University of Surrey, Faculty of Engineering and Physical Sciences, Department of Chemical and Process Engineering, Centre for Osmosis Research and Applications, Guildford, Surrey GU2 7XH, UK.
J Colloid Interface Sci. 2010 Jun 1;346(1):232-5. doi: 10.1016/j.jcis.2010.01.053. Epub 2010 Mar 1.
The effect of many-body interactions on the electrostatic force between spheres in an array of charged spherical particles has been quantified by solving the non-linear Poisson-Boltzmann equation (PBE) using a finite element method (FEM) model. The equation is solved for conditions of constant surface potential. The effect of the dimensionless Debye length scaled radius of the spheres on the electrostatic force between them has been determined and a significant reduction of the force is observed as the dimensionless Debye radius is decreased. Calculations based on the dimensionless separation distance between a pair of charged spheres in isolation confirm an exponential decay of the repulsive electrostatic force as the surface to surface separation distance is increased. In contrast, calculations based on an array of interacting spheres in certain critical packing conditions reveal considerable reduction in the magnitude of the repulsive electrostatic force at separation distances less than half the sphere radius. The latter results are explained by considering the directional cancellation effects of the electrical double layer between adjacent spheres placed in certain orientations within the array. This is believed to be a surprising many-body effect which has been overlooked in previous studies and whose validity can be used to explain the stability and strength of charged sphere arrays under certain critical geometric configurations.
通过使用有限元方法 (FEM) 模型求解非线性泊松-玻尔兹曼方程 (PBE)，定量研究了多体相互作用对带电球形粒子阵列中球体之间静电力的影响。该方程是在恒定表面电势条件下求解的。确定了无量纲德拜半径与球体之间静电力的关系，发现随着无量纲德拜半径的减小，静电力显著减小。基于一对孤立带电球体之间的无量纲分离距离的计算，证实了随着表面到表面分离距离的增加，排斥静电的力呈指数衰减。相比之下，基于在某些临界堆积条件下相互作用球体的阵列的计算表明，在小于球体半径一半的分离距离处，排斥静电的力的大小显著减小。考虑到在阵列中以某些取向放置的相邻球体之间的电双层的定向抵消效应，可以解释后者的结果。这被认为是一个令人惊讶的多体效应，在以前的研究中被忽视了，其有效性可以用来解释在某些临界几何配置下带电球体阵列的稳定性和强度。
