Chromatography Handbook Of Hplc - Katz Eksteen Schocnmakers Miller wiley Sons -110

k = 0 Hmin,app = 0.58R, Hmin,ec = 0.29 uopt,cap = 6.9(Du/R) Vopt,cap = 13.9\nk = 1 Hmin,app = 1.22R, Hmin,ec = 0.61 uopt,cap = 3.3(Du/R) Vopt,cap = 6.6\nk = 2 Hmin,app = 1.45R, Hmin,ec = 0.73 uopt,cap = 2.8(Du/R) Vopt,cap = 5.6\nk = 3 Hmin,app = 1.68R, Hmin,ec = 0.84 uopt,cap = 2.4(Du/R) Vopt,cap = 4.8\nk = 4 Hmin,app = 1.79R, Hmin,ec = 0.89 uopt,cap = 2.2(Du/R) Vopt,cap = 4.4\nk = ∞ Hmin,app = 1.91R, Hmin,ec = 0.96 uopt,cap = 2.1(Du/R) Vopt,cap = 4.2\n\nThe situation becomes more complicated when the resistance to mass-transfer term in the stationary phase becomes relevant; for example, in OTLC and GC using thick films (>0.5 um), notably of polar gum or immobilized stationary phases, in which the diffusion coefficients are much smaller than in phases that are not immobilized. In capillary GC using such phases, especially with thick films up to 5 um, the Ct term may be of the order of Cr or even larger. Other complications may arise in capillary columns with “rough” walls such as in support-coated and whisker-walled open tubular columns; however, the Golay equation can, as an approximation, be used here as well.\n\nThus, we see that for any extent of retention, and for small resistances to mass transfer in the stationary phase, the minimum plate height is not likely to exceed the column diameter, which implies reduced plate heights of close to 1. For k > 1 the optimum velocity in open tubular columns is about 5. In a dimensional sense, converting u to u, this implies that when working with mobile phases that allow fast diffusion of solutes, the absolute value of the (optimum) working velocity is higher than with slowly diffusing solutes in more viscous mobile phases. This is of eminent importance for GC, in which the use of light gases, such as hydrogen or helium as the carrier gas, allows faster analysis. Diffusion coefficients are about 4 times higher than with nitrogen as the carrier, which yields 2 times faster optimal velocities, and correspondingly shorter analysis times. Hm values are more or less independent of the identity of the carrier gas for any given height, provided the height is optimized. Thus, the faster analyses with the light carrier gases at optimum conditions are not more efficient. At velocities other than uopt, the identity of the mobile phase is important in determining the Ct term. At higher velocities, carrier gases of relatively high molecular mass will yield relatively high H values, because of larger Cr values.\n\ntmax,app = uopt/Hm or in reduced terms tmax = Vp/Hm. This is the time necessary to produce maximum efficiency and thus maximum resolution (see Sec. II.D) from the column. Note, by the way, that this characteristic time is closely related to the Ct terms: tmax = uopt/Hm = 2(Cr + Ct) for both Guoy and van Deemter type of equations.\nWith Eq. (56a,b) we find\ntmax = (R2/Du)I(f(k)/12) and tmax = f(k)/48\nThis characteristic time for maximum resolution sets a natural lower limit to the practical analysis time (the retention time of the last component), which [apart from a retention factor 1/(1 + k)] is determined by the optimum velocity. Indeed, lowering the velocity below uopt would lead to a strong increase of the plate height by molecular diffusion (the f term becomes important) and thus to a loss in resolution at the additional cost of an increased residence, retention or analysis time tu = tr > tmax. With an increase in the mobile-phase velocity, we find some room for improvement (i.e., lowering the analysis time), because from the Golay and van Deemter equations, and from the retention equation using L = (u/m)Ht it is found that:\n\t tg = tpk(1 + k) = (L/(uopt)(1 + k) + k)(H/(uopt)(1 + k)\nwhich shows that for practical purposes it is the ratio of plate height and mobile-phase