Surface Instabilities and
Topological Phase Transitions in Soft Solids
Abstract:
Soft solids, such as hydrogels and elastomers, can develop
intricate, reticulated folding patterns in their surfaces and
interfaces when compressed. The formation and evolution of these
patterns---which resemble the sulcus patterns on our
brains---can be understood as a first order phase transition
between a flat surface and a surface with many sharply creased
folds, or sulci. The transition has well defined binodal and
spinodal points as well as an energy of transformation; however,
a droplet of the new phase (a single sulcus) does not have
a discernible phase boundary and so cannot be described with a
local order parameter. Rather, the transition is topological in
nature: the surface or interface folds to self-contact
(expelling the softer elastomer without tearing in the case of
an interface), eliminating the free surface or interface. I will
explain how these peculiar phase transitions arise in a
prototype model of a soft solid, the neo-Hookean model of
rubber, and how patterns form and evolve as an unusual kind of
phase separation. These interfacial phase transitions break from
the Landau-Ginzburg picture because the polyconvex form of the
neo-Hookean free energy forbids the formation of phase
boundaries, but does not forbid phase transitions.