Molecular Orientation in Deformed Bimodal Networks. 1. Theory

Expressions for the molecular orientation of long and short chains in bimodal networks, S_L and S_S, are derived based on the theory developed by Kloczkowski et al. (Macromolecules 1991, 24, 3266) for regular bimodal phantom networks and compared with those (S_L° and S_S°) occurring in corresponding unimodal networks. The changes in segmental orientation of the respective chains in bimodal networks relative to their unimodal counterparts, expressed as the ratio S_L/S_L° or S_S/S_S°, are shown to be independent of macroscopic strain and intrinsic chain configurational characteristics but depend essentially on network topology and composition. The latter are accounted for by two variables: the ratio ξ of the molecular weights of short chains to that of long chains, and the number ϕ_S and ϕ_L of short and long chains at each junction. Results of the formulation show that the long (short) chains in the bimodal network orient more (less) than those in the corresponding unimodal network. These differences in the orientation behavior of the two chains arise from differences in fluctuations of chain dimensions that, in turn, affect the microscopic strain of each component. Predictions of the theory are compared in the following paper with results of Fourier transform infrared measurements on well-defined poly-(dimethylsiloxane) networks.