Experimental design and re-parameterization of the Neue-Kuss model for accurate and precise prediction of isocratic retention factors from gradient measurements in reversed phase liquid chromatography

The present work describes a re-parameterization of the Neue Kuss (NK) model for describing retention in liquid chromatography, and this re-parameterized model is used fit a large set of isocratic retention measurements with improved convergence properties relative to the original parameterization of the model. Next, an experimental design for retention measurements made using mobile phase gradient elution conditions is proposed for the purpose of obtaining accurate and precise NK parameters. Simulated retention data for mobile phase gradient elution conditions with two different levels of noise, as well as an essentially zero noise level were fit with the re-parameterized model. The results showed that the re-parameterized fits yielded average (absolute value) prediction errors for the parameters at the highest noise level of 7.16 % for S1,ref, 17.5 % for S2,ref and 6.19 % for kref. These errors were significantly smaller than those for the original parameterization of the NK model, where the errors were 23.2 % for S1, 24.9 % for S2 and 159 % for kw. Furthermore, isocratic retention factors predicted using these model parameters were found to have an average magnitude of error of 0.509 % for the re-parameterized model, as opposed to 6750 % for the model with the original parameterization. A further test of this approach was carried out for independent experimental measurements for five solutes and a C18 column. The average magnitude of error of the isocratic retention factors predicted from parameters obtained from fits of gradient data was 1.59 %, provided that the range of organic solvent compositions that the solute sampled in the mobile phase gradient experiments was consistent with the isocratic experiments. These results indicate that the reparameterization of the NK model allows for significant improvements in the fitting process, and that the proposed experimental design allows for NK parameters to be extracted from mobile phase gradients experiment that predict isocratic retention factors with an accuracy on the order of 1%.