Mass transfer equation for proteins in very high-pressure liquid chromatography

The mass transfer kinetics of human insulin was investigated on a 50 mm x 2.1 mm column packed with 1.7 microm BEH-C(18) particles, eluted with a water/acetonitrile/trifluoroacetic acid (TFA) (68/32/0.1, v/v/v) solution. The different contributions to the mass transfer kinetics, e.g., those of longitudinal diffusion, eddy dispersion, the film mass transfer resistance, cross-particle diffusivity, adsorption-desorption kinetics, and transcolumn differential sorption, were incorporated into a general mass transfer equation designed to account for the mass transfer kinetics of proteins under high pressure. More specifically, this equation includes the effects of pore size exclusion, pressure, and temperature on the band broadening of a protein. The flow rate was first increased from 0.001 to 0.250 mL/min, the pressure drop increasing from 2 to 298 bar, and the column being placed in stagnant air at 296.5 K, in order to determine the effective diffusivity of insulin through the porous particles, the mass transfer rate constants, and the adsorption equilibrium constant in the low-pressure range. Then, the column inlet pressure was increased by using capillary flow restrictors downstream the column, at the constant flow rate of 0.03 mL/min. The column temperature was kept uniform by immersing the column in a circulating water bath thermostatted at 298.7 and 323.15 K, successively. The results showed that the surface diffusion coefficient of insulin decreases faster than its bulk diffusion coefficient with increasing average column pressure. This is consistent with the adsorption energy of insulin onto the BEH-C(18) surface increasing strongly with increasing pressure. In contrast, given the precision of the height equivalent to a theoretical plate (HETP) measurement (+/-12%), the adsorption kinetics of insulin appears to be rather independent of the pressure. On average, the adsorption rate constant of insulin is doubled from about 40 to 80 s(-1) when the temperature increases from 298.7 to 323.15 K.