Definition

Molecular dynamics is a numerical simulation technique used to model the movement of a system of particles (nuclei of atoms, electrons, ions) over time in a particular or specific environment (temperature, pressure). In Newtonian mechanics (section 2.3.2), the particle (assimilated to a point mass) is subjected to a force (derived from an energy potential) that produces an acceleration on it [20,21]. The equations are numerically integrated using an infinitesimal time step (section 2.3.3), guaranteeing the conservation of the system's energy, typically from one to two femtoseconds. The simulation will then consist in calculating at each moment the position, velocity and acceleration of each of the particles, as well as the forces between particles, using the results obtained at the previous time. It should be noted that the size and time-scale accessible by molecular dynamics are in the order of a few tens of nanometers, and a few picoseconds.

Molecular dynamics applies both to the structural study of molecules and to large interacting systems. However, since computing capacities are limited, thus the number of particles in a simulation is also limited. For example, to simulate an infinite material in one, two or three dimensions, the particles will be placed in a periodic space: this is referred as a simulation box (section 2.3.4). When calculating the forces, this periodicity of the space must be taken into account. In practice, a distinction will be made in the interaction strength (section 2.3.5)

between short-range terms, which will not be affected by periodicity, i.e. only the closest particles will be taken into account, and a long-range term, which will need to take this into account. The long-range term is generally of the Coulomb type and will be calculated by the Ewald sum.

Equation of motion

As previously defined the MD method is a computer instrument that provides access to the time-dependent properties of a physical system. For this, it considers the atoms as a classical moving masses and has a velocity resulting from the forces applied on each atom. In Classical MD simulations atoms move according to the Newtonian equations of motion given by

F i = m i ãi (t) = m i dv i (t) dt = m i d 2 r i (t) dt 2 ; F i = @ @r i U (2.11) 30 Chapter 2 Ilham Essafri
with F i is the force acting on atom i, t is the time, v i , m i and r i is the velocity, the mass and the position of atom i and U is the potential energy.

Integration algorithm

The solution of the differential equation (2.11) describing the motion of each of the N atoms of a system requires, because of its complexity, the use of numerical resolution methods.The most commonly used algorithms in molecular dynamics are the Beeman algorithm, the Gear method, the Leapfrog algorithm and finally the Verlet algorithm presented in this thesis.

Velocity verlet algorithm: The integration algorithms are based on finite difference methods.

the concept of this method is to discretize the first or second order differential equations. Consequently, an algorithm that requires minimal computational effort is considered a good integrator.

However, it also needs to be stable and accurate as a function of time and to respect the physical invariant such as the energy and the total momentum of the system. In general, a good integrator is a compromise between accuracy and computational time. There are also different integration algorithms (Verlet simple [6], Verlet Leap-frog [22], Verlet velocity [23] , etc...) that can be used and which differ in the way Taylor's development is implemented. To this argument, we used the Verlet-velocity algorithm, which is presented below.

We suppose that our system of interests is composed of N atoms, each atom i is distinguished in space by its position ri , and we note r = {r 1 , r2 , ... rN } the space vector that conveys all the positions of the atoms. Similarly, ṽ = { ṽ1 , ṽ2 , ... ṽN } is the space vector that contains all the velocities. We note Fi the total force exerted on the atom i ( previously noted (F i )).

2m i t 2 + Fi (t + t 2m i t 2 + O( t 3 ) (2.14)
That is :

ṽi (t + t) = ṽi (t) + F i (t) + Fi (t + t) 2m i t + O( t 3 ) (2.15)
The equations (2.12) and (2.15) represent the Verlet Velocity algorithm. This algorithm is simple to use, accurate and stable, which explains its success in molecular dynamics simulation codes. However, it is also slightly more expensive than other algorithms, since the forces have to be calculated at t + t.

Periodic boundary conditions

The simulation box is in general a closed space. During the integration of motion equation the atoms close to the coin eventually leave outside. We must thus impose constraints on the surfaces to prevent this loss, and use a method to treat the leaving atoms, by reintegrating them into the box. As illustrated in Figure 2.2 the periodic boundary conditions (PBC ) are applied [24] to avoid these boundary effects. That consists in replicating the finite set of atoms distributed according to the three dimensions. Indeed, the aim of the periodic boundary is to generate a surfaceless system.

As shown in Figure2.2, when an atom or molecule moves in the central box, its images move in the same way in the replicated boxes. The number of atoms in the central box is then conserved.

There is no need to store the coordinates of all the images, only those of the atoms in the central box (that corresponds to the Cell 1 in Fig. 2.2). A given atom interacts with all other atoms in this infinite periodic system. This means that with the periodic boundary conditions the surface effect are removed and and infinite volume is created to represent a macroscopic system. In the 32 Chapter 2 Ilham Essafri case of an atom i at the ri position, there is a set of image atoms at the (r i +nL) positions, ñ is arbitrary vector of three numbers. Given the PBC the potential energy can be written as

U (r 1 , ...., rn ) = X i<j U (r ij ) + X n X i<j U (|r i rj + ñL|) (2.16)
As the system is pseudo-infinite, an effect is generated that requires to make approximations to calculate the potential pairwise interactions. To do so, a convention about how distances are calculated is made.

Minimum image convention

Through the so-called "minimal image" approximation, each atom i of the central cell interacts with the nearest image of all the other atoms j. The distance between particle i at ri and particle j at rj is rij =min(|r i -r j +ñL|) on all ñ. The circled atom in the primary cell (Cell 1 in Fig. 2.2)

interacts only with each of the other N-1 particles in the secondary cell or their closest images such that the interactions are limited to the cutoff radius, equation(2.17), where L is the box Chapter 2 Ilham Essafri length.

r c < L 2 (2.17)
It would be more realistic to include the interaction of each particle with all its image. Since we assumed that there is an infinite system, we need to choose a cut-off to perform calculations, which introduces truncation in potential, short range interaction (LJ ) and long range electrostatic interaction. A procedure to treat the electrostatic interaction have been established by EWALD [25] that divide the problem into two parts.

Molecular interactions

The first step of a molecular dynamics simulation is to determine how to simulate a physical system composed of N molecules. Knowing that each molecule of this system is made of atoms, and each atom interacts with its neighbor. Then, the atoms close to each other involve electrons, and this leads to an interaction. The main point here is to discover how this interaction between atoms can be modeled and simulated.

As mentioned previously (Eq. (2.11)), forces are derived as the gradients of the potential in terms of atomic displacements. The aim of molecular dynamics simulation is to choose the interaction potential: a function U(r 1 ,...r N ) of the atomic positions, representing the potential energy of the system. This function is generally constructed from the relative positions of atoms relative to each other. The most basic choice for U is to write it as a sum of interactions in pairs. This function characterizes the most relevant ingredient that contains physics in MD simulation.

The potential energy U basically has two contributions: intramolecular and intermolecular interactions. The "intramolecular" component represents the flexibility of the molecules and the "intermolecular" component describes the interactions between "unbound" atoms, i.e the atoms are separated by more than three bonds; that can be divided in two terms taking into account of the long and short range interactions, i.e Van der Waals and electrostatic interactions respectively.

Chapter 2 Ilham Essafri

Microstructure of binary mixtures in bulk and nanoconfined phases

Non-bonded interactions

The intermolecular interactions are expressed as a sum of Lennard-Jones and Coulomb potentials:

U ij (r) = X ia,jb 4✏ ia,jb " ✓ ia,jb)
r ia,jb

◆ 12 ✓ ia,jb) r ia,jb ◆ 6 # + X ia,jb 1 4⇡✏ 0 q ia q jb r ia,jb (2.18)
Thus the potential between two molecules i and j is defined as the sum of interactions between the sites a and b, on molecules i and j, respectively, with partial charges q ia and q jb , and the diameter Lennard-Jones ia,jb , energy ✏ ia,jb and relative distances r ia,jb .

a) The Lennard-Jones potential.

The first term of Eq. (2.18) is the Lennard-Jones potential (LJ), which characterizes van der Waals interactions and its behavior is presented in Figure 2.3. This potential represents the interaction energy between two non-bonded atoms according to their separation distance. The LJ potential has an attractive part in term of ( 1 r ) 6 at long distances and strong repulsion in term of ( 1 r ) 12 at short distances. The Lennard-Jones intermolecular parameters were derived using the Lorentz-Berthelot rules for mixing ab = p ✏ aa ✏ bb and ab = ( aa + bb )/2. The potential of Lennard-Jones (LJ) includes the attractive interaction of Van der Waals, which is prevalent at Chapter 2 Ilham Essafri long distances, and the electronic repulsion of Pauli, which is predominant at short distances, and which prevents the mutual interpenetration of electronic clouds of two atoms.

As illustrated in Figure 2.2 beyond r c the LJ potential is close to zero and the potential can be then truncated such that U (r c )=0. With the use of r c in the case of Lennard-Jones potential (LJ ), this truncation introduces a break in the calculation of the potential between two atoms, since it has a finite value for r ia,jb  r c and is zero for r ia,jb > r c . To avoid this problem, the potential is often shifted in order to vanish at the cut-off radius:

U (r) = 8 > < > : U LJ (r) U LJ (r c ) if r  r c 0 if r > r c (2.19)
b) Electrostatic interactions from the Ewald sum.

Unlike short Van der Waals interactions, the long range electrostatic interaction cannot be ignored at long distances. We suppose that our system is composed of N atoms placed in a cubic box. These atoms are subjected to periodic boundary conditions as shown previously. This means that we need to consider all interactions of the atoms with its periodic images. Ewald formalism is addressed in this calculation which it was developed by Ewald [25]. It is based on the following principle: if we consider a molecule placed in a central box, it will not only interact with neighbouring molecules but also with all its images located in the periodically reproduced cells. To calculate the position of an image box, a simple translation of a vector whose components represent an integer multiple of the dimensions of the central box can be used. This formalism is applied to the calculation of the interactions of the Colombians forces, and is the most used for the simulation of molecular dynamics.

The coulomb interaction energy of N atoms at locations r 1 , r 2 , r 3 , ..., r N and possessing point charges q 1 , q 2 , q 3 , ..q N respectively, is written as,

U elec = 1 4⇡✏ 0 X i,j q i q j |r ij | (2.20)
where r ij = r j r i , ✏ 0 is vacuum permittivity and the sum is over all atomic pairs (i, j). These atoms are subjected to periodic boundary conditions (P BC) as shown previously, which are 36 Chapter 2 Ilham Essafri

Microstructure of binary mixtures in bulk and nanoconfined phases described by three repeat vectors L x , L y and L z (forming a box). To simplify our notation, we will write L x , L y and L z , as L, where L represents the characteristic length of the simulation box. This means that whenever there is an atom q i at location r i , there are also atoms with charge q i at r i + n x L + n y L + n z L, where n x , n y , n z are arbitrary integers. In this case, we can

choose L = |L x | = |L y | = |L z |
and vectors n form a simple cubic lattice (n x , n y , n z ).

Then the total coulomb interaction energy for these atoms under PBC has to include the interactions between periodic images,

U elec = 1 4⇡✏ 0 X n X i,j q i q j |r ij + nL| (2.21)
The sum over all pairs can be rewritten into sums over all atoms, with a factor 1 2 to cancel the double-counting.

U elec = 1 4⇡✏ 0 1 2 X n 0 N X i=1 N X j=1 q i q j | rij + nL| (2.22)
where the 0 symbol is introduced to exclude the term j = i, if and only if n = 0. The infinite sum in equation 2.22 not only converges very slowly but also is conditionally convergent meaning that the result depends on the order of the summation. For this reason, there are several ways of proceeding in numerical simulation with truncation methods (spherical truncation, generalized reaction field, Wolf's sum, etc.), which in some cases provide simulation artifacts, or, in a more rigorous way, the Ewald's sum. In this thesis, we use the latter method, which is the most commonly used in numerical simulation research.

As shown in Fig. 2.4 the Ewald's sum transforms long-range interactions by summing the interaction energies of each charge of the first cell with all the periodic images and to improve the convergence by converting the function 1 r into two series, each converging more quickly according to the following principle:

1 r = (r) r + 1 (r) r (2.23)
So the aim is to define a function (r) that is in line with i) the rapid variations from 1 to Chapter 2 Ilham Essafri small r and ii) the long slow decay at distant r. In practical terms, this is expressed in the Ewald sum as a series in real space to consider the interactions inside and near the cell-unity and a series in reciprocal space for interactions with the other cells. The approach of the Ewald summation method is based on the expression (2.21). This equation is rewritten by introducing around each charge center a of each molecule i a charge distribution term ( diffusive charge) of the same quantity as the point charge q i and of the opposite sign. In this way, by adding the total cloud charge, the q i charge is completely nullified (Figure 2.4). As a result, the most commonly used form and, at the same time, the one originally used by Ewald formalism is a Gaussian distribution:

⇢ Gauss (r) = z ia ↵ 3 ⇡ 3 2 exp( ↵ 2 r 2 ) (2.24)
where ↵ is the gaussian distribution width. ↵ is chosen according to the system under study. To filter the interaction between neighbouring charges, this distribution acts as an ionic atmosphere.

The screened interactions are now short-ranged, and the total screened potential is calculated by summing over all the molecules in the central cube and all their images in the real space lattice of image boxes. For our case we followed the empirical relationship given in the DL_POLY manual [27] which is: ↵=3.2/(l min /2) with l min the length of the smallest side of the considered cubic box.

The electrostatic potential created by the site a of molecule i is the result of the non-screen q i charge. Eventually, the total electrostatic potential form in the Ewald's sum is expressed as ,

38

Chapter 2 Ilham Essafri

U T otal Elec = U S + U L U self = 1 4⇡✏ 0 1 2 X n 0 N X i=1 N X j=1 q i q j |r i r j + nL| erf c ✓ |r i r j + nL| p 2 ◆ + 1 2✏ 0 X k6 =0 e 2 k 2 /2 k 2 |S(k)| 2 1 4⇡✏ 0 1 p 2⇡ N X i=1 q 2 i (2.25)
where erfc(x) is a complementary error function (erfc

(x)=[2/ p ⇡] R exp[ t 2
]dt) that falls to zero with an increase of x. This sum physically translates into:

1. Replicating the atomic charges of the studied system in the three dimensions of the real space.

2. Considering each point charge of the real space as a Gaussian distribution of charges of opposite sign from the point charge (Figure 2.5, "Sum in the real space").

3. The representation of the Gaussian distribution of charges of real space in reciprocal space.

This last distribution of the opposite sign therefore serves to cancel out the Gaussian distributions (Figure 2.5, "Sum in reciprocal space").

In this way, as shown in Figure 2.5, the sum of the charges is converted into a sum of interactions between charges and Gaussian distributions.

Bonded interactions

Intramolecular interactions are described by several potentials, representing interactions between atoms linked by covalent bonds. The mathematical function forms used to describe these interactions are given by,

U T otal = X bonds K r (r r 0 ) 2 + X angles K ✓ (✓ ✓ 0 ) 2 + X torsion ( V 1 2 [1 + cos( )] + V 2 2 [1 cos(2 )] + V 3 2 [1 + cos(3 )] + V 4 2 [1 cos(4 )]) (2.26)
In this potential, these two atoms are coupled by the force that derives from a harmonic potential.

As depicted in Figure 2.6, the harmonic potential is provided by the first term in Equation (2.26).

In this expression, r is the interatomic distance between two atoms (Å), r 0 is is the equilibrium bond length (Å) and K r is the strength of the bonds (kcal/mol 2 ). The second term describes the flexibility of the considered triplet of atoms, with ✓ is the valence angle between the three atoms (in degrees), ✓ 0 is the equilibrium angle (in degrees) and K ✓ s the strength of valence angle (kcal/mol). The last term is the dihedral deformation energy term which refers to three bonds and therefore four consecutive atoms. In this equation, V 1 , V 2 , V 3 and V 4 are Fourrier constants and (in degrees) is the dihedral angle between the planes constructed by the four atoms.

40

Chapter 2 Ilham Essafri

Molecular parameters

A force field is a set of empirical parameters that describes the interactions between each atom.

Accuracy of computer simulations depends critically on these models parameters, which are mainly the force fields between the components. These force fields are expressed in terms of bond lengths, angles, torsion angles, Lennard-Jones potential, and partial atomic charges. These parameters are derived from spectroscopic and diffraction experiments, quantum chemical calculations or empirical parameterizations used to reproduce liquid properties, such as density.

The validity of a force field consists in reproducing other quantities that have not been used in the parameter adjustment process, for example, the thermodynamic properties of the mixing systems, the diffusion constants or the dynamic properties such as relaxation times. Currently, the most popular force fields are: CHARMM [28], AMBER [29], GROMOS [30], OPLS [31],

GAFF [32] and COMPASS [33].

Through these force fields, small organic molecules, polymers, proteins or membranes can be simulated. In this thesis study, we chose to use OPLS-AA [31] (Optimized potentials for liquid simulations-all atoms) developed by William L. Jorgensen, which has proven to be relevant for describing many structural, thermodynamic and dynamic properties of molecular solids and liquids.

Confined systems

Silica cylindrical nanopore with a hydrophilic surface was managed by applying the procedure proposed by Brodka and Zerda [34]. We generated a cylindrical cavity along the z axis of the cubic silica cell of (

Introduction and objectives

The hydrogen bond (HB), which is ubiquitous in self-assembly sciences including chemistry, biology, and physics, has been the subject of extensive investigation in the last 100 years. Among the HB former liquids, many works have been devoted on water to connect the structure with the macroscopic properties [6,9] and more especially its physical anomalies [10]. Alcohols are a class of HB liquids such that the molecules form the HB from their hydroxyl group (OH), whereas their hydrophobic moiety provides them an amphiphilic character [1][2][3]. Regarding the primary alcohols, HB leads to a chainlike structure which is less cohesive than the three-dimensional HB network of water, whereas the hydrophobic group is at the origin of the micellar structure (the molecular emulsion). This amphiphilic behavior leads to the structural heterogeneities at the nanoscale although the homogeneity and the full mixing are at the macroscopic scale. To microscopically characterize this heterogeneity and this microstructure, extensive experiments and simulations have been performed. The most studied alcohols are probably methanol and ethanol given their fascinating aqueous microscopic structure and their numerous applications.

Usually, the heterogeneity of these two alcohols was examined by progressively diluting the HB network by using water and to a lesser extent from an aprotic or organic solvent [4,5]. Indeed, the amphiphilic nature of the alcohols thereby solubilizes a large range of organic solvents that increases the heterogeneity and involves a strong deviation of thermodynamic properties from the ideal mixture behavior [5]. From the hexane-ethanol binary liquid mixture, Perera et al. have recently shown that the hydrogen-bonded structure persisted and induced a subsequent local segregation of ethanol [4] which allowed them to investigate the differences between clustering and heterogeneity [4] and structurally evidenced the heterogeneity from a prepeak in the structure factor. The presence of clusters then will be disconnected to the prepeak and to the heterogeneity.

More recently the concept of "simple disorder" was defined if the excess quantities are always smoothly varying functions of molar fraction, whereas the notion of "complex disorder" was connected to the local heterogeneity or molecular emulsion evidenced by sharp changes occurring in the excess quantities with change of sign. Actually, these recent concepts could be used to microscopically understand the nonideality of binary mixtures.

Alcohols are amongst the simplest of all organic molecules that undergo a conventional hydro-Chapter 3 Ilham Essafri gen bond [6]. They are known as self-associated liquids [7]. In mixture with hydrocarbons, they exhibit physical changes which is strongly attributed to their bifunctional nature [8][9][10][11]. Undoubtedly, the alcohol-hydrocarbon mixtures are extremely affected by the HB network created by the alcohol molecules [12]. Predicting the physical properties of entire binary mixture from the one of pure liquids is impossible due to the non-ideality. This is owing to the complicated ordering of liquids in the presence of polar and non polar media.

The determination of the correlation between structural characteristics of binary organic mixtures and the excess thermodynamic properties were the focus of many theoretical and experimental works. Furthermore, several authors attempted to relate experimentally the local micro-structure of various organic binary liquids to the intensity of the intermolecular interactions [13][14][15]. Well, despite advances in experimental techniques, it remains difficult to provide more information on these micro-structures inducing local inhomogeneities in the atomic level.

This local heterogeneity creates deviations from the ideal behavior of binary mixtures. If these micro-structures are evidenced by experimental measurements, their originalities are not well explained and it remains evident that improvements can still be made on the understanding of the structure of these liquids. This thesis helps to understand self-assemblies of associated liquids and their effects on the macroscopic properties. We consider then alcohols, given their identity covering a wide range of applications and their ability to self-organize. Notably, these systems are characterized by their highly directional interactions which tend to strongly associate the molecules. In our case, the non ideality behavior and local structure were explored from two types of mixtures. The first one is the TOL-alcohol system. This choice is mainly based on the ability of toluene molecules to create strong interactions with alcohol molecules as showed in our recent paper [16]. So, it so important to investigate our earlier findings for more alcohols liquids.

The second system is composed of CHX-alcohol. Interestingly, CHX molecules can create weak interactions, as dispersion forces, with alcohols and it also miscible at whole range concentrations as TOL liquid.

In this context, this thesis aims to investigate these two perspectives by studying various liquids from molecular simulation. We performed equilibrium molecular dynamics simulations of Ethanol (EtOH), Propanol (PrOH), Butanol (BuOH), Pentanol (PeOH), Toluene, Cyclohexane 50

Chapter 3 Ilham Essafri

Microstructure of binary mixtures in bulk and nanoconfined phases and their mixtures visiting the all-regions concentrations. Fundamentally these systems were studied in order to explore the effect of the dilution of the hydrogen bonding network by an apolar solvent. To achieve this goal, toluene (TOL) and cyclohexane (CHX) were used given their apolar character. Furthermore, these two apolar solvents were mixed with five types of alcohols in order to examine the carbon chain length effect on the hydrogen bond network of these alcohols.

