Lattice Model for Segmental Orientation in Deformed Polymeric Networks. 1. Contribution of Intermodular Correlations

Intermolecular contributions to segmental orientation in uniaxially deformed amorphous networks are formulated according to a lattice model. The network chains are represented as sequences of freely jointed rodlike segments each corresponding to a Kuhn segment. The length-to-width ratio, x, of the volume occupied by a Kuhn segment varies, depending on the type of the polymeric system. For polyethylene, this ratio is estimated to be about 2. The length-to-width ratios of Kuhn segments of flexible chains may in general be taken to lie between 1 and 3. The entropy of packing of such network chains in an oriented lattice is derived, and the orientation function is evaluated as a function of extension ratio, degree of swelling, and chain stiffness. The treatment is a generalization of the original work of DiMarzio in which the reduced flexibility or the relative stiffness of chain segments was not considered. Results of calculations show that for sufficiently flexible chains, i.e., for the chains composed of Kuhn segments of nearly spherical shape, intermolecular contributions to segmental orientation are of secondary importance compared to intramolecular effects and rapidly vanish with dilution upon swelling of the network with a solvent. Intermolecular interferences to segmental orientation lead to about a 10-15% increase in the observed orientation function in dry network chains with Kuhn segments of an axial ratio χ = 3.