Tricritical phenomena in quasibinary mixtures. VIII. Calculations from the van der Waals equation for binary mixtures

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Abstract
The van der Waals equation for binary mixtures has been used to calculate thermodynamic properties in the region of a tricritical point. Three different models have been used: (A) molecules of the same size, but different energies of interaction, and zero interchange energy; (B) mixtures of chain molecules using the Flory entropy of mixing; and (C) mixtures of chain molecules using the Flory entropy of mixing and the Prigogine chain entropy parameter c. The results from all three models are qualitatively similar, but model C comes closest to reproducing the experimental three-phase coexistence curves of binary and quasibinary mixtures of ethane with higher hydrocarbons (C17 to C20). However, the calculated susceptibilities yield a Griffiths first sum ∑1 that differs substantially from the experimental results; it is finite and nonzero at the tricritical point, as the extended classical theory predicts, and changes only slightly with increasing chain length. This supports our view that the discrepancies between theory and experiment are not associated with being too far from the tricritical point, and the conclusion that, since amplitude ratios are expected to be nonclassical, the experimental ∑1 is in fact divergent.