Simulation validation

Methanol mixtures

We report in Figure 3.1 (a) the density of the liquid phase as a function of x MeOH for both mixtures. In two cases the so-calculated densities are found in fair agreement with the experiments [11,17] that validates the so-used models to describe MeOH, CHX and TOL molecules and their combining interactions. Experimentally, CHX/MeOH mixture is well known to demix between x MeOH =0.2 and x MeOH =0.8. This tendency to segregate is highlighted in Figure 3.1 (c)

where snapshots of CHX/MeOH at x MeOH =0.1, 0.5 and 0.9 are reported. As shown in Figure 3.1 (c) the phase separation is well recovered at x MeOH =0.5 whereas at x MeOH =0.1 and 0.9 the systems are miscible. This result is in good agreement with the experimental immiscible region (Figure 3.1 a) that allows us to make confident to the so-used OPLS force field. Moreover, as evidenced in Figure 3.1 (a) the so-calculated densities with higher systems (4000 molecules) are found in good concordance with simulations of 500 molecules that involves a small impact of size effects what bears out our computational procedure. The mechanical equilibrium of MD simulations of 500 molecules was checked by calculating the profile of the total pressure according to z direction. Given the isotropy of our system, the profiles according to three x, y and z directions were found similar.

We report in x MeOH = 0.1, 0.5, and 0.9 such that methanol is represented in red, and CHX is represented in cyan. calculation, a deviation of 30-50 bar was obtained that is considered as correct in MD simulations. Indeed, the pressure is a macroscopic property and can be measured properly only as a time average. As shown in Fig. 3.2 (a) the pressure is constant along the z direction, highlighting that the mechanical equilibrium is well reached. As exhibited in Fig. 3.2 (a) the pressure oscillations are the same order of magnitude as that for the calculated pressure for the water reference system and that for the profile pressures reported in the literature [18]. The pressure profile was also calculated for x MeOH = 0.5 for a system of 4000 molecules. As highlighted in Fig. 3.2 (a) the pressure profile is in good concordance with the calculated pressure for the system of 500 molecules, which suggests that the studied systems of 500 molecules are physically relevant 52 Chapter 3 Ilham Essafri to capture the microscopic insights into both binary mixtures. Interestingly, Fig. 3.2 (a) shows that at x MeOH = 0.5, i.e., for the demixing system, the pressure profile is constant, highlighting the mechanical pressure [18][19][20][21] through the interface between methanol and cyclohexane.

Ethanol to pentanol mixtures

Unlike the mixture of methanol with CHX, the EtOH PrOH, BuOH and PeOH are fully miscible in CHX and in TOL [10,11,22,23]. mixtures [10,11,22,23]. The so-used OPLS-AA force field is then validated also for Ethanol, Propanol, Butanol and Pentanol molecules. It means that our numerical results it produce the real behavior of these liquids and conclusion can be drawn correctly.

Tert -butanol mixtures

The variation in density mixture of TOL/TBA and CHX/TBA binary liquids as a function of

x TBA that is obtained at 300K and 1 bar was plotted in Fig. are miscible with TBA at each concentration. The miscibility trend observed in Fig. 3.4 is in good agreement with experimental observations [11,24]. The so-use force field provides thus miscibility in fair agreement with experiments. Indeed, the simulated density is larger than the experimental value in both systems with a maximum difference of 9% which is considered as correct.

Chapter 3 Ilham Essafri

Microstructure of binary mixtures in bulk and nanoconfined phases the excess density) is higher than the TOL/MeOH one. These behaviors could be imputed to a change in the structural topology [25,26] leading to a structural heterogeneity or a difference in Chapter 3 Ilham Essafri the interactions between both components of the binary liquid mixture [27]. Actually, contrary to the miscible zone, in the immiscible region of the CHX/MeOH mixture the difference is due to the phase separation.

2) Ethanol to pentanol-cyclohexane and ethanol to pentanol-toluene

As shown in Fig. 3.3 (a), the calculated density of TOL/EtOH binary mixture exceeds the value of the ideal density. For concentrations from 0.1 to 0.8 and when the ethanol concentration reached 0.9, a decrease in density is observed in comparison with the ideal density. interestingly, an increase in density is observed when x EtOH < 0.6 while from x EtOH =0.6 the density reaches its maximum and begins to decrease gradually. However, the density of CHX/EtOH mixture exceeds the ideal density at x EtOH =[0.1,0.2] and from x EtOH =0.3 the density begins to decrease.

As observed from Fig. In order to measure the magnitude deviation of binary mixtures, we represent in Figures 3.5 Microstructure of binary mixtures in bulk and nanoconfined phases a negative excess density can be attributed to the predominance of the dispersion forces and dipolar dissociation over the specific interactions on CHX-Alcohols mixtures [28,29]. From thereon, In this case, the mixture will probably produce segregation in the local organisation of hydrophobic sites and hydrogen bonds. This means that the deviations are probably ascribable to the inefficient packing in the mixtures of these components as a result of their incompatible structures.

3) TBA-CHX and TBA-TOL Probably, the combination effect between ⇡ interaction and the structure of TBA molecules (auto-aggregator) may be responsible for these variations in non-ideality. It is interesting to mention that TBA molecules are known as auto-aggregating molecules. According to the study of Dixit et al. [30], TBA/Water mixture at a small concentration in TBA exhibits structural agglomeration, which causes anomalous behavior of physical properties. In our study, water is replaced by non polar solvents, leading to the absence of TBA-water hydrogen bonds. The differences in deviation highlighted from the negative excess density is may be caused by the specific microstructure due to the presence of clusters (i.e. self-assembly of molecules in finite groups).

As

4) Discussion

The non-ideality for both systems TOL/alcohols and CHX/alcohols was already found to be a for mixtures of alcohols with non-polar solvents, the anomalous behavior in the thermodynamic properties are typically related to two structural effects [34,35]. First one is the association of alcohol molecules through their hydrogen bonds and the second one is about the formation of complexes between alcohol and solvent non polar molecules.

In order to explore the structure of the so-studied binary liquids, we examined the microscopic structure of each component in the mixture and investigated the local heterogeneities between the different molecules that can be caused by clustering mechanisms. Indeed, the non-ideality is correlated with the microscopic local structure of the liquids constituting a mixture likely leading Chapter 3 Ilham Essafri 59 Microstructure of binary mixtures in bulk and nanoconfined phases to spatial heterogeneities that are probably responsible for such macroscopic behavior.

Structural heterogeneity

1) Methanol-cyclohexane and methanol-toluene Interestingly, as illustrated in Figure 3.7 for CHX/MeOH mixture, it seems that the immiscibility at low methanol concentration is due to the formation of the methanol pocket assimilated to a nucleation process leading to the formation of nanophases rich in methanol molecules such that the OH groups will be hidden from the organic solvent given of the lack of favorable interactions.

The progressive formation of nanophases as a function of x MeOH could then generate a structural heterogeneity. At high concentration in methanol of CHX/MeOH mixture (x MeOH =0.8) the miscibility is recovered due to the percolating of the methanol nanophases. Actually, in the miscible region, the progressive formation of these nanophases increases the heterogeneity and could explain the non-ideality of CHX/MeOH mixture. To quantify this spatial heterogeneity, the heterogeneity order parameter (HOP) [36,37] was calculated. The HOP value increases with the expansion of the spatial heterogeneity because a tighter packing of sites results in a smaller r ij , which leads to a larger HOP. Calculations were performed for both binary liquid mixtures.

According to the study of Wang et al., the HOP of ideal particles homogeneously distributed is lower than 15.74, and a heterogeneous system exhibits a HOP greater than 15.74 [36]. We report in Fig. 3 Let us mention that the microstructure is assimilated to the presence of the heterogeneities, and both terms will be subsequently used interchangeably. Whereas the spatial heterogeneity in the CHX-MeOH mixtures is the result of the local segregation and its propagation to strive for a total demixing, the molecular origin of the microstructure in the TOL-MeOH mixtures is then Chapter 3

Ilham Essafri yet to be determined. Interestingly, Fig. 3.8 highlights that the HOP of CHX and TOL (close to 15) is lower than the HOP of MeOH, which suggests a more homogenous distribution of the aprotic component in the mixtures.

2) Ethanol to Pentanol-Cyclohexane and Ethanol to Pentanol-Toluene i) Instantaneous configuration observation ii) Structural heterogeneity characterization In order to evaluate these microstructures, the heterogeneity order parameter (HOP) was calculated. We represent in growing as a function of concentration. These heterogeneities disappear when we approach the ethanol rich-region (x EtOH = 0.9), the system begins to structure homogeneously. The maxima of the excess density showed in Figure 3.5 (a) corresponds to a strong heterogeneity (HOP= 18 > 15.74). This result validates our first hypothesis at the origin of the non-ideality behavior.

Furthermore, a minimum of the excess density around x EtOH = 0. was previously highlighted.

3) TBA-CHX and TBA-TOL

We show in Figure 3.12 the structure of TOL/TBA and CHX/TBA mixtures as a function of three TBA concentrations (x TBA =0.2, x TBA =0.5, x TBA =0.8). At x TBA =0.2, TBA in TOL/TBA mixture show small pockets regularly distributed in the mixture. Figure 3.12 (a) showed the morphology of CHX/TBA molecules at x TBA =0.2. On the contrary, less distributed clusters are found through the CHX/TBA mixture. It seems that there are regions rich in clusters and regions without any pocket of TBA molecules. Fig. 3.12 (b) shows that both mixtures exhibit nanophases of small sizes which they are more extensive in CHX-TBA mixture. Furthermore, the microstructure in TBA rich-region is depicted in Fig. 3.12 (c). These configurations allow us to make difference between large and small nanophases formed in CHX-TBA and TOL-TBA mixtures, respectively. It is interesting to mention that TBA is more aggregated in CHX than in TOL. Then, the formation of these aggregations could explain the ideality behavior showed in both mixtures are locally distributed homogeneously except for TBA molecules in mixture with TOL at x TBA = 0.3. That is highlighted by the value of the HOP which exceeds the estimated value for homogeneous distributed sites. In this mixture, one can conclude that the non-ideality behavior depicted in Fig. 3.6 is strongly correlated to the formation of these aggregations. scale with the decrease of the TOL (or CHX) number density, but it actually decays to a smaller extent [2]. That is an obvious evidence of the microstructure and the partial mixing at the molecular scale [2]. In case of the CHX/MeOH mixture, this effect is higher because the increase in RDF intensity as a function of the decrease in x MeOH is more pronounced, suggesting an increase in the spatial heterogeneity in line with the HOP calculations and the miscible regions. Interestingly, this increase in intensity is similar to that observed in nano-confined media where the excluded volume involves an increase in the interfacial concentration of confined fluids [1,[38][39][40] and bears out the presence of nanophases. Let us mention that the similar behavior is also observed with the second peak but in a lesser extent. To investigate the interactions between MeOH and TOL(CHX), the radial distribution functions between the centres of mass were calculated in the miscible regions and reported in interaction between toluene and methanol molecules. This result sheds light on a preferential interaction between methanol and toluene. To identify it, we report in Figure 3.16 the RDF be- x MeOH =0.9 tween the centres of mass of the aprotic component and hydrogen atoms of hydroxyl and methyl groups of methanol. Let us mention that the centre of mass of both TOL and CHX molecule is close to the centre of the cycle. Figure 3.16 highlights a strong interactions between OH groups and toluene molecules because distance of 2.5 Å was found that is the same order of magnitude that a hydrogen bond. This result suggests then a hydrogen bond like interaction probably induced by the aromatic cycles. Actually, this strong interaction is probably at the origin of the toluene miscibility in methanol and the positive excess density [27]. In the CHX/MeOH mixtures the CHX molecules self-organize to form hydrophobic nanophases.

Molecular interactions

Chapter 3

Ilham Essafri

2) Ethanol to pentanol mixtures

The most likely reason at the origin of the mismatch between the density of the mixture and the ideal behavior is probably the formation of HB-induced aggregates. To verify this hypothesis, the radial distribution functions (RDFs) of the EtOH, PROH, BuOH, PeOH, TOL and CHX mass centers have been managed. Figure 3.17 presents the RDFs of CHX-CHX and TOL-TOL distances for CHX-EtOH, CHX-PrOH, CHX-BuOH and CHX-PeOH, and TOL-EtOH, TOL-PrOH, TOL-BuOH and TOL-PeOH mixtures at whole range concentrations. For the pure liquids, the RDFs are in good agreement with RDF measured from Neutron scattering [41]. In Fig. 3.17, the CHX-CHX RDF is reported for four binary mixtures. As shown in Fig. 3.17

RDF exhibits a first and a second peak located at a distance of 6.1 Å and 10.8 Å, respectively.

The first peak intensity changes from 2.67 to 3.52 for CHX-EtOH That involves the possibility of space filling decreases with an increase in the alkyl chain length of alcohol molecules. For toluene mixtures, the TOL-TOL RDFs displayed in Figure 3.17 show two large peaks. The first and second peak are located at distance of 5.9 Å and at 11.5 Å, respectively. The intensity of the first peak increases very slowly with the addition of alcohols molecules. The alkyl chain effect of alcohols is less marked compared to CHX/CHX mixtures.

As previously discussed the location of the first peak of TOL and CHX molecules are indicating a strong interaction of TOL molecules at 5.9 Å rather than that of cyclohexane at 6.1 Å. TOL-BuOH and TOL-PeOH as a alcohol mole fraction. Very interestingly, the RDFs between alcohol and TOL revealed two peaks with an evident shoulder in the first peak at short distances about 3.9 Å . This is characteristic of a strong interaction of TOL molecules with alcohol ones.

This interaction is absent with CHX, which highlights a difference in the local structure of these two types of mixtures (CHX-alcohols and TOL-alcohols). That is an evidence of the solvation of toluene from alcohol molecules. Eventually, the long range interactions seem to be similar for both mixtures. That could explain the positive deviation in excess densities for TOL/alcohols mixtures while the negative excess density could be attributed to the strong cluster domains created by both molecules (CHX and alcohols).

3) TBA mixtures x TBA =0.0 x TBA =0.1 x TBA =0.2 x TBA =0.3 x TBA =0.4

x TBA =0.5

x TBA =0.6

x TBA =0.7

x TBA =0.8

x TBA =0.9 The structure analysis has been also conducted for TBA-TOL and TBA-CHX mixtures. x TBA =0.1

x TBA =0.2 x TBA =0.3

x TBA =0.4

x TBA =0.5

x TBA =0.6

x TBA =0.7

x TBA =0.8

x TBA =0.9 x TBA =0.1

x TBA =0.2 x TBA =0.3

x TBA =0.4

x TBA =0.5

x TBA =0.6

x TBA =0.7

x TBA =0.8

x TBA =0.9 Microstructure of binary mixtures in bulk and nanoconfined phases

Dilution effect on hydrogen bonds network

Methanol mixtures

To characterize the microstructure in both mixtures the hydrogen bonds number per methanol molecule (nHB) was calculated. Hydrogen bonds were evaluated by considering the geometric criterion developed by Luzar and Chandler [42] such that the distance between hydrogen atom of one MeOH molecule and the oxygen atom of another one has to be smaller to 2.5 Å whereas the distance between two oxygen atoms of two MeOH molecules has to be smaller to 3.5 Å. We report in convergence [43,44]. Details of calculations can be found in Refs. [43,44]. We report in Fig.

TBA mixtures

r(Å)

x EtOH =0.1

x EtOH =0.5

x EtOH =0.9 x PrOH =0.1

x PrOH =0.5

x PrOH =0.9 x BuOH =0.1

x BuOH =0.5

x BuOH =0.9 x PeOH =0.1

x PeOH =0.5

x PeOH =0.9 The presence of ⇡ electrons in toluene molecules leads to the formation of weak intermolecular complexes [45][46][47][48][49][50]. The RDFs between toluene on alcohols showed a shoulder close to the first peak involving a favorable interaction. To evidence the alcohols affinity for TOL molecules, we report in Figure 3.24 the local surroundings of the aromatic ring of toluene molecules in the presence of different alcohols made by calculating RDFs between the hydroxyl group (HOC) of the alcohol and the aromatic ring of TOL. As shown in Fig. 3.24, the RDFs reveal a favorable Chapter 3 Ilham Essafri interaction between HOP and aromatic rings at very small distance of 2.46 Å that is in line with the loss of the hydrogen bonds of alcohols molecules evidenced in Figure 4.15. Interestingly, there is a very strong dilution of the hydrogen bonding network. While in CHX-alcohol systems, it is preserved with a very small loss in the connected HB pattern. 2) Ethanol to pentanol mixtures Microstructure of binary mixtures in bulk and nanoconfined phases of PeOH molecules that occupied more space in both mixtures. Non ideality behavior can ben then attributed to these micro-heterogeneities created by molecular clusters formed by alcohols which generated micro-strucutres of all systems at the molecular level.

Cluster analysis

3) TBA mixtures

Clusters versus heterogeneity

Recently, Perera et al. have suggested that the structural signature of the heterogeneity and then the microstructure of ethanol mixture were related to the observation of a pre-peak in the structure factor around 0.8 Å 1 [4]. More recently, Hureau et al., by studying tert-butanol, have established that the pre-peak was rather the structural signature of the presence of the closed clusters [3,39]. The structure factor [S(Q) such that Q is the momentum transfer vector] was calculated in both mixtures to structurally highlight the microstructure. All details of the structure factor calculation can be found elsewhere [3]. Let us mention that the value of S(Q = 0) was not evaluated because at Q = 0 Å 1 the system is poorly sampled, which explains that S(Q) begins from Q = 0.19 Å 1 . Indeed, Q = 0 Å 1 corresponds to the very high distance in the real space that was slightly sampled in our finite MD simulations.

We report in Figs. 3.31 (a) and 3.31 (b) the total structure factor of both TOL-MeOH and CHX-MeOH mixtures, respectively, as a function of the methanol concentration. The total structure factor corresponds to the case where all atoms were considered. In both mixtures, Fig. 3.31 exhibits the absence of a pre-peak that is contradicts the fact that the pre-peak could be the structural signature of the heterogeneity.

However, this result is in line with the fact that the pre-peak is connected to the closed clus- ters (5% of cyclic clusters in both mixtures). Indeed, physically, the pre-peak at low Q can be assigned to the mesoscale spatial correlations between the hydrophilic parts surrounded by a hydrophobic shell. This situation occurs from molecules with a large hydrophobic moiety such as tert-butanol [3] (TBA) or ethanol [51] (ETOH).

By using the previous data obtained from molecular simulation of TBA [3] and ETOH [51], we

Chapter 3

Ilham Essafri report in Fig. 3.32 the partial structure factor of the hydroxide groups. A partial structure factor allowed us to highlight the pre-peak of the total structure factor that becomes the main one [3].

Details of the calculation of thee partial structure factor can be found in Ref. [3]. As shown in Fig. 3.32, TBA and ETOH present a first peak at 0.8 Å 1 , contrary to MeOH, which presents a first peak located at 1.4 Å 1 The decrease of amplitude is the result of the decrease in the number of cyclic clusters. Indeed, in the TBA and ETOH liquids 95% and 15% of cyclic clusters were calculated, respectively, whereas in the pure methanol liquid, the rate of cyclic clusters is close to 5%. The shift from 0.8 to 1.4 Å 1 sheds light on range of mesoscopic correlations and on the size of clusters. Indeed, methanol has smaller cyclic clusters involving an increase in the range of the interactions. Additionally, in three pure TBA, ETOH, and MeOH liquids, the HOP was found e qual to 14.9, 7.1, and 15.0, i.e., below 15.74, involving an absence of heterogeneity.

In the pure liquids, this result indicates that the presence of clusters could be uncorrelated from the notion of heterogeneity, which is in line with the conclusion drawn by Perera et al. [4]. However, this result also suggests that the pre-peak will be a structural signature of the mesoscopic correlations between cyclic clusters, which is evidence of the heterogeneity of the microscopic scale.

The spatial heterogeneity of miscible liquid mixtures then would be the result of the local structural disruption of the homogenous structure in the pure liquid. Indeed, as observed in Fig. 4.14, by progressively increasing the toluene concentration, the initial hydrogen-bonding network corresponding to a homogenous structure is then locally broken due to the favorable toluene-methanol interactions leading to the spatial heterogeneity. As the toluene concentration increases, the heterogeneity increases to reach a maximum around x MeOH = 0.5 (see Fig. Microstructure of binary mixtures in bulk and nanoconfined phases

Dynamical properties

In this part, the rotational and translational motion have been investigated. Translational dynamics has been studied by calculating the mean square displacement (MSD). We aim to investigate the so-observed structural anomalous from a dynamical standpoint. The rotational motion will be studied from the auto-correlation function of dipole moment C(t) and the relaxation times ⌧ will be calculated.

Self-diffusion coefficient

1) Ethanol to pentanol mixtures Table 3.1 reports the self-diffusion coefficients of pure components. A fair agreement with experimental results is observed for alcohols and for TOL and CHX molecules is showed with an error of about 13 % which is reasonable. In Table 3 3.33. Three concentrations are chosen in order to explore the non-ideality observed in Figure 3.3 from the density and the excess density. Furthermore, 0.1 and 0.9 are the mole fractions of alcohols are also studied to evaluate the poor and rich alcohols regions.

In Figure 3 TOL diffuses more faster than CHX at low and medium alcohol concentrations (x EtOH =0.1 and 0.5) while at x EtOH =0.9 a similar value is observed. At low concentration, alcohols in TOL diffuse two times faster than their pure behavior. On the contrary, alcohols molecules in CHX at a similar concentration diffuse two times slower than alcohols molecules in their pure state. This is due to the new environment offered by TOL and CHX in each case separately. This is means that the polarity (⇡ interaction) of apolar molecules mixed with alcohols impacts the self-diffusion. At x Alcohol =0.5, EtOH in (EtOH/TOL) mixture diffuses even more than EtOH molecules in CHX; At x EtOH =0.9, the molecules auto-diffuse similarly in both mixtures. Effectively, we have two close values to the pure self-diffusion coefficient. The study of the dynamics recorded in all these mixtures indicates that alcohols mixed with toluene Chapter 3 Ilham Essafri have a rapid motion when compared to alcohols in cyclohexane. Indeed, this observation points out that toluene creates strong molecular interactions and promotes the translational movement of molecular alcohols rather than cyclohexane.

