Wigner-Seitz model of charged lamellar colloidal dispersions
Wigner-Seitz model of charged lamellar colloidal dispersions
复制标题
带电层状胶体分散体的 Wigner-Seitz 模型
DOI：
10.1103/physreve.56.3137
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发表时间：
1997
影响因子：
2.4
通讯作者：
J. Hansen
中科院分区：
文献类型：
--
作者：
E. Trizac;J. Hansen
层状胶体颗粒的浓缩悬浮液（例如，G.粘土）是通过考虑一个单一的，均匀带电的，有限的血小板限制与共和抗衡离子的维格纳-塞茨（WS）细胞。该系统内处理泊松-玻尔兹曼理论，与适当的边界条件的WS细胞的表面上，应该考虑到相邻的血小板的限制效应。表达式获得的自由能，渗透压和分离压力和电容的局部静电势和合作和反的密度分布。线性化Poisson-Boltzmann（LPB）方程的显式解获得圆形和方形血小板放置在一个圆柱形或平行六面体细胞的中心。对于任何给定的体积（由血小板的宏观浓度确定）、血小板表面电荷和盐浓度，发现所得自由能作为细胞的纵横比的函数经历最小值。最佳的纵横比被发现是几乎独立的后两个物理参数。的渗透压和分离压被发现在自由能最小值相吻合，而总的四极矩的双电层形成的血小板和周围的合作和抗衡离子同时消失。渗透状态方程计算了各种物理条件。消失血小板浓度的限制被认为是在一些细节，和两个同轴的血小板之间的作用力计算在该限制作为其分离的函数。
A concentrated suspension of lamellar colloidal particles (e. g. clay) is modelled by considering a single, uniformly charged, finite platelet confined with co- and counterions to a Wigner-Seitz (WS) cell. The system is treated within Poisson-Boltzmann theory, with appropriate boundary conditions on the surface of the WS cell, supposed to account for the confinement effect of neighbouring platelets. Expressions are obtained for the free energy, osmotic and disjoining pressures and the capacitance in terms of the local electrostatic potential and the co- and counterion density profiles. Explicit solutions of the linearized Poisson-Boltzmann (LPB) equation are obtained for circular and square platelets placed at the centre of a cylindrical or parallelepipedic cell. The resulting free energy is found to go through a minimum as a function of the aspect ratio of the cell, for any given volume (determined by the macroscopic concentration of platelets), platelet surface charge and salt concentration. The optimum aspect ratio is found to be nearly independent of the two latter physical parameters. The osmotic and disjoining pressures are found to coincide at the free energy minimum, while the total quadrupole moment of the electric double-layer formed by the platelet and the surrounding co- and counterions vanishes simultaneously. The osmotic equation-of-state is calculated for a variety of physical conditions. The limit of vanishing platelet concentration is considered in some detail, and the force acting between two coaxial platelets is calculated in that limit as a function of their separation.