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공학박사 학위논문

차세대 이차전지용 흑연 및 리튬

금속 음극 소재에 대한 이론적 연구

Theoretical study on graphite and lithium metal as anode materials for

next-generation rechargeable batteries

2019 년 2 월

서울대학교 대학원

재료공학부

윤 갑 인

i

Abstract

Theoretical study on graphite and

lithium metal as anode materials for

next-generation rechargeable batteries

Yoon, Gabin

Department of Material Science and Engineering

College of Engineering

The Graduate School

Seoul National University

A worldwide drift for sustainable society has led to the intensive development of

the electrochemical energy storage system (ESS). Among the various ESSs, Li-ion

batteries (LIBs) have drawn widespread attention for various applications because

of their high energy density, power capability and stable cyclability. However, the

energy density of LIBs is limited and their production cost is unstable due to the

uneven worldwide distribution and the limited supply of Li. In this regard, it is of

great importance to search for electrodes for next-generation rechargeable batteries

in order to meet an ever-growing variety of demands and improve the energy

ii

storage performances. In this thesis, I present theoretical investigation on anode

materials for next-generation rechargeable batteries, particularly on the graphite for

Na-ion batteries and the metallic Li for Li metal batteries.

In Chapter 2, the mechanism of solvated-Na-ion intercalation in graphite is

investigated using in operando X-ray diffraction analysis, electrochemical titration,

real-time optical observation, and density functional theory (DFT) calculations.

The ultrafast intercalation is demonstrated in real time using millimeter-sized

highly ordered pyrolytic graphite, in which instantaneous insertion of solvated-Na-

ions occurs (in less than 2 s). The formation of various stagings with solvated-Na-

ions in graphite is observed and precisely quantified for the first time. The

atomistic configuration of the solvated-Na-ions in graphite is proposed based on

the experimental results and DFT calculations. The correlation between the

properties of various solvents and the Na ion co-intercalation further suggests a

strategy to tune the electrochemical performance of graphite electrodes in Na

rechargeable batteries.

In Chapter 3, through a systematic investigation of a series of alkali metal (AM)

graphite intercalation compounds (AM-GICs, AM = Li, Na, K, Rb, Cs) in various

solvent environments, I demonstrate that the unfavorable local Na–graphene

interaction primarily leads to the instability of Na-GIC formation but can be

effectively modulated by screening Na ions with solvent molecules. Moreover, it is

shown that the reversible Na intercalation into graphite is possible only for specific

iii

conditions of electrolytes with respect to the Na–solvent solvation energy and the

lowest unoccupied molecular orbital level of the complexes. I believe that these

conditions are applicable to other electrochemical systems involving guest ions and

an intercalation host and hint at a general strategy to tailor the electrochemical

intercalation between pure guest ion intercalation and co-intercalation.

In Chapter 4, various aspects of the electrochemical deposition and stripping of Li

metal are investigated with consideration of the reaction rate/current density,

electrode morphology, and solid electrolyte interphase (SEI) layer properties to

understand the conditions inducing abnormal Li growth. It is demonstrated that the

irregular (i.e., filamentary or dendritic) growth of Li metal mostly originates from

local perturbation of the surface current density, which stems from surface

irregularities arising from the morphology, defective nature of the SEI, and relative

asymmetry in the deposition/stripping rates. Importantly, I find that the use of a

stripping rate of Li metal that is slower than the deposition rate seriously

aggravates the formation of disconnected Li debris from the irregularly grown Li

metal. This finding challenges the conventional belief that high-rate

stripping/plating of Li in an electrochemical cell generally results in more rapid cell

failure because of the faster growth of Li metal dendrites.

Keywords : Energy storage, First-principles calculation, Continuum mechanics,

Batteries, Li metal anode, Graphite

Student Number : 2013-20611

iv

v

Table of Contents

Abstract ............................................................................................................ i

List of Figures............................................................................................... viii

List of Tables................................................................................................. xvi

Chapter 1. Introduction .................................................................................. 1

1.1 Motivation and outline..................................................................1

1.2 References .....................................................................................4

Chapter 2. Sodium intercalation chemistry in graphite ................................ 9

2.1 Introduction ..................................................................................9

2.2 Experimental and computational details ...................................122.2.1 Materials ............................................................................12

2.2.2 Electrode preparation and electrochemical measurements .............................................................................12

2.2.3 In Operando XRD analysis ................................................132.2.4 Calculation details .............................................................13

2.3 Result and Discussion .................................................................152.3.1 Staging behavior upon Na intercalation ...........................152.3.2 Solvated-Na-ion intercalation into graphite structure .....212.3.3 Solvent dependency of Na intercalation............................31

2.4 Conclusion...................................................................................46

2.5 References ...................................................................................47

vi

Chapter 3. Conditions for reversible Na intercalation in graphite: Theoretical studies on the interplay among guest ions, solvent, and graphite host..................................................................... 53

3.1 Introduction ................................................................................53

3.2 Computational details.................................................................57

3.3 Results and discussion ................................................................60

3.3.1 Understanding the origin of unfavorable Na intercalation into graphite .........................................................603.3.2 Conditions for reversible Na intercalation into graphite .74

3.4 Conclusion...................................................................................86

3.5 References ...................................................................................87

Chapter 4. Deposition and stripping behavior of lithium metal in electrochemical systems: Continuum mechanics

study............................................................................................................... 95

4.1 Introduction ................................................................................95

4.2 Computational details.................................................................99

4.3 Results and discussion .............................................................. 1024.3.1 Effect of deposition rate on Li growth behavior............. 1044.3.2 Effect of surface geometry on Li growth behavior ......... 1094.3.3 Effect of SEI layer properties on Li growth behavior .... 116

4.3.4 Consequences of repeated cycles of deposition and stripping.................................................................................... 130

4.4 Conclusion................................................................................. 135

4.5 References ................................................................................. 137

vii

Chapter 5. Summary ....................................................................................144

Abstract in Korean.......................................................................................147

Curriculum Vitae .........................................................................................150

viii

List of Figures

Figure 2-1. In operando synchrotron X-ray diffraction analysis of the structural

evolution of the ternary Na-ether-graphite system observed during electrochemical

solvated-Na-ion intercalation and deintercalation into/out of graphite in Na | 1M

NaPF6 in a DEGDME | graphite cell.

Figure 2-2. Expansion of highly ordered pyrolytic graphite (HOPG) along the c

axis with chemical Na-ether intercalation. (a) Real-time snapshots of HOPG under

direct contact with Na metal before and after exposure to 1 M NaPF6 in DEGDME

solution, (b) height of HOPG measured during the intercalation process, and (c)

schematic comparison of the height and c lattice parameter of graphite for

hypothetical stage 3 GIC, 2 GIC, and stage 1 GIC.

Figure 2-3. Geometry of solvated-Na intercalated graphite. (a) Weight change of

graphite measured at various state of charge and discharge. (b) Energy-dispersive

X-ray spectroscopy analysis of discharged sample. Calculated structure when (c)

one [Na-DEGDME]+ complex is and (d) two [Na-DEGDME]+ complexes are

intercalated in the interlayer spacing in graphite

Figure 2-4. Various configurations of [Na-DEGDME]+ solvation complex.

Energies relative to the most stable configuration are shown with each structure.

Figure 2-5. Various configurations of double complex intercalation of [Na-

DEGDME]+ in stage 1 structure.

ix

Figure 2-6. A model of triple complex intercalation of [Na-DEGDME]+ in stage 1

structure.

Figure 2-7. Calculated planar area of (a) [Na-DEGDME]+ and (b) graphene layer.

For convenience, rectangular shape of [Na-DEGDME]+ is assumed and

intermolecular interactions are considered in Figure 2-7a. The planar areas of [Na-

DEGDME]+ and graphene layer are 68.13 Å2 per complex, and 2.64 Å2 per carbon

atom, respectively.

Figure 2-8. In-plane charge distribution at graphene layer after the intercalation of

[Na-DEGDME]+ complex. Intercalated Na+ ions donate electrons to graphene layer,

forming an ionic bond with electrons from C-C bonds in graphene layer.

Figure 2-9. Na storage potential depending on solvent species. (a) Typical

charge/discharge profiles of graphite electrode with three electrolyte solvents (inset:

solvent molecules) in Na half-cell configuration. (b) X-ray diffraction (XRD)

patterns of solvated-Na intercalated graphite compounds and simulated XRD

patterns of expanded graphite with repeated distance of 11.66 Å with/without

intercalants of [Na-DEGDME]+ complex. (c) Intensity ratio of (002)/(003) when

three electrolyte solvents are intercalated into graphite with Na ions. (d) dQ dV-1

analysis of graphite electrode with three electrolyte solvents. (e) Schematic of the

screening effect of the solvent on the Na storage potential.

Figure 2-10. Mass change of the electrodes upon discharge when (a) TEGDME

x

and (b) DME solvents are used.

Figure 2-11. Typical charge/discharge profile and ex-situ XRD patterns using 1M

NaPF6 in TEGDME electrolyte.

Figure 2-12. Typical charge/discharge profile and ex-situ XRD patterns using 1M

NaPF6 in DEGDME electrolyte.

Figure 2-13. Typical charge/discharge profile and ex-situ XRD patterns using 1M

NaPF6 in DME electrolyte.

Figure 2-14. (a) Simulated XRD patterns of two different state of [Na-DEGDME]+

ordering in graphite host. Structures of ordered, disordered structures used in

simulation are described in (b), (c), respectively. Note that the intensity ratio of

(002) / (003) does not change, whereas several minor peaks in 11˚-22˚ range

emerge or diminish due to the change of [Na-DEGDME]+ ordering.

Figure 2-15. Cycle stability of graphite electrode in Na half cells. Graphite

working electrode, Na metal counter electrode, and 1M NaPF6 in DEGDME

electrolyte are used.

Figure 2-16. Cycle stability of graphite electrode in Na half cells. Graphite

working electrode, Na metal counter electrode are used. 1M NaPF6 in TEGDME,

DEGDME, DME electrolytes are used, respectively.

Figure 2-17. Ex-situ XRD and XPS analyses before and after cycling. (a) XRD

xi

patterns of graphite electrode before/after cycling. (b) XPS spectra of graphite

electrode before/after cycling.

Figure 2-18. SEM image of graphite electrode after cycling.

Figure 3-1. (a) �� values of AM-GICs in MC6 and MC8 structures (AM = Li, Na,

K, Rb, Cs). (b) Contributing factors to �� values of AM-GICs.

Figure 3-2. (a) ��,����� values upon lattice reconstruction from bcc structure to

MC6 and MC8 structures. (b) Relative ��,�������� upon AM intercalation and

charge transfer. (c) Relative �� between AM and a single layer of graphene. (d)

Relative �� between AM-solvent complexes and a single layer of graphene. The

energy scales in (b), (c), and (d) are referenced to the values obtained for Li.

Figure 3-3. Model structure for the calculation of pure interaction between AM and

the graphene layer. A vacuum slab of ~15 Å was used.

Figure 3-4. (a) Plane-averaged charge density of metal-adsorbed graphene.

Because of the nature of AMs, different characteristics of the charge distributions,

such as the peak of the planar charge density and distance from graphene at

maximum charge density, are observed. (b) Charge distribution of Li-adsorbed

graphene. All the AM-adsorbed graphene samples exhibited identical charge

distributions. Isosurface level is set to 0.005 e-/Å3.

Figure 3-5. (a) Plane-averaged charge density of [AM-DEGDME]-adsorbed

xii

graphene. Because of the screening effect of the solvent molecules, similar charge

distributions were observed for all the AMs. (b) Charge distribution of [Li-

DEGDME]-adsorbed graphene. All the [AM-DEGDME]-adsorbed graphene

samples exhibited identical charge distributions. Isosurface level is set to 0.03 e-/Å3.

Figure 3-6. (a) Cyclic voltammetry curves of various Na–solvent systems; 1 M

NaPF6 salts were used for all tests. (b) The solvent species used to investigate the

solvent dependency of the co-intercalation phenomenon (DME: ethylene glycol

dimethyl ether, DEGDME: diethylene glycol dimethyl ether, TEGDME:

tetraethylene glycol dimethyl ether, THF: tetrahydrofuran, DOL: dioxolane, DMC:

dimethyl carbonate, DEC: diethyl carbonate, EC: ethylene carbonate, PC:

propylene carbonate).

Figure 3-7. SEM image of graphite after discharge in 1 M NaPF6 in PC solvent.

The cleavages observed in the sample indicate the exfoliation of graphite.

Figure 3-8. (a) �� of Na–solvent complexes. (b) Energy diagram of [Na-DMEx]+

desolvation process. (c) ���� values of Na–solvent complexes. The ���� values

of potential candidates for feasible co-intercalation are highlighted in bold. (d)

LUMO levels of [Na-solvent]+ complexes. The Fermi level of graphite is shaded

green.

Figure 3-9. Summary of solvent dependency of the Na–solvent co-intercalation

behavior. The structure of Na-solvent co-intercalated graphite (upper right) is

xiii

adopted from ref. 18.

Figure 4-1. Evolution of Li deposits for different deposition rates. (a) Reference

model used for simulations. Geometry after initial deposition at (b) slow and (c)

fast deposition rates. The gray lines represent the initial geometry before deposition.

(d) Expected shape after continuous deposition at slow rate. The dotted circles

represent pores that could be generated after physical contact between deposits. (e)

Geometry after further deposition from (d). Deposits from neighboring bumps will

meet and eventually form a mossy-like shape, whereas the high-rate condition

yields vertical growth of Li with many branches, forming a needle-like shape. The

scale bars are 2-μm long. The utilization of Li is identical in (b) and (c). The

contour levels of the potential are displayed every 2.5 meV.

Figure 4-2. Snapshots for time-dependent Li electrodeposition using a relatively

slow rate.

Figure 4-3. Snapshots for time-dependent Li electrodeposition using a relatively

fast rate.

Figure 4-4. Models used for simulation with (a) triangular and (b) circular surface

shape.

Figure 4-5. Evolution of Li deposits starting from an initial surface geometry with

(a) triangular and (b) circular bumps. The gray lines represent the initial geometry

before deposition, and the scale bars are 2-μm long. The utilization of Li is

xiv

identical in (a) and (b), and the contour levels of potential are displayed every 2.5

meV.

Figure 4-6. Snapshots for time-dependent Li electrodeposition at the triangular

surface.

Figure 4-7. Snapshots for time-dependent Li electrodeposition at the circular

surface.

Figure 4-8. Model used for simulation with 200nm-thick SEI layers. Li ion

diffusivity in SEI layers is 100 times as sluggish as that in electrolyte. The

thickness and the Li ion diffusivity were controlled to see their effect in Li

deposition behavior.

Figure 4-9. Evolution of Li deposits with the presence of a 200-nm-thick surface

SEI layer. The Li ion concentration profile along the yellow dotted line is also

shown. The Li ion conductivity of the layer was set to (a) 100 times and (b) 10

times lower than that of the electrolyte. The gray lines represent the initial

geometry before deposition, and the scale bars are 1-μm long. The utilization of Li

is identical in (a) and (b), and the contour levels of potential in (a) and (b) are

displayed every 10 meV.

Figure 4-10. Li ion concentration and electrolyte potential profile in electrolyte

region using (a) single-ionic conducting and (b) bi-ionic conducting SEI layer.

Figure 4-11. Li deposition shape using single and bi-ionic conducting SEI.

xv

Figure 4-12. Li ion concentration and electrolyte potential profile in electrolyte

region using (a) single-ionic conducting and (b) bi-ionic conducting electrolyte. It

is assumed that the interface between the Li metal and the electrolyte is stabilized

without the formation of SEI layer.

Figure 4-13. Li deposition shape using single and bi-ionic conducting electrolyte.

It is assumed that the interface between the Li metal and the electrolyte is stabilized

without the formation of SEI layer.

Figure 4-14. Shape of Li deposits after a deposition simulation with 50 nm-thick

SEI layer.

Figure 4-15. Li stripping behavior from irregular deposit. Dead Li formation is

shown at the narrow point (black arrow) for the slow stripping condition. Complete

stripping was not achieved because of the failure of the solution converge,

presumably arising from the dynamic generation of singular points during the

stripping reaction. The scale bars are 1-μm long.

Figure 4-16. Stripping from artificially made model with narrow points.

xvi

List of Tables

Table 3-1. Comparison of c-lattice parameters obtained by experiments and PBE-

D3 calculation.

Table 3-2. Bond lengths of AMs in bcc lattice ���� and comparison of ���� to

the AM lattices in MC6 and MC8 structures in both ab- and c- directions.

Table 3-3. Bader charges of AMs in metal-adsorbed graphene.

Table 3-4. Material properties of investigated solvent.

xvii

1

Chapter 1. Introduction

1.1 Motivation and outline

The soaring demand for energy along with the exhaustion of fossil fuels and their

environmentally harmful outcome have led to the growing interest in the

sustainable energy source, including solar, wind and hydroelectric power

generation. These eco-friendly energy resources necessarily require an energy

storage system (ESS), since the energy production highly depends on the

environmental condition. In addition, as portable electronic devices from

cellphones to electric vehicles proliferate, the development of ESS becomes

indispensable. For a last few decades, Li-ion batteries (LIBs) which stores

chemical energy using reversible Li (de)intercalation to the electrode materials

have drawn widespread attention for their high energy density, power capability

and stable cyclability.1-3 However, the performance improvement of LIBs is slow in

progress, whereas the demands for high-performance ESSs are soaring as well as

diversifying. For instance, applications such as mobile devices and electric vehicles

require high energy density, while renewable energy plants need a large-scale and a

low-cost ESS. In this regard, the development of next-generation rechargeable

batteries is critical.

One of the promising candidates for post-LIBs is Na-ion batteries (NIBs), due to

their similar electrochemistry to the established LIBs. In addition, the low cost of

2

Na compared to Li, which comes from the accessibility of Na resources, makes

NIB a strong candidate for large-scale energy storage applications.4-10 However,

while graphite has been broadly utilized as a standard anode materials for LIBs

because of its high capacity and low cost, it has not been considered as an anode

for NIBs due to its inferior Na storage performance.11-13 In chapters 2 and 3, I

present the studies to reveal the underlying origin for the poor Na storage

performance of graphite by systematically investigating a series of alkali metal

graphite intercalation compounds (AM-GICs, AM = Li, Na, K, Rb, Cs).14-15 In

addition, I demonstrate the Na-solvent co-intercalation is an effective strategy for

reversible Na intercalation into graphite. Furthermore, with the aid of the

experimental measurements, the mechanism of solvated-Na-ion intercalation in

graphite is investigated. The formation of various stagings of solvated-Na-ions in

graphite is observed and precisely quantified, and the atomic arrangement of the

solvated-Na-ions in graphite is proposed based on experiments and DFT

calculations. Finally, I demonstrate that the reversible intercalation of solvated-Na-

ions in graphite is possible for specific solvents, which satisfy the conditions

regarding the Na-solvent solvation energy and the lowest unoccupied molecular

level of solvated-Na-ion complexes.

From a viewpoint of energy density, Li metal batteries which use metallic Li as an

anode have recently drawn extensive attention. While the conventional

intercalation-based anodes show limited gravimetric capacity (~370 mAh g-1)

3

because of the weight of the intercalation host, Li metal anode has a potential of

delivering the largest capacity (~3860 mAh g-1) and the lowest redox potential (-

3.04 V vs. standard hydrogen electrode), since it utilizes the reversible

electrochemical plating/stripping of Li metal.16 However, the safety issues arising

from the dendritic growth of Li prevents the practical application. Various physical

and chemical approaches have been applied to address this issue, however, the

stable cycle performance under practical operation conditions is not yet achieved.17-

29 In this respect, it is critical to understand the fundamentals of Li deposition and

stripping behavior. In Chapter 4, I present the fundamental investigation of Li

electrodeposition and stripping using continuum mechanics simulation.30 Key

factors affecting the electrochemical Li deposition/stripping behavior, such as the

reaction rate, shape of the electrode surface, conductivity and uniformity of the SEI

layer, and the effect of current density history were thoroughly controlled to

monitor their effect on the Li morphology evolution.

4

1.2 References

1. Tarascon, J. M.; Armand, M., Issues and challenges facing rechargeable

lithium batteries. Nature 2001, 414, 359-367.

2. Armand, M.; Tarascon, J. M., Building better batteries. Nature 2008, 451,

652-657.

3. Kang, K.; Meng, Y. S.; Breger, J.; Grey, C. P.; Ceder, G., Electrodes with

high power and high capacity for rechargeable lithium batteries. Science 2006, 311,

977-980.

4. Kim, S. W.; Seo, D. H.; Ma, X. H.; Ceder, G.; Kang, K., Electrode

Materials for Rechargeable Sodium-Ion Batteries: Potential Alternatives to Current

Lithium-Ion Batteries. Adv. Energy Mater. 2012, 2, 710-721.

