V N Karazin

Keywords: ionic-molecular systems, local structure, transport properties, ionic aggregation, Voronoi polyhedra

The objective of this thesis is to analyze the microscopic structure of the series ion-molecular systems that widely used for practical electrochemistry and to characterize the effect of the ion aggregation on the transport properties of these systems. By using molecular dynamics simulation, the following systems were investigated: (i) the solutions of lithium hexafluorophosphate in dimethyl carbonate / ethylene carbonate mixture (1:1), (ii) the solutions of spirobipyrrolidinium tetrafluoroborate in acetonitrile, and (iii) the mixtures of room-temperature ionic liquids (ILs) C 4 mimX (X= BF 4 -, PF 6 -, TFO -, TFSI -) with dipolar aprotic solvents such as acetonitrile, γ-butyrolactone and propylene carbonate.

For all the systems the aggregate analysis showed the formation of the ionic continuous network with the increase of electrolyte concentration. This affects significantly diffusivity and viscosity in these solutions.

Voronoi polyhedra analysis of ILs-solvent mixtures showed that below the IL mole fraction of about 0.2, the ions are well solvated by the solvent molecules, but above this mole fraction they start to form contact pairs, while the solvent molecules, expelled from the vicinity of the ions, self-associates.

RÉSUMÉ

L'objectif de cette thèse est d'analyser la structure microscopique des mélanges de liquide avec des solvants utilisés comme électrolytes dans les dispositifs électrochimiques afin de caractériser l'effet de l'agrégation des ions sur les propriétés de transport de ces systèmes. En utilisant la simulation de dynamique moléculaire, les systèmes suivants ont été étudiés: (i) les solutions de hexafluorophosphate de lithium dans le mélange carbonate de diméthyle / carbonate d'éthylène (1:1), (ii) les solutions de tétrafluoroborate de spirobipyrrolidinium dans l'acétonitrile, et (iii) les mélanges de liquides ioniques (ILs) C 4 mimX à température ambiante (X= BF 4 -, PF 6 -, TFO -, TFSI -) avec des solvants aprotiques dipolaires tels que l'acétonitrile, la γ-butyrolactone et le carbonate de propylène.

Pour tous les systèmes, l'analyse des agrégats a montré la formation d'un réseau ionique continu avec l'augmentation de la concentration de l'électrolyte.

Ceci affecte significativement la diffusivité et la viscosité dans ces solutions. L'analyse des polyèdres de Voronoi des mélanges ILs-solvants a montré qu'en dessous de la fraction molaire IL d'environ 0.2, les ions sont bien solv atés par les molécules de solvant, mais au-dessus de cette fraction molaire, ils commencent à former des paires de contact, tandis que les molécules de solvant, expulsées du voisinage des ions, s'autoassocient.

Mots clés : systèmes ioniques-moléculaires, structure locale, propriétés de transport, agrégation ionique, polyèdres de Voronoi. Chapter 1. General introduction Ionic-molecular systems represent a huge interest for the researchers as new advanced systems with high performances for the electrochemical needs. There are many different types of such systems of different cation and solvent nature. At the same time, many of them have maximum on the conductivity-concentration curve that remains to be explained.

Table of contents

List of abbreviations

This chapter gives a brief introduction to such ionic-molecular systems, as well as an overview of the problem and possible theories that can explain such behavior.

Today the global electricity consumption is constantly rising, which is caused by technology development and the constantly rising state of the global economy. 1,2 This have caused the growing demand for various energy storages, for which the advanced electrochemical systems with high performances are essential for proper and long-term functioning of these devices. Electrolyte systems with high electric conductivity and stability are required. At today's market there are numerous types of such systems that can fulfill these criteria.

Li-ion batteries are widely used when large energy density is needed, 3,4 e.g., in portable electronics, 5 hybrid electric vehicles, 6,7 etc. For these systems lithium salts are often mixed with alkylcarbonates such as ethylene, dimethyl, diethyl and ethyl-methyl carbonates, [8][9][10][11] which can optimize the operating temperature range and increase the conductivity of the Li + . 12 As for the lithium salts themselves, there are several numerous candidates such as LiBF 4 , LiPF 6 , LiTFSI, LiTDI, LiAsF 6 , CF 3 SO 3 Li, LiClO 4 , etc. 6,[13][14][15][16] From practical point of view LiPF 6 dissolved in the binary mixture of two solvents usually used. One of the solvents is considered to play a role in dissociating the cations and anions via high dielectric constant whereas the other in improving ionic movement via its low viscosity: ethylene carbonate (EC) and dimethyl carbonate (DMC) are one of the common examples of such a mixture. 17 During the last few decades electric double layer capacitors have shown themselves as promising charge storage devices too. [18][19][20][21][22] These types of systems have better power density, long cycle life compared to secondary batteries and also are safer in usage and Li-ion batteries. [23][24][25][26] Thus, such capacitors are often used in modern electric vehicles, smartphones, industrial power management, complex power systems, etc. [27][28][29][30] However, the widespread usage of these devices is hindered by their low energy density. 31 It is necessary to improve the energy density without sacrificing the high power density and long cycle life. Because the energy density is proportional to the square of the voltage, the organic electrolytes that have wide voltage window are used for high energy density applications. [32][33][34] Usually these electrolytes are dissolved in carbonate-based organic solvents, e.g., acetonitrile (AN) or propylene carbonate (PC). 31,34,35 AN is electrochemically stabile and has high conductivity while PC has high flash point, but low conductivity. And among different salts tetraethylammonium tetrafluoroborate (TEABF 4 ) is the most common one. [36][37][38] However, this electrolyte has a significant drawback of limited solubility in organic solvents.

1,1'-spirobipyrrolidinium tetrafluoroborate (SBPBF 4 ), on the other hand, has low viscosity and high solubility in many organic solvents, as well as good electrochemical stability and high value of conductivity. 34,39,40 Another type of systems that has been actively studied in recent decades along with traditional electrolyte ones is ionic liquids (ILs). They are known for a long time and gained mainstream popularity about 30 years ago. This was made possible by the commercial availability and the increased variability of the IL.

The first applications of ILs were as solvents for chemical reactions, 41,42 for catalysis with transition metals, 43 as a stationary phase in gas-liquid chromatography 44 and they are finding new improvements nowadays. [45][46][47][48][49][50][51][52][53][54][55][56] ILs, room-temperature ionic liquids, are molten salts usually composed of relatively large organic cations and organic or inorganic anions, where the ionic head groups (ammonium, imidazolium, sulfate, sulfonate etc.) are attached to non-polar (mostly alkyl) side chains which are liquid below 100 °C. Due to perspective properties such as nonvolatile, nonflammable, and nonexplosive, possess high chemical and thermal stability, large electrochemical potential window, high ionic conductivity, large liquid temperature range, negligibly low vapor pressure, ILs successfully used in many fields of science. The most studied application areas now are biological (antimicrobial ionic liquid-based materials [57][58][59] pharmaceutical (active medecine ingredients 60,61 ) chemical (molecular gas capture, such as H 2 S, H 2 , CO and CO 2 , [62][63][64][65][66] functional materials, [67][68][69][70][71] lubricants 72,73 ) Because of unique properties of ILs one of their main applications is electrochemistry where they used as electrolytes in different energy storage devices such as batteries, 17 solar cells, [74][75][76][77] supercapacitors, [START_REF] Esser | TiCl4 Dissolved in Ionic Liquid Mixtures from Аb Initio Molecular Dynamics Simulations[END_REF][START_REF] Shelepova | Structural similarity of an ionic liquid and the mixture of the neutral molecules[END_REF][START_REF] Sharma | How mixing tetraglyme with the ionic liquid 1-n-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide changes volumetric and transport properties: An experimental and computational study[END_REF] etc. The family of 1-alkyl-3-methylimdazolium (C n mim + ) ILs with perfluorinated anions like tetrafluoroborate (BF 4 -), hexafluorophosphate (PF 6 -), trifluoromethanesulfonate (TFO -), bis(trifluoromethane)sulfonimide (TFSI -) has proven to be good electrolytes for various electrochemical devices. [START_REF] Sharma | Effect of water on structure and dynamics of [BMIM][PF6] ionic liquid: An all-atom molecular dynamics simulation investigation[END_REF][START_REF] Sharma | Effect of alcohols on the structure and dynamics of [BMIM][PF6] ionic liquid: A combined molecular dynamics simulation and Voronoi tessellation investigation[END_REF][START_REF] Schröder | On the collective network of ionic liquid/water mixtures. III. Structural analysis of ionic liquids on the basis of Voronoi decomposition[END_REF][START_REF] Biswas | Microheterogeneity-Induced Vibrational Spectral Dynamics of Aqueous 1-Alkyl-3-methylimidazolium Tetrafluoroborate Ionic Liquids of Different Cationic Chain Lengths[END_REF][START_REF] Haberler | Hydrated ionic liquids with and without solute: The influence of water content and protein solutes[END_REF][START_REF] Rajbangshi | Cosolvent polarity dependence of solution structure in[END_REF][START_REF] Tsuzuki | Theoretical analysis of the hydrogen bond of imidazolium C2-H with anions[END_REF] The stopping factor for widespread use of ILs is their high viscosity that is one of the reasons of low ion mobility. To overcome this problem the mixing of ILs with molecular solvents is usually made.

Typical candidates for this purpose are AN, [START_REF] Tsuzuki | Magnitude and Directionality of Interaction in Ion Pairs of Ionic Liquids: Relationship with Ionic Conductivity[END_REF][START_REF] Hunt | Hydrogen bonding in ionic liquids[END_REF][START_REF] Hunt | Structural characterization of the 1-butyl-3-methylimidazolium chloride ion pair using ab initio methods[END_REF][START_REF] Fujii | Experimental evidences for molecular origin of low-Q peak in neutron/x-ray scattering of 1-alkyl-3-methylimidazolium bis(trifluoromethanesulfonyl)amide ionic liquids[END_REF] PC, [START_REF] Fujii | Liquid Structure of Room-Temperature Ionic Liquid, 1-Ethyl-3-methylimidazolium Bis-(trifluoromethanesulfonyl) Imide[END_REF][START_REF] Mondal | Quantitative prediction of physical properties of imidazolium based room temperature ionic liquids through determination of condensed phase site charges: A refined force field[END_REF][START_REF] Mondal | A Refined All-Atom Potential for Imidazolium-Based Room Temperature Ionic Liquids: Acetate, Dicyanamide, and Thiocyanate Anions[END_REF] γ-butyrolactone (-BL), 95- 98 dimethyl sulfoxide (DMSO), [START_REF] Fornefeld-Schwarz | Refractive Indices and Relative Permittivities of Liquid Mixtures of γ-Butyrolactone, γ-Valerolactone, δ-Valerolactone, or ε-Caprolactone + Benzene, + Toluene, or + Ethylbenzene at 293[END_REF]100 etc.

As it was mentioned, all of these systems have a wide range of use for electrochemical applications for batteries, supercapacitors, solar cells, etc. For this purpose, electroconductivity remains a crucial property for the investigation.

Lithium-type systems, alkylammonium electrolyte solutions and ILs with aprotic dipolar solvents -for all of them the electroconductivity has maximum at concentration of electrolyte. [START_REF] Fujii | Experimental evidences for molecular origin of low-Q peak in neutron/x-ray scattering of 1-alkyl-3-methylimidazolium bis(trifluoromethanesulfonyl)amide ionic liquids[END_REF][101][102][103][104][105][106][107][108][109] The traditional explanation for this phenomenon is the local structure changes in these systems (particularly, ion-ion and ion-solvent interactions) and the viscosity changes that both occurs at around the concentration where maximum of conductivity curve can be found. 110 Moreover, vibrational spectroscopic techniques and nuclear magnetic resonance (NMR) spectroscopy were used to analyze interactions in mixtures of imidazolium-based ILs with molecular solvents. [111][112][113][114][115][116][117][118][119][120][121][122][123] The findings indicate that noteworthy alterations in the vibration modes of C-H (or the ring of cations) and the 1 H chemical shift manifest at a certain IL concentration range where the conductivity undergoes changes. This phenomenon was linked to the adjustment, through modification of the mixture composition, of the equilibrium between different intercomponent interactions present in the mixtures, namely interionic (predominant at very high IL mole fractions), ion-solvent, and solvent-solvent interactions. Thus, the investigation of the microstructure of these systems remains a relevant task.

Theoretical approaches still cannot answer the question about these phenomena for solutions of different types. Especially considering the different nature of them: lithium and alkylammonium electrolytes are being solid salts under normal conditions and never can be studied in their "pure" liquid form unlike ILs. Nevertheless, numerous studies (in particularly, for ILs-solvent mixtures) have been made during last 30 years to study the ionic association and solvation processes and their correlation with the transport properties in order to understand the reasoning of this behavior. 109,[124][125][126][127][128][129] One of the concepts that can describe the maximum on the conductivity-electrolyte concentration curve states that ion pairs and aggregates exist in such systems. Indeed, if the system consists predominantly (or only for neat ILs) of ions, the one should expect high conductivity in the solution, but that's not the case in real systems as was mentioned earlier. The interpretation with ion-pairing indication 110 or aggregates formation (triplets, quadruplets and higher) 130 can help to interpret this observation. In this case the effective concentration of charge carriers in solution -free ions -becomes lower with the increasing of the electrolyte concentration which lowers the electroconductivity as well comparing to diluted solution.

Following this, the ion pairs do not contribute in the conductivity of the solution at all because of their neutral charge. But considering larger aggregates is a lot trickier. For instance, if triple ions are more likely to form in the solution than ion pairs, an increase in conductivity can be anticipated as they always possess a nonzero charge. [130][131][132] Also, the larger the aggregates in the solution, the lower the electroconductivity is. The overall structure and stability of the aggregates depend on the components of the solution itself, specifically, their interactions with each other and local structure as a result. 133 Another possible approach is the free volume theory, which posits that the rate of molecular diffusion is determined by the quantity of unoccupied space between the particles within the solution. 134,135 According to the free volume theory, total volume of a solution:

,

s occ f V V V   (2.1)
where V occ is occupied volume, V f is free volume.

The V f is distributed locally into so-called voids or holes between molecules and ions. These holes can be formed from other smaller ones, they have irregular shape, size and location and formed by a particular molecular distribution. Voids are constantly changing in the solution due to the molecules and ions displacement. Free volume is closely linked to the transport properties such as viscosity and conductivity. Studying the free volume in IL and its potential impact on its physicochemical properties establishes a connection between the IL's structure and its suitability for a particular application. 136,137 In order to investigate these approaches a classical molecular dynamics (MD) simulation technique is proposed. It allows to obtain a wide spectrum of physicochemical, transport and structural properties of simulated systems, including the ones that cannot be directly obtained from the experimental data or easily interpreted. 138 To investigate the local structure of the proposed systems, two methods have been suggested. The first one was studied by Bernardes and co-workers. 139- 141 It is based on the distance criteria to observe the formation of the aggregates in the solution. This method enables not only qualitative verification of the formation of aggregates but also quantitative exploration of the process in terms of the probability distribution of aggregation sizes in the solution. More details regarding this method are provided in Chapter 2.

The second method involves the algorithm proposed by Ruocco et al., 142 which generates a tessellation of the space without gaps or overlaps. This is achieved through Voronoi polyhedral (VP), which represent spatial points closer to one seed than to any other. The VP algorithm is based on a spatial set of seeds and can be used to investigate the local structure of the proposed systems. More details about this algorithm are provided in Chapter 2.

Organization of the thesis

In this thesis a set of classical MD simulations were performed to investigate the microscopic structure and transport properties of lithium (Li + ), 1-1'-spirobipyrrolidinium (SBP + ) and

Chapter 2. Methodology and computational details

In this chapter all the details of molecular dynamics simulations are provided. Two approaches for microscopic structure investigations are presented: (i) in terms of radial distribution functions (RDF), running coordination numbers (RCN) and (ii) Voronoi polyhedra (VP) analysis. The former ones were used for the detailed description of ion subsystems in terms ion aggregates. Special attention was paid to the algorithm of calculation of transport properties: viscosity and diffusion.

Molecular dynamics methodology

MD simulations have been performed at the temperature of 298.15 K. To set the size of the cubic simulation box, a short (i.e., 1 ns) run has been performed on the isothermal-isobaric NPT ensemble at 1 bar. The compositions of each set of systems are given in respective Chapters.

