Chromatography Handbook Of Hplc - Katz Eksteen Schocnmakers Miller wiley Sons -113

Mechanisms and Importance of Zone-Spreading 103\nexcluding the selection; see Sec. II.E.4, is considered as the stationary phase or, better, as the stationary \"region\" or \"zone\" [32]. Stagnant mobile phase within the particles would contribute to the common dead time tR, as measured with a (totally permeable, but nonretained) toy molecular sieve membrane. The usual LI/L ratio is thus a true measure of the interstitial mobile-phase velocity \u03c6. This is indeed the velocity that was meant to occur in all our equations so far, because we tacitly assumed that all internal pore space was occupied by a stationary phase, rather than a mobile phase. The usual LI/L1 ratio yields an average velocity smaller than 1, as ts includes time spent in the intraparticle stagnant phase. The difference between the two values, k0 = (tR * - t0) / tR and k = (tR * - t1) / tR, may be appreciable, as noted by Scott et al. [21-31]. For modern Partisanal and Zorbach columns, for example, k ~ 2k. This is not quite unexpected as, from the definitions of k0 and k, we find that k/k0 = [(tR * - t1) / (tR * - t0)](L/L1), where tR = ts + t'e + tS + tMU + tR, where tR and again eR = eI = eH and d = eH/e0R; (see Sec. II.A.) We see that k0 = 1 + (1/(1+d)) - (1)[(1/k0) or k0 = (1 + k - d)/(k). For eI = (nonporous particles) \u03c6 = 1 and k0 = k, but for typical porous particles we have eI = e0R = eS and so k0 = k + (1 + k) = 1 + 2k, which approaches 2 for large k values.\nIt is dangerous to simply replace k with k0 without a solid fundamental background, as done by Scott in the modified tCureur-Golay equation [see Eq. (58b)]. However, in the next section, we will treat this issue of porous particles further; it is proved from first principles that the substitution is correct.\nThe geometrical factor 7π/a2 from reference [21,31] contains the original, but outdated geometric factor b/2 after element b, but we prefer the use of the modified van Dermen and Golay C terms with the factor 2/3, as used by Purnell et al. [29,30] in Eq. (58a). We also added a correction factor x, accounting for the fact that the effective capillary radius is packed back into its equivalent diameter, as was assumed by Scott et al. (reiterating from our earlier discussion on the hydraulic radius concept [see Sec. II.E. 3.]) As R0/G, from this remark, we therefore know experimentally that y = 0.05. Equation (58a) for GC shows, however, an experimental value of x = 3/2, much larger than expected. Hence, the result of Scott et al., Eq. (58b), is suspect in its estimation of the numerical factor in the C term.\n(g) Plate Height from Porous Particles. The notion of stationary phase (region or zone) is necessary in the case of porous particles with stagnant mobile phase in the pores. The latter play a role in the residence time of all molecules, including mobile-phase molecules (tR, t0). Because there is slow and possibly strongly hindered molecular diffusion in the tortuous pores containing stagnant mobile phase, notably in LC, we may expect the occurrence of an additional C term. We designate this as Cmob because it concerns partitioning of slow molecules between two types of mobile-phase regions; namely, the interstitial and truly mobile region and the stagnant intraparticle region, with a portion coefficient of at the \"interface\" between the two regions. Indeed, in the literature, a poor agreement is found between experimental and theoretical contributions to the plate height stemming from the stationary phase (region; C term), especially for packing materials such as Partisil and Zorbach. A significant contribution from stagnant mobile phase may, therefore, be suspected.\nThe mobile phase potentially present in stagnant pores is not moving; therefore, it constitutes part of the stationary phase. Hence, as proposed by Scott [21,31], the term moving phase should be used for the fraction of the phase that actually moves, whereas the static phase would be appropriate for the fraction that is trapped in the pores. Thus, the retention equation should read, as in the former section: tR = t0 + tMU + tR, where tMU always indicates the total residence time in the mobile phase, including t0 in the interstitial, moving region and tMU in the static region inside the porous particles.\nThe true practical situation in LC is even more complicated because exclusion of larger solute molecules can easily occur, especially for silica-based materials with pore diameters ranging from as low as 1-3 Å, to as much as 1500-3000 Å. Open pores with diameters less