5. Kim, H.; Kim, H.; Ding, Z.; Lee, M. H.; Lim, K.; Yoon, G.; Kang, K.,

Recent Progress in Electrode Materials for Sodium-Ion Batteries. Adv. Energy

Mater. 2016, 6, 1600943.

6. Barpanda, P.; Ye, T.; Nishimura, S.; Chung, S. C.; Yamada, Y.; Okubo, M.;

Zhou, H. S.; Yamada, A., Sodium iron pyrophosphate: A novel 3.0 V iron-based

cathode for sodium-ion batteries. Electrochem. Commun. 2012, 24, 116-119.

7. Komaba, S.; Yabuuchi, N.; Nakayama, T.; Ogata, A.; Ishikawa, T.; Nakai,

I., Study on the Reversible Electrode Reaction of Na1-xNi0.5Mn0.5O2 for a

Rechargeable Sodium-Ion Battery. Inorg. Chem. 2012, 51, 6211-6220.

8. Yabuuchi, N.; Kajiyama, M.; Iwatate, J.; Nishikawa, H.; Hitomi, S.;

5

Okuyama, R.; Usui, R.; Yamada, Y.; Komaba, S., P2-type Nax[Fe1/2Mn1/2]O2 made

from earth-abundant elements for rechargeable Na batteries. Nat. Mater. 2012, 11,

512-517.

9. Kim, H.; Yoon, G.; Park, I.; Park, K. Y.; Lee, B.; Kim, J.; Park, Y. U.; Jung,

S. K.; Lim, H. D.; Ahn, D.; Lee, S.; Kang, K., Anomalous Jahn-Teller behavior in a

manganese-based mixed-phosphate cathode for sodium ion batteries. Energy

Environ. Sci. 2015, 8, 3325-3335.

10. Song, J.; Wang, L.; Lu, Y.; Liu, J.; Guo, B.; Xiao, P.; Lee, J.-J.; Yang, X.-

Q.; Henkelman, G.; Goodenough, J. B., Removal of Interstitial H2O in

Hexacyanometallates for a Superior Cathode of a Sodium-Ion Battery. J. Am. Chem.

Soc. 2015, 137, 2658-2664.

11. Kundu, D.; Talaie, E.; Duffort, V.; Nazar, L. F., The Emerging Chemistry

of Sodium Ion Batteries for Electrochemical Energy Storage. Angew. Chem. Int. Ed.

2015, 54, 3431-3448.

12. Yabuuchi, N.; Kubota, K.; Dahbi, M.; Komaba, S., Research Development

on Sodium-Ion Batteries. Chem. Rev. 2014, 114, 11636-11682.

13. Slater, M. D.; Kim, D.; Lee, E.; Johnson, C. S., Sodium-Ion Batteries. Adv.

Funct. Mater. 2013, 23, 947-958.

14. Yoon, G.; Kim, H.; Park, I.; Kang, K., Conditions for Reversible Na

Intercalation in Graphite: Theoretical Studies on the Interplay Among Guest Ions,

Solvent, and Graphite Host. Adv. Energy Mater. 2017, 7, 1601519.

15. Kim, H.; Hong, J.; Yoon, G.; Kim, H.; Park, K.-Y.; Park, M.-S.; Yoon, W.-

6

S.; Kang, K., Sodium intercalation chemistry in graphite. Energy Environ. Sci.

2015, 8, 2963-2969.

16. Choi, J. W.; Aurbach, D., Promise and reality of post-lithium-ion batteries

with high energy densities. Nat. Rev. Mater. 2016, 1, 16013.

17. Monroe, C.; Newman, J., The Impact of Elastic Deformation on

Deposition Kinetics at Lithium/Polymer Interfaces. J. Electrochem. Soc. 2005, 152,

A396-A404.

18. Chen, X.; Hou, T.-Z.; Li, B.; Yan, C.; Zhu, L.; Guan, C.; Cheng, X.-B.;

Peng, H.-J.; Huang, J.-Q.; Zhang, Q., Towards stable lithium-sulfur batteries:

Mechanistic insights into electrolyte decomposition on lithium metal anode.

Energy Storage Materials 2017, 8, 194-201.

19. Zu, C.; Azimi, N.; Zhang, Z.; Manthiram, A., Insight into lithium-metal

anodes in lithium-sulfur batteries with a fluorinated ether electrolyte. J. Mater.

Chem. A 2015, 3, 14864-14870.

20. Yan, K.; Lee, H.-W.; Gao, T.; Zheng, G.; Yao, H.; Wang, H.; Lu, Z.; Zhou,

Y.; Liang, Z.; Liu, Z.; Chu, S.; Cui, Y., Ultrathin Two-Dimensional Atomic Crystals

as Stable Interfacial Layer for Improvement of Lithium Metal Anode. Nano Lett.

2014, 14, 6016-6022.

21. Kazyak, E.; Wood, K. N.; Dasgupta, N. P., Improved Cycle Life and

Stability of Lithium Metal Anodes through Ultrathin Atomic Layer Deposition

Surface Treatments. Chem. Mater. 2015, 27, 6457-6462.

22. Kozen, A. C.; Lin, C.-F.; Pearse, A. J.; Schroeder, M. A.; Han, X.; Hu, L.;

7

Lee, S.-B.; Rubloff, G. W.; Noked, M., Next-Generation Lithium Metal Anode

Engineering via Atomic Layer Deposition. ACS Nano 2015, 9, 5884-5892.

23. Zheng, G.; Lee, S. W.; Liang, Z.; Lee, H.-W.; Yan, K.; Yao, H.; Wang, H.;

Li, W.; Chu, S.; Cui, Y., Interconnected hollow carbon nanospheres for stable

lithium metal anodes. Nat. Nanotechnol. 2014, 9, 618.

24. Lee, H.; Lee, D. J.; Kim, Y.-J.; Park, J.-K.; Kim, H.-T., A simple

composite protective layer coating that enhances the cycling stability of lithium

metal batteries. J. Power Sources 2015, 284, 103-108.

25. Li, N. W.; Yin, Y. X.; Yang, C. P.; Guo, Y. G., An Artificial Solid

Electrolyte Interphase Layer for Stable Lithium Metal Anodes. Adv. Mater. 2016,

28, 1853-1858.

26. Wang, X.; Hou, Y.; Zhu, Y.; Wu, Y.; Holze, R., An Aqueous Rechargeable

Lithium Battery Using Coated Li Metal as Anode. Sci. Rep. 2013, 3, 1401.

27. Lu, Y.; Tu, Z.; Archer, L. A., Stable lithium electrodeposition in liquid and

nanoporous solid electrolytes. Nat. Mater. 2014, 13, 961.

28. Lu, Y.; Tu, Z.; Shu, J.; Archer, L. A., Stable lithium electrodeposition in

salt-reinforced electrolytes. J. Power Sources 2015, 279, 413-418.

29. Ding, F.; Xu, W.; Graff, G. L.; Zhang, J.; Sushko, M. L.; Chen, X.; Shao,

Y.; Engelhard, M. H.; Nie, Z.; Xiao, J.; Liu, X.; Sushko, P. V.; Liu, J.; Zhang, J.-G.,

Dendrite-Free Lithium Deposition via Self-Healing Electrostatic Shield

Mechanism. J. Am. Chem. Soc. 2013, 135, 4450-4456.

30. Yoon, G.; Moon, S.; Ceder, G.; Kang, K., Deposition and Stripping

8

Behavior of Lithium Metal in Electrochemical System: Continuum Mechanics

Study. Chem. Mater. 2018, 30, 6769-6776.

9

Chapter 2. Sodium intercalation chemistry in

graphite

(The content of this chapter has been published in Energy & Environmental

Science. [Kim, H., Hong, J., Yoon, G. et al., Energy & Environmental Science 2015,

8, 2963-2969.] – Reproduced by permission of The Royal Society of Chemistry.)

2.1 Introduction

Graphite is capable of accommodating a wide range of guest species, including

alkali, alkaline-earth, and rare-earth elements; halogens; protons; and Lewis acids

between its sp2-bonded graphene layers.1 Its versatility also allows more than two

different guest species to be intercalated simultaneously in the host structure

through a co-intercalation process. Graphite intercalation compounds (GICs), the

product of the intercalation, exhibit distinctive physical and chemical properties

compared with pristine graphite. Their electronic/magnetic structures and optical

and catalytic properties significantly vary with the type of intercalant as well as its

concentration.2 For instance, the electrical conductivity of GICs drastically

increases along the c-axis (~104 times) compared to a/b-axes (~10 times) with a

high concentration of ionized guest species.3-5 The unique structure-property

relationship of GICs enables the diverse application of graphite and GICs for

energy storage and as catalysts and electrical/thermal conductors.6-10

10

Graphite has been widely used as a standard anode material in Li-ion batteries,

where it forms a series of binary GICs during intercalation and finally reaches the

stoichiometry of LiC6, delivering a high capacity. 11-12 However, thus far, graphite

has not been considered suitable for Na-ion batteries, an alternative system for

large-scale energy storage because of the thermodynamic instability of binary Na-

intercalated GICs.13-14 As a recent breakthrough, Jache et al. and our group

facilitated Na-ion storage in graphite using solvated-Na-ion intercalation, forming

ternary GICs.15-16 With the proper selection of the electrolyte, a significant amount

of sodium insertion was demonstrated to unexpectedly occur. The Na-ions are

stored and reversibly released in graphite for hundreds of cycles assisted by ether-

based electrolyte which shows a stability at the potential below 4.0 V (vs. Na).16

Nevertheless, understanding of the mechanism of solvated-Na-ion intercalation in

graphite remains limited because of the complexity of the system and the difficulty

of quantifying the intercalation of both the solvent molecules and Na ions. The lack

of understanding of how and when the Na ion intercalation occurs in graphite

prohibits the further advancement of this practically important anode material for

Na-ion batteries. Herein, we investigated the intercalation mechanism of Na in

graphite by precisely determining the crystal structures and stoichiometry of GICs

in the ternary Na-ether-graphite system using in operando X-ray diffraction (XRD)

analysis coupled with electrochemical titration. The formation of first-stage GICs

was directly visualized using real-time measurements of the graphite intercalation.

Density functional theory (DFT) calculations suggested a particular configuration

11

of the Na ions and solvent between the graphene layers, which involves the double

stacking of solvated-Na-ions. Furthermore, by introducing various solvents, we

propose a feasible strategy to tune the energy storage capability of solvated-ion-

intercalation-based electrodes.

12

2.2 Experimental and computational details

2.2.1 Materials

Natural graphite was purchased from Bay Carbon Inc. and used without any

modification or post-treatment. The electrolytes were carefully prepared to

maintain low H2O contents (<20 ppm). The Na salt (NaPF6) and molecular sieves

were stored in a vacuum oven at 180°C before use. The dried Na salts were

dissolved in electrolyte solvents, including diethylene glycol dimethyl ether

(DEGDME), tetraethylene glycol dimethyl ether (TEGDME), and

dimethoxyethane (DME) at 1 M. The solutions were stirred at 80°C for 2 days, and

molecular sieves were used to remove residual H2O from the electrolyte

solutions.to tune the energy storage capability of solvated-ion-intercalation-based

electrodes.

2.2.2 Electrode preparation and electrochemical measurements

Graphite electrodes were prepared by mixing the active material (natural graphite,

90 wt%) with polyvinylidene fluoride binder (PVDF, 10 wt%) in an N-methyl-2-

pyrrolidone (NMP) solvent. The resulting slurry was uniformly pasted onto Cu foil,

dried at 120°C for 1 h, and roll-pressed. The average electrode thickness was ~40

μm. Test cells were assembled in a glove box into a two-electrode configuration

with a Na metal counter electrode. A separator of grade GF/F (Whatman, USA)

was sonicated in acetone and dried at 120°C before use. Electrochemical profiles

13

were obtained over a voltage range of 2.5 to 0.001 V using a multichannel

potentio-galvanostat (WonATech).

2.2.3 In Operando XRD analysis

For in operando XRD analysis, the holed coin cells, which were sealed by kapton

film with epoxy, were used. In operando XRD patterns for graphite were collected

on the 5A XRD beamline at PLS-II. The wavelength of the X-ray beam was 0.7653

Å, and XRD patterns were recorded as a set of circles on a Mar 345-image plate

detector in the transmission mode for approximately 1 min of exposure time. The

storage ring was operated with an electron energy of 3.0 GeV and a current of 300

mA. The total recording time was approximately 2.6 min because of the scanning

time of the image plate and transferring time of the spectral information. The two

theta angles of all the XRD patterns presented in this article have been recalculated

to corresponding angles for λ = 1.54 Å, which is the wavelength of the

conventional X-ray tube source with Cu Kα radiation for ease of comparison with

other published results.

2.2.4 Calculation details

Geometric optimizations of [Na-ether]+ complexes were conducted with the DFT

platform using Gaussian 09 program.17 All the molecular structures were fully

relaxed with the B3LYP/6-311G level. Structural relaxations of stage 1 and stage 2

GICs were performed with the Vienna ab initio simulation package (VASP).18 We

14

used a projector-augmented wave (PAW) pseudopotential19, as implemented in

VASP, and the exchange-correlation energy was addressed using the Perdew-

Burke-Ernzerhof (PBE) parameterized generalized gradient approximation

(GGA).20 In addition, the semi-empirical dispersion potential (DFT-D2)21 was

implemented to describe the van der Waals (vdW) interactions of graphite. All the

GIC structures were relaxed until the total energy of the system converged within

0.01 eV/Å.

15

2.3 Result and Discussion

2.3.1 Staging behavior upon Na intercalation

To probe the structural evolution of graphite during the intercalation/deintercalation,

we obtained synchrotron-based XRD patterns of the electrode in operando (5A

XRD beamline at PLS-II). For the analysis, a coin-type Na half-cell with a pin-hole

containing an ~40-μm thick graphite electrode and ~100 μl of a 1 M NaPF6 in

diethylene glycol dimethyl ether (DEGDME) electrolyte was discharged and

charged under a current density of 20 mA g-1graphite. Each diffraction pattern was

collected within a time corresponding to the capacity of ~0.87 mAh g-1graphite (~2.6

min), which enabled the detection of the structural transformation even with the

minutest alteration of Na contents. Throughout the electrochemical sodiation and

desodiation, the pristine graphite transformed into multiple new phases involving

one- or two-phase reactions and was completely restored to the pristine state after a

cycle (Figure 2-1). The highly reversible structural transformation implies the

stable capacity retention of the graphite electrode, which will be further discussed

later.

Surprisingly, the evolution of the XRD patterns of the graphite electrode in Figure

2-1 indicates a typical staging behavior during electrochemical sodium insertion

and extraction even though co-intercalation was expected. The main (002) peak at

27° splits into two peaks, which can be indexed as (00l) and (00l+1).22 Applying

16

Bragg’s law, we determined the l-value using equations 1 and 2, which resulted in

equation 3.

�(���) =��

�and�(�����) =

��

��� (1)

�(���) sin �(���) = �(�����) sin�(�����) (2)

� =�

[��� ɵ�������� ɵ���

��] (3)

, where d(00l) and d(00l+1) are the d-spacing values of the (00l) and (00l+1) planes,

respectively. Ic is the c lattice parameter of each stage GIC corresponding to the

repeated distance.

During the initial period of sodiation, the graphite undergoes a one-phase-like

transformation, possibly with many different stages changing sensitively with a

small alteration of the Na content. The transformation continues until the specific

capacity of graphite reaches 31 mAh g-1graphite (Na: C = 1/72 or 1.5 hour), forming a

certain stage of n GIC, where the n value will be determined later. The

measurements of θ00l and θ00l+1 at this state suggest l = 5 according to equation 3;

thus, the two peaks are indexed as (005) and (006), respectively. The determination

of l also results in Ic from equation 1 above, which is plotted as a function of charge

and discharge in the middle of Figure 2-1. Between 1.5 and 2.2 h of sodiation (Na:

C = 1/50), a biphasic reaction begins to occur, as indicated in the inset box of

Figure 2-1 left, forming another phase of a stage o GIC at the expense of stage n

17

GIC. After the completion of the biphasic reaction into stage o GIC, a stage p GIC

evolves. A single phase of stage p GIC is observed after 4 h of sodiation,

corresponding to a wide range of Na/C from 1/28 to 1/21 with no significant

change in the XRD patterns. During the final step of sodiation, as the state of

discharge exceeds 91%, new peaks at 12–14° begin to appear. Although further

study is required for clarification, we expect that these new peaks originate from

the in-plane superstructural ordering of the Na ions and ether solvent molecules,

which will be discussed in detail later. Note that the c lattice parameters (Ic) of the

stage n, o, and p GICs correspond to 18.50, 15.06, and 11.62 Å, respectively. The

differences between the Ic values are approximately 3.44 Å, which is similar to the

interlayer distance of the pristine graphite (3.35 Å). This finding indicates that the

stage numbers n, o, and p are consecutive integers of p+2, p+1, and p, respectively.

Considering that Ic of stage p (11.62 Å) is less than four times the interlayer

distance of pristine graphite (3.35 Å×4 =13.4 Å), p should be less than 4.

To determine the final stage index p, we employed chip-type highly ordered

pyrolytic graphite (HOPG) with 10×10×1.5 mm dimensions (0.8° mosaic spread)

and monitored the height of the HOPG perpendicular to the basal plane in real time

using a digital camcorder while intercalating Na and DEGDME solvent (Figure 2-

2a). The HOPG chip was placed on the Na-metal foil and between the two Na-

metal cubes to make contact with the graphite layers in both the parallel and

vertical directions. The intercalation does not occur in the absence of the electrolyte

18

even though the HOPG and Na metal are physically in contact each other (the first

row of Figure 2-2a and Figure 2-2b). This result contrasts with the case of lithium

metal, where the physical contact between lithium metal and graphite leads to rapid

lithiation even in the absence of the electrolyte and confirms the thermodynamic

instability of the sodiated graphite. However, as soon as we inject the electrolyte

(row 2, column1 of Figure 2-2a), the HOPG of lateral size of 10 mm immediately

swells from the interface, indicative of the Na-ether co-intercalation. Note that this

visually noticeable intercalation occurs in less than 2 s. In a few minutes (85

seconds), the height of the HOPG converges to 278% of that of the pristine state. A

slight imbalance of the height results from the poor contact between the HOPG and

Na-metal cube, as indicated by the yellow triangle in Figure 2-2a (row 3, column 4).

By tightening up the contact along the a and b directions of HOPG, the expansion

further proceeded rapidly. This observation clearly demonstrates that the Na

diffusion occurs along the a and b axes of graphite. In the end, the height of the

HOPG was saturated at 346% of that of the pristine state. This value is remarkably

close to the theoretically estimated height expansion (347%), assuming the

formation of a stage 1 GIC with a c lattice parameter of 11.62 Å (Figure 2-2c).

Similar calculations assuming stage 2 or 3 GICs yielded height expansions of 173%

and 116%, respectively, strongly supporting the conclusion that p is 1. Thus, o and

n are 2 and 3, respectively.

19

Figure 2-1. In operando synchrotron X-ray diffraction analysis of the structural

evolution of the ternary Na-ether-graphite system observed during electrochemical

solvated-Na-ion intercalation and deintercalation into/out of graphite in Na | 1M

NaPF6 in a DEGDME | graphite cell.

20

Figure 2-2. Expansion of highly ordered pyrolytic graphite (HOPG) along the c

axis with chemical Na-ether intercalation. (a) Real-time snapshots of HOPG under

direct contact with Na metal before and after exposure to 1 M NaPF6 in DEGDME

solution, (b) height of HOPG measured during the intercalation process, and (c)

schematic comparison of the height and c lattice parameter of graphite for

hypothetical stage 3 GIC, 2 GIC, and stage 1 GIC.

21

2.3.2 Solvated-Na-ion intercalation into graphite structure

To better understand the solvated Na intercalation mechanism, we attempted to

quantify the number of intercalated DEGDME molecules per Na ion in the graphite

by monitoring the weight of the electrode. The weight changes of the graphite

electrode were checked at several states of charge and discharge (Figure 2-3a). To

exclude the weight change from the residual free solvents adsorbed on the

electrode surface, the graphite electrodes were dried at 60 °C for 24 h after being

disassembled from the coin cells. All the sampling procedures were conducted in

an Ar-filled glove box to prevent contamination. The dashed lines in Figure 2-3a

show the theoretical weight changes of the electrode when different numbers of

DEGDME molecules per Na ion (b-value) were assumed to be intercalated into the

graphite. It is apparent that the weight of the graphite electrode follows the b=1 line,

which corresponds to a 1:1 ratio of the DEGDME molecules and Na ions in the

GICs. The experimental values are slightly higher than the theoretical ones because

of the solid-electrolyte-interphase (SEI) formation upon discharge. This finding is

also supported by the energy-dispersive X-ray spectroscopy analysis (Figure 2-3b),

which indicates that the ratio of O to Na atoms in the GICs is approximately three,

confirming that one DEGDME molecule ((CH3OCH2CH2)2O) is intercalated with

one Na ion.