2) TBA mixtures

TBA mixtures

For the TBA/TOL and CHX/TBA mixtures, the evolution of the autocorrelation function of TBA dipole moment were reported as a function of time in Figure 3.36. The decay of the autocorrelation function of TBA molecules in TOLis found faster than CHX. As previously shown, CHX breaks the structure but does not break the nHB, rather it causes complexes formation. We think that the formation of large aggregates is at the origin of this slow rotational and translational motion showed. For the TBA/TOL binary mixture, the fact that there are more monomers could be an explanation of differences observed in both cases.

Chapter 3 Ilham Essafri 95

Microstructure of binary mixtures in bulk and nanoconfined phases TOL/TBA a)

x TBA =1. x TBA =0.9 x TBA =0.8 x TBA =0.7 x TBA =0.6 x TBA =0.5 x TBA =0. CHX/TBA

x TBA =1.

x TBA =0.9

x TBA =0.8

x TBA =0.7

x TBA =0.6 x TBA =0.5

x TBA =0.4

x TBA =0.3 x TBA =0.2 x TBA =0.1 This could be attributed to the evolution of the hydrogen bonding interactions in both mixtures.

It has appeared to be an important factor influencing the rotational motion of the total dipole moment of alcohols and their relaxation times [58]. As a result, a wait-and-switch [58] model has been developed to describe the rotational dynamics of liquids [58]. Through this model, a "waiting" time is necessary for the hydrogen bonding network to reorganize itself and find the next available site to "switch" from one hydrogen bond to another.

The "wait-and-switch" model [58] can be used to correlate the observations of the dilution of the hydrogen bonding network to the total dipole reorientation dynamics of alcohol-TOL and alcohol-CHX mixtures. The nHB of alcohols in all mixtures are given in sec. That generates a frequent "switch" of the liquid structure and, therefore, a faster relaxation response at higher TOL concentrations. The relaxation time of TBA molecules in CHX/TBA and in TOL/TBA is reported in Figure 3.38. As previously, slow relaxation time is observed for CHX/TBA systems while a rapid one evidenced in case of the TOL/TBA mixtures.

Conclusion

This work has focused on the exploration at the nanoscale of the non-ideality of methanol, ethanol, propanol, butanol, pentanol and tert-butanol in mixtures with toluene and cyclohexane by means of molecular dynamics simulations. Simulations fairly reproduced the experimental densities of all binary mixtures even at the miscibility region of methanol-cyclohexane binary mixtures. In all mixtures, the deviation from the ideal mixture behavior was observed and different intensities were recorded. In the case of toluene this non-ideality have been ascribed with the specific interactions between toluene and alcohol leading to a breaking in the hydrogen-bonding network involving clusters of different sizes and the spatial heterogeneity. Particularly, the immiscibility and the non-ideality (negative excess density) of the CHX-MeOH mixtures were the result of the unfavorable interactions between CHX and MeOH leading to a self-organizing of CHX molecules to form hydrophobic nano-phases at the origin of the structural heterogeneity in the miscible region. However, the non-ideality showed by ethanol, propanol, butanol, pentanol and tert-butanol (negative excess density except for low EtOH concentration) have been attributed to the hydrophobic character of CHX molecules with alcohols ones and the creation of largest clusters in comparison with alcohols in TOL. A strong dilution of the hydrogen bonding network by toluene molecules as well as cyclohexane molecules has been shown. Nanophases have been characterized in terms of pockets of linear clusters such that the difference in miscibility and in heterogeneity were understood in terms of cluster size and distribution for methanol-toluene and methanol-cyclohexane mixtures. Moreover, we have shown that the presence of clusters had to be uncorrelated from the notion of heterogeneity. Eventually, we have highlighted that the prepeak observed in the structure factor is independent of the degree of heterogeneity but is rather connected to the presence of cyclic clusters. Additionally, the dynamics of these liquids Chapter 3

were in line with the structural results given that a fast motion with a rapid relaxation times were shown by alcohol molecules in mixture with TOL whereas a slow motion with a long relaxation times of alcohols in CHX were captured. The results of this part allow us to differentiate between the intensity of the self-organization of liquids at their hydrogen bonding networks while distinguishing between ideal and non-ideal mixture in terms of microscopic local structuring. 100 Chapter 3 Ilham Essafri

Introduction

Liquids behavior in regions of several molecular diameters can change completely once confined.

More precisely, significant attention has been devoted to the structure and dynamics of nanoconfined water owing its crucial role in biosystems. Any confined fluid behaves differently with respect to volume due to the presence of wall surfaces and the finite size of the pore in one or more dimensions. In this work, we elucidates the impact of a hydrophobic and hydrophilic confinement on the hydrogen bonding (HB) network of polar liquids at the nanoscale. The understanding of such phenomena is of wide interest for the design of new materials that could be used for heterogeneous catalysis, membrane separation, lubrication, drug delivery and petroleum recovery with no energy cost.

According to knight [1] et al. the confinement effect on the physical properties of water is governed by the changes in the HB network of water that is impacted by the creation of liquid-silica surface HBs interactions. Kremer et al. [2] studied poly(propylene glycol) in bulk state and in confined media within a native (hydrophilic) and a silanized (hydrophobic) unidirectional silica nanopores with average diameters of 4, 6 and 8 nm. Astonishingly, they distinguished between the surface effect and the confinement effect. Molecules near the surface wall are subjected to the surface effect, and the molecules far from the surface wall are subject to confinement effect. These three decades the confinement effects on the physics of fluids have been been intensively studied [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].

Many new properties have been then discovered such as the giant diffusion of liquids [18][19][20], the apparition of new phases and new transitions [21][22][23][24], giant dielectric properties [13,14,[25][26][27],

the increase of optical properties [28], and the possible mixing of non-miscible mixtures [29].

These observations indicated that the classical understanding of the physics of liquids should be revisited in confined geometry. Whereas these effects have been largely investigated in the case of confined single components [3][4][5][6][7][8][9][10][11][12][13][14][15][16] and immiscible binary mixtures [30][31][32] less works have been devoted to the confinement of miscible liquid mixtures [17,33,34].

Recently, Muthulakshmi and coworkers reported an experimental evidence of a partial phase separation of an ethanol-water mixture confined in mesoporous silica using positron annihilation lifetime spectroscopy. They showed that a small fraction of the ethanol molecules seemed to be anchored at the silica surface [35]. A similar results was also established by Guo et Microstructure of binary mixtures in bulk and nanoconfined phases studied confinement of an ethanol-water mixture between two planar silica walls [16]. A partial and local separation between water and ethanol close to the silica surface were thus evidenced [16].

In the same time Schmitz et al. have exhibited that the glycol-water mixture could undergo an interfacial separation [36]. This phenomenon was also numerically observed by You et al. who exhibited a local demixing of binary hard-core Yukawa mixtures in a slitlike pore [37]. More recently, Krycka et al. displayed a separation between two confined apolar liquids [34]. Whereas these works only suggest a partial separation of two hydrogen bonds forming liquids or two apolar liquids near the solid surface. Morineau and coworkers have recently provided a direct experimental structural evidence of the microphase separation of macroscopically miscible liquids consisting of a hydrogen bonds forming liquid and an apolar one [17]. They showed that a mixture of toluene (TOL) and tert-butanol (TBA) with a TBA/TOL volume fraction composition of 56/44% can demix and form a core-shell organization in a confined medium, where this mixture is fully homogenous in the bulk phase [17]. Up to now, the physical mechanism ruling this phase separation at the nanometric scale stays unknown. In this context, we suggest that this structure is the result of a peculiar hydrogen bond network.

In this part, we deeply study the microscopic structure of pure and binary liquids and the possibility to control the micro-phase separation under nanoscale confinement. Additionally, we aim to explore the role of the hydrophobic/hydrophilic nanopore in the microphase separation.

To do so, we studied tert-butanol (TBA), toluene (TOL) and cyclohexane (CHX) and their binary mixtures as previously studied in the bulk phase, into confined media. The hydrophilic matrix is a water nanotube (WNT) characterized by OH heads that promotes the creation of strong interactions with liquids that form hydrogen bonds, such as TBA. In fact, the hydrophobic matrix is a carbon nanotube (CNT) that is characterized by carbon on its surface and can provide only weak interactions: couloumbiennes. Silica Nanopore (MCM-41) were used as weakly hydrophilic matrix. We also studied the effect of the pore size through the comparison between 2 radius sizes ( r = 1nm and r=2nm) for WNT and CNT.

Chapter 4 Ilham Essafri

Confinement versus heterogeneity

Confinement through the silica cylindrical nanopore

By combining contrast matching from neutron scattering and a core-shell model (CS), Hamid et al. showed that a mixture of toluene (TOL) and tert-butanol (TBA) with a TBA/TOL volume fraction composition of 56/44% confined in cylindrical silica (MCM-41) of radius of 24 Å can separate [17], whereas this mixture is fully homogeneous in the bulk phase. In this CS model, TBA and TOL are, respectively, located close to the silica surface and at the centre of the pore.

This peculiar structure is ascribed to the HBs between the TBA molecules and the silanol (SiOH).

In this part, we aim to capture this Core-Shell (CS) structure and clarify the microscopic driving force that governs it. MD simulations of pure TBA, pure TOL and TBA/TOL mixtures were thus conducted in confined phase. For consistency with the experiments, the confined medium corresponds to a cylindrical silica nanopore with a radius of 24 Å. Notably, a highly hydrophilic nanopore with a ratio of 7.5 OH/nm 2 was considered to intensify the hydrogen-bond interactions between TBA and the silica surface and to promote the CS organisation. Indeed, experimentally, a ratio of 2.5 -3.0 OH/nm 2 was measured.

Numerical evidence of the absence of a core-shell structure

We report in Figure 4.1 (a), the S HO of pure TBA and TBA/TOL mixture with a TBA/TOL molar fraction composition of 56/44% in the bulk and confined phases. This fraction was chosen for consistency with the concentration used in neutron diffraction experiments [17]. As shown in Figure 4.1 (a), in the bulk phase, the main peak that is located at approximately 0.8 Å 1

for pure TBA is slightly shifted toward 0.7 Å 1 for the mixture. The presence of this peak in both cases is related to the persistence of TBA clusters in the mixture. The lessening in intensity highlights a partial dilution of the aggregates i.e. a breaking of clusters. This situation was clarified by the calculation of cluster size, which shows a decrease in cluster size from 3.9 molecules per aggregate for the pure TBA to 2.9 in the TBA/TOL mixture. The calculation of cluster size is based on the hydrogen bond computation. The decrease in size of TBA aggregates in the mixture is then the result of dilution of the hydrogen bonding network (i.e. a rupture of the HB network) [38,39]. As shown in Microstructure of binary mixtures in bulk and nanoconfined phases for both confined situations (pure component and mixture) is similar to the position in the bulk phases. A decrease in intensity caused by the excluded volume is also observed [40]. This result appears to indicate that the long-range correlations of the TBA molecules in both confined and bulk phases are similar. Indeed, the cluster size of TBA aggregates in pure confined TBA is approximately 3.3 molecules per aggregate, whereas this value is 2.3 for the confined mixture.

This decrease in cluster size is the same order of magnitude in both confined and bulk phases.

These results show an absence of a CS organization. Indeed, in the case of a total demixing, the cluster size of TBA in both confined situations (pure TBA and TBA/TOL mixture) should be similar.

To highlight the local structure, the density profiles of the methyl groups of TBA (C T BA ) and carbon atoms of TOL (C T OL ) along the radial direction of the cylindrical pore are reported in Microstructure of binary mixtures in bulk and nanoconfined phases cylindrical nanopore), which emphases the absence of a CS organisation. To verify our numerical result reflecting an absence of segregation, the silica force field developed by Brodka and Zerda [42] was also considered. Figure 4.2 obviously shows an absence of core-shell organisation that demonstrates that the so-obtained structure is independent of the force field. Additionally, MD simulation of a TBA/TOL mixture with a TBA/TOL molar fraction composition of 35/65% was also considered. We report thus in To really highlight a possible micro phase separation, we report in 4.3 (c) and (d), the local molar fraction for both compositions. For both molar fractions, a homogenous mixture was observed at the centre of pore (from 0 to 5 Å). Into the layers, the increase in x T BA is compensated by a decrease in x T OL and reciprocally that involves a homogenous composition of TOL and TBA.

Validation of the force field and computational procedure

Interestingly, close to the silica surface (around 20 Å) a slight interfacial segregation is observed because x T BA = 1.0 in both cases. Although, a local demixing is highlighted close to the silica surface it does not propagate into the nanopore to form a CS structure. This is probably due to the weak hydrophilic interactions between the silica material and TBA. Interestingly, close to Furthermore, a long simulation (250 ns) of confined TBA/TOL with a TBA/TOL molar fraction composition 56/44% was also performed. In all cases, an absence of a CS structure is observed.

Additionally, an initial CS configuration with TBA close to the silica surface and TOL at the centre of pore was considered. After 0.7 ns the initial CS organisation was broken to obtain an heterogeneous mixture. This result shows that the CS organisation is unstable and that the so-obtained results are not MD-time dependent while our MD simulations are well converged.

Eventually, mean square displacement of TOL and TBA were also computed, both TBA and TOL molecules are moved of 24 and 15 Å along the axial and radial directions, respectively. This result shows that the simulation is ergodic and is long enough to allow the system to visit all of its energetically relevant states. How to thus explain the absence of the extinction of Bragg's peak (EBP) from neutron diffraction measurements [17] ? The CS organisation was highlighted by

Molecular interpretation of neutron scattering measurements

We report in To quantify this spatial heterogeneity, the heterogeneity order parameter was calculated [43,44]. As it mentioned before, the value of HOP increases with increasing spatial heterogeneity because a tighter packing of sites results in a smaller r ij , which leads to a larger HOP. Calculations were performed for both bulk and confined phases. For pure TBA and a TBA/TOL mixture in the bulk phase, HOP = 8.69 and HOP = 12.55, respectively. To verify that the so-calculated HOP is not affected by the layering organisation in the nanopore, the HOP was evaluated at the centre of the pore. For the confined TBA, a value of HOP = 16.93 was found, which indicates heterogeneity (>15.74), likely because of the confinement effect. For the confined TBA/TOL, HOP = 21.76. This strong increase with respect to the HOP of confined pure TBA clearly indicates the presence of strong heterogeneity, as previously observed in Figure 4.5 (a). These results shows that the absence of the extinction of Bragg's peak is in relation to the strong heterogeneity-inducing nanophases. This work allowed us to purpose another scenario that CS is one. MD simulations allowed us to clarify the confined structure by highlighting strong heterogeneity of the confined TBA/TOL mixture with respect to the bulk phase. This increase in heterogeneity with respect to the bulk phase is ascribed to the hydrophobic interactions of TOL and TBA with the silica surface. Indeed, as shown in To quantify the host-guest interactions, the isosteric heat of adsorption was computed for pure TBA and TOL at low loading. This result suggests a higher affinity of TOL with the silica surface, corroborating the hypothesis that the hydrophobic interactions rule the physisorption onto the silica nanopore, consistent with the so-observed structure. CHX/TBA mixture confined through a totally hydrophilic matrix and a totally hydrophobic matrix. Firstly, we study the microstructure of the so-mentioned mixtures in both nanopores of 2 nm pore size. In the second part, pore size effect on the microphase separation will be evaluated.

Strong and weak affinities impact

In Microstructure of binary mixtures in bulk and nanoconfined phases like structure for all liquids with a period that remains constant as the radius increases. The distance between two concentration peaks is approximately 5 Å. Interestingly, TOL showed the same layering behavior which means that TOL can be restored to its bulk organization after 2 layers in both confinement. This may be due to the fact that Toluene has ⇡-⇡ interactions and a methyl group that makes it interact in both forms of environments in two ways. TBA molecules in the WNT are the closest molecules in comparison with TOL and CHX that could have resulted from the creation of a strong interaction with the confining surface. Snapshots observations are extracted from simulations and presented in Figure 4.8 (a) to (c) and (a') to (c'). We observe a layering-like structure of confined pure TBA, TOL and CHX in both types of confinement as it illustrated by the radial profile represented in Figure 4.7.

In order to have a good description of the local strong or weak affinity showed in both nanotubes, we present in Figure 4.9 the comparison of the radial atomic profile of TOL, CHX and TBA. Furthermore, we aim to zoom out on the preferential orientation of the molecules in the first layer. That could explain the affinity between TBA and the surface in the hydrophilic confinement. That allows us to check the affinity of TOL with the CNT wall. As shown in Figure 4.9 (a), under hydrophobic confinement, we can observe that TBA's methyl parts point toward the surface contrary to the hydroxyl tail. Indeed, the carbon atoms of the methyl part of TBA are located around 16.5 Å while the oxygen and hydrogen atoms are located at 15 Å. This is evidenced by the structural snapshot in the same graph. As shown in Figure 4.9 (b), when we switch to the hydrophilic confinement in this case, we find an opposite behavior.

A first peak is highlighted at 19.5 Å but the atoms of the hydroxyl part of TBA are closely anchored to the surface although the TBA methyl group's carbons are positioned at 17 Å. This means that the hydroxide groups are oriented towards the wall surface while the methyl groups are founded behind. This change in structural behavior can be explained by the presence of hydrophobic interactions between the methyl groups of TBA molecules and the carbon atoms of CNT. In the case of WNT, this affinity with the surface of TBA hydroxyl groups can be probably attributed to the creation of hydrogen bond type interactions with the surface.

The radial profile of the carbon atoms of the aromatic part and the carbon of TOL's methyl group is shown in Figures 4.9 (c) and 4.9 (d). Microstructure of binary mixtures in bulk and nanoconfined phases and a second peak at 15 Å that depicts two different preferential locations close to the surface.

However the molecules are rather adsorbed on the surface from stacking interactions between aromatic cycles. In the WNT, the two peaks of carbon atom profiles of the aromatic part and the methyl part of the TOL are found at a similar distance around 18 Å (see Fig. 4.9 (d)).

This may be due to the creation of a strong interaction with the confining wall that requires a specific orientation. It is interesting to note that there is a broader peak observed in hydrophilic confinement that can be in favor of a specific structure close to the surface. Different preferred locations at the surface are illustrated by the presence of a large peak between 17 and 20 Å.

In the case of cyclohexane in hydrophobic confinement, we observe a very sharp peak around 16.8 Å with a shoulder at 15.5 Å which indicates that we have two preferred locations next to the confining surface. This can be explained by the creation of different hydrophobic interactions with the carbon nanotube (hydrophobic anchoring). In hydrophilic confinement the CHX has a broad peak ranging from 14.5 Å to 20 Å which emphasizes the fact that in hydrophilic confinement the CHX molecules do not have a preferential location near the surface. That's why we have a distance gap of 3 or 4 Å next to the surface.

Local demixing evidence of confined miscible mixtures

The behavior of binary mixtures of TOL/TBA and CHX/TBA confined in two frameworks is now studied and compared in this section. The local structure is described by the radial density profile showed in Figure 4.10. In Figure 4.10 (a)-(b), we provide the comparison in the radial density profile of TOL/TBA mixture in hydrophobic and hydrophilic confinement.

In a hydrophobic confinement, Fig. Microstructure of binary mixtures in bulk and nanoconfined phases the TOL shows a first main peak at 13 Å. There is microscopically a local demixing near the water surface. However, it should be noted that this mixture is fully miscible in the bulk phase.

Probably, this local demixing may be due to two major factors: confinement effect and strong interaction effect. This point will be detailed later. For both confinements, we found that molecules are arranged into layers, but showed different affinities near the wall surfaces. TOL has showed a very strong affinity with the wall surface in CNT better than TBA molecules in the case of a hydrophobic confinement. However, in a hydrophilic confinement, we observed the reverse phenomenon. These results indicates that, the chemistry of the wall surface affect the In addition, we examined the behavior of CHX/TBA inside CNT (hydrophobic) and WNT (hydrophilic). Microstructure of binary mixtures in bulk and nanoconfined phases confinement. In both confinements, CHX and TBA molecules form 4 layers. The CHX and TBA are located near the wall surface in the hydrophobic confinement while an important proportion of CHX molecules is captured near the surface. The behavior of CHX/TBA inside the nanowater seems to be slightly different . Specifically, a local de-mixing behavior is observed near the wall surface. Indeed, a large concentration of TBA molecules is found at 19.5 Å near the wall surface whereas CHX molecules are located at 17 Å.

To this point, we have observed that the type of confinement affects the organization of liquids within these nanopores. In the case of hydrophilic confinement, alcohol molecules are more attracted to the confining surface, whereas hydrophobic confinement is the hydrocarbons that prefer to be present in large quantities beside the surface. In order to understand this preferential structuring in both confinements, the atomistic radial density profile of TBA, TOL and CHX atoms along the nanopore radial direction have been managed.

