Approximation of the Results of Analysis of Thermally Unstable Compounds by Gas Chromatography Using Logistic Regression

Abstract

The decomposition of thermally unstable components in chromatograph sample injectors often occurs during gas chromatographic analysis. However, variations in the absolute areas of gas chromatographic peaks at different injector temperatures generally do not reveal this decomposition. This is due to the area discrimination effects, which are typical for samples introduced into capillary columns with flow splitting. This problem can be solved using relative peak areas, calculated in relation to thermally stable compounds. The relationships between the relative peak areas of unstable analytes and temperature (decreasing) and between those of their decomposition products and temperature (increasing) are characterized by the existence of two limits. Low-temperature limits correspond to the actual concentration of unstable compounds or their decomposition products in the samples, while high-temperature limits reflect the composition of samples under the hypothetical condition of the complete transformation of such analytes. These relationships can be approximated using the logistic regression equation, also known as sigmoidal approximation or Boltzmann approximation. To evaluate the applicability of logistic regression to processing the results of a gas chromatographic analysis of thermally unstable compounds, this study examines the potential for approximating the temperature dependence of ethyl diazoacetate peak areas in various solvents. The results confirm that the gas chromatographic analysis of this ester, as well as likely other diazocarbonyl compounds, can be performed without their significant decomposition at injector temperatures up to 200°C. The thermal decomposition of ethyl diazoacetate in its solutions with aliphatic alcohols is accompanied by the formation of ethyl esters of alkoxyacetic acids. These are products of the insertion of the intermediate ethoxycarbonyl carbene into O−H bonds of alcohols. A characteristic feature of logistic regression, specifically the argument value corresponding to the mean function value, indicates that the temperatures for the analyte’s half-life and the time of the formation of half of products are equal. This relationship allows these processes to be correlated with each other. A slight modification of the proposed method (adding a point corresponding to the zero peak area at a hypothetical high injector temperature) enables its application to the characterization of compounds with half-life temperatures above 300°C. This variation was used to evaluate the thermal stability or instability of halogen-substituted alkyl- and cycloalkyl-aromatic hydrocarbons under the conditions of gas chromatographic analysis.