Short Cyclic Structures in Polymer Model Networks: A Test of Mean Field Approximation by Monte Carlo Simulations

Abstract

A mean field rate theory description of the homo- and co-polymerization of $f$-functional molecules is developed, which contains the formation of short cyclic structures inside the network. The predictions of this model are compared with Monte-Carlo simulations of cross-linking of star polymers in solution. We find that homo-polymerizations are well captured by mean-field models at concentrations larger than one quarter of the geometrical overlap concentration. All simulation data can be fit using a single geometric parameter for cyclization. The simulation data reveal that within the range of parameters of the present study correlations among multiply connected molecules can be neglected. Thus, mean-field treatments of homopolymerizations are reasonable approximations, if short cycles are properly addressed. Co-polymerization is considered in the case of strict A-B reactions, where all reactive groups of individual molecules are either of type A or B. For these systems we find a clear influence of the local intermixing of A and B groups for all concentrations investigated. In consequence, mean-field models are less appropriate to describe the simulation data. The lack of ring structures containing an odd number of molecules as compared to homopolymerizations at the same extent of reaction allows for the formation of stable AB networks at concentrations one order of magnitude below the geometrical overlap concentration.