Hard sphere colloidal suspension of macroparticles in a multicomponent solvent

Abstract

Colloidal suspensions are represented as a mixture of macrospheres immersed in a multicomponent solvent of small spheres. The behavior of the macrospheres is analyzed on the basis of the Percus–Yevick theory when the ratios of the small to large sphere diameters go to zero at fixed packing fractions. Within the Baxter formalism the recent results of Biben and Hansen for the one component solvent are generalized. It is shown that the macrosphere suspension reduces to a one component system in which Baxter’s function goes exactly over to that of a one component adhesive sphere fluid. The expression for the adhesiveness is exactly expressed in terms of the packing fractions of the solute and the solvent components. Such a model permits the interpretation of the flocculation phenomenon induced by the addition of free polymers in a colloidal suspension.

Depletion effects in binary hard-sphere fluids

“…A manifestation of this inconsistency is that there is a difference between the pressure as computed from the virial equation of state, and as computed from the compressibility relation. A detailed discussion of these integral equations applied to a very asymmetric mixture of hard spheres can be found in reference [11], and partially in references [12][13][14]. We briefly summarize the most important theoretical predictions in the next section, and present a comparison with the results of numerical simulations for a size ratio y = σ s /σ l = 0.1.…”

A density functional approach to depletion interaction

“…It is precisely the latter that relates this result to the one obtained for hard spheres in reference [12]. Therefore the effective fluid can be referred to as the fluid of parallel adhesive hard cubes.…”

“…the limit in which the size of the small particles goes to zero while the effect of depletion is retained. This limit was already used [12] to show that the DCF of a mixture of hard spheres becomes that of a fluid of adhesive hard spheres in this limit. The possibility offered by our formalism is that of taking the limit on the functional to obtain a limiting functional for the effective fluid.…”

“…Actually this was the starting point from which the effective fluid was defined in reference [12]. Seen in this light, it appears as the result of the semi-grand ensemble choice, and equations (11) and (12) extend it to arbitrary phases.…”

“…In spite of that it is always possible to achieve it as a functional expansion in 'powers' of ρ S . To show this let us rewrite (12) as…”