Denton A R
Department of Physics, North Dakota State University, Fargo, North Dakota 58105-5566, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Sep;70(3 Pt 1):031404. doi: 10.1103/PhysRevE.70.031404. Epub 2004 Sep 30.
A nonlinear response theory is developed and applied to electrostatic interactions between spherical macroions, screened by surrounding microions, in charge-stabilized colloidal suspensions. The theory describes leading-order nonlinear response of the microions (counterions, salt ions) to the electrostatic potential of the macroions and predicts microion-induced effective many-body interactions between macroions. A linear response approximation [A.R. Denton, Phys. Rev. E 62, 3855 (2000)] yields an effective pair potential of screened-Coulomb (Yukawa) form, as well as a one-body volume energy, which contributes to the free energy. Nonlinear response generates effective many-body interactions and essential corrections to both the effective pair potential and the volume energy. By adopting a random-phase approximation (RPA) for the response functions, and thus neglecting microion correlations, practical expressions are derived for the effective pair and triplet potentials and for the volume energy. Nonlinear screening is found to weaken repulsive pair interactions, induce attractive triplet interactions, and modify the volume energy. Numerical results for monovalent microions are in good agreement with available ab initio simulation data and demonstrate that nonlinear effects grow with increasing macroion charge and concentration and with decreasing salt concentration. In the dilute limit of zero macroion concentration, leading-order nonlinear corrections vanish. Finally, it is shown that nonlinear response theory, when combined with the RPA, is formally equivalent to the mean-field Poisson-Boltzmann theory and that the linear response approximation corresponds, within integral-equation theory, to a linearized hypernetted-chain closure.
我们发展了一种非线性响应理论，并将其应用于电荷稳定的胶体悬浮液中，由周围微离子屏蔽的球形大离子之间的静电相互作用。该理论描述了微离子（反离子、盐离子）对大离子静电势的主导阶非线性响应，并预测了微离子诱导的大离子之间有效的多体相互作用。线性响应近似[A.R. 丹顿，《物理评论E》62，3855（2000）]产生了屏蔽库仑（汤川）形式的有效对势以及单体体积能，其对自由能有贡献。非线性响应产生有效的多体相互作用，并对有效对势和体积能进行了重要修正。通过对响应函数采用随机相位近似（RPA），从而忽略微离子相关性，我们推导出了有效对势、三重态势和体积能的实用表达式。发现非线性屏蔽会削弱排斥性对相互作用，诱导吸引性三重态相互作用，并改变体积能。单价微离子的数值结果与现有的从头算模拟数据吻合良好，并表明非线性效应随着大离子电荷和浓度的增加以及盐浓度的降低而增强。在大离子浓度为零的稀释极限下，主导阶非线性修正消失。最后，结果表明，当非线性响应理论与RPA相结合时，在形式上等同于平均场泊松 - 玻尔兹曼理论，并且在积分方程理论中，线性响应近似对应于线性化的超网链闭合。
