Charged Membranes: Poisson-Boltzmann theory, DLVO paradigm and beyond
Tomer Markovich, David Andelman, Rudi Podgornik
备注：
57 pages, 19 figures, From the forthcoming Handbook of Lipid Membranes: Molecular, Functional, and Materials Aspects. Edited by Cyrus Safinya and Joachim Radler, Taylor & Francis/CRC Press, 2016
In this chapter we review the electrostatic properties of charged membranes in aqueous solutions, with or without added salt, employing simple physical models. The equilibrium ionic profiles close to the membrane are governed by the well-known Poisson-Boltzmann (PB) equation. We analyze the effect of different boundary conditions, imposed by the membrane, on the ionic profiles and the corresponding osmotic pressure. The discussion is separated into the single membrane case and that of two interacting membranes. For one membrane setup, we show the different solutions of the PB equation and discuss the interplay between constant-charge and constant-potential boundary conditions. A modification of the PB theory is presented to treat the extremely high counter-ion concentration in the vicinity of a charge membrane. For two equally-charged membranes, we analyze the different pressure regimes for the constant-charge boundary condition, and discuss the difference in the osmotic pressure for various boundary conditions. The non-equal charged membranes is reviewed as well, and the crossover from repulsion to attraction is calculated analytically. We then examine the charge-regulation boundary condition and discuss its effects on the ionic profiles and the osmotic pressure for two equally-charged membranes. In the last section, we briefly review the van der Waals (vdW) interactions and their effect on the free energy between two planar membranes. We explain the simple Hamaker pair-wise summation procedure, and introduce the more rigorous Lifshitz theory. The latter is a key ingredient in the DLVO theory, which combines repulsive electrostatic with attractive vdW interactions, and offers a simple explanation for colloidal or membrane stability. Finally, the chapter ends by a short account of the limitations of the approximations inherent in the PB theory.
Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method
在简单剪切流中自由悬浮的初始球形胶囊的变形可以在小变形的极限下解析计算[D。Barthes-Bianca，J. M. Rallison，在线性剪切流中自由悬浮的胶囊的时间相关变形，J. Fluid Mech.113（1981）251-267]。这些解析近似被用来研究的网格镶嵌方法，空间分辨率，和离散δ函数的浸入边界法的数值结果上得到的耦合浸入边界格子Boltzmann有限元方法的影响。对于囊膜的描述，采用有限元法和Skalak本构模型[R。Skalak等人，红细胞膜的应变能函数。J. 13（1973）245-264]已经被使用。我们的主要目标是调查所提出的模型为小分辨率提供了一个良好的基础，有效而准确的模拟多个可变形的粒子浸没在流体中。我们得出的结论是，膜网格的细节，镶嵌方法和分辨率，只发挥次要作用。流体动力学分辨率，即，离散δ函数的宽度可以显著地影响模拟的精度。δ函数的离散化引入了人工长度尺度，其有效地改变了胶囊的半径和可变形性。我们讨论的可能性，减少计算时间的变形物体浸没在流体中的模拟，同时保持高精度。
Dielectric permittivity of water confined in stacks of charged lipid layers: extracting profiles from molecular dynamics simulations using a modified Poisson-Boltzmann equation
Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière（里昂第一大学，法国国家科学研究中心，光物质研究所）；UPR 22/CNRS, Institut Charles Sadron, Université de Strasbourg（斯特拉斯堡大学，法国国家科学研究中心查尔斯·萨德龙研究所）
Asymmetric electrostatic properties of an electric double layer: a generalized Poisson-Boltzmann approach taking into account non-uniform size effects and water polarization
