Spanning-tree models for A(f) homopolymerizations with intramolecular reactions

The spanning-tree approximation model is one of the models used for polymer izations with intramolecular reaction regardless of the size of the ring fo rmed. We present a modification of this model that uses more accurate inter nal estimates of the probabilities of intramolecular reaction. This require s limited Monte Carlo simulations of some molecular structures, resulting i n a hybrid probability model (a combined analytic and Monte Carlo model). W e then extend the spanning-tree model so that it may be used in the post-ge l region. We show three possible extensions of varying degrees of complexit y. The resulting models for stepwise A(f) homopolymerizations have been cod ed into programs that run on desktop PCs in a few seconds. The models calcu late the amount of intramolecular conversion, the weight-average molecular weight, the gel point, the weight fraction of soluble material, and the wei ght-average molecular weight of the sol fraction. We discuss the relative m erits of the modified spanning-tree model and its three post-gel extensions and show sample calculations for arbitrary homopolymerization systems. (C) 2000 Elsevier Science Ltd. All rights reserved.