Gradient plate number

The plate number in equation (4.56) corresponds to the value when the effective value of the capacity factor (equal to k when the band is at the column midpoint) is equal to the capacity factor in isocratic elution for the same column. The effective value of the capacity factor, k, is simply 1/1.15b. In most cases k, will be large and equation (4.57) is simplified by equating l/k, to zero. The resolution between two adjacent bands in a gradient program, again analogous to isocratic elution, is e q>ressed by equation (4.58)... 

N is the average column isocratic theoretical plate number is the retention factor at the point of elution controlling the bandwidths in gradient elution— Equation 5.5... 

A strategy for the optimization of gradient programs based on the actual retention behaviour of some sample components has been described by Jandera and Chura5ek [623, 624]. This approach relies on the possibility to calculate retention and resolution under gradient conditions from known retention vs. composition relationships and plate numbers. Both typical RPLC (eqn.3.45) and LSC (eqn.3.74) relationships can be accommodated in the calculations and linear, convex and concave gradients are all possible because of the use of a flexible equation to describe the gradient function. This equation reads... 

Flow is not constant Flow cannot be controlled easily Limited plate numbers Not always predictable or in agreement with theory Temperature gradients can exist Quantitation not as accurate as for column LC... 

It should be noted that Eqs. (1.7) and (1.8) are valid only if the migration velocity of a sample zone is constant during the elution, which means that the plate number can be determined only from isocratic chromatograms obtained at a constant composition of the mobile phase, temperature and flow rate. Plate number values evaluated from a gradient-elution chromatogram are subject to gross errors and have no real meaning. 

Pf is the instantaneous concentration of the strong eluting component in the mobile phase at the outlet of the column at the time the band maximum elutes from the column, Ri. R2 are the retention volumes of sample compounds with adjacent peaks, N is the number of theoretical plates determined under isocratic conditions and T, is the hold-up volume of the column. It should be noted that the correct plate number value cannot be determined directly from a gradient-elution chromatogram using Eq. (1.7) or Eq. (1.8), which assume a constant value of the retention factor A and hence can be applied for isocratic elution only. 

In addition to the gradient volume and to the column plate number gradient shape can be adjusted [85,94]. 

Fig. 1.30. (A) The resolution window diagram for the gradieni-elulion separalion of a mixture of eight phenyluiea herbicides on a Separon SGX. 1.5 tm. silica gel column (150 x 3.3 mm i.d.) in dependence on the initial concentration of 2-propanol in n-hcpiane at ihe slart of the gradicni. A. with optimum gradient volume Vc, - 10 ml. Column plate number N = 5000. compounds as in Fig. 1.23. (B. C) The separation of the eight phenylurea herbicides with optimised gradient-elution conditions (maximum resolution in (A)) with gradients from 12 to 38.6 2 2-propanol in n-hcptanc in 7 min (B) and from 25 to 37.5 2 2-propanol in fi-heptane in 5 min (C). Flow rale I ml/min.

NC = no change i = a factor < f L = column length = column diameter N = eolumn plate number = resolution Fm = column hold-up oIunie tK = retention lime (proportional to the run time) F = flow rate of the mobile phase A/r = pressure drop across the eolumn B. B = gradient steepness parameter, Eq. (I. .30). 

Fig. 3 Top The resolution window diagram for RP gradient elution separation of phenylurea herbicides on a Separon SGX Cl8 7.5-pm column (150 x 3.3 mm ID) in dependence on the initial concentration of methanol in water at the start of the gradient A with optimum gradient volume Vq = 13 mL. Column plate number A = 5000 sample compounds hydroxymetoxuron (1), desphenuron (2), phenuron (3), metoxuron (4), monuron (5), monolinuron (6), chlorotoluron (7), metobromuron (8), diuron (9), linuron (10), chlorobromuron (11), and neburon (12). Bottom The separation with optimized binary gradient from 24% to 100% methanol in water in 73 min. Flow rate = 1 mL/ min T=40°C.

Jandera, P. Churacek, J. Gradient elution in liquid chromatography II. Retention characteristics (retention volume, bandwidth, resolution, plate number) in solvent-programmed chromatography—Theoretical considerations. J. Chromatogr. 1974, 91, 223-235. 

The above-mentioned equation for n in fact is only valid for isocratic separations and if the peaks are symmetric the peak capacity is larger with gradient separations. Tailing decreases the peak capacity of a column. In real separations the theoretical plate number is not constant over the full k range. However, it is even more important to realize that a hypothetical parameter is discussed here. It is necessary to deal with peaks that are statistically distributed over the accessible time range. The theory of probabilities allows us to proceed from ideal to near-real separations. Unfortunately, the results are discouraging. 

A specific test mixture may be prepared for working in a special area, e.g. an aflatoxin mixture for aflatoxin determination. (However, a test mixture for the determination of the plate number should not include any peptides or proteins. These compounds need to be eluted by gradient, see Figure 18.7, whereas the plate number is calculated from an isocratic chromatogram.) In all other cases, a test mixture that satisfies the following criteria is needed ... 

Multidimensional liquid chromatography is preferred over gradient elution when a large plate number is required for a separation and for the analysis of complex mixtures which contain only a few adjacent components of interest. For these problems, single-column techniques are inherently inefficient, since only a small fraction of the column is actually in use at any given time. The multidimensional separation methods provide optimum efficiency for the separation of the components of interest while simultaneously minimizing the time spent in separating sample components of no particular interest. 

Flo. 19. Peak capacity (a) plate number iV and reduced velocity vvefsus gradient time. Calculations of model of Table Vlll for reversed-phase gradient elution of peptides. Column of Fig. 16 A0 O.3, — 1000, flow rate varied to maintain Kg constant 6). From Stadalius... 

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