Retention factor relationship

PD Ferguson, DM Goodall, JS Loran. Systematic approach to links between separations in capillary electrophoresis and liquid chromatography. IV. Application of binding constant-retention factor relationship to the separation of... 

Other cases, involving an arbitrary relationship between the solute retention factor and the modulator concentration can be handled analytically using the approaches of Frey [Biotechnol. Bioeng., 35, 1055 (1990)] and Carta and Striugfield []. Chromatogr, 605, 151 (1992)]. 

Where a, b, and c = van Deemter coefficients, dp = particle size of column, L = column length, Dm = diffusion coefficients of analytes, t = column dead time (depends on flow rate F), tg= gradient time (determines analysis time via tA = tg + t0), Ac = difference in concentrations of the organic modifier at the end and the beginning of the gradient (a continuous linear gradient is assumed), and B = slope of the linear relationship between the logarithm of the retention factor and the solvent composition. 

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. 

In addition to the above strategies, the use of higher column temperatures is another approach that may decrease analysis time and improve sample throughput. The relationship between the chromatographic retention factor, k, and separation temperature is shown in Equation 13.1 ... 

The relationship of the selectivity to the polarity of the analytes can be understood from the differences in the retention factors of homologous alkanols (Figure 3.12). The polar alkanols are relatively more retained on the non-endcapped bonded phases (LOC-ODS-NE and HIC-ODS-NE) because smaller-size alkanols can reach the unreacted silanol groups on the surface of silica gels. 

The relationship of the selectivity towards rc-electrons can be understood from the differences in the retention factors of polycyclic aromatic hydrocarbons (Figure 3.13). The difference in the retention factors on end-capped and non-endcapped stationary phase materials is less than that of alkylbenzenes. This is due to the water content of the stationary phase. The content may be higher in non-endcapped bonded phases. 

The general relationship between the type of solute and its retention can be seen by comparing the retention factors, k, of a set of standard compounds with their octanol-water partition coefficients, i.e. the logP value (listed in Table 4.1), as a measure of their relative solubility in water. The logarithm of the retention factor, log k, of these compounds measured in 50% aqueous acetonitrile on an octadecyl-bonded silica gel column shows a close linear relationship (Figure 4.1). 

This method was applied to the prediction of the retention factor of phenols. First, this method requires a relationship between log A and the van der Waals volume of a homologous series of alkyl compounds such as alkylbenzenes or alkylphenones. When alkylbenzenes are used as the standard, the value of B in Equation 6.8 should be altered to give a parallel relationship at a suitable position (E) on the y-axis for a different group of compounds. When B is moved to E for phenols, the log A values of para-alkylated phenols (y) are simply predicted from their van der Waals volume by the following equation ... 

The retention time of phenols was predicted in 70 and 60% acidic aqueous acetonitrile on an ODS silica gel column. The constants A, B, C, and D were obtained from the above equations. The result in 60% aqueous acetonitrile is shown in Figure 6.6. The correlation coefficients between the measured and predicted retention factors of substituted phenols in 60 and 70% acidic aqueous acetonitrile were 0.974 (n = 36) and 0.967 ( = 36), respectively. In this system, the values of the slopes, which indicate the relationship between the measured and predicted retention factors, were 0.81 and 0.94 in 60 and 70% acidic aqueous acetonitrile, respectively.32... 

Figure 6.7 Measurement of enthalpy using chromatography for the relationship between absolute temperature and retention factor.

Retention theory from the work of Lanin and Nikitin [55] (Equation 1.6) was adapted to describe the dependency of retention factors k) as a function of the mobile phase composition [53]. The concentration of the polar modifier is, besides the type, the primary variable for the optimization of the separation and can be described by competitive adsorption reactions of solute (i.e., sorbate) and polar modifier for which the following relationship can be applied (Equation 1.6)... 

For RPLC, the general strategy (Figure 3.10a) is less complex because no distinction between acidic and basic compounds is made. The optimization stage is also less complicated. In case of a baseline separation, the retention factor can be optimized based on the fact that a linear relationship is assumed between log k and the fraction... 

Neue and Carr [14] suggested that the overall retention factor k for bases on conventional silica RP columns could be described by the relationship... 

H is the plate height (cm) u is linear velocity (cm/s) dp is particle diameter, and >ni is the diffusion coefficient of analyte (cm /s). By combining the relationships between retention time, U, and retention factor, k tt = to(l + k), the definition of dead time, to, to = L u where L is the length of the column, and H = LIN where N is chromatographic efficiency with Equations 9.2 and 9.3, a relationship (Equation 9.4) for retention time, tt, in terms of diffusion coefficient, efficiency, particle size, and reduced variables (h and v) and retention factor results. Equation 9.4 illustrates that mobile phases with large diffusion coefficients are preferred if short retention times are desired. 

By simultaneous optimization of the percent organic modifier in the eluent and the column temperature to keep the retention factors fixed, very efficient, ultrafast separation can be achieved. The researchers conclude that for fast separations, the relationship between retention, temperature, and volume fraction of organic modifier needs to be taken into account. As the temperature increases, a lower volume of organic modifier is needed to speed up HPLC. Therefore, a highly retentive column... 

There is experimental evidence that dnder certain conditions RPC may possibly be used as an alternative method to evaluate a parameter equivalent to log P. Linear-relationships between logarithm of the retention factor and carbon number are anticipated in this optic and have been ob-... 

DL-Leucine, resolution of, 222, 262 Leucine encephalin, 290 LFER, see Linear free energy relationships LH-releasing hormone, 263, 290 Ligate, carbon number of, 153 Ligates, solute binding to, 213 Limiting retention factors, 239 Linear elution adsorption chromatography, 58... 

In the course of the investigation (146) it was also ex ined whether Eq. (13) should be replaced by a quadratic relationship between In k and do. but no marked improvement was found in the fit of retention factor composition data. 

The quasi-linear relationship between the logarithm of the retention factor and volume fraction organic cosolvent in the mobile lase seems to be the general rule in RPC. However, special effects can ur to cause this rule to be violated. Marked deviation from linearity was observed by Melander et al. (158) with retention data o poiy(ethylene glycol) derive-... 

In the case where the retention factor increases to a limiting value with no subsequent decrease at increasing hetaeron concentrations, i.e., the plot of k versus is a rectangular hyperbola because one of the terms in the denominator of Eqs. (69) and (72) vanishes, the. relationship between retention factor and hetaeron concentration for either of the two mechanisms takes the simple form... 

In spite of the preceding observation that eluite retention in RPC with hydrocarbonaceous bonded phases may not occur by partitio ng of the eluite between two liquid phases, theoretical considerations based on the solvophobic treatment of solvent effects shows that it might be possible to relate the observed retention factors to partition coefficients between water and an organic solverit. Such a relationship would be quite useful in light of the scale developed by Hansch and his co-workers (2/12, 283) to characterize hydrophobic properties of drugs and other biologically active... 

Fig. 59. A general representation of the binding of n molecules of hetaeron, L, to an eluite E. Each binding step has an associated equilibrium constant, Ki, for e formation of species containing / molecules of hetaeron from the reaction of a species containing i - 1 molecules of hetaeron with hetaeron. As a consequence, the retention factor can have a complex dependence on hetaeron concentration the relationship is given by Eq. (109).

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