Chromatography Handbook Of Hplc - Katz Eksteen Schocnmakers Miller wiley Sons -118

108\nTijssen\n\nin later years for which chemically bonded phases are used as the retentive stationary layer, have made clear that it is necessary to redefine the spatial extent of both phases, because there is no clear interface that separates both domains. In the latter case, the chemically modified surface of the carrier particles is grafted with chain-like molecules with different lengths (Cg and C15s, for example), with different surface coverages (from isolated flexible chains to \"hairy\" polymer brushes), and with varying capabilities to include molecules of the mobile phase itself, so that a pure and separate stationary phase no longer exists. Rather, a continuous change of concentrations exists if we look perpendicular onto the solid interface, for both stationary-phase chain segments, mobile-phase constituents, and solute molecules. In a review on this matter [39], it has been shown that a hydrodynamic layer thickness, rather than a geometric condition, defines the existence of a stationary phase next to a moving mobile phase. The same situation, probably to another extent, may be present at liquid-liquid interfaces, with mutual penetration of molecules from one phase to the other.\n\nIn these situations, rather than postulating equilibrium to exist at the \"interface,\" it seems more appropriate to remove the equilibrium condition and treat mass transfer in this region as being driven by concentration differences and a kinetic adsorption and desorption process, with rate constants k_ and k_a that represent the mass-transfer velocity such that the partition coefficient is now given by k_E = k_a/k_h. Advocates of this approach [for a short introduction see Ref. 401, among which Giddings [5], derive an additional term in the plate height equation, analogous to the valid for adsorption [see Eq. [33c]]. For capillary chromatography this contribution reads:\n\nH_interface = k[(k_a(1 + k_b)k_i)/(k_a + k_b) = C_interface(u_m)\n\nAlthough the physical meaning of the dispersion constant is still a matter of debate, it is possible to approximate this mass transfer coefficient using Gidding's nonequilibrium theory [5], to find that (40):\n\nk_u = (R_iC_m)|k|(1 + k)\n\na\nand so, the interfacial resistance C term in the plate height equation is strongly connected to the mobile-phase convective dispersion C_m term as we know it from the foregoing treatment:\n\nC_interface ~ C_m|k|(1 + k)\n\nWith this additional C term, the total plate height Eq. (55a) becomes extended to:\n\nH_ap = ΣH_i = B_ap(u_m) + C_mC_interface(u_m) + C_i(u_m)\n+ 2D_p/(u_m)(1 + 1/24)h(R_i)R(u_m) + (2/3)h(k_i/ D_i)\n\nwhere h(k) = f(k)(1 + 2k)(1 + K) replaces f(k) in the original Golay equation. From this, it appears that for almost the whole k range the C_m term is increased by a factor approaching 2 at high k values (k > 10), which certainly cannot be ignored. A decisive study on the subject of interfacial resistance still has not been performed; but the available experimental data [40] clearly points in favor of the proposed additional term.\n(b) Peak Shape and Partitioning. Although the presence of an overlapping nonresolved second component should always be considered, often asymmetrical peak shapes can be attributed to concentration effects in the partitioning mechanism, and to a far lesser extent, to adsorption, chemical reactions, and extracolumn band-spreading. Concentration effects are at the very basis of chromatographic separations, both in the partitioning process and the transport processes governing the peak dispersion. When considering the effect of concentration, one should realize that the overall concentration of migrating zones falls as the rod proceeds: the rate of the fall is rapid at first and reduces toward the column exit, where the detector is measuring the outlet concentrations, which are thus always smaller than those inside the column. Hence, even if the outlet concentration may be infinite dilution, the inside column