Inhomogeneities and local chain stretching in partially swollen networks

According to classic single-chain theories of rubber elasticity such as the affine or phantom models, the length N and the state of stretching R/R-0 of network chains are directly reflected in the magnitude of segmental orientation correlations, as quantified by a dynamic order parameter S proportional to R-2/N (this relation holds for chains in the bulk and theta solvent). S can be determined by suitable NMR techniques, and is a viable molecular probe of the network structure, as it is directly proportional to the elasticity modulus. Furthermore, previous studies (see Saalwachter et al., Soft Matter, 2013, XX, XXX, in this issue for a review) have convincingly demonstrated the validity of the phantom model for the prediction of S in equilibrium-swollen networks. We here investigate changes in the degree of local chain stretching reflected in S as a function of the degree of (partial) swelling Q V/V-0 in different networks prepared in bulk and in states of increasing dilution. Previous work has already revealed a non-monotonic dependence of S on Q, indicating strongly subaffine local deformation in the early stages of swelling. The width of the distribution in S is also accessible, and increases significantly during the early stage of swelling, indicating the well documented presence of swelling heterogeneities. We find that beyond this early stage, the network chains deform affinely. A back-extrapolation of the affine deformation range to zero swelling allows for conclusions on the actual crosslink density of the networks corrected for the effect of topological or packing constraints, which we refer to as the "phantom reference state" of a bulk network. Deviations of the network elasticity from this state constitute non-classical contributions, possible origins of which are discussed.