Excess thermodynamic functions of n-alkane mixtures. Prediction and interpretation through the corresponding states principle

Abstract

Using published reduction parameters for pure normal alkanes, the Prigogine corresponding states principle is extended to excess thermodynamic functions of n-alkane mixtures. All alkane segments have identical interactions (no end-effects), an assumption justified by the success of the treatment. The TCEp data of Trejo Rodriguez and Patterson (J. Chem. Soc., Faraday Trans. 2, 1982, 78, 491), for n-alkane mixtures through the composition range at 20, 40, 55 °C are given by a single reduced TCEp against T curve. Similarly, single curves against T of HE, GER and TSER represent literature HE, residual GE and residual TSE data through the composition ranges and at various temperatures for n-C6+ n-C16. The Flory and the Guggenheim–Huggins–Miller–Orr combinatorial SE approximations lead to equally successful corresponding states representations for TSER and GER. Maximum deviations from the corresponding states curves correspond to ca. 10 J mol–1 for HE, GE and TSE, and ca. 0.2 J K–1 mol–1 in CEp, indicating conformity of the excess functions with the corresponding states principle. The TCEp, HE, TSER and GER may be represented by a single Cp(T) curve for pure and mixed n-alkanes. The curve first decreases with increasing T corresponding to decreasing short-range orientational order in the liquid, then passes through a wide minimum and increases with T corresponding to an increase of free volume. The Cp function predicts all the complex temperature and composition dependences of CEp, HE, TSER and GER for a typical system, n-C6+ n-C16, as effects of orientational order and free volume. Experimental data available for numerous n-alkane systems at different temperatures are used to test the calculations of the following quantities: equimolar HE, finite concentration and infinite dilution activity coefficients (including polyethylene systems) and lower critical solution temperatures for polyethylene systems. Agreement with experiment is almost always within experimental error and is considerably better than with other predictive methods. Experimental data for the pure n-alkanes from n-C5 to polyethylene follow the corresponding states principle imperfectly, but give a Cp(T) curve which is of the same shape as that obtained from excess quantities, i.e.Cp indicates both orientational order and free volume effects. However, the magnitude of Cp is considerably greater and reasons for this difference are discussed.