高电位胶体颗粒强相互作用的近似表达式  

Approximate Expressions for Strong Interaction of Colloidal Particles with High Surface Potential

作　　者：陈崇钧[1] 罗根祥[2] 金军[3] 王好平[2] 

机构地区：[1]鞍山师范学院化学系 [2]抚顺石油学院材料科学系 [3]北京东方重质油技术开发公司,北京100081

出　　处：《物理化学学报》2001年第4期377-380,共4页Acta Physico-Chimica Sinica

摘　　要：When surface potential of the particles,ψ ,is high,sinh y can be approximated by≈ ey/2 in the nonlinear Poisson Boltzmann equation.Thus,we present a simple method of calculating the interaction force and energy per unit area between two dissimilar plates with high potentials at constant surface potential.These formulae could be applicable to the case of repulsive case,in which the derivative of y must vanish at an interior point,and a minimum ymin=u always exists.A turning point at～κ h≈ 2(π－ 1)e－ y1/2 for the repulsion or attraction between dissimilar planar surfaces.These formulae are divergent atκ h∞ ,and zero point atκ h≈ 2π .This means that they can only be used atκ h < 2π and accurate location is atκ h≤ 4. Agreement of the approximation for force,Eq.（ 13） ,is good with the exact numerical values of the interaction of dissimilar plates given by Devereux [6] for high surface potentials.For y1≥ 5κ h≤ 3.0 the relative errors of Eq.(13) are less than 5％ ,and forκ h≤ 3.5 relative errors are less than 10％ .For the interaction energy,Eq.(15),the applicable range extends toκ h=4.0.Beyond this range the error increases rapidly.The higher surface potential is the better the precision of Eq.（ 13） and Eq.( 15).The condition of the strong interaction has been satisfied.When surface potential of the particles, psi, is high, sinh y can be approximated by approximate to e(y)/2 in the nonlinear Poisson-Boltzmann equation. Thus, we present a simple method of calculating the interaction force and energy per unit area between two dissimilar plates with high potentials at constant surface potential. These formulae could be applicable to the case of repulsive case, in which the derivative of y must vanish at an interior point, and a minimum y(min) = u always exists. A turning point at similar to kappah approximate to 2(pi - 1)e-y(1)(/2) for the repulsion or attraction between dissimilar planar surfaces. These formulae are divergent at kappah-->infinity ,and zero point at kappah approximate to 2 pi. This means that they can only be used at kappah < 2 <pi> and accurate location is at kappah less than or equal to 4. Agreement of the approximation for force, Eq. (13), is good with the exact numerical values of the interaction of dissimilar plates given by Devereux ([6]) for high surface potentials. For y(1) greater than or equal to 5 kappah less than or equal to 3. 0 the relative errors of Eq. (13) are less than 5%, and for kappah less than or equal to 3. 5 relative errors are less than 10%.For the interaction energy, Eq. (15), the applicable range extends to kappah = 4. 0. Beyond this range the error increases rapidly. The higher surface potential is the better the precision of Eq. (13)and Eq. ( 15). The condition of the strong interaction has been satis fled.

关 键 词：平板型胶粒 高表面电位 相互作用能 相互作用力 稳定性 胶体颗粒 

分 类 号：O648.1[理学—物理化学]