Chromatography Handbook Of Hplc - Katz Eksteen Schocnmakers Miller wiley Sons -102

i = 1, for molecules that travel faster in the center of narrow interstitial flow channels than at the walls of those channels, caused by intrachannel velocity profiles (so-called trans-channel effect [1,5])\n\ni = 2, for molecules that move faster (or slower) in surrounding but neighboring channels, because of differences in shapes, widths, obstructions, and such, in the channel of interest (so-called short-range interchannel effect)\n\ni = 3, for molecules that undergo faster (or slower) transport in neighboring regions (covering some tens to hundreds of particles) owing to local packing irregularities, which may cause open voids or local porosity differences (stemming, e.g., from segregation of different-sized packing particles; so-called long-range interchannel effect)\n\ni = 4, for molecules that can penetrate potentially present pores within porous packing particles, in which intraparticle transport is necessarily slower than in the wider interstitial channels outside the particles (so-called transparticle effect)\n\ni = 5, for molecules near the column wall, at which packing density is generally lower than in the center of the packing (extending at least over several particle layers from the wall); consequently, higher velocities occur (so-called transcolumn or wall effect)\n\nAll the listed velocity differences contribute potentially to zone-broadening, and each is treated by Giddings in the described way of coupling the processes of flow and diffusion “in concert” as Giddings phrases it. The constants λ and α, reflecting the geometry of the packing on the different scales, are undoubtedly different for the mentioned regions over which the velocity differences exist, and each effect, when treated as an independent random-walk, generates its own and additive coupled plate height term.\n\nNone of these effects will produce a single, constant longitudinal effect to be identified in the eddy diffusion term D, and because there is no way to distinguish between (the effects show a gradual overlap, rather than being discrete and separate) we prefer the descriptive velocity profile effects to the single mobile-phase term, with the velocity profile factor k representing the overall velocity differences, combined with solute and convective radial mass transfer that counteracts the spreading from the velocity profile.\n\nIn fact, our expression for Ce is a good model for the unknown ω value for transcolumn processes in Giddings’ theory, the more important of the foregoing terms.\n\nDependence of the Mobile-Phase Terms on Partitioning. A difference between Eqs. (43) and (44) is further seen to be the factor f(k) in Eq. (43), which is not present in the total coupling equation [see Eq. 44]. This is a result of the derivations as made by the coupling theory, which see, thus foregoing listing of effects, concerns everything in the mobile phase except the distribution of stationary phases. As mentioned before, and as will become very clear in the section on capillary columns (see sec. II.E.4.e), uneven distribution of stationary phase in a cross section will result in a dependence of the velocity profile term of k. What is more, many experiments in LC (see, for example, Ref. 21) show a distinct k-dependence of the mobile-phase term. This is, probably, caused largely by the presence of dead end or stagnant pores within porous packing particles. Here, mobile phase is present and molecules trapped in these pores are also stagnant. Thus, these pores represent a kind of stationary (in fact, stagnant mobile) phase, where partitioning (with a partition coefficient K = 1) takes place with the surrounding flowing mobile phase. Trapped molecules can, however, escape only with a limited transfer rate, which is solely based on strongly hindered (in the tortuous pores) diffusion in the mobile phase. This would introduce an additional D term, Cmw, which is definitely dependent on k, and not easily distinguished from Ce [see II.E.4.g]. It should be stressed here, that the existence of these dead end pores filled with stagnant mobile phase can also play a positive role, notably in GC. If these pores were totally filled with stationary liquid, the transfer of mobile molecules toward the surrounding flowing mobile phase would dramatically longer and a large zone-broadening would result.\n\nIn conclusion of this section, we prefer the use of the physically well-supported Eq. (43) over the coupling Eq. (44), noting that the original success of the coupling theory by describi...