Micro-heterogeneities

In order to investigate the presence of micro-heterogeneity in pure and binary mixtures, we calculate the heterogeneity order parameter (HOP) of confined pure CHX, TOL and TBA and their binary mixtures within CNT and WNT. According to the study of Wang et al., the HOP for homogeneously distributed ideal molecules is lower than 15.74 and a heterogeneous system exhibits a HOP greater than 15.74 [43].

a) Pure liquids TBA, CHX and TOL showed a layer structure in both types of confinement. In hydrophobic confinement, the molecules of TOL, CHX that are close to the surface and TBA appears after. The TOL gives us a HOP value equal to 23.10 which indicates a local heterogeneity. Similarly, CHX's HOP is 22.66 which also shows spatial heterogeneity in the carbon nanotube. The TBA exhibits a high degree of heterogeneity compared to the two substances with an HOP of 24. Therefore, TBA in hydrophobic confinement is more inhomogeneous than TOL and CHX. In hydrophilic confinement, the HOP of CHX, TBA and TOL is 29.48, 29.29 and 29.11, respectively. This indicates a strong heterogeneous liquids under nanoscale confinement. Then, these heterogeneities could be explained by the confinement effect that induces by the surface-to-volume ratio.

b) TBA mixtures

The binary TOL/TBA mixture confined to the hydrophobic nanopore highlights a demixing behavior near the surface of the confinement. Snapshots show that the local formation of small nano-phases are present in both cases that is in line with heterogeneous mixtures. In hydrophobic confinement, the HOP of TBA and TOL are 25.15 and 25.18, respectively; these are significantly higher than 15.74 (homogeneous liquid) which highlights a strong heterogeneous distribution of TBA and TOL molecules in the mixture. Both components are heterogeneous in the mixture while at the same TBA concentration in bulk phase we showed that they are homogeneous. This is probably due to the confinement effect which tends to arrange molecules in layers from the confining surface and it keeps them away from their bulk behavior. In the hydrophilic confine-128 Chapter 4 Ilham Essafri

Microstructure of binary mixtures in bulk and nanoconfined phases ment, TOL is more heterogeneous than the TBA with a value of 29.66 while the TBA shows a value of 21.42. This may be due to the creation of strong interactions with the wall surface.

However, TOL is less heterogeneous in comparison with TOL in hydrophobic confinement.

In the case of CHX/TBA binary mixture confined within hydrophilic confinement, it showed local demixing behavior near the wall surface. The TBAs at the interface separate from the CHX molecules (see Fig. 4.10 (d)) which may result from the creation of small nanophases leading to strong heterogeneities. This was attributed to the perturbation of the wall surface on interfacial

TBAs. The HOP of CHX is 30.60 while TBA is 20.41 which points out a strong heterogeneity.

The closeness of TBA to the confining surface leads to significant local heterogeneity in CHX molecules which is organized in three layers. In addition, the preferential orientation of TBA molecules near the wall surface causes a spatial heterogeneity recorded in the HOP. The preference of TBA to self-orientate near the confining surface is affected by strong interactions that occur. Although, the perturbation of its bulk identity produce a strong internal disturbance. In the case of the hydrophobic confinement, there are non-local demixing behavior showed. We have both components at the surface with the formation of small nanophases which could generates spatial heterogeneities in the mixture. For CHX, the HOP is equal to 19.77 while the TBA is 22.78. Indeed, we note that both CHX and TBA are heterogeneous under nanoscale hydrophobic confinement. TOL and CHX are non-polar, non H-bonding van der Waals molecules that present no specific interaction with the WNT, no special intermediate range order in the liquids state.

While TBA is polar and provide hydrogen bonds type interaction which could interacts strongly with the surface. These two different interactions could be responsible for both mixtures showing high and low heterogeneity.

Hydrogen bonds number

The change in behavior of the TOL/TBA and CHX/TBA binary mixtures has been attributed to the chemistry of the wall surface. This elucidates the creation of hydrophobic type interactions with the CNT in TOL and in CHX liquids while a creation of hydrogen bond interaction between the WNT and TBAs were predicted.

Confinement effect on clustering phenomenon

As discussed previously, cluster number size is calculated by the modified Stoddard algorithm based on HBs criteria. According to our results, there are strong HBs dilution of TBA molecules in the hydrophilic surface while in hydrophobic pore the HBs are preserved in average. Figure 4.17 reports the comparison of TBA cluster (see Fig. 4.16 (a)) number as pure liquid in bulk and in confined media: WNT and CNT. In this figure, we can see that in the water nanotube there are more monomers than other n-mers (dimers, trimers, etc.). In this figure the number of TBA clusters in the bulk phase is compared to those restricted to the hydrophilic or hydrophobic matrix. Hydrophilic confinement generates more monomer than dimers, trimers and tetramers or pentamers in binary mixtures as well as in the pure state. In comparison with hydrophobic confinement, the number of clusters reveals the creation of larger clusters around 22 molecules and there are less monomers. This corroborates our hypotheses. As expected, TBA loses its self-associating power through hydrogen bonding in the carbon nanotube as it loses half of its hydrogen bonds by forming a bond with the surface of the water nanotube (very strong interaction). Such interaction with the surface is the major factor in the phase separation created at the surface.

Pore size effect

By decreasing the pore size, we can evaluate the impact of confinement size on local demixing and determine whether microphase separation can be produced at the nanoscale. The binary mixtures of TOL/TBA and CHX/TBA and their pure states are confined in a water nanotube that has a radius of 1nm and a carbon nanotube that has a radius of 1.15nm. nanotube surface which attracts more TBA molecules than TOL. So one may wonder why there is not a higher concentration of TBA in the water nanotube such as the carbon nanotube since water attracts more TBA to the surface? The answer lies in TBA's identity.

As previously shown in the bulk phase, TBA at any concentration promotes the creation of molecular aggregates that are approximately 3.8 molecules in size on average per aggregate. This behavior is expected to coexist in carbon nanotubes, which may explain the high concentration of TBA. Under hydrophobic confinement, the TBA has only weak interaction with the surface and therefore the TBA preserves its molecular aggregates properly. In hydrophilic confinement, TBA interacts strongly with the surface (this is given by the high density of OH at a very short distance from the surface) which could affect its self-organizing powers within the water nanotube.

In To understand the origin of these two nanostructures captured in the two binary mixtures in the hydrophilic confinement, the atomic density along the pore radius will be explored. The radial Microstructure of binary mixtures in bulk and nanoconfined phases previously. To characterize the interaction with the confining surface, the radial profile of the number of hydrogen bonds between TBA-Water molecules are shown in Figure 4. 22 (c-d). Interestingly, between 15 and 20 Å for both mixtures a hydrogen bond interaction is captured between the TBA and the confining water surface. The CHX/TBA in hydrophilic confinement showed a microphase separation where TBA are adsorbed on the surface and the CHX is in the center of the nanopore as exhibited by the radial density profile. From Figure 4.22 (c), we observe no hydrogen bond in the center of the nanopore that confirms the absence of TBA molecules in the center of the nanopore, but near the surface, we have found that TBA creates two hydrogen bond interactions, one with the water surface and one between its molecules. Figure 4. 22 (d) shows the profile of the nHB of TBA-TBA and TBA-water in the TOL/TBA mixture. In this figure, two peaks can be observed: the first is located at 1 Å and the second at 6.5 Å. This shows that the TBA molecules are connected to each other through the hydrogen bond within the nanopore.

Hydrogen bond

Interestingly, there is also a creation of a hydrogen bond with the confining surface at 9.5 Å.

All this shows that the microphase-separation is probably due to the creation of hydrogen bonding of TBA with the surface as shown previously. Size effect could be considered a key factor for the creation of microphase-separation at the nanoscale since it has not previously been observed with a larger pore size where one is only able to create local demixtion.

Tuning liquid-solid interactions

As previously reported recent experimental works suggested that the confinement into a cylindrical nanopore induced the microphase separation of a binary liquid, despite the miscible character of its bulk counterpart. A core-shell organization was evidenced such that one of the liquids was strongly anchored to the solid surface whereas the other one was confined at the center of the pore. At the same time, we showed in the previous sections a strong heterogeneity and the absence of core-shell organization. In this part, we refine the solid-liquid interactions to reproduce qualitatively the experimental adsorption isotherms of both single liquids as well as the microphase separation and capture the core-shell structure.

Chapter 4 Ilham Essafri

Force field refinement

To be in line with experiment, the confining medium corresponds to a cylindrical silica nanopore of radius of 24 Å. To reproduce the adsorption isotherms of the pure components the solid-liquid interactions were refined. The OPLS force field was used to model the TOL and TBA molecules as previous. Indeed, it was shown that the thermodynamic properties of TBA/TOL mixtures were closely reproduced from the OPLS model [45]. Whereas the intramolecular contributions (bonds, bending, and dihedral angles) were conserved as original, the partial charges were calculated using ab-initio calculations. Silica material was modeled by considering the ClayFF force field [46]. To refine the LJ parameters ruling the solid-liquid interactions, we began to predict the adsorption isotherm by considering the initial force fields.

Concerning the TBA adsorption through nanoporous silica, Fig. 4.23 shows a qualitative of F is that every partial derivative must be zero [47]. Optimized LJ parameters are provided in We have studied 7 compositions of TOL/TBA (x TBA =0, 0.24, 0.49, 0.51, 0.71, 0.83, 1.0). As shown in Figure 4.24 (b), for both pure components, a layering structure was observed due to the confinement effect at the nanometric scale [7]. Whereas three layers are observed for both cases, the interfacial TBA layer seems closer to the silica surface suggesting that the attractive interactions between the silica nanopore and TBA molecules are stronger. As shown in Figure 4.25 the hydroxide groups (OH) of the TBA molecules point towards the silica surface. The driving force of this interfacial anchoring is probably the result of the strong hydrogen bonding (HB) network between porous silica and TBA molecules. This point will be discussed later.

Interestingly, as shown in The formation of a first TBA layer anchored at the silica surface is induced by the strong hydrogen bonds between the silanol groups SiOH of the silica material and the OH groups of the TBA molecules. Indeed, hydrogen bonds number were computed by considering a geometrical criterium based on the quantum consideration [48] where two molecules are chosen as being hydrogen bonded only if their inter-oxygen distance is less than 3.5 Å, and simultaneously the oxygen-hydrogen is less than 2.5 Å. The profile of the hydrogen bonds number (nHB) per The insets illustrate the core-shell organization, the TBA (red color) close to the surface and the TBA/TOL (TOL is blue colored) mixture at the center of pore; from 0.83 to 0.24 the width of the interfacial layer decreases, whereas the concentration in TBA decreases at the center of pore. molecule was then reported in Figure 4.28 (b) for x TBA =0.24. As shown in Figure 4.28 (b) a peak of nHB was observed close to the silica surface beyond the bulk value. As observed in Figure 4. 28 (b) this peak is the result of two contributions, the hydrogen bonds (HB) between silica wall and the OH groups of TBA and HB between TBA molecules. That highlights a strong hydrogen bonding network between TBA and silica material that is at the origin of the core-shell organization.

To ensure this hypothesis, MD simulations through a weakly hydrophilic silica nanopore (WH) was carried out. mixture at the centre of pore. These results indicate that the highly hydrophilic surface induces a microphase separation of TBA/TOL mixture and could also suggest that a hydrophobic surface is not able to discriminate TBA and TOL molecules because TOL is fully hydrophobic.

However, Figure 4. 30 (d) shows that a carbon nanotube (CNT) is also capable to separate TBA and TOL by forming a core-shell structure such that TOL and TBA molecules are respectively preferentially located at the CNT surface and at the centre of pore. As shown in Figure 4.31 this separation is the result of a commensurate organization due to stacking interactions between benzenic cycles of CNT and TOL molecules. To go a little further, the curvature effect was also investigated. Indeed, as often shown the curvature induced by the cylindrical geometry can drastically impacted the physical properties in relation to the slitlike confinement [19,20]. We carried out then MD simulation of a TBA/TOL mixture with a TBA concentration of x TBA =0.5 confined through two silica slitlike pores such that the confinement in term of confined volume was conserved (two silica walls separated by a distance of 24 Å as illustrated in Figure 4.32 (a)).

As observed in Figure 4.32 (b) segregation between both liquids is observed highlighting that the separation is rather ruled by the interactions between the silica surface and TBA than the Chapter 4 Ilham Essafri [49], that the core-shell organization was also observed with a pore radius of 43 Å. Therefore, the solid-liquid interactions and more especially the solid-liquid hydrogen bonds seem to overcome the bulk ones whatever the pore diameter leading to the microphase separation and the core-shell structure.

Eventually, by comparing the structures obtained from the silica nanotube and from the CNT material (smoothness nanopore) we show that the core shell organization is independent of the surface roughness. Although, the core-shell structure is indirectly correlated to the capillary condensation the main mechanism is related to the wetting on the silica surface and then to the interfacial interactions between TBA/TOL and the SiOH. Therefore the microphase separation at the nanoscale cannot be related to any putative de-wetting phenomenon, nor could it be understood by considering solely the capillary condensation of the gas. Indeed, a vision of the intermolecular interactions and then the strength of wetting is needed to capture the origin of the microphase, what was performed in this work.

Conclusion

We have investigated the microscopic structure of TOL, TBA and CHX and their mixtures inside 2nm and 1nm pore size of CNT and WNT using MD simulations. We examined the confinement type dependency of these mixtures and their local properties. For both confinements, we found that molecules are arranged into layers, but showed different affinities near the wall surfaces. In the case of hydrophobic confinement, TOL displayed a very strong affinity to the wall surface in CNT better than TBA molecules. However, we observed the opposite in a completely hydrophilic confinement. TOL has showed a very strong affinity with the wall surface in CNT better than TBA molecules in the case of a hydrophobic confinement. However, in a totally hydrophilic confinement, we observed the inverse. These data suggest that the wall surface chemistry influences such molecules ' preferential layered organization near the surface.

We also found at this stage that the form of confinement affects the fluid organization within these nanopores. In the case of hydrophilic confinement, alcohol molecules are more attracted to the confining surface, whereas hydrophobic confinement is the hydrocarbons that prefer to be present in large quantities beside the surface. By tuning the surface chemistry of the nanopore Chapter 4 Ilham Essafri to mimic hydrophilic and hydrophobic confinement, we show that it is possible to control the structural characteristics of the core-shell structure.The molecular origin of the microphase separation is then ascribed to the strong hydrogen bonds and a commensurate arrangement between the confining material and both liquids. In this work, the TOL/TBA mixture that is homogenous in the bulk liquid phase was confined at the nanoscale into cylindrical pores. We showed that the nano-confinement can induce, under a few conditions, microphase separation of binary mixture with a core-shell organization in line with Neutron scattering experiments. Phase separation was evidenced by highlighting both liquid-liquid and liquid-solid interfaces by means of the profiles of the density of centre of mass and the local surface tension. By computing the radial profile of the hydrogen bonds number and by tuning the hydrophilicity of the surface of the silica nanopore we established that the phase separation was ruled at the molecular scale by the strong hydrogen bonds between TBA molecules and the silica material that favors the HB anchoring. Confinement through a carbon nanotube showed an inverse core-shell structure with TOL anchored at the solid surface highlighting an hydrophobic anchoring due to a commensurate organization implying the benzenic cycles stacking. These results shed light on the possibility to control the nanostructure of multicomponent fluids under confinement at the nanoscale by tuning the surface chemistry of nanopore. The nanoconfined phase separation seems to be independent to the pore size and is essentially connected to the strength of pore-fluid interactions.

As shown in Figure 4.29 (a) the microphase separation has not been established from a weakly hydrophilic pore whereas the core-shell structure was also recovered from a hydrophobic matrix (CNT) highlighting that the phase separation is unambiguously connected to the liquid-solid interactions. Determination of a theoretical model predicting the phase separation as a function of the strength of the solid-liquid interactions could be possible by tuning progressively (thermodynamic integration) the pore liquid interactions (Lennard-jones parameters and partial charges). However, it will be difficult to connect this model with the realistic materials where the interactions are too complexes. We think, that the so-developed strategy consisting in the refining of the pore-wall interactions by a comparison with experiment is probably the most relevant approach. Qualitatively, the microphase separation can be then predicted if one considers a mixture of an amphiphilic component and a hydrophobic one confined in pure hydrophilic 150 Chapter 4 Ilham Essafri

Microstructure of binary mixtures in bulk and nanoconfined phases and hydrophobic pores. Although the development of a theoretical model to predict the phase separation in a nanoconfined pore seems to be difficult to connect with realistic materials it is possible to predict the optimal conditions to observe the core-shell organization that means the maximal number of TBA molecules anchored at the surface.

Indeed the pore volume can be calculated as V pore = ⇡R 2 pore L z where R pore is the pore radius of the nanopore while L z is the height of the nanotube, the volume of the core region is V core = ⇡R 2 core L z such that R core is the radius of the core region. The volume of the interfacial zone, i.e., the shell can be then evaluated as

V pore = ⇡(R 2 pore R 2 core )L z such that R core = R pore e shell
with e shell corresponding to the thickness of the interfacial shell. e shell is computed from the density profile. From the density profiles calculations, we found that e shell =4 Å. If we consider the bulk density as the interfacial density the number of TBA molecules interfacially anchored can be calculated as N TBA,s = V shell .⇢ TBA,bulk . With R pore =12 Å and e shell =4 Å an interfacial saturation of N TBA,s = 57 was predicted. Therefore, for the TBA molar fraction corresponding to a number of TBA molecules less than N TBA,s the TBA will be fully anchored and a full core-shell organization will be observed (i.e., x TBA =0.71, 0.49 and 0.24). Beyond N TBA,s , TBA molecules will be also located in the centre of pore and in the intermediary layer. From simulations, we found that the solid interface is saturated for N TBA,s =56 molecules that bears out our previous structural model. In Eventually, the microphase separation raises exiting questions about its impact on the molecular dynamics and the liquid flow in nanochannel, as suggested by the recent report on multiple glassy dynamics [50]. Further insight about this aspect could be attained from ongoing experimental spectroscopy and molecular simulation studies.

Chapter 4 Ilham Essafri

Chapter 5

Summary and future research

Summary of the current work

The investigations conducted in the present thesis were intended to provide insight into the hydrogen bonding (HB) network at the nanoscale. Liquid-forming hydrogen bonding, linear and branched chain alcohols were investigated and mixed with apolar molecules (toluene and cyclohexane) to study the dilution of the HB network. The structure and dynamics of these binary mixtures have been then studied.

This work has focused on the exploration at the nanoscale of the non-ideality of methanol, ethanol, propanol, butanol, pentanol and tert-butanol in mixtures with toluene and cyclohexane by means of molecular dynamics simulations. Simulations fairly reproduced the experimental densities of all binary mixtures even at the miscibility region of methanol-cyclohexane binary mixtures. In all mixtures, the deviation from the ideal mixture behavior was observed and different intensities were recorded. In the case of toluene this non-ideality have been ascribed with the specific interactions between toluene and alcohol leading to a breaking in the hydrogen-bonding network involving clusters of different sizes and the spatial heterogeneity. Particularly, the immiscibility and the non-ideality (negative excess density) of the CHX-MeOH mixtures were the result of the unfavorable interactions between CHX and MeOH leading to a self-organizing of CHX molecules to form hydrophobic nano-phases at the origin of the structural heterogeneity in the miscible region. However, the non-ideality showed by ethanol, propanol, butanol, pen-tanol and tert-butanol (negative excess density except for low EtOH concentration) have been attributed to the hydrophobic character of CHX molecules with alcohols ones and the creation of largest clusters in comparison with alcohols in TOL. A strong dilution of the hydrogen bonding network by toluene molecules as well as cyclohexane molecules has been shown. Nanophases have been characterized in terms of pockets of linear clusters such that the difference in miscibility and in heterogeneity were understood in terms of cluster size and distribution for methanol-toluene and methanol-cyclohexane mixtures. Moreover, we have shown that the presence of clusters had to be uncorrelated from the notion of heterogeneity. Eventually, we have highlighted that the prepeak observed in the structure factor is independent of the degree of heterogeneity but is rather connected to the presence of cyclic clusters. Additionally, the dynamics of these liquids were in line with the structural results given that a fast motion with a rapid relaxation times were shown by alcohol molecules in mixture with TOL whereas a slow motion with a long relaxation times of alcohols in CHX were captured. The results of this part allow us to differentiate between the intensity of the self-organization of liquids at their hydrogen bonding networks while distinguishing between ideal and non-ideal mixture in terms of microscopic local structuring.

Toluene/tert-butanol and cyclohexane/tert-butanol were studied under nanoscale confinement. This systems choice is based on recent experimental observation where a micro-phase separation of toluene/tert-butanol miscible binary mixture were attributed to the hydrogen bonds interaction created between the alcohol molecules and the confining wall surface. Such binary liquids are miscible at any concentration and homogeneous on a microscopic scale. Confined toluene/tert-butanol mixture behavior within the MCM-41 silica cylindrical nanopore illustrated a clear spatial heterogeneity leading to the formation of nano-phases (segregation). While the confinement of the same mixture under a totally hydrophilic matrix as our nanopore prototype called a water nanotube, the behavior is different where local de-mixing behavior is captured near the wall surface. This was attributed to the creation of hydrogen bonds interactions between water molecules on the surface and tert-butanol molecules at the interface. However, toluene/tert-butanol has also been studied in the hydrophobic nanopore, the carbon nanotube.

A hydrophobic local de-mixing was highlighted for toluene/tert-butanol near the wall surface that is attributed to the hydrophobic anchoring of toluene molecules on the confining surface.

Chapter 5 Ilham Essafri

Interestingly, no de-mixing behavior was observed for cyclohexane/tert-butanol mixture within the carbon nanotube, which is a barely predictable because there is no favorable interactions between the confining surface and cyclohexane molecules. In the hydrophilic water nanotube, cyclohexane/tert-butanol mixture for the first time showed a local hydrophilic de-mixing near the wall surface. That was attributed to the hydrogen bonds interactions with tert-butanol and water molecules at the interface. At this point, the pore size effect was also explored. The results mentioned previously were obtained for a radius(size pore)=2nm. In a carbon nanotube of 1.15 nm pore size, the toluene/tert-butanol mixture has again shown de-mixing behavior even if the pore size is decreased. However, cyclohexane/tert-butanol has always indicated that there is no hydrophobic de-mixing behavior. In the water nanotube, there are significant differences in behavior once the pore size is reduced. In the water nanotube at 1nm pore size, toluene/tert-butanol mixture showed a strong hydrophilic de-mixing behavior. While cyclohexane/tert-butanol revealed a micro-phase separation under the hydrophilic nanopore (water nanotube). So far, no core-shell organization has been observed for the two mixtures confined in the three types of confinement. At such a point, we decided to study the adsorption isotherms of toluene/tert-butanol liquid mixture in order to quantify the surface interactions with the silica cylindrical nanopore (MCM-41). Finally, by improving the solid-liquid interactions, we are able to qualitatively reproduce the experimental adsorption isotherms of both single liquids, the micro-phase separation and the core-shell structure. The tuning of the surface chemistry of the nanopore in order to model the hydrophilic and hydrophobic confinement has shown that it is possible to control the structural characteristics of the core shell structure. The molecular origin of the micro-phase separation is then ascribed to the strong hydrogen bonds and a commensurate arrangement between the confining material and both liquids.

