To my family

List of Papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I Electrolyte Decomposition on Li-metal Surfaces from First-

Principles Theory Ebadi, M.; Brandell, D.; Araujo, C. M.; The Journal of Chemical Physics, 2016, 145(20): 204701.

II Insights into the Li-Metal/Organic Carbonate Interfacial Chemistry by Combined First-Principle Theory and X-ray Photoelectron Spectroscopy Ebadi, M.; Nasser, A.; Carboni, M.; Younesi, R.; Marchiori, C. F. N.; Brandell, D.; Araujo, C. M.; The Journal of Physical Chemistry C, 2019, 123 (1), 347–355.

III Density Functional Theory Modelling Interfacial Anode Re-actions of the LiNO3 Additive in Lithium-Sulfur Batteries by Means of Simulated Photoelectron Spectroscopy Ebadi, M.; Lacey, M. J.; Brandell, D.; Araujo, C. M.; The Jour-nal of Physical Chemistry C, 2017, 121, 23324.

IV Modelling the Polymer Electrolyte/Li-metal Interface by Molecular Dynamics Simulations Ebadi, M.; Costa, L. T; Araujo, C. M.; Brandell, D.; Electro-chimica Acta, 2017, 234, 43-51.

V An Interaction Model for Solid Polymer Electrolyte/Li Metal Interface: PEO as a case Study. Ebadi, M.; Lourenço, T. C.; Araujo, C. M.; Costa, L. T.; Bran-dell, D.; in manuscript.

VI Restricted Ion Transport by Plasticizing Side Chains in Pol-ycarbonate-Based Solid Electrolytes Ebadi, M.; Eriksson, T.; Mandal, P.; Costa, L. T.; Araujo, C. M.; Mindemark, J.; Brandell, D.; in manuscript.

VII Assessing Structure and Stability of Polymer/Lithium Metal Interfaces from First-Principles Calculations Ebadi, M.; Marchiori, C. F. N.; Mindemark, J.; Brandell, D.; Araujo, C. M.; Journal of Materials Chemistry A, 2019, 7, 8394.

VIII Understanding the Electrochemical Stability of Solid Poly-mer Electrolytes from Atomic-Scale Modelling Marchiori, C. F. N.; Ebadi, M.; de Carvalho, R. P.; Brandell, D.; Araujo, C. M.; in manuscript.

IX Initial Steps in PEO Decomposition on a Li Metal Electrode Mirsakiyeva, A.; Ebadi, M.; Araujo, C. M. ; Brandell, D.; Broqvist, P.; Kullgren, J.; Submitted to The Journal of Physical Chemistry C.

Reprints were made with permission from the respective publishers.

Comments on my contributions to the appended papers: For articles I, III, IV, and VII, I had the main responsibility for planning and performing calculations/simulations, analyzing the results, and writing the manuscripts. In paper II, I co-supervised a bachelor student who performed most of the DFT calculations, but I had the main responsibility of analyzing the results of the modelling part and wrote the manuscript (except the details of experimental measurements). In paper V, planning the project, performing the calculations, analyzing the results and writing the first draft of the manuscript was a joint work with T. C. Lourenço. For article VI, I performed all the simulations and had the main responsibility of planning the simulation part of the work. I wrote substantial parts of the manuscript (except the details of experimental measurements). In paper VIII and IX, I participated in planning the work, in all discussions of the results, and in the writing of the manuscript. Disclaimer: Part of this thesis is based on my licentiate thesis entitled “Mod-elling the electrolyte/lithium interface in Li metal batteries” (Uppsala Univer-sity, 2017).

Papers not included in the thesis

Mahmoodinia, M.; Ebadi, M.; Åstrand, P.-O.; Chen, D.; Cheng, H.-Y.; Zhu, Y.-A.; Structural and Electronic Properties of the Ptn–PAH Complex (n = 1, 2) from Density Functional Calculations, Physical Chemistry Chemical Physics, 2014, 16, 18586.

Xu, C.; Renault, S.; Ebadi, M.; Wang, Z.; Björklund, E.; Guy-omard, D.; Brandell, D.; Edström, K.; Gustafsson, T.; LiTDI: A Highly Efficient Additive for Electrolyte Stabilization in Lithium-Ion Batteries, Chemistry of Materials, 2017, 29, 2254-2263.

Renault, S.; Oltean, V.-A.; Ebadi, M.; Edström, K.; Brandell, D.; Dilithium 2-aminoterephthalate as a Negative Electrode Material for Lithium-ion Batteries, Solid State Ionics, 2017, 307, 1-5.

Contents

1. Introduction .......................................................................................... 131.1 Rechargeable lithium batteries ........................................................ 131.2 Li battery electrolytes ..................................................................... 14

1.2.1 Liquid electrolytes .................................................................. 141.2.2 Solid-state electrolytes ............................................................ 15

1.3 Electrode/electrolyte interfaces in Li metal batteries ....................... 171.4 Computational modelling of Li-metal batteries ............................... 171.5 Thesis outline ................................................................................. 19

2. Theory and computational methods ....................................................... 232.1 The many-body problem................................................................. 232.2 Density functional theory ............................................................... 24

2.2.1 The Hohenberg-Kohn theorems ............................................... 242.2.2 The Kohn-Sham ansatz ........................................................... 252.2.3 Exchange-correlation functional approximations ..................... 26

2.3 Basis sets........................................................................................ 272.4 Projector-augmented wave (PAW) method ..................................... 292.5 Solvent effects ................................................................................ 292.6 Computed X-ray photoelectron spectroscopy data........................... 302.7 Molecular Dynamics simulations .................................................... 31

2.7.1 Force fields ............................................................................. 332.7.2 Long range interactions ........................................................... 352.7.3 Ab initio molecular dynamics .................................................. 36

3. Molecular modelling of liquid electrolyte/Li metal interfaces ................ 373.1 Adsorption and decomposition of organic carbonates at the Li metal surface ........................................................................................ 373.2 Core-level binding energies of organic carbonates .......................... 393.3 Interfacial chemistry of the LiNO3 additive at the surface of Li metal…. ............................................................................................... 42

4. Molecular dynamics simulations of solid polymer electrolytes .............. 474.1 Structure and dynamic properties of an SPE/Li metal interface ....... 47

4.1.1 Structural properties ................................................................ 474.1.2 Dynamics ................................................................................ 48

4.2 Development of the interaction model for the PEO/Li metal interface ............................................................................................... 49

4.3 The role of plasticizing side-chains in polycarbonate-based electrolytes ........................................................................................... 51

4.3.1 Structural properties ................................................................ 524.3.2 Ion transport mechanisms ........................................................ 53

5. Solid polymer electrolyte reactivity/stability ......................................... 575.1 Polymer decomposition on the Li metal surface .............................. 575.2 The electrochemical stability of solid polymer electrolytes ............. 605.3 Initial steps in PEO decomposition on Li-metal .............................. 61

6. Conclusions .......................................................................................... 65

Sammanfattning på svenska ...................................................................... 67

Acknowledgements .................................................................................. 71

References ................................................................................................ 73

Abbreviations

ACF Auto correlation function AIMD Ab-initio molecular dynamic B88 Becke 1988 BCC Body centered cubic BE Binding energy BOMD Born-Oppenheimer molecular dynamics CLS Core level shift CN Coordination number CT Charge transfer DEC Diethyl carbonate DFT Density functional theory DMC Dimethyl carbonate DOS Density of state DZ Double zeta EC Ethylene carbonate ESW Electrochemical stability window FTIR Fourier transform infrared spectroscopy GGA Generalized gradient approximation GTO Gaussian type orbital HOMO Highest occupied molecular orbital LDA Local density approximation LIB Li-ion battery LJ Lennard-Jones LMB Li-metal battery LS Lattice sum LUMO Lowest unoccupied molecular orbital MD Molecular dynamics MSD Mean square displacement PAW Projector augmented-wave PBE Perdew, Burke and Ernzerhof PBEC poly(2-butyl-2-ethyltrimethylene carbonate) PBC Periodic boundary condition

PC Propylene carbonate PCM Polarizable continuum model PDOS Projected density of states PEO Poly(ethylene oxide) PHEC poly(2-heptyloxymethyl-2-ethyltrimethylene

carbonate) PME Particle mesh Ewald PTMC Poly(trimethylene carbonate) PW91 Perdew and Wang 1991 RDF Radial distribution function SEI Solid electrolyte interphase SPE Solid polymer electrolyte STO Slater type orbital TZ Triple zeta VASP Vienna ab initio simulation package VdW Van der Waals XPS X-ray photoelectron spectroscopy

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1. Introduction

1.1 Rechargeable lithium batteries Renewable energy resources have been the subject of many scientific studies over the last decades due to the increasing environmental concerns and deple-tion of fossil fuels. Development of advanced energy storage devices are re-quired to deliver energy on demand.1 Batteries have, in this context, been po-tential candidates for a wide range of applications including portable devices and electrification of the transport sector. Various electrochemical batteries have been developed since the invention of the first cell in the early 1800s, such as lead−acid, nickel−cadmium, nickel−metal hydride and rechargeable lithium batteries.2

Rechargeable lithium batteries − i.e., batteries utilizing Li metal as the neg-ative electrode material, in contrast to Li-ion batteries (LIBs) which employ intercalation anodes − are promising candidates for high energy density elec-trochemical storage devices. The Li metal electrode has a high theoretical ca-pacity and a low negative potential, thereby giving a very high energy density. Although the field of lithium-based battery chemistries were established around usage of Li metal as the negative electrode in the 1970s, the Li metal electrodes could then not be successfully implemented in commercial devices due to some serious challenges such as Li dendrite growth during charge/dis-charge cycling, low columbic efficiencies, and safety issues.3 Later, in the early 1990s, LIBs with graphite as the negative electrode were introduced to overcome the problems associated with the Li metal electrodes, and have since then dominated this field despite the lower energy density provided. The increasing demand on higher energy density for a number of products, not least vehicles, have however led to a renewed interest for employment of the Li-metal electrode. Moreover, in some of the Li metal battery (LMB) chem-istries currently being explored, the positive electrode comprises high capac-ity materials, for example sulfur (for Li–S batteries) or air (O2) electrodes (for Li–air batteries). This has triggered numerous studies on the development of LMBs during recent years.3–5 Figs. 1.1 a and b show the schematic diagrams of a typical LIB and a LMB, respectively. Several challenges in the applica-tion of Li metal as the negative electrode are also shown in this figure.

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Figure 1.1. Schematic diagram of (a) Li ion batteries; (b) Li metal batteries; (c) the typical morphology of Li dendrites and the major problems in Li metal batteries. Re-produced from Ref.4 with permission of The Royal Society of Chemistry.

1.2 Li battery electrolytes The electrolyte plays an important role in the battery where it is transferring charge in the form of ions between the two electrodes.6 It is desired that the electrolyte fulfills the following requirements:7 (1) being electronically insulating but ionically conductive; (2) proper ionic dissociation of the salt in the bulk media; (3) physical and chemical stability during cycling; (4) good thermal and electrochemical stabilities in a wide range of tempera-tures and voltages, necessary for the safety of the cell; (5) good wettability of electrodes and separators; (6) mechanical strength to mitigate lithium dendrite growth; (7) being non-costly. Therefore, implementing a successful electrolyte in the cell is not an easy task and has been the subject of much research over the years.8,9 In the following sections, important types of electrolytes in Li-based batteries are discussed.

