Department of Engineering and Chemical Sciences, Karlstad University, SE-651 88 Karlstad, Sweden.
J Chromatogr A. 2013 Jul 19;1299:64-70. doi: 10.1016/j.chroma.2013.05.041. Epub 2013 May 23.
The inverse method is a numeric method for fast estimation of adsorption isotherm parameters directly from overloaded elution profiles. However, it has previously only been used for isocratic experiments. Here we will extend the inverse method so it can be used for gradient elution too. This extended inverse method will make it possible to study the adsorption of substances whose retention factor vary strongly with the mobile-phase composition, like peptides and proteins, where the classic methods will fail. Our extended inverse method was verified using both simulations and real experiments. For simulated overloaded elution profiles we were able to determine almost exact Langmuir adsorption isotherm parameters with the new approach. From real experimental data, bi-Langmuir adsorption parameters were estimated using both the perturbation peak method and the extended inverse method. The shape of the acquired adsorption isotherms did match over the considered concentration range; however, the adsorption isotherm parameters found with the two methods were not the same. This is probably due to the fact that adsorption isotherm estimated with the inverse method is only a good approximation up to the highest eluted concentration in the used chromatograms. But this is not a serious drawback from a process point of view where the main objective is to make accurate predictions of elution profiles. The bi-Langmuir adsorption isotherm obtained with both methods could accurately predict the shape of overloaded elution profiles.
反演法是一种快速估计吸附等温线参数的数值方法，可以直接从过载洗脱曲线中得到。然而，它以前只被用于等度实验。在这里，我们将扩展反演法，使其也可用于梯度洗脱。这种扩展的反演方法将使研究保留因子随流动相组成强烈变化的物质（如肽和蛋白质）的吸附成为可能，而经典方法在这种情况下将失效。我们的扩展反演方法通过模拟和实际实验进行了验证。对于模拟的过载洗脱曲线，我们能够使用新方法几乎精确地确定朗缪尔吸附等温线参数。从实际实验数据中，使用扰动峰法和扩展反演法分别估计了双朗缪尔吸附参数。所获得的吸附等温线在考虑的浓度范围内形状匹配；然而，两种方法得到的吸附等温线参数并不相同。这可能是由于反演法估计的吸附等温线仅在所用色谱图中洗脱的最高浓度下是一个很好的近似，而不是从过程的角度来看一个严重的缺点。两种方法得到的双朗缪尔吸附等温线可以准确地预测过载洗脱曲线的形状。
