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

TL;DR

This study compares mean field rate theory predictions with Monte Carlo simulations for polymer network formation, highlighting the conditions under which mean-field models are accurate or less appropriate, especially considering cyclic structures and copolymerization effects.

Contribution

It introduces a mean field model that accounts for short cyclic structures in polymer networks and tests its validity against Monte Carlo simulations for homo- and co-polymerization.

Findings

Mean field models accurately predict homo-polymerization at high concentrations.

Simulation data fit well with a single geometric parameter for cyclization.

Co-polymerization shows significant deviations from mean-field predictions due to local intermixing.

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.