电化学电容器连续模型的建立与研究进展

doi:10.13208/j.electrochem.180409

摘要/Abstract

摘要： 电化学电容器（超级电容器）是一种兼具高能量密度和高功率密度的新型储能元件，它既具有传统电容器大电流快速充放电的特性，又具有蓄电池高储能密度的特性. 近几年，电化学电容器储能机理的研究和纳米结构电极复合材料的合成不断取得新突破，超级电容器的电化学性能得到了显著的提高. 为了更好地解析电化学电容器的工作特性，建立描述电容器内部浓度分布和电场的物理模型是一项非常重要的研究方法. 本文首先介绍电化学电容器理论基础，并论述近几年电化学电容器连续模型研究进展，最后阐述连续模型进一步发展的前景和挑战.

关键词: 电化学电容器, 储能机理, 纳米结构, 连续模型

Abstract: Electrochemical capacitors (supercapacitors) have been developed as a new type of energy storage device with high energy and power densities, which have the advantages of both fast charging-discharging as traditional capacitors and high energy density as batteries. Notable improvements in their electrochemical performance have been achieved in recent years owing to the recent advances in understanding of charge storage mechanisms and the development of advanced nanostructured materials. Recently, modeling and simulation of these supercapacitors has been applied as a useful approach to better understand the working mechanisms of the supercapacitors by describing the concentrations and electric fields inside the capacitors. Particularly, the continuous models for supercapacitors, which can provide insights into the mass transport and interfacial phenomena in supercapacitors under different operating conditions, have been drawing more and more attention. And there is no review article addresses this topic so far. This paper will try to summarize the basic theories of supercapacitors and the latest progresses in the continuous models for supercapacitors. The focus is the recent advances in the application of continuous models to optimize device parameters under different conditions. Meanwhile, the prospects and challenges associated with the continuous models in the future are also discussed. We believe that modelling of supercapacitors could help design the next-generation supercapacitors for versatile electronic devices.

Key words: electrochemical capacitors, charge storage mechanisms, nanostructured materials, continuous models

中图分类号:

O646
TQ152

鲁浩天，周静红，叶光华，周兴贵. 电化学电容器连续模型的建立与研究进展[J]. 电化学（中英文）, 2018, 24(5): 517-528.

LU Hao-tian, ZHOU Jing-hong, YE Guang-hua, ZHOU Xing-gui. Recent Advances in Continuous Models of Electrochemical Supercapacitors[J]. Journal of Electrochemistry, 2018, 24(5): 517-528.

