Isocratic retention factor

A characteristic of small-molecule liquid chromatography is the reversibility of their contacts with the stationary phase. The distribution equilibrium constant determines the duration of the stationary periods and, thus, the retention of the solute. With polymers, isocratic retention factors of normal degree (i.e., 1 gk 10) generally do not occur. A fractional alteration of elution conditions may cause transition from zero retention to infinity. As a rule of thumb, polymers either pass without retention or remain in the column. This off or on behavior produces the impression of irreversible fixation under the conditions of retention. 

Resolution. Maximizing selectivity, as part of the early stages of methods development, will result in the fastest methods since as flow rate is increased or column length is decreased, resolution will decrease. The resolution equation describes the key parameters. In equation (17-24), k is substituted for the isocratic retention factor, k, to give... 

Similar to the log D-pH profile, the distribution of the compounds in a chromatographic partition system is also influenced by the pH. Charged species have much shorter retention times than their uncharged parent compounds. Horvath et al. [105 described first the effect of solute ionisation on the retention of weak acids, bases and ampholytes on octadecyl silica, both theoretically and experimentally. They have found a similar equation to Eqs. (12.11) and (12.12) that describes the pH dependence of the isocratic retention factor (A) for weak acids as shown in Eq. (12.1.3) ... 

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. 

Symbols are identified in the text to the dwell time for the chromatograph (the time it takes a change in mobile phase composition to pass from the gradient mixer to the column inlet) and kz the isocratic retention factor in the terminal solvent for the gradient... 

The different organic modifiers used to derive the most suitable mobile phases lead to different parameters namely isocratic logfe and extrapolated logkw. The extrapolation method has no reality in terms of chromatographic behavior of solutes. However, mainly by correlation with log Pod (Eqs. 2 and 3) several studies have demonstrated the interest of these extrapolated retention factors as predictors of the lipophilicity of solutes. 

The logarithm for the capacity factor correlates well with known log P values obtained by the shake flask method. In practice, the k values are determined isocratically from 70 to 30% organic mobile phase and then extrapolated to 0%. Prior to determining the log P for an unknown compound, a set of structurally related molecules (standards) are analyzed to construct a correlation model between the logarithm of the retention factor and known log P values. The process is then repeated for the test compounds and their log P values determined from the mathematical relationship established for the standard compounds. 

First, we look at isocratic separations. Let us assume that the analysis can be accomplished within a retention factor of 10. We also suppose that the analysis is carried out with a typical reversed-phase solvent and a sample with a typical molecular weight of a pharmaceutical entity. In order to manipulate the analysis time, we will keep the mobile phase composition the same and vary the flow rate. The maximum backpressure that we will be able to apply is 25MPa (250 bar, 4000psi). In Figure 1, we have plotted the plate count as a function of the analysis time for a 5 J,m 15-cm column. We see that the column plate count is low at short analysis times and reaches a maximum at an analysis time of about 1 h. A further increase in analysis time is not useful, since the column plate count declines again. This is the point where longitudinal diffusion limits the column performance. The graph also stops at an analysis time of just under 5 min. This is the point when the maximum allowable pressure drop has been reached. 

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... 

FIGURE 15.11 Plots of the logarithmic retention factor of ovalbumin as a function of the reciprocal square root of the mobile phase ionic strength, l/yfl at different pH values 6.0 ( ), 7.0 ( ), and 8.0 (A). Experimental conditions Synchropak Q300 column, NaCl eluting salt under isocratic condition. Experimental data from Ref. [29]. (Reproduced with permission from Stahlberg, J. etal.. Ana/. Chem., 63, 1867, 1991.)... 

The quantity k is the retention factor of the solute, or its mass distribution constant. It allows the straightforward comparison of results obtained with different apparatus and is frequently used in chromatographic literature. The optimum value is k = 2 in isocratic elution. Here, on an average, the solute remains in the stationary phase twice as long as in the mobile phase. The probability of finding the solute in the mobile phase is 1 (1 + 2) = 0.33. 

Figure 5.13 Curves relating the isocratic composition (p ) to the net retention time under gradient conditions for various values of the isocratic capacity factor. Curves calculated on the basis of eqns.(3.45) and (3.46). Linear gradient 0 — 100% methanol in water. /0= 125 s. Figure taken from ref. [536]. Reprinted with permission. 

The variety of stationary phases available commercially and the lack of standardisation between different laboratories makes it difficult to compare the retention factors k directly as comparison of lipophilicity. Therefore different lipophilicity scales obtained from chromatographic data (isocratic or gradient elution) have been introduced. A calibration of the individual chromatographic system with compounds of known lipophilicity is used in all cases. 

Cj(cp) can be obtained e3q)erimentally from isocratic elution experiments at different Cp values, or from linear gradient elution experiments where the ratio G = pL/v is varied. In the latter case, the retention factor is obtained by differentiation of Eq. (16-190) from... 

Once the probe gradient is run, check the diode array purity and if LC-MS is available, run as well to check for peak homogeneity. If you have any known precursors or impurities, run them as well to ensure resolution from the main component and to make sure they are adequately retained. The main analyte should elute between k 2-5. If the main component elutes at A = 2-5 and is spectrally pure and the impurities all elute k > 1, the method is complete. If the retention factor of the impurities is below 1, then an isocratic hold at the initial organic composition should be implemented until the minor component (impurity) elutes k > 1 and then a linear gradient can be implemented. The method could be further optimized by increasing the flow rate as long as the backpressure limitation of the system has not been reached. A general rule of thumb is that the backpressure should not exceed 85% of the maximum backpressure for a particular HPLC system. 

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