Interpreting freezing point depression of stearic acid and methyl stearate

Freezing point depressions of binary systems including either stearic acid (SA) or methyl stearate (MES) were evaluated based on differential scanning calorimetry melting scans. The second binary component included a solvent from the group acetic acid, acetone, 2-butanone, and hexane. Vapor pressure as a function of liquid composition and temperature was used to measure vapor/liquid equilibrium. Activity coefficients were calculated from this data and models fit to the data to determine how well the models fit the solid–liquid equilibrium models.The Gibbs/Duhem equation and polymorphism of the melt transitions indicated that freezing point depressions were due to a combination of: (1) a reduction of activity of the triglyceride derivative in solution albeit with activity coefficients > 1.0, (2) incorporation of the solvent into the solid matrix for at least some of the mixtures, and (3) substantially different physical properties between the solid and liquid phases of the SA and MES. Different melting phenomena were observed in differential scanning calorimetry (DSC) scans depending upon the heteroatom functionality of the solvent.The empirical Margules, NRTL, and Wilson activity coefficient models fit data for the solvent activity coefficients well, while the UNIQUAC model combined with the predictive abilities of UNIFAC could not accurately predict activity coefficients. Despite questions on the fundamental interpretation of the data, modeling the activity coefficients for the solvent is sufficient to approximate the effect the solvent will have on the melting point depression. Relatively simple experiments following the total pressure of mixtures as a function of composition and temperature can be used to obtain activity coefficient model parameters for the Margules, NRTL, UNIQUAC, and Wilson.