Columns saturation capacity

The column saturation capacity is calculated from two chromatograms. One of these is made at analytical loads, whilst the other is run at a preparative loading. It is important that the load is chosen such that the peak due to the component of interest is not deformed by detector overload and that a reasonably large change in capacity factor is seen. It is recommended that a relative change of more than 10 or 15% in k is used. 

An alternative calculation uses Eq. (6). The efficiency for the overloaded peak was measured to be 303 plates. Substituting the values into Eq. (6) yields  

This gives a value of 340 mg for the column saturation capacity. As noted earlier, this method is used when column efficiencies are low and the approximation of an infinite efficiency is no longer possible. For most HPLC separations, Eq. (8) can be used with sufficient accuracy. 

It should be noted that the saturation capacity is determined for the column. Saturation capacities for other columns containing the same phase system can be calculated by multiplying this value by the ratio of the column volumes. If the weight of packing material in the column is known, the saturation capacity per gram of packing can be calculated. This can be used to compare different packing materials for a separation. 

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For preparative or semipreparative-scale enantiomer separations, the enantiose-lectivity and column saturation capacity are the critical factors determining the throughput of pure enantiomer that can be achieved. The above-described MICSPs are stable, they can be reproducibly synthesized, and they exhibit high selectivities - all of which are attractive features for such applications. However, most MICSPs have only moderate saturation capacities, and isocratic elution leads to excessive peak tailing which precludes many preparative applications. Nevertheless, with the L-PA MICSP described above, mobile phases can be chosen leading to acceptable resolution, saturation capacities and relatively short elution times also in the isocratic mode (Fig. 6-6). 

The critical parameters for separation by displacement are the displacer concentration, the loading factor (ratio of the sample size to the column saturation capacity) and the column efficiency. The choice of displacer is probably the most critical step. For correct development to occur the adsorption isotherm of the displacer must overlie those of the feed components. The concentration of the i PlAcer controls the separation time and... 

Lf is the loading factor, i.e., the ratio of the total amount of the components in the sample to the column saturation capacity... 

Other parameters characterizing a PFAR are the column breakthrough capacity, Bc, the column saturation capacity, Sc, and the column efficiency, E, of the PFIEBR, which are calculated with the following equations [105] ... 

The importance of the column saturation capacity in the design of chromatographic unit operations is that the amount loaded and the production rate are proportional to the capacity of the stationary phase for the product and its impurities. The column saturation capacity is defined for each species / as the amount loaded to create a monolayer coverage per unit weight or volume of packing medium. The Langmuir isotherm in Eq. (7.3) mathematically represents the equilibrium of the solute and the adsorbent with no solute-solute interactions. 

Direct determination of the column saturation capacity requires measurement of the adsorption isotherm. Use of methods such as frontal analysis, elution by characteristic point are classical techniques. Frontal analysis and elution by characteri.stic point require mg or gram quantities of pure product component. It is also possible to estimate the column saturation capacity from single-component overloaded elution profiles using the retention time method or using an iterative numerical method from a binary mixture [66J. 

From a practical point of view, it is likely to be sufficient to estimate the column saturation capacity using the retention time method from several single-component overloaded elution profiles. Part of the purpose of the screening tests is also to determine the impact of the column saturation capacity of the product for different mobile-phase systems, temperatures and packing media. Since the optimum amount loaded is a stronger function of the separation factor than the column saturation capacity, estimation of the column saturation factor over an exact measurement may be sufficient. It is likely to be sufficient to use only the product species saturation capacity as measures of the... 

Estimate or measure the column saturation capacity under several mobile-phase and stationary-phase conditions, including different temperatures. 

From calculation of the loading factor and using an estimated value for the column saturation capacity from the screening studies, the optimum amount loaded. for species / can be calculated, Eq. (7.13). 

The units for calculating the amount loaded. in g. the cross-sectional area S in cm, the column length L in cm and the column saturation capacity, in g/ml. Typical loading factors range from 0.5% to. ... 

Model unit operation to optimize operating -ariables (c.g. loading, bed length, flow rate and required plate count) ba.sed on thermodynamics (adsorption isotherm, separation factor, the column saturation capacity). 

The parameters reviewed here are (1) pressure, (2) column saturation capacity, (3) particle size, (4) separation factor, (5) retention factor, (6) crude cost, (7) solvent cost, (8) purity, and (9) diffusivity. The results presented here are adapted from previous work [73]. 

Fig. 7.11 illustrates for a 1000 mg/g and 5(X) mg/g column saturation capacity, pie charts for the fractional cost associated with the solvent, packing, system, labor and lost... 

Use of temperature to optimize the separation factor and the column saturation capacity is an important element in the experimental component of the optimization process. For compounds where the column saturation capacity is low and the separation factor can be made large, for example enantiomers, it may be important to consider carefully this trade-off. There are insufficient data in the literature to understand the... 

Fig. 7.11. Cost contributions at two column saturation capacities packing, solvent, lost crude, labor and system, (a) 1000 mg/g, and (b) 500 mg/g. Absolute cost /g, cost component, % fractional cost.

