Simulation and optimization of electrochemical double layer capacitors: effects of ion size and diffusion coefficient

doi:10.11949/0438-1157.20190421

Abstract

Abstract:

The low energy density of electrochemical double layer capacitors limits its application in the field of energy storage power. Organic electrolytes, as a key factor in improving the energy density of devices, are of great significance in studying the properties of conductive electrolytes. Ion size and diffusion coefficient in organic electrolyte are the critical factors in determining the energy density of electrochemical double layer capacitors. A dynamic model of electrochemical double layer capacitors was established to simultaneously account for transport process, Stern and diffuse layers and the saturation phenomenon of dielectric permittivity. The cyclic voltammetry measurement of electrochemical double layer capacitors was numerically simulated for different ionic solvation sizes and diffusion coefficients. The simulation results indicated that the specific capacitances were only affected by ionic solvation sizes at low scan rates, increasing significantly with decreasing ionic solvation size, whereas the ionic diffusion coefficients had no effect on the specific capacitances which were mainly controlled by the Stern layer at low scan rates. However, the specific capacitances, which were mainly controlled by the ionic transport within the diffuse layer at high scan rates, were simultaneously affected by ionic solvation sizes and diffusion coefficients. The specific capacitances increased considerably with increasing ionic solvation size or diffusion coefficient at high scan rates. Finally, the strategies for rational design of electrochemical double layer capacitors is proposed based on the simulation results.

Key words: electrochemical double layer capacitors, dynamic modeling, electrolytes, ionic solvation size, diffusion coefficient, optimal design

摘要：

电化学双电层电容器的低能量密度限制了其在储能动力等领域的应用，而有机电解液作为提升器件能量密度的关键因素，研究其导电电解质的特性具有重要的意义。通过构建电化学双电层电容器的动态模型，模拟了电化学双电层电容器的循环伏安曲线，并定量探究和解析了离子溶剂化尺寸和扩散系数对电容性能的影响。模拟结果表明：在低扫描速率情况下，电容性能主要受控于双电层结构特性，比电容随着离子溶剂化尺寸的减小而增大，而离子扩散系数对其电容性能没有影响；在高扫描速率情况下，电容性能会受控于离子传质过程，比电容随着离子溶剂化尺寸和离子扩散系数的增大而增大。并基于模拟计算和分析结果提出了理性设计和优化电化学双电层电容器的策略。

关键词: 电化学双电层电容器, 动态建模, 电解质, 离子尺寸, 扩散系数, 优化设计

CLC Number:

TQ 152

Haotian LU, Yiqin CHEN, Jinghong ZHOU, Zhijun SUI, Xinggui ZHOU. Simulation and optimization of electrochemical double layer capacitors: effects of ion size and diffusion coefficient[J]. CIESC Journal, 2019, 70(10): 4021-4031.

鲁浩天, 陈怡沁, 周静红, 隋志军, 周兴贵. 电化学双电层电容器动态模拟：离子尺寸及扩散系数的优化[J]. 化工学报, 2019, 70(10): 4021-4031.

Figures/Tables 10

Fig.1 Schematic of electric double layer capacitor modeling

Table 1 Parameters for elctric double capacitor dynamic state model simulation

Parameters	Value
minimum value of imposed potential/V	-0.5
maximum value of imposed potential/V	0.5
scan rate of cyclic voltammetry/(V·s^-1)	10,10²,10⁴,10⁵
cycle number	6
local temperature/K	298.5
bulk electrolyte concentration/(mol·L^-1)	1.0
solvated ion size/nm	0.4, 0.6, 0.8
diffuse layer thickness/μm	200
ion valency	1
initial diffusion coefficient of ions in electrolyte/(m²·s^-1)^[22]	3.17×10^-10
dielectric constant of electrolyte within diffuse layer^[27]	61.4
dielectric constant of electrolyte within Stern layer	6.5

Fig.2 Predicted cyclic voltammetry curves by simulation with different solvated ion diameters

Fig.3 Predicted specific capacitance variations at different scan rates by simulation with different solvated ion diameters

Fig.4 Predicted cyclic voltammetry curves by simulation with different ion diffusion coefficients

Fig.5 Predicted specific capacitance variations at different scan rates by simulation with different ion diffusion coefficients

