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电化学(中英文) ›› 2022, Vol. 28 ›› Issue (2): 2108471.  doi: 10.13208/j.electrochem.210847

所属专题: “理论计算模拟”专题文章 iSAIEC 2023 “AI for Electrochemistry”专题文章

• 教程 • 上一篇    下一篇

平衡、非平衡、交流状态下电化学双电层建模的初学者指南

张露露1,#, 李琛坤2,#, 黄俊3,*()   

  1. 1.中国科学技术大学化学与材料科学学院,安徽 合肥230026,中华人民共和国
    2.中南大学化学化工学院,湖南 长沙410083,中华人民共和国
    3.乌尔姆大学理论化学研究所,乌尔姆89069,德国
  • 收稿日期:2021-10-26 修回日期:2021-12-07 出版日期:2022-02-28 发布日期:2021-12-18

A Beginners’ Guide to Modelling of Electric Double Layer under Equilibrium, Nonequilibrium and AC Conditions

Lu-Lu Zhang1,#, Chen-Kun Li2,#, Jun Huang3,*()   

  1. 1. School of Chemistry and Materials Science, University of Science and Technology of China, Hefei 230026, Anhui, People’s Republic of China
    2. College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, Hunan, People’s Republic of China
    3. Institute of Theoretical Chemistry,Ulm University, 89069 Ulm Germany
  • Received:2021-10-26 Revised:2021-12-07 Published:2022-02-28 Online:2021-12-18
  • Contact: *Tel: (+49)15906819204, E-mail: jhuangelectrochem@qq.com.
  • About author:#Equal contribution.

摘要:

本文定位在一篇电化学双电层(EDL)理论建模方面入门级文章。我们首先简要介绍了EDL的基本特征,简述了EDL理论建模的发展历史,特别是D.C. Grahame之后近几十年的发展历史。然后,我们依次介绍了平衡状态和动态下不同复杂度的EDL模型。作为一篇入门级文章,我们尽可能详细地阐释理论模型的物理图像、假设、数学推导、形式分析、数值分析,并附上Matlab仿真代码。平衡状态下的模型包括Gouy-Chapman-Stern(GCS)模型,Bikerman-Poisson-Boltzmann(BPB)模型,和非对称离子尺寸模型。我们强调GCS模型和BPB模型在处理离子有限尺寸上存在一个微妙的不同。GCS模型通过人为引入Helmholtz平面来考虑离子有限尺寸,但在Helmholtz平面内及弥散层内却依然采用没有考虑离子尺寸效应的Poisson-Boltzmann理论,因而此处的离子浓度可以无限大。与之不同,BPB模型通过格子气体方法,能够自洽描述离子有限尺寸效应。不同以往直接采用Poisson-Nernst-Planck方程描述EDL动态行为,我们从EDL的巨势出发,运用基本的泛函分析方法,推导了一个考虑离子有限尺寸的EDL动态模型。这一理论方法拓展性好。读者可以根据研究对象的需要,建立不同复杂度的EDL动态模型。最后,我们基于EDL动态模型,推导了EDL的电化学阻抗谱理论模型,以试图向读者展示如何从一个时域物理模型出发,推导相应的阻抗谱物理模型。读者若想要踏进理论电化学这个美丽的花园,根据我们自己学习和研究的经验,一个可行的方式是拿起纸和笔来开始推导本文所介绍的这些模型。

关键词: 双电层, 平衡, 非平衡, 电化学阻抗谱, 物理建模

Abstract:

In electrochemistry, perhaps also in other time-honored scientific disciplines, knowledge labelled classical usually attracts less attention from beginners, especially those pressured or tempted to quickly jam into research fronts that are labelled, not always aptly, modern. In fact, it is a normal reaction to the burden of history and the stress of today. Against this context, accessible tutorials on classical knowledge are useful, should some realize that taking a step back could be the best way forward. This is the driving force of this article themed at physicochemical modelling of the electric (electrochemical) double layer (EDL). We begin the exposition with a rudimentary introduction to key concepts of the EDL, followed by a brief introduction to its history. We then elucidate how to model the EDL under equilibrium, using firstly the orthodox Gouy-Chapman-Stern model, then the symmetric Bikerman model, and finally the asymmetric Bikerman model. Afterwards, we exemplify how to derive a set of equations governing the EDL dynamics under nonequilibrium conditions using a unifying grand-potential approach. In the end, we expound on the definition and mathematical foundation of electrochemical impedance spectroscopy (EIS), and present a detailed derivation of an EIS model for a simple EDL. We try to avoid the omission of supposedly ‘trivial’ information in the derivation of models, hoping that it can ease the access to the wonderful garden of physical electrochemistry.

Key words: electric double layer, equilibrium, nonequilibrium, electrochemical impedance spectroscopy