Epidemic models for phase transitions: application to a physical gel

Abstract

Carrageenan gels are characterized by reversible sol-gel and gel-sol transitions under cooling and heating processes and these transitions are approximated by generalized logistic growth curves. We express the transitions of carrageenan-water system as a representative of reversible physical gels in terms of a modified Susceptible-Infected-Susceptible epidemic model as opposed to the Susceptible-Infected-Removed model used to represent the (irreversible) chemical gel formation in the previous work. We locate the gel point T-c of sol-gel and gel-sol transitions and we find that for the sol-gel transition (cooling) T-c > T-sg (transition temperature) i.e. T-c is earlier in time for all carrageenan contents and moves forward in time and gets closer to T-sg as the carrageenan content increases. For the gel-sol transition (heating) T-c is relatively closer to T-gsit is greater than T-gs i.e. later in time for low carrageenan contents and moves backward as carrageenan content increases.