1.2.1 Liquid electrolytes Non-aqueous organic liquids are solvents conventionally used in LIB electro-lytes. These solvents can generally be classified into two main groups: ethers (e.g. tetrahydrofuran, dioxolane, dimethoxyethane, tetraethylene glycol dime-thyl ether) and carbonates (e.g. ethylene carbonate (EC), propylene carbonate (PC), dimethyl carbonate (DMC), diethyl carbonate (DEC) and ethyl methyl carbonate).6,10 Lithium salts such as LiPF6, LiBF4, LiAsF6, LiN(SO2CF3)2 and LiSO3CF3 are dissolved into these solvents, forming the electrolyte and providing Li-ion conductivity.8

Liquid electrolytes usually have insignificant mechanical strength and poor thermal stability, and a narrow electrochemical stability window (ESW). These electrolytes are therefore not compatible with many high energy-

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density batteries. Several approaches have been implemented to tackle these problems with liquid electrolytes, not least electrolyte additives (e. g. LiNO3 in the case of Li–S batteries).7

1.2.2 Solid-state electrolytes Low molecular weight organic solvents have shown large difficulties in pre-venting the growth of Li dendrites during battery cycling and therefore suffer from safety risks. In order to prevent dendrite formation, the shear modulus of the electrolyte is required to be about twice that of the Li electrode.11 Thereby, solid-state electrolytes can be utilized with the Li metal. Generally, the thermal properties, chemical and electrochemical stabilities, and mechan-ical strength of solid-state electrolytes are better as compared to conventional liquid electrolytes. Solid-state electrolytes can be classified into three catego-ries; inorganic ceramics, polymer electrolytes and hybrids of these two groups.7 Ceramic electrolytes have shown to be highly effective in reducing the dendrite growth on the Li metal surface because of their high mechanical strength. Most examples of this group of solid state electrolytes consist of ox-ide or sulfide ceramics. Despite their benefits, however, there exists signifi-cant drawbacks for their application in devices, such as brittleness, interfacial compatibility and high costs.7

Solid polymer electrolytes (SPEs) can provide interfacial compatibility and are also more cost-effective if compared with ceramic electrolytes. The major challenge of SPEs is instead their low intrinsic ionic conductivity.7 That ether-based polymers such as poly(ethylene oxide) (PEO) could be employed as electrolytes were discovered more than four decades ago by Wright and coworkers,12 while Armand and coworkers pioneered the application of PEO in the field of lithium batteries.13–17 Since then, numerous studies have been conducted on polyether based SPEs in Li based batteries. There are many ways to tailor SPE materials to their desired properties. For example, the me-chanical properties of PEO can be improved by using cross-linked polymer networks.18,19 Block-copolymers of PEO and polystyrene have also attracted significant attention in this context.20 These block-copolymers consist of soft and hard blocks, forming Li+-conducting channels in a rigid network which can provide mechanical strength that prevent Li dendrite growth.

The ionic conductivity mechanism in SPEs are complicated due to the complexity in structure and dynamics of these host materials. The underlying mechanism can be demonstrated by the free volume model, shown in Fig. 1.2 for PEO–type electrolytes. The local segmental motion of the polymer chains can provide free volume in direct vicinity of the moving chain segment. This free volume can lead to Li+ ions hopping from one coordination site to another by an intermolecular coordination to the lithium ions.21

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Figure 1.2. Energy profile and schematic illustration of the ion transport mechanism within (PEO-type) polymer electrolytes based on the free volume model. Reproduced from Ref.21 with permission of The Royal Society of Chemistry.

Although the field of SPEs has been dominated by PEO and polyether based polymers, ‘alternative’ host materials such as polycarbonates (high molecular weights analogue of the commonly used linear alkyl carbonate solvents), pol-yesters and polynitriles have attracted considerable interest in recent years. These exhibit promising performances for application in Li–based batteries.22 Similar to PEO, modifications of these alternative host materials, such as the addition of side-chains or nano-particles, have also been investigated in order to generate a more flexible polymer matrix and increase the ionic conductiv-ity.22

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1.3 Electrode/electrolyte interfaces in Li metal batteries The interface between the electrode and electrolyte is highly important for the performance of Li-metal batteries. The high reactivity of Li-metal with the organic electrolyte solvents normally used leads to a thin layer of electrolyte decomposition products on the surface of Li prior to cycling and/or during the first charge/discharge cycles. If this layer is electronically insulating and ion-ically conductive, it can, in principle passivate the Li metal surface. This film was first recognized by Peled23 and is known as the solid electrolyte interphase (SEI) layer. Several models have been proposed for the SEI layer, and can typically be categorized into either a double layer model24 or a mosaic structure model,25 or combinations thereof.26

The formation of the SEI – and analogous on the positive electrode – occurs when the redox potential gap of the electrodes is larger than the ESW of the electrolyte. In this case, electron transfer reactions can occur between the elec-trodes and the electrolytes which lead to electrolyte reduction/oxidation at the negative/positive electrode.27

The SEI layer has both advantageous and disadvantageous properties in the battery cell. This film obviously changes the morphology of the Li metal sur-face and leads to a lower columbic efficiency and higher internal resistance. The SEI can, however – if it is stable – function as a protective layer on the Li metal and inhibit further reactions between the Li metal electrode and the electrolyte.3

Li metal, however, has a very negative potential and redox reactions therefore normally occur between the electrode and the liquid electrolyte. Generally, the SEI in LMBs contains deposited products from the parasitic reactions between Li ions, anions and solvent on the surface of the Li metal. X-ray photoelectron spec-troscopy (XPS) and Fourier transform infrared (FTIR) spectroscopy are com-monly used experimental techniques for identification of the SEI layer on Li metal.3,4,6,8 According to these studies, the SEI film is assumed to have an inner and an outer layer. The inner layer, primarily comprising inorganic salts, is built up from two-electron reduction processes. The major inorganic compounds are Li2O,28 Li2S/Li2S2,29,30 LiOH, LiF,31–34 LiI,32 Li3N,29 and Li2CO3,35 depending on electrolyte salt, solvent and additives. The outer SEI layer mainly contains or-ganic species formed by one electron reduction processes.6,36 The major organic compounds on the surface of Li metal have been found to be ROLi, RCOOLi, ROCOLi, RCOO2Li, and ROCO2 Li (R = alkyl groups).3

1.4 Computational modelling of Li-metal batteries In addition to experimental studies in the field of Li batteries, modelling tech-niques have been applied to investigate various properties in these complex

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systems. The development of computer power has led to the possibility of modelling more complicated systems and improve the quality of computa-tional studies. While earlier studies mostly have focused on bulk electrolyte properties, including both organic liquid electrolytes and polyether-based pol-ymer electrolytes,37 less attention has been given to the interfaces.

The complexity of the SEI layer makes it challenging to investigate the details of its formation mechanism only by experimental techniques. Hence, theoretical studies have been quite helpful for this purpose, especially at the molecular level.38–43 Molecular simulations of SEI formation and the decom-position of organic carbonate solvents were pioneered by Balbuena and coworkers.38–40,44 In these studies, however, it is primarily the reactivity of bulk electrolyte systems that have been investigated, without implementing any physical model of the electrodes. More recently, computationally de-manding simulation methods such as density functional theory (DFT) based ab-initio molecular dynamic (AIMD) methodologies have been employed to study the SEI formation in the presence of electrode surfaces.41,42,45 Most of these computational studies have focused on the SEI formation at elec-trode/electrolyte interfaces (primarily considering graphite as negative elec-trode) through two-electron mechanisms. 41,46

There have also been a limited number of computational studies on the Li-metal electrode/electrolyte interface. The electrochemical properties of the Li metal/EC solvent interface have for example been investigated, employing an implicit solvent model within the DFT framework.47 The mechanical and elec-trochemical properties of the two interfaces LiF/Li and Li2CO3/Li for the inner layer of the SEI have also been studied by DFT methods.48 Moreover, the stability of organic and inorganic SEI components, lithium carbonate (Li2CO3) and lithium ethylene dicarbonate, on Li metal have been addressed.49 In more recent studies, the interfaces of ionic liquids and Li metal have been explored by AIMD simulations which have addressed the ionic decomposi-tion reactions in this type of electrolytes.50,51

A notable number of studies have also been carried out by first principles calculations on inorganics solid state electrolytes and the interfaces with Li metal. In these studies, ionic conductivity, electrochemical stability and inter-facial reactivity have been predicted.52,53

For SPEs, specifically molecular dynamics (MD) simulations have been widely applied.54,55 The MD studies on SPEs in Li batteries have mostly fo-cused on high molecular weight PEO polymer with different Li salts.56 Dif-ferent force fields have been used57–59 (including some polarizable force fields60,61) for modelling amorphous linear and branched PEO of different mo-lecular weights, at different temperatures, and with various Li salts and con-centrations. MD simulations have for example been performed to study crys-talline PEO-based electrolytes,62 polyelectrolytes with tethered anions63 (i.e., ionomers) and SPEs containing ceramic nanoparticles.64 The ionic

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conductivity mechanisms in some alternative host materials such as polyesters have been investigated by MD simulations in order to explain the higher ionic conductivity of PEO compared to the alternative polymers.65 Through these simulations, it has been shown that the higher number of solvation sites of Li ions available in PEO is the main reason of its comparatively high conductiv-ity.65 It has then concluded that the solvation sites connectivity and ionic con-ductivity are strongly correlated.

So far, however, the major parts of the molecular modelling studies on SPE materials have been performed on bulk polymer electrolytes, and there exist only a handful of examples of studies on SPE/electrode interfaces. For in-stance, the structural and dynamical properties of the PEO/V2O5 interface have been compared with the bulk-like parts of the electrolyte performing MD simulations,66 and the interface between PEO and TiO2 has been investigated using a quantum chemistry-based force field.67 Here, it was seen that the TiO2 surfaces have dramatic effects on the PEO density. The conformational and structural relaxations of the polymer located in the interface regions decreased compared to the bulk-like regions, which clearly addresses the importance of these types of investigations.

1.5 Thesis outline Li metal is indeed an ideal candidate as the negative electrode for rechargeable Li batteries. However, the high reactivity with the electrolytes, the dendrite growth and the low coulombic efficiency have for long time constituted the main obstacles for implementation of Li metal in practical applications. To overcome these problems, a better understanding of the SEI layer formation process and its stability in different electrolyte systems is necessary. With the aid of first principle electronic structure calculations and MD simulations, powerful tools exist to investigate these topics on the molecular level. Com-putational studies combined with experimental investigations can lead to a viable route towards realization of Li-metal batteries. The overriding goal of this thesis work is to explore stability/reactivity, structural properties and dy-namics of the liquid electrolytes and (mainly) SPEs in the bulk or at the Li metal negative electrode by molecular modelling techniques, in order to give insights into these complex systems at the atomistic level.

There are a number of different modelling techniques available for the study of materials and electrochemical processes in battery systems, each con-fined to different time and length scales due to the differences in approxima-tions and the differences in approach. Using several of these techniques – and couple them – is the basis of multi-scale modelling.68 A schematic figure for multiscale modelling is presented in Fig. 1.3, where the different studies in the thesis are highlighted.

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This thesis comprises nine different computational studies of Li metal/elec-trolyte interfaces and novel electrolyte systems intended for use with Li-metal. Two levels of techniques have been employed throughout the thesis work: DFT calculations and MD simulations (further discussed in the next section; theory and computational methods). In the first step, paper I, DFT calculations were performed on different common organic carbonate solvents and a Li metal negative electrode. The decomposition of these solvent molecules, rel-evant for the early stages of the SEI growth, was thereby studied. This then served as a basis for implementing a more novel approach to reproduce ex-perimental XPS results in paper II, and also for electrolytes comprising the LiNO3 additive, in paper III. Especially in paper II, direct comparisons of the simulated XPS results from DFT and experimentally measured counterparts are performed in order to give new insights into the complex experimental peak assignment.

The remainder of the thesis is focused on molecular modelling studies of SPE-based systems. First, a LiTFSI-doped PEO-based polymer electrolyte at the surface of a lithium metal was studied by employing MD simulations in paper IV. The structural properties and the ionic conductivity of the SPE on the surface of Li metal are compared with those of the bulk SPE. Then, in order to improve the interaction model of PEO electrolyte and the Li metal surface, a new interaction model for the SPE and Li-metal electrode is proposed in paper V. It is shown that the potentials used in the description of the systems indeed has significant impact on the results obtained through the simulations.

Figure 1.3. The hierarchy for multiscale modelling approaches for various length and time scales.

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Bulk ionic transport in SPEs was studied in a combined modelling-experi-mental study in paper VI. Specifically, the effect of side-chains on the ionic conductivity mechanisms of polycarbonate SPEs was explored by MD simu-lations. It is found that side-chains have a hindering effects on the Li ion dif-fusion and lead to lower ionic conductivity in the polymer hosts.

Due to the limitations of common classical MD simulations in modelling bond breaking of the materials, DFT and AIMD simulations were applied in paper VII to study the interaction of both PEO and several alternative host materials at the surface of the Li metal. A better understanding of the interac-tions of these different SPE host materials with the surface of the electrode at atomistic level is highly important for the performance of the battery, while it can also provide information about the early stages of SEI layer formation in these systems, which are difficult to study experimentally. The inclusion of salts interacting with the polymer units studied in paper VII was thereafter taken into account in paper VIII. In this study, the redox potentials of the electrolytes have been obtained by DFT calculations to better estimate the ESW of the SPE systems. In paper IX, the interaction of PEO and the possible decomposition reactions of the molecular units of this polymer at pristine Li metal, and partial and fully oxidized Li metal are performed by DFT method-ology.

