The Published Version of Our Paper in The Journal of Physical Chemistry C 

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Electrolytes in Batteries: Fundamentals

Electrolytes are a crucial component for all electrochemical devices as discussed above. Electrolytes are composed by salts (solutes) dissolved in solvents and they act as the con-ductive medium which transfer the charges or ions between the electrodes. Performances of the devices depend on both the electrolyte and electrode materials. The electrolyte material must be chemically compatible when the electrodes to avoid stability issues and the chemical reactions taking place in the electrolyte control both quantity and speed of the energy released towards the electrodes. Also, electrolytes must be highly stable or completely inert when on contact with the electrode surface, otherwise they fail to produce high energy densities. The reaction rate of the reductive and oxidative decomposition is controlled by the electrolyte concentration.
In order to develop better electrolytes a few issues should be considered [12]: 1) tem-perature range for stability. For instance, the EC solvent is solid at room temperature, therefore affecting conductivity and reactivity of the salt, e.g., LiPF6; 2) flammability, it is therefore crucial to consider safety problems; 3) solvent efficiency in dissolving lithium salts; and 4) considerable loss of concentration of lithium-ion in electrolytes, because those lithium ions are involved in the formation of SEI. The electrolyte must therefore fulfil many requirements, such as being environment friendly, inert toward electrode substrates and cell separator, highly efficient for oxidative and reductive decomposition, and show a good ionic conductivity.
Electrolytes in Batteries: Electrolytes are in close interaction with both electrodes and play a crucial role in LIBs. They provide the ion-conductive medium of the lithium-ion battery, where the Li+ shuttles between the electrodes. The electrolytes must be characterized a high chemical stability, that prevents decomposition when oxidizing at the cathode or reducing at the anode. Some important properties, like non-toxicity, low melting point, high boiling point, the absence of explosive reaction, are required for a good electrolyte in batteries applications. Three types of electrolytes have been used in batteries: aqueous, non-aqueous and solid.
An aqueous electrolyte consists of a strong acid or base, due to the more polarity those exist as ions like positive and negative in solution. These electrolytes are stable in particular voltage ranges, while beyond these limits, they start to decompose. The stability of the provided voltage is controlled by the electrolyte composition degree of purity. High ionic conductivities can be achieved in aqueous electrolytes when dielectric constant and solvating power of the materials are reasonably high.
Non-aqueous electrolytes are formed by carbonate solvents with common lithium salts such as LiBF4, LiClO4, LiPF6, LiAsF6, LiTFSI (lithium bis-(trifluoromethane sulfonyl) iodide) and LiBOB (lithium bis-oxalato borate). The conductivity of non-aqueous elec-trolytes are in the range of 10−2-10−3 Scm−1. More specifically, these electrolytes are non-aqueous aprotic (unable of acting as proton donors) organic solvents, combined with lithium salts. They are characterized by low toxicity and melting point, good ion conductivity and electrochemical stability towards the electrodes. The two classes of electrolytes that have been used in batteries are: i) linear alkyl carbonates (dimethyl