Effect of excluded volume on segmental orientation correlations in polymer chains

Abstract

We study the impact of excluded volume interactions on the orientation statistics of chain segments in polymer gels, and show that nuclear magnetic resonance (NMR) experiments provide a direct and unique measure of excluded-volume effects on the chain statistics. In particular we consider the tensor order parameter, which can be expressed as the second Legendre polynomial of the segment orientation with respect to a fixed end-to-end distance vector and which is directly related to the residual coupling constant obtained in NMR experiments. We provide analytical results for the case of single chains in a good solvent and for semidilute solutions. Computer simulations using the bond fluctuation model are applied to compare with the analytical predictions. 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 multiple-quantum NMR methods to both end-linked and randomly cross-linked polymer networks are in excellent agreement with this prediction. The initial decay of the tensor order parameter as observed in experiments at low and intermediate degrees of swelling can be explained as a solvent effect without making additional assumptions about constraint release processes during swelling.

Segmental Order Parameters and Swelling in Polymer Networks

“…We like to add that the experimental findings are in excellent agreement with results of computer simulations using the bond fluctuation method presented in Ref. 10.…”

“…2. For the dilute solution the so‐called Fisher distribution has to be used 7, 9, 10. Moreover, in this case it has to be shown that the behavior of the end segment is characterstic for the overall chain 10…”

The Non‐effect of Polymer‐Network Inhomogeneities in Microgel Volume Phase Transitions: Support for the Mean‐Field Perspective

“…This indicates that the structural influence (elastic chain length) on the RDC dominates over the geometrical (stretching) constraint. However, the situation is probably complicated by the existence of spatial inhomogeneities with different swelling capacities, and we can conclude that the microscopic NMR results cannot support a mean‐field picture, because otherwise, D res,eq ∼ q –3/2 would have to be fulfilled …”

Inhomogeneities and Chain Dynamics in Diene Rubbers Vulcanized with Different Cure Systems

“…On the other hand, the NMR analysis of the samples from Figure 6 after swelling in toluene lead in all cases to very broad distributions of dipolar couplings, completely covering up the significant differences between them, in agreement with our works on poly(dimethylsiloxane) networks. [83][84][85] This pinpoints that NMR analyses addressing matrix inhomogeneities should be performed on unswollen samples.…”