Capacity factor relationship

Now that we have defined capacity factor, selectivity, and column efficiency we consider their relationship to chromatographic resolution. Since we are only interested in the resolution between solutes eluting with similar retention times, it is safe to assume that the peak widths for the two solutes are approximately the same. Equation 12.1, therefore, is written as... 

The relationship between capacity factor and analysis time can be advantageous when a separation produces an acceptable resolution with a large b. In this case it may be possible to decrease b with little loss in resolution while significantly shortening the analysis time. 

Many chromatographic systems show linear relationships between the logarithm of the capacity factor and the reciprocal of the column temperature (van t Hoff plots) [255,258-261]. In thermodynamic terms the interaction of the solute with the stationary phase can be described by... 

Figure 1.9 illustrates the relationship between resolution, the separation factor, the average capacity factor and the column efficiency for some real chromatographic peaks [lOS]. The central portion of the figure illustrates how resolution increases with the capacity factor for a fixed separation factor and column efficiency. At first the resolution increases quickly as the... 

Hamisch, M., Mockel, H.J., Schulze, G. (1983) Relationship between log Pow shake-flask values and capacity factors derived from reversed-phase HPLC for n-alkylbenzenes and some OECD reference substances. J. Chromatogr. 282, 315-332. 

Opperhuizen, A. (1987) Relationships between octan-l-ol/water partition coefficients, aqueous activity coefficients and reversed phase HPLC capacity factors of alkylbenzenes, chlorobenzenes, chloronaphthalenes and chlorobiphenyls. Toxicol. Environ. Chem. 15, 349-364. 

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. 

The capacity factor k is equal to njnm where ns is the total moles of X in stationary phase and nm is the total moles of X in the mobile phase. Based on this relationship, we can formulate the following equations ... 

Relationships such as Eqs. (45) and (46) have been utilized extensively in correlating solubility properties (such as gas/liquid and liquid/liquid partition coefficients), retention volumes in gas/solid chromatography, capacity factors in high-pressure liquid chromatography, etc.199 200 For instance, gas/liquid partition coefficients for each of 35 different liquid stationary phases were represented with R > 0.985.205 Other applications have been in biochemical and pharmacological areas,199 200 e.g., enzyme inhibition and pollutant effects. 

Miyake, K., Mizuno, N., and Terada, H. Effect of hydrogen bonding on the high-performance liquid chromatographic behaviour of organic compounds. Relationship between capacity factors and partition coefficients,/. Chromatogr., 439 227-235,1988. 

C Yamagami, M Yokota, N Takao. Hydrogen bond effects of ester and amide groups in heteroaromatic compounds on the relationship between the capacity factor and the octanol-water partition coefficients. J. Chromatogr. A 662 49-60 (1994). 

The plots of log k vs. log P w and the plots of log k (v) vs. log k (z) were studied for seven cephalosporins. A linear relationship was obtained in micellar solution and in microemulsion solution (Tables 3 and 4). The results obtained indicate that the capacity factor determined by EKC could be used both as parameter to characterize the partition behavior of drugs in ME and MC and as hydrophobic parameter instead of log Pow. k appears to be an evident parameter, and it shows a better diversification than P w. In the 1-octanol/water system, we did not found high values of the partition coefficients. In contrast, the ME systems used provide a better characterization of the drugs according to their hydrophilic/lipophilic properties. 

DK Lloyd, A Ahmed, F Pastore. A quantitative relationship between capacity factor and selector concentration in capillary electrophoresis and high-performance liquid chromatography evidence from the enantioselective resolution of benzoin using human serum albumin as chiral selector. Electrophoresis 18 958-964, 1997. 

Other relationships derived from the preceding equations can be used to express resolution. These relationships are used to express resolution as a function of one parameter or another or, alternatively, to accommodate simplifications. Therefore, equations (1.25) and (1.26) are often used (equation (1.26) is obtained from (1.24) when w = w2). Equation (1.26) shows the influence on resolution of the efficiency, the capacity factor and the selectivity. 

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