Future research

As an extension of this research, it could be more complementary to study other binary miscible liquids within hydrophilic and hydrophobic nano-pores as well as their transport inside nanochannels. It is interesting to correlate the structure to the dynamics of liquids at this scale. In addition to that, the study of filling processes by imbibition in order to evaluate the impact of 160 Chapter 5 Ilham Essafri empirical relaxation function, given that it allows gauging in a simple way deviations from the 'canonical' single exponential behavior by means of parameter K .

A.9 Mean square displacement (MSD)

A.9.1 Definition

The mean square displacement of atoms in a simulation can be easily computed by its definition:

MSD = D |r(t) r(0)| 2 E (A.10)
where h• • • i denotes here averaging over all the atoms (or all the atoms in a given subclass). Care must be taken to avoid considering the 'jumps' of particles to refold them into the box when using periodic boundary conditions as contributing to diffusion.

The MSD contains information on the atomic diffusivity. If the system is solid, MSD saturates to a finite value, while if the system is liquid, MSD grows linearly with time. In this case it is useful to characterize the system behavior in terms of the slope, which is the diffusion coefficient • La première partie se concentre sur l'étude des liquides binaires en phase Bulk : l'objectif de cette partie est de décrire correctement la structure des mélanges liquides ainsi que leurs propriétés physiques et d'en établir un lien. De plus, cette partie permettra aussi de valider les champs de forces utilisé, donc l'idée c'est d'avoir une référence « phase Bulk » afin de mieux appréhender les modifications en « phase confinée ».

• La 2 ème partie concerne l'étude des mélanges binaires en phase confinée: l'objectif est d'étudier la structuration de ces mélanges sous confinement nanométrique et de répondre à la question de l'auto-organisation de ces mélanges à l'échelle nanométrique.

II. Microstructure des mélanges liquides binaires de méthanol non idéal Onze fractions molaires en MeOH (x MeOH ) ont été étudiées {0, 0,1, 0,2, 0,3, 0,4, 0,5, 0,6, 0,7, 0,8, 0,9, 1}.

Résultats de la Phase Bulk

Nous rapportons sur la figure 1 De x TBA = 0,24 à 0,83, la figure 4 (de la figure 4a-d) montre que les molécules de TBA ont été adsorbées près de l'interface constituant une première couche, alors que les molécules de toluène sont situées juste après. Pour x TBA = 0,83, les deuxième et troisième couches correspondent à une phase de mélange homogène rappelant le milieu en Bulk. De manière très intéressante, la figure 4 met en évidence le développement progressif de deux phases à mesure que la concentration de TBA diminue. En effet, pour x TBA = 0,71, les molécules TBA sont presque uniquement localisées à proximité de la surface de la silice dans la première couche adsorbée sans molécules de TOL.

Pour x TBA = 0,49 qui correspond à la concentration où l'organisation noyau-coquille a été observée expérimentalement, la séparation en micro-phase est presque complète. Il est intéressant de noter que la distance entre les pics de TOL et de TBA semble diminuer en fonction de la diminution de la fraction molaire de TBA. En effet, alors que sur la figure 4a

Discussion

Dans ce travail, nous avons montré que le nano-confinement peut induire, dans quelques conditions, une séparation en micro-phase du mélange binaire avec une organisation noyau-coquille conforme aux expériences de diffusion neutronique.

3. 1

 1 Simulated and experimental self-diffusion coefficient of pure liquids in 10 9 m 2 /s at T=300K and P=1 Bar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.1 Crossed Lennard-Jones parameters. CH3 is the carbon of the methyl groups of toluene, CH the carbon of the CH groups of toluene, and C the carbon without hydrogen atoms in toluene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 List of Figures 2.1 Timeline of numerical studies conducted between 1967 and 2013. . . . . . . . . . 2.2 Two dimensional Periodic Boundary Conditions scheme for a cubic box. The simulation box is indexed 1 while the image boxes are indexed 2, 3, 4, 5, 6, 7, 8 and 9. When an atom leaves the boundaries of the cell (1 ! 2) its image in the opposite image cell enters the cell (3 ! 1). . . . . . . . . . . . . . . . . . . . . . . 2.3 Profile of the Lennard-Jones potential. . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Schematic representation of the Ewald method of constructing the periodic cell network, [26]. A) Ewald sum replicated the simulation box to convergence, B)Radial cutoff methods to reach convergence for the larger systems. . . . . . . . . . . . . 2.5 The elements of Ewald's summation of a one-dimensional system. The Gaussian is normalized by unit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Description of intra and inter-atomic interactions in a force field. . . . . . . . . . 2.7 Schematic representation of carbon nanotube (CNT), the silica cylinrical nanopore (MCM-41) and the water nanocavity (WNC) used in this work. . . . . . . . . . . 3.1 Simulated and experimental density (a) and the excess density (b) of the CHX-MeOH and TOL-MeOH mixtures as a function of x MeOH at 300 K and 1 bar. The uncertainties about the density are too small to be represented. (c) Snapshots of binary mixture at x MeOH = 0.1, 0.5, and 0.9 such that methanol is represented in red, and CHX is represented in cyan. . . . . . . . . . . . . . . . . . . 3.2 a) Profiles of the total pressure along the z direction for three methanol concentrations of CHX/MeOH mixtures and for water at 1bar and 300K. . . . . . . . . 3.3 Simulated and experimental densities of a) TOL/EtOH + CHX/EtOH, b) TOL/PrOH + CHX/PrOH and c) TOL/BuOH + CHX/BuOH and d) TOL/PeOH + CHX/PeOH as a function of x Alcohol at 300K and 1 bar. . . . . . . . . . . . . . . . . . . . . . 3.4 Simulated density of TOL/TBA and CHX/TBA as a function of x TBA at 300K and 1 bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 The excess densities of a) TOL/EtOH + CHX/EtOH, b) TOL/PrOH + CHX/PrOH and c) TOL/BuOH + CHX/BuOH and d) TOL/PeOH + CHX/PeOH as a function of x Alcohol at 300K and 1 bar. . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Excess density of TOL/TBA and CHX/TBA mixtures as a function of x TBA at 300K and 1 bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Snapshot of the CHX-MeOH mixture at x MeOH = 0.2. . . . . . . . . . . . . . . . 3.8 HOP as a function of the molar fraction in MeOH for both CHX-MeOH and TOL-MeOH mixtures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 Snapshot structure of Ethanol, Propanol, Butanol and Pentanol with Toluene at x Alcohol =[0.1,0.3,0.5]. Red and cyan colours describe alcohols and Toluene molecules, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.10 Snapshot structure of Ethanol, Propanol, Butanol and Pentanol with Cyclohexane at x Alcohol =[0.1,0.3,0.5]. Blue and cyan colours describe alcohols and Cyclohexane molecules, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11 Heterogeneity order parameter of binary mixture with toluene and cyclohexane as a function of alcohol concentration: a) for TOL/EtOH + CHX/EtOH, b) for TOL/PrOH + CHX/PrOH, c) for TOL/BuOH + CHX/BuOH and d) for TOL/PEOH + CHX/PeOH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.12 Snapshot of the TOL-TBA mixture at a) x TBA =0.2, b) x TBA =0.5 and c) x TBA =0.8 and CHX-TBA mixture at a) x TBA =0.2, b) x TBA =0.5 and c) x TBA =0.8. The same notation of Figure 3.7 is used. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.13 HOP as a function of the molar fraction in TBA for both CHX-TBA and TOL-TBA mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.14 Radial distribution functions between centers of mass of the aprotic component for both CHX-MeOH (a) and (b) TOL-MeOH mixtures. The vertical dashed line represents the position of the first peak. . . . . . . . . . . . . . . . . . . . . . 3.15 Radial distribution functions between centers of mass of aprotic component and methanol for both CHX-MeOH (a) and TOL-MeOH (b) mixtures in the miscible regions. The dashed circles highlights the peaks located around 3.5 Å. . . . . 3.16 Radial distribution functions between the center of mass of the aprotic molecules and the hydrogen atoms of OH (HOC) and CH 3 (H 3 C) groups of methanol for x MeOH = 0.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.17 Radial distribution functions between centers of mass of the aprotic component for both (a) CHX-EtOH and (b) TOL-EtOH mixtures, (c) CHX-PrOH and (d) TOL-PrOH mixtures, (e) CHX-BuOH and (f) TOL-BuOH mixtures and (a) CHX-PeOH and (b) TOL-PeOH mixtures. The vertical dashed line represents the position of the first peak. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.18 Radial distribution functions between centers of mass of the aprotic component and alcohols for (a) CHX-EtOH and (b) TOL-EtOH mixtures, (c) CHX-PrOH and (d) TOL-PrOH mixtures, (e) CHX-BuOH and (f) TOL-BuOH mixtures and (a) CHX-PeOH and (b) TOL-PeOH mixtures. The vertical dashed line represents the position of the first peak and the dashed circles highlights the shoulder position. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.19 Radial distribution functions between centers of mass of the aprotic component for both CHX-TBA (a) and (b) TOL-TBA mixtures. The vertical dashed line represents the position of the first peak. . . . . . . . . . . . . . . . . . . . . . . . 3.20 Radial distribution functions between centers of mass of aprotic component and tert-btanol (TBA) for both CHX-TBA (a) and TOL-TBA (b) mixtures. The vertical dashed line represents the position of the first peak. . . . . . . . . . . . 3.21 (a) nHB per methanol molecule as a function of the methanol concentration. (b) KBIs as a function of the methanol concentration for both TOL-MeOH and CHX-MeOH mixtures. In panel (b) the right axis corresponds to the MeOH-MeOH KBI for the CHX-MeOH mixture. . . . . . . . . . . . . . . . . . . . . . . Chapter 0 Ilham Essafri Microstructure of binary mixtures in bulk and nanoconfined phases 3.22 Number of the hydrogen bonds per alcohol molecule in a) EtOH/TOL, EtOH/CHX, b) PrOH/TOL, PrOH/CHX, c) BuOH/TOL, BuOH/CHX and d) PeOH/TOL, PeOH/CHX as a function of alcohol concentration.. . . . . . . . . . . . . . . . . . 3.23 nHB per TBA molecule as a function of the TBA concentration. . . . . . . . . . 3.24 Radial distribution function of center of mass of the Aromatic part of Toluene molecules and the hydroxyl part of the alcohol (HOC): EtOH, PrOH, BuOH and PeOH as a function of alcohol concentration. . . . . . . . . . . . . . . . . . . 3.25 Cluster size probability as a function of the MeOH concentration in logarithmic scale in both TOL-MeOH (a) and CHX-MeOH (b). . . . . . . . . . . . . . . . . . 3.26 Illustrations of opened and closed clusters highlighted with the yellow solid lines. Red and cyan correspond to the oxygen atoms and methyl groups, respectively. . 3.27 Cluster number as a function of the MeOH concentration for the dimers, trimers, tetramers, and pentamers in both TOL-MeOH (a) and CHX-MeOH (b). (c) Number of higher clusters for both TOL-MeOH and CHX-MeOH mixtures. . . . 3.28 Cluster number as a function of the EtOH concentration for monomers, dimers, trimers, tetramers, and pentamers in (a) TOL/EtOH and CHX/EtOH, (b) TOL/PrOH and CHX/PrOH, (c) TOL/BuOH and CHX/BuOH and (d) TOL/PeOH and CHX-PeOH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.29 Representative cluster of TBA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.30 Cluster number as a function of the TBA concentration for the monomers, dimers, trimers, tetramers, and pentamers in both TOL-TBA (a) and CHX-TBA (b). . . 3.31 Total structure factor of the TOL-MeOH (a) and CHX-MeOH (b) mixtures as a function of methanol concentration. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.32 Partial structure factor of the oxygen atom of the OH group of methanol, ethanol, and tert-butanol liquids at 1 bar and 300 K. . . . . . . . . . . . . . . . . . . . . . 3.33 Self-diffusion coefficients for a) TOL,CHX) +EtOH, b) TOL,CHX) +PrOH, c) TOL,CHX) +BuOH and d) TOL,CHX) +PeOH. . . . . . . . . . . . . . . . . . . 3.34 Self-diffusion coefficients for TOL/TBA and CHX/TBA mixtures. . . . . . . . . . 3.35 Evolution of the dipole moment autocorrelation function with composition in a) EtOH/TOL, b) EtOH/CHX, c) PrOH/TOL, d) PrOH/CHX, e) BuOH/TOL, f) BuOH/CHX, g) PeOH/TOL and h) PeOH/CHX. . . . . . . . . . . . . . . . . . . 3.36 Evolution of the dipole moment autocorrelation function with composition in a) TBA/TOL, b) TBA/CHX. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.37 Variation of relaxation times in a) EtOH/TOL + EtOH+CHX, b) PrOH/TOL + PrOH/CHX, c) BuOH/TOL + BuOH/CHX and d) PeOH/TOL + PeOH/CHX as a function of alcohol concentration. . . . . . . . . . . . . . . . . . . . . . . . . 3.38 Variation of relaxation times in TBA/TOL + TBA/CHX as a function of TBA concentration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 (a) Partial structure factors of hydrogen atoms of OH groups of TBA, SHO of pure liquids and of TBA/TOL mixture with a TBA/TOL molar fraction composition of 56/44% at 298 K and 1 bar in the confined and bulk phases. (b) Profiles of radial density of carbon atoms of TOL, hydrogen atoms of the OH group of TBA and carbon atoms of the methyl group of TBA in the TBA/TOL mixture with a TBA/TOL molar fraction composition of 56/44% . . . . . . . . . . .

  (b) Profiles of radial density of centre of mass of TOL and TBA confined into the silica nanopore with a TBA/TOL molar fraction composition 35/65%. . . . . . . 4.4 Profiles of radial density of centre of mass of hydrogenated (OH) and deuterated (OD) TOL and TBA confined into the silica nanopore with a TBA/TOL molar fraction composition 56/44% and with a deuterated/hydrogenated composition 50/50% for TOL and TBA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 (a) Connolly's surface of confined TBA (red)/TOL(cyan) mixture in the cylindrical nanopore in different directions. (b) Isotherms of adsorption of pure TBA and TOL in the silica framework. (c) Illustration of confined TBA (red)/TOL(cyan) mixture in the cylindrical nanopore for four relative pressures. For clarity, the silica framework is omitted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Illustration of TBA (red)/TOL(cyan) mixture in the bulk phase for a TBA/TOL molar fraction composition 56/44%. . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 a) Radial density profile of pure confined TBA, TOL and CHX within a) Carbon nanotube (CNT) with r= 2nm and b) Water nanotube (CNT) with r= 2nm. 4.8 Illustrations of pure (a)-(d) TBA, (b)-(e) TOL and (c)-(f) CHX confined in CNT and in WNT, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9 Atomic radial density profile of pure TBA (oxygen, hydrogen (HO part) and carbon of (CH 3 ) and TOL (carbon atoms of aromatic ring) and CHX (carbon atoms) confined within CNT (a,c,e) and within WNT (b,d,f), respectively. . . . . 4.10 Radial density profile of TBA/TOL within a) carbon nanotube and b) water nanotube (r=20 Å). a-1) and b-1) are atomic radial profiles of TBA (oxygen, hydrogen (HO part) and carbon of 3CH 3 ) and TOL (carbon atoms of aromatic ring and carbon atoms of methyl group) in hydrophobic and hydrophilic confinement, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.11 Snapshot illustration of TOL/TBA mixture within a) and c) CNT (r=2nm) in axial and radial directions, respectively and b) and d) WNT (r=2nm) in axial and radial directions, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.12 Radial density profile of CHX/TBA within a) carbon nanotube and b) water nanotube (r=20 Å). c) and d) are are atomic radial profiles of TBA (oxygen, hydrogen (HO part) and carbon of 3CH 3 ) and CHX (carbon atoms) in hydrophobic and hydrophilic confinement, respectively. . . . . . . . . . . . . . . . . . . . . 4.13 Snapshots of a) CHX/TBA within CNT and b) CHX/TBA within WNT. . . . . 4.14 Radial hydrogen bond number (nHB) profile of pure and mixed TBA within a) CNT and b) WNT respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.15 Radial hydrogen bond number (nHB) profile of TBA-TBA and TBA-Water in a) TOL/TBA mixture and b) CHX/TBA mixture. . . . . . . . . . . . . . . . . . 4.16 Presentation of molecular aggregates in TBA confined in a nanopore. . . . . . . 4.17 Comparison of the cluster number of pure TBA in Bulk and in confined media. . Chapter 0 Ilham Essafri 4.18 a) Radial density profile of pure confined TBA, TOL and CHX within a) Carbon nanotube (CNT) with r = 1.15 nm and b) Water nanotube (CNT) with r = 1nm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.19 Snapshot observations and radial density profiles of a,b) TOL/TBA confined within carbon nanotube (CNT) with r= 11.5 Å and c,d) CHX/TBA confined within carbon nanotube (CNT) with r= 11.5 Å. . . . . . . . . . . . . . . . . . . . 4.20 Snapshot observations and radial density profiles of a,b) TOL/TBA confined within water nanotube (WNT) with r= 10 Å and c,d) CHX/TBA confined within water nanotube (WNT) with r= 10 Å. . . . . . . . . . . . . . . . . . . . . . . . . 4.21 a) Profile of the radial density of hydrogen and oxygen atoms of hydroxide group (HO) of TBA, and carbon atoms of CHX. b) Profile of the radial density of hydrogen and oxygen atoms of hydroxide group (HO) of TBA, and carbon of benzenic cycle (C aromatic ) and methyl group (CH 3 ) of TOL. . . . . . . . . . . . . . . 4.22 Hydrogen bond number profile of TBA in TOL/TBA a) in CHX/TBA b) within CNT and the Hydrogen bond number profile of TBA in CHX/TBA c) in TOL/TBA d) within WNT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.23 Adsorption isotherm of the TBA/TOL mixture confined in the silica nanopore as a function of the relative pressure such that P 0 is the saturation pressure vapor of TBA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.24 b) Density profiles of the center of mass of pure TBA and TOL confined into the nanoporous silica material obtained at 308 K and 1 bar. . . . . . . . . . . . . 4.25 Density profiles of OH groups, carbon atoms of TBA molecules and SiOH groups in case of x TBA =1.0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.26 Profiles of radial density of the center of mass of TBA and TOL molecules for x TBA = 0.83 (a), 0.71 (b), 0.49 (c), and 0.24 (d). The insets illustrate the coreshell organization, the TBA (red color) close to the surface and the TBA/TOL (TOL is blue colored) mixture at the center of pore; from 0.83 to 0.24 the width of the interfacial layer decreases, whereas the concentration in TBA decreases at the center of pore. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.27 Profiles of radial density of the hydrogen atoms of the OH and CH3 groups of TBA and hydrogen atoms of CH 3 group of TOL for x TBA = 0.83 (a), 0.71 (b), 0.49 (c), and 0.24 (d). The dashed circle represents the interpenetration region of TOL molecules in the interfacial layer. . . . . . . . . . . . . . . . . . . . . . . . 4.28 b) Profiles of the hydrogen bonds number per TBA molecules along the radial direction of the silica cylindrical nanopore. . . . . . . . . . . . . . . . . . . . . . . 4.29 a) Profile of the radial density of center of mass of TBA and TOL molecules confined into the weakly hydrophilic silica nanopore. b) Profile of the radial density of tertiary carbon (C t ), hydrogen atom of hydroxide group (HO) of TBA, and carbon of benzenic cycle (C) and methyl group (CH 3 ) of TOL. . . . . . . . . 4.30 c) Profile of the radial density of TBA and TOL liquids confined into a water nanotube (WNT) with a pore radius of 12 Å. d) Profile of the radial density of TBA and TOL liquids confined into a carbon nanotube (CNT) with a pore radius of 12 Å. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.31 Snapshot illustrating the confinement of TOL molecules in the carbon nanotube of pore radius of 12 Å. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Chapter 0 Ilham Essafri Microstructure of binary mixtures in bulk and nanoconfined phases 4.32 a) Illustration of the confined TOL (cyan color) and TBA (red color) for x TBA = 0.5, between two silica walls separated by a distance of 24 Å. Red and yellow colors correpond to the oxygen and silicon atoms. b) Profile of the axial density of centers of mass of TBA and TOL molecules confined between two silica slabs separated by a distance of 24 Å. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 4.33 Profiles of radial density of the center of mass of TBA and TOL molecules for x TBA = 0.50 for three pore radii (R = 6, 12, and 18 Å) . . . . . . . . . . . . . .

1960s [ 1 ]Figure 2 . 1 :

 121 Figure 2.1: Timeline of numerical studies conducted between 1967 and 2013.

Figure 2 . 2 :

 22 Figure 2.2: Two dimensional Periodic Boundary Conditions scheme for a cubic box. The simulation box is indexed 1 while the image boxes are indexed 2, 3, 4, 5, 6, 7, 8 and 9. When an atom leaves the boundaries of the cell (1 ! 2) its image in the opposite image cell enters the cell (3 ! 1).

Figure 2 . 3 :

 23 Figure 2.3: Profile of the Lennard-Jones potential.

Figure 2 . 4 :

 24 Figure 2.4: Schematic representation of the Ewald method of constructing the periodic cell network, [26]. A) Ewald sum replicated the simulation box to convergence, B)Radial cutoff methods to reach convergence for the larger systems.

