Segmental Order Parameters and Swelling in Polymer Networks

We study segmental order parameters in polymer networks in good solvent. In particular we consider the tensor order parameter which characterizes the degree of orientational order of segments and which is directly related to the residual coupling constant obtained in NMR-experiments. Using a simple relation between the order parameter and the force acting on the chain end at a given extension we derive an universal relation for the order parameter for concentrations above the overlap threshold. Considering polymer gels at the equilibrium state of swelling we predict a unique relation between the tensor order parameter and the correlation length (blob size) of the gel. Experiments applying multi-quantum NMR-methods to both end-linked and randomly cross-linked polymer networks are in excellent agreement with this prediction. We critically discuss the widely used Flory-Rehner model of network swelling and show that initial decay of the tensor order parameter as observed in experiments at low degrees of swelling can be explained as a solvent effect without making additional assumptions about constraint release processes during swelling.