Statistical Mechanic and Phenomenological Approaches to Isomeric Effects in Thermodiffusion

We present a model that explains variance in the thermodiffusion of hydrocarbon isomers in binary liquid mixtures. The model relies on material transport equations for binary nonisothermal liquid systems that were derived through a nonequilibrium thermodynamic approach in a previous work, coupled with one of two methods: (i) use of equilibrium chemical potentials for each component under conditions of constant pressure, derived using statistical mechanics or (ii) use of the temperature derivative of chemical potential expressed phenomenologically as molecular entropy. The model is evaluated using Soret coefficients (S) measured in binary solutions of heptane isomers in benzene. The statistical mechanic approach yields moderately acceptable agreement with experimental data. The phenomenological approach, which relies on both measured and calculated values of molecular entropy from the literature, yields values of S centered around the experimental data, with the scatter likely due to poor precision in the measured or calculated values of entropy. For the latter case, we identify several methods for calculating entropy that yield good agreement with experimental data.