All simulations have been carried out using the GROMACS 2019.4 software package. 1 The temperature and the pressure have been kept constant by means of the velocity-rescaling thermostat 2 with the relaxation time of 0.1 ps, and the Berendsen barostat 3 with the relaxation time of 0.5 ps, respectively. Equations of motion have been integrated using the leap-frog algorithm with a time-step of 0.5 fs. All interactions have been truncated to zero beyond the center-center cutoff distance of 1.2 nm. The long-range part of the electrostatic interaction has been accounted for by the particle mesh Ewald method, 4 while that of the Lennard-Jones interaction has been treated by the conventional shifted force technique.

The Lennard-Jones parameters corresponding to unlike pairs of atoms have been calculated by the standard Lorentz-Berthelot combination rules. 5 After equilibrating the systems in the NPT ensemble, simulations of 10 ns have been performed in the NVT ensemble using the equilibrium density determined from the constant pressure run. All set of systems were simulated at least five times from new independent randomly created configuration. The last 1 ns of the trajectory of these simulations have then been used for the detailed structural analyses while full 10 ns trajectories were used for transport properties calculation.

Microscopic structure

Radial distribution function

A quantitative description of the structure of liquids can be made with the help of radial distribution function (RDF). As a result of the interaction of particles with each other, the position of each particle depends on the location of the others. The correlation between the mutual arrangement of particles is described by the RDF. It is a pair correlation function, which can show how the investigated system is packed with the particles.

A RDF specifies the probability of finding an observed particle at a certain distance from the reference particle for all directions, relative to the uniform density of the observed particle. This uniform density is the density of observed particles that would be present if they were uniformly distributed throughout the simulation cell. Thus, the value of the RDF larger than 1 indicates the higher probability of finding the observed particle at certain distance from reference particle than on average. The RDF usually determined as 𝑔(𝑟):

6     2 , 4 ij ij j N r V g r r r N    (2.1)
where r is the distance between particles,   ij N r is the average number of observed particles j in a sphere with a thickness r at the distance of r from the reference particle, N j is the total number of particles j, V is the volume of the system.

The example of RDF is shown at Figure 2.1, from which several important observations can be made. At very small distances, the value of the 𝑔(𝑟)

approaches zero, which indicates that the probability of finding a particle at that distance is very low due to the strong repulsive interactions between the particles.

This behavior reflects the effective size or diameter of the atoms. Next, there are several peaks that show the most probable distances between observed and reference particles. Usually, the most probable distance between neighbor particles is of most interest. It is equal to the position of the first peak on the RDF.

Also, shoulders can appear near the peaks as seen at the example. It indicates additional probability of location of observed particles regarding to the reference one. In combination with the peaks itself the shoulders can usually give additional information about local organization in investigated systems. Also peaks and shoulders indicate such known "shells" of neighbors -a regions where the two types of particles investigated are packed in some order around each other. The border of such shells can be determined as the respective minimum on the RDF.

The occurrence of peaks and shoulders at long range distances indicates a high degree ordering in the investigated system. Lastly, at the very long range every RDF becomes equal to the value of 1, which states for uniform or average density of the observed particle.

Running coordination number

One of the simplest characteristics of the structure in the liquid along with the RDF is running coordination number (RCN). A RCN shows how many observed particles can be found in certain range around the reference particle. It can be obtained by integrating 𝑔(𝑟) in spherical coordinates to the distance r.

Thus, the RCN can be determined as 𝑛(𝑟): 7,8    

Aggregate analysis

In order to study the association of ions one should to identify the criterion by which two ions can be considered as a part of one aggregate (or cluster, associate). Such a criterion was proposed in different works 9,10 as the distance between coordination centers of respective ions. Thus, two ions were considered to belong to the same associate if their respective centers are located at the equal or lower distance that was chosen as a criterion from each other. 11 After the definition of the criterion, the neighbor list of each cation and anion was determined for each configuration during the simulation at each timestep. The obtained neighbor list was later used to establish the connectivity between ions in the system. Important to note that mainly differently charged ions are coordinating around each other (anions around cations and vice versa). This means that the resulting clusters are constructed from the ions of altering charge that have the distance between them that fulfill the determined criterion.

Finally, the statistical analysis was applied to determine the characteristics of clusters. One of such statistical functions can be a size distribution of the aggregates 𝑃(𝑛). It shows the probability of finding an ion in an aggregate of size n:

    1 , C n j n A j P n CN    (2.3)
where   n A j is the number of aggregates of size n for a given configuration j, C is the total number of configurations acquired during the simulation, N is the total number of cations and anions combined in the simulation box.

The size distribution of the aggregates 𝑃(𝑛) is shown at Figure 2.3. From the graph, it is possible to observe the probability of cluster occurrence in the system for each cluster size. Expanding this picture to the whole concentration range can give the insight into the local organization of ionic subsystem and clusterization processes. In this case size clusters of 1 (isolated ions) and of numbers close to N are the most interesting for the analysis. For example, the domination of clusters of size one can point out the domination of solvation effects over association in the system. If the concentration of ions will increase, the transition from small clusters to large aggregates can occur which specifies the change in the preferable interactions from solvation to the ionic association. Aggregate analysis has been performed by AGGREGATES 3.2.0 software package. 12 To better represent the results of the clusterization the average number of association n can be obtained. In general case, one can calculate it as follows:

  1 N i i i n n P n    . ( 2
      0 . vv C t v v t  (2.5)
According to the ergodic hypothesis, the time average for the equilibrium system coincides with the ensemble average. For direct analysis and comparison of particle dynamics, it is more convenient to use the normalized ACF of linear velocity

  vv C t :       2 . 0 vv vv C t C t v  (2.6)
At the same time, for an equilibrium system, the average square of the speed of particles is related to their mass and average temperature by the ratio:

  2 3 0 . B k T v m  (2.7)
The coefficient of translational self-diffusion of atoms (molecules, ions) in a liquid can be found using the Green-Kubo relation:

  0 1 . 3 vv D C t dt    (2.8)

Viscosity

For the viscosity a nonequilibrium periodic perturbation method has been used. 13 To sum it up, molecular dynamic simulation is carried out in the 3D periodic cell with the external force in x direction a(z). According to the Navier-Stokes's equation:

  2 , u u u a p u t               (2.10)
where u is the velocity of the liquid, p is pressure of the fluid, ρ is the density of the fluid, t is time, η is viscosity. Because force is applied only in the x direction, the velocity along y and z will be zero:

      2 2 . x x x u z u z a z t z          (2.11)
The velocity profile as well as acceleration should be periodic because of the periodic system in the simulations. Thus, the cosine function can be used for this purpose:

    cos , x a z kz   (2.12) 2 , z k l   (2.13)
where l z is the height of the box,  is the acceleration amplitude of the external force. The viscosity then can be obtained:

2 . V k     (2.14)
The measured viscosity greatly depends on the parameter . To obtain the viscosity at zero acceleration few viscosities for different accelerations should be obtained. Then plotting the viscosities versus the amplitudes allows to obtain shear viscosity for =0 via extrapolation.

Voronoi analysis

In a three-dimensional space of seeds, the Voronoi polyhedral (VP) of a given seed is the locus of the spatial points that are closer to this seed than to any other one. 14,15 Thus, by calculating the Voronoi tessellation, the space can be unambiguously divided between the seeds. This way, the VP of each seed corresponds to the volume element that belongs to this particular seed. In other words, the volume of a VP represents the space available around its central particle. Conversely, the reciprocal volume of a VP can be the measure of the local density around this particle. Further, considering that the vertices of the VP are the spatial points that are equally far from the four nearest seeds, they mark the centers of the largest spherical voids located between the particles.

In applying the Voronoi analysis for multi-atomic particles, such as the cations, anions, and solvent molecules in the mixtures considered here, the seeds are associated with chosen atoms of these particles.

In performing Voronoi analysis and determining the VP around representative sites of each component of the mixture, the algorithm proposed by Ruocco et al. 16 has been used. To calculate the volume of the VP of a given site, first the vertices pertaining to each face of the polyhedron have been determined and sorted according to their sequence along the perimeter of this face. 17 The VP faces have then been divided to elemental triangles, determined by their first, j th and (j+1) th vertex, and the VP itself has been divided to elemental tetrahedra, one face of which is one of these elemental triangles, and the fourth vertex is the position of the atom around which the VP is centered. 17 In this study, the following metric properties have been evaluated, 𝑋: the volume of the Voronoi polyhedra, 𝑉, the local density around the central particle, 𝜌 = 1/𝑉, and the radii of the spherical voids between the particles, 𝑅, simply as the distances of the VP vertices from the central atom. For each of these metric quantities, the distribution was calculated, 𝑃(𝑋). Further, to characterize the change of the shape of these distributions with the mixture composition, the mean value was also evaluated, 〈𝑋〉, standard deviation, 𝑋, and skewness parameter, 𝑚 ⁄ (𝑋) of these quantities. The skewness parameter, characterizing the asymmetry of the distribution, is defined as: 18,19

  3 2 3 3 2 2 , M m M  (2.14)
where M n is the n th moment of the distribution. The value of this parameter helps to evaluate the asymmetry of the corresponding distribution. Thus, in the case of symmetric distribution, the value of the skewness parameter is unity, values below or above 1 indicate that the distribution extends more to lower (negative skew) or higher (positive skew) values. 18,19 The composition dependence of these values can shed some additional light to the change of the local structure with the mixture composition. Indeed, in previous papers it was shown that the occurrence of a maximum of the standard deviation of the reciprocal volume as a function of either the temperature or the composition is a signature of large density fluctuation (i.e., occurrence of low and high density domains, where the local density around the particles that are located at the boundary of these domains is fluctuating more than those located at the core of them). [20][21][22] Further, the analysis of the VP volume or density distribution when one of the two components (here the IL ions or the solvent) is disregarded in the analysis can provide some additional insight into the self-association of the like components in the mixtures. 17 This way, the VP volume distribution reflects the spatial distribution of the non-disregarded component only, and self-associates of the disregarded component appear as large voids in the analysis. 17 Thus, similarly to the case of one component systems with large density fluctuations, 23 were used: minima on the RDFs and the minima on the second derivative of the RCNs. For the second set of criteria the massive aggregation was spotted from the concentration of 1.0 M and higher which in agreement with the experimental conductivity value. Also, the criteria to take SSIPs into account seem to overestimate the aggregation. The diffusion coefficients for all components of the solutions and viscosity of simulated systems were also obtained. The diffusion coefficients for all components are decreasing and viscosity values are non-linearly increasing with the salt concentration increase. These findings and the drastic viscosity increase at 1.0 M and at higher concentrations of LiPF6 are in agreement with the experimental conductivity values.

Introduction

Lithium-ion batteries are widely used in various portable devices. [1][2][3][4][5] They were leading the technological revolution in the electrochemistry for the last decades. The combination of electrode materials, electrolyte solvents and, of course, salts can hugely impact the battery performance. [5][6][7][8][9][10][11][12][13][14][15][16][17] Practical electrolyte should be electrochemically stable, have high ionic conductivity, transference number, good electrochemical and thermal stability, low volatility, flammability, toxicity and be cheap in the production. 18 Polar organic molecules such as dimethyl carbonate (DMC) and ethylene carbonate (EC) are one of the most common solvents in lithium batteries. 6,[19][20][21] Binary mixtures of solvents proved to be useful in improving electrolyte behavior for different temperatures and in optimizing electrochemical and physical properties. 22,23 Electrolytes with EC known to form a stable solid electrolyte interface on anodes that can prevent electrolyte decomposition. 24 EC also has high dielectric constant and relative viscosity. That is why linear DMC with low viscosity and dielectric constant usually paired with the cyclic ester like EC: the overall viscosity of such mixture is lower than of pure EC, the mixture can still dissolve lithium salts because of high dielectric constant of EC and, most importantly, the ionic conductivity of such system improves. 25 As for the salt, LiPF 6 has a large dissociation degree in organic carbonate solvents, which results in an excellent ionic conductivity for the electrolyte.

Due to these reasons organic polar electrolytes was studied by variety techniques with the accent on electrochemical application. These studies include such methods as vibrational spectroscopy, X-ray diffraction, 26 photoelectron spectroscopy, 27,28 neutron scattering, 29 NMR, 30 etc. Although as was mentioned the combination of LiPF 6 with carbonate solvents leads to better electroconductivities of such systems, one needs to choose the composition of the components attentively because the conductivity dependence has maximum on the concentration curve. [31][32][33] One of the most common commercial used solutions of LiPF 6 in DMC/EC (1:1) binary has the peak electrical conductance at 1 M. 33,34 This maximum usually explained via local structure changes in the solution, 35 although the literature data are of a qualitative nature without a detailed analysis of the contribution of ion aggregation to the formation of a maximum on the concentration curve of electrical conductivity.

In this Chapter, MD simulations are used to obtain microstructural and transport properties for LiPF 6 in DMC/EC (1:1) binary mixture of various salt concentration. In addition, the aggregate analysis has been performed to study the features of ionic clusterization in lithium salt solutions. The Chapter is organized as follows. In sec. 2 details of the details of molecular dynamics simulation and force field development for solvent molecules is provided. In sec. 3 the main results are showed and discussed further in the section. In sec. 4 the main conclusions are presented.

Methodology

Details of molecular dynamics simulation

MD simulations of the LiPF 6 and binary mixtures of DMC/EC (1:1) have been performed at five different compositions. To calculate the exact number of the ions and solvent molecules for the MD simulation from the molarities the experimental densities, ρ, of the LiPF 6 in DMC/EC (1:1) binary mixture were used. 36,37 The number of the different particles in cubic box and molar concentration of the LiPF 6 in the simulated systems are collected in Table 3.1.

The total number of Li + cations and PF 6 -anions were always equal to 100.

Two systems of pure solvents (DMC and EC) were also simulated (with the number of molecules of 500 for each). Pure EC system was simulated at the temperature of 313.15 K because at 298.15 K this solvent is solid substance.

All simulations were performed as described in Chapter 2.

Force field refinement

The structure of the PF 6 -anion and DMC and EC solvent molecules along with the atomic labeling scheme is shown at The labeling of solvent molecules used in potential models is also shown.

For the Li + the potential model directly from OPLS-AA 38 has been used.

For the PF 6 -anion the potential model from Canongia Lopes et al. 39 was taken.

As a first step the LigParGen 40 was used to develop Lennard-Jones (LJ) parameters, as well as bond, angle, and dihedral angle parameters based on the OPLS-AA 38,41,42 force field for both DMC and EC.

In current study according potential models have the following functional form of the total potential energy:

            5 2 2 , , 0, 0, 0 12 6 , , 0 cos 2 2 1 cos 4 4 angles bonds dihedral n r ij ijk tot ij ij ijk ijk n ijkl ij ijk ijkl n improper non ij ij i j ijkl ijkl s ijkl ij ijkl ij ij ij ij k k U r r C q q k n r r r                                                              , bonded  (3.1)
where k is the force constant for bond stretching (r), angle bending (θ),

proper and improper dihedral (ϕ), respectively, ε and σ are the Lennard-Jones energy and the distance parameters, respectively, and q stands for the fractional charges of the interaction sites. For proper dihedral

180 o ijkl ijkl    
.

Optimization of the geometry and calculation of partial charges of atoms was carried out using the software package Gaussian16 43 at M062X-AUG\-cc-PVTZ level. The algorithm for calculating partial atomic charges according to Breneman was applied. 44,45 The charges obtained are presented in the Table 3.2.

But the results for diffusion coefficients of these potential models in pure solvents are much lower than the experimental ones. For pure DMC diffusion coefficient, D, was equal to 1.5⸱10 -5 cm/s 2 , for pure EC -0.5⸱10 -5 cm/s 2 .

Experimental values are 2.6⸱10 -5 cm/s 2 (at 303 K) and 0.8⸱10 -5 cm/s 2 respectively.

