Electrostatistics of counter-ions at and between planar charged walls: From Poisson-Boltzmann to the strong-coupling theory
Electrostatistics of counter-ions at and between planar charged walls: From Poisson-Boltzmann to the strong-coupling theory
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DOI：
10.1007/s101890170039
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发表时间：
2001-08-01
影响因子：
1.8
通讯作者：
Netz, RR
中科院分区：
文献类型：
--
作者：
Netz, RR
Poisson-Boltzmann(PB)方法给出了在低反离子价态、低表面电荷密度和高温的弱耦合极限下，宏观带电物体周围的反离子密度和宏观带电物体之间的作用力的渐近精确的分布。本文利用场论方法，导出了在强耦合(SC)的相反极限下变得精确的理论。在形式上，它对应于标准的维里扩张。长程发散使得均匀块体系统的维里展开难以处理，导致电解质溶液自由能密度的低密度展开中的非解析性。我们证明了对于宏观带电物体的非均匀密度分布函数的情况，这些发散可以通过逸度幂的系统展开来重整化。对于单个平面带电体壁，我们得到了Sc极限中的反离子密度分布，与预测代数衰变的PB结果相反，并与以前发表的数值结果一致。类似地，在存在多价反离子的情况下，高电荷板在Sc限制下相互吸引，形成静电束缚状态，与PB限制相反，在PB限制下，相互作用总是排斥的。通过考虑PB和SC理论的下一个主要修正，我们估计了这两个理论的有效范围。
The Poisson-Boltzmann (PB) approach gives asymptotically exact counter-ion density profiles around macroscopic charged objects and forces between macroscopic charged objects in the weak-coupling limit of low counter-ion valency, low surface-charge density, and high temperature. In this paper we derive, using field-theoretic methods, a theory which becomes exact in the opposite limit of strong coupling (SC). Formally, it corresponds to a standard virial expansion. Long-range divergences render the virial expansion intractable for homogeneous bulk systems, giving rise to non-analyticities in the low-density expansion of the free-energy density of electrolyte solutions. We demonstrate that for the case of inhomogeneous density distribution functions at macroscopic charged bodies these divergences are renormalizable by a systematic expansion in powers of the fugacity. For a single planar charged wall, we obtain the counter-ion density profile in the SC limit, which decays exponentially, in contrast to the PB result, which predicts algebraic decay, and in agreement with previously published numerical results. Similarly and highly charged plates in the presence of multivalent counter-ions attract each other in the SC limit and form electrostatically bound states, in contrast to the PB limit, where the interaction is always repulsive. By considering next-leading corrections to both the PB and SC theories, we estimate the range of validity for both theories.