修正的Poisson-Nernst-Planck模型及其库仑和硬球关联
Modified Poisson-Nernst-Planck model with Coulomb and hard-sphere correlations
摘要：
我们提出了一个修正的Poisson-Nernst-Planck模型，该模型在自由能泛函中同时包含了长程库仑关联和短程硬球关联，使得该模型能够准确描述复杂环境和纳米尺度约束下的离子输运.考虑电介质的极化的库仑关联通过求解广义Debye-Hückel方程来处理，该方程是一个格林函数方程，测试离子的相关能由自格林函数描述。硬球相关模型通过修改的基本测量理论。由此产生的模型可用于超出平均场论的问题，如可变介电介质，多价离子和强表面电荷密度的问题。采用Wentzel-Kramers-Brillouin近似求解了广义Debye-Hückel方程，并研究了两平行介质表面间的电解质。与其他改进模型相比，新模型更准确地与基于粒子的模拟一致，并捕获界面附近离子结构的物理性质。
英文摘要：
We develop a modified Poisson-Nernst-Planck model which includes both the long-range Coulomb and short-range hard-sphere correlations in its free energy functional such that the model can accurately describe the ion transport in complex environment and under a nanoscale confinement. The Coulomb correlation including the dielectric polarization is treated by solving a generalized Debye-Hückel equation which is a Green's function equation with the correlation energy of a test ion described by the self Green's function. The hard-sphere correlation is modeled through the modified fundamental measure theory. The resulting model is available for problems beyond the mean-field theory such as problems with variable dielectric media, multivalent ions, and strong surface charge density. We solve the generalized Debye-Hückel equation by the Wentzel-Kramers-Brillouin approximation, and study the electrolytes between two parallel dielectric surfaces. In comparison to other modified models, the new model is shown more accurate in agreement with particle-based simulations and capturing the physical properties of ionic structures near interfaces.
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