We further built model structures to illustrate how the Na ions and DEGDME

molecules are co-intercalated in the graphite electrode, given that one Na ion is

22

intercalated into graphite with one DEGDME molecule. Because it is generally

believed that the cation and solvent molecules are co-intercalated, maintaining the

solvation complex form into graphite,16, 23-25 the most stable solvation structure of

the [Na-DEGDME]+ complex was first determined using first-principles

calculations (see Figure 2-4). The most stable [Na-DEGDME]+ complex is the

form where three oxygen atoms of DEGDME are simultaneously coordinating Na

ions, as illustrated in Figure 2-4. Maintaining this initial complex form in the

graphite, various configurations of stage 1 GICs were calculated (Figure 2-5), and

three representative models that most sensitively affect the interlayer space of GICs

were selected for comparison (Figure 2-3c, d, and Figure 2-6). One model consists

of a stage 1 GIC with single [Na-DEGDME]+ complex intercalation in the middle

of the graphite gallery (Figure 2-3c). Another model consists of double stacked

[Na-DEGDME]+ complexes located at one-third and two-thirds of the height of the

gallery space (Figure 2-3d). The final model contains triple stacked [Na-

DEGDME]+ complexes in the space (Figure 2-6). Among all the candidate

configurations, the double stacking of the complex was observed to be the most

energetically stable model structure, as described in Figure 2-3d. When we

consider the planar area density of the [Na-DEGDME]+ complex (68.13 Å2 per

complex) within a graphene layer (2.64 Å2 per carbon atom), the maximum Na

concentration in the stage 1 GIC is [Na-DEGDME]C25.8, [Na-DEGDME]C12.9, and

[Na-DEGDME]C8.6 for the single, double, and triple stacking models, respectively

(see Figure 2-7). Note that the experimental capacity of the graphite electrode was

23

~110 mAh g-1graphite, which corresponds to one [Na-DEGDME]+ complex per 21

carbon atoms, i.e., [Na-DEGDME]C21. This value exceeds the maximum density of

the single stacking [Na-DEGDME]+ complex model, confirming that the

intercalation geometry of the graphite electrode cannot be the single stack model

and is more likely to be the double or triple stack model. To further confirm the

structure of Na-DEGDME-graphite GICs, we compared the calculated interlayer

distances of the three different models with the experimentally observed value. The

three staging models resulted in interlayer distances of 7.43 Å, 11.98 Å, and 16.40

Å, respectively. Considering that the c lattice parameter of the stage 1 GIC is 11.62

Å, as measured by XRD analysis (see Figure 2-1), the second model with double

stacking of the complex is much more acceptable with only 3.1 % of a difference

(Figure 2-3d) compared with the other models.

The thermodynamic stability of the proposed structure (Figure 2-3d) was

investigated by DFT calculations to further support our model structure. We found

that the reaction enthalpy of [Na-DEGDME]+ co-intercalation into graphite is -0.87

eV, confirming that the co-intercalation of Na and DEGDME into graphite is

feasible. We also confirmed that the formation of triple stack model is

thermodynamically unstable, whereas the formation of double stack model is

thermodynamically favorable. We note that the vibrational, configurational,

rotational entropies of [Na-DEGDME]+ complex can play an important role in the

reaction Gibbs free energy. However, since [Na-DEGDME]+ stays freely both

24

before and after the insertion reaction, we believe that vibrational and rotational

entropy change will have limited effect on reaction free energy. The contribution of

configurational entropy is also negligible, considering that [Na-DEGDME]+

intercalants densely occupy the interlayer space between graphene layers.

We further examined the charge interaction between the intercalated [Na-

DEGDME]+ complex and graphene layers. The yellow region in Fig. 2-3d shows

the charge gained after [Na-DEGDME]+ intercalation (isosurface of 0.017 e-/Å3). A

major portion of the electron cloud, which belongs to the solvent molecules, resides

in approximately one-third and two-thirds of the unit cell height because of the

electron transfer from the solvating Na ions. Some portion of electrons from the Na

ions also moves toward the graphene layers, forming ionic bonds with electrons

donated from C-C bonds in the graphene layers (see Figure 2-8), which was

similarly observed in Li intercalated graphite.26

25

Figure 2-3. Geometry of solvated-Na intercalated graphite. (a) Weight change of

graphite measured at various state of charge and discharge. (b) Energy-dispersive

X-ray spectroscopy analysis of discharged sample. Calculated structure when (c)

one [Na-DEGDME]+ complex is and (d) two [Na-DEGDME]+ complexes are

intercalated in the interlayer spacing in graphite

26

Figure 2-4. Various configurations of [Na-DEGDME]+ solvation complex.

Energies relative to the most stable configuration are shown with each structure.

27

Figure 2-5. Various configurations of double complex intercalation of [Na-

DEGDME]+ in stage 1 structure.

28

Figure 2-6. A model of triple complex intercalation of [Na-DEGDME]+ in stage 1

structure.

29

Figure 2-7. Calculated planar area of (a) [Na-DEGDME]+ and (b) graphene layer.

For convenience, rectangular shape of [Na-DEGDME]+ is assumed and

intermolecular interactions are considered in Figure 2-7a. The planar areas of [Na-

DEGDME]+ and graphene layer are 68.13 Å2 per complex, and 2.64 Å2 per carbon

atom, respectively.

30

Figure 2-8. In-plane charge distribution at graphene layer after the intercalation of

[Na-DEGDME]+ complex. Intercalated Na+ ions donate electrons to graphene layer,

forming an ionic bond with electrons from C-C bonds in graphene layer.

31

2.3.3 Solvent dependency of Na intercalation

To understand the correlation between the Na solvation and intercalation, we

conducted electrochemical measurements using three different linear ether solvent

species with varying chain lengths (i.e., DME, DEGDME, and TEGDME) in

Figure 2-9. Notably, the specific capacity and shape of the charge/discharge

profiles were not greatly affected by the solvent species despite their different

molecular sizes and weights. The coordination number of complexes in each case

(DME/Na and TEGDME/Na ratios) was observed to be close to unity, which is

analogous to the Na-DEGDME electrolyte system (see Figure 2-10). The ex situ

XRD analyses of each electrode also revealed similar staging behavior with

intercalation, as observed in Figure 2-11, 2-12, and 2-13.

Even the XRD patterns of the fully discharged samples in Na-TEGDME, Na-

DEGDME, and Na-DME systems were almost identical, exhibiting sharp (002) and

(003) peaks at 15.2° and 22.9° with the same c lattice parameters of 11.62 Å

(Figure 2-9b). This finding implies that the chains of each solvent in [Na-ether]+

complexes do not stretch along the c direction and thus do not affect the spacing of

graphene layers, in accordance with the complex model suggested above. The

observed XRD patterns match well with the simulated ones from the double

stacking model in Figure 2-3d with [Na-ether]+ complexes residing parallel to the

graphene layers at one-third and two-thirds of the height of the gallery. We

observed that the ordering of [Na-DEGDME]+ complexes in the model structure

32

result in minor peaks in the 11˚–22˚ region in the simulated XRD patterns. These

peaks rise and diminish as the degree of ordering is artificially modified (see

Figure 2-14). This finding supports the presence of the in-plane superstructural

ordering of [Na-DEGDME]+ complexes at highly discharged graphite electrodes

and is consistent with the experimental result in Figure 2-1. Note that in Figure 2-

9b, the (002)/(003) peak ratios differ among the Na-DME, Na-DEGDME, Na-

TEGDME systems. The relative intensity of the (003) peak linearly increases with

the length of the solvent, as observed in Figure 2-9c for both simulations and

experiments. As the peak intensity of the (003) plane is determined by the electron

density in the plane, the higher electron density offered by the solvent with the

longer chain, i.e., Na-TEGDME, results in the smallest (002)/(003) peak intensity

ratio in Figure 2-9c.

Note that the Na storage potential increases as the chain length of the solvent

species increases. Voltage plateaus were observed at 0.59, 0.65, and 0.77 V (vs. Na)

in DME, DEGDME, and TEGDME, respectively (Figure 2-9d). This correlation

provides strong evidence for solvated-Na-ion intercalation. The solvent-dependent

Na storage voltage is attributable to the screening effect by the solvent molecules.

Generally, the Na storage voltage is described by the energy difference between

pristine (here, graphite) and intercalated products (here, the Na-solvent-graphite

compound). In our case, the energetics of the intercalated products primarily

determines the difference in the overall Na storage voltage, given the same pristine

33

material. Because neutral molecules in the graphite galleries can stabilize the

intercalated product by screening the repulsion between positively charged Na

ions,27 a stronger screening effect is expected with longer chain solvent species,

which in turn will increase the Na storage potential (Figure 2-9e).

It remains unclear why these unique phenomena are observed only in

electrochemical systems using specific solvents (i.e., DME, DEGDME, and

TEGDME). This solvent dependency of solvated-ion intercalation phenomenon is

also reported in Li-graphite systems,28-30 where various behaviors such as binary,

ternary intercalation and exfoliation of graphite are observed depending on the

solvent species. Although further study is needed, a possible interpretation is that

the linear ether solvents strongly solvate Na ions primarily because of the enhanced

affinity between the solvent and Na ions resulting from the so-called chelate

effect.31-32 Considering Na ion solvation with two distinctive groups of oxygen-

containing solvents, (i) solvents with a linear chain such as the linear ethers used in

this work and (ii) solvents without a linear chain such as cyclic ethers or carbonates,

multiple oxygen atoms in one solvent molecule can more efficiently surround the

Na ion if group (i) solvents are used due to the geometric flexibility. This behavior

will stabilize the solvation structure, as calculated in this work. To achieve a similar

solvation enthalpy (i.e., to provide the same donor power with solvent molecules)

with group (ii) solvents, more than one solvent molecule is required to form a

similar Na-O local environment because of their geometric limitation. In these two

34

cases, the enthalpy of solvation is approximately the same because similar donor

power is provided. However, there is a major difference in the two reactions, that is,

the number of species participating in each reaction. Solvation with group (i)

solvents involves two species (one solvent molecule and one Na ion) to form one

solvation complex; however, more than two species (more than one solvent

molecules and one Na ion) should participate in the latter to provide a similar Na-O

local environment. Therefore, if we compare the loss of the entropy of disorder in

the two cases, less entropy of disorder is lost in solvation with group (i) solvents,

resulting in more favorable solvation.

It is worthy of noting that a remarkably high reversibility in the co-intercalation is

possible for the Na-ether-graphite system even with the exceptionally large volume

change of the electrode. It is generally known that the volume change greatly

affects the cycle performance of the electrode for rechargeable batteries.33 The

large volume change of the electrode gradually degrades the structure of the

electrode, leading to severe performance decay. For example, the poor cycle

stability of a few important electrode materials, such as Si and SnO2, is attributed

to their large volumetric change.34-35 Although the graphite electrode undergoes an

exceedingly large volume change of 347% upon charge/discharge, it exhibits

excellent cycle stability up to 2,500 cycles (see Ref. 16 and Figure 2-15 and Figure

2-16). Note that no noticeable structure degradation in either the bulk or surface of

the graphite electrode was observed after cycling in the Na-DEGDME electrolyte

35

system (Figure 2-17 and Figure 2-18). We attribute the excellent reversibility to (i)

the formation of ionic binding between Na and the graphene layer, as observed in

Figure 2-8 despite the large expansion of the gallery space preventing the

exfoliation of graphene layers, and (ii) the much more stable solvation complex in

the graphite gallery compared with the propylene-carbonate-based solvation

complex, wherein intercalated propylene carbonate solvents are decomposed into

gas phases and readily exfoliate graphene layers.36-38 For more practical

applications of ternary GIC systems, it also needs to investigate Na-containing

electrolytes with better oxidative stability (>4.0 V vs. Na).

There have also been some reports on the electrochemical storage of cations in host

materials, which can be switched on with the aid of proper solvents similar to our

system, indicative of the importance of the role of electrolyte solvents.16, 39-40 In this

respect, our work enriches the pool of electrode materials, which has been limited

to the binary systems of guest ion-host materials, to versatile ternary systems of

guest ion-solvent-host materials. These findings will lead us to further

investigations toward energy-storage materials using solvated-ion intercalation.

36

Figure 2-9. Na storage potential depending on solvent species. (a) Typical

charge/discharge profiles of graphite electrode with three electrolyte solvents (inset:

solvent molecules) in Na half-cell configuration. (b) X-ray diffraction (XRD)

patterns of solvated-Na intercalated graphite compounds and simulated XRD

patterns of expanded graphite with repeated distance of 11.66 Å with/without

intercalants of [Na-DEGDME]+ complex. (c) Intensity ratio of (002)/(003) when

three electrolyte solvents are intercalated into graphite with Na ions. (d) dQ dV-1

analysis of graphite electrode with three electrolyte solvents. (e) Schematic of the

screening effect of the solvent on the Na storage potential.

37

Figure 2-10. Mass change of the electrodes upon discharge when (a) TEGDME

and (b) DME solvents are used.

38

Figure 2-11. Typical charge/discharge profile and ex-situ XRD patterns using 1M

NaPF6 in TEGDME electrolyte.

39

Figure 2-12. Typical charge/discharge profile and ex-situ XRD patterns using 1M

NaPF6 in DEGDME electrolyte.

40

Figure 2-13. Typical charge/discharge profile and ex-situ XRD patterns using 1M

NaPF6 in DME electrolyte.

41

Figure 2-14. (a) Simulated XRD patterns of two different state of [Na-DEGDME]+

ordering in graphite host. Structures of ordered, disordered structures used in

simulation are described in (b), (c), respectively. Note that the intensity ratio of

(002) / (003) does not change, whereas several minor peaks in 11˚-22˚ range

emerge or diminish due to the change of [Na-DEGDME]+ ordering.

42

Figure 2-15. Cycle stability of graphite electrode in Na half cells. Graphite

working electrode, Na metal counter electrode, and 1M NaPF6 in DEGDME

electrolyte are used.

43

Figure 2-16. Cycle stability of graphite electrode in Na half cells. Graphite

working electrode, Na metal counter electrode are used. 1M NaPF6 in TEGDME,

DEGDME, DME electrolytes are used, respectively.

44

Figure 2-17. Ex-situ XRD and XPS analyses before and after cycling. (a) XRD

patterns of graphite electrode before/after cycling. (b) XPS spectra of graphite

electrode before/after cycling.

45

Figure 2-18. SEM image of graphite electrode after cycling.

46

2.4 Conclusion

We investigated the solvated-ion intercalation chemistry of the ternary GIC system

of Na-ether-graphite, which has been poorly understood because of its complexity

compared with the simple binary GIC system of Li-graphite. In operando XRD-

electrochemical analysis and direct visualization coupled with DFT calculations

revealed the structural evolution of the graphite during the solvated-Na

intercalation. The Na intercalation occurs through multiple staging reactions, which

finally form first-stage GICs within a wide range of Na/C from 1/28 to 1/21 with

excellent reversibility. We proposed that the intercalated Na ions and ether solvents

are in the form of [Na-ether]+ complexes double stacked in parallel with graphene

layers in the graphite galleries. The correlation between the solvent species and

intercalation suggests the possible tunability of Na storage properties. The Na

storage potential increases as the chain length of the solvent species increases

because of the stronger screening effects of longer solvent molecules on the

repulsion between positively charged Na ions in the discharge product. This work

suggests that various unexplored ternary intercalation systems of guest ion-solvent-

host materials can provide unlimited opportunities to design electrodes with

superior performances beyond that of conventional electrode materials of

rechargeable batteries.

47

2.5 References

1. Ebert, L. B., Intercalation compounds of graphite. Annu. Rev. Mater. Sci.

1976, 6, 181-211.

2. Dresselhaus, M. S.; Dresselhaus, G., Intercalation compounds of graphite.

Adv. Phys. 1981, 30, 139-326.

3. Weller, T. E.; Ellerby, M.; Saxena, S. S.; Smith, R. P.; Skipper, N. T.,

Superconductivity in the intercalated graphite compounds C6Yb and C6Ca. Nat.

Phys. 2005, 1, 39-41.

4. Sugihara, K., c -axis conduction in graphite intercalation compounds.

Phys. Rev. B 1988, 37, 4752-4759.

5. Sugihara, K., c-axis conductivity and thermoelectric power in graphite

intercalation compounds. Phys. Rev. B 1984, 29, 5872-5877.

6. Cheng, H.; Sha, X.; Chen, L.; Cooper, A. C.; Foo, M.-L.; Lau, G. C.;

Bailey Iii, W. H.; Pez, G. P., An Enhanced Hydrogen Adsorption Enthalpy for

Fluoride Intercalated Graphite Compounds. J. Am. Chem. Soc. 2009, 131, 17732-

17733.

7. Grüneis, A.; Attaccalite, C.; Rubio, A.; Vyalikh, D. V.; Molodtsov, S. L.;

Fink, J.; Follath, R.; Eberhardt, W.; Büchner, B.; Pichler, T., Angle-resolved

photoemission study of the graphite intercalation compound KC8: A key to

graphene. Phys. Rev. B 2009, 80, 075431.

8. Kanetani, K.; Sugawara, K.; Sato, T.; Shimizu, R.; Iwaya, K.; Hitosugi, T.;

48

Takahashi, T., Ca intercalated bilayer graphene as a thinnest limit of

superconducting C6Ca. Proc. Natl. Acad. Sci. U. S. A. 2012, 109, 19610-19613.

9. Conti-Ramsden, M.; Nkrumah-Amoako, K.; Brown, N.; Roberts, E. L.,

The oxidation of aqueous thiols on a graphite intercalation compound adsorbent.

Adsorption 2013, 19, 989-996.

10. Park, S.; Ruoff, R. S., Chemical methods for the production of graphenes.

Nat. Nanotechnol. 2009, 4, 217-224.

11. Nishi, Y., Lithium ion secondary batteries; past 10 years and the future. J.

Power Sources 2001, 100, 101-106.

12. Aurbach, D.; Ein Eli, Y., The Study of Li Graphite Intercalation ‐ ‐

Processes in Several Electrolyte Systems Using In Situ X Ray Diffr‐ action. J.

Electrochem. Soc. 1995, 142, 1746-1752.

13. Nobuhara, K.; Nakayama, H.; Nose, M.; Nakanishi, S.; Iba, H., First-

principles study of alkali metal-graphite intercalation compounds. J. Power

Sources 2013, 243, 585-587.

14. Wang, Z.; Selbach, S. M.; Grande, T., Van der Waals density functional

study of the energetics of alkali metal intercalation in graphite. RSC Adv. 2014, 4,

4069-4079.

15. Jache, B.; Adelhelm, P., Use of Graphite as a Highly Reversible Electrode

with Superior Cycle Life for Sodium-Ion Batteries by Making Use of Co-

Intercalation Phenomena. Angew. Chem. Int. Ed. 2014, 53, 10169-10173.

16. Kim, H.; Hong, J.; Park, Y.-U.; Kim, J.; Hwang, I.; Kang, K., Sodium

49

Storage Behavior in Natural Graphite using Ether-based Electrolyte Systems. Adv.

Funct. Mater. 2015, 25, 534-541.

17. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.;

Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.;

Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.;

Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.;

Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.;

Montgomery Jr., J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M. J.; Heyd, J.;

Brothers, E. N.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.;

Raghavachari, K.; Rendell, A. P.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.;

Rega, N.; Millam, N. J.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo,

C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi,

R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.;

Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas,

Ö.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, Gaussian,

Inc.: Wallingford, CT, USA, 2009.

18. Kresse, G.; Furthmüller, J., Efficiency of ab-initio total energy

calculations for metals and semiconductors using a plane-wave basis set. Comput.

Mater. Sci. 1996, 6, 15-50.

19. Blöchl, P. E., Projector augmented-wave method. Phys. Rev. B 1994, 50,

17953-17979.

20. Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient

50

Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865-3868.

21. Grimme, S., Semiempirical GGA-type density functional constructed with

a long-range dispersion correction. J. Comput. Chem. 2006, 27, 1787-1799.

22. Seel, J. A.; Dahn, J. R., Electrochemical Intercalation of  PF 6 into

Graphite. J. Electrochem. Soc. 2000, 147, 892-898.

23. Sirisaksoontorn, W.; Adenuga, A. A.; Remcho, V. T.; Lerner, M. M.,

Preparation and Characterization of a Tetrabutylammonium Graphite Intercalation

Compound. J. Am. Chem. Soc. 2011, 133, 12436-12438.