参考文献

[1] Wang Y G, Song Y F, Xia Y Y. Electrochemical capacitors: Mechanism, materials, systems, characterization and applications[J]. Chemical Society Reviews, 2016, 45(21): 5925-5950.
[2] Miller J R, Simon P. Materials science: Electrochemical capacitors for energy management[J]. Science, 2008, 321(5889): 651-652.
[3] Simon P, Gogotsi Y, Dunn B. Where do batteries end and supercapacitors begin?[J]. Science, 2014, 343(6176): 1210-1211.
[4] Augustyn V, Come J, Lowe M A, et al. High-rate electrochemical energy storage through Li+ intercalation pseudocapacitance[J]. Nature Materials, 2013, 12(6): 518-522.
[5] Burke A. Ultracapacitors: Why, how, and where is the technology[J]. Journal of Power Sources, 2000, 91(1): 37-50.
[6] Simon P, Gogotsi Y. Materials for electrochemical capacitors[J]. Nature Materials, 2008, 7(11): 845-854.
[7] Frackowiak E. Carbon materials for supercapacitor application[J]. Physical Chemistry Chemical Physics, 2007, 9(15): 1774-1785.
[8] Pandolfo A G, Hollenkamp A F. Carbon properties and their role in supercapacitors[J]. Journal of Power Sources, 2006, 157(1): 11-27.
[9] 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.
[10] Zhang L L, Zhao X S. Carbon-based materials as supercapacitor electrodes[J]. Chemical Society Reviews, 2009, 38(9): 2520-2531.
[11] Conway B E. Electrochemical supercapacitors: Scientific fundamentals and technological applications[M]. New York: Kluwer Academic/Plenum Publishers, 1999.
[12] 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.
[13] Chmiola J, Largeot C, Taberna P L, et al. Desolvation of ions in subnanometer pores and its effect on capacitance and double-layer theory[J]. Angewandte Chemie-International Edition, 2008, 47(18): 3392-3395.
[14] Chmiola J, Yushin G, Dash R, et al. Effect of pore size and surface area of carbide derived carbons on specific capacitance[J]. Journal of Power Sources, 2006, 158(1): 765-772.
[15] Frackowiak E, Béguin F. Carbon materials for the electrochemical storage of energy in capacitors[J]. Carbon, 2001, 39(6): 937-950.
[16] Gryglewicz G, Machnikowski J, Lorenc G E, et al. Effect of pore size distribution of coal-based activated carbons on double layer capacitance [J]. Electrochimica Acta, 2005, 50(5): 1197-1206.
[17] Vix G C, Frackowiak E, Jurewicz K, et al. Electrochemical energy storage in ordered porous carbon materials[J]. Carbon, 2005, 43(6): 1293-1302.
[18] Guo Y, Yu L, Wang C Y, et al. Hierarchical tubular structures composed of Mn-based mixed metal oxide nanoflakes with enhanced electrochemical properties[J]. Advanced Functional Materials, 2015, 25(32): 5184-5189.
[19] Chen Y M, Li Z, Lou X W. General formation of M_xCo_(3-x)S₄ (M=Ni, Mn, Zn) follow tubular structures for hybrid supercapacitors[J]. Angewandte Chemie International Edition, 2015, 54(36): 10521-10524.
[20] Yu L, Guan B Y, Xiao W, et al. Formation of yolk-shelled Ni-Co mixed oxide nanoprisms with enhanced electrochemical performance for hybrid supercapacitors and lithium ion batteries[J]. Advanced Energy Materials, 2015, 5(21): 1500981.
[21] Li L, Peng S, Wu H B, et al. A flexible quasi-solid-state asymmetric electrochemical capacitor based on hierarchical porous V₂O₅ nanosheets on carbon nanofibers[J]. Advanced Energy Materials, 2015, 5(17): 1500753.
[22] Yu X Y, Yu L, Lou X W. Metal sulfide hollow nanostructures for electrochemical energy storage[J]. Advanced Energy Materials, 2016, 6(3): 1501333.
[23] Helmholtz H. Studien über electrische grenzschichten[J]. Annalen der Physik, 1879, 243(7): 337-382.
[24] Huang J, Qiao R, Sumpter B G, et al. Effect of diffuse layer and pore shapes in mesoporous carbon supercapacitors [J]. Journal of Materials Research, 2011, 25(8): 1469-1475.
[25] Huang J, Sumpter B G, Meunier V. Theoretical model for nanoporous carbon supercapacitors[J]. Angewandte Chemie International Edition, 2008, 47(3): 520-524.
[26] Huang J, Sumpter B G, Meunier V, et al. Curvature effects in carbon nanomaterials: Exohedral versus endohedral supercapacitors[J]. Journal of Materials Research, 2011, 25(8): 1525-1531.
[27] Gouy G. Sur la constitution de la charge electrique a la surfaced’ unelectrolyte[J]. Journal De Physique Théorique Et Appliquée, 1910, 9: 457-468.
[28] 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.
[29] Stern O. Zur theorie der elektrolytischen doppelschicht[J]. Zeitschrift für Elektrochemie und Angewandte Physikalische Chemie, 1924, 30(21/22): 508-516.
[30] Bikerman J J. Structure and capacity of electrical double layer[J]. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1942, 33(220): 384-397.
[31] Aranda R M J, Grosse C, López G J J, et al. Electrokinetics of suspended charged particles taking into account the excluded volume effect[J]. Journal of Colloid and Interface Science, 2009, 335(2): 250-256.
[32] López G J J, Aranda R M J, Grosse C, et al. Equilibrium electric double layer of charged spherical colloidal particles: Effect of different distances of minimum ion approach to the particle surface[J]. Journal of Physical Chemistry B, 2010, 114(22): 7548-7556.
[33] López G J J, Aranda R M J, Horno J. Excluded volume effect on the electrophoretic mobility of colloidal particles[J]. Journal of Colloid and Interface Science, 2008, 323(1): 146-152.
[34] López G J J, Horno J,Grosse C. Poisson-Boltzmann description of the electrical double layer including ion size effects[J]. Langmuir, 2011, 27(23): 13970-13974.
[35] López G J J, Horno J, Grosse C. Equilibrium properties of charged spherical colloidal particles suspended in aqueous electrolytes: Finite ion size and effective ion permittivity effects[J]. Journal of Colloid and Interface Science, 2012, 380(1): 213-221.
