论文标题

改良的泊松玻璃到玻璃体方程和不均匀离子流体中的宏观力量

Modified Poisson-Boltzmann equations and macroscopic forces in inhomogeneous ionic fluids

论文作者

Budkov, Yu. A., Kolesnikov, A. L.

论文摘要

我们提出了一种基于热力学扰动理论的现场理论方法,并在其中提出了不均匀离子流体的巨大热力学潜力,作为任意参考流体系统的静电潜力的功能。我们获得了修改后的泊松玻璃到达方程,作为获得功能的Euler-Lagrange方程。将Noether定理应用于该功能,我们得出了与各自修改的Poisson-Boltzmann方程一致的应力张量的一般平均场表达。我们得出作用在浸入离子液中的介电或导电体上的宏观表达。特别是,我们得出了缝孔中离子流体的分离压力的一般平均场表达。我们将开发的形式主义应用于描述三种实际重要性的离子流体模型:不可极化的模型(包括众所周知的泊松 - 波尔兹曼和泊松式 - 弗米方程),可极化模型(离子携带非零的永久性偶极或静态极性化),以及众所周知的poisson poisson-boltzmannequation(包括众所周知的poisson-boltzmannequation)。对于这些模型,我们获得了修改的泊松托架方程和各自的应力张量,这对于不同的应用可能很有价值,在这种情况下,有必要估计作用于介电或导电物体(电极,胶体,胶体,膜,膜,{\ it eft eft effertostic的宏观或导电物体)的宏观力。

We propose a field-theoretical approach based on the thermodynamic perturbation theory and within it derive a grand thermodynamic potential of the inhomogeneous ionic fluid as a functional of electrostatic potential for an arbitrary reference fluid system. We obtain a modified Poisson-Boltzmann equation as the Euler-Lagrange equation for the obtained functional. Applying Noether's theorem to this functional, we derive a general mean-field expression for the stress tensor consistent with the respective modified Poisson-Boltzmann equation. We derive a general expression for the macroscopic force acting on the dielectric or conductive body immersed in an ionic fluid. In particular, we derive a general mean-field expression for the disjoining pressure of an ionic fluid in a slit pore. We apply the developed formalism to describe three ionic fluid models of practical importance: nonpolarizable models (including the well-known Poisson-Boltzmann and Poisson-Fermi equations), polarizable models (ions carry nonzero permanent dipole or static polarizability), and models of ion-dipole mixtures (including the well-known Poisson-Boltzmann-Langevin equation). For these models, we obtain modified Poisson-Boltzmann equations and respective stress tensors, which could be valuable for different applications, where it is necessary to estimate the macroscopic forces acting on the dielectric or conductive bodies (electrodes, colloids, membranes, {\it etc}.) together with the local electrostatic potential (field) and ionic concentrations.

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