Prediction of overloaded concentration profiles under ultra-high-pressure liquid chromatographic conditions

In this study, overloaded elution profiles under ultra-high-pressure liquid chromatographic (UHPLC) conditions and accounting for the severe pressure and temperature gradients generated, are compared with experimental data. The model system consisted of an C18 column packed with 1.7-µm particles (i.e., a UHPLC column) and the solute was 1,3,5-tri‑tert-butylbenzene eluted with a mobile phase composed of 85/15 (v/v) acetonitrile/water. Two thermal modes were considered, and the solute was eluted at the very high inlet pressures necessary to achieve a highly efficient and rapid chromatographic process, as provided by using columns packed with small particles. However, the high inlet pressure and high linear velocity of the mobile phase caused the production of a significant amount of heat, and consequently, the formation of axial and radial temperature gradients. Due to these gradients, the retention and the mobile phase velocity were no longer constant. Thus, simple mathematical models consisting only of the mass balance equations are unsuitable to properly model the elution profiles. Here, the elution concentration profiles were predicted using a combined two-dimensional heat and mass transfer model, also including the calculation of the mobile phase velocity distribution. The isotherm adsorption model was the bi-Langmuir isotherm model with Henry constants that depended on the local temperature and pressure in the column. These adjustments allowed us to precisely account for changes in the shape and retention of the overloaded concentration profiles in the mobile phase. The proposed model provided accurate predictions of the overloaded concentration profiles, demonstrating good agreement with experimental profiles eluted under severe pressure and temperature gradients in the column even in the most extreme cases where the pressure drops reached 846 bar and the temperature gradients equaled 0.15 K mm^-1 and 0.95 K mm^-1 in the axial and the radial directions, respectively. In such cases 36 % decrease of the retention factor was observed along the column and 2 % increase in radial direction. These changes, combined with the velocity distribution, shifted the overloaded elution profile's shock towards the center of the column, advancing approximately 3 mm from its initial position close to the column wall. Ultimately, this resulted in the broadening of the elution band.