[36] Borukhov I, Andelman D, Orland H. Steric effects in electrolytes: A modified poisson-boltzmann equation[J]. Physical Review Letters, 1997, 79(3): 435-438.
[37] Borukhov I, Andelman D, Orland H. Adsorption of large ions from an electrolyte solution: A modified Poisson-Boltzmann equation[J]. Electrochimica Acta, 2000, 46(2/3): 221-229.
[38] Silalahi A R J, Boschitsch A H, Harris R C, et al. Comparing the predictions of the nonlinear Poisson-Boltzmann equation and the ion size-modified Poisson-Boltzmann equation for a low-dielectric charged spherical cavity in an aqueous salt solution[J]. Journal of Chemical Theory and Computation, 2010, 6(12): 3631-3639.
[39] Biesheuvel P M, Van Soestbergen M. Counterion volume effects in mixed electrical double layers[J]. Journal of Colloid and Interface Science, 2007, 316(2): 490-499.
[40] Biesheuvel P M, Lyklema J. Sedimentation-diffusion equilibrium of binary mixtures of charged colloids including volume effects[J]. Journal of Physics Condensed Matter, 2005, 17(41): 6337-6352.
[41] Biesheuvel P M, Leermakers F A M, Stuart M A C. Self-consistent field theory of protein adsorption in a non-Gaussian polyelectrolyte brush[J]. Physical Review E-Statistical, Nonlinear, and Soft Matter Physics, 2006, 73(1): 011802.
[42] Alijó P H R, Tavares F W, Biscaia E C. Double layer interaction between charged parallel plates using a modified Poisson-Boltzmann equation to include size effects and ion specificity[J]. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2012, 412: 29-35.
[43] Tresset G. Generalized Poisson-Fermi formalism for investigating size correlation effects with multiple ions[J]. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2008, 78(6): 061506.
[44] Huang J, Sumpter B G, Meunier V. A universal model for nanoporous carbon supercapacitors applicable to diverse pore regimes, carbon materials, and electrolytes[J]. Chemistry, 2008, 14(22): 6614-6626.
[45] Dickinson E J F, Compton R G. Diffuse double layer at nanoelectrodes[J]. Journal of Physical Chemistry C, 2009, 113(41): 17585-17589.
[46] Henstridge M C, Dickinson E J F, Compton R G. On the estimation of the diffuse double layer of carbon nanotubes using classical theory: Curvature effects on the Gouy-Chapman limit[J]. Chemical Physics Letters, 2010, 485(1/3): 167-170.
[47] Hamou R F, Biedermann P U, Erbe A, et al. Numerical simulation of probing the electric double layer by scanning electrochemical potential microscopy[J]. Electrochimica Acta, 2010, 55(18): 5210-5222.
[48] Hamou R F, Biedermann P U, Erbe A, et al. Numerical analysis of Debye screening effect in electrode surface potential mapping by scanning electrochemical potential microscopy[J]. Electrochemistry Communications, 2010, 12(10): 1391-1394.
[49] Wang H, Varghese J, Pilon L. Simulation of electric double layer capacitors with mesoporous electrodes: Effects of morphology and electrolyte permittivity[J]. Electrochimica Acta, 2011, 56(17): 6189-6197.
[50] Booth F. The dielectric constant of water and the saturation effect[J]. The Journal of Chemical Physics, 1951, 19(4): 391-394.
[51] Booth F. Dielectric constant of polar liquids at high field strengths[J]. The Journal of Chemical Physics, 1955, 23(3): 453-457.
[52] Wang H N, Pilon L. Accurate simulations of electric double layer capacitance of ultramicroelectrodes[J]. Journal of Physical Chemistry C, 2011, 115(33): 16711-16719.
[53] Wang H, Pilon L. Mesoscale modeling of electric double layer capacitors with three-dimensional ordered structures[J]. Journal of Power Sources, 2013, 221: 252-260.
[54] Kilic M S, Bazant M Z, Ajdari A. Steric effects in the dynamics of electrolytes at large applied voltages. II. Modified Poisson-Nernst-Planck equations[J]. Physical Review E-Statistical, Nonlinear, and Soft Matter Physics, 2007, 75(2): 021503.
[55] Adamczyk Z, Belouschek P, Lorenz D. Electrostatic interactions of bodies bearing thin double-layers II. exact numerical solutions[J]. Berichte der Bunsengesellschaft für Physikalische Chemie, 1990, 94(12): 1492-1499.
[56] Wang H, Thiele A, Pilon L. Simulations of cyclic voltammetry for electric double layers in asymmetric electrolytes: A generalized modified Poisson-Nernst-Planck model[J]. Journal of Physical Chemistry C, 2013, 117(36): 18286-18297.
[57] Girard H L, Wang H N, D'entremont A L, et al. Physical interpretation of cyclic voltammetry for hybrid pseudocapacitors[J]. Journal of Physical Chemistry C, 2015, 119(21): 11349-11361.
[58] Girard H L, Wang H N, D'entremont A L, et al. Enhancing faradaic charge storage contribution in hybrid pseudocapacitors[J]. Electrochimica Acta, 2015, 182: 639-651.
[59] Girard H L, Dunn B, Pilon L. Simulations and interpretation of three-electrode cyclic voltammograms of pseudocapacitive electrodes[J]. Electrochimica Acta, 2016, 211: 420-429.
[60] Mei B A, Munteshari O, Lau J, et al. Physical interpretations of Nyquist plots for EDLC electrodes and devices[J]. The Journal of Physical Chemistry C, 2018, 122(1): 194-206.
[61] Wu Z, Li L, Yan J M, et al. Materials design and system construction for conventional and new-concept supercapacitors[J]. Advanced Science, 2017, 4(6): 1600382.
[62] Mei B A, Pilon L. Three-dimensional cyclic voltammetry simulations of EDLC electrodes made of ordered carbon spheres[J]. Electrochimica Acta, 2017, 255: 168-178.
[63] Mei B A, Li B, Lin J, et al. Multidimensional cyclic voltammetry simulations of pseudocapacitive electrodes with a conducting nanorod scaffold[J]. Journal of the Electrochemical Society, 2017, 164(13): A3237-A3252.