Justification of statistical overlap theory in programmed temperature gas chromatography: Thermodynamic origin of random distribution of retention times

A specific distribution of compounds' standard-state changes of enthalpy and entropy between mobile and stationary phases in programmed temperature gas chromatography (PTGC) is shown to produce the Poisson distribution of retention times often postulated in statistical-overlap theory (SOT). A three-part model is proposed, in which the enthalpy change is Poisson distributed, the average entropy change depends on the enthalpy change, and the actual entropy change varies in a uniformly random manner about the average entropy change. To test the model, the entropy and enthalpy changes of 350 aliphatic and aromatic hydrocarbons in petroleum were calculated with commercial GC software. These changes are shown to follow the three-part model. The model then was used with Monte Carlo methods to mimic the enthalpy and entropy changes. The substitution of the mimicked enthalpy and entropy changes into an equation for the retention temperature in PTGC is shown to produce a Poisson distribution of retention times that is statistically significant. This finding establishes a scientific link between the thermodynamics governing retention in PTGC and the superficially ad hoc assumption of the Poisson retention time distribution in SOT, Similar thermodynamic distributions are found for flavors and fragrances and for tetrachlorodibenzo-p-dioxins and furans, which follow SOT based on the Poisson distribution, but not for polychloronaphthalenes, which do not follow that SOT.