Gradient steepness parameter

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... 

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). 

S = 3.6 is a better value for cyanopropylsiloxane-bonded phases in above relationships) tg = gradient elution time b = gradient steepness parameter ko = isocratic retention factor for the solute in the starting solvent composition k v = estimated isoctratic retention factor for water as the mobile phase volume fraction of strong solvent (%B / 100) and M = solute molecular mass. 

Experimental values of /for several small-molecule solutes are plotted in Fig. 5a as a function of the gradient-steepness parameter 6. A similar plot for insulin as the solute is shown in Fig. 5b. A finsd expression for band width in RPLC can then be obtained from Eqs. (8), (9), (48), and (50) ... 

The gradient-steepness parameter b of Eq. (6) is of central importance to an understanding of gradient elution. It can be related to separation conditions and Eq. (2) as follows ... 

Here is the dead volume of the column (equal to toF), and f is the mobile-pht flow rate. The average value of il for the band during gradient migration (k, the value of k when the solute reaches the column midpoint) is directly determined from the gradient-steepness parameter. 

The gradient-steepness parameter b for ion exchange is given by Eq. (16), which involves the ion-exchange gradient parameter r (Eq. (17)]. Oilcula-tion of r (needed in order to calculate b and requires a value of c. 

It should be pointed out that the analysis shown here is valid only if the gradient steepness parameter is the same for the neighboring peaks under consideration. If this were not the case, no simple general conclusions can be drawn for the dependence of resolution on gradient parameters. 

Fig. 4. Plots of log Ic versus based on gradient experiments for /3-endorphin-related peptides 7, 8, 10, 11,14-15. The plots were derived from best-fit analysis to the data points obtained from gradient elution experiments, where tQ = 20, 30, 40, 60 and 120 min and / = ml/min. Column, developmental octadecylsilica, dp= 6/im, Pd = 13 nm, 25 cm x 4.6 mm ID. Solvent A, 0.1 % trifluoroacetic add (TFA) in water solvent B, 0.1% TFA in water-acetonitrile (50 50). See Table 2 for the code to polypeptide structure and for the calculated slope parameter S and log k values. Note the changes in band spacing for peptides 7, 8, 10 and 11 which illustrate the potential for selectivity manipulation through changes in the gradient steepness parameter, b. From [4].

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