高电位胶体颗粒强相互作用的近似表达式

When surface potential of the particles, ,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 ～kh≈2(??1)e－y1/2 for the repulsion or attraction between dissimilar planar surfaces.These formulae are divergent at 阧∞,and zero point at kh≈2 .This means that they can only be used at 阧 < 2 and accurate location is at kh ≤ 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 ≥5 kh ≤ 3.0 the relative errors of Eq.(13) are less than 5％,and for kh ≤ 3.5 relative errors are less than 10％.For the interaction energy,Eq.(15),the applicable range extends to kh =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.

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

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 at κ h ∞ ,and zero point at κ h≈ 2π .This means that they can only be used at κ h 　　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 for κ h ≤ 3.5 relative errors are less than 10％ .For the interaction energy,Eq.(15),the applicable range extends to κ 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.