Rapid optimization of gradient liquid chromatographic (LC) separations often utilizes analyte retention modelling to predict retention times as function of eluent composition. However, due to the dwell volume and technical imperfections, the actual gradient may deviate from the set gradient in a fashion unique to the employed instrument. This makes accurate retention modelling for gradient LC challenging, in particular when very fast separations are pursued. Although gradient deformation has been addressed in method-transfer situations, it is rarely taken into account when reporting analyte retention parameters obtained from gradient LC data, hampering the comparison of data from various sources. In this study, a response-function-based algorithm was developed to determine analyte retention parameters corrected for geometry-induced deformations by specific LC instruments. Out of a number of mathematical distributions investigated as response-functions, the so-called “stable function” was found to describe the formed gradient most accurately. The four parameters describing the model resemble the statistical moments of the distribution and are related to chromatographic parameters, such as dwell volume and flow rate. The instrument-specific response function can then be used to predict the actual shape of any other gradient programmed on that instrument. To incorporate the predicted gradient in the retention modelling of the analytes, the model was extended to facilitate an unlimited number of linear gradient steps to solve the equations numerically. The significance and impact of distinct gradient deformation for fast gradients was demonstrated using three different LC instruments. As a proof of principle, the algorithm and retention parameters obtained on a specific instrument were used to predict the retention times on different instruments. The relative error in the predicted retention times went down from an average of 9.8% and 12.2% on the two other instruments when using only a dwell-volume correction to 2.1% and 6.5%, respectively, when using the proposed algorithm. The corrected retention parameters are less dependent on geometry-induced instrument effects.

梯度液相色谱（LC）分离的快速优化通常利用分析物保留模型来预测保留时间与洗脱液组成的关系。但是，由于驻留体积和技术缺陷，实际梯度可能会以所用仪器独有的方式偏离设定的梯度。这使得针对梯度液相色谱的准确保留模型具有挑战性，尤其是在进行非常快速的分离时。尽管在方法转移的情况下已解决了梯度变形问题，但在报告从梯度LC数据获得的分析物保留参数时却很少考虑到梯度变形，从而妨碍了对各种来源数据的比较。在这个研究中，开发了一种基于响应函数的算法，以确定通过特定LC仪器校正了几何形状引起的变形的分析物保留参数。在研究作为响应函数的许多数学分布中，发现了所谓的“稳定函数”，可以最准确地描述所形成的梯度。描述模型的四个参数类似于分布的统计矩，并且与色谱参数有关，例如驻留体积和流速。然后，可以使用特定于仪器的响应函数来预测在该仪器上编程的任何其他梯度的实际形状。为了将预测的梯度纳入分析物的保留模型中，对模型进行了扩展，以促进无限数量的线性梯度步骤可以数值求解方程式。使用三种不同的LC仪器证明了快速梯度明显梯度变形的重要性和影响。作为原理证明，使用在特定仪器上获得的算法和保留参数来预测在不同仪器上的保留时间。当仅使用驻留体积校正时，预测保留时间的相对误差从其他两种仪器的平均值分别为9.8％和12.2％降至使用所提出算法时的2.1％和6.5％。校正后的保留参数较少依赖于几何形状引起的仪器效果。使用在特定仪器上获得的算法和保留参数来预测不同仪器上的保留时间。当仅使用驻留体积校正时，预测保留时间的相对误差从其他两种仪器的平均值分别为9.8％和12.2％降至使用所提出算法时的2.1％和6.5％。校正后的保留参数较少依赖于几何形状引起的仪器效果。使用在特定仪器上获得的算法和保留参数来预测不同仪器上的保留时间。当仅使用驻留体积校正时，预测保留时间的相对误差从其他两种仪器的平均值分别为9.8％和12.2％降至使用所提出算法时的2.1％和6.5％。校正后的保留参数较少依赖于几何形状引起的仪器效果。