Kwon GW, Won YS, Yoon BJ
Department of Chemical Engineering, Pohang University of Science and Technology, Pohang, 790-784, Korea
J Colloid Interface Sci. 1998 Sep 15;205(2):423-432. doi: 10.1006/jcis.1998.5675.
Electrostatic interactions are computed for three-dimensional regular arrays of spheres. Tetrahedral array of four spheres, octahedral array of six spheres, cubic array of eight spheres, and periodic arrays of spheres in body-centered cubic (BCC) and face-centered cubic (FCC) structures are considered. Based on the linearized Poisson-Boltzmann equation the electrostatic free energy is computed for both constant surface potential and constant surface charge conditions. Facilitating the complex geometry of the problem, the boundary element method is used. Test results for two-sphere interactions are in excellent agreement with existing exact solutions even at very small Debye length. The results for multisphere interactions are compared with those obtained by the pairwise additivity approximation. For BCC and FCC arrays comparison is made to the results from the pairwise additivity approximation and from the spherical cell model. At small Debye length the pairwise additivity approximation predicts the interactions reasonably well. At large Debye length, however, the cell model furnishes much better estimates. In addition, the electrostatic free energy difference between BCC and FCC structures at given particle concentration is found to be too small to assess any physical significance. Copyright 1998 Academic Press.
计算了球体三维规则阵列的静电相互作用。考虑了四个球体的四面体阵列、六个球体的八面体阵列、八个球体的立方体阵列以及体心立方（BCC）和面心立方（FCC）结构的球体周期性阵列。基于线性化的泊松 - 玻尔兹曼方程，计算了恒定表面电势和恒定表面电荷条件下的静电自由能。为便于处理该问题的复杂几何形状，采用了边界元法。即使在非常小的德拜长度下，双球体相互作用的测试结果与现有的精确解也非常吻合。将多球体相互作用的结果与通过成对加和近似法得到的结果进行了比较。对于BCC和FCC阵列，将结果与成对加和近似法以及球形单元模型的结果进行了比较。在小德拜长度下，成对加和近似法能较好地预测相互作用。然而，在大德拜长度下，单元模型提供了更好的估计。此外，发现在给定粒子浓度下，BCC和FCC结构之间的静电自由能差太小，无法评估任何物理意义。版权所有1998年，学术出版社。
