考慮粒子大小與強交互作用之新泊松-玻爾茲曼方程

Abstract

研究離子擴散的行為在很多應用問題上扮演重要的角色，如生物離子通道等等，而泊松-玻爾茲曼方程便是描述此行為的模型且被廣泛應用。隨著奈米科技的發展，許多新的結果被發現。然而，這些結果卻無法用泊松-玻爾茲曼方程解釋，因此有了Bo Li 的模型。本論文研究Poisson-Nernst-Planck 方程with steric effects 的穩定態，New Poisson-Boltzmann 方程with steric effects，並且證明可以從此模型推得Li 的模型。

Studying the transport of ions plays an important role in many problems, such as ion channels. Over the past decades, original Poisson-Boltzmann (PB) equation was widely used to describe the electrolyte solutions. However, due to the development of nanotechnology, some new experiment outcomes were found but could not be described. Therefore, Li’s model was constructed. In this work, we further investigate a new Poisson-Boltzmann (PB) type equation called the PB_ns equation, which is derived from the steady-state of the Poisson-Nernst-Planck system with steric effects and shows that PB_ns equation can reduce to Li’s model.