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2. Theory and computational methods

2.1 The many-body problem The main goal of most quantum chemical approaches is to solve the time-independent, non-relativistic Schrödinger equation:†

where is the Hamilton operator for a molecular system with M nuclei and N electrons in the absence of magnetic or electric fields. The operator is defined as:

(2.2)

where is the position of the ith electron, and is the position of the Ath nucleus. The first and second terms are kinetic energies of electrons and nu-clei, respectively. The third term refers to the attractive electrostatic interac-tions between electron and nuclei. The fourth and fifth terms are contributions of the electron-electron and nucleus-nucleus repulsions, respectively. All equations in this section are written in the system of atomic units. In this sys-tem, the mass of an electron, , the modulus of its charge, |e|, (Planck’s constant) divided by , and , the permittivity of the vacuum, are all set to unity. Therefore, physical quantities are expressed as multiples of these constants.

The mass of the nucleus is significantly greater than the mass of the elec-tron even for the lightest nucleus, the proton. This fact led to the Born-Oppen-heimer approximation, which makes Eqs. (2.1) and (2.2) simpler. In this ap-proximation, the nuclei are assumed to be fixed and their kinetic energy is † The context and notations for the DFT description in this thesis are primarily based on the descriptions in ref. 80.

( 2.1)

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consequently zero. The nucleus-nucleus repulsive term is also constant. Eqs. (2.1) and (2.2) is then transformed to the electronic Hamiltonian:

( 2.3)

The solution of the above equation results in the electronic wave function and the electronic energy . To obtain the total energy of the system,

the constant repulsive potential energy of the nuclei should be added to this energy. By means of the Born-Oppenheimer approximation, the Schrödinger equation is simplified, but there is nevertheless no straightforward solution for it and it can only be solved exactly for the hydrogen atom. For any other systems with more electrons, approximations are required in order to tackle the complexity of this equation. Different approaches have been proposed over the years such as the Hartree-Fock approximation and DFT. The DFT formalism is further discussed in the following section.

2.2 Density functional theory

2.2.1 The Hohenberg-Kohn theorems The modern formulation of DFT was introduced in 1964 by Hohenberg and Kohn.69 Their first theorem elegantly proved that all the properties of the sys-tem can be obtained by the ground state electron density of the system. DFT is based on two theorems:

Theorem I: For any system of interacting particles in an external potential , the potential is determined uniquely, except for a constant, by

the ground state particle density . Theorem II: A universal functional for the energy in terms of the

density can be defined, valid for any external potential . For any particular , the exact ground state energy of the system is the global minimum value of this functional, and the density that minimizes the functional is the exact ground state density .‡

Based on the first theorem, the ground state energy as a functional of ground state electron density ( can be written as:

( 2.4)

In this expression, the potential energy due to nuclei-electron attraction is sys-tem dependent, , and the other terms are universal since they are independent of N, RA, and ZA:

‡ The statements of the two theroems are written exactly as in ref. 136.

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( 2.5)

The universal part is called the Hohenberg-Kohn functional which consists of kinetic energy term ( ) and electron-electron interactions ( ). This universal part can be further written as:

( 2.6)

in which is expressed as classical coulomb part ( ) and non-classi-cal term . In , only the second term is known. If also and are known, the Schrödinger equation can be solved exactly. The second Hohenberg-Kohn theorem states that the true ground state density of the system gives the lowest energy. This can be found by utilizing the va-riational principle:

( 2.7)

in which is a trial density and by satisfying the boundary conditions of , .

2.2.2 The Kohn-Sham ansatz In 1965, Kohn and Sham proposed an approach to consider the kinetic energy of the non-interacting reference system with the same density as the real interacting system.70 The non-interacting kinetic energy is not equal to the kinetic energy of the real system. Therefore, Kohn and Sham applied a new separation of the universal functional:

( 2.8)

where is the so-called exchange-correlation energy and defined as:

≡ ( 2.9)

The interacting kinetic energy is included in the exchange correlational en-ergy. The Schrödinger equation is then rewritten as:

( 2.10)

where is the Kohn-Sham orbital. The unknown part is and the potential due to the exchange-correlation energy is . is defined as the derivative of the with respect to the electron density:

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( 2.11)

A flowchart for the self-consistent field procedure in DFT methodology is shown in Fig. 2.1.

Figure 2.1. The self-consistent field cycle in DFT.

2.2.3 Exchange-correlation functional approximations The main challenge when performing DFT calculations is to find a good-enough exchange correlation functional. So far, there have been many ap-proaches to express exchange-correlation functionals. One of the most com-mon is the local density approximation (LDA). In this approximation, it is assumed that can be written as:

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( 2.12)

where is the exchange-correlation energy per particle of a uniform electron gas of density . This energy per particle is weighted with the probability that there in fact is an electron at this position in space. The

term can be separated into the exchange and correlation contribu-tions:

( 2.13)

LDA, however, shows over-binding in molecular systems and extended solids and can therefore be less helpful for many problems within computational chemistry. It is rather used by solid-state physicists. To improve the LDA ap-proximation, the gradient of the charge density has been considered in addi-tion to . This approach is called the generalized gradient approximation (GGA). Many different functionals based on GGA have been proposed, e.g. those by Becke (B88),71 by Perdew and Wang (PW91) 72 and by Perdew, Burke and Ernzerhof (PBE).73 PBE functional were applied in papers I, II, III, VII and IX of this thesis.

One of the challenges in LDA and GGA exchange-correlation functionals is their failure in describing van der Waals long range interactions. In order to improve this shortcoming, one approach is to add dispersion correction ex-plicitly to the functional. In papers I, II, III, and VII, DFT-D374 was used to consider long range interactions. It was found that the D3 dispersion correc-tion provide the best trade-off between computational cost and the correction for the adsorption energy of the molecules adsorbed at the surface of the Li metal. The functionals M062X75 and wB97XD,76 which include long range interactions, were applied in papers V and VIII, respectively.

2.3 Basis sets One of the approximations in ab initio methods is to use a basis set in order to express an unknown function such as a molecular orbital in terms of set of known functions. If a basis set is complete, this approach is not an approxi-mation. However, a complete basis set means an infinite number of functions which is almost impossible to handle in calculations.77 On the other hand, the smaller the basis set is, the poorer it can model the unknown function. More-over, the type of basis functions to express the unknown function is also im-portant, and the more accurate this function is, the required number of func-tion decreases. Basis functions can be classified into two main groups: Slater type orbital (STOs) and Gaussian type orbitals (GTOs).78,79 STOs and GTOs are proportional to and , respectively, in which is the orbital exponent (controlling the size of the function) and is the radius. GTOs

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have a problematic behavior near the nucleus as compared to STOs, and they also fall quite rapidly and less accurate far from the nucleus. The number of GTOs required to obtain a certain accuracy is about three times that of STOs but are on the other hand computationally more efficient. Therefore, con-tracted Gaussian functions built from a linear combination of GTOs are nor-mally applied. 77,80

Selecting an appropriate basis set for electronic structure calculations de-pends on the number of terms included in the system under study, the required accuracy and the computational cost. The main categories of basis sets are based on the number of functions, and are called double zeta (DZ), triple zeta (TZ), and so on. To consider extra angular flexibility, polarization functions are taken into account by using higher angular momentum. Diffusion func-tions can also be added to the basis sets in systems with loosely-bound elec-trons, or when the desired properties depend on the wave function tail.77

In this thesis, in the case of the finite systems such as polymeric molecules, GTO-based basis sets such as Pople basis sets, Karlsruhe-type basis sets and correlation consistent basis sets implemented in the Gaussian software81 have been used.

The basis sets discussed so far are used to express the atomic orbitals in finite systems. However, in the case of extended systems such as a unit cell with periodic boundary conditions, different type of basis functions are re-quired. Based on the periodicity of the crystal lattice, Bloch’s theorem defines a good quantum number, the crystal momentum and the boundary condition for the single particle wave function:§

( 2.14)

where is a direct lattice vector. The boundary condition is satisfied in the following general solution:

( 2.15)

where is the reciprocal lattice vector. The plane waves are the eigenfunc-tions of the kinetic energy operator. The plane-wave expansion of the Kohn-Sham orbitals is truncated in a way so that the individual terms all lead to kinetic energies lower than a specified cut-off energy:

( 2.16)

Solids often contain electrons and nuclei which interact strongly through Cou-lomb potentials, with the core electrons being strongly bonded to the nuclei. The pseudopotential approximation assumes that the core electrons are fixed. The corresponding ground-state wave-function (pseudo wave functions) § Ref. 137 has been used for the general descriptions in this part.

29

represents the valence electrons outside a specific core radius. These pseudo wave functions are smooth and well-behaved when using only low planewaves. This is the reason for the popularity of plane-waves for the pseudo-wave functions.

It should be noted that although plane wave basis sets have primarily been applied for periodic systems, they can also be used for molecular systems by a supercell approach, where the molecule is placed in an appropriately large unit cell.82

2.4 Projector-augmented wave (PAW) method The projector-augmented wave (PAW)83 method offer computational effi-ciency of the pseudopotential method as well as the accuracy of the full-po-tential linearized augmented-planewave method. Moreover, this method en-sures the orthogonality between valence and core functions. The PAW method implemented in the plane wave code of Vienna ab initio simulation package (VASP)84 have been used for the plane wave DFT calculations performed in this thesis work.

In the PAW method, the all-electron wave function, is derived by means of a linear transformation of the pseudo wave function.85 The pseudo wave functions, are variational quantities. is identical to all electron wave function ( ) in the region between the PAW spheres around the atoms. However, inside the spheres, is an approximation of the exact wave func-tion used as a computational tool.

2.5 Solvent effects The models studied in this thesis have primarily been considered in the gas phase (vacuum), which are often useful but not always realistic. In order to take the solvation phases into account, solvent molecules can be considered either explicitly or by implicit models. In the implicit model, the solvent is represented by a uniform polarizable medium with a dielectric constant. Po-larizable continuum models (PCMs) are highly efficient in this sense, and are implemented in the Gaussian package. These were considered in paper VIII. In PCM, the effect of the fluid is captured by considering the electronic system in an appropriately chosen dielectric cavity. Solvation effects in papers I and VII were considered suing VASPsol,86,87 which is the implementation of an implicit solvation model into the plane wave VASP code.

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2.6 Computed X-ray photoelectron spectroscopy data Core electrons, electrons in orbitals very close to the nucleus, can provide information about the atom-specific chemical environment. The energy re-quired to remove a core electron from an atom is referred to as core-level binding energy (BE). The core-level BEs can be experimentally obtained by XPS measurements. XPS is a common surface sensitive spectroscopic tech-nique to study chemical compositions and electronic states of many materials since the pioneering contributions of Siegbahn and co-workers.88,89 Experi-mentally, the kinetic energy of electrons (Ekin) which result from bombarding a beam of photons towards a sample, are measured. In the case of gas phase molecules:90

( 2.17)

In case of solids and their surfaces, the term of a work function , i.e., the energy needed to remove an electron from the surface to the vacuum, is also required in the formula:90

( 2.18)

In DFT calculations, core level BEs can be calculated by three different models: complete screening picture, transition state method, and initial ap-proximations. Initial approximations treat the unperturbed system before re-moving the electron from a core state.91 Complete screening and transition-state models both include the initial and final states effects (the perturbed state after removing an electron from the core). The total energies of the systems are used in the complete screening picture while the energy eigenvalues are considered in the transition state model.91 In this thesis (papers II and III), the transition state method78,92 (known as the Janak-Slater transition state method) has been used to calculate the BEs.

