非点电荷离子模型的静电相互作用的理论与模拟

An important direction within an area of electrostatics of soft-matter systems is to go beyond the standard Poisson-Boltzmann equation by incorporating correlations neglected in the mean-field level of description. In the weak-coupling limit correlations act as corrective contribution, are important for dielectric discontinuities, then, in the strong-coupling limit correlations dominate physics, in which case, the standard Poisson-Boltzmann model loses any predictive power. Another important direction is to retain the mean-field level of description and instead focus on details of a structure of an ion. In standard Poisson-Boltzmann equation an ion is represented as a point-charge. There are two problems with this description. First of all, such a representation is not completely physical, since, according to its prediction, to separate two opposite charges from zero to any finite separation would require an infinite force. This leads to collapse of opposite ions, which becomes problematic for models that attempt to go beyond the mean-field description, calling for some sort of regularization. The second reason is that a point-charge description is not complete enough for large class of emerging systems in soft-matter. An important example is ion-specificity, where ions of the same valance charge but different, size, shape, polarizability exhibit different behaviors. These extra features of an ion are more than just a corrective contribution. Like correlations of the strong-coupling limit they give rise to counterintuitive phenomena, such as charge inversion and attraction between the same charged surfaces. Models that capture an ion structure are still lacking. Together with the lack of models, we lack proper understading of how structure leads to these counterintuitive behaviors. These interests lead to various problematic issues, such as, how to handle combination of short-range non-electrostatic interaction, say hard-core interactions, with long-range electrostatic forces. Or, how to handle or even simulate polarizability. This proposal deals precisely with these issues. For some cases the mean-field level of description is sufficient and one can learn a great deal from it. Other situations, like combination of hard-core interactions with electrostatics are more challenging, but there still remains a lot of room for producing creative solutions that have not been pursued. Finally, this proposal wants to take advantage of emerging methods of field-theoretical simulations, formulated for polymers, to cope with problems of polarizability encountered in standard Monte-Carlo simulation.

软物质体系静电学研究的一个重要方向是加入关联效应来改进标准泊松玻尔兹曼方程（PBE）的平均场描述。在弱耦合极限下，关联效应可以作为修正项；而在强耦合极限下，PBE失去了预测能力。另一个重要方向是保留平均场描述，而着重于离子结构的细节。PBE中离子用点电荷描述。然而点电荷在一些情况下是非物理的，如将距离为零的异性电荷拉开需要无限大的力。此外，点电荷不能够描述所有感兴趣的软物质体系，例如离子特异性。离子的这些特性不能够用简单的修正项来表示。如同强耦合极限下的关联效应一样，这导致了一些反常现象，如电荷反转和同性带电表面相吸。目前还没有能够准确描述离子结构的模型，且对离子结构与这些反常现象之间关系的理解仍不充分。本项目将解决与此相关的一些问题。首先平均场描述研究简单的体系。然后提出创新方案来处理硬球势和静电势的混合模型。最后汲取新发展的用于聚合物的场论模拟方法来处理蒙特卡罗模拟中极化率的计算问题。

本项目研究基于软物质和生命体系最基础的相互作用来源—静电相互作用。我们提出了一种适用非均质流体的无规相近似（RPA）的密度泛函框架，并称之为广义RPA (GRPA)。 GRPA构成了对平均场的校正，它对于稠密流体（在大量粒子重叠的情况下更准确）而言更加准确。可以处理长程库仑势和短程非静电相互作用的混合体系。我们首次找到鞍点周围辅助磁场的谐波波动与RPA的密度函数公式之间的联系， 证明GRPA与基于场论框架处理电荷粒子的变分高斯近似完全一致。考虑可穿透球体系统随着相互作用的增加转变为刚性球系统，我们进一步将RPA应用于可穿透球体系统，以更深入地研究RPA相对于强和弱耦合极限的不足和限制。通过研究对称相互作用下的单相和两相流体系统，发现虽然RPA是一种非微扰模型，但并不适合强耦合区间。RPA在平均场层面引入修正，但并没有扩大平均场适用的范围。我们还研究在涂抹电荷过度屏蔽的电荷表面双层结构，并通过观察Kirkwood交叉探索双层结构与电解质体性质的联系。我们发现正如Kirkwood线将体溶液划分为单调衰减和振荡衰减的流体,它类似地将电荷反转分为两个主要区域，包含和不包含振荡电荷密度分布。因最初的振荡如同远场现象，最终发展为成熟的分层电荷密度。总之本项目发展了新的模型方法，并通过对不同离子结构的研究为像电荷反转和带同种电荷的表面间吸引相互作用这样的反常现象提供了新的见解。