24. Yamada, Y.; Usui, K.; Chiang, C. H.; Kikuchi, K.; Furukawa, K.; Yamada,

A., General Observation of Lithium Intercalation into Graphite in Ethylene-

Carbonate-Free Superconcentrated Electrolytes. ACS Appl. Mater. Interfaces 2014,

6, 10892-10899.

25. Moon, H.; Tatara, R.; Mandai, T.; Ueno, K.; Yoshida, K.; Tachikawa, N.;

Yasuda, T.; Dokko, K.; Watanabe, M., Mechanism of Li Ion Desolvation at the

Interface of Graphite Electrode and Glyme–Li Salt Solvate Ionic Liquids. J. Phys.

Chem. C 2014, 118, 20246-20256.

26. Yoon, G.; Seo, D.-H.; Ku, K.; Kim, J.; Jeon, S.; Kang, K., Factors

Affecting the Exfoliation of Graphite Intercalation Compounds for Graphene

Synthesis. Chem. Mater. 2015, 27, 2067-2073.

27. Kovtyukhova, N. I.; Wang, Y.; Berkdemir, A.; Cruz-Silva, R.; Terrones,

M.; Crespi, V. H.; Mallouk, T. E., Non-oxidative intercalation and exfoliation of

graphite by Brønsted acids. Nat. Chem. 2014, 6, 957-963.

51

28. Mizutani, Y.; Abe, T.; Inaba, M.; Ogumi, Z., Creation of nanospaces by

intercalation of alkali metals into graphite in organic solutions. Synth. Met. 2001,

125, 153-159.

29. Yamada, Y.; Takazawa, Y.; Miyazaki, K.; Abe, T., Electrochemical

Lithium Intercalation into Graphite in Dimethyl Sulfoxide-Based Electrolytes:

Effect of Solvation Structure of Lithium Ion. J. Phys. Chem. C 2010, 114, 11680-

11685.

30. Abe, T.; Kawabata, N.; Mizutani, Y.; Inaba, M.; Ogumi, Z., Correlation

Between Cointercalation of Solvents and Electrochemical Intercalation of Lithium

into Graphite in Propylene Carbonate Solution. J. Electrochem. Soc. 2003, 150,

A257-A261.

31. Schwarzenbach, G., Der Chelateffekt. Helv. Chim. Acta 1952, 35, 2344-

2359.

32. Hancock, R. D.; Martell, A. E., The Chelate, Cryptate and Macrocyclic

Effects. Comments Inorg. Chem. 1988, 6, 237-284.

33. Park, Y.-U.; Seo, D.-H.; Kwon, H.-S.; Kim, B.; Kim, J.; Kim, H.; Kim, I.;

Yoo, H.-I.; Kang, K., A New High-Energy Cathode for a Na-Ion Battery with

Ultrahigh Stability. J. Am. Chem. Soc. 2013, 135, 13870-13878.

34. Chan, C. K.; Peng, H.; Liu, G.; McIlwrath, K.; Zhang, X. F.; Huggins, R.

A.; Cui, Y., High-performance lithium battery anodes using silicon nanowires. Nat.

Nanotechnol. 2008, 3, 31-35.

35. Kim, H.; Kim, S.-W.; Park, Y.-U.; Gwon, H.; Seo, D.-H.; Kim, Y.; Kang,

52

K., SnO2/graphene composite with high lithium storage capability for lithium

rechargeable batteries. Nano Res.2010, 3, 813-821.

36. Buqa, H.; Würsig, A.; Goers, D.; Hardwick, L. J.; Holzapfel, M.; Novák,

P.; Krumeich, F.; Spahr, M. E., Behaviour of highly crystalline graphites in lithium-

ion cells with propylene carbonate containing electrolytes. J. Power Sources 2005,

146, 134-141.

37. Wagner, M. R.; Albering, J. H.; Moeller, K. C.; Besenhard, J. O.; Winter,

M., XRD evidence for the electrochemical formation of in PC-based electrolytes.

Electrochem. Commun. 2005, 7, 947-952.

38. Dey, A. N.; Sullivan, B. P., The Electrochemical Decomposition of

Propylene Carbonate on Graphite. J. Electrochem. Soc. 1970, 117, 222-224.

39. Pan, H.; Lu, X.; Yu, X.; Hu, Y.-S.; Li, H.; Yang, X.-Q.; Chen, L., Sodium

Storage and Transport Properties in Layered Na2Ti3O7 for Room-Temperature

Sodium-Ion Batteries. Adv. Energy Mater. 2013, 3, 1186-1194.

40. Hu, Z.; Zhu, Z.; Cheng, F.; Zhang, K.; Wang, J.; Chen, C.; Chen, J., Pyrite

FeS2 for high-rate and long-life rechargeable sodium batteries. Energy Environ. Sci.

2015, 8, 1309-1316.

53

Chapter 3. Conditions for reversible Na intercalation

in graphite: Theoretical studies on the interplay

among guest ions, solvent, and graphite host

(The content of this chapter has been published in Advanced Energy Materials.

[Yoon, G. et al., Advanced Energy Materials 2017, 7(2), 1601519.] – Reproduced

by permission of 2016 WILEY VCH Verlag GmbH & Co. KGaA, Weinheim‐ .)

3.1 Introduction

Intercalation of guest ions in crystals is the key fundamental reaction behind

modern rechargeable batteries. Graphite is the most widely used anode material in

Li-ion batteries (LIBs) because of its capability to store Li ions via intercalation. Its

high capacity and low redox potential to store Li ions combined with its low raw

material cost has made graphite one of the most successful anode materials for

LIBs to date.1-3 Recent studies have suggested that graphite can also serve as a

promising anode for K-ion batteries (KIBs) because of the intercalation capability

of the numerous K ions in its structure.4-6 Moreover, Rb and Cs ions, which are also

elements in the alkali group of the periodic table, are known to be capable of

intercalating into the graphite host.7 However, it has been widely reported that a

similar alkali ion, Na+, cannot be intercalated into the graphite host, and no stable

Na–C binary compound has been formed. The inability of graphite to store Na ions

54

has prohibited its use as an anode for Na-ion batteries (NIBs), an attractive post-

LIB energy storage system candidate, for many years.8-11 The dissimilar

intercalation behavior of alkali ion insertions into graphite results in significantly

different electrochemical performance of graphite electrodes in LIBs, NIBs, and

KIBs, and the fundamental origin of this varying behavior remains unclear.

Several theoretical studies have been conducted to investigate the stability of Na

intercalation into graphite.12-15 Nobuhara et al. observed that stage 1 Na-graphite

intercalation compounds (Na-GICs), such as NaC6 and NaC8, are unstable based on

density functional theory (DFT) calculations using the Perdew–Burke–Ernzerhof

(PBE) parameterization of the generalized gradient approximation (GGA) and

attributed the stress caused by the stretching of C–C bond lengths to the unstable

Na-GICs.12 Computational work performed by Okamoto also demonstrated that the

formation of NaC6 and NaC8 is unfavorable regardless of the selection of

exchange-correlation functionals in DFT, and this behavior was attributed to the

high redox potential of Na/Na+.13 Recently, Wang et al.14 and Liu et al.15 conducted

a more detailed investigation to understand the Na instability in graphite by

deconvoluting the formation energy (��) of Na-GICs into three factors using

Hess’s law: the reconstruction energies of the (i) alkali metal (AM) and (ii) graphite

framework upon GIC formation and (iii) the remaining �� . Although these

researchers noted that factor (iii) is responsible for the Na instability in the graphite

host, the underlying chemistry was not clear because factor (iii) in their works is

55

simply the sum of all energy contributions other than the reconstruction of the AM

and graphite. In addition, a very recent experimental study reported that Na ions

can be inserted into graphite when an appropriate solvent molecule co-intercalates

simultaneously.16-20 According to these reports, only specific solvent species, such

as linear ethers and their derivatives, make the reversible Na–solvent co-

intercalation phenomenon possible. Although this report suggests an alternative

approach to utilize graphite as a promising anode for NIBs, it indicates that the

interaction between the guest ion and intercalation host is complex and can be

significantly altered by the presence of solvent molecules. Furthermore, the

observation that some solvent molecules are more effective in promoting co-

intercalation implies a multipart interaction among the Na ions, graphite host, and

solvent molecules.

In this work, we explore the interplay among the guest ions, solvent, and graphite

host and attempt to broaden our understanding of the alkali-ion intercalation into

graphite. Based on a systematic investigation of AM-GIC (AM = Li, Na, K, Rb, Cs)

formation, it is demonstrated that the particularly repulsive local interaction

between Na ions and the graphene layer compared with that of all other alkali ions

dominantly destabilizes binary Na-GICs. Moreover, it is also shown that the

repulsive interaction can be significantly reduced when solvent molecules are co-

intercalated. We further investigate the solvent dependency of the Na intercalation

and propose conditions for reversible Na–solvent co-intercalation. We believe that

56

by unveiling the underlying mechanism for the Na–solvent co-intercalation, this

work extends our understanding of the co-intercalation chemistry in the graphite

host and provides insight into the design of a better system to utilize not only

graphite but also other intercalation-based hosts as electrode materials for

rechargeable batteries.

57

3.2 Computational details

Information on the geometries, ��s, and electronic structures of AM-GICs was

obtained by performing DFT calculations using the Vienna Ab initio Simulation

Package (VASP).21 Exchange-correlation energies were described using spin-

polarized GGA parameterized using the PBE functional.22 We used projector

augmented wave (PAW) pseudopotentials as implemented in VASP.23-24 A standard

pseudopotential is used for C, and s semi-core states are treated as valence states

for alkali metals except for Na, which requires a very high cutoff energy. We

confirmed that the use of standard Na pseudopotential had a negligible effect on

formation energies. For charge density analysis, s semi-core states are treated as

valence states for Na. A plane-wave basis set was used with an energy cutoff of 500

eV (800 eV for charge density analysis), A plane-wave basis set was used with an

energy cutoff of 500 eV, and geometric relaxations were performed until the

remaining force in the system converged within 0.02 eV Å-1. To describe the van

der Waals force between graphene layers in the AM-GICs, we adopted the method

suggested by Grimme et al. (DFT-D3).25 The validity of the DFT-D3 scheme was

confirmed by calculation of the structural properties of graphite, LiC6, and KC8 and

comparison with experimental values (Table 3-1). We note that, when using van der

Waals functional, hard pseudopotential and a very high cutoff energy ensures the

acccurate description of several layered systems, but the results from our

conditions are reasonably accurate enough to be taken considering the advantage of

58

computational cost. The structures, ��s, and lowest unoccupied molecular orbital

(LUMO) levels of [Na-solventx]+ complexes were calculated using the Gaussian 09

code.26 All the molecules were optimized at the B3LYP/6-311G (3df) level of

theory.27-28

59

��������� (Å) ����� (Å) ���� (Å)

DFT-D3 3.46 3.76 5.30

Exp. 3.3629 3.7130 5.357

Table 3-1. Comparison of c-lattice parameters obtained by experiments and PBE-

D3 calculation.

60

3.3 Results and discussion

3.3.1 Understanding the origin of unfavorable Na intercalation into graphite

To investigate the thermodynamic stability of stage 1 AM-GICs, the �� values of

MC6 and MC8 (M = Li, Na, K, Rb, Cs) were calculated, as shown in Figure 3-1. ��

is defined as

�� = ���� − � × �� − �� ,

where ���� (� = 6 or 8) denotes the energy of the MCx formula unit, �� is the

energy of graphite per carbon atom, and �� is the energy of the

thermodynamically stable metallic phase of M per metal atom. The initial

structures (i.e., the interlayer ordering of graphene and metal layers) of MC6 and

MC8 were adopted from experimental reports on LiC630 and KC8.

31 Consistent with

the previous findings, the calculations confirmed that the formation of binary Na-

GICs is energetically unfavorable, whereas other AMs form stable stage 1 binary

GICs.7, 12-15 We also note that the composition of stable stage 1 AM-GICs differs

among AMs. As the intercalant becomes larger, the MC8 composition is preferred;

LiC6 is more stable than LiC8, whereas K, Rb, and Cs prefer to form KC8, RbC8,

and CsC8, respectively. The detailed reason for this trend will be discussed in the

following sections.

To obtain a better understanding of the Na instability in the formation of AM-GICs,

we categorized the possible factors that were expected to have major effects on ��

61

of the AM-GICs. Because stage 1 AM-GICs are composed of alternating metal and

graphene layers, it is reasonable to expect that the structural deviation of the AMs

and graphite from their pristine states greatly contributes to the total ��s. For

example, it is mathematically possible to extract the energy penalty of partial metal

decohesion or graphite deformation, as illustrated in Figure 3-1b (1,2). In addition,

the formation of an AM-GIC involves local interaction between the constituting

single layer of graphene and AM (the adsorption of metal on graphene in Figure 3-

1b). These three possible major contributing factors to the formation of AM-GICs

are schematically illustrated in Figure 3-1b. We note that similar approaches have

been used by a few research groups.14-15 These researchers also decomposed the

total �� into contributing components using Hess’s law, where the components

were the destabilization energies of the AMs and graphite framework, which

correspond to 1 and 2 in Figure 3-1b of our model, and the remainder of ��. The

previous studies defined the remainder energy as the binding energy15 or energy

gained from charge transfer,14 however, the remainder energy mathematically

includes all the energy contributions except for the reconstruction energies of the

AMs and graphite framework. In our model, we exclusively extracted the local

interaction between the AM and graphene layers from the remainder energy to

more precisely quantify the contribution.

We first calculated the destabilization energy of metal reconstruction (��,�����)

using the following equation:

62

��,����� = ��,��� − ��,��� .

Here, ��,��� is the energy of the metal within a reconstructed lattice (either MC6

or MC8 lattice) per metal atom and ��,��� is the energy of the equilibrium bcc

AM per atom. Figure 3-2a demonstrates that ��,����� first decreases and then

slightly increases as the size of the AM increases, with minimum values at K and

Rb for MC6 and MC8, respectively. This behavior of ��,����� is closely related to

the difference in bonding distances between the AM atoms in GIC frameworks and

pristine bcc metals. As observed in Table 3-2, AMs in AM-GICs should have a

fixed distance to each other within the ab-plane at the given intercalation sites in

MC6 (4.32 Å) or MC8 (4.93 Å), whereas the equilibrium bond distances of AMs in

bcc metals are 2.97, 3.63, 4.57, 4.90, and 5.32 Å for Li, Na, K, Rb, and Cs,

respectively. K and Rb exhibit the smallest lattice mismatch along the ab-plane in

the MC6 and MC8 structures, respectively, and thus have the smallest ��,�����.

This result also explains the trend that larger intercalants prefer to form MC8, as

observed in Figure 3-1a. Considering the large equilibrium interatomic distances of

Rb and Cs in pristine metals (>> 4.5 Å), the intercalation sites with small metal–

metal distance (4.32 Å in MC6) would generate a strong repulsion among

intercalated metals; thus, the MC8 structure with larger metal–metal distance is

preferred. Nevertheless, no anomaly is observed in the trend of ��,����� for Na

intercalation in either GIC structure and does not account for the instability of Na

intercalation.

63

Next, we investigated the destabilization energy of the graphite framework upon

AM insertion, ��,��������, which is defined as

��,�������� = ��,��� − �� ,

where ��,��� is the energy of graphite with the reconstructed lattice per C atom

and �� is the energy of pristine graphite per C atom. In the calculation of ��,���,

we injected electrons into the system to describe the charged graphite framework in

GICs as the charge transfer arises because of the nature of AM ionization in the

host upon AM insertion. Figure 3-2b shows the relative ��,�������� assuming the

electrons are fully transferred from AM to graphite regardless of the metal species.

For comparison, the energies were rescaled with respect to that of the graphite

structure in LiC6. ��,�������� decreases as the interlayer distance between

graphene layers increases according to the basic electromagnetic principle that the

electrostatic repulsion between charged species is inversely proportional to the

distance between them. This monotonous trend of ��,�������� also does not

explain the peculiar Na instability.

The local interaction between AM ions and the graphite framework was probed

within a simplified model consisting of a single layer of graphene and a metal atom

(Figure 3-3). The interaction energy �� is defined as

�� = ����������� − �� − ��������� ,

where ����������� is the energy of the metal-adsorbed graphene, �� is the

64

energy of the metal atom, and ��������� is the energy of the single layer of

graphene. The relative values of �� with respect to �� of the Li adsorption are

plotted in Figure 3-2c. Unlike the previously investigated factors (��,����� and

��,��������), Na ion binding to a single graphene layer is uniquely unstable by ~0.5

eV compared with that using other AMs.32 The trend of �� also corresponds

remarkably well to that of �� of GICs (Figure 3-1a), strongly suggesting that the

basic interaction between a single metal ion and graphene layer dominates the trend

and affects the instability of Na-GIC formation. To understand this abnormal

phenomenon, we examined the local charge redistribution by performing Bader

analysis and compared the amount of charge transferred for all AM species (Table

3-3). All the AMs exhibited Bader charges of more than +0.89, indicating that the

interaction between a metal atom and graphene layer is primarily ionic. Despite the

high ��,��, the amount of charge transfer falls in a similar range of 0.89–0.91

electrons per atom regardless of the metal species. We further investigated the

distribution of the transferred charges by calculating the plane-averaged charge

densities (Figure 3-4). However, the distributions of additional charges from AMs

were also similar to each other, implying that the unfavorable interaction between

Na ions and graphene does not simply arise from classical electrostatic interaction

or its derivatives. We note that the trends of atomization energy and ionization

energy are also monotonous for AM series. Nevertheless, our calculations of the

energy components hitherto clearly indicate that the basic unfavorable local

65

interaction between a single Na ion and graphene layer is the underlying reason for

the unstable Na-GIC formation. However, the intrinsic aspect of Na ion adsorption

on a carbon layer that leads to this anomaly remains unclear, and is only speculated

to arise from the basic materials property, rather than the classical electrostatic

interaction.

Based on our calculations, it can be assumed that if the unfavorable local

interaction between Na ions and graphene layers is mitigated, graphite may become

capable of accommodating Na ions in its framework. One plausible approach is to

dilute the direct interaction between AM ions and graphene with the inclusion of

screening moieties. In this respect, recent experimental reports on the reversible Na

intercalation behavior in graphite using the Na-solvent co-intercalation

phenomenon16-20 can also be explained by the screening effect of the intercalated

solvent molecules, which prevents direct Na ion–graphene interaction. To elucidate

the nature of the Na–solvent co-intercalation, we recalculated �� between the

AM–solvent complex and graphene layer (Figure 3-2d). Diethylene glycol

dimethyl ether (DEGDME) was used as a solvent molecule in the calculation

because it has been experimentally reported to be reversibly co-intercalated in

graphite with Na.16-20 Unlike the trend of �� between the pure AM and graphene

layer in Figure 3-2c, the Na-solvent complex did not exhibit noticeable instability

in its interaction with the graphene layer. This observation was further supported by

the calculation of the plane-averaged charge density, where the charge distribution

66

was dominated by the solvent molecule in the AM–solvent complexes, thus

effectively screening the AMs (Figure 3-5). Because of the presence of the solvent

molecule, the individual characteristics of the AM ions are significantly lost,

resulting in an almost identical interaction with the graphite host and finally the

Na–solvent co-intercalation in graphite. Indeed, our preliminary calculation using

the structure model obtained from our previous work18 resulted in a negative

formation energy of Na-DEGDME co-intercalated graphite (-0.87 eV), indicating

the feasible co-intercalation of Na and DEGDME into graphite.

67

Figure 3-1. (a) �� values of AM-GICs in MC6 and MC8 structures (AM = Li, Na,

K, Rb, Cs). (b) Contributing factors to �� values of AM-GICs.

68

Figure 3-2. (a) ��,����� values upon lattice reconstruction from bcc structure to

MC6 and MC8 structures. (b) Relative ��,�������� upon AM intercalation and

charge transfer. (c) Relative �� between AM and a single layer of graphene. (d)

Relative �� between AM-solvent complexes and a single layer of graphene. The

energy scales in (b), (c), and (d) are referenced to the values obtained for Li.

69

Table 3-2. Bond lengths of AMs in bcc lattice ���� and comparison of ���� to

the AM lattices in MC6 and MC8 structures in both ab- and c- directions.

70

Figure 3-3. Model structure for the calculation of pure interaction between AM and

the graphene layer. A vacuum slab of ~15 Å was used.

71

*Electronegativity : C (2.55) Li (0.98) Na (0.93) K (0.82) Rb (0.82) Cs (0.79)

Table 3-3. Bader charges of AMs in metal-adsorbed graphene.

72

Figure 3-4. (a) Plane-averaged charge density of metal-adsorbed graphene.

Because of the nature of AMs, different characteristics of the charge distributions,

such as the peak of the planar charge density and distance from graphene at

maximum charge density, are observed. (b) Charge distribution of Li-adsorbed

graphene. All the AM-adsorbed graphene samples exhibited identical charge

distributions. Isosurface level is set to 0.005 e-/Å3.

