Liu Bo-Tau, Hsu Jyh-Ping
Department of Chemical and Materials Engineering, National Yunlin University of Science and Technology, Yunlin, Taiwan.
J Chem Phys. 2008 Mar 14;128(10):104509. doi: 10.1063/1.2888994.
The electrical potential for the case of two identical, planar parallel particles immersed in a salt-free medium, where the ionic species in the counterions come solely from those that dissociated from the surfaces, is evaluated. Analytical expressions for the electrical potential, the concentration of counterions, and the electrical energy are derived. We show that in a salt-free dispersion, if the separation distance between two particles is sufficiently far, the electrical repulsive force dominates, that is, the total energy is positive and does not have a secondary minimum, which is not the case for a dispersion where both coions and counterions are present. Also, the conditions used to calculate the critical coagulation concentration in the classic Derjaguin-Landau-Verwey-Overbeek theory become inappropriate and the Derjaguin approximation is inapplicable. We show that if the surface charge density exceeds approximately 0.04 Cm(2), the stability of a salt-free dispersion remains essentially the same. If the surface charge density is sufficiently high, the maximum separation distance between two particles below which coagulation occurs is in the ranges of [0,1 nm] and [1,7 nm] for the cases where the Hamaker constant is 10(-20) and 10(-19) J, respectively.
研究了两个相同的平面平行粒子浸没在无盐介质中的电势情况，其中反离子中的离子种类仅来自于从表面解离的那些离子。推导了电势、反离子浓度和电能的解析表达式。我们表明，在无盐分散体系中，如果两个粒子之间的分离距离足够远，电排斥力起主导作用，即总能量为正且不存在次级最小值，而对于同时存在同离子和反离子的分散体系则并非如此。此外，经典的德亚金 - 朗道 - 韦弗 - 奥弗贝克理论中用于计算临界凝聚浓度的条件变得不合适，德亚金近似也不适用。我们表明，如果表面电荷密度超过约0.04 C/m²，无盐分散体系的稳定性基本保持不变。如果表面电荷密度足够高，对于哈梅克常数分别为10⁻²⁰ J和10⁻¹⁹ J的情况，两个粒子之间发生凝聚的最大分离距离分别在[0,1纳米]和[1,7纳米]范围内。
