Formation of gels and complexes by pairwise interacting polymers

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Abstract
Pairwise bonding between polymers in solution may lead to network formation - e.g. double helical junction zones in biopolymer gels, or association between polyacids and polybases. The equilibrium length distribution of bonded sequences to be expected in a branched network structure is obtained here by modification of helix-coil transition theory for linear chains. In the limit of infinite chains a « pairing transition » is observed at a finite temperature. At this point the mean length of the bonded sequences diverges and the system changes from a network to a solution of perfectly paired molecules. Subsequent aggregation of these pairs is then probable. Kinetic equations are developed to represent the helix formation reactions in gels and in single chains. These are compared to Monte Carlo simulations. In a network neighbouring bonded sequences will share only one of their two chains and may therefore not merge. Whilst the fraction of chain which is bonded rises smoothly to its equilibrium value, the number of bonded sequences per molecule (which is related to the network modulus) is found to pass through a maximum if the equilibrium bonded fraction is large. This suggests the possibility of high modulus,