73

Figure 3-5. (a) Plane-averaged charge density of [AM-DEGDME]-adsorbed

graphene. Because of the screening effect of the solvent molecules, similar charge

distributions were observed for all the AMs. (b) Charge distribution of [Li-

DEGDME]-adsorbed graphene. All the [AM-DEGDME]-adsorbed graphene

samples exhibited identical charge distributions. Isosurface level is set to 0.03 e-/Å3.

74

3.3.2 Conditions for reversible Na intercalation into graphite

The calculations above successfully demonstrate that the inclusion of screening

moieties such as solvent molecules can negate the peculiar interaction between Na

and graphite. However, note that experimental reports on the reversible

intercalation of Na–solvent complexes into graphite have been limited to certain

solvent species such as linear ethers and their derivatives.16-20 This fact indicates

that the negating effect by solvation does not always guarantee reversible

intercalation into graphite and is dependent on the solvent selection. Our

preliminary experiment on the Na–solvent co-intercalation behavior also suggests

that the co-intercalation into graphite is only practical for linear ethers, as described

in Figure 3-6a, after testing various solvent species (linear/cyclic ethers and

carbonates, as shown in Figure 3-6b). For example, although electrochemical

activity was clearly observed when using a propylene carbonate (PC) electrolyte

during a reduction process, no oxidation occurred, indicative of irreversible

intercalation and subsequent side reactions, such as the exfoliation of graphite

observed in the scanning electron microscopy (SEM) image in Figure 3-7, which is

similar to the Li–PC electrolyte system.33-36 Previous studies of the Li–PC

electrolyte system suggested that the exfoliation with Li insertion is due to the

instability of the solvated Li in the solvent, proposing the donor number of solvents

(or corresponding Li solvation energy) as a determining factor of the co-

intercalation.34, 37-38 However, according to our analysis in Table 3-4, an explicit

75

comparison between the donor number of solvents and the electrochemical activity

does not reveal a clear trend in the Na–graphite system. Cyclic ethers have higher

donor numbers than linear ethers; however, they do not exhibit the co-intercalation

phenomenon (Figure 3-6a). This indiscrepancy between the donor number and the

electrochemical activity could arise from the different ionic size between Na ion

and SbCl5 ion, which is used for the derivation of donor number. The different

ionic size of solute ions could result in the different solvation structure between

Na-solvent complex and SbCl5-solvent complex, possibly leading to the different

solvation enthalpy and the disagreement of the solvation energy (derived from the

solvation enthalpy of Na) and the donor number (derived from the solvation

enthalpy of SbCl5). Previous work by Gutmann revealed this steric effect for the

case of small vanadyl ion.39 Therefore, the direct estimation of electrochemical

activity with the donor number of solvents without considering the Na solvation

energy is not reliable.

To verify the conditions for the co-intercalation and solvent dependency in the Na–

graphite system, the thermodynamic stability of Na–solvent complexes was first

estimated by calculating the solvation energy �� values in various solvents and

comparing them with experimental observations. Based on previous works, it was

speculated that the high stability of the solvated Na ion would tend to prevent the

desolvation process and promote the co-intercalation.34, 40 �� was defined as

�� = �[�����������]� − � × �������� − ���� ,

76

where �[�����������]� is the energy of the Na–solvent complex, �������� is the

energy of the solvent molecule, and ���� is the energy of the Na ion. Because the

solvation number � can vary in a dynamic situation in the electrolyte, various �

values were applied to each solvent species, and the maximum � was adopted

from experimental observations in Li solvation chemistry.41-43 Note that the

interaction with anions in Na salts is neglected.17 Figure 3-8a presents the

calculated �� values of all the investigated Na–solvent complexes. When a Na ion

is solvated by a single solvent molecule, i.e., � = 1, a relatively stronger solvation

(red bars in Figure 3-8a) is observed between Na and the solvent, which follows

the order of linear ethers (�� < -2 eV), cyclic carbonates (-1.80 eV < �� < -1.75

eV), linear carbonates (-1.55 eV < �� < -1.44 eV), and cyclic ethers (-1.41 eV <

�� < -1.20 eV). Linear ethers strongly solvate Na ions because they contain

multiple oxygen atoms in their structure that can simultaneously stabilize the Na

ion. This trend of the solvation strength among different solvent molecules is

consistent with the experimental findings that co-intercalation is more frequently

observed in ether-based electrolyte systems. As � increases (blue and black bars in

Figure 3-8a), the Na ion is further stabilized for all solvents because of the

increased Na–O coordination. Based on the �� values at each step, the desolvation

energy ���� values of the Na–solvent complexes were calculated using the

following equation, as shown in Figure 3-8b:

����,� = �[�������������]� + �������� − �[�����������]�.

77

The results are described in Figure 3-8c. For all the solvent species, ����,� is

higher than ����,�, which indicates that the desolvation of one solvent molecule

from [Na-solvent]+ requires more energy than that from [Na-solvent2]+. This

phenomenon occurs because the interaction between the Na ion and second solvent

molecule is shielded by the first-neighboring solvent molecule, which leads to a

weaker interaction.44 The considerably smaller second (or third) ���� compared

with the first one results in the highly coordinated complexes being partially

desolvated before intercalation and the intercalated complexes generally having �

= 1.18 According to the ���� results in Figure 3-8c, the highest ���� of the [Na-

solvent2]+ complexes (� = 2) was 1.50 eV. Considering that the electrochemical

co-intercalation of [Na-solvent2]+ (� = 2) was never observed for such solvents,

this finding suggests that �� > 1.5 eV is required to achieve stable co-intercalation

from the �� perspective alone. Therefore, solvents such as dimethyl carbonate

(DMC), dioxolane (DOL), and tetrahydrofuran (THF) would not provide

sufficiently stable solvation of Na ions for the co-intercalation even in the first

solvation coordination. In addition, the absence of electrochemical activity of the

Na–graphite system under diethyl carbonate (DEC, �� of 1.55 eV) and ethylene

carbonate (EC, �� of 1.75 eV) electrolytes (as observed in Figure 3-6a) indicates

that �� = 1.75 eV is also not sufficiently high for the co-intercalation. This finding

roughly narrows down the candidate solvent molecules suitable for co-intercalation

with respect to ���� to ethylene glycol dimethyl ether (DME), DEGDME,

78

tetraethylene glycol dimethyl ether (TEGDME), and PC, as indicated in bold in

Figure 3-8c. We note that the presence of solid electrolyte interphase (SEI) layers

could also affect the co-intercalation behavior of bulky Na-solvent complexes by

blocking their insertion. However, the recent report showed the reversible

intercalation of Na and DEGDME in the presence of preformed SEI layers.20 In

addition, since the composition of SEI layers varies depending on the electrolytes

used and is not yet fully understood, the explicit investigation on the effect of SEI

layers is beyond our scope, and will be conducted in the following work along with

experiments.

In addition to the stability of Na–solvent complexes with respect to �� itself, the

intercalated complexes should remain chemically stable in graphite galleries for the

reversible Na–solvent co-intercalation because there is a possibility of their

chemical decomposition after the initial co-intercalation. To estimate the relative

stability of each solvent molecule in graphite, we simply calculated the LUMO

levels of the [Na-solvent]+ molecules and compared their relative positions with

respect to the Fermi level of the graphite (the green shaded region in Figure 3-

8d).45 The highest occupied molecular orbital levels were not considered because

the additional electron extraction from the electropositive [Na-solvent]+ molecule is

not likely to occur in the graphite host. Figure 3-8d plots the calculated LUMO

levels of the candidates for the Na–solvent co-intercalation, which reveals that the

LUMO levels of the [Na-linear-ether]+ complexes (in a blue shaded circle) are

79

mostly higher than the others. The LUMO levels of [Na-DEGDME]+ and [Na-

TEGDME]+ are higher than the Fermi level of graphite, indicating that it would be

difficult for electrons to be injected into these complexes (or for complexes to be

reduced) and is less likely to initiate the decomposition reaction and subsequent

degradation of graphite. The [Na-PC]+ complex exhibits the lowest LUMO level

which is substantially lower than the Fermi level of graphite, implying more facile

chemical reduction upon co-intercalation. We note that uncertainty in the Fermi

level of graphite could arise upon the formation of GICs with the structural

reorganization of the graphite framework, as described in Figure 3-1b (2); therefore,

the reversible intercalation of [Na-DME]+, whose LUMO level is relatively close to

the Fermi level of graphite, could still be possible. The instability of [Na-PC]+

complex is analogous to previous experimental observations for Li–PC co-

intercalation,46-48 where the intercalated Li–PC undergoes electrochemical

decomposition accompanying the evolution of a gas phase, leading to the

exfoliation of graphite. In our own experiment, we also observed that Na-

intercalated graphite in a PC electrolyte is not stable (Figure 3-7). Several

cleavages were generated in the sample because of the exfoliation of graphite from

the decomposition of the intercalated complexes. This finding suggests that the

chemical stability of [Na-solvent]+ complexes in graphite, which can be roughly

speculated from the relative position of the LUMO, is necessary for the reversible

co-intercalation.

80

The Na–solvent co-intercalation behavior into graphite is schematically

summarized in Figure 3-9 with respect to the thermodynamic and chemical

stabilities of Na–solvent complexes. Our results indicate that among the candidates

considered, [Na-linear-ether]+ complexes could be reversibly intercalated into

graphite because of their high �� of Na and chemical stability in graphite. If �� is

too small, Na–solvent complexes easily desolvate before the intercalation and/or

further intercalation does not proceed because Na alone cannot form a GIC. Even

with the high ��, the complex in the graphite host should be chemically stable to

prevent the decomposition of the Na–solvent GIC and to ensure the reversible co-

intercalation. When the complex is not stable, the chemical decomposition

involving gas evolution may lead to the exfoliation of graphite upon co-

intercalation.

81

Figure 3-6. (a) Cyclic voltammetry curves of various Na–solvent systems; 1 M

NaPF6 salts were used for all tests. (b) The solvent species used to investigate the

solvent dependency of the co-intercalation phenomenon (DME: ethylene glycol

dimethyl ether, DEGDME: diethylene glycol dimethyl ether, TEGDME:

tetraethylene glycol dimethyl ether, THF: tetrahydrofuran, DOL: dioxolane, DMC:

dimethyl carbonate, DEC: diethyl carbonate, EC: ethylene carbonate, PC:

propylene carbonate).

82

Figure 3-7. SEM image of graphite after discharge in 1 M NaPF6 in PC solvent.

The cleavages observed in the sample indicate the exfoliation of graphite.

83

Table 3-4. Material properties of investigated solvents.

84

Figure 3-8. (a) �� of Na–solvent complexes. (b) Energy diagram of [Na-DMEx]+

desolvation process. (c) ���� values of Na–solvent complexes. The ���� values

of potential candidates for feasible co-intercalation are highlighted in bold. (d)

LUMO levels of [Na-solvent]+ complexes. The Fermi level of graphite is shaded

green.

85

Figure 3-9. Summary of solvent dependency of the Na–solvent co-intercalation

behavior. The structure of Na-solvent co-intercalated graphite (upper right) is

adopted from ref. 18.

86

3.4 Conclusion

We attempted to understand the thermodynamic instability of Na intercalation into

graphite by investigating various AM-GICs (AM = Li, Na, K, Rb, Cs). Our

calculations indicated that the unstable Na-GIC formation can be attributed to the

peculiarly unfavorable local Na–graphene interaction. Screening of Na with solvent

molecules was observed to be an effective strategy to promote Na intercalation

because it prevents the direct interaction between Na and graphene. Based on an

investigation of the solvent dependency in the reversible co-intercalation, we

proposed that the high �� of Na and chemical stability of Na–solvent complexes

are critical for the reversible co-intercalation. This claim was further supported by

comparing experimental results on the electrochemical activity with the calculated

thermodynamic and chemical stabilities of Na–solvent complexes. The

relationships among the guest ions, solvent, and intercalation host observed in this

study can be extended to general intercalation-based electrochemical systems and

hint at an effective strategy to optimize the system performance.

87

3.5 References

1. Goodenough, J. B.; Park, K.-S., The Li-Ion Rechargeable Battery: A

Perspective. J. Am. Chem. Soc. 2013, 135, 1167-1176.

2. Etacheri, V.; Marom, R.; Elazari, R.; Salitra, G.; Aurbach, D., Challenges

in the development of advanced Li-ion batteries: a review. Energy Environ. Sci.

2011, 4, 3243-3262.

3. Ji, L.; Lin, Z.; Alcoutlabi, M.; Zhang, X., Recent developments in

nanostructured anode materials for rechargeable lithium-ion batteries. Energy

Environ. Sci. 2011, 4, 2682-2699.

4. Komaba, S.; Hasegawa, T.; Dahbi, M.; Kubota, K., Potassium

intercalation into graphite to realize high-voltage/high-power potassium-ion

batteries and potassium-ion capacitors. Electrochem. Commun. 2015, 60, 172-175.

5. Luo, W.; Wan, J.; Ozdemir, B.; Bao, W.; Chen, Y.; Dai, J.; Lin, H.; Xu, Y.;

Gu, F.; Barone, V.; Hu, L., Potassium Ion Batteries with Graphitic Materials. Nano

Lett. 2015, 15, 7671-7677.

6. Jian, Z.; Luo, W.; Ji, X., Carbon Electrodes for K-Ion Batteries. J. Am.

Chem. Soc. 2015, 137, 11566-11569.

7. Dresselhaus, M. S.; Dresselhaus, G., Intercalation compounds of graphite.

Adv. Phys. 2002, 51, 1-186.

8. Kundu, D.; Talaie, E.; Duffort, V.; Nazar, L. F., The Emerging Chemistry

of Sodium Ion Batteries for Electrochemical Energy Storage. Angew. Chem. Int. Ed.

88

2015, 54, 3431-3448.

9. Yabuuchi, N.; Kubota, K.; Dahbi, M.; Komaba, S., Research Development

on Sodium-Ion Batteries. Chem. Rev. 2014, 114, 11636-11682.

10. Slater, M. D.; Kim, D.; Lee, E.; Johnson, C. S., Sodium-Ion Batteries. Adv.

Funct. Mater. 2013, 23, 947-958.

11. Kim, S.-W.; Seo, D.-H.; Ma, X.; Ceder, G.; Kang, K., Electrode Materials

for Rechargeable Sodium-Ion Batteries: Potential Alternatives to Current Lithium-

Ion Batteries. Adv. Energy Mater. 2012, 2, 710-721.

12. Nobuhara, K.; Nakayama, H.; Nose, M.; Nakanishi, S.; Iba, H., First-

principles study of alkali metal-graphite intercalation compounds. J. Power

Sources 2013, 243, 585-587.

13. Okamoto, Y., Density Functional Theory Calculations of Alkali Metal (Li,

Na, and K) Graphite Intercalation Compounds. J. Phys. Chem. C 2014, 118, 16-19.

14. Wang, Z.; Selbach, S. M.; Grande, T., Van der Waals density functional

study of the energetics of alkali metal intercalation in graphite. RSC Adv. 2014, 4,

4069-4079.

15. Liu, Y.; Merinov, B. V.; Goddard, W. A., Origin of low sodium capacity in

graphite and generally weak substrate binding of Na and Mg among alkali and

alkaline earth metals. Proc. Natl. Acad. Sci. 2016, 113, 3735-3739.

16. Jache, B.; Adelhelm, P., Use of Graphite as a Highly Reversible Electrode

with Superior Cycle Life for Sodium-Ion Batteries by Making Use of Co-

Intercalation Phenomena. Angew. Chem. Int. Ed. 2014, 53, 10169-10173.

89

17. Kim, H.; Hong, J.; Park, Y.-U.; Kim, J.; Hwang, I.; Kang, K., Sodium

Storage Behavior in Natural Graphite using Ether-based Electrolyte Systems. Adv.

Funct. Mater. 2015, 25, 534-541.

18. Kim, H.; Hong, J.; Yoon, G.; Kim, H.; Park, K.-Y.; Park, M.-S.; Yoon, W.-

S.; Kang, K., Sodium intercalation chemistry in graphite. Energy Environ. Sci.

2015, 8, 2963-2969.

19. Zhu, Z.; Cheng, F.; Hu, Z.; Niu, Z.; Chen, J., Highly stable and ultrafast

electrode reaction of graphite for sodium ion batteries. J. Power Sources 2015, 293,

626-634.

20. Jache, B.; Binder, J. O.; Abe, T.; Adelhelm, P., A comparative study on the

impact of different glymes and their derivatives as electrolyte solvents for graphite

co-intercalation electrodes in lithium-ion and sodium-ion batteries. Phys. Chem.

Chem. Phys. 2016, 18, 14299-14316.

21. Kresse, G.; Furthmüller, J., Efficiency of ab-initio total energy

calculations for metals and semiconductors using a plane-wave basis set. Comput.

Mater. Sci. 1996, 6, 15-50.

22. Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient

Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865-3868.

23. Blöchl, P. E., Projector augmented-wave method. Phys. Rev. B 1994, 50,

17953-17979.

24. Kresse, G.; Joubert, D., From ultrasoft pseudopotentials to the projector

augmented-wave method. Phys. Rev. B 1999, 59, 1758-1775.

90

25. Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H., A consistent and accurate

ab initio parametrization of density functional dispersion correction (DFT-D) for

the 94 elements H-Pu. J. Chem. Phys. 2010, 132, 154104.

26. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.;

Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.;

Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.;

Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.;

Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.;

Montgomery Jr., J. A.; Peralta, J. E.; Ogliaro, F.; Bearpark, M. J.; Heyd, J.;

Brothers, E. N.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.;

Raghavachari, K.; Rendell, A. P.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.;

Rega, N.; Millam, N. J.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo,

C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi,

R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.;

Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas,

Ö.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, Gaussian,

Inc.: Wallingford, CT, USA, 2009.

27. Becke, A. D., Density functional thermochemistry. III. The role of exact ‐

exchange. J. Chem. Phys. 1993, 98, 5648-5652.

28. McLean, A. D.; Chandler, G. S., Contracted Gaussian basis sets for

molecular calculations. I. Second row atoms, Z=11–18. J. Chem. Phys. 1980, 72,

5639-5648.

91

29. Trucano, P.; Chen, R., Structure of graphite by neutron diffraction. Nature

1975, 258, 136-137.

30. Guerard, D.; Herold, A., Intercalation of lithium into graphite and other

carbons. Carbon 1975, 13, 337-345.

31. Rüdorff, W.; Schulze, E., Über Alkaligraphitverbindungen. Z. Anorg. Allg.

Chem. 1954, 277, 156-171.

32. Rytkönen, K.; Akola, J.; Manninen, M., Density functional study of alkali-

metal atoms and monolayers on graphite (0001). Phys. Rev. B 2007, 75, 075401.

33. Moon, H.; Tatara, R.; Mandai, T.; Ueno, K.; Yoshida, K.; Tachikawa, N.;

Yasuda, T.; Dokko, K.; Watanabe, M., Mechanism of Li Ion Desolvation at the

Interface of Graphite Electrode and Glyme–Li Salt Solvate Ionic Liquids. J. Phys.

Chem. C 2014, 118, 20246-20256.

34. Yamada, Y.; Takazawa, Y.; Miyazaki, K.; Abe, T., Electrochemical

Lithium Intercalation into Graphite in Dimethyl Sulfoxide-Based Electrolytes:

Effect of Solvation Structure of Lithium Ion. J. Phys. Chem. C 2010, 114, 11680-

11685.

35. Xu, K.; von Cresce, A., Interfacing electrolytes with electrodes in Li ion

batteries. J. Mater. Chem. 2011, 21, 9849-9864.

36. Kim, H.; Yoon, G.; Lim, K.; Kang, K., Graphite as versatile electrode for

rechargeable batteries. Chem. Commun. 2016, 52, 12618-12621.

37. Inagaki, M.; Tanaike, O., Determining factors for the intercalation into

carbon materials from organic solutions. Carbon 2001, 39, 1083-1090.

92

38. Abe, T.; Mizutani, Y.; Tabuchi, T.; Ikeda, K.; Asano, M.; Harada, T.; Inaba,

M.; Ogumi, Z., Intercalation of lithium into natural graphite flakes and heat-treated

polyimide films in ether-type solvents by chemical method. J. Power Sources 1997,

68, 216-220.

39. Gutmann, V., Coordination chemistry in non-aqueous solutions. Springer-

Verlag: 1968.

40. Abe, T.; Kawabata, N.; Mizutani, Y.; Inaba, M.; Ogumi, Z., Correlation

Between Cointercalation of Solvents and Electrochemical Intercalation of Lithium

into Graphite in Propylene Carbonate Solution. J. Electrochem. Soc. 2003, 150,

A257-A261.