In order to improve the results for the solvent potential models and to reproduce transport properties of pure molecular liquids the OPLS-AA models were modified. Lowering the effective molecule radius can improve the diffusion coefficients. Thus, the Lennard-Jones parameters of H atoms of DMC and EC were replaced with the GAFF force field ones. 46,47 The GAFF  parameter is almost two times lower than such of OPLS-AA force field. This approach can give transport properties closer to the experimental ones. The Lennard-Jones parameters and charges of the DMC and EC are shown in the Table 3.2. 3.3. For the potential models with the H parameters from GAFF the results are close to the experimental values. For further MD simulations these modified potential models were selected. a -for 303 K. As was stated in the literature, contact ion pairs (CIP) and solvent shared ion-pair (SSIP) may occur in the solutions of lithium salts. 33,53,54 The latter are formed when the solvent molecule (DMC or EC for investigated solutions) is located between cation and anion. After the first minimum all of the RDFs have wide plateau until approximately 0.6 nm, and second maximum occurs only at 0.91 nm, second minimum -at 1.04 nm. The wide region, related to the formation of SSIPs, of uncertain position of PF 6 -anion relatively to Li + cation (0.6 nm -1.0 nm on RDFs) can be explained with the packing of solvent molecules around the cation. It was proposed that solvent molecules are arranged around the Li + cation in a way that leaves large holes between them. The anions can penetrate into these empty spaces quite closely to the cation. 33,53,54 It was expected that the coordination numbers for cation-solvent interaction will decrease while the cation-anion ones will increase with the increasing of the LiPF 6 concentration. The EC carbonyl O atoms are competing with the PF 6 - anions for the coordination with the Li + cation. But in the case of DMC its number is independent of the concentration of the salt. It remains ~1.8 for all systems while for Li-P it increases from 0.1 to 1.6 and for EC it decreases from 4 to 2 with the increasing of LiPF 6 concentration in DMC/EC binary mixture. This is caused by higher molecular dipole moment of EC comparing to DMC. Also, EC molecule is smaller and can be packed more efficiently in the Li + first coordination sphere than wide and linear DMC. The average total coordination number remains 5.5-6.0 regardless of the concentration. These results are in agreement with previous MD simulations. 59

k , kJ/(mol⸱nm 2 ) 0 r , nm r k , kJ/(mol⸱nm 2 ) C 1 -O 1 C 1 -O 1-2 C 2 -C 3 C 2 -O 2 C 3 -O 3 C 2 -H 1-2 C 2 -H 1-3 C 3 -H 3-4 C 3 -H 4-
 , deg k  , kJ/(mol⸱rad 2 ) 0  , deg k  , kJ/(mol⸱rad 2 ) O 1 -C 1 -O 1-2 C 1 -O 2 -C 2 C 1 -O 3 -С 3 С 2 -С 3 -O 3 C 3 -C 2 -O 3 С 2 -С 3 -H 3-4 С 3 -С 2 -H 1-2 O 2 -C 1 -O 3
O 2 -C 2 -H 1-2 O 2 -C 2 -H 1-3 O 3 -C 3 -H 3-4 O 3 -C 3 -H 4-6 H 1 -C 2 -H 2 H 3 -C 2 -H 1-2 H 3 -C 3 -H 4 H 4 -C 3 -H 5 H 6 -C 3 -H 4-
 , kJ/mol n s  , deg k  , kJ/mol n O 1 -O 2 -C 1 -O 3 O 3 -C 1 -O 1 -O 2 180.0 43.932 2 180.0 43.932 2 Dihedral 0 C , kJ/mol 1 C , kJ/mol 2 C , kJ/mol 3 C , kJ/mol 4 C , kJ/mol 5 C , kJ/mol DMC C 1 -O 2 -C 2 -H 1-3 C 1 -O 3 -C 3 -H 4-6 O 1 -C 1 -O 2 -C 2 O 1 -C 1 -O 3 -C 3 C 2 -O 2 -C 1 -O 3 C 3 -O 3 -C 1 -O 2
.0 EC C 1 -O 2 -C 2 -O 3 C 1 -O 3 -C 3 -O 2 C 1 -O 2 -C 2 -H 1-2 C 1 -O 3 -C 3 -H 3-4 O 1 -C 1 -O 2 -C 2 O 1 -C 1 -O 3 -C 3 C 2 -O 2 -C 1 -O 3 C 3 -O 3 -C 1 -O 2 O 2 -C 2 -C 3 -O 3 O 2 -C 2 -C 3 -H 3-4 O 3 -C 3 -C 2 -H 1-2 H 1-2 -C 2 -C 3 -H 3-4 -2.

Aggregate analysis

To analyze the formation of the aggregates on the solution two distance criteria are proposed. The first is the first minimum in cation-anion RDF (0.45 nm, As mentioned in sec. 3.3.1, the Li + cation has very strong cation-solvent interaction to the point that EC and DMC molecules are dominating its first coordination sphere. Also, as were discussed, Li + cation can form SSIPs with anions. Thus, it is necessary to investigate this type of ion pairing in these systems.

For the second set of criteria the second minimum on cation-anion RDF (1.04 nm, For the first set the results are pretty similar for both criteria chosen. The ions are mostly isolated from each other in 0.1 M solution of LiPF 6 in DMC/EC

(1:1) binary mixture. With the increasing of the salt concentration, one can see that more and more aggregates of different sizes start to appear. Nevertheless, at the 2.0 M concentration still the size of biggest ionic associate is 19 for both criteria. This fact ones again proves the strong solvation effect comparing to the association which is still not dominant even at high concentrations of salt.

For the second set of criteria the ions mostly are isolated or are in small clusters in 0.1 M solution of LiPF 6 in DMC/EC (1:1) binary mixture. With the increasing of the salt concentration more and more aggregates of different sizes start to appear. For 0.5 M the so-called "transition" state appears for the first criterion that is defined by numerous aggregates of different sizes in solution at the same time. It indicates that the system will form a network of solvent-shared ion pairs with the further salt concentration increase. Indeed, at 1.0 M almost all of the ions are part of this aggregation network for both criteria. At 2.0 M all ions in the system are forming one large aggregate.

To illustrate the general result among all concentrations for both set of criteria the average number of associations were obtained (Figure 3.13). For the first set it can be seen that both criteria are similar in their values. Also, there are not any massive association processes indicated in the systems for all concentrations of LiPF 6 . For the second set of criteria the massive aggregation can be seen beginning from the 1.0 M LiPF 6 concentration. The ionic conductivity is related to the effective concentration of the charge carriers in the solution according to the Nernst-Einstein relation. 60 The formation of CIPs and SSIPs in the solution and the formation of the ionic clusters as a result reduces the number of charge carriers and thus lowers conductivity. That is why the concentration at which the massive clusterization of ions in aggregate analysis occurs for the second set of criteria is close to the concentration at which the experimental conductivity has maximum at its curve. 33 Also, it should be stated that the second set of criteria in the analysis overvalues the distance to take SSIPs into account as can be seen at Figure 3.12 and 3.13. If all (or almost all) the ions are part of one aggregate, the concentration of effective charge carriers should be very low, to the point where no conductivity should be observed.

Transport properties

The transport properties were studied in terms of diffusion coefficients of all the components of the LiPF 6 in DMC/EC binary mixture systems as well as their shear viscosity. The obtained values are presented at Figure 3.14.

Here it is seen the decreasing of all diffusion coefficients as the concentration of LiPF 6 increases from 0.1 M to 2.0 M. Also, it can be seen that diffusion coefficients of solvent molecules are approximately two times larger than of ions. The values of coefficients for both solvents are similar to each other with less solvated DMC being higher. Simultaneously, the viscosity of the system increases according to a nonlinear dependence and at highest concentrations investigated it reaches rather huge values of ~35 cP. These results approve the appearing of the large cluster in the simulated system with the formation of SSIPs in solution beginning after the 1.0 M concentrations of LiPF 6 after which the viscosity is drastically changes.

Diffusion coefficients of ions is one of the factors that affects the electric conductivity as stated by Nernst-Einstein relation. 60 Diffusion coefficients decrease together with the drastic non-linear increase of the viscosity at nearly 1.0 M of LiPF 6 concentration confirms the presence of the maximum of experimental electroconductivity at this concentration value. 33

Conclusions

In the present Chapter LiPF 6 in DMC/EC (1:1) binary mixture solutions of five different concentrations have been studied with classical MD simulation technique. The potential models for DMC and EC molecules were optimized in this work from the combination of two different force fields: OPLS-AA and GAFF in order to properly reproduce the transport properties of these solvents.

The structure has been analyzed in terms of cation-anion and cation-solvent RDFs and RCNs. The snapshot from the trajectory files of the simulation confirmed the RDF and RCN data and shoved that Li + cations tend to form contact ion pairs as well as solvent-shared ion pairs.

The RCNs showed that total coordination number of the cation for the first coordination sphere remains 5.5-6.0 for all concentrations. In particular, for DMC it remains ~1.8, while for EC it decreases from 4 to 2 and for PF 6 -anion it increases from 0.1 to 1.6 with the increasing of the salt concentration. This indicates that EC solvent and anions are competing for the position in first coordination sphere.

For the ionic aggregate analysis two set of criteria were proposed (based on the fact of formation of CIPs and SSIPs). For them two different distances were used: minima on the RDFs and the minima on the second derivative of the RCNs.

As with the first set of criteria only small aggregates were spotted in the system, the previous statement was confirmed that LiPF 6 give preference to formation of solvent-shared ion pairs in DMC/EC (1:1) binary mixtures. The massive aggregation for the second set of criteria was spotted beginning from the concentration of 1.0 M for both criteria. The results for distances of minimum on the RDFs or minimum on the second derivative on the RCNs are not differ significantly. Also, the distances taken for the second set of criteria seem to overestimate the aggregation.

Lastly, the transport properties of simulated systems were obtained. The diffusion coefficients for all components are decreasing and viscosity values are non-linearly increasing with the salt concentration increase. The drastic non-linear increase of the viscosity from nearly 1.0 M and for higher concentrations of LiPF 6 also occurs. These findings are consistent with the maximum of experimental electroconductivity at this concentration value.

Introduction

Electric double-layer capacitors (EDLCs) or supercapacitors were considered as one of the most promising energy storing devices recently. [1][2][3][4][5][6][7] Their main benefits are high power density, long lifetime (cycle time) and fast charge/discharge process. Also, EDLCs usually have up to 1000 times higher power density as well as better safety comparing to Li-ion batteries. [8][9][10][11] One of the main properties that determine the great performance of supercapacitors is conductance of the electrolyte. As a result, developing the new electrolyte systems with high conductance and wide operating temperature ranges remains the relevant task.

The development of such systems involves the use of electrolyte salts with large electrochemical stability windows. Typically, the acetonitrile (AN) is used as a solvent for such systems due to low viscosity and wide electrochemical window. 12,13 As for the salt, ideally, it should have large electrochemical stability window, high ionic conductivity as well as ionic mobility and good solubility in organic solvents. Also, it should be inexpensive and environmentally friendly.

The most common salt in practical usage is tetraethylammonium tetrafluoroborate (TEABF 4 ). [14][15][16][17][18][19] But one of the most favorable candidates among electrolytes that possess all of the above criteria is spiro-1,1'-bipyrrolidinium tetrafluoroborate (SBPBF 4 ) salt. [20][21][22][23][24] It has higher solubility in organic solvents as well as SBPBF 4 in AN solutions have a higher conductivity value comparing to TEABF 4 . 20,25,26 In published works it was proven that maximum of conductivity concentration dependence of electrolyte (or ionic liquids) in organic solvents exists. 25,27,28 This phenomenon was related to the viscosity increase in such systems. 29 It was also reported that it can be due to the formation of ion associates at a high electrolyte concentration. 30 Still, all literature does not provide a detailed analysis of ionic aggregation process influence on the existence of conductivity maximum on the concentration curve.

Thus, in this Chapter the detailed analysis of structural and transport properties of SBPBF 4 in AN solutions of seven different concentrations using classical molecular dynamics (MD) simulation is presented. The aggregate analysis was performed to analyze the ionic subsystem of the solutions.

Additionally, the transport properties of the systems were obtained. The Chapter is organized as follows. In sec. 2 details of molecular dynamics simulation is provided as well as description of the cation force field development and validation. In sec. 3 the results of the simulation and their discussion are showed.

In sec. 4 the main conclusions are presented.

Methodology

Details of molecular dynamics simulation

In the current work the series of classical MD simulations were performed.

The simulated systems of SBPBF 4 in AN of different concentrations with a certain composition (Table 4.1.) were presented as a cubic box with periodic boundary conditions in all directions. Total number of ion pairs for each composition was always equal to 100.

To obtain the total number of ions and solvent molecules from the molarities the experimental density values were used. 31 For the cation conformers analysis, the infinite diluted solution was simulated for 1 ns.

To validate the cation potential model the infinite diluted solutions (Table 4.1.) were simulated for 50 ns for 5 independent runs with a total statistic of 250 ns. For each run the ions and solvent molecules were put in the simulation box with a random seed.

All other simulations were performed as described in Chapter 2. The structure of the cation, anion and solvent as well as labeling of the cation is shown at The BF 4 -potential model was taken from. 32 The acetonitrile model was taken from Koverga et al. 33 The Breneman method (ChelpG). 35,36 The charges of conformers are shown in The potential model was generated from the GROMOS54a7 force field. 37 For this force field potential models have the following functional form of the total potential energy:

            2 2 , , 2
angles bonds r ij ijk tot ij ij ijk ijk ij ijk dihedral nonbonded ij ij i j ijkl ijkl s ijkl ijkl ij ij ij ij k k U r r C C q q k n r r r                                       (4.1)
where k is the force constant for bond stretching (r), angle bending (θ),

proper and improper dihedral (ϕ), respectively, C6 and C12 are the Lennard-Jones parameters and q stands for the fractional charges of the interaction sites.

The first step in the unification of the data obtained for further creation of a potential model of the SBP + cation was the averaging of the partial charges of hydrogen atoms at a common carbon atom. It allowed to further unify all of three charge sets into one for all hydrogen atoms of SBP + in dependence with the number of conformers of different types that were observed in MD simulation in accordance with the equation 4.2:

3 1 , n in i n q P q    (4.2)
where 𝑖 is the atom in SBP + cation, 𝑛 is the number of conformer (1-3), n P is the probability to find the n th conformer in the solution, in q is the charge of the atom 𝑖 in the SBP + cation of the n th conformer.

The simulation for infinite diluted solution (Table 4 Using the charges after the two iterations of averaging the MD simulation for the same system but with long simulation time as described in previous section (infinite diluted solution, Table 4.1) was conducted. As a result, the diffusion coefficient of 1.64⸱10 -5 cm 2 /s was obtained. Experimental value of SBP + cation in the infinite diluted solution was calculated from the experimental value of limiting conductance 38,39 For all concentrations of the SBPBF 4 in AN similar behavior can be observed. The first maximum of RDF is constant for all simulated systems and is equal to approximately 0.50 nm. The RDF curve has some kind of shoulder (which more clearly resembles the local maximum for higher concentrations) with its peak at 0.63 nm. These values and RDF curve shape in these regions shows two possible configurations of cation-anion relative disposition near each other which was confirmed by analyzing GROMACS trajectory files from molecular dynamic simulations via VMD program package 40 (Figure 4.4). The maximum at 0.50 nm corresponds to axial relative position (BF 4 -is near nitrogen atom between pyrrolidinium rings) and the shoulder at 0.63 nm -to the equatorial relative position (BF 4 -is near one of the pyrrolidinium rings, in its plane). The minimum on RDF is at approximately 0.75 nm. This will be used later as the association criteria because at this distance the cation can interact with anions in both position types described earlier. The heights of peaks are decreasing with the increasing of SBPBF 4 concentration. The similar results were obtained in other MD simulations. 31,41 To study the solvation of the cation the RDF between the nitrogen atom of SBP + and the nitrogen atom of AN for all concentrations were obtained.

r , nm r k , kJ/(mol⸱nm 4 ) N 1 -C 6,9 N 1 -C 3,7 C 2 -C 5 C 4 -C 8 C 2 -C 6 C 9 -C 4 C 3 -C 8 C 5 -C 7 C 2 -H
3 -N 1 -C 7 C 3 -N 1 -C 9 C 6 -N 1 -C 7 C 6 -N 1 -C 3 C 7 -N 1 -C 9 C 6 -N 1 -
2 -C 5 -C 7 C 3 -C 8 -C 4 C 5 -C 2 -C 6 C 9 -C 4 -C 8 C 2 -C 5 -H C 4 -C 8 -H C 2 -C 5 -H C 4 -C 8 -H C 3 -C 8 -H C 7 -C 5 -H C 3 -C 8 -H C 7 -C 5 -H C 5 -C 2 -H C 8 -C 4 -H C 5 -C 2 -H C 8 -C 4 -H C 6 -C 2 -H C 9 -C 4
 , kJ/mol n N 1 -C 3 -C 8 -C N 1 -C 7 -C 5 -C N 1 -C 6 -C 2 -C N 1 -C 9 -C 4 -C C 3 -N 1 -C 6 -C C 3 -N 1 -C 7 -C C 3 -N 1 -C 9 -C C 6 -N 1 -C 3 -C C 3 -C 8 -C 4 -C C 3 -C 8
According to Figure 4.5, the position of first maximum at 0.42 nm as well as small local maximum at 0.56 nm. These two peaks also can be explained in similar way as ones in cation-anion RDF: the axial (0.42 nm) and equatorial (0. Such a big difference in these numbers is due to the size of the solvent molecules versus anions. The PF 6 -anion is larger than the solvent molecule. Also, it cannot be packed as tightly as the AN molecule which has linear structure.

