SALT FRACTIONATION EFFECT FOR SPHERICAL MACROIONS

Ordered structures and void formation in systems of highly charged sph erical macroions are investigated using the Sogami potential. The cruc ial feature of the treatment is the salt fractionation effect; Sogami theory combined with the Dirichlet boundary condition (constant surfac e potential) yields a definite prediction for the distribution of simp le electrolyte between the macroion-rich and macroion-poor regions. Th e treatment is restricted to the extreme case of an equilibrium betwee n an ordered structure and voids. The voids are found to be stable in the range between alpha kappa = 0.816 and alpha kappa = 3.05, where a is the radius of the particles and kappa is the inverse Debye screenin g length. In this range, added simple electrolyte fractionates between the macroionic crystals and the voids, accumulating strongly in the v oids. Added electrolyte does not fractionate outside this range, leadi ng to an extraordinary regime below alpha kappa = 0.816 and to a homog eneous liquid-like structure above alpha kappa = 3.05. Within the rang e, the hypothesis that the relevant interaction kappa in the crystals is determined solely by the fractionated simple salt leads to a defini te prediction for the variation in the lattice parameter with added sa lt. This prediction is in quantitative agreement with recent USAXS mea surements and with a physically realistic value for the surface potent ial of the charged spheres. It is noted that the standard DLVO theory of colloid stability has nothing whatsoever to say about these interes ting phenomena.