carbonate (DMC), ethyl methyl carbonate (EMC), and diethyl carbonate (DEC)) and ii) cyclic alkyl carbonates (ethylene carbonate (EC), vinylene carbonate (VC), and propy-lene carbonate (PC)). A large number of studies have been devoted to their decompo-sition, electrochemical properties, and the formation and structure of the first solvation shell around lithium ions[33, 41–44]. Due to lower dielectric constant and lower solvating power of some solvents, the formation of ion pairs is enhanced, resulting in a lower ionic conductivity. Indeed, in this case ions are bound to each other and no longer freely diffuse in solution. At present, mixtures of solvents with different compositions are used to enhance the conductivity, and to achieve good low temperature performances. Pure solvents and solvent mixtures are discussed in the following sections.
Carbonates such as EC and PC have failed to be used as solvents in lithium-air batteries because of their decomposition reaction with O2. In particular, super-oxides or radicals are formed during initial reduction of O2[45]. Less volatile ether-based compounds such as dimethylether(DME) or larger ether compound electrolytes have been preferred as good candidates for lithium-air batteries [46, 47].
Beyond carbonates, silicon liquids have also received substantial attention. Several stud-ies have focused on carbonate-modified electrolytes [48–50], siloxane and silyl ether[35, 51, 52] and ethylene-glycol[53–55] compounds. Instead of carbonate solvents mixed with lithium salts, polymer and copolymer electrolytes have also been considered, formed by poly(ethylene)oxide (PEO) and lithium salts (LiPF6 or LiCF3SO3)[56–58].
In the past 15 years, Ionic Liquids (IL) [59–61] have attracted much attention as lithium-ion battery electrolytes. Indeed, ILs are interesting alternatives to organic solvents in batteries due to their unique properties such as electrochemical stability, low or no tox-icity, low flammability, low vapour-pressure properties, high charge density and tunable polarity. ILs with a melting temperature higher or close to room temperature are called room-temperature ionic liquids (RTILs). ILs are charged molecules and other than some advantages, it has relatively high viscosity which will affect the ionic conductivity. ILs are entirely comprised of cation with basis amines such as pyridinium, imidazolinium , piperidinium, pyrrolidinium and morpholinium [62–64]. The anion can be inorganic like BF−4, PF−6, CN− or AsF−6. The IL properties also based on the nature of the substituents whose affect the ionicity and salt solubility. The alkyl chain lengths[62] or branching chain length increases the conductivity of the IL upto 1 mScm−1.
The peculiar effect of ion-ion interactions, molecular charge distribution and molecu-lar shapes are the main properties of IL in both bulk solutions and at the interfaces. Contrary to what happens in normal solvents, the ion-pair effects are not predominant in ILs, and therefore the molar conductivity rises up to 0.1 Scm2mol−1. ILs also have low dielectric constant and vapour pressure. ILs show, however, moisture sensitivity, properties associated with halogen atoms and moderately high viscosity.
Different classes of ILs are used in a large electrochemical window and can achieve high charge densities. A virtually infinite number of IL electrolytes can be produced, by mixing different ILs or mixing ILs with other inorganic or organic polar solvents.
In the following section, we start our discussion of the organic solvents most used in applications as the main component of electrolytes.