Aggregate analysis

To analyze the presence of ionic clusters two different distance criteria have been chosen. The first criterion is the first minimum on the interionic RDF (0.75 nm, Figure 4.2). In this case all anions in the first coordination sphere are involved, including those in equatorial position because they can form weak hydrogen bonds with the cation even if they do not interact with the nitrogen atom of SBP + directly. 41 The second criterion was determined from the second derivative of the cation-anion RCN that was discussed earlier (Figure 4.6). As can be seen in the Figure 4.8, the first minimum is approximately at 0.53 for all concentrations. This minimum indicates some region where RCN comes to the beginning of the plateau (or soft incline) on its curve. Also, it is strict criteria as it does not include the equatorial anions (see Figure 4.4) in the cluster determination. The size distribution of the associates for both criteria can be found in The first criterion (0.75 nm) shows that at 1.0 M the huge increase of number of different cluster types can be observed. At this concentration of the salt the system is in the transition state from free ions and small aggregates to large associates. Starting from the 1.5 M almost all of the ions in the system associated in large clusters. The most concentrated solution is considered the one large aggregate without free ions.

For the second criterion (0.53 nm) the most diluted system (0.5 M of SBPBF 4 ) contains mostly isolated ions and small aggregates. Up until 2.5 M the system looks similar, the aggregates sizes are increase. 3.0-3.5 M concentration represents transition state when large aggregates start to appear. In the highest concentration, although, a huge number of ions are forming big aggregates, are still forming relatively small associates and are temporary left out of the big cluster.

To better illustrate the results, the average numbers of association for all the criteria (Figure 4.10) were calculated. According to the Nernst-Einstein relation, 42 the charge carrier concentration affects the conductivity value directly. The formation of the aggregates removes the ions (charge carriers) from the solution and, thus, should lower the electric conductivity. The rapid increasing of association process for SBPBF 4 in AN mixture is occurring at 1.0-1.5 M for first criterion and after that all of the ions are forming one large aggregate (Figure 4.10). 43 For the second criterion the size of aggregates starts to increase rapidly at 2.5 M, but even at 3.5 M the system is still not totally associated yet. In this case, the second criterion seems more correct. The first criterion seems to overvalues the aggregation as if all the ions are part of one large aggregate, the conductivity should be zero due to the charge carrier absence. The results for the second criterion correlate with the experimental conductivity for SBPBF 4 in AN which have the maximum that occurs at 2.0 M concentration of salt. 25,28,39 The conductivity depends on the concentration of the charge carriers in the solution and diffusion coefficients of the ions according to the Nernst-Einstein equation. 42 Diffusion coefficients decrease and viscosity begin to drastically nonlinearly increase at nearly 2.0 M of SBPBF 4 confirms the presence of the maximum of experimental electroconductivity at this concentration value. 25, 28, Aggregate analysis was performed with the use of two different criteria.

The second criterion is stricter, without considering the equatorial position of the anions relatively to the cations. As a result, the existence of ionic clusters in SBPBF 4 in AN systems was confirmed. For the first criterion the massive aggregation occurs at the concentration of SBPBF 4 in AN at 1.5 M while for the second criterion the average number of association begins to increase at the same region where the experimental conductivity curve changes its behavior which indicates that this criterion is the correct choice for such an analysis.

The transport properties were investigated via diffusion coefficients of solution components and viscosity of simulated systems. Obtained viscosity values are matching the experimental ones. Diffusion coefficients of all components are decreasing while the viscosity of the system continuously increasing with the salt concentration increase. The obtained results show a good correlation with the association analysis and in accordance with the occurrence of the concentration conductivity maximum in the experiment.

Introduction

Ionic liquid (IL) mixtures with molecular solvents can be considered as electrolyte solutions, for which their structure and properties are determined by the balance of types of interactions between all particles in the solution (cation, anion and solvent), which determine the existence of ionic associates and highorder aggregates. [1][2][3][4][5][6] In this context, the main feature of binary systems based on IL is that the constituent ions are polyatomic and, as a rule, asymmetric. As a result, the interactions mentioned above should be considered as anisotropic, having a predominant localization around some molecular fragment (center of interaction). [7][8][9] Another important feature of these systems in comparison with ordinary solutions of electrolytes is the complete miscibility of IL with many molecular solvents, which makes it possible to obtain mixtures corresponding to either a solution of such a liquid in a molecular solvent or a solution of a molecular solvent in an ionic liquid.

Intermolecular interactions in mixtures of two liquids of different nature can be showed as a gradual transition from the "first pure liquid" to the "second pure liquid" through intermediate compositions. Thus, the task boils down to the following question: which ranges of composition correspond to the abovementioned areas, and which intermolecular interactions are decisive. 10 For pure ILs, there is currently no generally accepted picture of their structure due to the indirect nature of the methods used. It is widely believed that in the liquid state the structure of imidazolium ionic liquids is determined by strong interionic Coulomb interactions, which are relatively effectively shielded away from the central ion (i.e., are quite local). It is also assumed that a significant contribution is made by the three-dimensional network of hydrogen bonds between counterions. [11][12][13][14][15] The strength and structure of this network are determined by the nature (polarizability, polarizing action, size, etc.) of the anion. 16 The above-mentioned considerations about the structure of pure components indicate the presence of two main phenomena in which a redistribution of the equilibrium between possible ion-ion, ion-molecular and intermolecular interactions can be manifested when the composition changes.

These are ionic association and ionic solvation. 6,[17][18][19][20] These phenomena can be understood as the gradual destruction of large ionic associates (the basic structural units of pure ionic liquids) into smaller ones, up to ion pairs. Subsequently, ion pairs completely dissociate into "free" ions in dilute solutions as a result of interaction with the solvent. Such an interaction can be both specific (localized ion-molecular interactions) and non-specific (the effect of the accumulation of a significant amount of solvent capable of forming an environment similar to a pure solvent). 21 The phenomena of ionic association and solvation are manifested at the microscopic level in the redistribution of electron density in the corresponding areas of interaction and, therefore, in changes in the corresponding force constants. Among the currently known experimental methods that can detect such effects, NMR 17,[22][23][24][25] and vibrational (IR and Raman) spectroscopy [26][27][28] should be singled out. The first can reveal information about the change in the electronic microenvironment of each chemically non-equivalent nucleus and the relative location for some nuclei, while the second investigates changes in the constants of the dipole moment, polarizability, changes in the microenvironment of atoms participating in the studied vibrational mode. 17,29 The association and solvation are also reflected in the "statistical" microstructure of such binary mixtures. Currently, only various methods of diffraction of X-rays and neutrons can provide experimental data on the such microstructure in different time and size scales. Also, they are quite expensive and not always available, as well as difficult from the point of view of data processing.

As well, usually there is only one IL-solvent system under investigation 30,31 which means that the approach for studying such objects should be wider and more universal. Molecular dynamics (MD) simulation can help solve these problems, and this method can also complete the picture with information not available from experiment. [32][33][34] In this Chapter MD simulation of 12 mixtures of ILs (1-butyl-3methylimidazolium C 4 mim + cation coupled with BF 4 -, PF 6 -, TFO -and TFSI - anions) with molecular solvents (AN, PC and -BL) of six IL mole fractions were performed. The molecular structures of the objects are presented at

Details of molecular dynamics simulation

The simulations of the binary mixtures (total of 12 systems) of four ILs of C 4 mim + cation with different anions (BF 4 -, PF 6 -, TFO -and TFSI -) in three aprotic dipolar molecular solvents (AN, PC and -BL) have been performed. Six different compositions of the mole fraction of the ILs from 0.05 to 0.30 for each binary mixture were selected in a way that the total number of ion pairs for each composition was always equal to 100. The number of the different particles of the ILs in the simulated systems are collected in Table 5.1. The ILs have been described by the potential model of Mondal and Balasubramanian, 35,36 while for the solvent molecules the potential model of Koverga et al. 37,38 has been used. According to classical MD formalism, these potential models have the following functional form of the total potential energy:

        5 2 2 , , 0, 0, 0 12 6 0 cos 2 2 4 , 4 angles bonds dihedral n r ij ijk tot ij ij ijk ijk n ijkl ij ijk ijkl n nonbonded ij ij i j ij ij ij ij ij k k U r r C q q r r r                                                        (5.1)
where k is the force constant for bond stretching (r), angle bending (θ), torsion (ϕ), respectively, ε and σ are the Lennard-Jones energy and the distance parameters, respectively, and q stands for the fractional charges of the interaction sites. For torsion angle

180 o ijkl ijkl    
. Indices i, j, k and l run through the interaction sites of the particles, while the subscript '0' refers to the equilibrium value of the bond lengths and angles. The potential model of ILs can be regarded a refinement of the CLaP force field. [39][40][41] Thus, while the bond and angle parameters have been retained, the torsional parameters have been adapted to the Ryckaert-Bellemans analytical expression. 42 Further, the charge distribution of the ions has been optimized in order to improve the agreement with the experimental thermodynamic and transport properties of the studied ILs. Thus, the ions of the IL carry a net charge that depends on the anion. 35,36 The potential models used here were previously validated by their ability of reproducing the basic experimental physicochemical properties of the systems. 35,36 5.3. Results and discussion

Structural properties

With the aim to study the cation-anion interaction, the interionic RDFs and RCNs of IL-solvent binary mixtures were analyzed. To fully consider these interactions the respective atoms for cations and anions should be chosen. Also, these points in space need to take into consideration all the coordination centers of cations and anions at once. For the C 4 mim + cation the most positive charge localized at the H-sites around imidazolium ring. Given this fact the center of the ring (CoR) is usually chosen as a reference point for the analysis. [43][44][45] Due to different structure, shape and symmetry of the anions their positions (X) for the analysis will be the follows: B atom in BF Here the similar curves were obtained for all IL mole fractions, meaning the positions of the peaks and minima do not depend on the concentration of the IL. Furthermore, their positions do not vary at all for the same IL in different solvents. The first maxima for various anions occur at 0.49 nm (BF 4 -), 0.51 nm (PF 6 -) and 0.52 nm (TFO -). For the TFSI -anion the situation is more complicated as there are two peaks at relatively low distances, 0.44 nm and 0.62 nm respectively. Also, these peaks have lower intensity comparing to other ILs. The first maximum in this case corresponds to the CoR-N interaction when N atom is located directly near the center of the ring or the H-atoms of the ring (the distances in both cases are similar). At the same time the second peak indicates the CoR-N the case of all TFSI -systems the curves values do not increase until at bigger distances.

Aggregate analysis

The ionic aggregates existence was analyzed via two different criteria. First criterion is the first minimum on the cation-anion RDF (Figure 5. This distance corresponds approximately to the area where the RCN curve starts to change its shape to the plateau after the initial rapid increase (first maximum on the RDF; second for the systems with TFSI -anion as described in the previous section). The values are next: 0.53 nm (BF 4 -), 0.56 nm (PF 6 -), 0.57 nm (TFO -) and 0.69 nm (TFSI -).

The results of the clusters formation probability for all mixtures of all mole fractions can be found in Figures 5.6-5.17 for the first and second criteria respectively. With the further increase of mole fraction of the ILs all the systems start to form large aggregates that include most of the ions in the mixture can be observed. The existence of such huge continuous polar network, however, still allows small clusters or even isolated ions to exist in systems. Most probably these small aggregates lose the connectivity with the huge cluster, but their low probabilities of formation prove that it is a temporary phenomenon. At the highest observed concentration, nevertheless, the ions are part of one massive associate.

It shows that at the first distance criterion (minimum on the interionic RDF) the aggregate formation is overestimated in the mixture as there are no charge carriers left in this case and thus there should be no conductivity at these mole fraction of the ILs. However, the experimental results show otherwise. [48][49][50][51] As for the second criteria, it shows that transition to the massive association occurs only at the highest IL mole fraction of 0.30 (for TFSI --at 0.20-0.25).

However, for the binary mixtures with AN the tendency for larger clusters formation appears at lower IL mole fraction compared to PC and -BL mixtures.

This shows that AN demonstrates a weaker ion-solvent interaction, allowing ions at lower concentration form a continuous polar network regardless of the chosen criteria.

To better illustrate the clusterization processes the average numbers of associations were obtained for all systems ( The diffusion coefficients were compared to the experimental data for cations and solvent molecules (and also for anions for the systems with PF 6 -). 53 For the binary mixtures with AN the obtained coefficients are very close to the experimental ones for all of the components of the analysis. For the systems with PC and -BL the obtained diffusion coefficients have in general higher values comparing to the experiment by 20%, especially for the higher concentrations. For all systems the diffusion coefficients of the solvent molecules are higher than of the cation or anions, while the latter are close to each other for almost all systems and IL mole fractions. Also, the coefficients of the components in the systems with AN molecules are 3-5 times higher than with other two solvent molecules. For all PC systems the general trend is almost similar diffusion coefficient for anion and solvent molecule. For the C 4 mimBF 4 in PC simulated system the anion diffusion coefficient is even higher in the most diluted solution.

On the other hand, this behavior cannot be observed in the experimental data.

The viscosities at Figure 5.20 are increasing with the IL mole fraction increase by a non-linear dependance. Although, the values for all systems do not show any drastic changes at respective mole fractions where the experimental conductivity has maximum.

As the Nernst-Einstein relation shows, not only concentration of the charge carriers influence the conductivity but the diffusion coefficients as well. 52 The behavior of calculated diffusion coefficients from the simulation for ions is in agreement with this statement.

Conclusions

In current chapter twelve ILs (C 4 mim + with BF 4 -, PF 6 -, TFO -and TFSI -)

with

Introduction

The mixtures of room temperature ionic liquids (ILs), consisting of 1-butyl-3-methylimidazolium cations (C 4 mim + ) and perfluorinated anions, such as tetrafluoroborate (BF 4 -), hexafluorophosphate (PF 6 -), trifluoromethylsulfonate (TFO -), and bis(trifluoromethanesulfonyl)imide, (TFSI -), with aprotic dipolar solvents, such as acetonitrile (AN), propylene carbonate (PC), or gamma butyrolactone (-BL), are adequate candidates to be used in electrochemical applications. As a consequence, these mixtures have been extensively studied by several experimental techniques in order to understand their macroscopic properties. [1][2][3][4][5][6][7][8][9][10][11][12][13] The existing array of experimental physicochemical data as well as spectroscopic results point out the significant changes occurring in the local structure of these mixtures at low IL mole fraction (x IL ~ 0.2) values. Indeed, the conductivity values go through a maximum around this composition, with higher values in the mixtures of these ILs with AN. Furthermore, vibrational spectroscopic technics, such as IR, Raman, and nuclear magnetic resonance (NMR) spectroscopy were used to analyze the interionic and ion-solvent interactions in mixtures of imidazolium-based ILs with molecular solvents [14][15][16][17][18][19][20][21][22][23][24][25][26] The results show that significant changes in the C-H (or the cation ring) vibration modes as well as the 1 H chemical shift occur at low IL content. This was correlated with the modulation, by changing the mixture composition, of the balance between intercomponent interactions, such as interionic (dominating at very high IL mole fractions), ion-solvent, and solvent-solvent interactions in the mixtures.

In accordance with these findings, molecular dynamics (MD) simulation results revealed that there is a crossover between the cation-anion, cation-solvent and anion-solvent average distances that occurs at low x IL values, where cation-solvent interactions overcome those between the cations and anions. 27 As a continuation of this analysis, to explain the composition dependence of the physicochemical properties, vibrational (i.e., IR and Raman) and NMR spectra of such mixtures, the changes of the local structure as a function of the mixture composition are characterized. These structural changes may be captured using appropriate statistical functions that characterize the local environment of the components in more detail than what is provided by their radial distribution functions. The main idea is, therefore, to evaluate the distribution functions by averaging over part of the total three-dimensional space. Appropriate methods in this respect include statistical geometry approaches, where the local structure is characterized by the statistical analysis of the Voronoi polyhedra (VP) around the individual particles, obtained by a specific tessellation, such as the Voronoi tessellation, in three-dimensional space. This approach is free from any arbitrary parameter that is used in many other methods, such as, e.g., the lattice heterogeneity analysis of Wang et al., 28 where the simulation space was divided into small cells the width of which was equal to the position of the minimum between the first and second peaks in the butyl-butyl radial distribution function.