Figure 2 . 5 :

 25 Figure 2.5: The elements of Ewald's summation of a one-dimensional system. The Gaussian is normalized by unit.

Figure 2 . 6 :

 26 Figure 2.6: Description of intra and inter-atomic interactions in a force field.

Figure 2 . 7 :

 27 Figure 2.7: Schematic representation of carbon nanotube (CNT), the silica cylinrical nanopore (MCM-41) and the water nanocavity (WNC) used in this work.

Fig. 2 .

 2 Fig. 2.7). The inner surface coverage of silanol groups was about 7.5 nm 2 , which corresponds to highly hydrated protonated silica pore. Armchair CNT of radius (12 and 20) Å with a pore length of 50 Å was modeled by considering the uncharged force field developed by Werder et al.Water nanotube was built by carving a cylindrical nanopore of radius(10, 12 and 20) Å into an equilibrated cubic water box with a length box of 60 Å. Water molecules were modeled by considering the TIP4P/2005 model and were considered as frozen[35].

Figure 3 .Figure 3 . 1 :

 331 Figure 3.1: Simulated and experimental density (a) and the excess density (b) of the CHX-MeOH and TOL-MeOH mixtures as a function of x MeOH at 300 K and 1 bar. The uncertainties about the density are too small to be represented. (c) Snapshots of binary mixture atx MeOH = 0.1, 0.5, and 0.9 such that methanol is represented in red, and CHX is represented in cyan.

Figure 3 .

 3 Figure 3.2: a) Profiles of the total pressure along the z direction for three methanol concentrations of CHX/MeOH mixtures and for water at 1bar and 300K.

Figure 3 .

 3 3 shows us the evolution of the simulated densities as a function of the alcohol concentrations. The uncertainties about the density are too small to be represented. Figures3.3 a-d) shows a good agreement with experimental results for all

3 . 4 .Figure 3 . 3 :

 3433 Figure 3.3: Simulated and experimental densities of a) TOL/EtOH + CHX/EtOH, b) TOL/PrOH + CHX/PrOH and c) TOL/BuOH + CHX/BuOH and d) TOL/PeOH + CHX/PeOH as a function of x Alcohol at 300K and 1 bar.

Figure 3 . 4 :

 34 Figure 3.4: Simulated density of TOL/TBA and CHX/TBA as a function of x TBA at 300K and 1 bar.

3. 3

 3 Non-ideality and structural heterogeneity 3.3.1 Non-ideality 1) Methanol-cyclohexane and methanol-toluene As exhibited in Figure 3.1 (a), the density of the TOL/MeOH mixture presents a monotonic evolution as a function of x MeOH whereas the CHX/MeOH mixture shows a minimum around x MeOH =0.5. Additionally, both mixtures present a deviation of same order of magnitude in relation to the ideal density. Very interestingly, the CHX/MeOH mixture also presents a nonideal behavior in the miscible regions (x MeOH =0.1; 0.9). To quantify this non-ideality, we report in Figure 3.1 (b) the excess density of the mixtures as a function of x MeOH . The excess density was evaluated as the difference between the simulated and the ideal densities. As exhibited in Figure 3.1 (b) the CHX/MeOH and the TOL/MeOH mixtures display a negative and a positive excess density, respectively. Moreover, Figure 3.1 (b) shows that both TOL/MeOH and CHX/MeOH mixtures present a change in monotony of the excess density. Furthermore, in the two miscible and immiscible zones the non-ideality of CHX/MeOH mixture (absolute value of

  3.3 (a), the TOL/EtOH and CHX/EtOH mixtures are presenting strong deviation from ideality behavior.In Figure3.3 (b) we report the density behavior of TOL/PrOH and CHX/PrOH binary systems as a function of x PrOH . Both mixtures present a non-ideality behavior at the whole range concentrations, although the intensity of the observed deviation differs from one mixture to the other. For TOL/PrOH mixtures, there is a small increase in density relative to ideality by varying the propanol concentration from 0.1 to 0.5. Beyond x PrOH =0.5, the density begins to decrease slightly. For CHX-PrOH system, a monotonic deviation is observed. From Figure3.3 (c), the simulated densities of TOL/BuOH and CHX/BuOH mixtures are close to the ideality.Both of these two systems are weakly non-ideal. In Figure3.3 (d), the variation of the density in TOL-PeOH mixture is practically ideal with a slight decrease compared to the ideal density at x PeOH =[0.2, 0.4]. The so-calculated densities in CHX/PeOH systems are not very far from the ideal behavior. The same trend is also observed for the simulated densities with a parabolic shape around ideality.

Figure 3 . 5 :

 35 Figure 3.5: The excess densities of a) TOL/EtOH + CHX/EtOH, b) TOL/PrOH + CHX/PrOH and c) TOL/BuOH + CHX/BuOH and d) TOL/PeOH + CHX/PeOH as a function of x Alcohol at 300K and 1 bar.

  (a)-(d) will be discussed later. For solutions with toluene, such behavior suggests that alcohols form complexes with toluene, i.e toluene molecules probably create strong interactions with alcohol ones, leading to breaking of structuring HB framework created by alcohols molecules. Contrary to positive deviation, Chapter 3 Ilham Essafri 57

3 . 6 .Figure 3 . 6 :

 3636 Figure 3.6: Excess density of TOL/TBA and CHX/TBA mixtures as a function of x TBA at 300K and 1 bar.

Figure 3 . 7 :

 37 Figure 3.7: Snapshot of the CHX-MeOH mixture at x MeOH = 0.2.

Figure 3 . 8 :

 38 Figure 3.8: HOP as a function of the molar fraction in MeOH for both CHX-MeOH and TOL-MeOH mixtures.

Figure 3 .

 3 Figure 3.9 and 3.10 describe the molecular arrangement of CHX/alcohols and TOL/alcohols binary mixtures at x alcohol =[0.1,0.3,0.5]. From Figure 3.10, strong local arrangement was observed for CHX molecules in presence of Ethanol. The local arrangement is defined as the agglomeration of the same type of molecule in the mixture. In the CHX/EtOH mixtures, the high excess densityshowed in Fig.3.5 (a) could be explained from these specific agglomerations. Figures 3.9 depicts that CHX and EtOH molecules do not mix very well and the presence of irregular organization in the mixture was captured. Concerning the TOL/EtOH (Figure3.9) mixture a homogeneous mixture was evidenced with less irregularities as a function of concentration. As shown in Figure3.9 EtOH and TOL form nanophases which are smaller than those of the CHX/EtOH system. Indeed, the resulting microstructure of both mixtures are different and could be responsible of the non-ideality behavior as we discussed previously. PrOH mixtures (Figures 3.9 and 3.10) show less structural inhomogeneities in comparison with EtOH ones (this is viewed by the way that (TOL,CHX) and (EtOH, PrOH) molecules are packed together). The associated tendency of PrOH molecules are favored in presence of CHX molecules rather than TOL which leads to a formation of largest cluster in CHX/PrOH mixture. This suggests that in the case of TOL/PrOH, more molecules highlighted the creation of small clusters. These differences in clustering behavior of both components could be relevant to understand the density deviations observed (Figures3.3 (b) and 3.5 (b)). The structural arrangement of CHX/BuOH and TOL/BuOH binary mixtures is also provided. In these mixtures, we start to observe the influence of the increase of the alkyl chain on the local structure. Indeed, a specific micro-structure is less observed and small clusters are formed in both mixtures in comparison with EtOH and PrOH ones. Regarding to the BuOH mixture, a good distribution of alcohol molecules in the mixture is observed. In CHX/BuOH mixtures, rich regions of CHX molecules are evidenced, while butanol crosses these

Figure 3 . 9 :

 39 Figure 3.9: Snapshot structure of Ethanol, Propanol, Butanol and Pentanol with Toluene at x Alcohol =[0.1,0.3,0.5]. Red and cyan colours describe alcohols and Toluene molecules, respectively.

Figure 3 . 10 :

 310 Figure 3.10: Snapshot structure of Ethanol, Propanol, Butanol and Pentanol with Cyclohexane at x Alcohol =[0.1,0.3,0.5]. Blue and cyan colours describe alcohols and Cyclohexane molecules, respectively.

Figure 3 . 11 :

 311 Figure 3.11: Heterogeneity order parameter of binary mixture with toluene and cyclohexane as a function of alcohol concentration: a) for TOL/EtOH + CHX/EtOH, b) for TOL/PrOH + CHX/PrOH, c) for TOL/BuOH + CHX/BuOH and d) for TOL/PEOH + CHX/PeOH.

  Figure 3.11 (a)-(d) the HOP of all binary mixtures at whole range concentration. First, as it depicted in Fig. 3.11 (a), the HOP of pure EtOH is 14.8 that indicates a Chapter 3 Ilham Essafri homogeneous liquid; when we add CHX, the EtOH molecules begin to show local inhomogeneities,

Figure 3 .

 3 Figure 3.11 (d) shows the HOP of CHX/PeOH and TOL/PeOH binary mixtures as a function of x PeOH . In the case of pure PeOH, the HOP has a small value of HOP = 14.76 < 15.74 which corresponds to a homogeneous liquid. The HOP of PeOH doesn't change in TOL/PeOH mixture, except at x PeOH = 0.4, it becomes heterogeneous. That corroborates the quasi-ideality behavior of the TOL/PeOH mixture at whole range concentration with a minimum excess density atx PeOH = 0.4. This minimum could be attributed to this spatial microstructure. On the other hand, the PeOH in PeOH/CHX mixtures shows a strong heterogeneity with the increase of PeOH quantity in the mixture (x PeOH < 0.6). Indeed, one may argue that CHX favor the persistence of aggregated PeOH molecules at low alcohol concentrations. These organizations in CHX/PeOH could be responsible for the strong deviations showed in the excess density compared to the TOL/PeOH deviations.

Fig 3 . 6 .Figure 3 . 12 :

 36312 Fig 3.6. In order to investigate these structural organization, the HOP parameter was calculated.The Figure3.13 reports the HOP of CHX-TBA and TOL-TBA binary mixtures. Molecules in

3. 4 . 1 Figure 3 . 14 :

 41314 Figure 3.13: HOP as a function of the molar fraction in TBA for both CHX-TBA and TOL-TBA mixtures

  x MeOH =0.1 x MeOH =0.2 x MeOH =0.8 x MeOH =0.9

Figure 3 . 15 :

 315 Figure 3.15: Radial distribution functions between centers of mass of aprotic component and methanol for both CHX-MeOH (a) and TOL-MeOH (b) mixtures in the miscible regions. The dashed circles highlights the peaks located around 3.5 Å.

Figure 3 .

 3 Figure 3.15. As shown in Figure 3.15 (a) the location of the first peak is found around 6 Å

  TOL-H(H 3 C-COH) TOL-H(HOC-CH 3 ) CHX-H(H 3 C-COH) CHX-H(HOC-CH 3 )

Figure 3 . 16 :

 316 Figure 3.16: Radial distribution functions between the center of mass of the aprotic molecules and the hydrogen atoms of OH (HOC) and CH 3 (H 3 C) groups of methanol for x MeOH = 0.9.

, 2 .

 2 67 to 3.45 for CHX-PrOH, 2.67 to 3.33 for CHX-BuOH and 2.67 to 3.07 for CHX-PeOH, however the peak position remains nearly unaltered. All CHX-CHX RDF peaks are sharps and well-defined. From the concentration dependence of the (CHX-CHX) RDFs, a slight increase in the value of the first peak is reported, which is probably an indication of the space filling of the CHX molecules with the addition of alcohols in the mixture. The second peak that is located at 10.8 Å with a smaller dependence in concentration. The alkyl chain effects of alcohols on cyclohexane are shown by a decrease in the intensity of the first peak value from 3.52 to 3.03, from CHX-EtOH to CHX-PeOH mixtures.

Figure 3 . 18 presentsFigure 3 . 17 :Figure 3 . 18 :

 318317318 Figure 3.17: Radial distribution functions between centers of mass of the aprotic component for both (a) CHX-EtOH and (b) TOL-EtOH mixtures, (c) CHX-PrOH and (d) TOL-PrOH mixtures, (e) CHX-BuOH and (f) TOL-BuOH mixtures and (a) CHX-PeOH and (b) TOL-PeOH mixtures. The vertical dashed line represents the position of the first peak. Chapter 3 Ilham Essafri 73

Figure 3 . 19 :

 319 Figure 3.19: Radial distribution functions between centers of mass of the aprotic component for both CHX-TBA (a) and (b) TOL-TBA mixtures. The vertical dashed line represents the position of the first peak.

Figure 3 .

 3 Figure 3.19 reports the RDFs between TOL and CHX molecules as a function of TBA molecules.The CHX-CHX RDFs showed two peaks, one located at 6.1 Å and second located at 10.8 Å. The change in TBA concentration does not affect the peaks positions. For the TOL-TOL RDFs there

Figure 3 . 20 :

 320 Figure 3.20: Radial distribution functions between centers of mass of aprotic component and tert-btanol (TBA) for both CHX-TBA (a) and TOL-TBA (b) mixtures. The vertical dashed line represents the position of the first peak.

Figure 4 .

 4 14 (a) nHB as a function of x MeOH for both mixtures. Concerning the CHX/MeOH mixture, Figure4.14 (a) shows a slight monotonic decrease in nHB because we move from 1.8 to 1.6 whereas a strong diminution is observed in case of the TOL/MeOH mixture that loses 1 hydrogen bond by moving from 1.8 to 0.8. Concerning the CHX/MeOH mixtures, the progressive formation of nanophases allows to conserve the hydrogen bonds number constant during the diluting. Indeed, the MeOH molecules are gathered in clusters, such that the OH groups are hidden from the CHX. In case of the TOL/MeOH mixture, the hydrogen bonding network is broken in favor of the interactions between TOL and MeOH molecules. That could suggest an increase in the dispersed MeOH molecules. This organization could be in line with an increase of small MeOH clusters (monomers and dimers) contrary to the CHX mixture where larger clusters could be favored. The increase in number of monomers and dimers in the TOL/MeOH mixture will be in accordance with the decrease of nHB. To be thorough, the analysis of the molecular interactions through Kirkwood-Buff integrals (KBIs) was carried out for both TOL-MeOH and CHX-MeOH mixtures. KBIs were calculated from corrected RDF calculations by considering the recent development purposed by Kruger and coworkers improving the KBIs'

4. 14 (Figure 3 .

 143 Figure 3.21: (a) nHB per methanol molecule as a function of the methanol concentration. (b) KBIs as a function of the methanol concentration for both TOL-MeOH and CHX-MeOH mixtures. In panel (b) the right axis corresponds to the MeOH-MeOH KBI for the CHX-MeOH mixture.

Figure 4 .

 4 Figure 4.15 (b) in both mixtures. The nHB in CHX-PrOH mixtures decreases from 1.8 to 1.45 while in TOL-PrOH it decreases from 1.8 to 0.7 which highlights a strong dilution of the HB network. The PrOH molecules as EtOH ones depict a strong affinity with TOL molecules rather than CHX molecules. Additionally, the evolution of nHB of BuOH molecules in CHX and TOL was also investigated and reported in Figure 4.15 (c). Very interestingly, the addition of TOL molecules decreases the nHB of BuOH molecules. The nHB of BuOH varies very slowly with the addition of CHX to the mixture, which is illustrated by the fact that there is no disturbance of the HB network of BuOH molecules over the entire concentration range (it varies from 1.8 to 1.5).Figure 4.15 (d) presents the nHB of PeOH molecules in both mixtures as a function of

Figure 4 .

 4 15 (d) presents the nHB of PeOH molecules in both mixtures as a function of PeOH concentration. We observe from Figure 4.15 (d) that nHB of PeOH decreased from 1.7 to 1.46 in CHX mixture and from 1.7 to 0.8 in TOL mixture which highlights a strong HB dilution by TOL molecules. The decrease in nHB of PeOH molecules in mixture with TOL are attributed to the high solvation degree in TOL molecules.

Figure 3 .Figure 3 .

 33 Figure 3.23 shows the evolution of TBA HB number in CHX and TOL mixtures.. As showed in Figure 3.23 HB number of TBA in CHX varied from 1.7 to 1.45 and in TOL changed from 1.7 to 0.8. This highlights a strong dilution of HB network by TOL rather than CHX. The breaking in HB generates more free hydroxyl groups in the mixture whereas in CHX a strong connection between TBA molecules is observed. As it evidenced from snapshots, a clustering phenomena are also observed with TOL. We can relate this dilution of nHB of TBA in TOL by the attracting forces between TOL and TBA. For CHX, large nano-domains of different cluster sizes are formed.

Figure 3 . 24 :

 324 Figure 3.24: Radial distribution function of center of mass of the Aromatic part of Toluene molecules and the hydroxyl part of the alcohol (HOC): EtOH, PrOH, BuOH and PeOH as a function of alcohol concentration.

Figure 3 . 25 :Figure 3 . 26 :Figure 3 . 27 :

 325326327 Figure 3.25: Cluster size probability as a function of the MeOH concentration in logarithmic scale in both TOL-MeOH (a) and CHX-MeOH (b).

Figure 3 .

 3 Figure 3.28 compares the cluster number of ETOH (a), PrOH (b), BuOH (c) and PeOH (d) in TOL with those obtained in CHX as a function of alcohol concentration. The main results obtained in the CHX/EtOH and TOL/EtOH mixtures are reported as the change in monotony of deviations, the presence of higher heterogeneity in the CHX/EtOH systems compared to TOL/EtOH and the high dilution effect of TOL instead of CHX with notable interactions between the TOL aromatic group and the hydroxyl moieties in the alcohol molecules. All of these outcomes covered the fact that clusters can formed in both mixtures with more or less separated nanophases inducing spatial heterogeneities. Figure 3.28 reports the evolution of clusters number of EtOH in both mixtures as a function of EtOH concentration. EtOH in TOL produces more monomers than other cluster sizes while EtOH in CHX promotes the formation of larger clusters. This is corroborated by the presence of different cluster size in CHX involving spatial heterogeneities as it observed in Figure 3.11. On the other hand, cluster analysis for TOL/PrOH and CHX/PrOH systems were reported in Figure 3.28 (b). PrOH in TOL showed small clusters (dimers and trimers) with a larger number in monomers, whereas PrOH in CHX exhibits less monomers but the same size of dimers, trimers, tetramers and pentamers. Cluster number of BuOH in CHX and TOL is managed in Figure 3.28 (c).Figure 3.28 (c) highlights the formation

Figure 3 .Figure 3 . 28 :

 3328 Figure 3.28: Cluster number as a function of the EtOH concentration for monomers, dimers, trimers, tetramers, and pentamers in (a) TOL/EtOH and CHX/EtOH, (b) TOL/PrOH and CHX/PrOH, (c) TOL/BuOH and CHX/BuOH and (d) TOL/PeOH and CHX-PeOH.

Figure 3 .

 3 Figure 3.30 (e) presents the evolution of TBA cluster number in both mixtures as a function of TBA. A representative cluster from the mixture is shown in Fig. 3.29. TBA molecules in solutions with TOL are presenting more monomers than more large clusters. A notable amount of Tetramers are highlighted in this mixture at whole range concentration. TBA clusters in x TBA < 0.6 are showing more monomers than tetramers, for example at x TBA =0.3 there are 38 monomers, 10 tetramers 9 dimers. In comparison with CHX/TBA mixture, we conclude that the majority part of TBA molecules are grouped in clusters, i.e. assembling in tetramers clusters. This corroborates with our first results depicted in MeOH mixture at the first part of this Chapter. Interestingly, in CHX-TBA mixture, a progressive increase in the number of cluster were captured as a function of TBA concentration.

Figure 3 . 29 :Figure 3 . 30 :

 329330 Figure 3.29: Representative cluster of TBA

Figure 3 . 31 :

 331 Figure 3.31: Total structure factor of the TOL-MeOH (a) and CHX-MeOH (b) mixtures as a function of methanol concentration.

Figure 3 . 32 :

 332 Figure 3.32: Partial structure factor of the oxygen atom of the OH group of methanol, ethanol, and tert-butanol liquids at 1 bar and 300 K.

3 . 8 )

 38 Figs.3.7 and in 3.8 the non-ideality of the toluene-methanol mixture is quasi correlated to the HOP evolution and then to its structural heterogeneity.

Figure 3 . 33 :

 333 Figure 3.33: Self-diffusion coefficients for a) TOL,CHX) +EtOH, b) TOL,CHX) +PrOH, c) TOL,CHX) +BuOH and d) TOL,CHX) +PeOH.

Figure 3 .

 3 Figure 3.33 (b) shows the diffusion coefficients of different components in TOL/PrOH and CHX/PrOH mixture as a function of x PrOH and we observe a faster diffusion of PrOH as EtOH in TOL in comparison with CHX. That corroborates, that our assumption about the preferential formation of monomers in PrOH/TOL binary mixture rather than PrOH/CHX one. Furthermore, TOL mostly interacts with PrOH molecules that allows us to observe an increase of dynamics, while CHX shows similar diffusion behavior as pure value. In Figure 3.33 (c), a fast diffusion of BuOH in both mixtures are observed such that D (PrOH) TOL >

Figure 3 .Figure 3 . 34 :

 3334 Figure3.34 reports the self-diffusion coefficients of TOL/TBA and CHX/TBA mixtures as a functions of concentration. Experimental self-diffusion coefficients were plotted for TOL/TBA which they are higher than those observed in this work and may be due to the fact that our measurements are carried out at a higher temperature than that used in their experiments. The agreement with experimental results was satisfactory. From Figure3.34, TBA in TOL shows

3. 7 . 2

 72 Rotational diffusioni) Dipole moment autocorrelation function C(t) Ethanol to pentanol mixtures We report in Fig. 3.35 the dipole moment autocorrelation function of EtOH, PrOH, BuOH and PeOH in mixtures in presence with TOL and CHX respectively.

Figure 3 .

