Retention time prediction in temperature-programmed, comprehensive two-dimensional gas chromatography: modeling and error assessment.

In this paper we present a model relating experimental factors (column lengths, diameters and thickness, modulation times, pressures and temperature programs) with retention times. Unfortunately, an analytical solution to calculate the retention in temperature programmed GC × GC is impossible, making thus necessary to perform a numerical integration. In this paper we present a computational physical model of GC × GC, capable of predicting with a high accuracy retention times in both dimensions. Once fitted (e.g., calibrated), the model is used to make predictions, which are always subject to error. In this way, the prediction can result rather in a probability distribution of (predicted) retention times than in a fixed (most likely) value. One of the most common problems that can occur when fitting unknown parameters using experimental data is overfitting. In order to detect overfitting situations and assess the error, the K-fold cross-validation technique was applied. Another technique of error assessment proposed in this article is the use of error propagation using Jacobians. This method is based on estimation of the accuracy of the model by the partial derivatives of the retention time prediction with respect to the fitted parameters (in this case entropy and enthalpy for each component) in a set of given conditions. By treating the predictions of the model in terms of intervals rather than as precise values, it is possible to considerably increase the robustness of any optimization algorithm.
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