Retention Factor k

Equation 2.6 indicates that retention time is proportional to k. 

Note that by multiplying both sides by the flow rate, F, a similar equation for VR is obtained  

Chromatography is a thermodynamically based method of separation, where each component in the sample is distributed between the mobile phase 

Moles ofX in stationary phase Moles ofX in mobile phase 

These factors are varied to affect the degree of resolution of a given separation. However, a practical approach to improve resolution is to adjust first the retention factor to an acceptable value and then improve the efficiency. Finally, if required, the selectivity is changed. 

The distribution of a solute between the stationary and mobile phases affects the rate at which it migrates through a column or bed. The resultant distribution constant (Ku) is defined as the ratio between the concentrations of the solute molecules in the stationary phase (CJ relative to those in the mobile phase (C, )  

Substituting these concentrations with the numbers of molecules (Ns and N, ) per unit volume (V, and V, ) and rearranging terms, equation (9) becomes  

The ratios NJN, and V, /Vs are defined as the retention factor, and the phase ratio, p, respectively. The retention factor is also a measure of the time a solute molecule spends in the stationary phase relative to the time it spends in the mobile phase and thus is related to the retention time of the solute  

The magnitude of is a function of the solute chemical and physical properties, the stationary and mobiles phases, and the column temperature. Also, solute retention is increased by increasing the amount of the stationary phase relative to that of the mobile phase. A large k is indicative of a slowly moving solute band, which improves the resolution between it and those of other solutes but also results in its broadening. In practice, optimum values of k are between 2 and 6, although values between 1 and 10 can be used. 

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Different tests for estimation the accuracy of fit and prediction capability of the retention models were investigated in this work. Distribution of the residuals with taking into account their statistical weights chai acterizes the goodness of fit. For the application of statistical weights the scedastic functions of retention factor were constmcted. Was established that random errors of the retention factor k ai e distributed normally that permits to use the statistical criteria for prediction capability and goodness of fit correctly. 

The main equation of the model describes the dependence of retention factor, k, from surfactant concentration, c and modifier concentration, c ... 

According to Equation 3, the resolution of two peaks in column separation is controlled by three major variables retention defined in terms of the retention factor k column efficiency expressed as the number of theoretical plates N and selectivity characterized by the selectivity factor a [48] ... 

Practically, the retention factor k of a neutral solute can be calculated from MEKC measurements ... 

There has been an attempt to measure the peak capacity in 1DLC and 2DLC by assigning a range of useful retention time between the unretained marker that elutes at ti and some stated value of the retention factor k leading to a zone at tf and plugging in a value for the peak width W. This number is useful but will never be equal to the number... 

In the simplest scheme of 2D HPLC, effluent of the first dimension (lst-D) was directly loaded into an injector loop (500 pL) of the 2nd-D HPLC for 28 s, and 2 s were allowed for injection. This operation was accompanied by the loss of lst-D effluent for 2 s out of 30 s in each cycle. The flow rate of 10 mL/min allowed the elution of solutes having retention factors (k values) up to 8 for the 2nd-D within the 30-s separation window, with f0 of 3.5 s. Figure 7.7 a and b shows the chromatograms for the 1 st-D and the 2nd-D, respectively, obtained for a mixture of hydrocarbons and benzene derivatives. The lst-D chromatogram showed many overlapping peaks. PAHs were eluted as mixtures from the FR column, and some are separated in the 2nd-D. 

Ten columns of the 24 available in a cartridge were employed to analyze all compounds in duplicate. Uracil, was employed as a dead volume marker (tO) needed for the evaluation of retention factor [k = (tr - t0)/t0]. Two additional columns were used for simultaneous analysis of the unknown. Values for the log of the capacity factor k were calculated for every compound at each percent organic content of the mobile phase log k = log [(tr - t0)/t0. For each compound, a plot of log k versus percent acetonitrile was used to calculate log k w (log k at 0% acetonitrile). 

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 ... 

Using the retention data and the chromatogram shown in Fig. 14.8, tabulate the following for each peak retention time ( r), adjusted retention time (t K), retention factor (k), partition coefficient (Kc) and number of theoretical plates (N). The column phase ratio was 250 and the gas hold up time ( m) was 0.995 min. 

Table 4. Retention factors k and column efficiencies N for an unretained thiourea and retained compound amylbenzene in columns packed by different methods [53] ...

PARTITION COEFFICIENTS (P ), RETENTION FACTOR (K) AND MOBILITY DATA OF DYE INTERMEDIATES MEASURED WITH A PHOSPHATE-(TTAB) BUFFER AT PH 5.0 ... 

Common standard compounds for reversed phase columns are toluene and naphthalene, which have retention factors, k, of about 3. The eluent modifier is methanol or acetonitrile at a concentration of 50-80%, depending on the hydrophobicity of the stationary phase material. For other stationary phase materials, corresponding analytes, with k = 3-5, can be used. 

