Geometric thermodynamics of collapse of gels

Stimulus-induced volumetric phase transition in gels may be potentially exploited for various bioengineering and mechanical engineering applications. Since the discovery of the phenomenon in the 1970s, extensive experimental research has helped understand the phase transition and related critical phenomena. However, little insight is available on the evolving microstructure. In this article, we aim at unravelling certain geometric aspects of the micromechanics underlying discontinuous phase transition in polyacrylamide gels. Towards this, we use geometric thermodynamics and a Landau-Ginzburg type free energy functional involving a squared gradient, in conjunction with Flory-Huggins theory. We specifically exploit Ruppeiner's approach of Riemannian geometry-enriched thermodynamic fluctuation theory, which was previously employed to investigate phase transitions in van der Waals fluids and black holes. The framework equips us with a scalar curvature that is typically indicative of certain aspects of the microstructure during phase transition. Since previous studies have indicated that curvature divergence relates to correlation length divergence, we infer that the gel possesses a heterogeneous microstructure during phase transition, i.e., at critical points. Curvature also provides an insight into the universality class of phase transition and the nature of polymer-polymer interactions.