相反电荷体的Poisson-Boltzmann：一个显式推导
Poisson-Boltzmann for oppositely charged bodies: an explicit derivation
摘要：
离子溶液中带电体之间的相互作用是胶体物理中的一个普遍问题，也是研究蛋白质、核酸、膜等生物体系静电相互作用的中心课题。这个问题通常从两个平行带电板的简单一维模型开始描述。针对这一问题存在几种不同的方法，侧重于不同的特征。在许多情况下，施加在板上的压力的一个直观的表达式，其中包括静电加上渗透贡献。我们提出了一个明确的和自洽的推导这个公式的一般情况下的任何电荷密度的板和任何盐溶液，在泊松-玻尔兹曼理论的框架内获得。我们还表明，取决于外部约束，正确的热力学势可以不同于通常的PB自由能。由此产生的表达式预测，不对称，带相反电荷的板，存在一个非平凡的平衡位置与板分离的有限距离。因此，它是至关重要的，为了研究相应的能量最小的动力学稳定性，以获得其明确的依赖于板的电荷密度和离子浓度。1975年，Ohshima [Ohshima H.，胶体与聚合物科学253，150-157（1975）]，但令人惊讶的是，这个重要的结果似乎被忽视了今天。我们检索Ohshima获得的表达式在一个更简单的形式主义，更熟悉的物理界，并给出了物理解释所观察到的行为。
英文摘要：
The interaction between charged bodies in an ionic solution is a general problem in colloid physics and becomes a central topic in the study of biological systems where the electrostatic interaction between proteins, nucleic acids, membranes is involved. This problem is often described starting from the simple one-dimensional model of two parallel charged plates. Several different approaches to this problem exist, focusing on different features. In many cases, an intuitive expression of the pressure exerted on the plates is proposed, which includes an electrostatic plus an osmotic contribution. We present an explicit and self-consistent derivation of this formula for the general case of any charge densities on the plates and any salt solution, obtained in the framework of the Poisson-Boltzmann theory. We also show that, depending on external constraints, the correct thermodynamic potential can differ from the usual PB free energy. The resulting expression predicts, for asymmetric, oppositely charged plates, the existence of a non trivial equilibrium position with the plates separated by a finite distance. It is therefore crucial, in order to study the kinetic stability of the corresponding energy minimum, to obtain its explicit dependence on the plates charge densities and on the ion concentration. An analytic expression for the position and value of the corresponding energy minimum has been derived in 1975 by Ohshima [Ohshima H., Colloid and Polymer Sci. 253, 150-157 (1975)] but, surprisingly, this important result seems to be overlooked today. We retrieve the expressions obtained by Ohshima in a simpler formalism, more familiar to the physics community, and give a physical interpretation of the observed behavior.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