The retention factor, k, is the basic value in chromatography, and is related to the void volume (dead volume). The void volume is the space inside the column, where no retention of solutes has occurred and can be measured on a chromatogram, as shown in Figure 1.3. The void volume is about half the total volume of the column when it is packed with porous stationary phase materials. In practice, the effective void experienced by the analyte is smaller because the molecular mass of the analyte is usually much greater than that of the eluent molecule. In a model of porous stationary phase material, the pores can be represented as V-shape valleys (Figure 3.8), where region a is a support, such as... 

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). 

FIGURE 1.4 Dependencies of retention factors k on counterion (i.e., phosphate) concentration [X]. Experimental conditions Mobile phase, methanol-sodium dihydrogenphosphate buffer (50 50 v/v) (pHa 6.5 adjusted in the mixture with sodium hydroxide) flow rate, 1 mLmin temperature, 25°C CSP, 0-9-[3-(triethoxysilyl)propylcarbamoyl]-quinine bonded to silica [30] column dimension, 150 x 4 mm ID. 

FIGURE 1.5 pH -effect on retention factors k and separation factors a. CSP 0-9- tert-butylcarbamoyl)quinine bonded to sihca column dimension, 150 x 4 mm ID eluent, methanol-ammonium acetate buffer (80 20, v/v) (adjusted with acetic acid) temperature, 25°C 1 mL min sample, N-benzoyl-leucine (Bz-Leu). (Reproduced from M. Lammerhofer et al., American Laboratory, 30 71 (1998). With permission.)... 

On the other hand, optionally added co-ions of the eluent may also interfere with the ion-exchange process through competitive ion-pairing equilibria in the mobile phase. The effect of various amines added as co-ions to the polar-organic mobile phase was systematically studied by Xiong et al. [47]. While retention factors of 9-fluorenylmethoxycarbonyl (FMOC)-amino acids were indeed affected by the type of co-ion, enantioselectivities a and resolution values Rs remained nearly constant. For example, retention factors k for FMOC-Met decreased from 17.4 to 9.8 in the order... 

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)... 

In Equation 1.15, q represents the adsorbed amount of solute, ns and qs are the saturation capacities (number of accessible binding sites) for site 1 (nonstereoselect-ive, subscript ns) and site 2 (stereoselective, subscript s), and fens and bs are the equilibrium constants for adsorption at the respective sites [54]. It is obvious that only the second term in this equation is supposed to be different for two enantiomers. Expressed in terms of linear chromatography conditions (under infinite dilution where the retention factor is independent of the loaded amount of solute) it follows that the retention factor k is composed of at least two distinct major binding increments corresponding to nonstereoselective and stereoselective sites according to the following... 

FIGURE 4.1 Effect of the plate number (N), the separation factor (a ), and the retention factor (k) on resolution (Rs). (Adapted from Sandra, P.J. 1989. High Resolut. Chromatogr. 12 82-86. With permission.)... 

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. 

While retention time is used for peak identification, it is dependent on the flow rate, the column dimension, and other parameters. A more fundamental term that measures the degree of retention of the analyte is the capacity factor or retention factor (k ), calculated by normalizing the net retention time (% > retention time minus the void time) by the void time. The capacity factor measures how many times the analyte is retained relative to an unretained component. ... 

In the System Suitability section, different parameters are described which can be applied in order to check the behavior of the CE system. The choice of the appropriate parameters depends on the mode of CE used. The system suitability parameters include retention factor (k) (only for MEKC), apparent number of theoretical plates (N), symmetry factor (Af), resolution (Rs)> Rtea repeatability, migration time repeatability, and signal-to-noise ratio. Practical equations to calculate different system suitability parameters from the electropherograms are presented, which are also included in Table 3. 

Fio. 38. Plot of the algorithm of the retention factor, k, and log P, the water-/i>octanol partition coefficient of eight amino acids. The chromatographic data were obtained on 3 ftm LiChrosorb kP-8, 230 x 4.6 mm i.d. eluierit 0.1 M aqueous phosphate buffer, pH 6.7, T 70 C. Eluites Trp, tryptophan Phe, phenylalanine Leu, leudne Val. valine Tyr, tyrosine Lys, lysine Ala, alanine Gly, glycine. Reprinted with permission from Molnar and Horvith QOS). 

The chromatographic retention factor, k, is related to the equilibrium constant for adsorption to a solid phase or distribution between liquid mobile and stationary phases by the well-known expression... 

As in chromatography, the retention factor (k ) in MEEKC is defined as the ratio of the number of moles of the solute in the micellar pseudostationary... 

The retention factor k of charged solutes can be determined from migration time data using Eq. (3) (10,11) ... 

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