A model to simulate the gas chromatographic separation in the presence of a spatial thermal gradient is presented. This model is developed from existing models for the prediction of retention times in temperature programmed GC. It is based on basic fluid mechanics of gasses in capillaries to describe the properties of the mobile phase and a thermodynamic model to describe retention of solutes in a stationary phase. This model is expanded to incorporate a spatial thermal gradient. The development of the peak width during the chromatographic separation is modeled by a differential equation, which uses the solute residency, the inverse of the solute velocity, instead of the solute velocity. The presented model is compared to measurements of n-alkanes with conventional temperature programmed GC-FID and to measurements with a hyper-fast flow-field thermal gradient GC (FF-TG-GC) coupled with a MS. The FF-TG-GC enables the use of a spatial thermal gradients. For temperature programmed GC-FID, without spatial thermal gradients, calculated retention times are mostly within 1% of measured values. For the FF-TG-GC-MS with a thermal gradient the simulation showed a deviation of the spatial thermal gradient from a linear to a nonlinear gradient, which could be confirmed by measuring the shape of the spatial gradient. The calculated retention times for the nonlinear gradient are also mostly within 1% of measured values. Calculated peak widths are smaller than measured peak widths by 10 to 15% in the case of the conventional GC-FID and by 30 to 50% for the FF-TG-GC-MS. The relation between the measured and calculated variances shows a linear correlation which can be used to correct the calculated variance and peak width. With this correction the difference for the peak widths is reduced to 4-10% for the conventional GC and below 10% for the majority of solutes with exceptions for early and late eluted n-alkanes (up to 25% difference).

中文翻译：

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空间热梯度气相色谱的模拟。

提出了一种在空间热梯度存在下模拟气相色谱分离的模型。该模型是根据现有模型开发的，用于预测温度编程GC中的保留时间。它基于毛细管中气体的基本流体力学来描述流动相的特性，并基于热力学模型来描述溶质在固定相中的保留。对该模型进行扩展以合并空间热梯度。用微分方程对色谱分离过程中峰宽的发展进行建模，该方程使用溶质停留时间（溶质速度的倒数）而不是溶质速度。将该模型与使用常规温度编程的GC-FID对正构烷烃的测量结果以及与MS结合使用超快速流场热梯度GC（FF-TG-GC）的测量结果进行比较。FF-TG-GC可以利用空间热梯度。对于温度编程的GC-FID，没有空间热梯度，计算出的保留时间大部分在测量值的1％以内。对于具有热梯度的FF-TG-GC-MS，模拟显示空间热梯度从线性梯度到非线性梯度的偏差，可以通过测量空间梯度的形状来确认。计算出的非线性梯度保留时间也大多在测量值的1％之内。对于常规GC-FID，计算出的峰宽比测量峰宽小10％至15％，对于FF-TG-GC-MS，其计算峰宽小30％至50％。测得和计算出的方差之间的关系显示出线性相关性，可用于校正计算出的方差和峰宽。通过这种校正，常规气相色谱的峰宽差异降低到4-10％，而大多数溶质的峰宽差异降低到10％以下，早期和晚期洗脱的正构烷烃除外（差异高达25％）。