Fundamental chromatographic equations designed for columns packed with very fine particles and operated at very high pressures. Applications to the prediction of elution times and the column efficiencies

The wall temperatures of three Acquity-BEH-C18columns (2.1 mm x 50, 100, and 150 mm) and the temperature of the incoming eluent were maintained constant at 289 K, using a circulating water heat exchanger. The retention times and the band broadening of naphtho2,3-a]pyrene were measured for each column as a function of the flow rate applied. Pure acetonitrile was used as the eluent. The flow rate dependence of neither elution volumes nor bandwidths can be accounted for by classical models of retention and HETP, respectively, since these models assume columns to be isothermal. Because the heat generated by friction of the eluent against the column bed increases with increasing flow rate, the column bed cannot remain isothermal at high flow rates. This heat is evacuated radially and/or longitudinally by convection, conduction, and radiation. Radial and axial temperature gradients are formed, which are maximum and minimum, respectively, when the temperature of the column wall is kept uniform and constant. The retention times that we measured match well with the values predicted based on the temperature distribution along and across the column, which we calculated and on the temperature dependence of the retention for the same column operated isothermally (i.e., at very low flow rate). The rate of band spreading varies along non-isothermal columns, so the HETP can only be defined locally. It is a function of the axial coordinate. A new contribution is needed to account for the radial thermal heterogeneity of the column, hence the radial distribution of the flow velocities, which warps the elution band. A new model, based on the general dispersion theory of Aris, allows a successful prediction of the unusually large bandwidths observed with columns packed with fine particles, operated at high flow rates, hence high inlet pressures.