Budkov Yury A, Kalikin Nikolai N, Kolesnikov Andrei L
School of Applied Mathematics, HSE University, Tallinskaya st. 34, 123458 Moscow, Russia.
G. A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, 153045, Akademicheskaya st. 1, Ivanovo, Russia.
Phys Chem Chem Phys. 2022 Jan 19;24(3):1355-1366. doi: 10.1039/d1cp04221a.
Polymeric ionic liquids are emerging polyelectrolyte materials for modern electrochemical applications. In this paper, we propose a self-consistent field theory of a polymeric ionic liquid on a charged conductive electrode. Taking into account the conformational entropy of rather long polymerized cations within the Lifshitz theory and electrostatic and excluded volume interactions of ionic species within the mean-field approximation, we obtain a system of self-consistent field equations for the local electrostatic potential and average concentrations of monomeric units and counterions. We solve these equations in the linear approximation for the cases of a point-like charge and a flat infinite uniformly charged electrode immersed in a polymeric ionic liquid and derive analytical expressions for local ionic concentrations and electrostatic potential, and derive an analytical expression for the linear differential capacitance of the electric double layer. We also find a numerical solution to the self-consistent field equations for two types of boundary conditions for the local polymer concentration on the electrode, corresponding to the cases of the specific adsorption absence (indifferent surface) and strong short-range repulsion of the monomeric units near the charged surface (hard wall case). For both cases, we investigate the behavior of differential capacitance as a function of applied voltage for a pure polymeric ionic liquid and a polymeric ionic liquid dissolved in a polar organic solvent. We observe that the differential capacitance profile shape is strongly sensitive to the adopted boundary condition for the local polymer concentration on the electrode.
聚合物离子液体是用于现代电化学应用的新兴聚电解质材料。在本文中，我们提出了一种关于带电导电电极上聚合物离子液体的自洽场理论。考虑到在 Lifshitz 理论中相当长的聚合阳离子的构象熵以及在平均场近似下离子物种的静电和排除体积相互作用，我们得到了关于局部静电势以及单体单元和抗衡离子平均浓度的自洽场方程组。我们针对浸没在聚合物离子液体中的点状电荷和平坦无限均匀带电电极的情况，在线性近似下求解这些方程，推导了局部离子浓度和静电势的解析表达式，并推导了双电层线性微分电容的解析表达式。我们还针对电极上局部聚合物浓度的两种边界条件找到了自洽场方程的数值解，这两种情况分别对应于不存在特异性吸附（中性表面）以及带电表面附近单体单元存在强短程排斥（硬壁情况）。对于这两种情况，我们研究了纯聚合物离子液体以及溶解在极性有机溶剂中的聚合物离子液体的微分电容随外加电压的变化行为。我们观察到，微分电容曲线形状对所采用的电极上局部聚合物浓度的边界条件非常敏感。