The Voronoi method was successfully applied to analyze the local structure of a number of different systems, such as hard sphere [29][30][31][32][33] and Lennard-Jones liquids, 34- 38 molten salts 39,40 and metals, 41,42 water [43][44][45][46][47][48][49] under different thermodynamic conditions, including supercooled, 46,49,50 supercritical 47,48,51 and negative pressure ones, 44 other neat molecular liquids 43,52 and their binary mixtures, 50,[53][54][55][56][57] ternary mixtures of spherical particles, 58 supercritical fluids, 47,48,[59][60][61] polymers, 62,63 hydrated salts, 64 amphiphiles, 65 peptides, 66 biomacromolecules, 67 lipid membranes [68][69][70][71][72] and also neat ILs [73][74][75][76][77] as well as their mixture with each other [START_REF] Esser | TiCl4 Dissolved in Ionic Liquid Mixtures from Аb Initio Molecular Dynamics Simulations[END_REF][START_REF] Shelepova | Structural similarity of an ionic liquid and the mixture of the neutral molecules[END_REF] and with molecular solvents. 75,[START_REF] Esser | TiCl4 Dissolved in Ionic Liquid Mixtures from Аb Initio Molecular Dynamics Simulations[END_REF][START_REF] Sharma | How mixing tetraglyme with the ionic liquid 1-n-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide changes volumetric and transport properties: An experimental and computational study[END_REF][START_REF] Sharma | Effect of water on structure and dynamics of [BMIM][PF6] ionic liquid: An all-atom molecular dynamics simulation investigation[END_REF][START_REF] Sharma | Effect of alcohols on the structure and dynamics of [BMIM][PF6] ionic liquid: A combined molecular dynamics simulation and Voronoi tessellation investigation[END_REF][START_REF] Schröder | On the collective network of ionic liquid/water mixtures. III. Structural analysis of ionic liquids on the basis of Voronoi decomposition[END_REF][START_REF] Biswas | Microheterogeneity-Induced Vibrational Spectral Dynamics of Aqueous 1-Alkyl-3-methylimidazolium Tetrafluoroborate Ionic Liquids of Different Cationic Chain Lengths[END_REF][START_REF] Haberler | Hydrated ionic liquids with and without solute: The influence of water content and protein solutes[END_REF][START_REF] Rajbangshi | Cosolvent polarity dependence of solution structure in[END_REF] In this chapter on the basis of molecular dynamics simulations, a detailed Voronoi analysis of the local structure around the hydrogen atoms of the C 4 mim + cation in mixtures of ILs of this cation with four perfluorinated anions, such as BF 4 -, PF 6 -, TFO -and TFSI -, and three aprotic dipolar solvents, such AN, PC and -BL is presented. The structure of these molecules and molecular ions, along with the atomic labelling scheme, is shown in Figure 6.1. As the C 4 mim + cation is large and asymmetric, different atoms of it are regarded as centers of the Voronoi polyhedra. Indeed, the formation of polar and non-polar domains around the imidazolium ring and butyl chain of the cation gives a hint that there are specific local distributions around these groups of the cation. 75 In particular, in ILs bearing 1-alkyl-3-methlylimidazolium cations it is commonly accepted that H 2 and, to a less extent also H 4 and H 5 are the main hydrogen bonding sites of the cation. [START_REF] Tsuzuki | Theoretical analysis of the hydrogen bond of imidazolium C2-H with anions[END_REF][START_REF] Tsuzuki | Magnitude and Directionality of Interaction in Ion Pairs of Ionic Liquids: Relationship with Ionic Conductivity[END_REF][START_REF] Hunt | Hydrogen bonding in ionic liquids[END_REF][START_REF] Hunt | Structural characterization of the 1-butyl-3-methylimidazolium chloride ion pair using ab initio methods[END_REF] Further, the literature data converges to show that these hydrogen atoms interact preferentially with the F (BF 4 -and PF 6 -) and O (TFO -and TFSI -) atoms of the anions. 13,27,[START_REF] Fujii | Experimental evidences for molecular origin of low-Q peak in neutron/x-ray scattering of 1-alkyl-3-methylimidazolium bis(trifluoromethanesulfonyl)amide ionic liquids[END_REF][START_REF] Fujii | Liquid Structure of Room-Temperature Ionic Liquid, 1-Ethyl-3-methylimidazolium Bis-(trifluoromethanesulfonyl) Imide[END_REF] cation in the analyses is also shown.

Details of molecular dynamics simulation

MD simulations of the binary mixtures of four ILs, consisting of the C 4 mim + cation and the BF 4 -, PF 6 -, TFO -, or TFSI -anions, with three aprotic dipolar molecular solvents, i.e., AN, PC and -BL, have been performed for 13 different compositions, including the neat ionic and molecular liquids. The cubic basic box always consisted of 864 structural units (both ion pairs and solvent molecules).

The number of the different particles and mole fraction of the IL in the simulated systems simulated are collected in Table 6.1. The ILs have been described by the potential model of Mondal and Balasubramanian, [START_REF] Mondal | Quantitative prediction of physical properties of imidazolium based room temperature ionic liquids through determination of condensed phase site charges: A refined force field[END_REF][START_REF] Mondal | A Refined All-Atom Potential for Imidazolium-Based Room Temperature Ionic Liquids: Acetate, Dicyanamide, and Thiocyanate Anions[END_REF] while for the solvent molecules the potential model of Koverga et al. [START_REF] Koverga | A new potential model for acetonitrile: Insight into the local structure organization[END_REF][START_REF] Koverga | Local structure and hydrogen bonding in liquid γ-butyrolactone and propylene carbonate: A molecular dynamics simulation[END_REF] has been used -the same potential models that were used and described in Chapter 5.

Results and discussion

Volume of the Voronoi polyhedra

The VP volume distributions considering all the components of the mixture, 𝑃 (𝑉), are shown in Figures A1-A5 of the Supporting Information (SI), as obtained when describing the position of the C 4 mim + cation by that of the H 2 , H 4 , H 5 , H B and H M hydrogen atoms, respectively (for the labelling of the atoms, see Figure 6.1.). The obtained distributions, apart from those corresponding to neat molecular solvents, are not of Gaussian shape, but exhibit a slowly decaying tail at large volume values. With decreasing x IL , the distributions shrink and shift to lower volumes, while the tail at large volumes progressively smears out and the distributions become less asymmetric. Further, the extent of this asymmetry is higher when the TFSI -anion is present in the mixture, independently from the chosen molecular solvent. In order to quantify the shift and asymmetry of these distribution, the composition dependence of the mean value and skewness parameter (see equation 6.2) of the 𝑃 (𝑉) distributions are presented in This finding indicates that in neat ILs the local structure is more packed around the latter sites than around the former ones. When adding the solvent to the ILs, the 𝑚 ⁄ value decreases non-linearly, and the decay occurs with considerably lower rate in the x IL range between 1 and 0.2 than for further dilution of the IL. In dilute mixtures of the ILs, the rate of decrease is similar for all the sites chosen to represent the position of the cation. Of note is that in the presence of the TFSI - anion, a maximum of 𝑚 ⁄ occurs around the x IL value of 0.2.

In principle, the value of 𝑚 ⁄ is determined by the shape of the 𝑃 (𝑉) In the case of the 𝑃 (𝑉), the skewness parameter decreases with increasing x IL (Figure 6.4.). This decrease occurs with two markedly different rates, a low one at high IL mole fractions (i.e., between 1 and 0.2), inferring that the local structure of the ions corresponding to the neat ILs is not altered strongly by the solvents molecules in this composition range, and a high one for lower IL 123 content. This strong decrease of the skewness parameter at x IL < 0.2 is noticeably steeper when the IL is mixed with AN than with the other solvents. This difference is related to the different extent of self-association of the solvent molecules. Thus, the weak interaction between the ions and AN favors the self-association of the AN molecules, while the strong interactions between the PC or -BL molecules and the ions reduces the extent of self-association of the molecular solvent.

distribution
Further, the difference between the rate of decrease observed with different anions reflects the different strength of the interaction of these anions with the C 4 mim + cation (mainly visible in the mixture in AN). A16, respectively. Upon dilution of the ILs, these distributions shift to higher values, reflecting simply the fact that the number density of the molecular solvents is higher than that of the ILs. It is also seen that, among the molecular solvents considered, AN, while among the anions considered, TFSI -corresponds to the largest shift, although the choice of the anion has a smaller effect in this respect. This trend is also seen from Figure 6.6, showing the IL mole fraction dependence of the mean value of the 𝑃 (𝜌) distribution in all systems simulated. Again, the rate of decrease of 〈𝜌 〉 with increasing x IL is considerably larger below the IL mole fraction of about 0.2 than above this value. It is also seen that the difference between the density fluctuation values calculated considering the different H atoms of the cation is rather small in the presence of PF 6 -and TFSI -, while it is considerably larger in the presence of BF 4 - and TFO -anions. This finding clearly indicates that the distribution of the solvent molecules around these sites depends on the interaction between the cations and the anions. The persistence of this difference even at low IL mole fractions (in particular, in systems consisting of BF 4 -and TFO -anions) indicates that the solvent is still not completely solvating the ions, and the interaction of the oppositely charged ions, although strongly weakened with respect to that in neat IL, is still not negligible.

This physical picture can be further refined by analyzing the composition dependence of the density fluctuation considering only the solvent molecules in the analysis, ∆𝜌 (Figure 6.11). As is seen, the values of this parameter go through a maximum at x IL ~ 0.2, and this maximum is the highest when AN is the solvent, independently from the choice of the anion. Clearly, when disregarding the cations and anions in the analysis, the ions are transformed to empty holes, the size of which is depending on the extent of solvation of the disregarded ions by the solvent molecules. This solvation is modulated by the balance between the interionic, ion-solvent, and solvent-solvent interactions. Thus, the increasing solvent density fluctuation observed upon addition of IL to the neat solvent indicates different extent of solvation of the oppositely charged ions, while the maximum of the ∆𝜌 values corresponds to the maximum difference between the solvation of the cations and anions by the solvent molecules. Above this composition, the interaction between cations and anions becomes dominant over that between the ions and solvent molecules. Thus, further dilution of the solvent leads to stronger interionic interaction, and hence the disregarding of the ions in the analysis creates more and more regular holes, leading eventually to the observed decrease of the density fluctuation of the solvent molecules.

Finally, the fact that the ∆𝜌 values are higher for AN than for the other solvents indicates that the interaction of AN with the ions is weaker than that of the other two solvents considered here, presumably because of the smaller dipole moment of AN than that of PC and -BL. [START_REF] Reichardt | Solvents and Solvent Effects in Organic Chemistry[END_REF][START_REF] Fornefeld-Schwarz | Refractive Indices and Relative Permittivities of Liquid Mixtures of γ-Butyrolactone, γ-Valerolactone, δ-Valerolactone, or ε-Caprolactone + Benzene, + Toluene, or + Ethylbenzene at 293[END_REF] As a consequence, in AN the importance of the interionic interaction relative to the ion-solvent interactions is larger than in the other two solvents, leading to the expulsion of the AN molecules, to a certain extent, from the vicinity of the ions, and eventually to the formation of self-associates of the AN molecules. This larger self-association leads then to larger density fluctuations in AN than in the other two molecular solvents considered. The analysis of the 𝑃 (𝑅) distributions (Figures A23-A27) shows that the size of the voids is larger in the neat ILs than in the molecular solvents, reflecting both the different size of the ions and solvent molecules, and also the fact that the solvent molecules are more closely packed in their neat liquid than the ions. The shape of the 𝑃 (𝑅) distribution is Gaussian in both neat systems, the fluctuation being larger in the neat ILs. When diluting the ILs, the 𝑃 (𝑅) distributions retain their Gaussian shape and shift slightly towards smaller 𝑅 values in the x IL range between 1 and 0.2. In some of the mixtures, the peak position shifts smoothly towards that in the pure solvent, while the Gaussian-like shape of the distribution is retained in the entire composition range. However, in mixtures consisting of either AN molecules or TFSI -anions, a shoulder emerges at the low 𝑅 side of the peak and turns gradually to a separate peak upon further dilution. Of note is that, simultaneously with the turning of this shoulder to the main peak, occurring roughly at the same position as that in the neat solvent, the previous peak gradually turns to a shoulder at the high 𝑅 side of the distribution. The occurrence of these shoulders indicates self-association of the components, as the local environment around a certain fraction of the voids is markedly different than that around other voids. 100 In particular, the fact that the shoulder at low 𝑅 values occurs roughly at the same position as the peak in the neat solvent indicates that a certain fraction of the voids in the mixtures are in a local environment that is very similar to that in the neat solvent. On the other hand, the shoulder at the high 𝑅 side occurs at markedly different position than the peak in the neat IL, indicating the lack of a considerable number of voids that are in a neat IL-like local environment. Thus, our findings reveal stronger self-association of the solvent molecules than that of the ions. Considering that, among the three molecular solvents considered, this behavior is only seen in AN, the present result clearly confirms our previous finding concerning larger density fluctuations of AN than that of the other solvents (see sec. 6.3.2), and stresses that, due to its somewhat weaker interaction with the ions, AN self-associates more than the other two molecular solvents considered.

Additional information in this respect can be gained again when one of the components is discarded in the analysis. Thus, the self-association of the solvent molecules can be further addresses by analyzing the 𝑃 (𝑅) distributions, calculated by taking only the ions into account while disregarding the solvent molecules in the calculation. These distributions (Figures A28-A32 The 𝑃 (𝑅) distributions, obtained by taking only the solvent molecules into account in the analysis (Figure A33) show an overall shift to higher 𝑅 values with increasing x IL , reflecting again the trivial effect of dilution. More importantly, upon dilution of the solvent, the 𝑃 (𝑅) distribution turns out to be bimodal, exhibiting a second peak the intensity and position of which are mole fraction dependent. In the low mole fraction range of the discarded ions, this second peak emerges as a shoulder in the high 𝑅 side of the main peak, while at higher IL mole fractions it gradually turns to a broad peak, located at large void radius values.

Simultaneously, the height of the first peak gradually decreases, and ultimately it turns to a shoulder of the large 𝑅 peak, however, unlike the other peak, it always appears at the same position. This peak (or shoulder) is thus given by voids that are surrounded by solvent molecules in all direction, and its presence even at high dilution of the solvent molecules indicates the persistence of solvent domains (inside which the voids are in the same local environment as in the neat solvent), and hence self-association of the solvent molecules up to relatively large IL mole fractions. On the other hand, the peak at large 𝑅 values is given by voids that are in a mixed local environment, i.e., surrounded both by solvent molecules and ions, and the shift of its position to larger values with increasing IL mole fraction marks the increasing mole fraction of the ions even in their mixed local environment. from the vicinity of the ions, form self-associates. This self-association is stronger in the case of AN than of the other solvents considered, because, due to its smaller dipole moment, AN has a weaker interaction with the ions than the other ones.

Similarly, this solvent self-association is stronger in the presence of TFSI -than of the other anions considered. All these results stress that the local structure, and thus also the physicochemical properties of the IL-solvent mixtures are eventually governed by the delicate interplay of the interionic and solvent-ion interactions.

Conclusions and perspectives

This thesis presents a molecular dynamics description of the transport properties and the local structure in three different type of systems (with lithium salts, alkylammonium salts and solutions with ionic liquids) that can be used as advanced electrochemical systems for energy store devices. All of these systems have maximum at the electroconductivity-concentration curve but as for today there is still no constant theory or quantitative approach to investigate the reasoning behind these phenomena. Understanding the undergoing processes that cause such behavior is crucial task on the way of successful use of such solutions and their analogues in practical aspects.

  List of abbreviations .................................................................................. Chapter 1. General introduction ................................................................

Figure 2 . 1 .

 21 Figure 2.1. Example of cation-anion (N-F) radial distribution function at various molar concentrations of SBPBF 4 in AN mixture.

2 )

 2 The example of the RCN is shown at Figure 2.2. The observations based on the running coordination number (RCN) heavily rely on the interpretation of the respective RDF due to their definition. The first coordination sphere is limited at the distance of the first minimum on the RDF. The plateaus (or soft incline) at the RCN curve in the same region show the stale composition of particles in the frame of that sphere.

Figure 2 . 2 .

 22 Figure 2.2. Example of cation-anion (N-F) running coordination numbers at various molar concentrations of SBPBF 4 in AN mixture.

Figure 2 . 3 .

 23 Figure 2.3. Example of probability distributions of aggregate sizes for 0.5 M (left) and 3.0 M (right) concentrations of SBPBF 4 in AN mixture with 0.53 nm as a distance criterion.

Figure 3

 3

Figure 3 . 1 .

 31 Figure 3.1. Structure of the PF 6 -anion and molecular solvents of DMC and EC.

  for density, self-diffusion coefficient and enthalpy of vaporization for systems of pure solvents in the comparison with the experimental data are shown in the Table

3. 3 .

