Kornyshev Alexei A
Section of Theoretical and Experimental Physical Chemistry, Department of Chemistry, Faculty of Natural Sciences, Imperial College London, SW7 2AZ London, U.K.
J Phys Chem B. 2007 May 24;111(20):5545-57. doi: 10.1021/jp067857o. Epub 2007 May 1.
Applications of ionic liquids at electrified interfaces to energy-storage systems, electrowetting devices, or nanojunction gating media cannot proceed without a deep understanding of the structure and properties of the interfacial double layer. This article provides a detailed critique of the present work on this problem. It promotes the point of view that future considerations of ionic liquids should be based on the modern statistical mechanics of dense Coulomb systems, or density-functional theory, rather than classical electrochemical theories which hinge on a dilute-solution approximation. The article will, however, contain more questions than answers. To trigger the discussion, it starts with a simplified original result. A new analytical formula is derived to rationalize the potential dependence of double-layer capacitance at a planar metal-ionic liquid interface. The theory behind it has a mean-field character, based on the Poisson-Boltzmann lattice-gas model, with a modification to account for the finite volume occupied by ions. When the volume of liquid excluded by the ions is taken to be zero (that is, if ions are extremely sparsely packed in the liquid), the expression reduces to the nonlinear Gouy-Chapman law, the canonical result typically used to describe the potential dependence of capacitance in electrochemical double layers. If ionic volume exclusion takes more realistic values, the formula shows that capacitance-potential curves for an ionic liquid may differ dramatically from the Gouy-Chapman law. Capacitance has a maximum close to the potential of zero charge, rather than the familiar minimum. At large potenials, capacitance decreases with the square root of potential, rather than increases exponentially. The reported formula does not take into account the specific adsorption of ions, which, if present, can complicate the analysis of experimental data. Since electrochemists use to think about the capacitance data in terms of the classical Gouy-Chapman theory, which, as we know, should be good only for electrolytes of moderate concentration, the question of which result is "better" arises. Experimental data are sparse, but a quick look at them suggests that the new formula seems to be closer to reality. Opinions here could, however, split. Indeed, a comparison with Monte Carlo simulations has shown that incorporation of restricted-volume effects in the mean-field theory of electrolyte solutions may give results that are worse than the simple Gouy-Chapman theory. Generally, should the simple mean-field theory work for such highly concentrated ionic systems, where the so-called ion-correlation effects must be strong? It may not, as it does not incorporate a possibility of charge-density oscillations. Somehow, to answer this question definitely, one should do further work. This could be based on density-functional theory (and possibly not on what is referred to as local density approximation but rather "weighted density approximation"), field theory methods for the account of fluctuations in the calculation of partition function, heuristic integral equation theory extended to the nonlinear response, systematic force-field computer simulations, and, most importantly, experiments with independently determined potentials of zero charge, as discussed in the paper.
离子液体在带电界面于储能系统、电润湿装置或纳米结门控介质中的应用，如果对界面双层的结构和性质没有深入理解，就无法进行。本文对关于这个问题的现有工作进行了详细的批判。它提倡这样一种观点，即未来对离子液体的考虑应该基于稠密库仑系统的现代统计力学或密度泛函理论，而不是依赖于稀溶液近似的经典电化学理论。然而，本文提出的问题将比给出的答案更多。为了引发讨论，文章从一个简化的原始结果开始。推导了一个新的解析公式，以合理化平面金属 - 离子液体界面双层电容对电势的依赖性。其背后的理论具有平均场特征，基于泊松 - 玻尔兹曼晶格气体模型，并进行了修正以考虑离子占据的有限体积。当离子排除的液体体积被视为零时（即，如果离子在液体中极其稀疏地堆积），该表达式简化为非线性古依 - 查普曼定律，这是通常用于描述电化学双层中电容对电势依赖性的经典结果。如果离子体积排除采用更现实的值，该公式表明离子液体的电容 - 电势曲线可能与古依 - 查普曼定律有显著差异。电容在接近零电荷电势处有一个最大值，而不是常见的最小值。在高电势下，电容随电势的平方根减小，而不是指数增加。所报道的公式没有考虑离子的特异性吸附，如果存在这种吸附，会使实验数据分析变得复杂。由于电化学家习惯于根据经典的古依 - 查普曼理论来思考电容数据，而我们知道该理论仅适用于中等浓度的电解质，所以就出现了哪个结果“更好”的问题。实验数据稀少，但快速查看这些数据表明新公式似乎更接近实际情况。然而，这里的观点可能会出现分歧。实际上，与蒙特卡罗模拟的比较表明，在电解质溶液的平均场理论中纳入受限体积效应可能会得到比简单的古依 - 查普曼理论更差的结果。一般来说，对于这种高浓度离子系统，简单的平均场理论是否适用呢？在这种系统中所谓的离子关联效应肯定很强。可能不适用，因为它没有考虑电荷密度振荡的可能性。不知何故，要明确回答这个问题，还需要进一步开展工作。这可以基于密度泛函理论（可能不是所谓的局域密度近似，而是 “加权密度近似”）、在配分函数计算中考虑涨落的场论方法、扩展到非线性响应的启发式积分方程理论、系统力场计算机模拟，以及最重要的是如本文所讨论的具有独立确定的零电荷电势的实验。
