Retention factors and

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. 

Retention Factor and Saturation Capacity of Nortriptyline and 2-Naphthalenesulfonic Acid in Various Buffers... 

The hyperbolic reladonship between the logarithm of the retention factor and the carbon load of octadecyl sOica stationary phase is illus-... 

The uncertainty in the measurement of elution time / or elution volume of an unretained tracer is another potential source of error in the evaluation of thermodynamic quantities for the chromatographic process. It can be shown that a small relative error in the determination of r , will give rise to a commensurate relative error in both the retention factor and the related Gibbs free energy. Thus, a 5% error in leads to errors of nearly 5% in both k and AG. An analysis of error propagation showed that if the... 

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-... 

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-... 

Gant et al. (175) examined the effect of temperature on resolution and on selectivity, retention factors, and plate number, which determine the magnitude of resolution. They found that these data can be used together with the lempeniliire dependence of solvent viscosity to optimize iinaivsis rate with required resolution. This is of particular interest when RFC is used for automated repetitive analyses of lar e numbers of samples. 

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... 

The ratio of the two virtual lengths defines a parameter called the electrophoretic velocity factor k, which is analogous to the chromatographic retention factor and it is expressed as [140] ... 

As evidenced by the above equation, the distribution coefficient can be directly calculated from the retention factor and other easily measurable parameters. It is also worth noting that when the concentration of the micellar phase is sufficiently low, the denominator at the last term of the above equation can be approximated to be equal to unity and the retention factor is linearly proportional to the concentration of the surfactant into the BGE. Accordingly, Equation 6.46 is rewritten as... 

EKC in the reversed direction mode is performed when analytes and pseudostationary phase move at different velocities in the same direction, which is opposite to that of EOF. In this case, retention factor and resolution are expressed by the following equations [211] ... 

The separation of two compounds A and B is studied by HPLC on a column of type RP-18. The mobile phase is a binary mixture of water and acetonitrile. A linear relationship exists between the logarithm of the retention factor and the % of acetonitrile within the binary mixture (H20/CH3CN). 

In MLC, the mobile phase consists of surfactants at concentrations above their critical micelle concentration (CMC) in an aqueous solvent with an alkyl-bonded phase (52). Retention behavior in MLC is controlled by solute partitioning from the bulk solvent into micelles and into stationary phase as well as on direct transfer from the micelles in the mobile phase into the stationary phase. Eluent strength in MLC is inversely related to micelle concentration. A linear relationship exists between the inverse of retention factor and micelle concentration. Similar to what is observed in RPLC, a linear relationship exists between retention in MLC and , the volume fraction of the organic modifier. Modeling retention in MLC is much more complicated than in RPLC. The number of parameters is important. Micelles are obviously a new domain in both liquid chromatography and electrophoresis. Readers interested in the topic will appreciate Ref. 53, a special volume on it. 

Case 1. The electrophoretic mobilities and the corresponding M-factors of the two components are identical. Since their chromatographic retention factors and thus their M/c are different, their MCec,packed will also be different so that X and Y are separable by CEC, e.g., components A and B are both neutral, differing only in their chromatographic retention factors and comigrating when X = 0 as illustrated in Fig. 1.12. The separation of A and B improves with increasing X and optimum separation is achieved when X is 0.9, i.e., the detection window is located immediately after the retaining frit as in conventional CEC columns. 

Case 2. The chromatographic retention factors and the M/c of X and Y in this case are identical. Since their electrophoretic mobilities and MCe are different, there MCec will be different too and the two components can be separated in CEC, e.g., components B and C have the same chromatographic retention factors, but different electrophoretic mobilities. Hence, they are separated by virtue of differential electrophoretic migration as illustrated in Fig. 1.12. 

Case 3. X has a smaller chromatographic retention factor and a higher electrophoretic mobility in the EOF direction than Y. So M/Cix> Micj and MCe,X> Mcejiti the two segments. Thus, MCec,X> MCec,Yin both the segments so that chromatographic and the electrophoretic forces act in concert to facilitate the separation of X and Y... 

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