41. Matsui, T.; Takeyama, K., Li+ adsorption on a metal electrode from

glymes. Electrochim. Acta 1998, 43, 1355-1360.

42. Soetens, J.-C.; Millot, C.; Maigret, B., Molecular Dynamics Simulation of

Li+BF4- in Ethylene Carbonate, Propylene Carbonate, and Dimethyl Carbonate

Solvents. J. Phys. Chem. A 1998, 102, 1055-1061.

43. Glover, W. J.; Larsen, R. E.; Schwartz, B. J., Nature of Sodium

Atoms/(Na+, e−) Contact Pairs in Liquid Tetrahydrofuran. J. Phys. Chem. B 2010,

114, 11535-11543.

44. Grossfield, A.; Ren, P.; Ponder, J. W., Ion Solvation Thermodynamics

from Simulation with a Polarizable Force Field. J. Am. Chem. Soc. 2003, 125,

15671-15682.

45. Shiraishi, M.; Ata, M., Work function of carbon nanotubes. Carbon 2001,

93

39, 1913-1917.

46. Buqa, H.; Würsig, A.; Goers, D.; Hardwick, L. J.; Holzapfel, M.; Novák,

P.; Krumeich, F.; Spahr, M. E., Behaviour of highly crystalline graphites in lithium-

ion cells with propylene carbonate containing electrolytes. J. Power Sources 2005,

146, 134-141.

47. Wagner, M. R.; Albering, J. H.; Moeller, K. C.; Besenhard, J. O.; Winter,

M., XRD evidence for the electrochemical formation of in PC-based electrolytes.

Electrochem. Commun. 2005, 7, 947-952.

48. Xu, K., Nonaqueous Liquid Electrolytes for Lithium-Based Rechargeable

Batteries. Chem. Rev. 2004, 104, 4303-4418.

94

95

Chapter 4. Deposition and stripping behavior of

lithium metal in electrochemical systems: Continuum

mechanics study

(The content of this chapter has been published in Chemistry of Materials. Adapted

with permission from [Yoon, G. et al., Chemistry of Materials 2018, 30, 6769].

Copyright (2018) American Chemical Society.)

4.1 Introduction

The use of Li metal as an electrode in rechargeable batteries offers an unparalleled

opportunity to boost the energy density of current lithium-ion batteries, as Li metal

is capable of delivering the largest theoretical capacity (~3860 mAh g−1) at the

lowest redox potential (−3.04 V vs. standard hydrogen electrode) of anode

materials known to date.1-2 However, the practical application of a Li metal anode

remains far from realization because of issues arising from the dendritic growth of

Li metal during electrochemical cycling, which raise serious safety concerns.3-7 For

instance, irregularly grown Li metal such as filaments on the anode or Li metal

debris detached from the electrode can penetrate the separator and contact the

cathode, resulting in an internal short circuit and thermal runaway. In addition,

repeating the formation and removal of Li dendrites inevitably exposes a fresh

surface of Li metal, which constantly consumes the electrolyte to form an

96

unusually thick solid electrolyte interphase (SEI) layer on the electrode.8-9 These

undesirable phenomena continuously deteriorate the coulombic efficiency, causing

premature cell failure.

Several strategies have been adopted experimentally to address these issues. One

widely used approach is the introduction of a mechanically robust layer at the

surface to physically suppress the uncontrolled growth of Li dendrites.10-20 Various

physical coatings such as Al2O3, Li3PO4, solid Li ion conductors, h-BN, and

different types of carbon have been used as a protection layer for the Li metal

surface, resulting in some improvements.13-19 Electrolyte additives such as

fluoroethylene carbonate and LiNO3 have also been adopted to induce the

formation of a dense and mechanically stable SEI layer to protect the Li surface.11-

12 Alternatively, attempts have been made to control the flux of Li ions near the

electrode surface. The addition of Li halide salts was successfully demonstrated to

selectively enhance Li ion transport at the interface of the electrode, stabilizing the

electrodeposition.20-21 Cs ions dissolved in the electrolyte could more evenly

distribute the flux of Li ions near the Li metal surface because of the resulting

electrostatic repulsive force.22 The use of vertically aligned Cu microchannels

exhibited the enhanced cycling and rate performance of Li deposition and stripping

due to the regulation of the current density distributions along the microchannel

walls.23 Although these treatments were partly successful in enhancing the stability

of the Li metal anode, as confirmed by the prolonged cycle life, the thin protection

97

layers were eventually cracked by the morphological growth of Li metal. In

addition, attempts to control the local Li flux near the electrode surface could not

ultimately suppress the propagation of dendrites, especially at high current rates

and large utilization levels, leading to cell failure. Moreover, the intrinsic inhibition

of dendritic growth for extended cycles under practical operation conditions has yet

to be achieved.

In this respect, it is important to revisit the fundamentals of Li electrodeposition

and stripping in an electrochemical system. Indeed, some theoretical studies have

aimed to understand the basic Li deposition behavior. Mayers et al. modeled the Li

deposition behavior in a particle-based theory, using coarse-grained simulation

based on diffusion-limited aggregation theory.24 Rosso and Chazalviel et al.

investigated the initial nucleation and growth of Li dendrites using an analytical

continuum model of the system.25-28 By interpreting the evolution of the ion

concentrations in a simplified uniform one-dimensional model, they suggested that

the ion concentration at the electrode would fall to zero after a certain time, called

Sand’s time (referring to the original work by Sand29), after which the potential on

the electrode surface would start to diverge. In addition, it was claimed that at

Sand’s time, the dendrites begin to appear to escape the instability of the system.27

Later, optical microscopy analysis revealed that the dendritic growth of Li metal

occurred after Sand’s time.30 Although these works regarding Sand’s time

successfully describe the initiation of Li dendrites and offer important insight into

98

the conditions of abnormal growth, a comprehensive understanding of the effects

of the practical conditions of Li deposition and stripping in the electrochemical

systems (such as the applied current rates or the history of the current rates and

surface properties of the electrode) on the formation of the initial morphology,

growth behavior, and propagation of the Li dendrites remains lacking.31 A

systematic understanding of the Li growth mechanisms and behaviors with respect

to the various experimental conditions would potentially enable practical

application of Li metal batteries.

In this work, we investigate the key factors affecting electrochemical Li deposition

and stripping by performing continuum mechanics simulations to monitor the

evolution of the Li morphology on the electrode. The rate of Li deposition/stripping,

shape of the electrode surface, conductivity and uniformity of the SEI layer, and

effect of the current density history on Li deposition/stripping were studied as

representative practical parameters affecting the geometry of Li deposits. Our

findings here not only elucidate the quantitative Li growth behaviors under various

applied electrochemical conditions but also provide insight into the possible origins

of different shapes of Li deposits and the formation of electrically isolated Li metal

debris.

99

4.2 Computational details

All the simulations on lithium electrodeposition were conducted using the

electrodeposition module with tertiary current distribution and Nernst–Planck

interface in COMSOL Multiphysics.32 The behaviors of the charged species in an

electrolyte were treated using the Nernst–Planck equation with the assumption of

charge conservation described below:

�� = −��∇�� − �������∇��

������

= 0.

Here, �� is the flux of the ionic species i, �� is the diffusion coefficient, �� is

the concentration, �� is the valence, �� is the mobility, �� is the electrolyte

potential of each species, and � is the Faraday constant. The contribution of

convection to the flux was neglected. The material balances were conserved using

the following mass conservation law:

�����

+ ∇ ∙ �� = 0.

The reaction kinetics at the electrode surface were described using the

concentration-dependent Butler–Volmer equation:

� = �� ��� exp �����

��� − �� �

−����

����,

100

where �� is the exchange current density; �� and �� are the dimensionless

concentrations of the reduced and oxidized species, respectively; �� and �� are

the anodic and cathodic charge transfer coefficients, respectively; � is the

activation overpotential; � is the gas constant; and � is the temperature. The

resulting electrodeposition was assumed to occur in the normal direction to the

boundary with a velocity �:

� =�

��

�

�,

where � and � are the molar mass and density of Li, respectively.

The equations above govern the ion transport behavior in the electrolyte and the

electrodeposition reaction at the electrode/electrolyte surface. All the other

boundaries were treated as insulating, as described by the following equation:

�� ∙ � = 0.

Here, � represents the vector normal to each boundary.

Each charge transfer coefficient was set to 0.5 and the temperature was fixed at 300

K in all the simulations. The initial Li ion diffusion coefficient in the electrolyte

was set to 7.5 × 10−11 m2 s−1, which is close to the values for conventional

electrolytes.33 We used an initial Li ion concentration of 1 M, and the overpotential

for Li deposition was kept in the range of 0.4–0.7 V to control the rates of the

deposition and stripping reaction. The other input parameters were systematically

101

controlled to monitor the effect of variables, such as the rate of Li deposition, shape

of the electrode surface, SEI layer conductivity and uniformity, and repeating cycle

of Li deposition and stripping. To elucidate how the specific variables in

electrochemical cells affect the Li metal evolution on the electrode, the conditions

were independently imposed in the following simulations.

102

4.3 Results and discussion

The standard model used for the overall simulation is described in Figure 4-1a.

Because a reaction on an ideally flat and clean surface necessarily results in

uniform and monotonous deposition, we intentionally built a surface with reference

bumps to induce irregularity of the ion flux, which better reflects the general

experimental conditions. Using this model as an initial geometry, the evolution of

Li deposition behavior was comparatively examined under diverse conditions.

103

Figure 4-1. Evolution of Li deposits for different deposition rates. (a) Reference

model used for simulations. Geometry after initial deposition at (b) slow and (c)

fast deposition rates. The gray lines represent the initial geometry before deposition.

(d) Expected shape after continuous deposition at slow rate. The dotted circles

represent pores that could be generated after physical contact between deposits. (e)

Geometry after further deposition from (d). Deposits from neighboring bumps will

meet and eventually form a mossy-like shape, whereas the high-rate condition

yields vertical growth of Li with many branches, forming a needle-like shape. The

scale bars are 2-μm long. The utilization of Li is identical in (b) and (c). The

contour levels of the potential are displayed every 2.5 meV.

104

4.3.1 Effect of deposition rate on Li growth behavior

The initial deposition on the electrode with the reference bumps (2 × 2 × 2 μm) was

performed using a relatively slow rate and is described as a reference in Figure 4-

1b. In the conditions of slow deposition and stripping, we applied the overpotential

of 0.4 V to the system, while a higher overpotential of 0.7 V was applied for fast

deposition and stripping. In the figure, the background color indicates the local Li

ion concentration in the electrolyte, the green lines are equipotential lines, and the

red arrows represent the intensity and direction of the Li ionic current density. It is

apparent that the Li deposition was locally concentrated at the corners of the

surface bumps. More in-depth examination of this initial stage (see Figure 4-2 for

time-dependent geometry evolution) revealed that the ionic current densities were

higher around the corners, making them preferential deposition sites. However, the

Li ion concentration at the corner did not drop to zero at the surface because of the

relatively low current density, and the Li deposit was rather spherical, covering the

corner. However, when a high current rate was applied, as shown in Figure 4-1c,

the Li deposition occurred much more vertically toward the counter electrode,

which was accompanied by the formation of a number of branches. The

equipotential lines (green lines) shown in Figure 4-1c are significantly denser than

those in Figure 4-1b around the corner (or the forefront of the Li branches after the

growth), indicating that a strong electric field was locally developed, inducing a

high flux of the Li ionic current. For this high-rate deposition, even a small

105

inhomogeneity would induce a non-negligible disturbance of the current

distribution and a correspondingly high localized ionic current density, leading to

directional growth toward the counter electrode as well as the formation of

branches (Figure 4-3). Another significant difference from the low-rate condition

was the depletion of the Li ion concentration to zero near the surface of the

electrode, shown by the dark blue color in Figure 4-1c. This depletion of Li ions at

the surface and simultaneous observation of directional and branching growth of Li

metal agrees well with the early theoretical work of Chazalviel.27

Even though the initial growth under the slow deposition conditions (Figure 4-1b)

was less directional, the continuing deposition under this condition would result in

physical contact among neighboring deposits on the side, as shown in Figure 4-1d.

It is noteworthy that the merging of the growing deposits inevitably involves the

formation of a porous structure underneath the growing forefront of the Li metal, as

indicated by the dotted circles in the figure. Even if the electrodeposition

proceeded further, the inner areas with the dotted circles would not participate in

the deposition reaction and would not be filled in, as illustrated in Figure 4-1e.

However, further deposition occurs mostly at the forefront of the Li deposits,

giving the neighboring deposits a chance to grow and merge again. Repeating this

process would lead to an overall porous geometry, resembling the mossy shape of

Li metal deposits observed experimentally.30

Based on the results for different current rates, it can be concluded that the initial

106

deposition occurs primarily at deposition seeds where the equipotential lines are

densely distributed for geometric reasons, followed by their evolution into different

forms depending on the current rate. The slow deposition condition does not induce

severe preferential deposition at regions of minor irregularity, leading to less

directional growth; however, a porous structure eventually develops because of the

initial uneven geometry. In contrast, at high current rates, preferential deposition

with the formation of a number of branches is easily triggered even by a small

inhomogeneity, and the complete depletion of Li ions is often observed at the

surface of the electrode, leading to unidirectional and dendritic growth of Li metal.

107

Figure 4-2. Snapshots for time-dependent Li electrodeposition using a relatively

slow rate.

108

Figure 4-3. Snapshots for time-dependent Li electrodeposition using a relatively

fast rate.

109

4.3.2 Effect of surface geometry on Li growth behavior

As local geometric irregularities were observed to act as seeds for the abnormal

growth of Li, we attempted to understand the effect of the initial surface geometry

using different surface shapes during Li deposition. Triangular- and circular-shaped

bumps were compared with the previous case of square-shaped bumps, as shown in

Figure 4-4. All the other parameters were the same as those for Figure 4-1c. Figure

4-5a shows the final shape of the Li deposits starting from the surface with

triangular bumps. Dendritic growth appeared to occur from the exposed corner of

the triangular bump. Because of the densely populated equipotential lines around

the sharp corners, the preferential depositions led to extremely directional and

branching growth of Li metal (Figure 4-6). Notably, the final length of the dendritic

deposits was much longer than that observed in Figure 4-1c, implying that the

shape and number of initial seeds are important factors in determining the length

and size of dendrites in the Li deposition. However, the deposition on the surface

with smooth circular bumps yielded quite uniform and dense growth, as shown in

Figure 4-5b. The lack of irregular areas on the surface resulted in well-distributed

current along the smooth surface with a large area without current concentrations at

certain points, which resulted in a shorter length of deposits, as shown in Figure 4-

7. However, if the deposition proceeds further and the surface irregularities are

accumulated, points with high local current density are generated accompanied by

the evolution of filamentary growth with branches. Fast deposition will also

110

accelerate the onset of the branching growth, therefore, the irregular deposition can

be eventually observed at the smooth surface after an extended deposition.

Nevertheless, a smoother initial surface delays the onset of branching, providing

more space for the dense and uniform deposition of Li within a certain utilization

level.

111

Figure 4-4. Models used for simulation with (a) triangular and (b) circular surface

shape.

112

Figure 4-5. Evolution of Li deposits starting from an initial surface geometry with

(a) triangular and (b) circular bumps. The gray lines represent the initial geometry

before deposition, and the scale bars are 2-μm long. The utilization of Li is

identical in (a) and (b), and the contour levels of potential are displayed every 2.5

113

meV.

114

Figure 4-6. Snapshots for time-dependent Li electrodeposition at the triangular

surface.

115

Figure 4-7. Snapshots for time-dependent Li electrodeposition at the circular

surface.

116

4.3.3 Effect of SEI layer properties on Li growth behavior

In the previous sections, we used simple models consisting of Li metal electrodes

and an electrolyte for the electrodeposition without the presence of additional

phases on the interface. However, it is widely known that a SEI layer is typically

generated at the surface of electrodes because of the decomposition of the

electrolyte, and this layer plays a crucial role in battery operation.1, 34 Typical SEI

layers in practical cells exhibit low electrical conductivities and reasonably high Li

ion conductivities; thus, they prevent further electrochemical decomposition of the

electrolyte while allowing the passage of Li ions. The salts, solvent, and electrode

materials used in the cell significantly affect the properties of the SEI layers such

as the constituting elements, electrical conductivity, and Li ion diffusivity, thereby

affecting the performance of the electrochemical cell. To account for this SEI layer,

we introduced an artificial layer at the surface of the electrode with different

transport properties, as shown in Figure 4-8. A 200-nm-thick interphase layer with

a Li ion diffusivity 100-times-lower than that of the electrolyte was adopted as a

reference model in the calculations, considering that the Li ion diffusivity in a solid

medium (e.g., constituents of SEI or solid-state electrolyte) is generally orders of

magnitudes lower than that in liquid electrolytes.35

Figure 4-9a depicts the Li deposition behavior with the presence of the SEI layer

on the electrode. The most notable difference compared with the previous results is

that the Li growth is much more dendritic, indicating that the tendency for

117

preferential deposition is far greater under this condition. It should be noted that

Figure 4-9a shows Li deposits deposited at a relatively lower deposition rate

(applied overpotential of 0.5 V) than that used for the previous cases (0.7V)

because the use of the same deposition rate as that in Figure 4-1c and 4-5 yielded

severe branching growth even from the initial stage. The dramatic color change

near the surface of the electrode in Figure 4-9a provides a clue about the cause of

this phenomenon, as the Li ion concentration was much higher outside the SEI

layer and rapidly decreased within the SEI layer upon approaching the electrode

surface. Because the transport of Li ions is comparatively hampered within the SEI

layer, the supply of Li ions to the electrode surface was not sufficiently rapid for

the incessant reaction, inducing the significant concentration gradient within the

SEI layer. The right panel in Figure 4-9a shows the Li ion concentration along the

vertical line across the interface, which also confirms the abrupt decrease of the Li

ion concentration in the SEI layer. Under this severe concentration gradient

condition, even a small protrusion of Li metal would cause significant distortion of

the equipotential lines of the ionic flux, resulting in a high local current density

near the protrusion and triggering dendritic growth. The dendritic growth of Li

metal not only occurred near the original corner region but also in other areas, as

shown in Figure 4-9a, indicating that minor protrusions could also induce dendritic

growth even at slow current rates.

Since the SEI layer in the simulation was simply described by presenting a surface

118

layer with reduced ionic diffusivity compared with that of the electrolyte, the

diffusion in the SEI layer retains a characteristic bi-ionic conducting property of

the conventional liquid electrolyte, where both Li ion and anion are mobile.

However, considering that typical SEI layer is mostly composed of inorganic

compounds, its single-ionic conducting characteristic should be carefully examined.

In this regard, we conducted a simulation using the SEI layer with single-ionic

conducting nature, while maintaining all other conditions identical. Figure 4-10

compares the Li ion and the potential profile in the electrolyte region, when single

and bi-ionic conducting SEI layer is adopted, respectively. Since the anions are

immobile in single-ionic conductor, Li ion concentration gradient is not observed

in the SEI as shown in Figure 4-10a. In addition, the potential gradient becomes

linear, indicating that the Ohmic drop in the SEI is the sole source inducing the

potential profile. On the other hand, the potential gradient is parabolic in bi-ionic

conducting SEI, implying that both Ohmic drop and the Li ion concentration

gradient affect the potential profile. This difference leads to slightly less severe

branching growth of Li metal with the single-ionic SEI layer. Nevertheless, the

branching growth is still observed, because sluggish SEI acts as high resistance

regardless of its conducting nature, resulting in steep Ohmic drop in SEI layer, as

described in Figure 4-11. The high local current density is thus induced at the

surface, and the generation of minor protrusions leads to the branching growth as

discussed in previous sections.

119

Our observations hitherto consistently suggest that the high local current density at

the surface induced by the steep potential gradient leads to the unwanted branching

growth of Li. Nevertheless, the findings above propose that the potential gradient

near the surface can be regulated using the single-ionic conductor SEI layer, since

it diminishes the effect of the Li concentration gradient. The impact would be more

dramatic for ideal solid electrolytes with purely single-ion conducting

characteristics, particularly for the case when the Li metal and solid electrolytes are

stabilized without the formation of SEI layer. In this case, as described in Figure 4-

12, the Ohmic drop is the sole source determining the potential profile in the

electrolyte region. It would result in the linear potential gradient near the solid

electrolyte interface without the Li ion concentration gradient, thus much smoother

Li metal growth can be achieved (Figure 4-13). Moreover, it implies that the

thickness of the single ionic conductor (or solid electrolyte) could be an important

design criteria for the uniform Li deposition, since the linear potential gradient near

the surface would be governed by the thickness of the electrolyte with a given

applied voltage. The observations in Figure 4-9a imply that the presence of the SEI

layer can substantially affect the deposition behavior and trigger unwanted

morphological Li metal growth because of the inferior ionic transport that induces

severe Li concentration gradients within the SEI layer. In this respect, we further

examined the effect of properties of the SEI layer, such as the Li ion diffusivity and

layer thickness, on Li metal growth on the electrode. Figure 4-9b shows the

morphological evolution of the Li deposits when an SEI layer with higher Li ion

120

diffusivity (10 times faster than that of the SEI layer in Figure 4-9a) was adopted.

