重新审视Poisson-Boltzmann理论：电荷表面、多价离子和板间力
Revisiting the Poisson-Boltzmann theory: charge surfaces, multivalent ions and inter-plate forces
摘要：
Poisson-Boltzmann（PB）理论被广泛用于深入了解带电胶体和生物系统，以及阐明分子间力的基本性质。许多工作致力于在过去的研究PB相关的功能，并确认他们的实验。在这项工作中，我们探讨了不同边界条件下的板间力的性质。我们处理的情况下，恒定的表面电荷，恒定的表面电位和混合边界。静电相互作用之间的相互作用，有吸引力的反离子释放，和排斥范特霍夫贡献分别讨论每种情况下。最后，我们讨论了吸引力和排斥力之间的交叉恒定的表面电荷的情况下是如何影响的存在下，多价反离子，其中它示出的吸引力的相互作用的范围与价增长。
英文摘要：
The Poisson-Boltzmann (PB) theory is extensively used to gain insight on charged colloids and biological systems as well as to elucidate fundamental properties of intermolecular forces. Many works were devoted in the past to study PB related features and to confirm them experimentally. In this work we explore the properties of inter-plate forces in terms of different boundary conditions. We treat the cases of constant surface charge, constant surface potential and mixed boundaries. The interplay between electrostatic interactions, attractive counter-ions release, and repulsive van 't Hoff contribution are discussed separately for each case. Finally, we discuss how the crossover between attractive and repulsive interactions for constant surface charge case is influenced by the presence of multivalent counter-ions, where it is shown that the range of the attractive interaction grows with the valency.
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