  Stimulus-induced volumetric phase transition in gels may be potentially
exploited for various bio-engineering and mechanical engineering applications.
Since the discovery of the phenomenon in the 1970s, extensive experimental
research has helped in understanding the phase transition and related critical
phenomena. Yet, 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 that has been
previously employed to investigate phase transitions in van der Waals fluids
and black holes. The framework equips us with a scalar curvature that relates
to the microstructural interactions of a gel during phase transition and at
critical points. This curvature also provides an insight into the universality
class of phase transition and the nature of polymer-polymer interactions.