Organic Solvents and Salts

In this section we briefly discuss the pure solvents we have considered in this work, EC, DMC and PC, and their physical properties. We also discuss previous work on the Li+-carbonate interaction. In particular we will first focus on the bibliography reporting mostly theoretical calculation without a specific salt in pure clusters. Next we will present additional results highlighting the role played by chosen from the chosen Li salts ( LiPF6, LiClO4, LiBF4, and others).

Physical Properties of Ethylenecarbonate (EC), Dimethylcar-bonate (DMC), Propylenecarbonate(PC)

Among all organic solvents, the most widely used in LIBs cyclic and linear carbonates. In particular, the EC solvent is very commonly used as the main component in electrolytes, due to its high dipole moment (4.9 D), dielectric constant (ε ∼ 89), and miscibility with most of the non-aqueous solvents [65, 66]. Some physical properties of the EC are shown in Table 7.1. At room temperature EC is solid (melting point temperature 36.4◦), therefore it is mixed with other carbonate solvents in order to lower the overall melting point temperature. In most cases, a small percentage of linear carbonates, like DMC, is added to EC to turn the resulting mixture into the liquid state at room temperature. DMC is chosen because of its low viscosity, low boiling point and low dielectric constant (values are shown in Table 7.1). The combination of EC and DMC in different concenrations forms a homogeneous mixture characterized by low viscosity and high ion conductivity. This mixture is stable up to 5.0 V at the cathode surface.
The PC solvent is another attractive cyclic carbonate, characterized by a higher dielectric constant (ε ∼ 64.9) than linear carbonates. The ionic conductivity and static stability over a wide temperature range, make PC as a preferred solvent for lithium. PC is a five member ring molecule, like EC with an extra methyl group in the side chain. However, PC behaves differently than EC. For instance, several studies have shown that EC plays an important role in the formation of the Solid Electrolyte Interfaces (SEI), which in particular protects, protects graphite anodes from further decomposition. The SEI is formed during the first slow charge of a battery, and the quality of its strcuture strongly impacts the lifetime of the system. In contrast, in systems only containing pure PC, no SEI is effectively formed on the graphite electrode surface [67]. Also, PC undergoes a susceptible reduction reaction after a single electron transfer [68] from lithium which impacts the cycling efficiency of the system. Despite these issues, PC molecule has also been considered as a promising solvent due to high anodic stability. In fact, the first commercial battery (produced by Sony and co.) was developed based on a PC solvent electrolyte. Structure and some physical properties of PC are shown in Table 7.1. Based on the data shown in the Table, PC appears to have a slightly higher viscosity than EC, therefore PC cannot lower the viscosity of EC as DMC does.
In the last decades, several theoretical an experimental work has been published on the coordination properties of EC, PC and DMC with Li+ ions. In fact, the understanding of the solvation properties of carbonate electrolytes with Li+ is crucial to understand a number of physical phenomena occurring in LIBs, like transport properties, stability in redox environment, and degradations phenomena. For instance, Masia et al., [69] studied the solvation structure of Li+ with EC molecules, using DFT and MD methods. The DFT results have shown that a 4-coordinated complex Li+(EC)4, is the dominant species. Similarly, they also found the same coordination number ( Li+(EC)4) in MD simulations. A similar result have been obtained by Wang et al.,[70] by a DFT study, confirming the Li+(EC)4 species as the most stable complex for the Li+(EC)1-4 series. They also studied the Li+(DMC)1-3 complexes and found that Li+(DMC)3 is the most stable conformation. Moreover they have also studied addition and substitution reaction on mixed complexes with EC and DMC solvents, concluding that the addition of DMC to the Li+(EC)n with n=1-3 complexes is favourable, while substitution of DMC to the Li+(EC)2 complex is forbidden. According to Hiroto et al.,[71] studies on EC with Li+ ion by AIMD (ab-initio molecular dynamics), the Li+ ion is solvated by four EC molecules in the first solvation shell. In the case of Li+(EC)5, only four molecules are coordinated with Li+ ion while the 5th molecule displaced with an average distance of 5.09 ˚A from the Li+ ion. Similar results have been obtained by Cho et al.,[72]by DFT calculations. In both papers the authors conclude that the maximum coordination number in the first solvation sphere is 4 and additional EC molecules can be only arranged in the second solvation shell.
Mahesh et al., [73] studied the Li+ ion with EC solvent by DFT and MD simulation. Gibbs free energy were computed using B3LYP/6-311++G(d,p) on the addition reac-tion of EC to Li+(EC)n (where n = 0 to 5) cluster gives negative values or spontaneous reactions for Li+(EC)1-4 clusters and positive Δ G value for the Li+(EC)5 complex. Therefore, they concluded that the formation of a coordination shell with 5 molecules is energetically unfavourable. Also, the AIMD simulation revealed that the coordination number is 4 around Li+ ion within a range of ∼4 ˚A. They also reported that there is no exchange of EC molecules once the solvation structure is formed. The same authors also published in following work [74] for PC complexes that Li+(PC)3 is the leading compo-nent, by calculating Gibbs free energy formation. From heat of formation and Gibbs free energy calculations, they concluded that EC acts as a better solvent than PC. Using the same discussion on ΔG energies, with different DFT approaches, Balbuena et al.,[34] and Wang et al., agreed on the same conclusions, thus confirming a maximum coordi-nation number of 4 for Li+(EC)n solvation and explaining that Li+(PC)4 is unlikely to exist and Li+(PC)2, Li+(PC)3 are the main components in solution.
Mostly, the conventional electrolytes consists of lithium salt like LiPF6, LiClO4, LiBF4 etc, and a binary or ternary mixture of carbonates.

