Mechanism of Microgel Formation via Cross-Linking of Polymers in Their Dilute Solutions: Mathematical Explanation with Computer Simulations

Abstract

The formation of poly(vinyl alcohol) microgels by γ-ray irradiation was previously studied by static and dynamic light scattering methods to obtain respectively the radius of gyration (Rg) and the hydrodynamic radius (R h ). It was proposed that the mechanism of this microgel formation was an intermolecular cross-linking step followed by an intramolecular cross-linking process. Presented herein is a mathematical model for interpreting the values of R g and R h , in which the Kirkwood theory of the friction factor was employed. To mimic the known extensions of brushes, a set of bias parameters were employed for the purpose of making a directional preference in generating the configurations of both parent and branch chains. The simulations with this simple model are in very good agreement with the proposed mechanism of microgel formation in the poly(vinyl alcohol) system. Justification of using the bias parameters is supported by computationally intensive Brownian dynamics simulations of a collection of 216 beads with a Velcro pair potential, i.e., a short-range attractive pair potential that acts as a formation of a chemical bond between the beads. The advantage of the bias walk model is that it allows one to explore different molecular configurations on a smaller computer and thus to select an appropriate set of parameters for more extended and time-consuming simulations on mainframe computers.