A new accurate quadratic equation model for isothermal gas chromatography and its comparison with the linear model

Abstract

The gas holdup time (tM) is a dominant parameter in gas chromatographic retention models. The difference equation (DE) model proposed by Wu et al. (J. Chromatogr. A 2012, http://dx.doi.org/10.1016/j.chroma.2012.07.077) excluded tM. In the present paper, we propose that the relationship between the adjusted retention time tRZ′ and carbon number z of n-alkanes follows a quadratic equation (QE) when an accurate tM is obtained. This QE model is the same as or better than the DE model for an accurate expression of the retention behavior of n-alkanes and model applications. The QE model covers a larger range of n-alkanes with better curve fittings than the linear model. The accuracy of the QE model was approximately 2–6 times better than the DE model and 18–540 times better than the LE model. Standard deviations of the QE model were approximately 2–3 times smaller than those of the DE model.

Determination and evaluation of gas holdup time with the quadratic equation model and comparison with nonlinear models for isothermal gas chromatography

“…General characteristics of the QE model were discussed in our previous paper [34]. The present study focused on the characteristics related to t MT and comparison with other nonlinear models.…”

“…The accuracy of a curve fitting for the t MCH4 and t MM with the LE model was poor [34]. To compare the accuracy of curve fittings of Eq.…”

“…It is commonly known that increasing the degree of or parameters in the equation will result in an improvement of fitting ability. The Δ Ī values from both the CE and LOG models [25, 30] with four parameters were equivalent to that from the QE model [34] with three parameters only. The reason is that the less accurate t M values counteracted the fitting power of the aforementioned 4-parameter equations.…”

“…The t MCH4 and t MNe values were obtained experimentally [10,33,34]. Published raw retention times were used to calculate t M [10,25,30,33].…”

“…the difference equation (DE) and quadratic equation (QE) models recently proposed by Wu et al [33,34]. The DE model [33] excludes the influence of t M and expresses the accurate retention behavior of n -alkanes.…”