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

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Abstract

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.

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I. G. Zenkevich

St. Petersburg University, Institute of Chemistry

Author for correspondence.
Email: izenkevich@yandex.ru
Russian Federation, St. Petersburg

T. A. Kornilova

St. Petersburg University, Institute of Chemistry

Email: izenkevich@yandex.ru
Russian Federation, St. Petersburg

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2. Fig. 1. Dependences of absolute peak areas of ethyl diazoacetate on the evaporator temperature for solutions (a) in n-heptane (b) and 2-propanol in the range from 150 to 280°C. See text for comments.

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3. Fig. 2. Dependences of the absolute peak areas of (a) (1-methyl-1-chloroethyl)benzene and (b) 1-methylethenylbenzene on the evaporator temperature in the range from 150 to 300°C (according to data from [15]).

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4. Fig. 3. Dependences of the absolute peak areas of thermally stable (1-methyl-2-chloroethyl)benzene [15] on the temperature of the gas chromatograph evaporator in the range from 150 to 300°C with a split of the carrier gas flow (a) 10:1 and (b) 5:1.

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5. Fig. 4. Approximation of the temperature dependence of the ratios of the peak areas of ethyl diazoacetate (EDA) and n-dodecane (standard) for a solution in n-heptane: left asymptote 0.176 ± 0.004, right asymptote –0.002 ± 0.005, middle of the curve (inflection point T(1/2)) 247 ± 11°C.

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6. Fig. 5. Approximation of the temperature dependence of the ratios of the peak areas of ethyl diazoacetate and the standard in different solvents. The internal standard in cases (a) and (d) is n-octane (impurity in n-heptane), in the others – n-dodecane: (a) n-heptane: left asymptote 1.69 ± 0.02, right -0.01 ± 0.01, inflection point 246 ± 14°C; (b) carbon tetrachloride: left asymptote 2.08 ± 0.02, right asymptote –0.03 ± 0.02, inflection point 244 ± 11°C; (c) methanol: left asymptote 2.10 ± 0.07, right asymptote –0.06 ± 0.10, inflection point 244 ± 15°C; (d) 2-propanol: left asymptote 24.6 ± 0.8, right asymptote –1.3 ± 1.2, inflection point 248 ± 14°C; (e) 2-methyl-1-propanol: left asymptote 7.77 ± 0.06, right asymptote –0.47 ± 0.12, inflection point 246 ± 12°C; (e) 3-methyl-1-butanol: left asymptote 2.65 ± 0.04, right asymptote 0.47 ± 0.11, inflection point 252 ± 11°C.

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7. Fig. 6. Fragment of the chromatogram of a solution of ethyl diazoacetate in 2-propanol at an evaporator temperature of 240°C: A – ethyl diazoacetate; B – ethyl ester of isopropoxyacetic acid, RI 911 ± 3; C – isopropyl ester of ethoxyacetic acid (presumably), RI 934 ± 3.

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8. Fig. 7. Approximation of the temperature dependence of the ratios of the peak areas of ethyl esters of alkoxyacetic acids and the standard in different solvents. The internal standard in the case of (a) is n-octane (impurity in n-heptane), (b) and (c) is n-dodecane: (a) ethyl isopropoxyacetate (EIPA, solution in 2-propanol): left asymptote 0.1 ± 0.4, right asymptote 3.8 ± 0.5, middle of the curve 242 ± 11°C; (b) ethyl isobutoxyacetate (EIBA, solution in 2-methyl-1-propanol): left asymptote 0.01 ± 0.03, right asymptote 1.12 ± 0.05, middle of the curve 243 ± 8°C; (c) ethyl isoamyloxyacetate (EIAA, solution in 3-methyl-1-butanol): left asymptote -0.04 ± 0.06, right asymptote 1.94 ± 0.23, middle of the curve 251 ± 17°C.

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9. Fig. 8. (a) Temperature dependence of the relative peak areas of 1-chlortetralin (standard – n-tridecane). Calculation of logistic regression parameters is impossible (the inflection point is not reached). (b) Illustration of the possibility of calculating logistic regression parameters with the artificial addition of the point Srel = 0 for T = 500°C. The left asymptote is 3.48 ± 0.11, the inflection point is 356 ± 20°C.

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10. Fig. 9. Temperature dependence of relative peak areas of (1-chloroethyl)benzene (standard – ethylbenzene). Calculation of logistic regression parameters is impossible (weak dependence close to linear; inflection point not reached). Artificial addition of the point Srel = 0 for Tlimit = 400°C allows us to estimate the left asymptote (Srel ≈ 2.25) and (with low accuracy) T(1/2) ≈ 400°, which approximately corresponds to the thermal stability limit of this compound.

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11. Scheme 1. Thermal transformations of a-diazocarbonyl compounds.

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12. Scheme 2. Probable mechanism of thermal destruction of substituted N-(2-hydroxybenzyl)amines.

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