 3 35 shows that molecules rotationally are disrupting in presence of TOL and CHX. the rotational motion of total dipole moment of alcohols increases when they are diluted with TOL rather than CHX.That is illustrated by a fast decay of the autocorrelation functions of EtOH, PrOH, BuOH and PeOH with the addition of TOL. A lesser effect on the rotational behavior were observed in CHX mixtures. These observations underpin our results suggesting a fast dynamics of alcohol molecules in presence of TOL in comparison with slow dynamics observed in CHX. The dynamics could be attributed to the microscopic aggregation of molecules leading to a strong micro-heterogeneity in the system showed by Figure3.11. It is interesting to mention that the high dilution of the hydrogen bonding network of alcohols in the mixture with TOL are somehow the first factor that was impacted the resulting structures.

1 Figure 3 . 35 :

 1335 Figure 3.35: Evolution of the dipole moment autocorrelation function with composition in a) EtOH/TOL, b) EtOH/CHX, c) PrOH/TOL, d) PrOH/CHX, e) BuOH/TOL, f) BuOH/CHX, g) PeOH/TOL and h) PeOH/CHX.

Figure 3 . 36 :

 336 Figure 3.36: Evolution of the dipole moment autocorrelation function with composition in a) TBA/TOL, b) TBA/CHX.

Figure 3 .

 3 37 (a), (b), (c) and (d) shows that alcohols in TOL are rapidly oriented compared to the same alcohols in CHX. Alcohols in TOL showed a short relaxation times and a long relaxation times were demonstrated by alcohols in CHX.

Figure 3 . 37 :

 337 Figure 3.37: Variation of relaxation times in a) EtOH/TOL + EtOH+CHX, b) PrOH/TOL + PrOH/CHX, c) BuOH/TOL + BuOH/CHX and d) PeOH/TOL + PeOH/CHX as a function of alcohol concentration.

Figure 3 . 38 :

 338 Figure 3.38: Variation of relaxation times in TBA/TOL + TBA/CHX as a function of TBA concentration.

Figure 4 .

 4 1 (a) , the position of the main peak of S HO 112 Chapter 4 Ilham Essafri

  Figure 4.1 (b). Given the excluded volume effect caused by the confinement in the radial direction, a layering structure is observed for both TBA and TOL, with a maximum density near the silica surface located at 24 Å. For both TBA and TOL, four layers are observed; these layers are related to the size of the molecules. As shown in Figure 4.1(b), the TOL and TBA molecules sample all positions from r = 0 to r = 20 Å (r is the radial position extending into the

Figure 4 . 1 :

 41 Figure 4.1: (a) Partial structure factors of hydrogen atoms of OH groups of TBA, SHO of pure liquids and of TBA/TOL mixture with a TBA/TOL molar fraction composition of 56/44% at 298 K and 1 bar in the confined and bulk phases. (b) Profiles of radial density of carbon atoms of TOL, hydrogen atoms of the OH group of TBA and carbon atoms of the methyl group of TBA in the TBA/TOL mixture with a TBA/TOL molar fraction composition of 56/44%

Figure 4 .

 4 1 (b) depicts a slight shoulder of HO density at r = 20 Å, whereas a large amount of TBA is located from the centre of the pore to 16 Å. In contrast, the carbon atoms of the methyl groups of TBA and the benzenic cycles of TOL are closer to the silica surface than the HO atoms, which suggests hydrophobic anchoring[41]. This structural behaviour is the result of the preferential hydrogen bonding of TBA between two TBA layers[41]. Using a CS model, Hamid et al. have shown that TBA preferentially adsorb on the silica surface. This discrepancy between both works shows that other models can be envisaged to fit the experimental data. Indeed, in their work, Hamid et al. used three models (TBA at the centre, TBA at the interface and homogenous case).

Figure 4 . 2 :

 42 Figure 4.2: Illustration of confined TBA (red)/TOL(cyan) mixture into the cylindrical nanopore obtained from the force field developed by Brodka and Zerda [42]. For clarity, silica framework is removed. This Figure shows that TBA (red colour) and TOL (cyan colour) molecules sample as well the surface as centre of pore.

Figure 4 .

 4 3 (a) and (b), the radial density of TBA and TOL for both 35/65% and 56/44% molar fraction composition. As shown in Figure 4.3 (a) and (b) for both molar compositions TOL and TBA molecules are located at the same position that highlights an absence of full demixing and a CS organisation. 114 Chapter 4 Ilham Essafri Microstructure of binary mixtures in bulk and nanoconfined phases

Figure 4 . 3 :

 43 Figure 4.3: a) Profiles of radial density of centre of mass of TOL and TBA confined into the silica nanopore with a TBA/TOL molar fraction composition 56/44% such as the silica framework is described with the model of Brodka and Zerda [42]. (b) Profiles of radial density of centre of mass of TOL and TBA confined into the silica nanopore with a TBA/TOL molar fraction composition 35/65%.

Figure 4 . 4 :

 44 Figure 4.4: Profiles of radial density of centre of mass of hydrogenated (OH) and deuterated (OD) TOL and TBA confined into the silica nanopore with a TBA/TOL molar fraction composition 56/44% and with a deuterated/hydrogenated composition 50/50% for TOL and TBA.

Figure 4 .

 4 5 (a), a representation of the Connolly surface of TBA and TOL in the confined TBA/TOL mixture. As observed in Figure 4.5 (a), the confined TBA/TOL mixture appears to be heterogeneous given the presence of TBA and TOL nanophases. Indeed, Figure 4.5 (a) clearly depicts alternating TBA and TOL phases related to a local demixing, highlighting an absence of homogeneity.

Figure 4 .

 4 1(a), the carbon atoms of both compounds preferentially adsorb onto the surface. A hydrophobic and hydrophilic network (related to HBs) can develop from the first adsorbed TOL and TBA molecules, driving local demixing, as shown in Figure4.5 (a) contrary to the bulk phase where the mixture is homogeneous (see Figure4.6). Therefore, this local demixing, which induces strong heterogeneity, is likely the physical process observed from neutron scattering measurements[17]. To understand the mechanism of formation of local demixing, grand-canonical Monte Carlo (GCMC) simulationsChapter 4 Ilham Essafri

Figure 4 . 5 :

 45 Figure 4.5: (a) Connolly's surface of confined TBA (red)/TOL(cyan) mixture in the cylindrical nanopore in different directions. (b) Isotherms of adsorption of pure TBA and TOL in the silica framework. (c) Illustration of confined TBA (red)/TOL(cyan) mixture in the cylindrical nanopore for four relative pressures. For clarity, the silica framework is omitted.

Figure 4 .

 4 5 (c) shows snapshots of gradual nanopore filling by the TBA/TOL mixture with a TBA/TOL molar fraction composition of 56/44%. As shown in Figure 4.5 (c), no specific organisation is observed regardless of the pressure. However, local segregation and formation of nanophases are observed, and the sizes of the nanophases increase spatially with increasing pressure. Therefore, the heterogeneous 118 Chapter 4 Ilham Essafri

Figure 4 .

 4 7(a)-(b) the radial density profiles of confined pure TBA, TOL and CHX are reported.

Figure 4 .

 4 7(a)-(b) compares the radial density behavior of these three components within hydrophobic (Fig. 4.7 (a)) and hydrophilic (Fig. 4.7 (b)) nanopores. Interestingly, Figures 4.7

  (a)-(b) indicate strong inhomogeneity in the density distribution of these liquids under both confinements. Furthermore, a formation of several layers around the wall surface are also observed.In the CNT (see Fig.4.7 (a)) TOL in comparison with TBA and CHX is the closest molecule to the wall surface. This strong affinity with the CNT wall surface is attributed to the aromatic ring of TOL. This indeed promotes the interaction with the carbon atoms of the nanotube that could explain the strongest preferential layering of TOL near the wall surface. Interestingly, TOL pseudo-periodic modulation showed in the local density has been seen to propagate into the confined volume but it damped and gradually disappears. This means that TOL gradually loses memory of the wall and tends to assume again the bulk structure. However, the hydrophilic

Figure 4 . 7 :

 47 Figure 4.7: a) Radial density profile of pure confined TBA, TOL and CHX within a) Carbon nanotube (CNT) with r= 2nm and b) Water nanotube (CNT) with r= 2nm.

  Figure 4.9 compares the local atomic density of pure TBA, TOL and CHX within the two confinements.

Figure 4 . 8 :

 48 Figure 4.8: Illustrations of pure (a)-(d) TBA, (b)-(e) TOL and (c)-(f) CHX confined in CNT and in WNT, respectively.

Figure 4 . 9 :

 49 Figure 4.9: Atomic radial density profile of pure TBA (oxygen, hydrogen (HO part) and carbon of (CH 3 ) and TOL (carbon atoms of aromatic ring) and CHX (carbon atoms) confined within CNT (a,c,e) and within WNT (b,d,f), respectively.

Figure 4 .

 4 9 (c) shows a preferred locations of the aromatic part of TOL with the hydrophobic wall surface. This figure shows a peak at 16.

Figure 4 .

 4 10 (a) shows a layering structure of TOL and TBA molecules along the nanopore radial direction. Obviously, near the wall surface between 17 Å and 15 Å, a local-demixing seems to be drawn inside the mixture. On the other hand, we provide the radial density profile of the same mixture confined within a water nanotube. As we can noticed from Figure 4.10 (b), we have a layering structure inside the water nanotube. In this case, the TBA molecules are located near the confining surface with a very weak percentage of TOL molecules. Moreover, Figure 4.10 (b) shows us a strong affinity near the wall surface between the TBA molecules and the water nanotube; this is evidenced by a peak at 18 Å and Chapter 4 Ilham Essafri 123

Figure 4 . 10 :

 410 Figure 4.10: Radial density profile of TBA/TOL within a) carbon nanotube and b) water nanotube (r=20 Å). a-1) and b-1) are atomic radial profiles of TBA (oxygen, hydrogen (HO part) and carbon of 3CH 3 ) and TOL (carbon atoms of aromatic ring and carbon atoms of methyl group) in hydrophobic and hydrophilic confinement, respectively.

Figure 4 . 11 :

 411 Figure 4.11: Snapshot illustration of TOL/TBA mixture within a) and c) CNT (r=2nm) in axial and radial directions, respectively and b) and d) WNT (r=2nm) in axial and radial directions, respectively.

Figure 4 .

 4 Figure 4.11 presents the confined media snapshots obtained from both mixtures which corroborates our first observations. For TOL/TBA mixture confined in hydrophobic nanopore Figure 4.11 a,c) illustrates the formation of small nano-phases in TOL and TBA which highlights a non-mixing behavior inside the mixture. For TOL/TBA confined in the WNT, snapshots observations indicates the presence of local de-mixing behavior near the wall of the water nanotube which highlights a micro-phase separation near the wall surface (see Figure 4.11 b,d). In the axial direction Fig. 4.11 d), we observe more TBA molecules adsorbed on the surface with weak proportion of TOL molecules that is in line with the results evidenced from the radial profile.

Figure 4 . 12 :

 412 Figure 4.12: Radial density profile of CHX/TBA within a) carbon nanotube and b) water nanotube (r=20 Å). c) and d) are are atomic radial profiles of TBA (oxygen, hydrogen (HO part) and carbon of 3CH 3 ) and CHX (carbon atoms) in hydrophobic and hydrophilic confinement, respectively.

Figure 4 .

 4 12 shows CHX/TBA mixture under a) hydrophobic and (b) hydrophilic 126 Chapter 4 Ilham Essafri

Figure 4 . 13 :

 413 Figure 4.13: Snapshots of a) CHX/TBA within CNT and b) CHX/TBA within WNT.

Figure 4 .

 4 Figure 4.13 highlights a microphase separation near the surface which confirms our conclusions drawn from the radial density profile (TBA peak at 18 Å and CHX peak at 16.5 Å). This suggest that the TBA molecules create strong interactions with the wall surface. However, this effective description does not fully address the microscopic origin of the local demixing behavior.

Figure 4 .

 4 14 presents the hydrogen bond number of TBA molecules in pure and in mixture with TOL and CHX in CNT and in WNT. As depicted from Chapter 4 Ilham Essafri

Figure 4 .

 4 Figure 4.14 (a), the hydrogen bonds of TBA are not changing along the radial direction for pure TBA and for mixed TBA. Whereas a maximum of two bonds per TBA molecule are captured in the hydrophobic confinement. Interestingly, the CNT were extremely a good protector of the hydrogen bond number despite some failure near the surface. In WNT (see Figure 4.14 (b)), confined pure TBA shows approximately a value of 1.3 HBs per TBA molecule. This means a small decrease of the nHBs which is approximately equal to 1.7 in the bulk phase. This could probably results from the confinement effect on TBA topology structure. However, the profile of nHBs of TBA in mixture with CHX and with TOL indicates a high HB dilution which means that TBA loses the half of the HBs (nHB ' 0.8). This is corroborated by the high dilution of the hydrogen bonding number of TBA molecules along the radial direction and near the wall surface.

Figure 4 . 14 :

 414 Figure 4.14: Radial hydrogen bond number (nHB) profile of pure and mixed TBA within a) CNT and b) WNT respectively.

Figure 4 .

 4 15 compares the radial profiles of the hydrogen bond of TBA-TBA and TBA-Water in (a) TOL/TBA and (b) CHX/TBA. From Figure4.15 (a) we observe a strong dilution of TBA's hydrogen bonding network, which is basically made up of two hydrogen bonded neighbors. In TOL/TBA confined in the water nanotube at x T BA =0.6, there is a significant decrease from nHB=1.51 to nHB=0.8. In the same figure, the average number of hydrogen bonds between the TBA and the nanopore surface is zero from 0 to 15 Å. From 15 Å (next to the confining surface), a hydrogen bond of TBA molecules is created near the surface, this is indicated by a peak that is located at 19.8 Å at a height corresponds to nHB=0.65. In the second figure, in the CHX/TBA mixture, the same behavior is observed. From these two Figures we observe a decrease of nHB within WNT as well as a creation of HB interaction with the surface. While in CNT, a very slow decrease of nHB is evidenced.

Figure 4 . 15 :Figure 4 . 16 :

 415416 Figure 4.15: Radial hydrogen bond number (nHB) profile of TBA-TBA and TBA-Water in a) TOL/TBA mixture and b) CHX/TBA mixture.

Figure 4 . 17 :

 417 Figure 4.17: Comparison of the cluster number of pure TBA in Bulk and in confined media.

4. 5 . 1

 51 Pure TBA, TOL and CHX

Figure 4 .Figure 4 .

 44 Figure 4.18 present the radial density profile of TOL, TBA and CHX liquids confined within a) CNT as hydrophobic nanopore and b) WNT as hydrophilic matrix. From Fig. 4.18 (b) we observe two distinct peaks for TBA, TOL and CHX which highlights a layered structure. Interestingly, first peak of TBA is located at 8 Å, peak of TOL is about 7.5 Å and peak of CHX is about 7 Å, this indicates a strong affinity with the surface of the water nanotube with TBA molecules as previously observed (Fig. 4.7 (b)). While in CNT, the local structure of these pure liquids differs from that of the hydrophilic confinement which is depicted in Figure 4.7 (a).Surprisingly, TOL shows a first significant peak at 8 Å and three other small peaks at 6.5, 4 and 3 Å respectively. This indicates a significant decrease in the production of distinct layered structures as observed earlier. Obviously, there is a fairly strong surface effect on TOL, which

4. 5 . 2

 52 TOL/TBA and CHX/TBA binary mixturesThe local structure of the confined binary mixtures is described by the radial density profile.The observed behaviour of TOL/TBA and CHX/TBA confined in the hydrophobic matrix is displayed in Figure4.19. Figure4.19 presents the radial profile of the density of the TOL and TBA in the TOL/TBA mixture (c) and the density of the CHX and TBA in the CHX/TBA mixture (d) with a TBA concentration equal to 0.9. As illustrated in Figure4.19 (c), there are two peaks of TBA and a single peak of TOL. An interesting fact is that the only peak of TOL is located at 7.8 Å while the central peak of TBA is located at 7 Å. This indicates that the TOL/TBA mixture separates nearby the confining surface. From our method of creating confined systems, it is evident that despite the poor affinity of TBA to the carbon nanotube, we have more TBA than TOL in the matrix. By observing the topology of this confined mixture, also shown in Figure4.19 (c), we can see that all the molecules of TOL are at the end of the carbon nanotube. This allows us to conclude that at this concentration of TBA all the TOL molecules that have entered into confinement are captured by the surface while the TBA had no option except to fill the space and approach its behavior in a pure state. The high concentration[START_REF] Dawass | Kirkwood-buff integrals from molecular simulation[END_REF] Chapter 4 Ilham Essafri

Figure 4 . 19 :

 419 Figure 4.19: Snapshot observations and radial density profiles of a,b) TOL/TBA confined within carbon nanotube (CNT) with r= 11.5 Å and c,d) CHX/TBA confined within carbon nanotube (CNT) with r= 11.5 Å.

Figure 4 . 20 :

 420 Figure 4.20: Snapshot observations and radial density profiles of a,b) TOL/TBA confined within water nanotube (WNT) with r= 10 Å and c,d) CHX/TBA confined within water nanotube (WNT) with r= 10 Å.

Figure 4 .

 4 20 (d), the radial profile of the CHX/TBA density reveals two layers of CHX and a single layer of TBA. The TBA peak is located at 8.5 Å and the two CHX peaks are located at 6.5 Å and 2.5 Å , this highlights a micro-phase separation near the surface. All the molecules of TBA[START_REF] Takahashi | Why is benzene soluble in water? role of oh/⇡ interaction in solvation[END_REF] Chapter 4 Ilham EssafriMicrostructure of binary mixtures in bulk and nanoconfined phases are at the surface while CHX is at the center of the pore. Interestingly, this micro-separation is also captured on the CHX/TBA topology image given in the same figure.

Figure 4 .

 4 Figure 4.21: a) Profile of the radial density of hydrogen and oxygen atoms of hydroxide group (HO) of TBA, and carbon atoms of CHX. b) Profile of the radial density of hydrogen and oxygen atoms of hydroxide group (HO) of TBA, and carbon of benzenic cycle (C aromatic ) and methyl group (CH 3 ) of TOL.

Figure 4 .

 4 21 (a) depicts the atomic radial density profile of oxygen and hydrogen atoms of the hydroxyl part of TBA molecules as well as the carbons atoms of CHX molecules. In CHX/TBA mixtures, where a micro-phase separation was captured, the atomic density profile highlights a strong anchoring of TBA molecules by their hydroxyl parts on the surface where a peak is recorded at 9.8 Å. On the other hand, the first peak of carbon atoms of CHX is captured at 7 Å which points out the micro-phase separation results showedChapter 4 Ilham Essafri 137

Figure 4 . 22 :

 422 Figure 4.22: Hydrogen bond number profile of TBA in TOL/TBA a) in CHX/TBA b) within CNT and the Hydrogen bond number profile of TBA in CHX/TBA c) in TOL/TBA d) within WNT.

Figure 4 .

 4 Figure 4.22 shows the profiles of the average number of TBA hydrogen bonds in the two binary mixtures in hydrophobic confinement (a) and (b), and in hydrophilic confinement (c) and (d). As previously reported, the TOL/TBA in CNT has showed a layering structure. From

Figure 4 .

 4 Figure 4.22 (a) a two broad peaks are captured at 8.5 Å and 1 Å which corresponds to 1.4 HBs per TBA molecule in average. This confirms that the observed layering structure correlates to the resulting nHB peaks that emphasize the predicted pattern between the TBA molecules in the hydrophobic confinement.Figure 4.22 (b) depicts the same behavior of CHX/TBA mixture

Figure 4 .

 4 22 (b) depicts the same behavior of CHX/TBA mixture in the hydrophobic confinement. 138 Chapter 4 Ilham Essafri Microstructure of binary mixtures in bulk and nanoconfined phases

Figure 4 . 23 :

 423 Figure 4.23: Adsorption isotherm of the TBA/TOL mixture confined in the silica nanopore as a function of the relative pressure such that P 0 is the saturation pressure vapor of TBA

Figure 4 .

 4 25 this HB anchoring leads to a peculiar organization such that hydrophobic and hydrophilic (HB) domains are disposed in alternating succession. These results should probably impact the molecular structure of confined mixture. The density profile of the SiOH groups is also reported in Figure 4.25. As shown in Figure 4.25 the SiOH profile Chapter 4 Ilham Essafri

Figure 4 .Figure 4 . 25 :

 4425 Figure 4.24: b) Density profiles of the center of mass of pure TBA and TOL confined into the nanoporous silica material obtained at 308 K and 1 bar.

Figure 4 . 26 :

 426 Figure 4.26: Profiles of radial density of the center of mass of TBA and TOL molecules for x TBA = 0.83 (a), 0.71 (b), 0.49 (c), and 0.24 (d).The insets illustrate the core-shell organization, the TBA (red color) close to the surface and the TBA/TOL (TOL is blue colored) mixture at the center of pore; from 0.83 to 0.24 the width of the interfacial layer decreases, whereas the concentration in TBA decreases at the center of pore.

Figure 4 .

 4 29 (a) shows that the weak ability of WH to establish interfacial hydrogen bonds between the silanol groups and the TBA molecules explains the absence of microphase[START_REF] Pratt | Self-diffusion in water and monohydric alcohols[END_REF] Chapter 4 Ilham Essafri

Figure 4 . 27 :

 427 Figure 4.27: Profiles of radial density of the hydrogen atoms of the OH and CH3 groups of TBA and hydrogen atoms of CH 3 group of TOL for x TBA = 0.83 (a), 0.71 (b), 0.49 (c), and 0.24 (d). The dashed circle represents the interpenetration region of TOL molecules in the interfacial layer.

Figure 4 .

 4 Figure 4.28: b) Profiles of the hydrogen bonds number per TBA molecules along the radial direction of the silica cylindrical nanopore.

Figure 4 .

