Approximation of the results of gas chromatographic analysis of thermally unstable compounds using logistic regression

Decomposition of thermally unstable analytes in the chromatograph injector is not uncommon in the practice of gas chromatographic analysis. However, as a rule, it cannot be detected by variations in the absolute areas of gas chromatographic peaks at different injector temperatures. This is hindered by the effects of area discrimination typical of sample dosing into capillary columns with flow division. The problem can be solved using relative peak areas calculated with respect to thermally stable compounds. Dependences of relative peak areas of unstable analytes on temperature (decreasing), as well as of their degradation products (increasing), are characterized by the presence of two limits. The low-temperature limits correspond to the real contents of unstable compounds or their degradation products in samples, and the high-temperature limits correspond to the composition of samples at hypothetically complete transformation of such analytes. Such dependences can be approximated by the logistic regression equation (otherwise – sigmoidal approximation or Boltzmann approximation). To test the applicability of logistic regression for processing the results of gas chromatographic analysis of thermally unstable compounds, the possibilities of approximating the temperature dependence of the peak areas of ethyldiazoacetate in various solvents were analyzed in the present work. The results confirm that gas chromatographic analysis of this ester and, apparently, of other diazocarbonyl compounds without their appreciable decomposition is possible at injector temperatures up to 200°C. The thermal destruction of ethyldiazoacetate in its solutions in aliphatic alcohols is accompanied by the formation of ethyl esters of alkoxyacetic acids – products of the introduction of intermediately formed ethoxycarbonylcarbene into the O–H bonds of alcohols. Such a characteristic of logistic regression as the value of the argument corresponding to the average value of the function indicates that the half-life temperatures of the initial analyte and “half-formation” of the products are the same, which makes it possible to correlate these processes with each other. A slight modification of the proposed method (addition of a point corresponding to the zero peak area at a hypothetical high injector temperature) makes it possible to extend it to characterize compounds with half-life temperatures higher than 300°C. Such a variant was used to test the thermal stability/instability of halogen derivatives of alkyl- and cycloalkylaromatic hydrocarbons under conditions of gas chromatographic analysis.