Gradient steepness

Band broadening is also affected by the gradient steepness. This effect is expressed in Table 16-14 by a band compression factor C, which is a fnuctiou of the gradient steepness and of equilibrium parameters. Since C < 1, gradient elution yields peaks that are sharper than those that would be obtained in isocratic elution at

[Pg.1536]

In Eq. (7), X is an auxiliary parameter, u is the linear velocity of the mobile phase, Cc is critical concentration of the displacing salt, Z is the effective charge on the solute ion divided by the charge on the mobile phase ion and B is the gradient steepness. 

Fig. 14 a, b. Effect of gradient steepness on the very fast separation of polystyrene standards in a molded monolithic poly(styrene-co-divinylbenzene) column (Reprinted with permission from [121]. Copyright 1996 Elsevier). Conditions column, 50 mm x8 mm i.d., mobile phase, linear gradient from 100% methanol to 100% tetrahydrofuran within a 1 min b 12 s, flow rate, 20 ml/min, peaks represent polystyrene standards with molecular weights of 9200,34,000 and 980,000 (order of elution), 3 mg/ml of each standard in tetrahydrofuran, injection volume 20 pi, UV detection, 254 nm... 

Run the scouting gradient, then narrow the gradient range so that the earliest peak elutes after t() + dwell time (tD) and the last peak elutes near the final solvent concentration. The gradient steepness should be maintained in the narrowed gradient. 

Evaporation from drops of liquid is generally much faster than from a plane surface, on account of the geometry of the system aiding the concentration to fall steeply away from the surface, and so making the concentration gradient steep. 

A gradient elution should be described by the initial and the final mobile-phase compositions, by the gradient shape, and by the gradient steepness. A step gradient is often convenient when strongly retained solutes are not the solutes of interest. 

Although many columns and eluants can be used for gradient elution, the conditions used in Figs. 2.16 and 2.17 are recommended as a good starting point. The HPIC-ASSA (5 i) separator with sodium hydroxide eluant provides the optimum combination of efficiency, selectivity, and speed without an unacceptable baseline slope. If fewer ions than the 36 shown in Fig. 2.16 need to be separated, the gradient steepness can be increased to reduce the run time. 

For components which are eluted under ideal gradient conditions (i.e. those components that appear neither at the very beginning nor after the end of the actual gradient in linear solvent strength gradients, it can be shown that the median capacity factor kg is inversely proportional to the gradient steepness parameter, defined as [428]... 

It appears from eqn.(4.68) that if the flow rate and the span of the gradient are kept constant, the gradient steepness parameter (6) is inversely proportional to the duration time (tG) of the gradient, and, hence, that the median capacity factor ( cg) is directly proportional to tG. Therefore, under these conditions, in gradient elution tG may take the place of the capacity factor kg in the resolution equation and eqn.(4.67) may be rewritten as... 

In this equation kin is the capacity factor, which the solute would show under isocratic conditions (i.e. an elution at a constant mobile phase composition) corresponding to the composition at the inlet of the column at the time t that has elapsed since the start of the gradient. ka is the capacity factor at the start of the gradient (t = 0),b the gradient steepness parameter, and t0, as usual, the hold-up time of the column. 

A comparison of this equation with eqn.(5.5) shows that the gradient steepness parameter b is a function of the solute (through S), the gradient program (through B) and of the column (through t0) ... 

Figure 5.12 Expected capacity factor (k) under isocratic conditions that correspond to the composition at the column inlet at t= t.—2t0, as a function of the gradient steepness parameter b. Figure calculated according to ref. [528],...

The optimal slope of the gradient also follows from the LSS concept, since it was shown by Snyder et aL [616] that optimum values for the gradient steepness parameter b are in the range 0.2 relationship between retention and composition over the range 1 < k< 10 can be described by... 

FIGURE 7-22. Effect of gradient steepness upon resolution. The retention depends upon the steepness. The steeper the gradient, the lower the retention and the sharper the peaks. (Reproduced with permission from LC Resources, Inc.)... 

Numerous researchers have dedicated their efforts to understanding the relationship between peptide and protein molecular properties (molecular mass and charge, hydrophobicity, surface charge anisotropy, surface area) and their retention in CEC as a function of field strength, gradient steepness, temperature, and variables related to surface characteristics of the stationary phase. So far, however, no reliable and comprehensive theory is available to model and predict peptide and protein retention, and the need to interface CEC with mass spec-... 

Indicating that concentration gradients of RTVc/c produce a dlffuslophoretlc velocity that Is similar to the electrophoretic velocity In a potential gradient Steep concentration gradients can, for Instance, be created across thin membranes, or near electrodes when electrode reactions take place. 

Fig. 1.28. Effects of the gradient steepness (gradient time) (three top chromatograms), of the initial concentration of the stronger eluent, methanol or acetonitrile in water (three middle chromatograms) and of the gradient shape (two bottom chromatograms, (A) convex, (B) concave) on the reversed-phase gradient-elution separation of ten fluorescent derivatives of homologous n-alkylamines (methyl- to n-decyl-) on a LiChrosorb RP-18, 10 pm. column (3(X) x 4.0 mm i.d.). Other operation conditions and compounds as in Fig. 1.25.

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