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

Mechanisms and Importance of Zone-Spreading 103 excluding the skeleton; see Sec. IIE.4.B, is considered as the stationary phase or, better, as the stagnant mobile phase, which contributes to the common dead time \\( t_0 \\), as measured with a (totally permeable, but non-retained) tow molecular sieve matrix. The ratio \\( L_{1.1} \\) is thus a true measure of the interstitial mobile-phase velocity \\( u_m \\). 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 \\( L_{1.1} \\) ratio yields an average velocity smaller than \\( u_m \\), that includes time spent in the intraparticle stagnant phase. The difference between the two values, \\( k_0 = (t_r - t_0)/t_r \\) and \\( k = (t_r - t_m)/t_r \\), may be appreciable, as noted by Scott et al. [21,31-33]. For modern Partisani and Zorbak columns, for example, \\( k \\) is 2k. This is not quite unexpected as, from the definitions of \\( k_0 \\) and \\( k \\), we find that \\( k/k_0 = [\\( \\textit{1}/t_r - 1/t_m \\)]/(1/t_r) \\), where \\( t_r = t_m + t_0 \\), and again \\( k_{0, m} = \\delta = \\delta_{ewob} \\) (see Sec. II.A); we see that \\( k/k_0 = 1 + (1/{1/k_0}) \\). \\( k_0 = (1 + k)^{-1} \\). For \\( k = (nonporous particles) \\) \\( \\phi = 1 \\) and \\( k_0 = k \\), but for typical porous particles we have \\( e_{i} = e_{0} = 2/3 \\), and so \\( k = k + 1 = k + 2 \\) approaches 2 for large \\( k \\) values. It is dangerous to simply replace \\( k \\) with \\( k \\) without a solid fundamental background, as done by Scott in the modified van Deemter–Gulay 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. The important factor of Eq. (58b) in references [21,31] contains the original, but outdated geometric factor \\( 7\\pi/8 \\) after van Deemter, but we prefer the use of the modified van Deemter and Golay C terms with the factor 2/3, as used by Purnell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 in packed beds is clearly not the theoretical diameter, as was assumed by Scott et al. The effective radius is better estimated from our earlier discussion on the hydraulic radius concept [see Sec. (3.7)]. \\( 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_m term. (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 \\( u_m \\). 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 C_m because it concerns partitioning of solute 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 \\( k \\) 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 Zorbak. A significant contribution from stagnant mobile phase may, therefore, be suspected. The 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 term stagnant phase would be appropriate for the fraction that is trapped in the pores. Thus, the retention equation should read, as in the former section: \\( t_r = t_0 + t_m + t_u \\), where \\( t_m = t_0 + t_u \\), always indicates the total residence time in the mobile phase, including \\( t_0 \\) in the interstitial, moving region and \\( t_u \\) in the static region inside the porous particles. The 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