Temperature dependence of the Kovلts retention index: Convex or concave curves

The non-linearity in the temperature dependence of the Kováts index, I (the formation of convex or concave curves) was characterized by the second derivative, d2I/dT2. The expression deduced on a purely mathematical–physicochemical basis is d2I/dT2 = [2TΔS(CH2)dI/dT − 100δΔCp]/TΔG(CH2). The solute-dependent factor for dI/dT, d2I/dT2, and the extreme temperature in the I vs. T relationship is δΔCp, which is the molar solvation heat capacity difference between the solute and a hypothetical n-alkane which elutes at the same time as the given solute, while the solvent-dependent factors are the solvation entropy and free energy of the methylene unit, ΔS(CH2) and ΔG(CH2). Experimentally, convex I vs. T curves with a minimum are formed when δΔCp ≫ 0, while concave ones with a maximum are observed when δΔCp ≪ 0. In the event of a linear temperature dependence, the former equation can be simplified: dI/dT = 100δΔCp/2TΔS(CH2). The deviation from linearity (higher d2I/dT2) increases with increasing δΔCp values. The model equations were tested from the dataset published by the Kováts group on C78 (19,24-dioctadecyldotetracontane), POH (18,23-dioctadecyl-1-untetracontenol), PCN (1-cyano-18,23-dioctadecyluntetracontane) and TMO (1,38-dimethoxy-17,22-bis-(16-methoxyhexadecyl)-octatriacontane) and by present measurements on the Innowax phase.