Effective forces between macroions in highly charged colloidal suspensions

It is shown based on the systematic theory recently developed for charge-st abilized colloidal suspensions of interacting Brownian particles with Coulo mb interactions that the effective Force between highly charged colloidal m acroions can be written as F-eff(r) = k(B)TZ(2)l(B)(2){Z(2) exp[-(Z/q)(1/2)r/lambda(D)] - q(2) exp(-r/ lambda(D))}(r/r(4)), where lambda(D) = (4 pi n(c)q(2)l(B))(-1/2) is the Debye screening length, Ze the charge of macroions, -qe the charge of counterions, l(B) the Bjerrum length, and n(c) the number density of counterions. This force consists of two parts. The first part results from the long-range, Coulomb interaction s between macroions and is repulsive over a short range of distances betwee n macroions. The second part results from the pair correlations due to the long-range, Coulomb interactions between macroions and counterions and is a ttractive over a broad range of distances between macroions. This force is expected to describe the ordering phenomena in highly charged colloidal sus pensions. [S1063-651X(99)50903-3].