Mass transfer kinetics in the chromatography of insulin variants under nonlinear conditions

Experimental data regarding the thermodynamics and kinetics of adsorption of lispro, an insulin variant, onto a YMC ODS-A column, from an aqueous solution of acetonitrile (31%) and TFA are reinterpreted, using a more complex model of the mass transfer kinetics. The adsorption behavior follows the Toth isotherm model, suggesting either a strongly heterogeneous surface or, rather, that when insulin molecules adsorb they contact the surface along different areas of the molecule. The lumped pore diffusion (POR) model of chromatography accounts well for the band profiles. The internal mass transfer resistances are higher than expected, which suggests that intraparticle diffusion is slower. Furthermore, the pore diffusion coefficient increases with decreasing sample size. That surface diffusion accounts for the mass transfer kinetics inside particles explains these results. Assuming that the gradient of the surface concentration is the driving force of surface diffusion, it is possible to account very well for the band profiles of samples of widely different sizes, using a single value of the surface diffusivity.