In this model, which is an extension to DFT,92 the Kohn-Sham eigenvalue ( ) is a linear function of , and the following relation can be considered to obtain the BEs:

( 2.19)

The implementation of the PAW method in the VASP code has been used in this thesis for the partial occupancies in order to calculates BEs for the Ja-nak-Slater transition state method:84,93

( 2.20)

in which is the energy of the selected half occupied core level orbitals. Moreover, in paper II, the core-level BEs were also aligned with the vacuum level. This has been performed by calculating the electrostatic potential, Evac,

31

in the vacuum region of a supercell containing the free molecules and equiv-alently for molecules adsorbed on the Li surface. The binding energies rela-tion is then rewritten as:

( 2.21)

2.7 Molecular Dynamics simulations One of the popular and widely used computational approaches to study chem-ical transport processes and provide insights to the dynamics of chemical sys-tems is MD simulations. The MD method is, generally, the numerical solva-tion of the classical Newtonian equations of motion for a system at finite tem-perature.94,95 One of the most challenging part of the MD simulations is the calculation of the interatomic forces. In classical MD, the forces are calculated from empirical potentials (force fields) which can either be parametrized by fitting to experimental data or by ab initio calculations of smaller models of the system under study.94,95 Despite the great success of the classical MD method in various types of ma-terials, not least polymers and biological systems, it also possess some inher-ent limitations. One important point about force fields is that charges are con-sidered as fixed parameters and therefore, the electronic polarizations are not taken into account.94,95 Polarizable models have been introduced in order to tackle this limitation and have so far been successfully applied in several stud-ies, although at higher computational costs. There exists, however, some chal-lenges in using these models as well, such as lack of transferability and stand-ardizations. Another important limitation of classical MD is that it is not pos-sible to straight-forwardly or accurately simulate the bond breaking and for-mation with these methods. In order to overcome these limitations, first principles methods such as AIMD can be applied, in which forces are obtained ‘on the fly’ from electronic structure calculations. Although higher accuracy can be achieved by AIMD simulations, the high computational cost is a severe limitation for this type of calculation.94,95 Atomic nuclei can due to their high weight approximately be considered as classical particles, and Newton’s equation of motion, , can therefore be used to study the dynamics of the system:77

( 2.22)

in which V is the potential energy at position r (vectors of Cartesian coordi-nates for all particles).

To integrate the equation of motion, the finite difference method is used where the partial derivatives are approximated by Taylor expansions. One

32

integration method commonly used in MD simulations is the Verlet algo-rithm96 and its velocity-explicit variants, e.g., the leap-frog97 and the velocity Verlet algorithms.98 In the Verlet algorithm:

( 2.23)

( 2.24)

The Verlet algorithm can lead to truncation errors due to the finite preci-sions. This is the results of adding , which is a small number, to

, and is the difference of two large numbers. Another disad-vantage of Verlet algorithm is that the velocities do not appear explicitly.77 These problems are met in the leap-frog algorithm:97

( 2.25)

( 2.26)

The numerical accuracy of the leap-frog algorithm is better than the Verlet algorithm, and the velocity term appears explicitly. The disadvantage is that the velocity and positions are not known at the same time.77 In the velocity Verlet algorithm,98 this problem is removed:

( 2.27)

( 2.28)

The NVE ensemble can be generated naturally by MD simulations in which temperature and pressure will fluctuate while the number of particles (N), vol-ume (V) and system energy (E) are fixed. The temperature of the system is defined based on the average kinetic energy:

( 2.29)

Other ensembles such as NPT or NVT can be also generated by MD simula-tions. In the MD simulations of this thesis (papers IV, V and VI), NVT and NPT ensembles have been considered. A thermostat procedure can be applied in which the system is coupled to a heat bath, and the energy of the system consequently change gradually with a suitable time constant. The rate of the heat transfer is controlled by a coupling parameter , while the kinetic energy of the system is altered by scaling the velocities:77

33

( 2.30)

( 2.31)

Different available thermostat methods include the scheme of Berendsen,99 the Andersen thermostat,100 the extended ensemble Nosé-Hoover scheme,101,102 and a velocity-rescaling scheme.103 The velocity-rescaling tem-perature coupling has been used in papers IV and VI. The Nosé-Hoover ap-proach was used to control the temperature in paper V. Also the pressure can be approximately constant by instead coupling to a pres-sure bath. In this case, the volume of the system is changed by scaling all coordinates:

( 2.32)

( 2.33)

in which the constant is the compressibility of the system. Two common methods for pressure coupling are Berendsen99 and Parrinello-Rahman pres-sure104 coupling (which have been used in papers IV and VI). The Lagran-gian105 approach was used to control pressure in paper V.

2.7.1 Force fields A classical force field is a simple analytical model to express the interactions between atoms in a system, and is composed of several components:

( 2.34)

In this function, the first four terms are the bonded or covalent terms. , , , and terms are related to bond stretching,

bond-angle bending, dihedral-angle torsion and improper dihedral-angle bending (out-of-plane distortions) in the molecules under study. The last two terms are the non-bonded terms: and for the Coulomb (electro-static) and the van der Waals (vdW) interactions, respectively. A schematic illustration of different contributions in the force field is shown in Fig. 2.2. A number of classical force field covering a large range of atomic, molecular and ionic compounds have been proposed over the years. Here, the OPLS106 force field has been used in paper IV, V and VI.

34

Figure 2.2. Schematic illustration of the terms defined in a classical fixed-charge force field, i.e. bond stretching (Ebond), bond-angle bending (Eangle), dihedral angle torsion (Etorsion), and improper dihedral-angle bending (Eimproper) as well as van der Waals (EvdW) and electrostatic (Eele) interactions. Reprinted with permission from ref. 107. Copyright 2018 American Chemical Society. The bond stretching term in the force field can be defined as:

( 2.35)

in which is the force constant of the bond i, is the bond length, and is the reference bond length. The bond angle bending is described as:

( 2.36)

Here, is the value of bond angle and is the reference bond angle. The torsional dihedral-angle term in the OPLS force field is expressed as:

( 2.37)

where is the force constant of torsion i and is the torsional angle. For OPLS and AMBER force fields, the standard dihedral-angle torsional term is used for the out-of-plane distortions. The vdW interactions can be expressed by using a 12–6 Lennard-Jones (LJ) functional:

( 2.38)

with

( 2.39)

( 2.40)

Here, and are the distance between atoms i and j, and the LJ param-eters, respectively. In order to obtain LJ parameters between different atom types, combination rules are often applied based on the arithmetic mean of σ

35

and the geometric mean for ϵ, or the geometric mean for both σ and ϵ depend-ing on the force field type.

The LJ potential is a popular way to describe vdW interactions, but other forms also exist, such as Morse and Buckingham potentials. In paper V, where an interaction model for the SPE with the Li metal surface is developed, the vdW parameters for the SPE atoms with the metal surface have been calcu-lated through quantum mechanical calculations. The obtained results were fit-ted to the best possible potential function, which in this case was the Morse function:

( 2.41)

where De, a and re are the depth and width of the potential and the equilibrium distance, respectively. Furthermore, in the classical force field, the pairwise Coulomb interaction be-tween point charges of atom i and j are considered:

( 2.42)

where , , and are the partial charge, the dielectric constant, the back-ground dielectric permittivity (typically set to 1 for atomistic systems), and the distance between atoms i and j, respectively. Fixed charges are taken into account in these types of force fields while polarization is not considered. In order to reproduce the structure and transport properties of ions in the SPE in papers V and VI, charge scaling has been considered for ions. This method has been commonly used in MD simulations of SPEs in order to avoid exces-sive ion pairing and clustering, instead of using computationally expensive polarizable force fields.59,108

2.7.2 Long range interactions To avoid edge effect in the finite systems, periodic boundary conditions (PBC) are applied in which molecules are considered in a (normally cubic) box duplicated in all directions. Thereby, if a molecule exits from one side of the box, its mirror image will enter from the other side.77 The pairwise vdW and electrostatic interactions of a system with N particles scales as N2, which is computationally expensive. To reduce the computational cost, a cut-off dis-tance is considered within which the interactions are taken into account, while they are neglected or treated with long range approaches outside.107

For long range electrostatic interactions, similar to vdW interactions, a cut-off distance can be defined. It has been reported that the truncation of electro-static interactions can lead to significant artifacts.109 Some computationally efficient alternative methods have also been proposed, including lattice sum (LS) methods which is appropriate for totally periodic systems. LS methods

36

for electrostatic potential include for example Ewald summation, which splits the electrostatic interactions in short-range and long-range parts, and a more efficient method, the particle-mesh Ewald (PME), which reduce the compu-tational costs.107 The PME method was used in papers IV-VI in the thesis.

2.7.3 Ab initio molecular dynamics As mentioned earlier, AIMD permits bond forming-breaking while also con-sidering polarization effects, which is a great advantage as compared to clas-sical MD. In the ideal form of AIMD calculations, it is assumed that the sys-tem has N nuclei and Ne electrons. The Born–Oppenheimer approximation is also taken into account and the dynamics of nuclei is considered classically on the ground-state electronic surface.110 Similar to Eq. (2.2), the total Ham-iltonian is , in which the terms are the electronic kinetic energy, the electron–electron repulsion, the electron–nuclear attraction, the nuclear kinetic energy and the nuclear–nuclear repulsion, respectively. The classical dynamics of the nuclei is:110

( 2.43)

Here, is the nuclear mass and the ground state energy eigenvalue at the nuclear configuration R. As discussed in the DFT section, the ground state electronic problem cannot be solved exactly and approximations are required. One common electronic structure method to be used for AIMD calculation is the DFT methods. The most straightforward type of AIMD is Born-Oppen-heimer MD (BOMD). In BOMD, Eq. (2.43) is integrated numerically and the forces are obtained by minimizing the energy functional at each time step. A high level of accuracy is required to fulfill the energy conservation in the BOMD approach, which makes this method computationally expensive. An alternative method is Car–Parrinello Molecular Dynamics, which was intro-duced to increase the computational efficiency by avoiding the wave function optimization at each MD step.111 In paper VII, when studying the possible bond decompositions of polymer molecules on the surface of the Li metal, DFT-based BOMD simulations implemented in VASP have been applied.

37

3. Molecular modelling of liquid electrolyte/Li metal interfaces

In this section, the key results of papers I-III are presented and discussed, focusing on DFT studies of liquid electrolyte/Li metal interfaces.

3.1 Adsorption and decomposition of organic carbonates at the Li metal surface

Common organic carbonate solvents, EC, PC, DMC, and DEC, were consid-ered in paper I. The optimized structures of these solvent molecules are shown in Fig. 3.1.

Figure 3.1 Optimized structures of the solvent molecules EC (a), PC (b), DMC (c), and DEC (d). Reprinted with permission from ref. 112. Copyright 2019 American Chemical Society.

In order to model the Li metal surface, three different low index surface ori-entations (100), (110) and (111) were considered from the experimentally de-termined body centered cubic (bcc) lattice of Li.113 The surface energies of (100) and (110) orientations were found to be clearly lower than that for the (111) plane, while the surface energy for (100) is slightly lower than that for (110) surface (see Fig. 2 in paper I). Therefore, Li (100) was considered for

38

the adsorption and reaction of the organic carbonate molecules. Different ad-sorption sites/configurations were studied: ‘bridge’, ‘top’ and ‘parallel’ to the surface of the Li metal (see Fig. 4 in paper I).

The calculated adsorption energies for the solvents on all positions are pre-sented in Fig. 3.2. The most favorable adsorption configuration for cyclic sol-vents (EC and PC) was found to be parallel to the surface with the carbonyl O atom of the solvent molecule (O1) at the bridge site. However, linear sol-vents (DMC and DEC) were most stable at the bridge site and vertical to the surface. An elongation of carbonyl bond distances (C1–O1) compared to the isolated solvents was observed, while the bond distances for the ethereal part of the molecules (C1–O2) were shorten. Electron transfer from the Li atom of the surface to the orbital of the carbonyl group is likely the reason for the elongation of the C1–O1 bond distance.

Figure 3.2 Adsorption energies of the solvents on the Li (100) surface for different sites. Reproduced from 114, with the permission of AIP publishing.

The initial formation of what could be considered the “inner layer” of the SEI in this system, formed from decomposition of organic carbonate solvents on the Li metal surface, was also been studied in paper I. The decomposition mechanisms considered here have been proposed in previous studies on pris-tine graphite and Li metal, but only for EC electrolyte.41,46 The products of these reduction pathways are reported in Table 3.1. Pathways a and b do (in all cases) refer to a cleavage of the C2-O2 and C1-O2 bonds in the carbonate solvents, respectively (see Fig. 3.1). The decomposition reaction energies, which were calculated from the difference between the energy of the intact solvent molecules and the energies of the decomposed solvents on the Li sur-face, are shown as relative energies in Table 3.1. Both pathways a and b are energetically favorable for the decomposition of cyclic solvents, with pathway b being slightly more favorable for EC. The difference between the energies of the two pathways are higher for PC. Interestingly, the CO molecule pro-duced in pathway b of the cyclic carbonates diffused somewhat into the Li metal surface after geometry optimization. For the linear solvents, pathway a

39

is found to be energetically more favorable. This is in accordance with a pre-vious computational study on the reductive decomposition of DMC and DEC. 44 The amount of charge transfer from the Li surface to the decomposed sol-vents, which was calculated using Bader charge analyses, indicate 2e- reduc-tions processes in all investigated pathways (Table 3.1).

