Polymer networks: principles of formation, structure and properties
Polimery 2000, No 7-8, 456
SummaryThis paper discusses the results of two types of theoretical investigations into the formation, structure and properties of polymer networks. First, to predict the value of the initial elastic modulus, it is important to be able to model, statistically, the molecular growth leading to network formation. A Monte-Carlo network polymerisation algorithm has been developed. It uses Flory-Stockmayer random-reaction statistics with intermolecular reaction allowed on a correctly weighted basis. The algorithm simulates, as a function of extent of reaction, the formation of all of the connections in a reaction mixture and counts all the ring structures. It also enables polymerisations and network structures to be simulated efficiently up to complete reaction. Comparisons of predictions from the algorithm with experimental data from end-linking polymerisations show the importance of accounting for the whole distribution of sizes of ring structure in determining reductions in elastic modulus. An important new factor, x, is introduced in the interpretation of experimental data. It is the fractional loss in elasticity per chain in loop structures larger than the smallest (eqns. 13–15, figs. 7, 8). The second type of investigation shows that Monte-Carlo simulations (fig. 10) of the elastic behaviour of chains in networks, using realistic (R-I-S) network-chain models, are able to reproduce experimentally observed deviations from Gaussian network behaviour in uniaxial extension (fig. 9). The finite extensibility of the network chains causes non-affine deformation of the mean-square network-chain end-to-end distance, even at moderate sample deformations (λ ≈ 1.5). An increase in the proportion of fully extended chains with increasing macroscopic strain gives rise to a steady decrease in the rate of network free-energy change with strain, causing a reduction in the network modulus. There is no need to invoke a transition from affine to phantom chain behaviour as deformation increases. For a complete understanding of the structure and elastomeric properties of polymer networks, both types of investigations need to be combined. Thus, the number and types of elastic-chains, including loop structures, and their entropy-deformation relationships would be known. The Network can then be deformed, and the values of initial modulus as well as stress-strain behaviour predicted.