Static structure factor of a suspension of charge-stabilized colloids: Application to liquid-glass transition phase diagram and to micellar solution

S. K. Lai, J. L. Wang, G. F. Wang
1999 Journal of Chemical Physics  
The charge-stabilized colloidal dispersion is modeled by a mixture of spherical charged hard spheres whose static partial structure factors were analytically solved by the mean spherical approximation ͑MSA͒. For point-like small ions ͑counterions and electrolyte͒, this so-called primitive model ͑PM͒ can be shown to yield exactly the same macroion-macroion structure factor S(q) as that of the effective one-component model ͑OCM͒. Such structural equivalence permits the use of the PM S(q) as input
more » ... he PM S(q) as input data to the idealized version of mode-coupling theory and hence the determination of the liquid-glass transition loci for a charge-stabilized colloidal dispersion. Numerically it is found that, for the whole boundary of the predicted liquid-glass transition loci, the portion of the line along 0ϽՇ0.43 reveals an inadequacy in the S(q) since its corresponding pair correlation function near the distance of contact approaches a negative value. This inherent shortcoming of the MSA has previously been noted mostly for the low-density (Շ0.1) and highly charged colloids, but now it is manifested in highly charged colloidal dispersions having a large . This MSA problem, in principle, can be remedied by the technique of rescaling the macroion size, provided in the course of rescaling one can deal concurrently the nonadditive contact radii relation between the macroions and small ions. Unfortunately, there are still technical difficulties and ambiguities in the handling of this latter kind of problem within the PM. This prompts us to suggest using the S(q) of the effective OCM of Belloni where such problem of nonadditive contact radii can be taken into account approximately. We contrast the liquid-glass transition phase boundary determined from the latter model with that of the PM, where the additive contact radii property is preserved throughout, to reveal qualitatively the uncertainties in the liquid-glass transition loci within the PM. Further evidences in support of this OCM can be seen from its successful interpretation for the S(q) of a micellar solution and for the charges of polystyrene spheres which are predicted in this work to agree reasonably with the theoretical values deduced from the density functional theory.
doi:10.1063/1.478645 fatcat:gd6tst2b7zaxrks45t2q7s5gke