 4 Figure 4.29: a) Profile of the radial density of center of mass of TBA and TOL molecules confined into the weakly hydrophilic silica nanopore. b) Profile of the radial density of tertiary carbon (C t ), hydrogen atom of hydroxide group (HO) of TBA, and carbon of benzenic cycle (C) and methyl group (CH 3 ) of TOL.

Figure 4 .

 4 Figure 4.30: c) Profile of the radial density of TBA and TOL liquids confined into a water nanotube (WNT) with a pore radius of 12 Å. d) Profile of the radial density of TBA and TOL liquids confined into a carbon nanotube (CNT) with a pore radius of 12 Å.

Figure 4 . 31 :

 431 Figure 4.31: Snapshot illustrating the confinement of TOL molecules in the carbon nanotube of pore radius of 12 Å.

Figure 4 .

 4 Figure 4.32: a) Illustration of the confined TOL (cyan color) and TBA (red color) for x TBA = 0.5, between two silica walls separated by a distance of 24 Å. Red and yellow colors correpond to the oxygen and silicon atoms. b) Profile of the axial density of centers of mass of TBA and TOL molecules confined between two silica slabs separated by a distance of 24 Å.

Figure 4 . 33 :

 433 Figure 4.33: Profiles of radial density of the center of mass of TBA and TOL molecules for x TBA = 0.50 for three pore radii (R = 6, 12, and 18 Å)

Figure 4 .

 4 26 (a), the molar fraction x TBA =0.83 corresponds to 79 TBA and 16 toluene molecules. Therefore other TBA molecules are distributed at the centre of pore and in the intermediate layer. As shown in Figure4.24 (b) the first layer is located between 0 and 3 Å, the second between 3 and 7.5 Å while the last is located between 7.5 and 12 Å. As the layer size corresponds to the molecule size and that TOL molecule is higher than TBA one, 3.5 Å vs 3.0 Å it appears that TOL molecules have no place at the centre of pore contrary to the intermediate layer where the layer size is 4.5 Å.

[ 1 ][ 2 ]

 12 Li S. Toward understanding the structural heterogeneity and ion pair stability in dicationic ionic liquids. Soft Matter, 10:9193, 2014. Alenka Luzar and David Chandler. Effect of environment on hydrogen bond dynamics in liquid water. Phys. Rev. Lett., 76(6):928-931, 1996. [3] Stoddard S. Identifying clusters in computer experiments on sytems of particles. J Comput Phys, 27:291, 1978. et objectifs Ces dernières décennies, les nanosciences et les nanotechnologies ont connu un essor très important dans tous les domaines, qui demande dans un premier temps la bonne compréhension de certains phénomènes à l'échelle nanométrique. Particulièrement, Il a été montré que la plupart de ces phénomènes sont contrôlés par le réseau de la liaison hydrogène, par exemple l'auto-assemblage, la formation d'agrégats ou de microémulsion, le repliement des protéines ou l'assemblage des protéines jusqu'au relargages de médicaments. Intéressement, avec l'avancée des nanosciences et des nanotechnologies on manipule beaucoup de liquides à l'échelle du nanomètres alors qu'il est devenu intéressant d'une manière impérative est bien d'essayer de revisiter notre compréhension de ces réseaux de liaison hydrogène à ces échelles là. L'objectif de ce travail est comprendre le rôle du réseau de liaison hydrogène des alcools à l'échelle nanométrique et est ce que ces réseaux de liaison hydrogène vont survivre sous confinement nanométrique ou ils vont transiter vers un autre type de réseau ou bien est ce que ces réseaux de liaison hydrogène vont être impacter par les effets de surface. Et essayer aussi de comprendre comment les propriétés de différents liquides formateurs de liaisons hydrogènes vont se modifier sous confinement nanométriques. Donc l'objectif principal de ma thèse était d'étudier la structure de différents liquides et leurs mélanges confinés à l'échelle nanométriques et essayer d'établir un lien entres les différentes propriétés de ces liquides avec leurs réseaux de liaison hydrogène. Donc le plan de ma thèse est composé de deux grandes parties :

1. Objectif : 2 .

 Objectif2 La non-idéalité des mélanges binaires est souvent liée à la nature des interactions entre les deux liquides et à l'hétérogénéité à l'échelle nanométrique de la microstructure. Lorsque l'un des liquides est un formateur de liaisons hydrogène et le second est aprotique, la dilution progressive du réseau de liaisons hydrogène conduit à un regroupement et des nano-phases. En considérant deux mélanges, toluène-méthanol et cyclohexane-méthanol, la non-idéalité et sa connexion avec la structure à l'échelle nanométrique et les interactions intermoléculaires sont étudiées numériquement. Contrairement au toluène totalement miscible dans le méthanol, le cyclohexane présente une plage d'immiscibilité élevée qui en fait un système pertinent pour étudier la nucléation (ségrégation locale) et sa propagation. Méthode : Phase BULK Le méthanol, le toluène et le cyclohexane ont été modélisés par le champ de force de tous les atomes flexible non polarisable pour les simulations liquides (OPLS). En effet, il a été récemment montré que les modèles OPLS étaient quantitativement reproduits aux propriétés thermodynamiques et interfaciales. Les interactions intermoléculaires sont composées de la répulsion-dispersion et des contributions électrostatiques modélisées respectivement par les potentiels de Lennard-Jones (LJ) et coulombiens. Les interactions électrostatiques ont été tronquées à 12 Å et calculées en utilisant la somme d'Ewald avec une précision de 10 -6 . Les interactions à courte distance ont été modélisées en utilisant le potentiel de Lennard-Jones en utilisant un seuil de 12 Å. Ici, les interactions entre des sites LJ différents de deux molécules ont été déterminées par la règle de combinaison de Lorentz-Berthelot. Les erreurs statistiques pour les propriétés calculées ont été estimées à l'aide de la méthode des moyennes de bloc. Des conditions aux limites périodiques ont été appliquées dans les trois directions. Des simulations MD ont été réalisées dans l'ensemble statistique NpT de telle sorte que N est le nombre de particules, T est la température, et p est la pression. Des simulations de dynamique moléculaire ont été effectuées à T = 300 K et p = 1bar en utilisant un pas de temps de 0,001 ps pour échantillonner 10 ns (phases d'acquisition et d'équilibrage). Toutes les simulations MD ont été réalisées à partir du progiciel DL_POLY en utilisant une combinaison des algorithmes de thermostat et barostat Velocity-Verlet et Nosé-Hoover. La configuration initiale a été construite par une distribution aléatoire de molécules de méthanol (MeOH), de toluène (TOL) et de cyclohexane (CHX).

  figure 1 (c) où des instantanés de CHX-MeOH à x MeOH = 0,1, 0,5 et 0,9 sont indiqués. Comme le montre la figure 1 (c), la séparation de phase est bien récupérée à x MeOH = 0,5, alors qu'à x MeOH = 0,1 et 0.9 les systèmes sont miscibles.

Figure 1 :

 1 Figure 1: Densité simulée et expérimentale (a) et excès de densité (b) des mélanges CHX-MeOH et TOL-MeOH en fonction de XMeOH à 300 K et 1 bar. Les incertitudes sur la densité sont trop faibles pour être représentées. (c) Images instantanées du mélange binaire à XMeOH = 0,1, 0,5 et 0,9 de sorte que le méthanol est représenté́ en rouge, et CHX est représenté́ en bleu.

Figure 2 :

 2 Figure 2: (a) Les profils de densité radiale des atomes de carbone de TOL, des atomes d'hydrogène du groupe OH de TBA et des atomes de carbone du groupe méthyle de TBA dans le mélange TBA/TOL avec une composition de fraction molaire de TBA/TOL de 56/44%, cette courbe montre une structure en couche et une absence d'une organisation en noyaucoquille. (b) Image instantanée de la structuration de liquides confinées, cette illustration montre un mélange TBA (rouge)/TOL (bleue) confiné dans le nanopore cylindrique. La structure du pore de silice est enlevée. Cette figure montre que les molécules de TBA (couleur rouge) et de TOL (couleur bleue) sont présentes à la surface et au centre du pore.

Figure 3 :

 3 Figure 3: Profils de densité des groupes OH, des atomes de carbone des molécules de tert-butanol (TBA) et des groupes SiOH dans le cas où XTBA = 1,0.

  , b la distance entre la densité interfaciale TOL et TBA (d TBA-TOL ) est d'environ 4 Å, la distance est fortement réduite à seulement ~ 1 Å pour x TBA = 0,49 et x TBA = 0,24. La différence dans le d TBA -TOL en fonction de la fraction molaire TBA est due à l'augmentation progressive de TOL. En effet, pour la fraction TBA inférieure à 0,5 correspondant à une interface solide insaturée dans les molecules TBA, la surface SiOH peut alors

  TOL. L'adsorption progressive en molécules TOL à la surface de la silice est alors à l'origine de la diminution de d TBA-TOL avec l'augmentation de la fraction TOL et est alors à l'origine de l'interpénétration des molécules TOL.

Figure 4 :

 4 Figure 4: Profils de la densité radiale du centre de masse des molécules de tert-butanol (TBA) et de toluène (TOL) pour xTBA = 0,83 (a), 0,71 (b), 0,49 (c) et 0,24 (d). Les images encadrées illustrent l'organisation noyau-coquille, le TBA (couleur rouge) près de la surface et le mélange TBA/TOL (TOL est de couleur bleue) au centre des pores ; de 0,83 à 0,24, la largeur de la couche interfaciale diminue, tandis que la concentration en TBA diminue au centre des pores.

  EtOH =0.6, both components in the mixture exhibit local heterogeneity because HOP (CHX) = 16.75 and HOP (EtOH) = 18.75 seem to be responsible for the strong deviation from the ideal mixing density. It can be concluded that heterogeneity could conduct such behavior. Second, the BuOH =0.2 0.6. A strong spatial heterogeneity (HOP= 19 > 15.74) is also evidenced for BuOH in mixture with CHX at x BuOH =0.2. It is necessary to remember that the HOP value increases when more sites are closer to each other, explain the difference in non-ideality behavior of CHX/BuOH and TOL/BuOH mixtures. Negative deviation are attributed to these heterogeneities. Moreover, the both aprotic solvents in the two mixtures are homogeneous.

		Microstructure of binary mixtures in bulk and nanoconfined phases
	heterogeneity could then
	66	Chapter 3	Ilham Essafri

At x

addition of TOL to EtOH molecules generates less heterogeneities regardless CHX/EtOH binary liquids. Interestingly, EtOH in TOL is homogeneous at low EtOH concentration (x EtOH =0.1) and in ethanol rich region (for x EtOH = 0.8 and 0.9). The HOP of both (CHX ; TOL) molecules are homogeneous in pure and in mixtures with EtOH, except for CHX at x EtOH = 0.6 it exhibits small local inhomogeneity as we've mentioned before.

In Figure

3

.11 (b), the HOP of pure PrOH is 15 that corresponds to a homogeneous phase.

The addition of CHX leads to spatial heterogeneity in PrOH for 0.2 < x PrOH < 0.7. At these concentrations, the excess density of CHX/PrOH mixture presents such that strong deviation.

At low and high alcohol concentrations (x PrOH =0.1 ; 0.8-0.9), the CHX/PrOH mixture approach the ideality behavior, that is in line with the homogeneous organization of PrOH molecules. The heterogeneity leads to then the negative deviation from ideality. Unlike CHX, TOL doesn't affect the homogeneity of PrOH molecules. Indeed, between x PrOH =0.3 and 0.5, PrOH molecules are locally heterogeneous because HOP at x PrOH = 0.3 is 16.5 greater than 15.74. On the contrary TOL molecules are homogeneously distributed in the mixture as the same as CHX (except for

x PrOH = 0.6 where the HOP(CHX)=15.

85 > 15.74)

. The HOP of each molecule in CHX/BuOH and TOL/BuOH mixtures are provided in Figure

3

.11 (c). One important point is that BuOH in both mixtures present a heterogeneous at x resulting in a higher value for more aggregated or clustered organization. Then, the resulting

  (about 2.6 % of EtOH in TOL and 2% of EtOH in CHX). As previously reported, TOL breaks the HB networking of EtOH molecules. The dynamics is then impacted by the EtOH monomers and dimers. However, CHX doesn't break the nHB even a slight decrease of nHB is observed in Figure3.23. The slow dynamics is probably governed by the molecular clustering phenomenon of different EtOH largest clusters such that tetramers and pentamers.

		Microstructure of binary mixtures in bulk and nanoconfined phases
	in both components
		5, we show a proportion of 7.6 % of EtOH monomers in TOL whereas 1.6
	% of monomers in CHX is evidenced. That could be at the origin of the slow motion of EtOH
	92	Chapter 3	Ilham Essafri

molecules in EtOH with CHX. In EtOH rich-regions (x EtOH =0.9) the motion of EtOH are similar to that in both aprotic solvent that is expected because there are the same rate of monomers

Table 4

 4 .1. Figure4.23 shows that the predicted adsorption isotherms are in fair agreement with those obtained from experiments[33]. Interestingly, Figure4.23 exhibits that the capillary condensation pressure is qualitatively reproduced for both TOL and TBA components. These results allowed us to be confident in these refined interactions.

		(Å)	✏(K)
	Si-CH3 3.6475 46.17061
	Si-CH	3.6725 47.54915
	Si-C	3.6725 47.54915

Table 4 .

 4 1: Crossed Lennard-Jones parameters. CH3 is the carbon of the methyl groups of toluene, CH the carbon of the CH groups of toluene, and C the carbon without hydrogen atoms in toluene

	4.6.2 Microscopic origin of microphase separation

Chapter 2 Ilham Essafri

Chapter A Ilham Essafri

Ethanol to pentanol mixtures

From TOL/TOL and CHX/CHX RDFs, we observe that CHX promotes the self-associating behavior of alcohol molecules, whereas TOL presents strong interaction with alcohols. Figure with the addition of CHX molecules, ranging from 1.8 to 1.6, and interestingly a small reduction in HB number is observed. EtOH in TOL solution exhibits a strong dilution of the hydrogen bonds number that is highlighted by a significant decrease in nHB of EtOH from 1.8 to 0.8. anchoring that occurs at low pressures could act as a 'germ' of the heterogeneity. Additional TBA and TOL molecules are progressively adsorbed through HBs and hydrophobic interactions, respectively, leading to TBA and TOL nanophases. Eventually, the growth of these nanophases induces local demixing and heterogeneity. This interfacial heterogeneity seems to be ruled by (i) the difference in silica/fluids interactions between TOL and TBA as suggested from the calculation of Q st and (ii) by the favourable hydrogen bonds between two TBA layers [38].

In this part, we showed that the nano-confinement induces strong heterogeneity, causing the absence of the extinction of Bragg's peak from neutron diffraction measurements. Our results illuminate another scenario based on the local segregation rather than a core-shell organisation of the confined TBA/TOL mixture. Ultimately, we show that the underlying mechanism is based on the formation and growth of a 'germ' of heterogeneity, leading to the formation of nanophases.

Although this study highlights an absence of a CS structure of the confined TBA/TOL binary liquid into the hydrophilic nanopores, it would be worthwhile to study the behavior of other confined mixtures, size pore effect and the confinement through a hydrophobic medium as the carbon nanotubes.

Role of hydrophobicity and hydrophilicity

Now, to provide a full picture of the microphase separation, two different confining surfaces were used in this part. We have studied the behavior of TOL/TBA and we have compared it with Chapter 4 Ilham Essafri filling on structuring could be an interesting vast area of research to enhance our understanding of the relation between structure-dynamics property inside the nano-porous materials.

Chapter 5 Ilham Essafri 161 Appendix structural and dynamical analysis

A.1 Total density

Density refers to how much matter is packed into a substance, and it's usually measured in grams per cubic centimeter (g/cm 3 ). Density is a measure that compares the amount of matter of an object to its volume. For example, an object with a lot of material in a certain volume has a high density. If an object is heavy and compact, it has a high density. Density is obtained by dividing the mass of an object by its volume. The structure of our molecular systems were first explored by density calculation. This is accomplished by a simple density calculation, applying this equation to our simulation trajectories:

Where <.> indicates the average value, the (n a , M a ) and (n b , M b ) are the number of molecules and the molar mass of the alcohol and the aprotic molecules respectively.

A.2 Radial distribution function:

The radial distribution function (RDF), (or pair correlation function) g(r) in a system of particles (atoms, molecules, colloids, etc.), describes how density varies as a function of distance from a reference particle. Radial distribution function analysis is an important feature to explore matters local order. It gave us a statistical description of atomic positions. Atomic arrangement can be described from this function. It can be measured experimentally by scattering experiments. The RDF is usually determined by calculating the distance between all particle pairs and binning them into a histogram. The histogram is then normalized with respect to an ideal gas, where particle histograms are completely uncorrelated. For three dimensions, this normalization is the number density of the system multiplied by the volume of the spherical shell, which mathematically can be expressed as g(r) = 4⇡r 2 ⇢dr, where ⇢ is the number density.

RDF was calculated from

is the number of i-j pairwise interactions located at r i j, V is the volume, r i j the distance between i and j particles, N i and N j the number of i and j particles and < . > is the statistical average.

A.3 Heterogeneity order parameter

The local structural order was investigated through the use of the heterogeneity order parameter (HOP) [1]. The HOP is defined as

where r ij is the distance between sites i and j and = L/Ns 1/3 , L is the simulation box length, and N s is the number of sites for which the HOP is being computed. The HOP value increases when more sites are closer to each other, resulting in a higher value for more aggregated or clustered geometries.

The HOP is so defined that it is topologically invariant with the absolute distances between sites, thus independent of the simulation box size L. Because the weights of the sites far from the target site decrease quickly with distance, the HOP approaches a constant with increasing Chapter A Ilham Essafri number of sites. Some ideal systems with sites that is uniformly distributed in a cubic box were constructed, and the HOP was computed for these systems with periodic boundary conditions applied. The HOP takes a fixed number of 15.7496 when the number of sites is larger than 1000.

A.4 Hydrogen bond number

Hydrogen bonds are non-covalent interactions occurrisng between the H atom of a dipolar molecule such as water, and the unshared electron pair of another atom (i.e., O or N). The definition of the hydrogen bond used in this thesis is based on the geometric criteria developed by Luzar and Chandler [2]. That is, an intermolecular pair is hydrogen bonded if the following conditions are fully satisfied.

1. The distance between oxygen atoms is less than R O O =3.6 Å.

The distance between donor hydrogen atom and acceptor oxygen atom is less than

3. The angle between the vector that connects the two oxygen atoms and the vector that connects donor intramolecular oxygen and hydrogen atoms is less than 30°.

A.5 Hydrogen-bonded clusters

Calculation of cluster size based on the hydrogen bonds is performed by considering the modified algorithm of Stoddard [3].

A.6 Partial structure factor

The structure factor (S Liq (Q)) was computed from eq.(A.3) where (Q) is the momentum transfer vector, N L the number of molecules of liquid, n L the number of atoms belonging of one liquid molecule, r km is the vector position r km = r mr k and b i the coherent diffusion length of atom i.

The brackets stand for time and isotropic average carried out over the angles of Q in spherical coordinates of a sum of the scattering intensity arising from every couples of atoms (✓, )

Microstructure of binary mixtures in bulk and nanoconfined phases . Thus, the structure factor is expressed by steradians corresponding to the cross section measured by neutron scattering. S Liq (Q) is normalised by the number of molecules (N L ) to compare the bulk and confined phases. Then the unit of eq.(A.3) is molecules by steradian.

A.7 Time correlation function of dipole moment

A.7.1 Definition

We define a time-correlation function as:

where the angle brackets represent an ensemble average and A is the dynamic variable of interest.

If we compare the value of A(t) with its value at zero time, A(0) the two values will be correlated at sufficiently short times, but at longer times the value of A(t) will have no correlation with its value at t=0. Information on relevant dynamical processes is contained in the time decay of C(t). The starting time is arbitrary so we can also discuss the ensemble average starting at any time, t.

Normalization may also be applied by dividing by <A(0)A(0) >. The normalized function is a decay from a value of one to some lower value (not always zero). It represents the loss of correlation with the initial value. The short time value is proportional to <A 2 >. The asymptotic long time value is proportional to < A > 2 as shown in the figure below.

A.7.2 The time-correlation function method

The decay shown in the figure is the average of a large number of trajectories. We can see that C(t) decays from < A 2 > to < A > 2 . This means that initially C(0) =< A(0)A(0) > which is clear from our definition. Note that this value is shown as 1.0 on the y-axis because of normalization. As time goes on the value of A(t) changes and becomes less correlated with Chapter A Ilham Essafri its value at time zero. At long enough times A(t) has no correlation and so its average value is <A(t)>. The average value of A at time zero is <A(0)>. These averages are both average values of A and should be the same. Thus, < A(0

The value of zero shown in the Figure above is arbitrary. The normalized long time value is < A(0) > 2 /<A(0)A(0)> and is less than one, but is zero only if <A(0)> = 0.

A.7.3 Dipole moment

Even though the total charge on a molecule is zero, the nature of chemical bonds is such that the positive and negative charges do not completely overlap in most molecules. Such molecules are considered to be polar because they possessed a permanent dipole moment. The dipole moment is given by,

Then, the time correlation function of dipole moment is expressed as,

A.8 Relaxation time of dipole moment

The relaxation function (t) is a linear function of a property of a system that evolves towards equilibrium after the sudden removal of a perturbation.

A.8.1 Debye model

where ⌧ D and ⌧ K is a parameter with the dimensions of time and K is 0 < K  1. In studies of the relaxation of complex systems, the Kohlrausch function is frequently used as a purely Abstract : The study of the hydrogen bonded liquids under nanoscale confinement were the focus of this thesis. By molecular dynamics simulations, we've investigated the physical behavior of binary liquids in bulk and nanoconfined phases. By tuning the surface chemistry of the nanopore to mimic hydrophilic and hydrophobic confinement, we show that it is possible to control the structural characteristics of the core-shell structure.

Thereon, a core-shell organization was evidenced such that one of the liquids was strongly anchored to the solid surface whereas the other was confined at the center of the pore.