In addition, the decomposition energies were calculated using an implicit solvent model (Table 3.1). Although the calculated decomposition energies in vacuum are slightly lower than those in the implicit solvent model, similar trends as in the vacuum model are observed in the solvation phase. Their dif-ferences can be attributed to an idealized situation in absence of any solvation phase, and consequently a more stable system. Table 3.1. Products from the decomposition pathways, relative energies (eV) in vac-uum and in an implicit solvent, and (charge transfer after the decomposition) for solvent decomposition reactions.

Solvent(pathway) Products for the pathway (Vac) EC (a) CO32-, C2H4 -4.61 -4.47 -2.36 EC (b) C2H4O22-, CO -4.76 -4.63 -1.95 PC (a) CO32-, C3H6 -4.34 -4.24 -2.25 PC (b) C3H6O22-, CO -4.77 -4.67 -1.94 DMC (a) CH3, O3C2H3 -3.11 -3.10 -2.01 DMC (b) OCH3, O2C2H3 -2.81 -2.79 -2.43 DEC (a) C2H5, O3C3H5 -2.69 -2.69 -2.08 DEC (b) OC2H5, O2C3H5 -2.67 -2.67 -2.14

The products from the decompositions of the electrolytes, which in turn form the SEI on the electrode, have significant effect on the performance of the battery. Therefore, this type of modelling study can yield insights into the de-tails of this layer and the mechanism of forming the components of this layer.

3.2 Core-level binding energies of organic carbonates In paper II, a combined DFT and experimental XPS study was performed to obtain the C 1s and O 1s core-level binding energies of organic carbonate molecules on the surface of Li metal. The BEs of C 1s and O 1s for organic carbonates before and after adsorption on the Li-metal surface for the most stable positions (found in paper I) were calculated and presented in Fig. 2 of paper II. The BEs for the corresponding systems with respect to the vacuum level were also computed (see Fig. S1 in paper II). It was found that the phys-ical chemistry of the systems in this study was better represented by the BE trends obtained with the Fermi level reference compared to the vacuum

40

reference. The computed core level shift (CLS) of C1 (Ccarbonyl), O1 (Ocarbonyl) and O2-3 (Oethereal) in the studied organic carbonates are reported in Table 3.2. It can be seen that there is a negative shift for Ccarbonyl and Oethereal, while a positive shift for Ocarbonyl can be seen in the BE values for all solvent molecules at the surface of Li metal. Different factors can be effective for the location of the simulated XPS peaks and the computed CLS. The correlations between BEs and either the local charge or the nearest neighbors’ potential were therefore analyzed separately (see Fig. 3 in paper II). The C 1s and O 1s BEs were found to be well corre-lated with the charge and electrostatic potential.

Table 3.2. C 1s and O 1s CLS of EC, PC, DMC, and DEC (Unit: eV)

The core-level BEs of the decomposed organic carbonate species on Li metal, based on the decomposition pathways discussed in the previous section (Table 3.1) were calculated and compared with the experimentally measured XPS data for these solvents. The computed and the experimentally measured C 1s and O 1s XPS spectra for these organic carbonates and the final structures for the considered decomposition pathways are shown in Fig. 3.3. The results for the decomposed products of cyclic carbonates from pathway a (i.e., decom-position through Cethereal−Oethereal bond cleavage) demonstrate an excellent agreement with the experimental spectrum in terms of shapes and order of BE peaks, particularly for the C 1s spectra. The BEs of pathway b (decomposition through Ccarbonyl−Oethereal) are in fairly good agreement with the experimental results. It should be noted that the CO molecule, a reaction product in pathway b, most likely cannot be detected experimentally since it is gaseous and the measurements are performed under vacuum. These results indicate that the products from both pathways, a and b, provide contributions to the experi-mental spectra. Similar to the cyclic carbonates, the BE peaks in pathway a for the linear carbonates are in better agreement with the experimental XPS. This combined computational-experimental methodology can be highly use-ful for exploring the interfacial chemistry in Li-metal batteries, since it can elucidate the measured XPS peaks and help to better understand the compo-nents having contributions in the peaks.

Solvent molecule C 1s (Ccarbonyl) O 1s (Ocarbonyl) O 1s (Oethe-

EC –0.43 0.50 –0.23 PC –0.29 0.39 –0.5

DMC –0.18 0.46 –0.61 DEC –0.11 0.30 –0.60

41

Figure 3.3. Decomposition pathways a and b and corresponding C 1s and O 1s XPS spectra calculated by DFT and measured experimentally; (a), (b), and (c) for EC; (d), (e), and (f) for PC; (g), (h), and (i) for DMC; and (j), (k), and (l) for DEC, respectively; the calculated binding energies of C 1s and O 1s are shifted 6−7 and 11 eV to lower values in the plot, respectively. The intensity of the calculated peaks is also adjusted in comparison to the experimental results (the intensity is multiplied by 2 × 103 and 3.5 × 103 for C 1s and O 1s, respectively). The hydrocarbon peak at 284.8 eV was selected as internal reference for the calibrations. Reprinted with permission from ref. 112. Copyright 2019 American Chemical Society.

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3.3 Interfacial chemistry of the LiNO3 additive at the surface of Li metal

Lithium nitrate (LiNO3) is a common electrolyte additive in Li−S batteries to protect the Li metal electrode from harmful side-reactions with dissolved pol-ysulfides.115 The electronic structure and stability of this additive at the sur-face of Li metal were studied by DFT calculations in paper III. LiNO2, Li3N and Li2N2O2 have been identified in previous experimental work as SEI layer components in the Li-S battery in presence of the LiNO3 additive.115–117 N2O and N2 gases have also been detected in LiNO3 containing Li-S cells.118 N2, N2O, LiNO2, Li3N, and Li2N2O2 molecules were thus considered on Li-metal. The most stable configurations of these molecules were reported in Fig. 1 of paper III. Interestingly, significant changes can be observed in the atomic and electronic structure of these molecules after adsorption on the Li metal sur-face. In most cases, the molecules decomposed and some of their fragments diffused into the Li surface. In the case of the Li3N molecule, a Li6N octahe-dral complex was formed after adsorption on the Li surface, in good agree-ment with reports of a stable cubic Li3N phase containing the Li6N octahe-dra.119,120 The N 1s core level BEs have also been calculated for all systems, and the XPS spectra for the adsorbed molecules on the Li metal surface and their corresponding gas phase molecules are presented in Fig. 2 of paper III. The peaks for N2, Li3N and Li2N2O2 exhibit shifts to higher BE values (posi-tive CLS). For other molecules, their decompositions and formation of new molecules render any comparison of the CLS with respect to the gas phase molecules meaningless. Although it is far from straightforward to interpret the core level BE shifts, different mechanisms have previously been proposed to describe the factors controlling these shifts, e.g. environmental charge density, hybridization, and screening effects.121,122 Bader charge analysis was performed in paper III to investigate the amount of charge transfer (CT) to/from N atoms after adsorp-tion of these molecules on the Li surface, because CT changes the electrostatic potential which a core electron experiences due to an electron in the valence orbital, and therefore leads to shifts of the core-level BEs of that atom.121 Pos-itive CLS while electrons are transferred to the N atoms means that other fac-tors such as hybridization have an effect on the location of the CLS peaks.122 The density of states (DOS) analysis shows a clear overlap (hybridization) between the s states of Li slab and the s and p states of the N (or O) atoms, leading to a delocalization of valence electron density on the adsorbents and the Li metal surface (see Fig. 1 in paper III).

In addition to the molecular Li3N, solid phases of Li3N on Li-metal were also studied. There are different stable phases of Li3N depending on pressure:

-Li3N with the space group is stable at ambient pressure, but trans-forms to -Li3N and -Li3N with the space groups and ,

43

respectively, at higher pressures.119,123 Another stable phase, -Li3N, with the space group of under ambient pressure, have also been reported in a more recent study.119,120 Here, two different phases, -Li3N and -Li3N, were investigated on a Li metal surface. The bulk crystal structures of -Li3N and -Li3N are shown in Figs. 3.4b and 3.4e, respectively. The overlap between

the N and Li states in both -Li3N and c-Li3N are shown in the PDOS plots of these crystal structures, which are presented in Figs. 3.4a and 3.4d, respec-tively.

The N1s XPS spectra of bulk Li3N phases are presented in Fig. 4 of paper III. The shift in the core level BE peak can be attributed to the different chem-ical environment in these bulk phases. The coordination number (CN) of the N atoms in the c-Li3N and -Li3N bulk structures are found to be 6 and 8, respectively. It seems that there is a correlation between the CNs and the BE values, since as the CN increases from 6 in c-Li3N to 8 in the -Li3N structure, the BE shifts to higher values. The calculated BEs for c-Li3N showed a better agreement with the experimental XPS peaks assigned to Li3N on Li metal electrodes,116,117 indicating that this is the phase preferentially formed in the Li−S battery system. A higher degree of overlap between the N(s), N(p), and Li(s) states in the α-Li3N than in the c-Li3N phase (see Figs. 3.4a and 3.4d) could be the reason for a higher BE for the α-Li3N phase.

Li3N/Li interfaces were built by considering the (100) orientation, which was found to be the most stable orientation for both -Li3N and c-Li3N slabs. The -Li3N(100)/Li(100) and c-Li3N(100)/Li(100) interfaces are presented in Figs. 3.4c and 3.4f, respectively. The N 1s core level BEs for the N atoms in three different regions, viz., interfacial, bulklike, and surface (the top layer of Li3N in contact with the vacuum layer) of the Li3N(100)/Li(100) slabs were calculated, and their corresponding XPS spectra are presented in Fig. 3.5.

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Figure 3.4. Projected DOS of α-Li3N, bulk-like and interfacial regions of α-Li3N(100)/Li(100) (a); the crystal structure of α-Li3N (b); the α-Li3N(100)/Li(100) interface (c). Projected DOS of c-Li3N, bulk-like and interfacial regions of c-Li3N(100)/Li(100) (d); crystal structure of c-Li3N (e); the c-Li3N(100)/Li(100) inter-face (f). The origin of the energy axis is set at the Fermi level. The density of states in (a) and (d) are scaled up two and four times, respectively. Reprinted with permis-sion from ref. 124. Copyright 2017 American Chemical Society. Interestingly, the BE shifts in the c-Li3N(100)/Li(100) interface are in the re-verse order with respect to the α-Li3N(100)/Li(100) interface for the interfa-cial and bulklike regions, indicating that the N atoms become more electron rich when approaching the surface in the α-Li3N(100)/Li(100) structure com-pared to the c-Li3N(100)/Li (100) interface. Furthermore, the average amount of CTs to the N atoms of the α-Li3N(100)/Li(100) and c-Li3N(100)/Li(100) interfaces, compared to their corresponding bulk phases, was found to be in-significant. The PDOS plots (Figs. 3.4a and b) exhibit a higher degree of over-lap between the N and Li(s) orbitals for the α-Li3N(100)/Li(100) interface than the c-Li3N(100)/Li(100), leading to a reduction of the electron densities on the N atoms in the α-Li3N(100)/Li(100) interface. This could be the reason for the increasing core level BEs in the α-Li3N(100)/Li(100) interface.

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Figure 3.5. Calculated N 1s XPS spectra for (a) α-Li3N (100)/Li (100) and (b) c-Li3N (100)/Li (100) interfaces. Reprinted with permission from ref. 124. Copyright 2017 American Chemical Society.

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4. Molecular dynamics simulations of solid polymer electrolytes

In this section, the results of papers IV-VI are summarized, focusing on clas-sical MD simulations of both bulk SPEs and the interface between SPEs and the Li metal electrode.

