(164e) Updating Classical Polymer Network Swelling Theory with Loop Defects

Precise swelling of polymer networks offers utility in applications ranging from controlled drug release to superabsorbent materials. Many applications, including actuation of pumps and valves in microfluidics or the variable release of encapsulated drugs in response to stimuli, require the ability to precisely predict the degree to which a network will swell. While the classical Flory-Rehner-Merrill-Peppas swelling equation is still widely used in many cases, it relies on the affine elasticity model which does not account for topological defects.

Recent work has shown that these defects, particularly primary and secondary loops, can significantly reduce the elasticity of the network and render predictions which are predicated on classical theories inaccurate. This work measured the impact loop defects have on the equilibrium swelling of a commonly used polymer network and updated the swelling equation to account for loops, leading to better swelling predictions. Building off of the Real Elastic Network Theory (RENT) developed for predicting linear viscoelasticity as a function of loop fraction, the Real Elastic Swelling Theory (REST) incorporates RENT as the elasticity model in the Flory-Rehner-Merrill-Peppas swelling equation in order to predict gel swelling as a function of loops.

To compare the predictions of the modified theory to the original, equilibrium swelling ratios were measured for a set of poly(ethylene glycol) (PEG) gels synthesized at varying polymer concentrations. The fraction of cross-link junctions with primary loops were previously measured for this system using network disassembly spectrometry, enabling direct correlation of equilibrium swelling to loop fraction. As expected, gels with a higher loop density demonstrated a higher degree of swelling due to a reduction of elastically effective strands which decrease the entropic penalty of stretching out the chains. The experimental results are compared to classical swelling equations, REST, and other defect-sensitive elasticity theories put forward in the field. 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 and enabling comparison across models without any fitting parameters. At all experimental concentrations tested, REST was more accurate than models which do not account for loops. Despite substantially increased accuracy in REST, persistent deviations suggest the need for further improvements in elasticity models, especially in the high defect regime.