Popović Marko, Šiber Antonio
Rudjer Bošković Institute, 10000 Zagreb, Croatia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Aug;88(2):022302. doi: 10.1103/PhysRevE.88.022302. Epub 2013 Aug 8.
We derive a modification of the Poisson-Boltzmann (PB) equation brought about by the finite and different sizes of mobile ions. The equation we obtain contains explicitly the size asymmetry of the electrolyte, enabling one to apply the PB approach to the cases where this effect may be of importance. We show that the modification we propose predicts the asymmetry of the double-layer capacitance. Our approach thus provides a transparent analytical framework for a previously proposed heuristic modification of the PB equation, which also predicts the same effect. In addition, a detailed exposition of the lattice-based calculation of the entropy, accounting for steric, spatial correlations, enables us to clearly pinpoint some of the drawbacks of such an approach, which are not entirely obvious in previous attempts to include the steric effects in the PB equation.
我们推导了由移动离子的有限且不同尺寸所导致的泊松 - 玻尔兹曼（PB）方程的一种修正形式。我们得到的方程明确包含了电解质的尺寸不对称性，使得人们能够将PB方法应用于这种效应可能很重要的情况。我们表明，我们提出的修正形式能够预测双层电容的不对称性。因此，我们的方法为之前提出的对PB方程的启发式修正提供了一个清晰的分析框架，该修正也能预测相同的效应。此外，对基于晶格的熵计算进行详细阐述，其中考虑了空间位阻和空间相关性，使我们能够清楚地指出这种方法的一些缺点，这些缺点在之前将空间位阻效应纳入PB方程的尝试中并不完全明显。
