Network Structure in Terms of Prepolymer and Curative Parameters

The structure of polymer networks is considered. The networks are assumed to be formed from the reaction of functional groups on low molecular weight telechelic polymers with a cross-linking agent. Relationships are derived between cross-link density and properties of the prepolymer mix such as functional group equivalent weight, functionality, and including the maximum or final extent of reaction of the functional groups and the gel content of the cured stock. At an equivalent reactant ratio of 1.0 to 1.0 and with the branch points uniting no more than three chain ends, the cross-link density in the gel was found to be proportional to the product of a concentration term, q, and a geometrical term, (1 − 1/fa − 1/fp), which is called the branching function. The absolute value of the network cross-link density in moles/g was found to be where q = equivalents of prepolymer functional groups per gram, fp = functionality of prepolymer, fa = functionality of cross-linking agent, CDF = cross-link decrease factor, a constant having a value between 0.42 and 0.66, and Wg = weight fraction of gel. The CDF term is the factor by which the cross-link density in the gel is decreased because of failure of the reaction to go to completion at the maximum degree of cure. At a reactant ratio of 1.0 this term was found to have the form where e is the maximum or final extent of the curing reaction in the gel, and ec is the extent of reaction at the gel point. At a reactant ratio of 1.0 the CDF term was constant over a wide range of functionalities. The extent of reaction in the gel was determined from a previously published equation of the form e2 = (1 − k)ec 2 + k. The value of the constant k was estimated to be 0.3 ± 0.1.