Because the Li ion transport through the SEI layer was faster, the bottleneck in the

supply of Li ions toward the electrode surface became less problematic. Therefore,

the concentration gradient within the SEI layer was less abrupt, as shown in the

right panel of the figure, and the resulting geometry displayed much smoother

growth compared with the previous case. Moreover, reduction of the SEI thickness

from 200 to 50 nm resulted in less severe dendritic growth of Li on the surface

(Figure 4-14), indicating the importance of the Li ion transport kinetics through the

SEI layer in the formation of Li dendrites. The diffusion length of Li ions in the

SEI layer is thought to be smaller for a thinner SEI layer; thus, the supply of Li

ions to the electrode surface becomes effectively facile, suppressing the build-up of

the concentration gradient within the SEI layer.

These results imply that inducing the formation of a highly conductive and thin SEI

layer on the electrode is of critical importance in tailoring the Li growth. The

formation of an ideal SEI layer with Li ion diffusivity equivalent to that in the

liquid electrolyte would prevent the development of an undesirably large

concentration gradient within the SEI layer, inhibiting the local high current

density near any possible protrusion. Tailoring the dielectric constant of the SEI

layer can also be an effective strategy for uniform Li growth, considering that the

medium with high dielectric constant screens the applied electric field and reduces

the effective electric fields, lowering the local current density. We note, however,

121

that this argument is only valid under the assumption that the reduction process

from Li ion to metallic Li is sufficiently fast on the electrode surface and not rate-

limiting. In addition, our current model system does not account for certain

properties of the SEI layer, such as its mixed-phase nature and mechanical

properties and the dynamic process of rupture and reformation at its surface.

Nevertheless, we believe that the interplay between the Li ion transport properties

in the SEI layer and the evolution of the dendrites observed in this simple system

can be applied to the local evolution of Li dendrites. Because SEI layers observed

in experiments are often irregular in terms of thickness and conductivity because of

the reasons described above, the local SEI region with sluggish Li ion transport is

expected to be more vulnerable to dendritic growth, serving as the weakest link,

according to our model studies. This speculation of non-uniform Li growth is

consistent with previous work showing that the non-homogenous nature of SEI

layers is more prone to trigger the irregular and dendritic growth of Li metal

deposits.36

122

Figure 4-8. Model used for simulation with 200nm-thick SEI layers. Li ion

diffusivity in SEI layers is 100 times as sluggish as that in electrolyte. The

thickness and the Li ion diffusivity were controlled to see their effect in Li

deposition behavior.

123

Figure 4-9. Evolution of Li deposits with the presence of a 200-nm-thick surface

SEI layer. The Li ion concentration profile along the yellow dotted line is also

shown. The Li ion conductivity of the layer was set to (a) 100 times and (b) 10

times lower than that of the electrolyte. The gray lines represent the initial

geometry before deposition, and the scale bars are 1-μm long. The utilization of Li

124

is identical in (a) and (b), and the contour levels of potential in (a) and (b) are

displayed every 10 meV.

125

Figure 4-10. Li ion concentration and electrolyte potential profile in electrolyte

region using (a) single-ionic conducting and (b) bi-ionic conducting SEI layer.

126

Figure 4-11. Li deposition shape using single and bi-ionic conducting SEI.

127

Figure 4-12. Li ion concentration and electrolyte potential profile in electrolyte

region using (a) single-ionic conducting and (b) bi-ionic conducting electrolyte. It

is assumed that the interface between the Li metal and the electrolyte is stabilized

without the formation of SEI layer.

128

Figure 4-13. Li deposition shape using single and bi-ionic conducting electrolyte.

It is assumed that the interface between the Li metal and the electrolyte is stabilized

without the formation of SEI layer.

129

Figure 4-14. Shape of Li deposits after a deposition simulation with 50 nm-thick

SEI layer.

130

4.3.4 Consequences of repeated cycles of deposition and stripping

Thus far, we have attempted to investigate the conditions that can trigger dendritic

growth of Li metal during deposition as well as the influencing factors. However,

unlike in typical metal electrodeposition processes, practical batteries are operated

for thousands of charge and discharge cycles, involving the same number of

repeated deposition and stripping processes. Therefore, it is of importance to probe

the progressive effects of the cycles of deposition and stripping on the Li growth

behavior, particularly when each deposition and stripping condition begins to

deviate from the given initial conditions. As a representative case, we applied a

reverse bias with different stripping rates for the Li deposits obtained after a single

deposition step and comparatively monitored the morphological evolutions.

Figure 4-15 shows the evolutions of the geometry of Li metal for two different

stripping conditions (right panels) starting from the Li deposit deposited at a fast

rate (left panel). When the stripping process was performed at a similarly fast rate

as the deposition, the morphology returned to the initial geometry with high

reversibility (no side reactions that could affect the nature of the

electrode/interface/electrolyte during the cycles were considered in the

calculations). This result was observed because the stripping reactions were the

most active at the corners or at points with large curvature, where the equipotential

lines were densely concentrated, as previously discussed for electrodeposition. This

preferential stripping therefore resulted in the stripping direction toward the

131

reduction of curved points, which is simply the reverse process of the deposition

and induced the recovery of the smooth surface. However, at a relatively low

current rate, isotropic stripping occurred uniformly throughout the Li deposits.

Although the uniform process was desirable during the deposition, stripping under

this condition can induce highly curved points in regions with irregular surfaces in

the deposits, as illustrated in Figure 4-15. In particular, isotropic thinning around

the necking region (as indicated by the black arrows) eventually led to the

separation of a fragment of Li deposits from the bulk electrode, producing Li debris.

To confirm that this thinning under slow stripping conditions causes the formation

of Li debris from the necking regions, we artificially built a model containing

similar regions and performed a stripping simulation. Figure 4-16 confirms that

analogous behavior was consistently displayed. This phenomenon, known as the

formation of ‘dead Li’, has been observed in many experiments and has been

blamed for the severe degradation of cycle stability and internal electrical

shortage.37-38 Our experimental results shown in Figure 4-15 and Figure 4-16

clearly demonstrate that the slow stripping of Li deposits with irregular shapes,

which are often formed after deposition at a fast rate, easily contributes to the

formation of dead Li. This finding implies that in a practical rechargeable battery,

the use of a different rate of charge and discharge within a cycle would pose a

higher risk for the formation of Li debris. Moreover, considering that the effective

current rates applied to the electrode may change as a result of side reactions,

which can cause the loss of the active electrode parts, similar issues may arise even

132

in batteries operating using a constant charge and discharge current rate and may be

aggravated with prolonged cycles.

133

Figure 4-15. Li stripping behavior from irregular deposit. Dead Li formation is

shown at the narrow point (black arrow) for the slow stripping condition. Complete

stripping was not achieved because of the failure of the solution converge,

presumably arising from the dynamic generation of singular points during the

stripping reaction. The scale bars are 1-μm long.

134

Figure 4-16. Stripping from artificially made model with narrow points.

135

4.4 Conclusion

In this work, we investigated the deposition and stripping behavior of Li metal in

an electrochemical cell considering various experimental conditions such as the

applied current rates, initial surface morphology, nature of the SEI layer, and

cycling process of deposition and stripping. Our findings confirmed that the

preferential Li growth occurs because of the disturbance of the local current density

resulting from the presence of irregular surface properties. In addition, the

tendency of preferential growth was particularly promoted for high deposition rates

because of the densely populated equipotential lines around the irregular surfaces.

The presence of a SEI layer was shown to generally promote the abnormal growth

of Li deposits even from minor protrusions. The nature of SEI layers with

relatively sluggish ionic transport properties compared with those of a liquid

electrolyte induced severe ionic concentration gradients near the electrode surface,

indicating the importance of engineering of the SEI to inhibit abnormal Li growth.

Finally, it was demonstrated that the history of the deposition/stripping processes

could sensitively affect the generation of Li metal debris. The stripping of irregular

deposits at slow rates induced thinning of the necking regions, thus increasing the

risk of the formation of dead Li. We believe that our findings not only elucidate the

quantitative Li growth behaviors under various electrochemical conditions but also

provide important clues about the basic mechanism of abnormal Li growth that

occurs during battery operation and causes premature failure of Li metal anodes. It

136

is our hope that these fundamental studies will aid in the development of effective

counter strategies to regulate the growth of Li metal and enable the use of high-

energy-density Li metal anodes.

137

4.5 References

1. Tarascon, J. M.; Armand, M., Issues and challenges facing rechargeable

lithium batteries. Nature 2001, 414, 359.

2. Choi, J. W.; Aurbach, D., Promise and reality of post-lithium-ion batteries

with high energy densities. Nat. Rev. Mater. 2016, 1, 16013.

3. Li, Z.; Huang, J.; Yann Liaw, B.; Metzler, V.; Zhang, J., A review of

lithium deposition in lithium-ion and lithium metal secondary batteries. J. Power

Sources 2014, 254, 168-182.

4. Zhang, K.; Lee, G.-H.; Park, M.; Li, W.; Kang, Y.-M., Recent

Developments of the Lithium Metal Anode for Rechargeable Non-Aqueous

Batteries. Adv. Energy Mater. 2016, 6, 1600811.

5. Guo, Y.; Li, H.; Zhai, T., Reviving Lithium-Metal Anodes for Next-

Generation High-Energy Batteries. Adv. Mater. 2017, 29, 1700007.

6. Wood, K. N.; Noked, M.; Dasgupta, N. P., Lithium Metal Anodes: Toward

an Improved Understanding of Coupled Morphological, Electrochemical, and

Mechanical Behavior. ACS Energy Lett. 2017, 2, 664-672.

7. Xu, W.; Wang, J.; Ding, F.; Chen, X.; Nasybulin, E.; Zhang, Y.; Zhang, J.-

G., Lithium metal anodes for rechargeable batteries. Energy Environ. Sci. 2014, 7,

513-537.

8. Qian, J.; Henderson, W. A.; Xu, W.; Bhattacharya, P.; Engelhard, M.;

Borodin, O.; Zhang, J.-G., High rate and stable cycling of lithium metal anode. Nat.

138

Commun. 2015, 6, 6362.

9. Zaban, A.; Aurbach, D., Impedance spectroscopy of lithium and nickel

electrodes in propylene carbonate solutions of different lithium salts A comparative

study. J. Power Sources 1995, 54, 289-295.

10. Monroe, C.; Newman, J., The Impact of Elastic Deformation on

Deposition Kinetics at Lithium/Polymer Interfaces. J. Electrochem. Soc. 2005, 152,

A396-A404.

11. Chen, X.; Hou, T.-Z.; Li, B.; Yan, C.; Zhu, L.; Guan, C.; Cheng, X.-B.;

Peng, H.-J.; Huang, J.-Q.; Zhang, Q., Towards stable lithium-sulfur batteries:

Mechanistic insights into electrolyte decomposition on lithium metal anode.

Energy Storage Materials 2017, 8, 194-201.

12. Zu, C.; Azimi, N.; Zhang, Z.; Manthiram, A., Insight into lithium-metal

anodes in lithium-sulfur batteries with a fluorinated ether electrolyte. J. Mater.

Chem. A 2015, 3, 14864-14870.

13. Yan, K.; Lee, H.-W.; Gao, T.; Zheng, G.; Yao, H.; Wang, H.; Lu, Z.; Zhou,

Y.; Liang, Z.; Liu, Z.; Chu, S.; Cui, Y., Ultrathin Two-Dimensional Atomic Crystals

as Stable Interfacial Layer for Improvement of Lithium Metal Anode. Nano Lett.

2014, 14, 6016-6022.

14. Kazyak, E.; Wood, K. N.; Dasgupta, N. P., Improved Cycle Life and

Stability of Lithium Metal Anodes through Ultrathin Atomic Layer Deposition

Surface Treatments. Chem. Mater. 2015, 27, 6457-6462.

15. Kozen, A. C.; Lin, C.-F.; Pearse, A. J.; Schroeder, M. A.; Han, X.; Hu, L.;

139

Lee, S.-B.; Rubloff, G. W.; Noked, M., Next-Generation Lithium Metal Anode

Engineering via Atomic Layer Deposition. ACS Nano 2015, 9, 5884-5892.

16. Zheng, G.; Lee, S. W.; Liang, Z.; Lee, H.-W.; Yan, K.; Yao, H.; Wang, H.;

Li, W.; Chu, S.; Cui, Y., Interconnected hollow carbon nanospheres for stable

lithium metal anodes. Nat. Nanotechnol. 2014, 9, 618.

17. Lee, H.; Lee, D. J.; Kim, Y.-J.; Park, J.-K.; Kim, H.-T., A simple

composite protective layer coating that enhances the cycling stability of lithium

metal batteries. J. Power Sources 2015, 284, 103-108.

18. Li, N. W.; Yin, Y. X.; Yang, C. P.; Guo, Y. G., An Artificial Solid

Electrolyte Interphase Layer for Stable Lithium Metal Anodes. Adv. Mater. 2016,

28, 1853-1858.

19. Wang, X.; Hou, Y.; Zhu, Y.; Wu, Y.; Holze, R., An Aqueous Rechargeable

Lithium Battery Using Coated Li Metal as Anode. Sci. Rep. 2013, 3, 1401.

20. Lu, Y.; Tu, Z.; Archer, L. A., Stable lithium electrodeposition in liquid and

nanoporous solid electrolytes. Nat. Mater. 2014, 13, 961.

21. Lu, Y.; Tu, Z.; Shu, J.; Archer, L. A., Stable lithium electrodeposition in

salt-reinforced electrolytes. J. Power Sources 2015, 279, 413-418.

22. Ding, F.; Xu, W.; Graff, G. L.; Zhang, J.; Sushko, M. L.; Chen, X.; Shao,

Y.; Engelhard, M. H.; Nie, Z.; Xiao, J.; Liu, X.; Sushko, P. V.; Liu, J.; Zhang, J.-G.,

Dendrite-Free Lithium Deposition via Self-Healing Electrostatic Shield

Mechanism. J. Am. Chem. Soc. 2013, 135, 4450-4456.

23. Shu-Hua, W.; Ya-Xia, Y.; Tong-Tong, Z.; Wei, D.; Jin-Yi, L.; Ji-Lei, S.;

140

Chang-Huan, Z.; Nian-Wu, L.; Cong-Ju, L.; Yu-Guo, G., Stable Li Metal Anodes

via Regulating Lithium Plating/Stripping in Vertically Aligned Microchannels. Adv.

Mater. 2017, 29, 1703729.

24. Mayers, M. Z.; Kaminski, J. W.; Miller, T. F., Suppression of Dendrite

Formation via Pulse Charging in Rechargeable Lithium Metal Batteries. J. Phys.

Chem. C 2012, 116, 26214-26221.

25. Rosso, M.; Gobron, T.; Brissot, C.; Chazalviel, J. N.; Lascaud, S., Onset

of dendritic growth in lithium/polymer cells. J. Power Sources 2001, 97-98, 804-

806.

26. Brissot, C.; Rosso, M.; Chazalviel, J. N.; Lascaud, S., Dendritic growth

mechanisms in lithium/polymer cells. J. Power Sources 1999, 81-82, 925-929.

27. Chazalviel, J. N., Electrochemical aspects of the generation of ramified

metallic electrodeposits. Phys. Rev. A 1990, 42, 7355-7367.

28. Rosso, M.; Chassaing, E.; Chazalviel, J. N.; Gobron, T., Onset of current-

driven concentration instabilities in thin cell electrodeposition with small inter-

electrode distance. Electrochim. Acta 2002, 47, 1267-1273.

29. Sand, H. J. S., III. On the concentration at the electrodes in a solution,

with special reference to the liberation of hydrogen by electrolysis of a mixture of

copper sulphate and sulphuric acid. Philos. Mag. 1901, 1, 45-79.

30. Bai, P.; Li, J.; Brushett, F. R.; Bazant, M. Z., Transition of lithium growth

mechanisms in liquid electrolytes. Energy Environ. Sci. 2016, 9, 3221-3229.

31. Park, J.; Jeong, J.; Lee, Y.; Oh, M.; Ryou, M.-H.; Lee, Y. M., Micro-

141

Patterned Lithium Metal Anodes with Suppressed Dendrite Formation for Post

Lithium-Ion Batteries. Adv. Mater. Interfaces 2016, 3, 1600140.

32. "COMSOL Multiphysics Reference Manual, version 5.3", COMSOL, Inc,

www.comsol.com.

33. Valøen, L. O.; Reimers, J. N., Transport Properties of LiPF6-Based Li-Ion

Battery Electrolytes. J. Electrochem. Soc. 2005, 152, A882-A891.

34. Verma, P.; Maire, P.; Novák, P., A review of the features and analyses of

the solid electrolyte interphase in Li-ion batteries. Electrochim. Acta 2010, 55,

6332-6341.

35. Peled, E., The Electrochemical Behavior of Alkali and Alkaline Earth

Metals in Nonaqueous Battery Systems—The Solid Electrolyte Interphase Model.

J. Electrochem. Soc. 1979, 126, 2047-2051.

36. Moon, S.; Park, H.; Yoon, G.; Lee, M. H.; Park, K.-Y.; Kang, K., Simple

and Effective Gas-Phase Doping for Lithium Metal Protection in Lithium Metal

Batteries. Chem. Mater. 2017, 29, 9182-9191.

37. Yang, C.-P.; Yin, Y.-X.; Zhang, S.-F.; Li, N.-W.; Guo, Y.-G.,

Accommodating lithium into 3D current collectors with a submicron skeleton

towards long-life lithium metal anodes. Nat. Commun. 2015, 6, 8058.

38. Yun, Q.; He, Y.-B.; Lv, W.; Zhao, Y.; Li, B.; Kang, F.; Yang, Q.-H.,

Chemical Dealloying Derived 3D Porous Current Collector for Li Metal Anodes.

Adv. Mater. 2016, 28, 6932-6939.

142

143

144

Chapter 5. Summary

In this thesis, anode materials for next-generation rechargeable batteries were

theoretically investigated. The contents include (i) the observation of Na-solvent

co-intercalation into graphite and the investigation on the intercalation mechanism,

(ii) the theoretical understanding on the thermodynamic instability of Na

intercalation into graphite and the conditions for reversible Na-solvent co-

intercalation, and (iii) the continuum mechanics study on the deposition and

stripping behavior of Li metal considering various experimental conditions.

In the first part, the solvated-ion intercalation chemistry of the ternary GIC system

of Na-ether-graphite, which has been poorly understood because of its complexity

compared with the simple binary GIC system of Li-graphite, was thoroughly

investigated. In operando XRD-electrochemical analysis and direct visualization

coupled with DFT calculations revealed the structural evolution of the graphite

during the solvated-Na intercalation. The Na intercalation occurs through multiple

staging reactions, which finally form first-stage GICs within a wide range of Na/C

from 1/28 to 1/21 with excellent reversibility. It is proposed that the intercalated Na

ions and ether solvents are in the form of [Na-ether]+ complexes double stacked in

parallel with graphene layers in the graphite galleries. The correlation between the

solvent species and intercalation suggests the possible tunability of Na storage

properties. The Na storage potential increases as the chain length of the solvent

species increases because of the stronger screening effects of longer solvent

145

molecules on the repulsion between positively charged Na ions in the discharge

product.

In the second part, the origin of the thermodynamic instability of Na intercalation

into graphite was revealed by investigating various AM-GICs (AM = Li, Na, K, Rb,

Cs). DFT calculations indicated that the unstable Na-GIC formation can be

attributed to the peculiarly unfavorable local Na–graphene interaction. Screening of

Na with solvent molecules was observed to be an effective strategy to promote Na

intercalation because it prevents the direct interaction between Na and graphene.

Based on an investigation of the solvent dependency in the reversible co-

intercalation, we proposed that the high �� of Na and chemical stability of Na–

solvent complexes are critical for the reversible co-intercalation. This claim was

further supported by comparing experimental results on the electrochemical

activity with the calculated thermodynamic and chemical stabilities of Na–solvent

complexes.

In the last part, the deposition and stripping behavior of Li metal in an

electrochemical cell considering various experimental conditions such as the

applied current rates, initial surface morphology, nature of the SEI layer, and

cycling process of deposition and stripping was investigated. It was confirmed that

the preferential Li growth occurs because of the disturbance of the local current

density resulting from the presence of irregular surface properties. In addition, the

tendency of preferential growth was particularly promoted for high deposition rates

146

because of the densely populated equipotential lines around the irregular surfaces.

