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 ...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.展开更多
文摘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.