 3 Results and discussion 3.3.1. Structural properties Structural properties of LiPF 6 in DMC/EC (1:1) binary mixture were analyzed in terms of radial distribution functions (RDF) and running coordination numbers (RCN). For all RDFs the center atom P of anion as well as most electronegative atom of solvent (the carbonyl O atom for DMC and EC) has been chosen for the analysis. The cation-anion RDFs for all systems are presented in Figure 3.2. Here similar curves for all of the concentrations of LiPF 6 in DMC/EC binary mixture can be seen. The first high sharp peak indicates a structured first coordination shell with maximum at approximately 0.34 nm. It corresponds to the classical MD simulation results with a polarizable force field of LiPF 6 in DMC/EC.48 The small shoulder on all curves with its local maximum near 0.29 nm can be detected. This indicates the occurrence of different mutual cation-anion configuration at these Li-P distance values. The example of cation-anion relative disposition at these distances was obtained from GROMACS trajectory files via VMD program package52 and shown at Figure3.3. The first maximum of RDFs here (0.34 nm) corresponds to the monodentate linkage of the anion to the cation when Li + is close to only one of the F atoms of anion. Thus, the local maximum of shoulder (0.29 nm) corresponds to the position of anion when Li + is close to two or even three F atoms of anion at the same time (bidentate and tridentate linkage respectively). The first minimum of RFDs is approximately at 0.45 nm.

Figure 3 . 2 .

 32 Figure 3.2. Cation-anion (Li-P) radial distribution functions at various molar concentrations of LiPF 6 in DMC/EC (1:1) binary mixture. The vertical dashed line corresponds to the first coordination shell.

Figure 3 . 3 .

 33 Figure 3.3. Example of (Li(PF 6 ) 2 ) -associate with monodentate (0.35 nm) and bidentate (0.29 nm) linkage of the anion to the cation. The respective Li-P distances are shown as well.

  Similar phenomenon can be observed in our investigation. The example of such configuration if shown at Figure 3.4. The height of each peak at RDF decreases with the increase of the salt concentration.

Figure 3 . 4 .

 34 Figure 3.4. Example of cation coordination shell with two anions that formed solvent-shared pairs. The respective Li-P distances are shown as well.

Figure 3 . 5 .

 35 Figure 3.5. Cation-solvent (Li-O DMC ) radial distribution functions at various molar concentrations of LiPF 6 in DMC/EC (1:1) binary mixture. The vertical dashed line corresponds to the first solvation shell.

Figure 3 . 6 .

 36 Figure 3.6. Cation-solvent (Li-O EC ) radial distribution functions at various molar concentrations of LiPF 6 in DMC/EC (1:1) binary mixture. The vertical dashed line corresponds to the first solvation shell.

Figure 3 . 7 .

 37 Figure 3.7. Cation-anion (Li-P) running coordination numbers at various molar concentrations of LiPF 6 in DMC/EC (1:1) binary mixture. The vertical dashed line corresponds to the first coordination shell.

Figure 3 . 8 .

 38 Figure 3.8. Cation-solvent (Li-O DMC ) running coordination numbers at various molar concentrations of LiPF 6 in DMC/EC (1:1) binary mixture. The vertical dashed line corresponds to the first solvation shell.

Figure 3 . 9 .

 39 Figure 3.9. Cation-solvent (Li-O EC ) running coordination numbers at various molar concentrations of LiPF 6 in DMC/EC (1:1) binary mixture. The vertical dashed line corresponds to the first solvation shell.

Figure 3 . 2 )

 32 Figure 3.2) which indicates the first coordination sphere around the Li + cation. The second criterion was determined by the minimum at the second derivative of cation-anion RCN (0.35 nm, Figure 3.10). This value shows the distance at which the RCN curve comes into plateau regime at which the coordination number have almost no change at all. Further in the Chapter they will be referred to as the first set of criteria.

Figure 3 . 10 .

 310 Figure 3.10. Second derivatives of cation-anion (Li-P) running coordination numbers at various molar concentrations of LiPF 6 in DMC/EC (1:1) binary mixture.

Figure 3 . 2 )

 32 Figure 3.2) was chosen as well as the second minimum on the second derivative of cation-anion RCN graphs (0.93 nm, Figure 3.10). Further in this Chapter they will be referred to as the second set of criteria. The results of the association analysis can be found in Figures 3.11and 3.12.

Figure 3 . 11 .

 311 Figure 3.11. Probability distributions of aggregate sizes of the first set of criteria with respective first (left) and second (right) criterion at various molar concentrations of LiPF 6 in DMC/EC (1:1) binary mixture.

Figure 3 . 12 .

 312 Figure 3.12. Probability distributions of aggregate sizes of the second set of criteria with respective first (left) and second (right) criterion at various molar concentrations of LiPF 6 in DMC/EC (1:1) binary mixture.

Figure 3 . 13 .

 313 Figure 3.13. Average numbers of association of the second set of criteria with respective first (left) and second (right) criterion at various molar concentrations of LiPF 6 in DMC/EC (1:1) binary mixture.

Figure 3 . 14 .

 314 Figure 3.14. Diffusion coefficients for cation, anions and solvent molecules and viscosity values at various molar concentrations of LiPF 6 in DMC/EC (1:1) binary mixture.

Chapter 4 .

 4 Microstructure and transport properties of 1-1'-spirobipyrrolidinium tetrafluoroborate in acetonitrile from molecular dynamics simulations For the solutions of 1-1'-spirobipyrrolidinium tetrafluoroborate (SBPBF4) in acetonitrile (AN) the maximum on conductivity concentration curve occurs at the concentration of salt at 2.0 M as was obtained the experimental data in the literature. Although this phenomenon is usually related to the ion association at a high electrolyte concentration, the detailed microscopic structure of the ion subsystem is not properly analyzed. Thus, in this Chapter SBPBF4 in AN of seven different concentrations were studied with classical MD simulation technique. For this purpose, the cation full-atom potential model has been developed on the base of GROMOS force field. To account several existing conformers of the cation in the solution, the several iterations of MD simulations and charge unification for hydrogen atoms of SBP + were performed. The structure was studied in terms of RDFs and RCNs. The cationanion (N-B) RDFs of mixtures of different concentrations shows the presence of two possible cation-anion relative disposition: axial (when the BF4 -anion is close to the nitrogen atom of the cation) and equatorial (when BF4 -anion is near one of the pyrrolidinium rings). The RCNs show that anions competing with the solvent molecules for the position in the first coordination shell around the cation: with the salt concentration increase the anion coordination number is increasing as well while the solvent coordination number is decreasing. Aggregate analysis with two different criteria (to take into account the equatorial anions and to not) confirmed the existence of ionic clusters in SBPBF4 in AN solutions. The first criterion showed the presence of massive aggregates at 1.5 M and higher. For the second criterion the average number of association starts to increase at the same concentration values as the maximum on the experimental conductivity curve is located. This indicates that the second criterion is the correct choice for such an analysis. The transport properties were investigated via diffusion coefficients of solution components and viscosity of simulated systems. The diffusion coefficients for ions and solvent molecules are decreasing and viscosity values are non-linearly increasing with the increasing of the salt concentration. The obtained results and the fact that calculated viscosity values are drastically non-linearly increasing from the concentration 2.0 M of the SBPBF4 are in agreement with the maximum of the experimental concentration conductivity curve.

Figure 4

 4

  starting point in the development of the cation potential model under consideration was the quantum-chemical calculations of three SBP + conformers: E-E (Envelope-Envelope conformer, in which the N atom in both pyrrolidine rings is outside the plane of the ring), T-E (one ring in the Twist conformation, the other in the Envelope) and T-T (both pyrrolidine rings in a Twist conformation). The conformers are presented at Figure 4.2. All quantumchemical calculations were performed using the Gaussian09 program 34 at the M06-2X/6-311++G(d,p) level; specific atomic charges were calculated by the

Table 4 . 2 .

 42 The energies obtained for the equilibrium geometries E-E, E-T and T-T are in good agreement with the literature data: the E-E conformation has the lowest energy, T-T is the highest, E-T occupies an intermediate position between the other two. The difference in energy between T-T and E-E conformers is equal to 14 kJ/mol, while E-T and E-E difference being on the order of 3-4 kJ/mol. The latter is comparable with the thermal energy 𝑅𝑇 equal to ~2.4 kJ/mol at 298.15 K. Thus, it can be possible for a cation to transit from E-T conformation to E-E and back during thermal motion in a liquid medium.

Figure 4 . 1 .

 41 Figure 4.1. Structure of the SBP + cation, BF 4 -anion and AN. The labeling of cation used in potential model is also shown.

Figure 4 . 2 .

 42 Figure 4.2. Structure of the SBP + cation conformers: Envelope-Envelope (left), Twist-Envelope (middle) and Twist-Twist (right).

. 1 .

 1 ) was conducted. At each frame during the simulation the values of the C-C-C-C angles of both pyrrolidine rings were recorded. If the value was 0±10°, the conformation of the ring was considered as an Envelope; if the value was 45±10°, the conformation was considered as a Twist. Other variations were discarded. After the simulation the distribution of conformers was obtained: T-T -0.08%, E-E -8.06%, E-T -91.86%. Due to the fact that E-T and E-E conformers can transform into one another as seen from the results of the quantum chemical calculations, the difference between their occurrence at more than 10 times seems unrealistic. It was decided to use the geometric parameters (bonds, angles, dihedrals) from the optimized geometry of lowest energy conformer (E-E) instead of the original from the GROMOS54a7 force field for further simulations. The previous step (simulation of infinite diluted solution with recording of the conformers occurrence) was repeated. New results seemed more realistic, and thus charges of hydrogen atoms were unified for this step (equation 4.2). After that, these unified charges were used for the new iteration of the unification. After two such iterations of charge averaging the difference in occurring of different conformers seemed negligible. Final distribution of conformers for SBP + in AN was: T-T -2.32%, E-E -46.48%, E-T -51.20%. These results seem realistic and prove the possible transition of SBP + from E-T conformation to E-E and vice versa during thermal motion. The charges obtained are presented inTable 4.2.

  Structural properties of SBPBF 4 in AN were analyzed in terms of radial distribution functions (RDF) and running coordination numbers (RCN). Because of quasispherical form of the ions their relative center atoms were chosen for the analysis: N for SBP + and B for BF 4 -. The cation-anion RDFs for all systems are presented in Figure 4.3.

Figure 4 . 3 .

 43 Figure 4.3. Cation-anion (N-B) radial distribution functions at various molar concentrations of SBPBF 4 in AN mixture. The vertical dashed line corresponds to the first coordination shell.

Figure 4 . 4 .

 44 Figure 4.4. Example of (SBP(BF 4 ) 2 ) -associate with axial (0.48 nm) and equatorial (0.63 nm) relative positions of anions. The respective N-B distances are shown as well.

  56 nm) positions of solvent molecules regarding cation. The first minimum is at the 0.66 nm indicates the first solvation shell around the cation. The peaks heights are remaining almost the same with the concentration increase of SBPBF 4 . Interesting to note that peak position as well as first minima on RDFs that indicate the boundaries of the first solvation shells do not depend on the concentration of the electrolyte.

Figure 4 . 5 .

 45 Figure 4.5. Cation-solvent (N-N AN ) radial distribution functions at various molar concentrations of SBPBF 4 in AN mixture. The vertical dashed line corresponds to the first solvation shell.

Figure 4 . 6 .

 46 Figure 4.6. Cation-anion (N-B) running coordination numbers at various molar concentrations of SBPBF 4 in AN mixture. The vertical dashed line corresponds to the first coordination shell.

Figure 4 . 7 .

 47 Figure 4.7. Cation-solvent (N-N AN ) running coordination numbers at various molar concentrations of SBPBF 4 in AN mixture. The vertical dashed line corresponds to the first solvation shell.

Figure 4 . 8 .

 48 Figure 4.8. Second derivatives of cation-anion (N-B) running coordination numbers at various molar concentrations of SBPBF 4 in AN mixture.

Figures

  Figures 4.9.

Figure 4 . 9 .

 49 Figure 4.9. Probability distributions of aggregate sizes with first (left) and second (right) criterion at various molar concentrations of SBPBF 4 in AN mixture.

Figure 4 . 10 .

 410 Figure 4.10. Average numbers of association for different criteria at various molar concentrations of SBPBF 4 in AN mixture.

39

 39

4. 4 Conclusions

 4 In the current work SBPBF 4 in AN solutions in a wide range of concentrations (0.5 M -3.5 M) were investigated with classical MD simulation technique. For this purpose, the cation full-atom potential model has been developed by authors. In order to account the existence of several conformers of the cation in the solution, the several iterations of MD simulations and charge unification for hydrogen atoms were performed. The final results after two iterations were taken into account. The SBP + cation diffusion coefficient is close to the one obtained from the experimental limiting molar conductivities. The structure was studied in terms of RDFs and RCNs. The cation-anion (N-B) RDFs of mixtures of different concentrations shows the presence of two possible cation-anion relative disposition: axial and equatorial. As the concentration of SBPBF 4 rises the composition of the cations first coordination shell changes: PF 6 -anions (coordination number changes from 1.4 to 4.2) are replacing AN solvent molecules (coordination number changes from 11.3 to 5.7) in it.

Figure 5 . 1 .

 51 The microstructure, clusterization and, finally, the transport properties of the systems have been studied. The Chapter is organized as follows. In sec. 2 details of the system setup is provided. In sec. 3 the results of the simulation are showed and discussed. In sec. 4 the main conclusions of the study of this Chapter are summed up.

Figure 1 .

 1 Figure 1. Structure of the ions and molecular solvents considered in this study.

  4 -, P atom in PF 6 -, middle of the C-S bond in TFO -(takes into account both O and F coordination sites) and N atom in TFSI -(takes into account N, O and F coordination sites). The interionic RDFs for all IL-solvent binary mixtures for all simulated systems are shown in Figure 5.2.

Figure 5 . 2 .

 52 Figure 5.2. Cation-anion (CoR-X) radial distribution functions of the mixtures at various mole fraction of ionic liquid. The position of the cation is described with center of imidazolium ring. The positions of anions (X) are: B atom in BF 4 -, P atom in PF 6 -, middle of the C-S bond in TFO -and N atom in TFSI -. The vertical dashed line corresponds to the first coordination shell.

Figure 5 . 4 .

 54 Figure 5.4. Cation-anion (CoR-X) running coordination numbers of the mixtures at various mole fraction of ionic liquid. The position of the cation is described with center of imidazolium ring. The positions of anions (X) are: B atom in BF 4 -, P atom in PF 6 -, middle of the C-S bond in TFO -and N atom in TFSI -. The vertical dashed line corresponds to the first coordination shell.

  2). This distance shows the border for the first coordination sphere where all of the anions are in strong interaction with the C 4 mim + cation. The second criterion is the minimum on the second derivative of the RCN curve (Figure5.5).

Figure 5 . 5 .

 55 Figure 5.5. Second derivatives of the cation-anion (CoR-X) running coordination numbers of the mixtures at various mole fraction of ionic liquid. The position of the cation is described with center of imidazolium ring. The positions of anions are: B atom in BF 4 -, P atom in PF 6 -, middle of the C-S bond in TFO -and N atom in TFSI -.

Figure 5 . 6 .

 56 Figure 5.6. Probability distributions of aggregate sizes with first (left) and second (right) criterion of the C 4 mimBF 4 in AN binary mixture at various mole fraction of ionic liquid.

Figure 5 . 7 .

 57 Figure 5.7. Probability distributions of aggregate sizes with first (left) and second (right) criterion of the C 4 mimBF 4 in PC binary mixture at various mole fraction of ionic liquid.

Figure 5 . 8 .

 58 Figure 5.8. Probability distributions of aggregate sizes with first (left) and second (right) criterion of the C 4 mimBF 4 in -BL binary mixture at various mole fraction of ionic liquid.

Figure 5 . 9 .

 59 Figure 5.9. Probability distributions of aggregate sizes with first (left) and second (right) criterion of the C 4 mimPF 6 in AN binary mixture at various mole fraction of ionic liquid.

Figure 5 . 10 .

 510 Figure 5.10. Probability distributions of aggregate sizes with first (left) and second (right) criterion of the C 4 mimPF 6 in PC binary mixture at various mole fraction of ionic liquid.

Figure 5 . 11 .

 511 Figure 5.11. Probability distributions of aggregate sizes with first (left) and second (right) criterion of the C 4 mimPF 6 in -BL binary mixture at various mole fraction of ionic liquid.

Figure 5 . 12 .

 512 Figure 5.12. Probability distributions of aggregate sizes with first (left) and second (right) criterion of the C 4 mimTFO in AN binary mixture at various mole fraction of ionic liquid.

Figure 5 . 13 .