Fig.6 Cation concentration at interface of Stern and diffusion layer with different solvated ion diameters

Fig.8 Cation concentration and potential gradient at interface of Stern and diffusion layer with linear sweep potential for different solvated ion diameters

Fig. 7 Cation concentration at interface of Stern and diffusion layer with different ion diffusion coefficients

Fig.9 Relation of potential gradient with cation concentration at interface of Stern and diffusion layer with different solvated ion diameters

References 37

1	Thounthong P , Raël S , Davat B . Energy management of fuel cell/battery/supercapacitor hybrid power source for vehicle applications[J]. Journal of Power Sources, 2009, 193(1): 376-385.
2	Conway B E . Transition from “supercapacitor” to “battery” behavior in electrochemical energy storage[J]. Journal of the Electrochemical Society, 1991, 138(6): 1539-1548.
3	Wang Y , Song Y , Xia Y . Electrochemical capacitors: mechanism, materials, systems, characterization and applications[J]. Chemical Society Reviews, 2016, 45(21): 5925-5950.
4	Zhong C , Deng Y , Hu W , et al . A review of electrolyte materials and compositions for electrochemical supercapacitors[J]. Chemical Society Reviews, 2015, 44(21): 7484-7539.
5	Chmiola J , Yushin G , Gogotsi Y , et al . Anomalous increase in carbon at pore sizes less than 1 nanometer[J]. Science, 2006, 313(5794): 1760-1763.
6	Sun G , Song W , Liu X , et al . Capacitive matching of pore size and ion size in the negative and positive electrodes for supercapacitors[J]. Electrochimica Acta, 2011, 56(25): 9248-9256.
7	Izadi-Najafabadi A , Yasuda S , Kobashi K , et al . Extracting the full potential of single-walled carbon nanotubes as durable supercapacitor electrodes operable at 4 V with high power and energy density[J]. Advanced Materials, 2010, 22(35): E235-E241.
8	Saito M , Kawaharasaki S , Ito K , et al . Strategies for fast ion transport in electrochemical capacitor electrolytes from diffusion coefficients, ionic conductivity, viscosity, density and interaction energies based on HSAB theory[J]. RSC Advances, 2017, 7(24): 14528-14535.
9	Largeot C , Portet C , Chmiola J , et al . Relation between the ion size and pore size for an electric double-layer capacitor[J]. Journal of the American Chemical Society, 2008, 130(9): 2730-2731.
10	武长城, 吴宝军, 段建, 等 . 电解质离子尺寸对超级电容器电化学性能的影响[J]. 天津工业大学学报, 2019, 38(1): 39-44.
	Wu C C , Wu B J , Duan J , et al . Influence of size of electrolyte ion on the electrochemical performanceof supercapacitor[J]. Journal of Tianjin Polytechnic University, 2019, 38(1): 39-44.
11	Simon P , Gogotsi Y . Materials for electrochemical capacitors[J]. Nature Materials, 2008, 7(11): 845-854.
12	Izadi-Najafabadi A , Futaba D N , Iijima S , et al . Ion diffusion and electrochemical capacitance in aligned and packed single-walled carbon nanotubes[J]. Journal of the American Chemical Society, 2010, 132(51): 18017-18019.
13	鲁浩天, 周静红, 叶光华, 等 . 电化学电容器连续模型的建立与研究进展[J]. 电化学, 2018, 24(5): 517-528.
	Lu H T , Zhou J H , Ye G H , et al . Recent advances in continuous models of electrochemical supercapacitors[J]. Journal of Electrochemistry, 2018, 24(5): 517-528.
14	Wang H , Pilon L . Physical interpretation of cyclic voltammetry for measuring electric double layer capacitances[J]. Electrochimica Acta, 2012, 64: 130-139.
15	Gouy M . Sur la constitution de la charge électrique à la surface d'un électrolyte[J]. Journal de Physique Théorique et Appliquée, 1910, 9(1): 457-468.
16	Chapman D L . A contribution to the theory of electrocapillarity[J]. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1913, 25(148): 475-481.
