Modeling the liquid-solid transition in saturated triglycerides*

Corkery \textit{et al.} have proposed that the high-temperature state of the triglyceride trilaurin (TL) is a Y-conformer, in which the three hydrocarbon chains are dynamically twisted with an average angle of $\sim $120\r{ } between them. Using computer simulations, we first show that the high-temperature state is indeed the Y conformation. We then develop a theory of the liquid-solid transition of this system, in which TL molecules are in a chair (h) conformation, with extended, possibly all-trans, chains at low-temperatures, and are in a Y conformation in the liquid phase at temperatures higher than the transition temperature, T*$\approx $319K. We map this ``h-Y model'' onto an Ising model in a temperature-dependent field, perform a mean-field approximation, and calculate the transition enthalpy, which is in good agreement with experiment. We also predict the temperature-dependence of the 1132 cm$^{-1}$ Raman band. Our results support the proposal that the liquid state is made up of molecules in the Y conformation.