4.1 Structure and dynamic properties of an SPE/Li metal interface

In paper IV, the structural and dynamical properties of a solid polymer elec-trolyte comprising PEO doped with LiTFSI salt were investigated in the pres-ence of a Li metal surface by MD simulations. Two different models were considered to describe the Li metal electrode: (i) an analytical wall potential model, implicitly describing the Li surface on both sides of the polymer elec-trolyte box, and (ii) an explicit Li atom surface model, which forms an inter-face with the electrolyte (see Fig. 1 in paper IV). Bulk polymer electrolyte was used as reference.

4.1.1 Structural properties Radial distribution functions (RDFs), which show the probability of finding a particle at a certain distance from another specific particle, were calculated for the O atoms of both PEO and LiTFSI against the Li+ ions (see Fig. 3 in paper IV). The RDFs indicate that a higher ordered structure for especially the anions of the electrolyte occurs in the presence of the Li surface. The cu-mulative CN were obtained from integration of the RDFs (see Fig. 4 in paper IV). The average CN for the oxygen atom of PEO and LiTFSI in the first shell around the Li+ ion is around 5 and 0.9, respectively. These results are in good agreement with both experimental studies using neutron diffraction on PEO/LiTFSI,125 and previous MD studies of PEO/LiTFSI.126

To further explore the effects of a Li metal surface on the molecular-level structure of the SPE, the structural properties of the electrolyte within 10 Å from the Li slab (defined as the ‘interface region’) were compared to that in the range 10-25 Å from the slab (defined as the ‘bulk region’). The calculated

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RDFs and CNs for the two regions were computed and reported in Fig. 5 and Fig. 6 of paper IV, respectively. The CNs are also shown in Fig. 4.1. It can be seen that the number of TFSI anions around Li+ in the bulk area of the elec-trolyte is smaller than in the interface region. The presence of the surface thereby leads to a more structured ionic arrangement in the interfacial region than in the bulk part.

The partial densities for Li+, TFSI and PEO were calculated with respect to the center of the box in the two models to evaluate the density of particles across the simulation box (see Fig. 7 in the paper). The density of Li+ and TFSI ions were observed to be significantly greater at the interfaces of the wall and slab models, indicating the formation of a “double-layer” close to the surface, which may hinder ionic transport through this layer. A similar phe-nomenon has also been reported in experimental work.127,128

Figure 4.1. CNs for Li+–O(TFSI) and Li+–O(PEO) in (a) the bulk region and (b) the interface region of the MD box. Reprinted from 129, Copyright (2017), with permis-sion from Elsevier.

4.1.2 Dynamics The dynamic properties of particles in the Li wall, Li slab, and bulk SPE mod-els were also studied in paper IV. The self-diffusion coefficients (Di) of the particles were obtained using the Einstein equation from the diffusive regions by mean square displacement (MSD) functions (see paper IV for the details of the calculations). The diffusion coefficients indicated that the motion of PEO and Li ions in both the Li slab and the bulk SPE model seem to be cou-pled, while the dynamics of TFSI is more independent of other species in the system. The dynamical properties of particles in the Li slab model were also compared between the interface region and the bulk-like region, and the MSD functions for these two different regions are presented in Fig. 4.2. Their dif-fusion coefficients display a lower mobility in the interface region than in the bulk-like domains, and it thus seems that the Li surface is slowing down the dynamics of the particles. This could well be correlated to the interfacial struc-ture, where more ion-ion interaction (pairing and clustering) is observed. This could be decisive in a Li-metal/SPE battery, since the structures, compositions

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and dynamics of particles in contact with the surface of the electrode are highly important for the functionality of the cell.

Figure 4.2. Mean square displacement (MSD) functions of the Li+ cation (a), PEO (b) and TFSI anion (c) at 400 K in the interface and bulk like parts of the MD simu-lation box. Reprinted from 129, Copyright (2017), with permission from Elsevier.

4.2 Development of the interaction model for the PEO/Li metal interface

In paper V, a more accurate force field was developed to study the interaction of the PEO-based electrolyte with the surface of the Li metal. The force filed parameters were obtained by quantum mechanical calculations in order to re-place the potentials for the interface studied in paper IV. The best fitted po-tential form to be used for the interactions between the electrolyte and the Li metal slab was found to be the Morse potential. The partial density distribu-tions of TFSI, Li+, and PEO, and snapshots from the simulations are shown in Fig. 4.3 for two systems; one with the LJ parameters (similar to paper IV) in Fig. 4.3a and one with the new force field (Morse potential), Fig. 4.3b. The resulting densities of the species are significantly higher closer to the surface, indicating aggregation of the particles in the interface region. It can be seen that for the LJ potential, a double layer is formed in the interface with TFSI being closer to the surface than the Li+ ion. On the other hand, in the model with the Morse potential, the double layers are closer to the surface, and with both the Li+ ion and TFSI being closer to the surface while PEO is located

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further away. The density number distributions in Fig. 4.3b are in accordance with the interaction energies calculated from quantum mechanics calculations (see Fig. 2 and Table S1 in paper V), in which the TFSI and the Li+ at the surface of the Li metal have higher interaction energies than the PEO frag-ment. It should be noted that while it seems that the distribution of ions is improved in the new model, some of the ions also diffused into the surface of the metal. This can be related to that the interaction parameters of the ions and the metals obtained from the quantum mechanics calculations are overesti-mated when transferred to the MD simulations. When illustrating the interface region of the two models (see Fig. 5a and b in paper V), closer contacts be-tween the electrode and the electrolyte were clearly displayed in case of using the Morse potential than the LJ potential.

Figure 4.3. Partial density distribution of Li+, PEO and TFSI in relation to the Z axis in the MD simulation using Lennard-Jones (LJ) interaction potentials (a) and Morse potentials (b), respectively.

In Fig. 4.4, the RDF for Li+ and the oxygens of PEO and TFSI in the bulk (from 4.5 to 9 nm along the z-axis) and interface regions (between 2.5 and 4.5 nm) for both models are reported. It can be seen that the RDFs of the Li+–O(PEO) and Li+–O(TFSI) in the bulk region for both models are similar. The significant difference between the two models is, as expected, in the interface region. A higher intensity of TFSI compared to PEO in the first coordination shell of the Li+ ion can be seen in the interface region than in the bulk region. Besides, several new peaks can be observed for the Li+–O(TFSI) from 0.3 nm due to the structured distribution of the ions close to the metal slab.

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Figure 4.4. The partial radial distribution function for the interactions Li+–O(TFSI) and Li+–O(PEO) in the bulk and interface regions for the simulations using the Len-nard-Jones potential and the parametrized Morse potential.

Due to more accurate interface force field parameters, it seems that the newly generated force field models the arrangement of particle more realistic com-pared to the old force field, which is vital for understanding the dynamics and compositions of SEI in the battery. In the context of solid-state batteries, this shows the importance of selecting and developing interface force field.

4.3 The role of plasticizing side-chains in polycarbonate-based electrolytes

In paper VI, three polycarbonate-based SPEs (shown in Fig. 4.5) were studied as alternative polymer host materials to the conventional PEO: Poly(tri-methylene carbonate) (PTMC), poly(2-butyl-2-ethyltrimethylene carbonate) (PBEC) and poly(2-heptyloxymethyl-2-ethyltrimethylene carbonate) (PHEC). Two of these polymers – PBEC and PHEC – have plasticizing side chains on the main chain of the polymer host. The plasticizing side-chains result in a lower glass transition temperature (Tg) which is expected to improve the ionic conductivity. However, the measured ionic conductivities of PBEC and PHEC are clearly lower than PTMC (see Fig. 2 in paper VI). The aim of this study was to obtain insights into the structural and dynamical properties of these three polymer hosts by MD simulations, and thereby to elucidate why the less flexible PTMC displayed higher conductivity.

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Figure 4.5. Structures of the three polymers PTMC, PBEC and PHEC.

4.3.1 Structural properties In order to investigate the first coordination shells around the Li ions in the three polymer hosts, RDFs (g(r)) and CN (n(r)) for Li+–Opolymer and Li+–OTFSI were calculated (see Fig. 4.6). It can be observed that the main-chain carbonyl oxygen and TFSI oxygen atoms are surrounding the Li ions in all three SPE systems. For PTMC, the average number of carbonyl oxygens and TFSI sur-rounding the Li+ ions in the first coordination shell (0.2 nm) is around 3 and 1–2, respectively. This is in agreement with previously reported results from MD simulations and NMR studies.130

Figure 4.6. Snapshots of Li+ ions with the surrounding polymer and TFSI anions within 2.5 Å observed in the MD simulations and radial distribution functions, g(r), with accumulated coordination number, n(r), for Li+–O in (a) PTMC, (b) PBEC, and (c) PHEC electrolytes, at 423 K. Red, light brown, green, blue, yellow and purple denote O, C, F, N, S and Li, respectively.

In PBEC, the first coordination shell around the Li+ ions is at the same dis-tance as in PTMC including oxygen atoms of TFSI and carbonyl oxygens of the polymer. However, as can be seen in Fig. 4.6b, the CN for TFSI is higher

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which indicates a higher degree of ion pairing than in PTMC. This is likely a result of the poorer solvating effect of the polymer as compared to PTMC. In PHEC, on the other hand, a similar pattern to PTMC is observed regarding the first coordination shell around the Li+ ion. Moreover, it can be seen in Fig. 4.6c that the side-chain ether oxygen in PHEC is not directly involved Li+ ion coordination. It has been reported in earlier studies that there exists a prefer-ential coordination to main-chain carbonate groups over single ether groups both in side-chains131 and in the main chain.132

4.3.2 Ion transport mechanisms In order to investigate the dynamics of the Li ions in the three polymer elec-trolytes, the contact autocorrelation function (ACF) of polymer-Li+ and TFSI-Li+ were computed (see supporting information of paper VI for the calculation details). The ACF depends on pair formation within a defined cut-off distance, and if the contact time between the selected particles is short, this function decreases sharply to lower values. Here, the contact distances for Li+ with carbonyl oxygen (Fig. 4.7a) and TFSI oxygen (Fig. 4.7b) are considered at 423 K within 2.5 Å. The results show that the contact time of Li+-O(carbonyl) and Li+-O(TFSI) are shorter in PTMC than PHEC and PBEC. The MSD func-tions of the carbonyl oxygen of the three polymers were also calculated at 423 K and are presented in Fig. 4.7c to investigate the correlation of Li+ ion mo-bility and the diffusion of Ocarbonyl. The MSD of the carbonyl oxygen is lower for PTMC than for PHEC, while the estimated Li+ diffusion coefficient at this temperature is higher in PTMC than in PHEC (see Table S3 of paper VI). This indicates that the Li+ transport in the side chain-containing PBEC and PHEC is more correlated to coupled ion–polymer motion (via interactions with carbonyl oxygens) than to changes in the coordination environment (solvation sites), while local changes in the structural environment are of higher importance for the active transport mechanism in PTMC.

To further investigate the nature of the polymer solvation sites and the pos-sible ion transport mechanisms in these polymer hosts, the changing coordi-nation environment of the Li cations during a simulation time of 200 ns was studied by monitoring the indices of coordinating carbonyl oxygens (within 2.5 Å) for randomly selected Li+ ions in the SPEs. The time-evolution plots are presented for individual Li+ ions in Fig. 4.8 a–c for the three different polymer hosts. In PTMC (Fig. 4.8 a), interchain hopping can be observed at several points throughout the simulation. Intrachain hopping, on the other hand, is a comparatively less frequent event, in agreement with a previous study on polyester based polymer electrolytes.65

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Figure 4.7. Contact correlation functions of Li+ and (a) carbonyl oxygen of the poly-mers and (b) TFSI oxygens. (c) MSD of carbonyl oxygens for the different polymer chains at 423 K.

In PBEC (Fig. 4.8 b), on the other hand, the lines are considerably more static, indicating that neither intrachain nor interchain hopping are significant. Therefore, the segmental diffusion of the polymer chain and its complexation is the main reason of ionic mobility in PBEC during the simulations. Also the plot for PHEC (Fig. 4.8 c) exhibits a more static pattern as compared to PTMC. These are strong indications on that the PTMC host provides sites to which the Li ions can jump frequently, which is not the case for PBEC or PHEC, which can explain the experimentally observed differences in conduc-tivity.