The presence of a SEI layer was shown to generally promote the abnormal growth

of Li deposits even from minor protrusions. The nature of SEI layers with

relatively sluggish ionic transport properties compared with those of a liquid

electrolyte induced severe ionic concentration gradients near the electrode surface,

indicating the importance of engineering of the SEI to inhibit abnormal Li growth.

Finally, it was demonstrated that the history of the deposition/stripping processes

could sensitively affect the generation of Li metal debris. The stripping of irregular

deposits at slow rates induced thinning of the necking regions, thus increasing the

risk of the formation of dead Li.

It is my hope that the fundamental studies on graphite anode will provide unlimited

opportunities to design electrodes with superior performances beyond that of

conventional electrode materials of rechargeable batteries. I also believe that the

relationships among the guest ions, solvent, and intercalation host observed in

these studies can be extended to general intercalation-based electrochemical

systems and hint at an effective strategy to optimize the system performance.

Finally, I hope that the continuum mechanics studies on Li metal anode will aid in

the development of effective counter strategies to regulate the growth of Li metal

and enable the use of high-energy-density Li metal anodes.

147

Abstract in Korean

초록

지속가능한 사회를 위한 전세계적인 노력에 발맞추어 전기화학적

에너지저장장치에 대한 연구가 활발하게 이루어지고 있다. 다양한

에너지저장장치 중, 리튬이온전지는 높은 에너지밀도, 출력 특성 및

우수한 수명으로 인해 현재 가장 널리 이용되고 있다. 그러나

리튬이온전지는 에너지밀도가 한계에 다다르고 있고, 지각 내 리튬

자원의 불균등한 분포로 인한 리튬의 제한된 공급 때문에 생산 단가가

불안정하다는 문제점을 가지고 있다. 따라서 에너지 저장 성능의 향상과

갈수록 증가하는 에너지저장장치의 수요를 충당하기 위해서 차세대

이차전지용 전극 소재에 대한 개발이 시급하다. 본 학위논문에서는

차세대 이차전지 시스템의 음극 소재 중 소듐이온전지용 흑연 음극재와

리튬금속전지용 리튬금속음극에 대한 이론적 연구를 소개한다.

제 2장에서는 용매화된 소듐 이온(solvated-Na-ion)이 흑연 내로

삽입되는 메커니즘을 반응 중의(operando) X선 회절 분석, 전기화학

적정, 실시간 광학 현미경 관찰, 제일원리 계산을 통해 관찰한다.

밀리미터 크기의 고배향성 흑연(highly oriented pyrolytic graphite)을

관찰하여 2초 이내의 짧은 시간 안에 용매화된 소듐 이온이 흑연 안에

148

삽입되는 것을 확인하고, 흑연 내의 용매화된 소듐 이온의 분포와

다양한 층간 배열 규칙(staging)을 처음으로 정량화한다. 실험 결과들과

제일원리 계산을 통해 용매화된 소듐 이온이 흑연 내에서 가지는 원자

단위의 배열을 제시하며, 다양한 용매들의 특성과 소듐 이온 삽입

현상의 상관관계를 분석하여 소듐이차전지용 흑연 전극의 성능을 조율할

수 있는 전략을 제안한다.

제 3장에서는 알칼리 금속 흑연 층간화합물에 대한 체계적인 연구를

통해 소듐 흑연 층간화합물의 열역학적 불안정성이 소듐과 그래핀의

국부적으로 불안정한 상호작용 때문임을 밝히고, 소듐 이온을 용매

분자로 감싸는 방식으로 불안정성을 해소할 수 있음을 보인다. 더

나아가, 특정 용매를 통해서만 흑연 내의 가역적인 소듐 삽입이

이루어짐을 밝히고, 그 용매의 조건을 소듐 용매화 에너지와 용매화된

소듐 이온의 최저준위 비점유 분자궤도(lowest unoccupied molecular

orbital)의 관점에서 제시한다. 제 3장에서 제안된 용매의 조건들은

삽입 반응의 숙주(intercalation host)와 이온(guest ion)이 존재하는

시스템에서 광범위하게 적용 가능할 것으로 예상되며, 순수한 이온의

삽입 반응과 용매화된 이온의 삽입 반응을 목적에 따라 맞추는 데

일반적인 기준이 될 것으로 기대된다.

제 4장에서는 리튬금속의 전기화학적 증착과 탈리 반응을 반응 속도,

149

전극 표면 구조, 고체 전해질 계면상(solid electrolyte interphase)의

특성 등 다양한 변수 하에서 관찰하여 불균일한 리튬 성장의 조건에

대해 조사한다. 시뮬레이션을 통해 불규칙적인 리튬 금속의 성장은 표면

전류밀도가 국부적으로 작은 불균일성을 보이기 때문임을 밝히고, 이는

표면 구조, 고체 전해질 계면상의 결함성, 그리고 증착/탈리 반응의

상대적인 비대칭성에서 기인함을 보인다. 더 나아가, 증착 속도보다

느린 속도로 탈리 반응이 진행될 때 리튬의 일부가 끊어져 떨어지는

현상을 관찰한다. 이러한 발견은 빠른 속도의 증착/탈리 반응이 더 이른

전지의 고장을 유발한다는 전통적인 해석에 반하는 결과이다.

주요어 : 에너지 저장장치, 제일원리 계산, 연속체 역학, 배터리,

리튬금속음극, 흑연

학번 : 2013-20611

150

Curriculum Vitae

Gabin Yoon

+82-10-3223-1641

lysine427@gmail.com

Education

Ph. D. course March 2013 – Present.

Department of Materials Science and Engineering

Seoul National University

Seoul, Republic of Korea

(Advisor: Prof. Kisuk Kang)

Visiting student June 2016 – November 2016

Ceder group

Lawrence Berkeley National Lab

Berkeley, CA, USA

(Advisor: Prof. Gerbrand Ceder)

151

B. S. March 2009 – February 2013

Department of Materials Science and Engineering

Seoul National University

Seoul, Republic of Korea

Research experiences

Ph. D. course (March 2013 – Present)

� Continuum mechanics studies on the Li metal electrodeposition/stripping

behavior

� First-principles evaluation of thermodynamics and kinetics of Li/Na-ion

rechargeable battery electrodes, including the investigation on the phase

stability, structural evolution upon Li/Na (de)intercalation, determination

of redox-active center (transition metal, oxygen anion) and activation

barriers of ion diffusion

� DFT studies on the Na-solvent co-intercalated graphite for the utilization

as an anode for Na-ion batteries

� Determination of exfoliation energies of graphite intercalation compounds

for graphene synthesis

152

� Evaluation on the catalytic activity of metal phosphides towards hydrogen

evolution reaction

Undergraduate course (March 2009 – February 2013)

� Synthesis of metal-graphene hybrid material for display application

Other experiences

� TA for Introduction to Materials Science and Engineering (2014 spring)

class

� TA for Self-design Experiments in Materials (2014 fall) class

Technical skills

� Computational software

- VASP, Gaussian09, COMSOL Multiphysics, LAAMPS, EspressoMD,

MATLAB

� Data processing and visualization

- VESTA, Materials Studio, VMD, OVITO, OriginPro, Microsoft office

153

� Programming language

- Python

Publications

† equal contribution

* corresponding authors

1. Deposition and stripping behavior of lithium metal in electrochemical

systems: Continuum mechanics study

Gabin Yoon, Sehwan Moon, Gerbrand Ceder, Kisuk Kang

Chemistry of Materials 2018, 30, 6769.

2. Na3V(PO4)2: a new layered-type cathode material with high water stability

and power capability for Na-ion batteries

Jongsoon Kim†, Gabin Yoon†, Hyungsub Kim, Young-Uk Park, Kisuk

Kang

Chemistry of Materials 2018, 30, 3683.

3. New 4V-class and zero-strain cathode material for Na ion batteries

Jongsoon Kim†, Gabin Yoon†, Myeong Hwan Lee, Hyungsub Kim,

Seongsu Lee, Kisuk Kang

154

Chemistry of Materials 2017, 29, 7826.

4. Using first-principles calculations for the advancement of materials for

rechargeable batteries

Gabin Yoon†, Do-Hoon Kim†, Inchul Park†, Donghee Chang, Byunghoon

Kim, Byungju Lee, Kyungbae Oh, Kisuk Kang

Advanced Functional Materials 2017, 27, 1702887.

5. Large-scale Synthesis of Carbon Shell-coated FeP Nanoparticles for

Robust Hydrogen Evolution Electrocatalyst

Dong Young Chung†, Samuel Jun†, Gabin Yoon†, Hyunjoong Kim, Ji Mun

Yoo, Kug-Seung Lee, Taehyun Kim, Heejong Shin, Arun Sinha, Soon Gu

Kwon*, Kisuk Kang*, Taeghwan Hyeon*, Yung-Eun Sung*

Journal of the American Chemical Society 2017, 139, 6669.

6. Conditions for reversible Na intercalation in graphite: Theoretical studies

on the interplay among guest ions, solvent, and graphite host

Gabin Yoon, Haegyeom Kim, Inchul Park, Kisuk Kang

Advanced Energy Materials 2017, 7, 1601519.

7. Anomalous Jahn-Teller behavior in manganese-based mixed-phosphate

cathode for sodium ion batteries

155

Hyungsub Kim†, Gabin Yoon†, Inchul Park, Kyu-Young Park, Byungju

Lee, Jongsoon Kim, Young-Uk Park, Sung-Kyun Jung, Hee-Dae Lim,

Docheon Ahn, Seongsu Lee, Kisuk Kang

Energy & Environmental Science 2015, 8, 3325.

8. Sodium intercalation chemistry in graphite

Haegyeom Kim†, Jihyun Hong†, Gabin Yoon†, Hyunchul Kim, Kyu-

Young Park, Min-Sik Park, Won-Sub Yoon, and Kisuk Kang

Energy & Environmental Science 2015, 8, 2963.

9. Factors affecting the exfoliation of graphite intercalation compounds for

graphene synthesis

Gabin Yoon, Dong-Hwa Seo, Kyojin Ku, Jungmo Kim, Seokwoo Jeon,

Kisuk Kang

Chemistry of Materials 2015, 26, 2067.

10. Atomistic investigation of doping effects on electrocatalytic properties of

cobalt oxides for water oxidation

Byunghoon Kim, Inchul Park, Gabin Yoon, Ju Seong Kim, Hyunah Kim,

Kisuk Kang

Advanced Science 2018, 5, 1801632

156

11. Graphitic carbon materials for advanced sodium ion batteries

Zheng-Long Xu†, Jooha Park†, Gabin Yoon, Haegyeom Kim, Kisuk Kang

Small Methods 2018, 1800227.

12. Native defects in Li10GeP2S12 and their effect on lithium diffusion

Kyungbae Oh, Donghee Chang, Byungju Lee, Do-Hoon Kim, Gabin

Yoon, Inchul Park, Byunghoon Kim, Kisuk Kang

Chemistry of Materials 2018, 30, 4995.

13. Extremely large, non-oxidized graphene flakes based on spontaneous

solvent insertion into graphite intercalation compound

Jungmo Kim, Gabin Yoon, Jin Kim, Hyewon Yoon, Jinwook Baek, Joong

Hee Lee, Kisuk Kang, Seokwoo Jeon

Carbon 2018, 139, 309.

14. Engineering solid electrolyte interphase for pseudocapacitive anatase TiO2

anodes in sodium ion batteries

Zheng-Long Xu, Kyungmi Lim, Kyu-Young Park, Gabin Yoon, Won Mo

Seong, Kisuk Kang

Advanced Functional Materials 2018, 28, 1802099.

157

15. Suppression of voltage decay through manganese deactivation and nickel

redox buffering in high-energy layered lithium-rich electrodes

Kyojin Ku†, Jihyun Hong†, Hyungsub Kim, Hyeokjun Park, Won Mo

Seong, Sung-Kyun Jung, Gabin Yoon, Kyu-Young Park, Haegyeom Kim,

Kisuk Kang

Advanced Energy Materials 2018, 8, 1800606.

16. Simple and effective gas-phase doping for lithium metal protection in

lithium metal batteries

Sehwan Moon†, Hyeokjun Park†, Gabin Yoon, Myeong Hwan Lee, Kyu-

Young Park, Kisuk Kang

Chemistry of Materials 2017, 29, 9182.

17. In Situ tracking kinetic pathways of Li+/Na+ substitution during ion-

exchange synthesis of LixNa1.5-xVOPO4F0.5

Young-Uk Park, Jianming Bai, Liping Wang, Gabin Yoon, Wei Zhang,

Hyungsub Kim, Seongsu Lee, Sung-Wook Kim, J. Patrick Looney, Kisuk

Kang*, Feng Wang*

Journal of the American Chemical Society 2017, 139, 12504.

18. Activating layered LiNi0.5Co0.2Mn0.3O2 as a host for Mg intercalation in

rechargeable Mg batteries

158

Yongbeom Cho, Myeong Hwan Lee, Hyungsub Kim, Kyojin Ku, Gabin

Yoon, Sung-Kyun Jung, Byungju Lee, Jongsoon Kim, Kisuk Kang

Materials Research Bulletin 2017, 96, 524.

19. Exploiting lithium-ether co-intercalation in graphite for high-power

lithium-ion batteries

Haegyeom Kim†, Kyungmi Lim†, Gabin Yoon, Jaehyuk Park, Kyojin Ku,

Hee-Dae Lim, Yung-Eun Sung, Kisuk Kang

Advanced Energy Materials 2017, 7, 1700418.

20. Amorphous cobalt phyllosilicate with layered crystalline motifs as water

oxidation catalyst

Ju Seong Kim†, Inchul Park†, Eun-Suk Jeong, Kyoungsuk Jin, Won Mo

Seong, Gabin Yoon, Hyunah Kim, Byunghoon Kim, Ki Tae Nam, Kisuk

Kang

Advanced Materials 2017, 29, 1606893.

21. Lithium-free transition metal monoxides for positive electrodes in lithium

ion batteries

Sung-Kyun Jung, Hyunchul Kim, Min Gee Cho, Sung-Pyo Cho, Byungju

Lee, Hyungsub Kim, Young-Uk Park, Jihyun Hong, Kyu-Young Park,

Gabin Yoon, Won Mo Seong, Yongbeom Cho, Myoung Hwan Oh,

159

Haegyeom Kim, Hyeokjo Gwon, Insang Hwang, Taeghwan Hyeon, Won-

Sub Yoon*, and Kisuk Kang*

Nature Energy 2017, 2, 16208.

22. Restoration of thermally reduced graphene oxide by atomic-level selenium

doping

Young Soo Yun, Gabin Yoon, Min Park, Se Youn Cho, Hee-Dae Lim,

Haegyeom Kim, Yung Woo Park, Byung Hoon Kim, Kisuk Kang*,

Hyoung-Joon Jin*

NPG Asia Materials 2016, 8, e338.

23. Highly stable iron- and manganese-based cathodes for long-lasting sodium

rechargeable batteries

Hyungsub Kim, Gabin Yoon, Inchul Park, Jihyun Hong, Kyu-Young Park,

Jongsoon Kim, Kug-Seung Lee, Nark-Eon Sung, Seongsu Lee, Kisuk

Kang

Chemistry of Materials 2016, 28, 7241.

24. A comparative study of graphite electrode using co-intercalation

phenomenon for rechargeable Li, Na and K batteries

Haegyeom Kim, Gabin Yoon, Kyungmi Lim, Kisuk Kang

Chemical Communications 2016, 52, 12618.

160

25. Lithium-excess olivine electrode for lithium rechargeable batteries

Kyu-Young Park, Inchul Park, Hyungsub Kim, Gabin Yoon, Hyeok-Jo

Gwon, Yongbeom Cho, Young Soo Yun, Jung-Joon Kim, Seongsu Lee,

Docheon Ahn, Yunok Kim, Haegyeom Kim, Insang Hwang, Won-Sub

Yoon, Kisuk Kang

Energy & Environmental Science 2016, 9, 2702.

26. Recent progress in electrode materials for sodium-ion batteries

Hyungsub Kim†, Haegyeom Kim†, Zhang Ding, Myeong Hwan Lee,

Kyungmi Lim, Gabin Yoon, Kisuk Kang

Advanced Energy Materials 2016, 6, 1600943.

27. Understanding origin of voltage hysteresis in conversion reaction for Na

rechargeable batteries: the case of cobalt oxides

Haegyeom Kim, Hyunchul Kim, Hyungsub Kim, Jinsoo Kim, Gabin

Yoon, Kyungmi Lim, Won-Sub Yoon, Kisuk Kang

Advanced Functional Materials 2016, 26, 5042.

28. Theoretical evidence for low charging overpotentials of superoxide

discharge products in metal-oxygen batteries

Byungju Lee, Jinsoo Kim, Gabin Yoon, Hee-Dae Lim, In-Suk Choi,

161

Kisuk Kang

Chemistry of Materials 2015, 27, 8406.

29. Highly durable and active PtFe nanocatalyst for electrochemical oxygen

reduction reaction

Dong Young Chung†, Samuel Woojoo Jun†, Gabin Yoon, Soon Gu Kwon,

Dong Yun Shin, Pilseon Seo, Ji Mun Yoo, Heejong Shin, Young-Hoon

Chung, Hyunjoong Kim, Bongjin Simon Mun, Kug-Seung Lee, Nam-Suk

Lee, Sung Jong Yoo, Dong-Hee Lim, Kisuk Kang, Yung-Eun Sung*,

Taeghwan Hyeon*

Journal of the American Chemical Society 2015, 137, 15478.

30. Structural effect on the oxygen evolution reaction in the electrochemical

catalyst FePt

Wonseok Jeong, Gijae Kang, Kyeyoup Kim, Gabin Yoon, Kisuk Kang,

Seungwu Han

New Physics: Sae Mulli 2015, 9, 878.

31. Ordered-mesoporous Nb2O5/Carbon composite as a sodium insertion

material

Haegyeom Kim†, Eunho Lim†, Changshin Jo, Gabin Yoon, Jongkook

Hwang, Sanha Jeong, Jinwoo Lee*, Kisuk Kang*

162

Nano Energy 2015, 16, 62.

32. Moisture Barrier Composites Made of Non-Oxidized Graphene Flakes

Jungmo Kim, Sung Ho Song, Hyeon-Gyun Im, Gabin Yoon, Dongju Lee,

Chanyong Choi, Jin Kim, Byeong-Soo Bae, Kisuk Kang, Seokwoo Jeon

Small 2015, 11, 3124.

33. Hierarchical atomic structure of Mn-based spinel cathode for Li-ion

batteries

Sanghan Lee, Gabin Yoon, Minseul Jeong, Min-Joon Lee, Kisuk Kang*,

Jaephil Cho*

Angewandte Chemie International Edition 2015, 54, 1153.

34. The Reaction Mechanism and Capacity Degradation Model in Lithium

Insertion Organic Cathodes, Li2C6O6, Using Combined Experimental and

First Principle Studies

Haegyeom Kim, Dong-Hwa Seo, Gabin Yoon, William A. Goddard III,

Yun-Sung Lee*, Won-Sub Yoon*, and Kisuk Kang*

The Journal of Physical Chemistry Letters 2014, 5, 3086.

35. High-Performance Supercapacitors Based on Defect-engineered Carbon

Nanotubes

Young Soo Yun, Gabin Yoon, Kisuk Kang, Hyoung-Joon Jin

163

Carbon 2014, 80, 246.

Award

1. Best graduation thesis award

Materials Science and Engineering, Seoul National University, 2018

Patent

1. Secondary battery containing auxiliary electrode sensor and detection

method for a short circuit of secondary battery

Kisuk Kang, Sehwan Moon, Gabin Yoon, Hyeokjun Park, Orapa

Tamwattana

Registration No. 10-1922992, 2018 (South Korea)

Application No. 16/052,455, 2018 (USA)

Conference presentations

International

1. Conditions for reversible Na intercalation in graphite: Theoretical studies

on the interplay among guest ions, solvent, and graphite host

International Battery Association 2018, Jeju, Korea

March 2018

2. First-principles studies on graphite intercalation compounds for graphene

164

exfoliation

2015 MRS Spring meeting & exhibit, San Francisco, CA, USA

April 2015

3. Computational studies on graphite intercalation compounds for graphene

exfoliation

ENGE 2014, Jeju, Korea

November 2014

4. First-principles studies on graphite intercalation compounds for graphene

exfoliation

15th Japan-Korea Students’ Symposium, Seoul, Korea

November 2014

Domestic

1. Theoretical studies on the reversible Na intercalation in graphite: Interplay

among guest ions, solvent, and graphite host

2017 Fall Conference of the Korean Institute of Metals and Materials,

Daegu, Korea

October 2017

165

2. New 4V-class cathode material for Na-ion batteries with zero-strain

2017 Fall Conference of the Korean Institute of Metals and Materials,

Daegu, Korea

October 2017