Mixtures of Organic Solvents

Among a variety of solvent electrolytes for LIBs, nowadays mixtures of carbonates con-taining EC are mostly used with success, due to the following reasons: i) even at high concentration of salt (up to 1.0 M), EC molecule can easily dissolve lithium salts, due to its high dielectric constant; ii) low melting point of the electrolyte; iii) low viscosity of linear carbonate electrolytes with improved chemical stability, ionic trans- port and dielectric permittivity; iv) high ionic conductivity at room temperature, which is higher than up to 10−3Ω−1cm−1 [75, 76] . This greatly impacts battery performances and is compatible with battery voltage. The mixture compositions are used in a wide tem-perature range for operations as well as storage applications and cell performance. The choice of the electrolyte is of crucial importance to develop better conventional devices. Therefore, the high dielectric constant of EC molecule is mixed with both liquid car-bonate solvent (such as linear carbonates) and PC (cyclic carbonate) to overcome these issues. The ternary mixt ures have been used to enhance at lower-temperature perfor-mance of batteries. Mixture of EC and DMC with LiPF6 allows the largest number of charge-discharge processes without loss of capacity.
In the past two decades, very extended research works have been published focusing on EC containing electrolytes. Before the 1970s, EC was used as a co-solvent in electrolytes, in order to obtain good ionic conductivity. In the 1970s, a little amount of PC was added, in order to lower the melting point of EC molecule resulting in a mixture high ionic conductivity in the bulk solution. In early 1990s, conventional LIBs employed with EC solvents and despite of EC high boiling point, little amounts of different co-solvents were added, including PC, THF (tetrahydrofuran), DEE (diethoxyethane). These solvents do not perform satisfactorily, due to the fact that PC causes side reactions affecting the irreversible capacity of the LIBs. Moreover, ether solvent are unstable during oxidation at the charged cathode. After 1994, Tarascon and Guyomard [77, 78] found that the linear carbonate DMC molecule acts as a better co-solvent with EC to form an effective electrolyte. Indeed, the addition of linear carbonate DMC to EC forms homogeneous mixtures re-sulting in the decreasing of EC melting temperature [78, 79]. As a result, EC viscosity becomes very low, enhancing ion transport mechanisms and, therefore, increasing ion conductivity. The addition of EC and PC solvents in adapted ratios has also been used to decrease the melting point of the electrolyte, due to the high permittivity and low melting temperature (-49◦) [80] of PC solvent. Further development and improvement of lithium ion batteries still implies to overcome limitations of the above binary mixtures, mainly due to low thermal stability of solvents and high vapour pressure. To date, there of lot of research works have been published in various mixtures with different salts that we discuss below. Some results could be dependent not only from the choice of the electrolyte mixture but also from the salts . For that reason we will discuss bibliography for each salt in separate paragraphs.

