Surface Potentials of Mixtures Containing Oddly Charged Colloids

Abstract

Charged surfaces and particles of the same sign never attract, but oppositely oppositely charged ones do. If the surface potentials of two colloids, namely ψA and ψB, differ in sign, the difference among representative exponentials, i.e., (exp+(zεΨA//kT) − exp−(zeψB/kT)), is solved by the Poisson–Boltzmann, P–B, equation. The procedure is simple to handle when |ψA| ≈ |ψB|. It is troublesome to address the problem when potentials largely differ from each other in modulus. To overcome these difficulties, the P–B equation was reformulated so that drawbacks inherent to its classical form are bypassed. The above relation was rewritten in a promptly readable mode. The similarities and differences met when |ψA| ≠ |ψB| are discussed. It is shown in which conditions the revised form of the P–B equation overlaps with the classical one. From the re-formulation, it is also possible to determine the electrostatic energy occurring among interacting colloid particles dispersed in a given medium.