Dispersion virial expansions

An analogy may be drawn between the phase behavior of weakly attractive monodisperse dispersions and that of conventional molecular systems provided coalescence and Ostwald ripening do not occur. The similarity arises from the common form of the pair potential, whose dominant feature in both cases is the presence of a shallow minimum. The equilibrium statistical mechanics of such systems have been extensively explored. As previously explained, the primary difficulty in predicting equilibrium phase behavior lies in the many-body interactions intrinsic to any condensed phase. Fortunately, the synthesis of several methods (integral equation approaches, perturbation theories, virial expansions, and computer simulations) now provides accurate predictions of thermodynamic properties and phase behavior of dense molecular fluids or colloidal fluids [1]. 

In the case of microemulsions and suspensions of spherical particles, it is usually more convenient to use the volume fraction, ((), of the dispersed particles as a measure of their concentration. By using the fact that ([) = pV, we can obtain the virial expansion ... 

As before, we consider the interaction of two flat plates coated by grafted polymeric layers. Once the interaction between the two flat surfaces is known, the Derejaguin approximation and virial expansion can be used to determine the stability of the spherical colloidal dispersion as described previously. 

The virial expansion for the osmotic pressure P of a colloidal dispersion reads... 

The generalization to a multicomponent solute is nontrivial, but for a homologous polymer with a dispersion in molecular weight, the resulting virial expansion for light scattering is just... 

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