To quantify the examples shown in the time-evolution plots (Fig. 4.8 a–c), the first coordination shell for all Li+ ions in every MD box was analyzed in every frame within a 200 ns trajectory. The number of unique solvation sites based on a 2.5 Å distance criteria were counted and are shown in Fig. 4.8d. It should be mentioned that the numbers in Fig. 4.8d are the different solvation sites (considering the different combination of index numbers of the carbonyl oxygens) that different Li ions encounter during the simulation time, and not their frequency of occurrence. Nevertheless, it can be clearly seen that the Li+ ions in PTMC move to many different solvating sites throughout the simula-tion in comparison to the other polymers. This is also in consistent with the ACF results discussed earlier. In contrast, the side chain-incorporating PBEC and PHEC systems show comparatively few interchanges of coordination

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sites, despite their lower Tgs. This explains how the flexibility-inducing side-chains primarily have a hindering effect on ionic transport.

Figure 4.8. Examples of Li+ coordination environments for (a) PTMC, (b) PBEC and (c) PHEC at 423 K. A single polymer (oligomer) chain is confined between two hor-izontal gray lines. Changing (blue) lines thereby represents a changing coordination sphere, while straight lines represent a fixed coordination throughout the simulation. If the (blue) coordination lines are within the same grey lines, it represents intra-chain coordination. (d) Number of unique coordination environments around Li+ throughout 200 ns trajectories in PTMC, PBEC and PHEC for all Li+ in the simulation boxes at 423 K.

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5. Solid polymer electrolyte reactivity/stability

SPE structure and dynamics are crucial for ionic transport, which is an essen-tial parameter for any electrolyte. However, these are not the only properties of interest for SPE-based battery systems. In papers VII-IX, the stability/re-activity of different SPEs are studied by DFT and AIMD simulations to un-derstand their chemical interactions with different electrode materials, primar-ily Li-metal. This is analogous to the interface reactivity studies in papers I-III, but for SPEs. The results of these studies are discussed in this section.

5.1 Polymer decomposition on the Li metal surface In paper VII, the interactions between the surface of Li metal with several polymers – all potential candidates for SPEs – were studied by first principles calculations. The investigated polymers are presented in Fig. 5.1.

Figure 5.1. Structures of the different polymers (oligomer fragments) investigated, including their terminal groups. Reproduced from Ref.133 with permission of The Royal Society of Chemistry.

The polymers showed some changes in their structures upon adsorption on the surface of lithium (mostly in their bond distances when in close contact with the surface; see Table 1 in paper VII). More significant changes could be ob-served for some polymers, not least for PAN which underwent a ring

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formation after adsorption. The optimized structures of these polymers at the surface of Li metal are shown in Fig. 5.2.

Figure 5.2. Optimized structures of (a) PEO (b) PVA (c) PEC (d) PEI (e) PCL (f) PTMC and (g) PAN oligomers on a Li (100) slab. Green, red, blue, brown and pink colors denote the Li, O, N, C and H atoms, respectively. Reproduced from Ref.133 with permission of The Royal Society of Chemistry. The calculated adsorption energies of the molecules on the Li metal surface can be found in Fig. 3 of paper VII. The implicit solvent model with two different dielectric constants, corresponding to the PEO polymer electrolyte and acetonitrile, respectively, were also applied. However, no changes in the trends of adsorption energies were observed by considering either of these (see Fig. 3 of paper VII), which supports the reliability of the results obtained in vacuum. Adsorption energy of PAN was found to be quite different from the other polymers. The stronger interaction of PAN with Li metal can be related to strong electron withdrawing characteristics of the nitrile group in this polymer, and can well be decisive for the use of PAN with Li-metal in a battery cell. The next highest adsorption energies are for the carbonyl contain-ing polymers; PEC, PTMC and PCL, respectively. The obtained adsorption energies for PVA and PEO were quite similar, while PEI displayed the weak-est adsorption capability. Adhesion of the polymers on the surface can be in-terpreted in two different ways: on the one hand, a stronger adhesion of the polymeric molecules on the surface can lead to a more stable interface be-tween the two materials, due to strong interactions, thereby providing good transfer of Li+ over the interface. On the other hand, the stronger adhesion also signals a thermodynamically favorable interaction, and can result in a reduc-tion of the molecule on the metal surface.

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To explore the early-stage interactions of the polymeric molecules with the Li metal surface, AIMD simulations were performed. Snapshots of the poly-mer/Li metal structure from AIMD simulations are shown in Fig. 5.3.

Figure 5.3. The final snapshots of AIMD simulations after 15 ps for (a) PEO (b) PVA (c) PEC (d) PEI (e) PCL (f) PTMC and (g) PAN at the Li (100) slab at 400 K. Repro-duced from Ref.133 with permission of The Royal Society of Chemistry. It can be seen that only PEC, PTMC and PCL clearly decomposed during the short time of these simulations. Both PEC (Fig. 5.3 c) and PTMC (Fig. 5.3 f) produced alkoxide and CO during the simulations. Similar fragments have been detected from one of the proposed reduction pathways for PTMC elec-trolyte at a graphite or Li metal interface in experimental studies.134 To further investigate the decomposition process of these three reactive polymers – PEC, PCL and PTMC – possible decomposition pathways analogous to liquid or-ganic carbonates (in paper I), were considered through Ccarbonyl–Oethereal and Cethereal–Oethereal bond breakings (Fig. 5.4). The Cethereal–Oethereal bond cleavage in the carbonate-containing (PEC and PTMC) oligomers turned out to be ther-modynamically more favorable, while Ccarbonyl–Oethereal bond breaking was ob-served in the AIMD simulations. The calculated DOS (see Fig. 6 in paper VII) of the products of the carbonate-producing pathway (pathway b) was also found to be better insulating compared to the alkoxide-producing pathway. Based on these results, it can be concluded that despite the decompositions of PEC and PTMC, the carbonate containing fragments are likely components of the inner part of SEI on Li-metal when using these SPEs, and that these have passivating properties.

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Figure 5.4. Decomposition energy for the degradation of PTMC, PEC and PCL at the Li metal surface. Reproduced from Ref.133 with permission of The Royal Society of Chemistry.

5.2 The electrochemical stability of solid polymer electrolytes

In paper VIII, the electrochemical stability window of the polymer hosts stud-ied in the previous section were determined computationally in their pristine form and after formation of complexes with three different Li-salts commonly used in SPEs: LiTFSI, lithium bis(fluorosulfonyl)imide (LiFSI) and lithium trifluoromethanesulfonate (LiCF3SO3). The redox potentials of the polymer-host materials and their salt complexes were calculated by DFT (see Fig. 5.5). The details for calculating the redox potentials can be found in paper VIII. It seems that most of the pristine polymers should be stable vs. the Li-metal electrode, since their reduction potential is estimated to be below that of Li+/Li (although that of PAN is very close, and PCL, PEC and PTMC are not that far either from the Li+/Li potential).

A significant reduction can be seen in the ESW for polymer:LiTFSI and polymer:LiFSI complexes, mainly due to the downward shift of the reduction potential, while the oxidation potential did not change significantly upon salt complex formation. On the other hand, the polymer:LiCF3SO3 complexes showed small changes in the ESW compared with the corresponding pristine

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polymers. The results in Fig. 5.5 indicated that the inclusion of LiTFSI and LiFSI salts lead to significantly more reactive systems with the Li metal elec-trode for most polymers, and that decomposition products are likely to be found on the electrode surfaces. However, the polymer:LiCF3SO3 complexes seems to be more stable in contact with the Li metal.

Figure 5.5. P/P- and P+/P redox pairs potentials for SPEs comprising (a) poly-mer:LiTFSI complexes, (b) polymers:LiFSI complexes, (c) polymers:LiCF3SO3 com-plexes, all showed in solid lines with filled symbols. The dashed lines with open sym-bols show the redox pair potentials for pristine polymer hosts, while the dashed hori-zontal lined show the redox potentials for the isolated salt and the solid grey line the Li+/Li potential (-3.04 V). All potential values are referred to SHE.

5.3 Initial steps in PEO decomposition on Li-metal PEO is still the archetypical SPE polymer host, and it is therefore interesting to explore its reactivity on Li-metal in detail. PEO is also considered to be stable at the Li-metal electrode,135 which was also indicated in papers VII and VIII. In paper IX, the thermodynamics of decomposition reactions of PEO on a Li-metal surface were investigated.

The thermodynamic analysis based on DFT calculations in this study is shown in Fig. 5.6. The calculated chemical potential ( ) for PEO(g) as a function of the oligomer size n is reported in Fig. 5.6a and displays that the oxidative power of the oligomer rapidly converges to the asymptotic value of -7.13 eV as the chain length increases. In order to investigate the oxidizing power which transforms lithium metal into Li2O, Li2O2 or Li2O4, the formation energy of these compounds were computed based on . The results are shown in Fig. 5.6b for all LixOy species. It can be seen that for the rather low oxidative power of PEO, only Li2O and Li2O2 are thermodynamically stable, while Li2O4 is also stable at higher values. Therefore, the formation of bulk Li2O(s) can be expected when PEO chains are in contact with Li(s). Besides, the Li2O2(s) phase is also stable, and might be formed if enough space is avail-able to be occupied by the larger peroxide ions.

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Figure 5.6. (a) The oxidation power of PEO(g) as function of chain length n. (b) For-mation energy for lithium oxide, peroxide and superoxide versus the chemical poten-tial of oxygen. (c) Monolayer interface energy upon oxidation of the Li(100) surface as function of the chemical potential of oxygen (same legend as in (b)). The dashed zones in (b) and (c) corresponds to the chemical potential for individual PEO chains of varying lengths. The thin dashed line in (c) is the surface energy for the clean Li(100) surface. The energies of the formation of monolayers of Li2O or Li2O2 on top of the Li(100) metal surface were calculated and are presented as a function of in Fig. 5.6c. The Li2O monolayer formation was found to be the most stable phase, as in the bulk compounds. These results suggest that lithium oxide (Li2O) should be the primary product when PEO interacts with a Li metal surface. By further analysis of the forced PEO decompositions on the surface of the Li metal (via two different routes presented in Fig. 5a of paper IX), the following full decomposition reaction can be proposed:

( 5.1)

This reaction was found to be strongly exothermic with an average energy gain of 2.42 eV per O atom (ΔE = -2.42 eV).

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To investigate the interactions of PEO with the oxidized Li surface, PEO ad-sorption and decomposition through the same route as on pristine Li metal, were studied on a partly (or fully) oxidized Li(100) surface. It was found that the decomposition process was still exothermic on the partially oxidized sur-face, but associated with a severe distortion of the surface (see Fig. 5b paper IX). Interestingly, in the case of a fully oxidized Li2O(111) surface, the initial decomposition step was endothermic. This is expected, since if further oxida-tion occurs, a Li ion with a higher oxidation state should be formed, which is impossible. This means that even if PEO reacts spontaneously with Li-metal, the resulting Li2O layer formed is passivating the surface properly, thereby rendering an electrochemically stable interface.

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6. Conclusions

Electrolytes and their interfaces with the Li metal electrode are highly im-portant for the construction of functional LMBs. In this thesis, DFT and MD simulations were used to provide insights into the atomistic world of these two complex components of the battery – and their even more complex inter-play. Two groups of electrolytes were considered: liquid electrolytes and (pri-marily) SPEs.

The static DFT modelling applied in this thesis gave knowledge about a variety of properties, including the adsorption energies of electrolyte mole-cules at the Li metal surface, their electronic structures and interfacial proper-ties, and the more likely decomposition pathways of the electrolytes. Gas phase modelling of electrolytes and interfaces using DFT was found to be a reliable approach which offered a good trade-off between computational costs and accuracy, and more expensive continuum solvent models did not display any relevant advantages.

Both static DFT and AIMD simulations could provide a deeper understand-ing of the polymeric molecules when interacting with the Li metal surface. Considering the short time scale of the AIMD simulations, the obtained results with this methodology should primarily be considered as the very initial steps of the SEI formation in the SPE-based systems, but are nevertheless vital for the build-up of these surface layers. Moreover, the computed DOS could show whether the polymer system was electronically insulating or not also after de-composition reactions at Li metal. Although the small system size renders it difficult to directly transfer these insights to the real systems (which display much larger interlayer thicknesses), the applied DFT methodology can pro-vide good insights into which polymers could provide thin and passivating surface layers on the battery electrodes. The results obtained in this way can serve as a starting point for larger screening studies of both polymer and liquid electrolyte systems to investigate their potential functionality on electrode sur-faces.

By performing relatively efficient plane wave DFT calculations, direct comparisons between the computed XPS and experimentally measured data of organic carbonates were carried out. Although the SEI layer formed in real LMB systems is quite complex, this thesis showed that this approach is feasi-ble, and could well be used as a predictive tool for a better understanding of

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the fragments contributing to the experimental XPS peaks and possible elec-trolyte degradation mechanisms.