 513 Figure 5.13. Probability distributions of aggregate sizes with first (left) and second (right) criterion of the C 4 mimTFO in PC binary mixture at various mole fraction of ionic liquid.

Figure 5 . 14 .

 514 Figure 5.14. Probability distributions of aggregate sizes with first (left) and second (right) criterion of the C 4 mimTFO in -BL binary mixture at various mole fraction of ionic liquid.

Figure 5 . 15 .

 515 Figure 5.15. Probability distributions of aggregate sizes with first (left) and second (right) criterion of the C 4 mimTFSI in AN binary mixture at various mole fraction of ionic liquid.

Figure 5 . 16 .

 516 Figure 5.16. Probability distributions of aggregate sizes with first (left) and second (right) criterion of the C 4 mimTFSI in PC binary mixture at various mole fraction of ionic liquid.

Figure 5 . 17 .

 517 Figure 5.17. Probability distributions of aggregate sizes with first (left) and second (right) criterion of the C 4 mimTFSI in -BL binary mixture at various mole fraction of ionic liquid.

Figure 5 .

 5 18). The figure displays in more compact way the same results that were discussed earlier. Here for the first criterion ions in AN systems form massive aggregates at 0.15 mole fraction of ILs already, in -BL and PC mixtures -at 0.20 and 0.25 respectively. For the second criterion the ions in the systems are separated from each other or forming small aggregates until ~0.15-0.20 mole fraction of the ILs. After that mole fraction ILs in mixtures tend to form bigger aggregates. For the BF 4 -, PF 6 -and TFO -in PC this trend is not so pronounced. The massive aggregation process occurs only in TFSI - systems for the second criterion and only at highest concentration of 0.30. The AN systems at this concentration at the transition stage, however for the5.3. Transport propertiesThe diffusion coefficients and shear viscosities were obtained for all the IL mole fractions for all systems. The results are presented atFigures 5.19 and 5.20 respectively.

Figure 5 . 19 .

 519 Figure 5.19. Diffusion coefficients for cation, anions and solvent molecules in comparison with the experimental data 53 of the mixtures at various mole fraction of ionic liquid.

Figure 5 . 20 .

 520 Figure 5.20. Viscosities of the mixtures at various mole fraction of ionic liquid.

  molecular solvents (acetonitrile, propylene carbonate, and gamma butyrolactone) binary mixtures were studied by the molecular dynamics simulation technique. The microstructure of the mixtures was studied in the framework of radial distribution functions and running coordination numbers. The RDFs and RCNs show the particular behavior in AN and TFSI -systems. For TFSI-system the cation-anion (CoR-N) RDFs curves showed two peaks with similar intensities. It was shown that they represent the position when the nitrogen atom of the anion is close to the imidazolium ring and when nitrogen atom of TFSI -not directly interacting with the ring, but instead the oxygen atoms do. The cation-anion coordination numbers changed in similar values for the same ionic liquids in different solvents: for AN it varies from ~1.2 to ~3.6, for PC -from 0.6 to 3.0 and for -BL -from 0.8 to 3.1 with the increasing mole fraction of the ILs. Also, data obtained were used to conduct a quantitative aggregate analysis with two different distance criteria (first minimum of RDF and minimum of the second derivative of the RCN respectively) to compare the results with each other. The analysis with the first criterion shows the formation of the massive cluster at ~0.15, 0.20 and 0.25 IL mole fraction for AN and for with -BL respectively. Thus, this criterion seems to overrate the aggregation process in the mixtures. With the second, stricter distance criteria the formation of big aggregates in the systems starting to occur at the same mole fractions of the ILs where the experimental conductivity curves change their behavior and the maximum occurs. It proves that the reason Chapter 6. Local Structure of Mixtures of Imidazolium-Based Ionic Liquids and Molecular Solvents from Molecular Dynamics Simulations and Voronoi Analysis While the physicochemical properties as well as the nmR and vibration spectroscopic data of the mixtures of ionic liquids (ILs) with molecular solvents undergo a drastic change around the IL mole fraction of 0.2, the local structure of the mixtures pertaining to this behavior remains unclear. In this Chapter, the local structure of twelve mixtures of 1-butyl-3methylimidazolium cation (C4mim + ) combined with perfluorinated anions, such as tetrafluoroborate (BF4 -), hexafluorophosphate (PF6 -), trifluoromethylsulfonate (TFO -), and bis(trifluoromethanesulfonyl)imide, (TFSI -), and aprotic dipolar solvents, such as acetonitrile (AN), propylene carbonate (PC), and gamma butyrolactone (-BL) is studied by molecular dynamics simulations in the entire composition range, with an emphasize on the IL mole fractions around 0.2. Distributions of metric properties corresponding to the Voronoi polyhedra of the particles (volume assigned to the particles, local density, radius of spherical voids) are determined, using representative sites of the cations, anions and the solvent molecules, to characterize the changes in the local structure of these mixtures. By analyzing the mole fraction dependence of the average value, fluctuation, and skewness parameter of these distributions, the present study reveals that, around the IL mole fraction of 0.2, the local structure of the mixture undergoes a transition between that determined by the interionic interactions and that determined by the interactions between the ions and solvent molecules. It should be noted that the strength of the interactions between the ions and the solvent molecules, modulated by the change in the composition of the mixture, plays an important role in the occurrence of this transition. The signature of the change in the local structure is traced back to the nonlinear change of the mean values, fluctuations and skewness values of the metric Voronoi polyhedra distributions.

Figure 6 . 1 .

 61 Figure 6.1. Structure of the ions and molecular solvents considered in this study. The labelling of the H atoms used to describe the position of the C 4 mim +

Figures 6 .

 6 Figures 6.2 and 6.3, respectively, as obtained in all systems simulated. As is seen from Figure 6.2, with decreasing mole fraction of the IL, the mean volume of the VP, 〈𝑉 〉, shifts to lower values, and it does not depend on which H atom is chosen to represent the position of the cation. The extent of this shift is the largest in the presence of the TFSI -anion and AN, while it is the smallest in the mixture of C 4 mimBF 4 and PC. Of note is that the rate of the shift is somewhat lower in the x IL range between 1 and 0.2 than below x IL = 0.2. This change of the rate of decrease of the mean volume value is a signature of changes occurring in the local structure around the components of the mixture.

Figure 6 . 2 .Figure 6 . 3

 6263 Figure 6.2. IL mole fraction dependence of the average value of the VP volume, 〈𝑉 〉, obtained considering all the ions and molecules in the analysis.

Figure 6 . 3 .

 63 Figure 6.3. IL mole fraction dependence of the skewness parameter of the VP volume distributions, 𝑚 ⁄ , obtained considering all the ions and molecules in the analysis.

  at large and small volume values. The decrease of the 𝑚 ⁄ is thus correlated with the decrease of the dominant, long decaying tail of the 𝑃 (𝑉) distribution at the large volume side of the peak, and the concomitant increase of the contributions to small VP volume values. However, when the 𝑚 ⁄ value goes through a maximum, not only the large volume tail of the overall 𝑃 (𝑉) distribution is decreasing (see Figs.A1-A5), but the contributions to the small volume part of the distribution (closely packed local structures) also have to decrease, and this latter decrease overweighs that at the large volume side (loosely packed local structures). For further dilution of ILs, the 𝑚 ⁄ values decrease and infer that these distributions are shaped by the local structure of the solvent molecules, which is more packed than that of the ILs.To go further in the investigation of the effect of composition on the local structure in IL-solvent mixtures, the 𝑃 (𝑉) and 𝑃 (𝑉) distributions by taking into account only the ions and only the solvent molecules, respectively, in the analysis were calculated. The 𝑃 (𝑉) distributions, obtained by describing the position of the cation by that of the H 2 , H 4 , H 5 , H B and H M hydrogen atoms, are shown in FiguresA6-A10, respectively, while the 𝑃 (𝑉) distributions are shown in FigureA11. The distributions broaden drastically and become progressively more asymmetric with increasing mole fraction of the disregarded component, developing an exponentially decaying tail (transformed to a line by the logarithmic scale) at large volume values. The occurrence of this exponentially decaying tail is a clear sign of the self-association behavior of both the ions and the solvent molecules.53,[START_REF] Zaninetti | The Voronoi tessellation generated from different distributions of seeds[END_REF] To quantify the development of this tail, the skewness parameter of the 𝑃 (𝑉) and 𝑃 (𝑉) distributions as a function of the IL mole fraction were plotted in Figures 6.4 and 6.5, respectively.

Figure 6 . 4 .

 64 Figure 6.4. IL mole fraction dependence of the skewness parameter of the VP volume distributions, 𝑚 ⁄ , obtained considering only the ions, while disregarding the solvent molecules in the analysis.

Figure 6 . 5 .

 65 Figure 6.5. IL mole fraction dependence of the skewness parameter of the VP volume distributions, 𝑚 ⁄ , obtained considering only the solvent molecules, while disregarding the ions in the analysis.

Figure 6 . 6 .

 66 Figure 6.6. IL mole fraction dependence of the average value of the reciprocal VP volume, characterizing the local density, 〈𝜌 〉, obtained considering all the ions and molecules in the analysis.

Figure 6 . 7 .

 67 Figure 6.7. IL mole fraction dependence of the standard deviation of the reciprocal VP volume distribution, ∆𝜌 , obtained considering all the ions and molecules in the analysis.

Figure 6 . 8 .

 68 Figure 6.8. IL mole fraction dependence of the average value of the reciprocal VP volume, characterizing the local density, 〈𝜌 〉, obtained considering only the ions, while disregarding the solvent molecules in the analysis.

Figure 6 .

 6 Figure 6.8 and 6.9 show that the rate of the density change with the composition is again considerably larger below the x IL value of 0.2 than at higher IL mole fractions. Such a rapid change of the density suggests the presence of large density fluctuations in the system (in a clear analogy with critical phenomena). This point can be clarified by analyzing the corresponding density fluctuations.

Figure 6 . 9 .

 69 Figure 6.9. IL mole fraction dependence of the average value of the reciprocal VP volume, characterizing the local density, 〈𝜌 〉, obtained considering only the solvent molecules, while disregarding the ions in the analysis.

Figure 6 . 10 .

 610 Figure 6.10. IL mole fraction dependence of the standard deviation of the reciprocal VP volume distribution, ∆𝜌 , obtained considering only the ions, while disregarding the solvent molecules in the analysis.

Figure 6 . 11 .

 611 Figure 6.11. IL mole fraction dependence of the standard deviation of the reciprocal VP volume distribution, ∆𝜌 , obtained considering only the solvent molecules, while disregarding the ions in the analysis.

6. 3 . 3 .

 33 Radius of the voidsThe analysis of the distribution of the radius of spherical voids between the particles can provide some additional insight into the local environment of the components in these mixtures. The 𝑃 (𝑅) and 𝑃 (𝑅) distributions, obtained by considering all particles and only the ions, respectively, in the analysis, describing the position of the cation by that of the H 2 , H 4 , H 5 , H B and H M hydrogen atoms are shown in FiguresA23-A27 and Figures A28-A32, respectively, while the 𝑃 (𝑅) distributions, obtained by considering only the solvent molecules and disregarding the ions are shown in FigureA33.

  Figures 6.12 and 6.13, respectively. Both parameters remain almost unaffected when the ILs are diluted from their neat liquid to their mole fraction of about 0.2, while their values increase drastically for further dilution. Of note is that these values are independent from the choice of the representative atom that describes the position of the cation.

Figures 6 . 12 .

 612 Figures 6.12. IL mole fraction dependence of the average value of the spherical voids' radius distribution, calculated as the distance of the VP vertices from the center of the polyhedra, 〈𝑅 〉, obtained considering only the ions, while disregarding the solvent molecules in the analysis.

Figures 6 . 13 .

 613 Figures 6.13. IL mole fraction dependence of the standard deviation of the spherical voids' radius distribution, calculated as the distance of the VP vertices from the center of the polyhedra, ∆𝑅 , obtained considering only the ions, while disregarding the solvent molecules in the analysis.

  Figure A2. Volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when all components are taken into account in the analysis. The position of the cation is described with ring H 4 hydrogen of C 4 mim + . The F (BF 4 -and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figure A3 .

 A3 Figure A3. Volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when all components are taken into account in the analysis. The position of the cation is described with ring H 5 hydrogen of C 4 mim + . The F (BF 4 -and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figure A4 .

 A4 Figure A4. Volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when all components are taken into account in the analysis. The position of the cation is described with alkyl H M hydrogen of C 4 mim + . The F (BF 4 -and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figure A5 .

 A5 Figure A5. Volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when all components are taken into account in the analysis. The position of the cation is described with alkyl H B hydrogen of C 4 mim + . The F (BF 4 -and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figures A6 .

 A6 Figures A6. Volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when only the ions are taken into account, and the solvent molecules are disregarded. The position of the cation is described with ring H 2 hydrogen of C 4 mim + . The F (BF 4 -and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figures A7 .

 A7 Figures A7. Volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when only the ions are taken into account, and the solvent molecules are disregarded. The position of the cation is described with ring H 4 hydrogen of C 4 mim + . The F (BF 4 -and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figures A8 .

 A8 Figures A8. Volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when only the ions are taken into account, and the solvent molecules are disregarded. The position of the cation is described with ring H 5 hydrogen of C 4 mim + . The F (BF 4 -and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figures A9 .

 A9 Figures A9. Volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when only the ions are taken into account, and the solvent molecules are disregarded. The position of the cation is described with alkyl H M hydrogen of C 4 mim + . The F (BF 4 -and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figures A10 .

 A10 Figures A10. Volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when only the ions are taken into account, and the solvent molecules are disregarded. The position of the cation is described with alkyl H B hydrogen of C 4 mim + . The F (BF 4 -and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figures A11 .

 A11 Figures A11. Volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when only the solvent molecules are taken into account. The N and O atoms describe the position of the AN, PC and -BL, respectively.

Figure A12 .

 A12 Figure A12. Reciprocal volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when all components are taken into account in the analysis. The position of the cation is described with ring H 2 hydrogen of C 4 mim + . The F (BF 4 -and PF 6 -) and the O (TFO - and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figure A13 .

 A13 Figure A13. Reciprocal volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when all components are taken into account in the analysis. The position of the cation is described with ring H 4 hydrogen of C 4 mim + . The F (BF 4 -and PF 6 -) and the O (TFO - and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figure A14 .

 A14 Figure A14. Reciprocal volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when all components are taken into account in the analysis. The position of the cation is described with ring H 5 hydrogen of C 4 mim + . The F (BF 4 -and PF 6 -) and the O (TFO - and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figure A15 .

 A15 Figure A15. Reciprocal volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when all components are taken into account in the analysis. The position of the cation is described with alkyl H M hydrogen of C 4 mim + . The F (BF 4 -and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figure A16 .

 A16 Figure A16. Reciprocal volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when all components are taken into account in the analysis. The position of the cation is described with alkyl H B hydrogen of C 4 mim + . The F (BF 4 -and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figures A17 .

 A17 Figures A17. Reciprocal volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when only the ions are taken into account, and the solvent molecules are disregarded. The position of the cation is described with ring H 2 hydrogen of C 4 mim + . The F (BF 4 - and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figures A18 .

 A18 Figures A18. Reciprocal volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when only the ions are taken into account, and the solvent molecules are disregarded. The position of the cation is described with ring H 4 hydrogen of C 4 mim + . The F (BF 4 - and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figures A19 .

 A19 Figures A19. Reciprocal volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when only the ions are taken into account, and the solvent molecules are disregarded. The position of the cation is described with ring H 5 hydrogen of C 4 mim + . The F (BF 4 - and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figures A20 .

 A20 Figures A20. Reciprocal volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when only the ions are taken into account, and the solvent molecules are disregarded. The position of the cation is described with alkyl H M hydrogen of C 4 mim + . The F (BF 4 - and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figures A21 .

 A21 Figures A21. Reciprocal volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when only the ions are taken into account, and the solvent molecules are disregarded. The position of the cation is described with alkyl H B hydrogen of C 4 mim + . The F (BF 4 - and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figures A22 .

 A22 Figures A22. Reciprocal volume distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when only the solvent molecules are taken into account. The N and O atoms describe the position of the AN, PC and -BL, respectively.

Figure A23 .

 A23 Figure A23. Vertex radius distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when all components are taken into account in the analysis. The position of the cation is described with ring H 2 hydrogen of C 4 mim + . The F (BF 4 -and PF 6 -) and the O (TFO - and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figure A24 .

 A24 Figure A24. Vertex radius distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when all components are taken into account in the analysis. The position of the cation is described with ring H 4 hydrogen of C 4 mim + . The F (BF 4 -and PF 6 -) and the O (TFO - and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figure A25 .

