Updating classical swelling theory with loops: experiments and real elastic swelling theory

Understanding the effect of loop defects on polymer network properties is an important step to improving the accuracy of predictions. Equilibrium swelling ratios were measured for a set of gels with known loop fractions, extending prior work on loop counting with network disassembly spectroscopy. As expected, loopier gels demonstrated a higher degree of swelling due to a reduction of elastically effective strands. Building off of the Real Elastic Network Theory (RENT) developed for predicting linear viscoelasticity as a function of loops, the Real Elastic Swelling Theory (REST) incorporates RENT as the elasticity model in the classical Flory-Rehner swelling equation. To avoid error in estimation of the Flory-Huggins chi parameter, a non-dimensional master equation was derived, demonstrating a collapse across all good solvents. For gels with loop densities low enough to accurately assume loops were not correlated, REST was more accurate than models that do not account for loops. Despite the increased accuracy in REST, persistent deviations suggest the need for further improvements in elasticity models, especially in the high defect regime.