Statistical thermodynamics of polydisperse fluids

Abstract

The statistical mechanical formalisms for dealing with mixtures containing an infinite number of components are discussed. The partition function and the thermodynamic properties can be easily generalized from the corresponding results for pure substances when the polydisperse fluid is studied in a four-dimensional space. The chemical potential field acts along the additional coordinate: the composition axis. A perturbation theory for narrow distributions is developed. A small parameter measuring the width of the chemical potential function is used within a semigrand ensemble. An equivalent, hybrid expansion expresses the results in terms of the variance of the composition distribution.

Flexible chain molecules in the marginal and concentrated regimes: Universal static scaling laws and cross-over predictions

“…The basis of semigrand ensembles 30,31 is a resummation of the grand canonical partition function in terms of molecular species identities. As a starting point we take the grand canonical partition function ⌶ for a multicomponent mixture containing c components:…”

Liquid-Liquid Equilibrium of Copolymer Solutions with Broad and Asymmetric Chemical Distributions

“…Kehlen and Ratzsch [1], and later Salacuse and Stell [2], Gualtieri et al [3], and Briano and Glandt [4], developed continuous thermodynamics based directly on continuous distribution functions to describe phase equilibria of complex multicomponent systems, such as polydisperse Since random copolymers show polydispersity with respect to the chemical composition in addition to the usual polydispersity with respect to the molecular weight, continuous thermodynamics was generalized to divariate distribution functions by Ratzsch, Kehlen, and Browarzik [5]. The double integrals for determining the cloud-point curve and the shadow curve of a copolymer solution may be calculated analytically by using a generalized Stockmayer distribution.…”

Semigrand Canonical Monte Carlo Simulation; Integration Along Coexistence Lines

“…The notion of a semigrand ensemble has its roots in the work of Griffiths and Wheeler [l], who developed and applied it for the study of critical phenomena in mixtures (one might even argue that the concept goes back to the Ising model). The idea was rekindled in the work of Briano and Glandt [ 2 ] , which formed the foundation for the first (off-lattice) Monte Carlo simulations in the ensemble, conducted by Kofke and Glandt [3-51. At about the same time Sariban and Binder [6] applied semigrand Monte Carlo simulation to study a lattice model of polymer mixtures.…”