EC,PC,DMC + LiClO4

Earlier experimental Raman spectroscopic studies by Hyodo et al., [81] in 1989 focused on the local structure of Li+ ion solvation in EC and PC with LiClO4 salt. They proposed a coordination number around 4 for Li+ in EC with a high concentration of 1 M LiClO4 and this value becomes 4.9 at lower concentration, 0.1 M LiClO4. Moreover, they also examined EC:PC mixtures. They reported 3.3 EC molecules and 0.7 molecules of PC at higher concentration (5:1). On the other hand Li+-EC molecule coordination decreases with increasing the molar ratio of PC. At 1:1 ratio, the number of EC molecule coordinated to Li+ is 1.9 ( on a total coordination number 3.8) meaning that in this case both EC and PC are bound to Li+ in a 50:50 ratio and there is no preferential solvation in the first solvation shell. Nevertheless, theoretical studies by Klassen et al., [76] investigating the heat of formation of the reactions of Li+ ion with EC and PC, showed that EC/ Li+ has a higher solvation energies than PC/ Li+. They concluded that EC selectively solvates Li+ in the EC/PC/ LiClO4 solutions. Also DFT and MD studies on LiClO4 with EC, PC and mixtures by Balbuena et al. [82], demonstrated that EC tends to substitute PC in the first solvation shell. They also demonstrated that the EC molecules have a coordination number of 4.1 with LiClO4 in diluted solutions, but it decreases to 3.8 in concentrated solutions. Also, the coordination numbers are 4 and 4.4 in the mixture of EC:PC in 1:1 and 3:1 ratio, respectively. In the first solvation shell, they found 38% of PC bound to Li+ ion in the 1:1 mixture, and 16% in the 3:1 mixture.
Lithium ion solvation in EC with LiClO4 has been studied by Cazzanelli et al. [83], using NMR techniques, with a concentration defined by the ratio R=[ Li+ ]/[EC]. They found a solvation number ∼7 at R=0.1 concentration, while at higher concentration (R= 0.33), the Li+-EC complex formed with ∼3 solvent molecules. Most of the work cited above therefore suggest that the coordination is around 4 for Li+(EC)n. In contrast, Huang et al., [84] studied the solvation of LiClO4 in EC by Raman and IR spectroscopy and suggested that the average solvation number for Li+ ions in EC is 6. Also, Matsuda et al., [85] measured the solvation of Li+ ion in EC and PC with LiClO4 by Electrospray Ionization – Mass spectroscopy (ESI-MS) and showed that Li+(EC)2 and Li+(EC)3 are the main solvation species in 1 mM LiClO4 solution. Similar result were obtained for PC molecules. In 2002 Inaba et al., [86] studied the linear carbonate (DEC and DMC) co-solvents effect on EC-based solutions, with 1 M LiClO4 by Atomic Force Microscopy (AFM). They reported that 4.6 is the apparent solvation number of Li+ in EC and this sol-vation number decreases to 4.2 (3.1 EC+1.1 DEC) and 3.1 (2.9 EC + 0.2 DMC) in EC:DEC(1:1) and EC:DMC(1:1) solutions, respectively. Their results revealed that EC molecule dominantly participate in the first solvation shell over linear carbonates.

EC, PC, DMC + LiBF4

The molecular dynamics simulation studies of Soetans et al., [87] focused on LiBF4 salt in EC, DMC and PC. They performed simulation on Li+- (EC), Li+- (DMC) and Li+-(PC) at different temperatures, in simulations boxes containing 214 solvent molecules for one Li+ and one BF4–, corresponding to 0.1 M concentration. They showed that the typical solvation shell is formed by both EC and PC around Li+, with a coordination number of 4.
On the other hand, the MD studies of Prezhdo et al., [88] reported that 6 individual carbonate molecules (EC, PC and DMC) can coordinate around Li+ ion at low con-centration (0.1 M) of LiBF4. The coordination decreases to 5 at 1 M concentration. They also described the solvation shell for binary mixtures. Particularly in PC-DME mixtures, lithium ion was found to coordinate with 6 PC molecules, due to absence of the C=O group in DME. In the case of EC-DMC mixtures, 5 EC and 1 DMC molecule were found to solvate Li+ ion. At higher concentrations, they also found some interac-tion with the counter anion. In particular, they discussed that the counter anion BF4– acts as a monodentate in PC-DME mixtures, and as a bidentate ligand in EC-DMC mixtures.
Sono et al., [89] studied the solvation of Li+ ion in PC solutions with LiBF4 salt, by Raman and NMR techniques. They reported that Li+ ion is bound to 1.08 PC molecules, at a concentration over 1 M. This small coordination number is evidence of a more important formation of contact-ion pairs of Li+- BF4–. Recent studies on LiBF4 in PC by Sono et al., [90] demonstrated that at 1 M concentration the total coordination can be attributed as 2.66 for Li+-O(PC) and 1.38 for Li+-F (BF4–). The Li+- PC coordination number increases to 3.14 in 0.5 M concentration, while Li+-F decreases to 0.91, which means that the counter anion BF4– interaction is smaller in the first solvation shell.

