Chemical clusters in polymer networks

Abstract

Chemical (topological) clusters in polymer networks have been defined as covalently bonded assemblies of units of a certain kind, for instance ‘hard’ units among the soft ones. For theoretical characterization, two methods have been used: (a) the theory of branching processes (TBP) by which the structures are generated from monomer units and (b) the generalized kinetic theory with a Monte-Carlo simulation of the process. The clusters are characterized by their average sizes and average number of issuing soft bonds (cluster functionality) and conditions where the clusters grow to infinity. Using the TBP, the characterization is based on classification of the bonds connecting units as hard → hard, hard → soft, soft → hard and soft → soft. The cluster size and functionality as a function of conversion are determined by the initial composition of the system, the rules of bond formation and the relative reactivities of functional groups. Under certain conditions, the hard clusters can grow to infinity. Method (b) allows us additionally to treat the long-range connectivity effects as well as to simulate the steric excluded volume effect by making the effective reactivity of a group dependent on the cluster size. The exclusion from the reaction of a larger fraction of groups in larger clusters makes the distribution narrower, shifts the gel point to higher conversions and causes the critical exponents to deviate from their classical values. The implications of the existence of hard clusters on equilibrium elasticity are discussed.