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

Abstract

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, d 2 I/d T 2. The expression deduced on a purely mathematical–physicochemical basis is d 2 I/d T 2 = [2 TΔ S(CH 2)d I/d T − 100 δΔ C p]/ TΔ G(CH 2). The solute-dependent factor for d I/d T, d 2 I/d T 2, and the extreme temperature in the I vs. T relationship is δΔ C p, 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, Δ S(CH 2) and Δ G(CH 2). Experimentally, convex I vs. T curves with a minimum are formed when δΔ C p ≫ 0, while concave ones with a maximum are observed when δΔ C p ≪ 0. In the event of a linear temperature dependence, the former equation can be simplified: d I/d T = 100 δΔ C p/2 TΔ S(CH 2) . The deviation from linearity (higher d 2 I/d T 2) increases with increasing δΔ C p 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.