The thesis is devoted to the study of the phase behavior and fractionation effects of colloidal and polymer systems in bulk and random porous media.
The major challenge for a theoretical description of the phase behavior of polydisperse mixtures is due to the functional dependence of Helmholtz free energy of the system on the distribution function of species. As a result, phase equilibrium conditions are formulated in terms of the set of an infinite number of equations, e.g. chemical potential for each value of the continuous species index should be the same in each of the coexisting phases. Solution of such a set of equations for Helmholtz free energy of arbitrary form is next to impossible. We have extended and applied the scheme developed to calculate the phase diagrams of polydisperse mixtures described by the truncatable free energy (TFE) models, i.e., the models with Helmholtz free energy defined by the finite number of the moments of the species distribution function. The latter feature of the TFE models enables one to formulate the phase equilibrium conditions in terms of a finite set of equations for these moments.
To calculate the phase behavior of colloidal system, which is represented by polydisperse hard sphere Morse mixture, we propose an extension of the second-order Barker-Henderson perturbation theory. The theory is used to describe the liquid–gas phase behavior of the mixture with different type and different degree of polydispersity. In addition to the regular liquid–gas critical point, we observe the appearance of the second critical point induced by polydispersity. At high degree of polydispersity, several new features in the topology of the two-phase diagram have been observed: the cloud and shadow curves intersect twice and each of them forms a closed loop of the ellipsoidal-like shape with the liquid and gas branches of the cloud curve almost coinciding. With polydispersity increase, the two critical points merge and finally disappear. Approaching a certain limiting value of the polydispersity index, the cloud and shadow curves shrink and disappear. Beyond this limiting value, polydispersity induces the appearance of the three-phase equilibrium at lower temperatures. The same phase behavior we obtain for other colloidal system, which is represented by polydisperse hard sphere Yukawa mixture in the framework of high temperature approximation (HTA) and mean spherical approximation (MSA). In general, good agreement was observed between predictions of the two different theoretical methods, i.e., HTA and MSA. Our results confirm qualitative predictions for two- and three-phase coexistence obtained earlier within the framework of the van der Waals approach.
Also we have studied the phase behavior of polydisperse Yukawa hard-sphere fluid confined in random porous media. The study is carried out using extension and combination of the HTA and scaled particle theory (SPT). We propose an analytical expression for the radial distribution function of the hard-sphere fluid in the hard sphere random matrix. Due to the confinement, polydispersity effects are substantially enhanced. At an intermediate degree of fluid polydispersity and low density of the matrix, we observe two-phase coexistence with two critical points, and cloud and shadow curves forming closed loops of ellipsoidal shape. With the increase of the matrix density and the constant degree of polydispersity, these two critical points merge and disappear, and at lower temperatures the system fractionates into three coexisting phases. A similar phase behavior was observed in the absence of the porous media caused, however, by the increase of the polydispersity.
To study the liquid-gas phase behavior of polymer system, which is represented by polydisperse hard-sphere square-well chain fluid confined in the random porous media, we propose and apply an extension of Wertheim’s thermodynamic perturbation theory and its combination with SPT. Thermodynamic properties of the reference system, represented by the hard sphere square-well fluid in the matrix, are calculated using corresponding extension of the second-order Barker-Henderson perturbation theory. We study effects of polydispersity and confinement on the phase behavior of the system. While polydispersity causes increase of the region of phase coexistence due to the critical temperature increase, confinement decreases the values of both critical temperature and critical density making the region of phase coexistence smaller. This effect is enhanced with the increase of the size ratio of the fluid and matrix particles. Fractionation effects of colloidal and polymer systems in bulk and random porous media also have been studied. The degree of fractionation depends on temperature. In all cases, particles with larger values of the polydispersity attribute are fractionated into a high-density (liquid) phase, and particles with lower values are fractionated into a low-density (gas) phase.