 A25 Figure A25. Vertex radius distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when all components are taken into account in the analysis. The position of the cation is described with ring H 5 hydrogen of C 4 mim + . The F (BF 4 -and PF 6 -) and the O (TFO - and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figure A26 .

 A26 Figure A26. Vertex radius distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when all components are taken into account in the analysis. The position of the cation is described with alkyl H M hydrogen of C 4 mim + . The F (BF 4 -and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figure A27 .

 A27 Figure A27. Vertex radius distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when all components are taken into account in the analysis. The position of the cation is described with alkyl H B hydrogen of C 4 mim + . The F (BF 4 -and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figures A28 .

 A28 Figures A28. Vertex radius distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when only the ions are taken into account, and the solvent molecules are disregarded. The position of the cation is described with ring H 2 hydrogen of C 4 mim + . The F (BF 4 - and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figures A29 .

 A29 Figures A29. Vertex radius distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when only the ions are taken into account, and the solvent molecules are disregarded. The position of the cation is described with ring H 4 hydrogen of C 4 mim + . The F (BF 4 - and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figures A30 .

 A30 Figures A30. Vertex radius distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when only the ions are taken into account, and the solvent molecules are disregarded. The position of the cation is described with ring H 5 hydrogen of C 4 mim + . The F (BF 4 - and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figures A31 .

 A31 Figures A31. Vertex radius distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when only the ions are taken into account, and the solvent molecules are disregarded. The position of the cation is described with alkyl H M hydrogen of C 4 mim + . The F (BF 4 - and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figures A32 .

 A32 Figures A32. Vertex radius distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when only the ions are taken into account, and the solvent molecules are disregarded. The position of the cation is described with alkyl H B hydrogen of C 4 mim + . The F (BF 4 - and PF 6 -) and the O (TFO -and TFSI -) atoms describe position of the anion while the N and O atoms describe the position of the AN, PC and -BL, respectively.

Figures A33 .

 A33 Figures A33. Vertex radius distributions of the Voronoi polyhedra of the components of the mixtures at various mole fraction of ionic liquid, when only the solvent molecules are taken into account. The N and O atoms describe the position of the AN, PC and -BL, respectively.

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Chapters 3, 4 and 5 provide a detailed MD simulation study of LiPF 6 in dimethyl carbonate (DMC) / ethylene carbonate (EC) mixture, SBPBF 4 in acetonitrile (AN) and the mixtures of room-temperature ionic liquids C 4 mimX (X = BF 4 -, PF 6 -, TFO -, TFSI -) with dipolar aprotic solvents such as AN, γbutyrolactone (-BL) and propylene carbonate (PC) respectively. The local environment, association analysis as well as transport properties were obtained, results were discussed in details in these three Chapters.

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Table 3 .

 3 1. The composition of the simulated systems of LiPF 6 in DMC/EC (1:1)

	binary mixture.
	LiPF6	Number	Number	Number	Number	𝛒, 36, 37
	concentration	of Li +	of PF6 -	of DMC	of EC	g/cm 3
	0.1 M			6707	6707	1.21
	0.5 M			1318	1318	1.25
	1.0 M	100	100	664	664	1.29
	1.5 M			420	420	1.33
	2.0 M			308	308	1.36

Table 3 .

 3 2. Charge distribution, q, Lennard-Jones parameters, σ and ε, intramolecular parameters, k i , for DMC and EC. Asterisk represents the Lennard-Jones parameters of the GAFF for H atoms that replaced the original ones.

	DMC

Table 3 .

 3 2 continued

	123.4	694.544	123.4	694.544
	116.9	694.544	116.9	694.544
	116.9	694.544	116.9	694.544
			109.5	418.4
			109.5	418.4
			110.7	313.8
			110.7	313.8
	118.18	584.923	118.18	584.923

Table 3 . 3 .

 33 Observed density, ρ, self-diffusion coefficient, D, and enthalpy of vaporization, H , and share viscosity, η, calculated at 298.15 K for DMC and at 313.15 K for EC in comparison with the results obtained through experimental measurements.

		DMC (298.15 K)	EC (313.15 K)
	Property	MD	Exp.	MD	Exp.
	ρ, g/dm 3	1038	1057 48	1294	1321 48
	D⸱10 , cm 2 /s	2.2	2.6 49,a	0.6	0.8 49
	H , kJ/mol	35.5	38.0 50	54.8	60 51

Table 4 .

 4 1. The composition of the simulated systems of SBPBF 4 in AN.

	SBPBF4	Number of	Number of	Number of	𝛒, 31 g/cm 3
	concentration	SBP +	BF4 -	AN
	Infinite diluted solution	1	-	500	0.77
	0.5 M			3483	0.82
	1.0 M			1603	0.87
	1.5 M			977	0.92
	2.0 M	100	100	664	0.97
	2.5 M			476	1.02
	3.0 M			350	1.07
	3.5 M			261	1.12
	4.2.2. Potential model: development and validation

Table 4 .

 4 2. Partial charges of the SBP + E-E, T-E and T-T conformers as well as the unified charges after 2 iterations.

	Atom	E-E	E-T	T-T	Unified
	N 1	0.113039	0.119648	0.135923	0.1169112
	C 2	-0.126957	-0.121679	-0.097901	-0.1236403
	C 3	-0.131967	-0.034286	-0.04368	-0.0799324
	C 4	-0.126957	-0.136825	-0.097901	-0.1314238
	C 5	0.043744	-0.014057	-0.097896	0.0110940
	C 6	-0.006476	0.006529	-0.043667	-0.0005663
	C 7	-0.131967	-0.120269	-0.04368	-0.1241190
	C 8	0.043744	-0.063084	-0.097896	-0.0141010
	C 9	-0.006476	-0.067939	-0.043667	-0.0388354
	H 10	0.079814	0.078743	0.068921	0.0856346
	H 11	0.088551	0.09497	0.106933	0.0856346
	H 12	0.109316	0.084141	0.087525	0.0948084
	H 13	0.108487	0.080274	0.094215	0.0948084
	H 14	0.088551	0.11117	0.106933	0.0915560
	H 15	0.079814	0.085588	0.068921	0.0915560
	H 16	0.070155	0.085205	0.068921	0.0561472
	H 17	0.027229	0.038017	0.106933	0.0561472
	H 18	0.094146	0.073641	0.087524	0.0846835
	H 19	0.087439	0.084163	0.094211	0.0846835
	H 20	0.109316	0.112409	0.094215	0.1114084
	H 21	0.108487	0.11661	0.087525	0.1114084
	H 22	0.070155	0.06509	0.068921	0.0666926
	H 23	0.027229	0.099173	0.106933	0.0666926
	H 24	0.087439	0.105045	0.094211	0.1013758
	H 25	0.094146	0.117722	0.087524	0.1013758

Table 4 .

 4 from the Nernst-Einstein equation. It is equal to 1.71⸱10 -5 cm 2 /s which means that the results from the MD simulations are close to experimental value. The potential model parameters of SBP + are shown in the Table 4.3.

	Atom	C6, kJ⸱nm 6 /mol	C12, kJ⸱nm 12 /mol
	N 1	2.4364096⸱10 -3	2.319529⸱10 -6
	C 2-9	2.3406244⸱10 -3	4.937284⸱10 -6
	H 10-25	8.464⸱10 -5	1.5129⸱10 -8
	Bond	0

3. Lennard-Jones parameters, C6 and C12 and intramolecular parameters, k i , for SBP + .

Table 4 .

 4

		0.151024	5430000
		0.150106	5430000
		0.155113	3081900
		0.155113	3081900
		0.153367	7150000
		0.153367	7150000
		0.152751	7150000
		0.152751	7150000
	10-11	0.109085	12300000
	C 3 -H 12-13	0.109085	12300000

Table 5 . 1 .

 51 Composition of the systems simulated.

	IL mole fraction Number of	Number of	Number of
		cations	anions	solvent molecules
	0.05			1900
	0.10			900
	0.15 0.20	100	100	566 400
	0.25			300
	0.30			232

Table 6 . 1 .

 61 Composition of the systems simulated.

	IL mole fraction Number of	Number of	Number of
		cations	anions	solvent molecules
	0.00	0	0	864
	0.02	17	17	847
	0.05	43	43	821
	0.10	86	86	778
	0.15	130	130	734
	0.20	173	173	691
	0.30	259	259	605
	0.40	346	346	518
	0.50	432	432	432
	0.60	518	518	346
	0.70	605	605	259
	0.80	691	691	173
	1.00	864	864	0

ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to my supervisors, Profs.

Abdenacer Idrissi and Oleg Kalugin, for their unwavering support, guidance and

encouragement throughout my PhD journey. Without Nacer's tireless efforts and patience, my defense at the University of Lille would not have been possible. I am also deeply grateful to Oleg for introducing me to the scientific world and providing invaluable guidance and ideas throughout all the years of my PhD research. I would also like to thank Profs. Oleg Prezhdo and Ari Paavo Seitsonen for their invaluable insights and feedback as my reviewers. My research would not have been possible without the support of the Ukrainian government, who provided me with basic scholarships, as well as Erasmus+ and MobLilEx research mobility grants for the opportunity to perform my research in Lille I am also grateful to Université Côte d'Azur and University of Warsaw, and particularly Dr. Kamil Polok, for providing

As can be seen from the figure, the diffusion coefficients of all ions and molecules with the increasing salt concentration become lower. Also, it can be noted that the diffusion coefficients of the relatively small and neutral molecules of AN are two times larger for those of SBP + and BF 4 -for almost all concentration range.

Viscosity perfectly fit the experimental data. 31 At concentration of approximately 2.0 M of SBPBF 4 the calculated viscosity increases drastically, indicating the inner processes of ionic aggregation that happen in the same concentration range.

Chapter 5. Microstructure and transport properties of imidazolium-based ionic liquids and molecular solvents from molecular dynamics simulations Binary mixtures based on aprotic dipolar solvents like acetonitrile (AN, propylene carbonate (PC) or gamma butyrolactone (-BL) with room-temperature ionic liquids are widely used in the modern electrochemistry. These systems have maximum on the electroconductivity as well as other changes in diluted solutions confirmed by the nmR and vibration spectroscopic data, there is no such theory that can explain these phenomena. In current chapter twelve ILs (C4mim + with BF4 -, PF6 -, TFO -and TFSI -) with molecular solvents (AN, PC and -BL) mixtures were studied by the molecular dynamics simulation technique. The local structure of the mixtures was studied in the framework of RDFs and RCNs that showed the particular behavior in AN and TFSI -systems. For TFSI -system the presence of two peaks on the RDFs with similar intensities were observed. The mutual arrangement of cation and anion corresponding to observed on the RDFs interatomic distances were investigated: they represent the position when the nitrogen atom of the anion is close to the imidazolium ring and when nitrogen atom of TFSInot directly interacting with the ring, but instead the oxygen atoms do. The cation-anion coordination numbers changed for mixtures with AN from ~1.2 to ~3.6, for PC -from 0.6 to 3.0 and for -BL -from 0.8 to 3.1 with the increasing mole fraction of the ILs. Also, the association analysis with two different distance criteria have been performed. It showed the formation of the massive clusters at ~0.15, 0.20 and 0.25 IL mole fraction for AN, PC and for -BL respectively for the first criterium. These findings points out the overestimation of the aggregation process. With the second, stricter criterion the formation of big aggregates in the systems starting to occur at similar mole fractions of the ILs where the experimental conductivity curves have maximum. To analyze the transport properties the diffusion coefficients of all the components and shear viscosity for all binary mixtures were obtained.

The diffusion coefficients show good agreement with experimental data. Although, the viscosity values didn't show any particular behavior.

interaction when N atom of TFSI -not directly interacting with the ring, but instead the oxygen atoms do. The example snapshot from the MD simulation trajectory files was obtained via VMD program package 46 (Figure 5.3). These findings prove the quantum chemical calculations from the literature data. 47 The first minima of RDFs for various anions are as follows: 0.70 nm (BF 4 -), 0.74 nm (PF 6 - ), 0.73 nm (TFO -) and 0.77 nm (TFSI -). Also, for PF 6 -. The behavior of the intensities of the peaks also changes in different ILs-solvent combinations. For all systems with AN the intensity becomes lower with the increasing of the ILs mole fraction. Also, for TFSI -system these changes are the lowest. Similar situation can be observed for all PC-containing systems where peak intensity do not change with the mole fraction of the ILs. Nernst-Einstein relation postulates that conductivity depends on the concentration of the charge carriers in the solution. 52 Ionic aggregation reduces its concentration and effectively causes the drop in the conductivity value. As seen from the Figure 5.18, the mole fractions of rapid increase in the aggregates formation are the same as the conductivity maxima are located: at ~0.10 for AN systems and at ~0.20 for PC and -BL ones. [48][49][50][51] of such drastic changes in the conductivity particular lies in the local structure of the ILs and solvent molecules.

To analyze the transport properties the diffusion coefficients of all the components and shear viscosity for all binary mixtures were obtained. The diffusion coefficients show good agreement with experimental data, especially for the systems with AN. The viscosity values didn't show any particular behavior at the mole fraction of the ILs range where the experimental conductivity maximum occur.

concentration of SBPBF 4 in AN at 1.5 M while for the second criterion the average number of association begins to increase at the same region where the experimental conductivity curve changes its behavior which indicates that this criterion is the correct choice for such an analysis. The transport properties were investigated via diffusion coefficients of solution components and viscosity of simulated systems. Obtained viscosity values are matching the experimental ones.

Diffusion coefficients of all components are decreasing while the viscosity of the system continuously increasing with the salt concentration increase. The obtained results show a good correlation with the association analysis and in accordance with the occurrence of the concentration conductivity maximum in the experiment.

Next, twelve ILs (C 4 mim + with BF 4 -, PF 6 -, TFO -and TFSI -) with molecular solvents (AN, PC, and -BLF) binary mixtures were studied by the molecular dynamics simulation technique. The microstructure of the mixtures was studied in the framework of radial distribution functions and running coordination numbers. The RDFs and RCNs show the particular behavior in AN and TFSI - systems. For TFSI-system the cation-anion (CoR-N) RDFs curves showed two peaks with similar intensities that represent the position when the nitrogen atom of the anion is close to the imidazolium ring and when nitrogen atom of TFSI -not directly interacting with the ring, but instead the oxygen atoms do. The cationanion coordination numbers changed in similar values for the same ionic liquids in different solvents: for AN it varies from ~1.2 to ~3.6, for PC -from 0.6 to 3.0 and for -BL -from 0.8 to 3.1 with the increasing mole fraction of the ILs. Also, data obtained were used to conduct a quantitative aggregate analysis with two different distance criteria (first minimum of RDF and minimum of the second derivative of the RCN respectively). The analysis with the first criterion shows the formation of the massive cluster at ~0.15, 0.20 and 0.25 IL mole fraction for AN and for with -BL respectively. Thus, this criterion seems to overrate the aggregation process in the mixtures. With the second, stricter distance criteria the formation of big aggregates in the systems starting to occur at the same mole fractions of the ILs where the experimental conductivity curves change their behavior and the maximum occurs. To analyze the transport properties the diffusion coefficients of all the components and shear viscosity for all binary mixtures were obtained. The diffusion coefficients show good agreement with experimental data, especially for the systems with AN. The viscosity values didn't show any particular behavior at the mole fraction of the ILs range where the experimental conductivity maximum occur.

Finally, the local structure in twelve mixtures of ILs was also studied via distributions of several metric characteristics (i.e., volume, reciprocal volume, characteristic of the local density, and vertex distance, marking the radius of the largest spherical void) of the Voronoi polyhedra. A drastic change in the behavior of the calculated properties at this composition was found, proving that these changes concern the local structure around the particles. The results show that below the IL mole fraction of about 0.2, the ions are well solvated by the solvent molecules, but above this mole fraction they start to form contact pairs, while the solvent molecules, expelled from the vicinity of the ions, form self-associates. This self-association is stronger in the case of AN than of the other solvents considered, because, due to its smaller dipole moment, AN has a weaker interaction with the ions than the other ones. Similarly, this solvent selfassociation is stronger in the presence of TFSI -than of the other anions considered. All these results stress that the local structure, and thus also the physicochemical properties of the IL-solvent mixtures are eventually governed by the delicate interplay of the interionic and solvent-ion interactions.

As for the general results, both of the approaches -association analysis via distance criterion of cluster formation and Voronoi polyhedral analysis -allow to investigate the local structure of the simulated systems of different types. Also, the crucial role of the processes that occur in the microenvironment of ions and solvent molecules were confirmed.