The calculated ESWs of pristine polymers (without Li metal surface; paper VIII) predicted well the reactivity of these polymers, and were generally in a good agreement with the results from these polymers when interacting with the Li metal surface (paper VII). However, the addition of LiFSI and LiTFSI salts to the polymer molecules predicted lower reduction stability against the Li metal, as compared to the salt-free polymers. The polymer-salt interactions thus appears to be vital when estimating the reactivity of SPE systems.

In order to capture larger size and time scales, classical MD could be a helpful tool in both interfacial and bulk electrolyte modelling. The structural properties and ionic transport of SPEs were investigated using this modelling tool. Comparing the structural properties and dynamics of particles in the bulk electrolytes with those in the interfacial region illustrated the impact from the Li surface on the electrolyte properties. For example, particles in the interfa-cial region displayed slower dynamics and formed an ionic ‘double layer’ in vicinity of the Li metal surface. It should also be realized that the obtained results from MD simulations are directly dependent on the accuracy of model potentials. Hence, a new model potential was developed in this study in order to describe the SPE/Li metal interactions more accurately and with a better agreement with the experimental results. This highlights the need for better force fields when modelling the electrolytes and especially for the interfaces. In this context, further development for the force field expressing the Li metal is still required. MD simulations could then provide information about ion transport mechanisms over the interface, which is highly important for the performance of SPE-based LMBs.

In this thesis work, both strength and shortcomings have been shown for the application of several modelling techniques in the exploration of Li-metal batteries. The main conclusion is that both DFT and MD simulations could be utilized to study a large range of properties in these complex systems, such as initial stages of SEI formation at the atomistic level, and dynamical properties in the interfacial regions. Hopefully – and most likely – will future research build upon these results. A major challenge in modelling of these complex systems is then to consider the different length and time scales which are re-quired for achieving more accurate results on all system levels in the battery, and to this end couple these modelling methodologies. It is in this context vital to consider a hierarchical model to obtain relevant properties from different modelling scales, and also to develop novel computational tools for this pur-pose. While this thesis have generated vital insights obtained by both DFT, AIMD and classical MD as separate techniques, the future of battery model-ling appears to be multi-scaled.

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Sammanfattning på svenska

De miljömässiga problemen associerade med behovet av att reducera kon-sumtionen av fossila bränslen har skapat ett livfullt forskningsfält avseende alternativa energiresurser. I detta sammanhang är utveckling av energilagring en framkomlig strategi för att leverera energi när det behövs. Batterier är en av lovande form av energilagring, vilka används brett i samhället. Bland de olika sorters batterier som utvecklats över åren så har litium-baserade batte-rier, speciellt litiumjon-batterier (LIB), visat stor potential för tillämpningar som mobiltelefoner, bärbara datorer och mer nyligen elektromobilitet. Batte-rier består av elektrolyt, positiva och negativa elektroder. I ett LIB är grafit vanligtvis det negativa elektrodmaterialet.

Trots den lyckade kommersialiseringen av LIB så finns ett stort behov av batterier med högre energidensitet, speciellt för elektrifiering av transportsek-torn, vilket har lett forskare till att söka efter alternativa elektrodmaterial. Li-tiummetall är en intressant kandidat som negativ elektrod p.g.a. några unika egenskaper: den lägsta elektrokemiska potentialen, hög specifik kapacitet och låg densitet. Detta elektrodmaterial kan kombineras med till exempel svavel, syre eller interkalationsföreningar som positiva elektroder.

Litiummetall-elektroder användes i batterier redan före grafitelektroder in-troducerades, men har stora utmaningar i form av säkerhetsrisker och låg pre-standa. Det har gjort att detta elektrodmaterial inte lyckats kommersiellas för storskaliga applikationer på samma sätt som LIB. Därför har forskningen kring litiummetall-batterier (LMB) främst fokuserat på att öka prestandan av detta elektrodmaterial samt skapa stabilare elektrolyter vilka kan användas med litiummetall. En av de viktigaste delarna av litiumbatterier som har stor påverkan på batteriets prestanda är ytan mellan elektroden och elektrolyten. Metalliskt litium är väldigt reaktivt, vilket medför att elektrolyter ofta bryts ner i kontakt med elektroden och bildar ett lager bestående av olika föreningar baserat på sammansättningen av elektrolyten. Denna film kallas SEI-lagret (efter ”solid electrolyte interphase”). Många analyser av lagret av nedbryt-ningsprodukter har gjorts genom åren, men det finns fortfarande en rad obe-svarade frågor om detta komplicerade gränsskikt.

Modelleringstekniker är kraftfulla verktyg för att undersöka batteriers egenskaper och kompletterar ofta experimentella studier. Det finns ett antal olika modelleringstekniker tillgängliga för att studera material och elektroke-miska processer i batterisystem vilka fokuserar på olika tid- och längdskalor.

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Täthetsfunktionalteori (DFT) – som är en variant av kvantmekaniska be-räkningar – har blivit en populär och framgångsrik beräkningskemisk metod. DFT-metoder kan tillämpas för att modellera system med färre än några hundra atomer. För att studera dynamiken och intermolekylära interaktioner av ett system med tusentals atomer appliceras i stället molekyldynamik-simu-leringar (MD). Dessa två grupper av molekylmodelleringstekniker är använda i studierna i denna avhandling. Avhandlingen omfattar beräkningsstudier av gränsskikt mellan litiummetall och nya elektrolytsystem som är aktuella för användning med litiummetall. Första delarna av resultaten i avhandlingen fokuseras på vätskeelektrolytsy-stem. DFT-beräkningar utfördes på olika vanliga organiska karbonatlösnings-medel och en litiummetallyta för att studera lösningsmedlens nedbrytning och deras interaktion med elektrodytan på atomnivå. Röntgenfotoelektronspekt-roskopi (XPS), som är en vitt använd teknik för att studera och analysera ytor, utnyttjades också för dessa system för att jämföra de beräknade resultaten med de experimentella. Detta sätt användes också för att beräkna XPS-spektra av elektrolyter innehållande additivet LiNO3, som används i litium-svavel batte-rier. Resultaten av dessa XPS-mätningar och -beräkningar kunde ge detalje-rade insikter i ytkemin i dessa system. Jämförelser av beräknad XPS-data med experimentella resultat visades vara hjälpsamma för att få information om de mer realistiska mekanismerna för elektrolytnedbrytning på ytan.

Vätskeelektrolyter är inte stabila i kontakt med den reaktiva litiummetall-ytan, och därför lider LMB av säkerhetsrisker tillsammans med denna sorts elektrolyt. Ett alternativ som uppvisat stor potential för säkrare LMB är att i stället använda fasta polymerelektrolyter (SPE). SPE är definierade som salt-lösningar i ett polymerbaserat värdmaterial som har god mekanisk stabilitet och som därmed kan anses vara fast. Resterande del av avhandlingen fokuse-ras på molekylära modelleringsstudier av SPE-baserade system. Dynamiska och strukturella egenskaper av vanliga SPE bestående av LiTFSI-dopad polyetylenoxid (PEO) studerades med MD-simuleringar. In-formation om struktur och dynamik av polymerer och salt vid elektrodytan kan vara avgörande för att få bättre batterier. För att förbättra interaktionsmo-dellen som definieras i MD-simuleringarna av PEO-elektrolyten och litium-metallytan föreslogs också en ny potentialmodell mellan SPE:n och litiumme-tall. Det visades att potentialerna som användes i beskrivningen av systemen faktiskt har signifikant påverkan på de resultat som erhålls i simuleringarna.

Jontransport i bulken av olika SPE studerades i en kombinerad studie in-kluderande både modellering och experiment. En av begränsningarna med SPE är deras låga jonkonduktivitet, och därför har olika sätt prövats för att öka den. Ett sätt är att ha sidokedjor på huvudkedjan av polymererna, vilket kan leda till högre polymerflexibilitet vilket därmed kan öka jonledningen. Effekten av sidokedjor på de jonledningsmekanismerna i SPE bestående av polykarbonat utforskades med MD-simuleringar. Det upptäcktes att

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sidokedjor hindrar effekten av Li+ diffusion och därmed ledde till lägre jon-konduktiviteter, vilket inte var förväntat. MD-simuleringarna visade att poly-meren utan sidokedjor har fler ställen för litiumjoner att binda till än polyme-rerna med sidokedjor.

Till följd av begränsningarna hos klassiska MD-simuleringar avseende för-mågan att modellera bindningsbrytningar användes även DFT och ab initio MD-simuleringar (AIMD) för att studera interaktionen av PEO-molekyler och flera enheter av alternativa polymera värdmaterial på ytan av litiummetall. Det upptäcktes då upptäcktes att vissa polymerer (såsom polykarbonater) de-graderade på ytan av litiummetallen, medan några andra var mer stabila. Vi-dare analys av dessa system visade att även de degraderade polymererna kunde skydda ytan p.g.a. att degraderingsprodukterna bildade ett elektriskt isolerande lager på ytan av litiummetallen, vilket därmed stoppar vidare re-duktion av elektrolyt.

Inkludering av interaktioner mellan salt och polymer togs hänsyn till i en annan studie, då redoxpotentialen av elektrolyterna erhölls med DFT-beräk-ningar för att bättre uppskatta den elektrokemiska stabiliteten av olika SPE-system. Dessa resultat gav nya insikter om den elektrokemiska stabiliteten av polymer-salt-komplex, vilket kan guida framtida elektrod- och elektrolytde-sign. Nedbrutna polymerer på ytan av litiummetall kan också bilda en film vars kemi är effektiv för interaktionen mellan elektrolyt och metallyta. Därför utforskades litiumytor som oxiderats av PEO genom DFT-beräkningar. Det upptäcktes då att bildandet av en film Li2O från nedbruten PEO är termody-namiskt gynnsam på ytan av litiummetall.

Sammanfattningsvis så kunde beräkningssätten använda i denna avhand-ling ge insikter om strukturer och dynamiken av elektrolyt/litium ytor, och även mekanismerna för jontransport och strukturella egenskaper hos SPE. Kunskapen som fåtts i den här avhandlingen kan spela en viktig roll för att stabilisera och kontrollera battericeller på atomär nivå, och förhoppningsvis fungera som en guide vid design av nya batterimaterial.

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Acknowledgements

First of all, I would like to thank my supervisor Daniel Brandell for his con-sistent support and motivations during this PhD project. I’ve been always im-pressed by his quick feedback on manuscripts or requests regarding the pro-ject. I would also like to thank my co-supervisor, Moyses Araujo for his kind supports and helpful discussions for this PhD project. I would also like to thank Kristina Edström for welcoming me into the ÅABC group. I am thankful to all my collaborators/co-authors of the studies included in the thesis, for their help and sharing their knowledge; Luciano Costa, Reza Younesi, Matthew Lacey, Jonas Mindemark, Cleber Marchiori, Marco Car-boni, Tuanan C. Lourenço, Therese Eriksson, Prithwiraj Mandal, Rodrigo de Carvalho, Antoine Nasser, Amina Mirsakiyeva, Jolla Kullgren, and Peter Broqvist. I would like to thank the TriLi group, Kristina, Torbjörn, Leif, Daniel, Hel-ena, Matz, Reza, Erik, and Ruijun for useful meetings and discussions. I am grateful to all past and present colleagues at the ÅABC, structural and inorganic chemistry for creating the great work environment. Special thanks to Alina, Gabi, Shruti, Fernanda, Siham and Chenjuan for all happy moments, fika and lunches. I miss our lunch discussions! Erik, Burak and Ruijun, thanks for the company in courses, conferences and at work. I would also like to thank Erik for translating the summary of this thesis to Swedish. Thank you, Burak and Johan Cedervall, it was nice to share the office with you. Many thanks to Giane Damas, for all interesting discussions and fun times. It was so nice to have you here! Finally, I would like to thank my family members for their support even from long distance. I would like to thank my dad, for always being confident in me and motivate me to achieve my goals. My mom, who is sadly no longer with us, for her love and unlimited support. Thanks to my lovely sisters, for always being my best friends. Last but not least, I would like to thank my dear hus-band, Mehdi. Thank you so much for your supports and always encouraging me to pursue my dreams. Thank you for all scientific discussions. Without you, this thesis could not be written.

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