A trade-off between hardness and stretchability of associative networks during the sol-to-gel transition

The trade-off between hardness and stretchability is a cornerstone of materials science. Balancing this trade-off is important in the molecular design of both chemical and physical networks. In this study, we report the quantitative trade-off at the molecular level for physical networks. Namely, we analyze, based on the reversible gelation model, a scaling relationship between the characteristic terminal relaxation modulus G(c) in linear viscoelasticity and the stretch ratio lambda(max) at the stress overshoot during the nonlinear elongation flow for unentangled randomly associative polymers, i.e., lambda(max) similar to G(c)(-0.17) and lambda(max) similar to G(c)(-0.33) in the mean-field and critical-percolation regimes, respectively. We use sulfonated polystyrene having different alkali counterions as a model system to test the relationship. The exponent of lambda(max) similar to G(c)(-0.25) seen in the experiment is in between the two theoretical values. We also discuss the quantitative deviation with respect to the size distribution of the network strands. (c) 2023 The Society of Rheology.