Zaboronsky A O, Kornyshev A A
Department of Chemistry, Faculty of Natural Sciences, Imperial College London, Molecular Sciences Research Hub, White City Campus, Wood Lane, London, W12 0BZ, United Kingdom.
J Phys Condens Matter. 2020 Jun 24;32(27):275201. doi: 10.1088/1361-648X/ab76e4.
Ising type models of charging of conductive nanopores with ions have already been proposed and investigated for single file cylindrical or single layer slit nanopores. In such pores, the state of ions, the coulombic interactions of which are exponentially screened by their images in pore walls, was named superionic. In the present work we extend the analysis of the superionic state to nanopores that can accommodate multiple rows of ions. By grouping multiple charges in the same row into 'supercharges', we map the arrangement of ions in polarised electrodes on a multi-row Ising model in an external field. We investigate one-, two- and three-row cases, which we solve exactly, using a purpose-built semi-numerical transfer matrix method. For pores of different radii, which can accommodate the corresponding number of ion rows, we calculate the dependence of the electrical capacitance and stored energy density on electrode potential. As in charging the single file pores, we find that in narrower pores higher energy densities can be achieved at low applied potentials, while wider pores perform better as the voltage is increased.
关于离子对导电纳米孔充电的伊辛型模型已经被提出并针对单列圆柱形或单层狭缝纳米孔进行了研究。在这类孔中，离子的状态，其库仑相互作用通过它们在孔壁中的镜像被指数屏蔽，被称为超离子态。在本工作中，我们将超离子态的分析扩展到可以容纳多排离子的纳米孔。通过将同一排中的多个电荷组合成“超电荷”，我们将极化电极中离子的排列映射到外部场中的多排伊辛模型上。我们研究了一排、两排和三排的情况，并使用专门构建的半数值转移矩阵方法精确求解。对于不同半径的孔，其可以容纳相应数量的离子排，我们计算电容和存储能量密度对电极电位的依赖性。如同对单列孔充电一样，我们发现，在较窄的孔中，在低施加电位下可以实现更高的能量密度，而随着电压升高，较宽的孔表现更好。