Table of contents :

1 Introduction and Motivations 
1.1 Introduction
1.2 Rechargeable Batteries
1.3 Electrolytes in Batteries: Fundamentals
1.4 Organic Solvents and Salts
1.4.1 Physical Properties of Ethylenecarbonate (EC), Dimethylcarbonate (DMC), Propylenecarbonate(PC)
1.5 Mixtures of Organic Solvents
1.5.1 EC,PC,DMC + LiClO4
1.5.2 EC, PC, DMC + LiBF4
1.5.3 EC, PC, DCM + LiTFSI
1.5.4 EC, PC, DMC + LiPF6
1.6 Motivation and Overview
2 Numerical Techniques 
2.1 Density Functional Theory
2.1.1 Outline of Electronic Structure Calculations
2.1.2 Schr¨odinger Equation
2.1.3 The Born-Oppenheimer (BO) Approximation
2.1.4 Hartree-Fock Theory
2.1.5 Thomas-Fermi Theory
2.1.6 Density Functional Theory (DFT)
2.1.6.1 Hohenberg and Kohn Theorems
2.1.6.2 The Kohn-Sham Formulation
2.1.6.3 Exchange-Correlation Functional
Local-Density Approximation (LDA)
Generalised-Gradient Approximation (GGA)
2.1.7 Basis Sets
2.1.8 Amsterdam Density Functional (ADF)
2.1.8.1 Formalism
2.1.8.2 Solvent Effects: Conductor-like Screening Model (COSMO)
2.2 Molecular Dynamics Simulations
2.2.1 Algorithm for integration of equation of motion
Quaternions method
2.2.2 Ensembles
Nos´e -Hoover Thermostat
Parrinello-Rahman Barostat
3 Study of Lithium ion Coordination with Carbonate Solvents 
3.1 Ethylene carbonate(EC)
3.2 Propylene carbonate (PC)
3.3 Dimethyl Carbonate (DMC)
3.4 Li+(EC)1−6 complexes
3.4.1 Structural Properties
3.4.2 Frequency and Mulliken Charge Analysis
3.4.3 Frontier Molecular Orbital(FMO) analysis
3.5 Li+(DMC)1−5 complexes
3.5.1 Structural Properties
3.5.2 Frequency and Mulliken Charge Analysis
3.5.3 Frontier Molecular Orbital(FMO) analysis
3.6 Li+(PC)1−5 complexes
3.6.1 Structural Properties
3.6.2 Frequency and Mulliken Charge Analysis
3.6.3 Frontier Molecular Orbital(FMO) analysis
3.7 Thermodynamic parameters of Li+(S)1−5 complexes: (S=EC,DMC and PC)
3.8 Solvent Mixtures
3.8.1 Binary Mixtures
3.8.2 Ternary Mixtures
3.9 Conclusions
4 Study of Counter Anion PF− 6 Effect on Li+-EC, -DMC and -PC complexes
4.1 Optimization of PF− 6 Anion
4.2 Possible interactions between Li+ and PF− 6 anion
4.3 Optimization of LiPF6
4.4 Effect of PF− 6 anion in Li+(EC)1−3 Complexes
4.5 Effect of PF− 6 anion in Li+(DMC)1−3 Complexes
4.6 Effect of PF− 6 anion in Li+(PC)1−3 Complexes
4.7 Stability of Clusters with anions
4.8 Conclusions
5 Coupling DFT and MD 
5.1 What we need MD for?
5.2 Molecular Dynamics Simulation
5.2.1 Effective Force Fields for EC, PC and DMC
5.3 The Published Version of Our Paper in The Journal of Physical Chemistry C
6 Conclusions and Perspectives 
7 Chapitre 1: Introduction et motivations
8 Chapitre 2: Techniques Num´eriques
9 Chapitre 3: Etude de Lithium ion Coordination avec Solvants des Carbonates
10 Chapitre 4: Etude de Contre-anion PF− 6 Effet sur Li+ -EC, -DMC et complexes -PC
11 Chapitre 5: Accouplement DFT et MD 16
12 Conclusions et Perspectives 
Bibliography 

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