17	Adamczyk Z , Belouschek P , Lorenz D . Electrostatic interactions of bodies bearing thin double-layers (Ⅰ): General formulation[J]. Berichte der Bunsengesellschaft für Physikalische Chemie, 1990, 94(12): 1483-1492.
18	Kilic M S , Bazant M Z , Ajdari A . Steric effects in the dynamics of electrolytes at large applied voltages (Ⅰ): Double-layer charging[J]. Physical Review E, 2007, 75(2): 021502.
19	Zhang L L , Zhou R , Zhao X S . Graphene-based materials as supercapacitor electrodes[J]. Journal of Materials Chemistry, 2010, 20(29): 5983-5992.
20	Senapati S , Chandra A . Dielectric constant of water confined in a nanocavity[J]. Journal of Physical Chemistry B, 2001, 105(22): 5106-5109.
21	Hantel M M , Weingarth D , Kötz R . Parameters determining dimensional changes of porous carbons during capacitive charging[J]. Carbon, 2014, 69: 275-286.
22	Sullivan J M , Hanson D C , Keller R . Diffusion coefficients in propylene carbonate, dimethyl formamide, acetonitrile, and methyl formate[J]. Journal of the Electrochemical Society, 1970, 117(6): 779-780.
23	Kovacs H , Kowalewski J , Maliniak A , et al . Multinuclear relaxation and NMR self-diffusion study of the molecular dynamics in acetonitrile-chloroform liquid mixtures[J]. Journal of Physical Chemistry, 1989, 93(2): 962-969.
24	Kalugin O N , Chaban V V , Loskutov V V , et al . Uniform diffusion of acetonitrile inside carbon nanotubes favors supercapacitor performance[J]. Nano Letters, 2008, 8(8): 2126-2130.
25	Nishikawa K , Fukunaka Y , Sakka T , et al . Measurement of LiClO₄ diffusion coefficient in propylene carbonate by moirá pattern[J]. Journal of the Electrochemical Society, 2006, 153(5): A830-A834.
26	Wang H , Varghese J , Pilon L . Simulation of electric double layer capacitors with mesoporous electrodes: effects of orphology and electrolyte permittivity[J]. Electrochimica Acta, 2011, 56(17): 6189-6197.
27	Daniels I N , Wang Z , Laird B B . Dielectric properties of organic solvents in an electric field[J]. Journal of Physical Chemistry C, 2017, 121(2): 1025-1031.
28	Pech D , Brunet M , Durou H , et al . Ultrahigh-power micrometre-sized supercapacitors based on onion-like carbon[J]. Nature Nanotechnology, 2010, 5(9): 651-654.
29	Cohen H , Cooley J . The numerical solution of the time-dependent Nernst-Planck equations[J]. Biophysical Journal, 1965, 5(2): 145-162.
30	Conway B E . Electrochemical Supercapacitors: Scientific Fundamentals and Technological Applications[M]. Springer Science & Business Media, 2013.
31	Wang H , Pilon L . Accurate simulations of electric double layer capacitance of ultramicroelectrodes[J]. Journal of Physical Chemistry C, 2011, 115(33): 16711-16719.
32	Qu Q T , Wang B , Yang L C , et al . Study on electrochemical performance of activated carbon in aqueous Li₂SO₄, Na₂SO₄ and K₂SO₄electrolytes[J]. Electrochemistry Communications, 2008, 10(10): 1652-1655.
33	Lee H Y , Goodenough J B . Supercapacitor behavior with KCl electrolyte[J]. Journal of Solid State Chemistry, 1999, 144(1): 220-223.
34	Reddy R N , Reddy R G . Sol-gel MnO₂ as an electrode material for electrochemical capacitors[J]. Journal of Power Sources, 2003, 124(1): 330-337.
35	Bazant M Z , Kilic M S , Storey B D , et al . Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions[J]. Advances in Colloid and Interface Science, 2009, 152(1/2): 48-88.
36	Jiang D E , Wu J . Unusual effects of solvent polarity on capacitance for organic electrolytes in a nanoporous electrode[J]. Nanoscale, 2014, 6(10): 5545-5550.
37	Chae W S , Gough D V , Ham S K , et al . Effect of ordered intermediate porosity on ion transport in hierarchically nanoporous electrodes[J]. ACS Applied Materials and Interfaces, 2012, 4(8): 3973-3979.

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