N. B. Ferapontov

Heterophase model of swollen cross-linked polyelectrolyte

Abstract In this paper we describe the heterophase model of a swollen particle of cross-linked polyelectrolyte in water. We also propose a new definition of a solution of cross-linked polyelectrolyte. We demonstrate that the activity of water in a solution of cross-linked polyelectrolyte depends on two independent parameters: the number of cross-links in the solution of the polyelectrolyte and the activity of water in the equilibrium state. Using a three-dimensional coordinate system, we illustrate the effect of these parameters on the amount and activity of water in the solution of cross-linked polyelectrolyte. The equilibrium between a solution of low-molecular-mass electrolyte and a solution of cross-linked polyelectrolyte is described from the standpoint of classical thermodynamics. We also present methods to calculate amounts and activities of components in the solution of cross-linked polyelectrolyte. In order to describe a solution of cross-linked polyelectrolyte, in addition to the concept of ‘isotherm of sorption of water’, it is necessary to introduce and define the term ‘isotherm of sorption of electrolyte’. Examples of such isotherms are provided as an illustration. We propose methodologies to experimentally determine several parameters of the model and present the results of calculations of amounts and activities of the components in a solution of cross-linked polyelectrolyte.

Interaction of cross-linked polyelectrolytes with solutions of low-molecular-weight electrolytes

We offer a method for calculation of the composition and the amount in solution of cross-linked polyelectrolyte. Methods to determine amounts and properties of the components in a solution of cross-linked polyelectrolyte are formulated from the viewpoint of a two-phase model and the law of interphase equilibria. An algorithm to calculate the composition of a solution of cross-linked polyelectrolyte was developed. We present the results of comparison of theoretical and experimental values and show that the heterophase model of the swollen gel can serve as a tool for description of such systems.

The properties of water in swollen cross-linked polystyrene sulfo acids

The properties of water in polystyrene sulfo acid gels with various cross-linking degrees were studied by optical volumetry and dynamic desorption porosimetry. The isotherms of water desorption obtained by dynamic desorption porosimetry coincided with isopiestic isotherms, which allowed this method to be recommended for the determination of the amount of water in polymer gels. Joint optical volumetry and dynamic desorption porosimetry studies showed that the interphase boundary in the cross-liked hydrophilic polymer-water system did not coincide with the visible gel boundary, because gels were two-phase systems, which contained water of two types, “free” and “bound.” The influence of the degree of polymer cross-linking on the amounts and properties of water of the two types was studied. It was shown that constants of water distribution in the polymer could be calculated from the dynamic desorption porosimetry data.

The properties of water in solutions of hydrophilic polymers

The properties of water in solutions of hydrophilic polymers were compared with those in solutions of their monomeric analogues. The properties of polar groups grafted to polymeric molecules were known to remain unchanged. A comparison of the properties of water in solutions of polymers and the corresponding monomers under equal conditions therefore allowed us to obtain information about the influence of polymeric bonds on the properties of water in solutions of polymers. Proceeding from this, we analyzed the influence of polymeric chains and three-dimensional polymeric network on the activity and concentration of water in solutions of polymers.

Analysis of the swelling or shrinking kinetics of crosslinked hydrophilic polymers by mathematical modeling

The developed kinetic physical and mathematical model of a crosslinked hydrophilic polymer swelling process in aqueous solutions of low molecular weight compounds is presented. The model was tested on 13 combinations of “polymer-solution”. The experimental results of measuring the swelling kinetics can be described by considering the flows caused by the difference in chemical potential of the water and solute inside/outside the swollen polymer, as well as the effect of elastic forces in the polymer. The calculation results are in a good agreement with experimental data.Graphical Abstract

The Effects of Polymer Properties and Solution Composition on the Distribution, Properties, and Amount of Water in Swollen Ion Exchangers

The effects of the composition and concentration of an external solution on the swelling degree of polystyrene-based ion exchangers crosslinked with different amounts of divinylbenzene have been analyzed within the heterophase model of polymer gel structure. It has been confirmed experimentally that, upon variations in the composition of the external solution, the swelling degree of polymers is determined by the content of “sorbed” water alone. Therewith, the volume of the external solution incorporated into the swollen polymer remains constant; i.e., it depends neither on an ionic form of an ion exchanger nor the concentration and composition of the external solution, but rather depends linearly on the polymer crosslinking degree. An algorithm has been proposed for calculating the volume of water in a polymer gel and some quantitative estimates have been presented.

Swelling Kinetics of Cross-Linked Polymer Gels Based on Polystyrene and Poly(vinyl alcohol) in Aqueous Solutions of Electrolytes and Sucrose

The swelling kinetics of polymer gels has been studied in water and aqueous solutions by optical micrometry. Cross-linked hydrophilic polymers based on polystyrene and poly(vinyl alcohol) have been used as gel-forming materials. The effects of the natures of the matrices and polar groups of the polymers and their cross-linking densities and granule sizes, as well as the properties of external phase, on the swelling kinetics of the polymer gels have been investigated. The experimental results have been processed in terms of a heterophase kinetic model. The applicability of the model to describing the behavior of all studied systems has been shown.

Kinetics of the swelling of a gel of cross-linked polyvinyl alcohol during the synthesis of copper-containing composite based on it

The kinetics of processes that occur during the chemical reduction of copper in a gel of polyvinyl alcohol (PVA) are described. It is shown that we can assess the processes occurring in the polymer from changes in the degree of swelling. The effects the nature of the precursor (precursor compound) has on the conditions of reduction are analyzed. It is found that crystals of reduced copper do not change the volume of PVA gel, which has a positive effect on the mechanical stability of the resulting composite.