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It is pointed out that the Ornstein–Zernike equations recently used by Madden in treating quenched-annealed mixtures are approximate. The exact equations are given and briefly discussed.

The statistical thermodynamics of polydisperse systems of particles is investigated. A Gibbs–Duhem relation is obtained and the equilibrium conditions relevant to a two-phase system are derived. Systems of hard spheres, and hard spheres with Kac tails, are treated as illustrative examples with analytic results given in the context of scaled-particle (Percus–Yevick) theory as well as the polydisperse generalization of the thermodynamic approximation of Mansoori et al. An exact treatment of the analogous one-dimensional systems is also given. Quantitative results using a Schultz distribution of diameters are presented. A model of interpenetrable particles introduced previously by one of us—the permeable-sphere model—is also considered. Its thermodynamics and pair distribution functions are shown to be exactly obtainable in the context of the Percus–Yevick approximation. For this model, polydispersivity in both particle size and particle impenetrability is considered analytically. The pair potential for this model is discontinuous at the interparticle diameter; generalization of the model for which the pair potential is continuous is also introduced as a model of an effective polymer–polymer potential.

We have studied a model of a complex fluid consisting of particles interacting through a hard core and a short range attractive potential of both Yukawa and square-well form. Using a hybrid method, including a self-consistent and quite accurate approximation for the liquid integral equation in the case of the Yukawa fluid, perturbation theory to evaluate the crystal free energies, and modecoupling theory of the glass transition, we determine both the equilibrium phase diagram of the system and the lines of equilibrium between the supercooled fluid and the glass phases. For these potentials, we study the phase diagrams for different values of the potential range, the ratio of the range of the interaction to the diameter of the repulsive core being the main control parameter. Our arguments are relevant to a variety of systems, from dense colloidal systems with depletion forces, through particle gels, nano-particle aggregation, and globular protein crystallization.

Potential distribution and coupling parameter theories are combined to interrelate previous solvation thermodynamic results and derive several new expressions for the solvent reorganization energy at both constant volume and constant pressure. We further demonstrate that the usual decomposition of the chemical potential into noncompensating energetic and entropic contributions may be extended to obtain a Gaussian fluctuation approximation for the chemical potential plus an exact cumulant expansion for the remainder. These exact expressions are further related to approximate first-order thermodynamic perturbation theory predictions and used to obtain a coupling-parameter integral expression for the sum of all higher-order terms in the perturbation series. The results are compared with the experimental global solvation thermodynamic functions for xenon dissolved in n-hexane and water (under ambient conditions). These comparisons imply that the constant-volume solvent reorganization energy has a magnitude of at most approximately kT in both experimental solutions. The results are used to extract numerical values of the solute-solvent mean interaction energy and associated fluctuation entropy directly from experimental solvation thermodynamic measurements.

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Using the replica method, we derive the thermodynamic relations for a fluid in equilibrium with a quenched porous matrix. In particular, t~e appropriate Gibbs-Duhem equation is obtained as well as the equivalence between grand canonical and canonical ensembles. The exact compressiblity and virial equations are derived. Whereas the compressibility equation remains a direct and practical way to obtain I. the adsorption isotherm, the virial equation involves terms which do not relate easily to the properties of the fluid/matrix system. This explains the inconsistency between previous theoretical predictions and computer simulation results.-,1

The kinetics of polymer growth and especially gelation are discussed for a system of reacting f-functional monomeric units. The gelation models of Flory and Stockmayer are examined, and their implications concerning sol–gel interaction after gelation has occurred are clarified. A new model, in which the gel does not cross link, is considered. A mathematical analysis shows that the onset of gelation is related to the formation of a shock-wave solution of the equation satisfied by the generation function.