Column saturation capacity, amount of compound to saturate the column packing... 

Column saturation capacity, based on volume of packing Column saturation capacity, based on weight of packing Interstitial linear velocity. L/pi Viscosity... 

Here n is the number of components in the system, coefficients a, and b, are the coefficients of the single-component Langmuir adsorption isotherm for component /. The coefficient bt is the ratio of the rate constants of adsorption and desorption, so it is a thermodynamic constant. The ratio ajb, is the column saturation capacity of component / [13],... 

Here q, is the solid phase concentration, C, is the mobile phase concentration and ati an,i btl bu, are isotherm parameters for the / th component. The column saturation capacity of the chiral site is defined as ... 

Since the Langmuir isotherm model is widely applicable, it is normal to take the column saturation capacity as a unit to measure the degree of column overload achieved, by reporting the actual amoimt injected as a fraction of the column saturation capacity. The loading factor, Ly, is defined for each component as the ratio of its amount in the sample to the column saturation capacity for that component ... 

As a consequence, the competitive Langmuir isotherm model offers no possibility to account for a reversal in the elution order of two components with increasing concentration. On the contrary, experimental results show that such an inversion is possible, and that it is not even unusual when the column saturation capacities of the two single-component isotherms are different. For example, experimental adsorption data and chromatograms of mixtures of tmns- and a s-androsterone show an inversion of the elution order when the sample size increases (see later. Figure 4.8 and the related discussion below) [9-11]. 

On the other hand, the quantitative prediction of competitive isotherm behavior for the components of binary mixtmes is not possible using the competitive Langmuir isotherm model when the difference between the column satmation capacities for the two components exceeds 5 to 10%. For example, the adsorption isotherms of pure cis- and trans-androsterone on sihca are well accoimted for by the Langmuir model [9]. However, the two column saturation capacities differ by 30%, due to the nearly flat structure of the trans isomer compared to the folded structure of the cis isomer. As a consequence, the competitive Langmuir model accounts poorly for the competitive adsorption data [9,10]. Much improved results are obtained with the more complex LeVan-Vermeulen isotherm (Section 4.1.5). Another approach could use the random adsorption site model, with different exclusion siuface areas for the competing molecules [12],... 

Finally, it can be shown that the multicomponent competitive Langmuir isotherm (Eq. 4.5) does not satisfy the Gibbs-Duhem equation if the column saturation capacities are different for the components involved [13]. This profound inconsistency may explain in part why this model does not accoimt well for experimental results. There are two very different alternative approaches to the problem of competitive Langmuir isotherms when the saturation capacities for the two pure compounds are different. Before discussing this important problem and an interesting extension of the competitive Langmuir isotherm, we must first present the competitive bi-Langmuir isotherm model. 

Figure 4.2 illustrates the best competitive adsorption isotherm model for benzyl alcohol and 2-phenylethanol [16]. The whole set of competitive adsorption data obtained using Frontal Analysis was fitted to obtain the Langmuir parameters column saturation capacity qs =146 g/1), equilibrium constant for benzyl alcohol bsA = 0.0143) and the equilibrium constant for 2-phenylethanol (bpE = 0.0254 1/g). The quality of the fit obtained with this simple model is in part explained by the small variation of the activity coefficients of the two solutes in the mobile phase when the solute concentrations increased from 0 to 50 g/1. The Langmuir competitive adsorption isotherm simplifies also in the case where activity coefficients are of constant value in both phases over the whole concentration range [17]. 

The conditions of validity of this isotherm model are the same as those of the competitive Langmuir isotherm, ideal behavior of the mobile phase and the adsorbed layer, localized adsorption, and equal column saturation capacities of both t3q>es of sites for the two components. The excellent results obtained with a simple isotherm model in the case of enantiomers can be explained by the conjunction of several favorable circumstances [26]. The interaction energy between two enantiomeric molecules in solutions is probably very close to the interaction energy between two R or two S molecules and their interactions with achiral solvents are... 

The agreement that was observed between the experimental results and the prediction of a competitive Langmuir model based on the use of single-component Langmuir isotherms in the case of the adsorption of enantiomeric derivatives of amino acids on immobilized serum albumin [26] is imusual. It demonstrates the validity of the competitive Langmuir model based on the use of the parameters of the single-component Langmuir model. However, as explained before, the experimental conditions are exceptionally favorable since the column saturation capacities for the two enantiomers are equal. Nevertheless, Zhou et ah have shown that it is possible, in certain favorable cases, to derive the equilibrium isotherms of the pure enantiomers and to calculate isotherm equilibrium data for any mixture of... 

Unfortunately, the available experimental results suggest that the column saturation capacity is often not the same for the components of a binary mixture, so Eq. 4.5 does not account accurately for the competitive adsorption behavior of these components [48]. A simple approach was proposed to turn the difficulty (next subsection). Although it is applicable in some cases, more sophisticated models seem necessary. Numerous isotherm models have been suggested to solve this problem. Those resulting from the ideal adsorbed solution (IAS) theory developed by Myers and Prausnitz [49] are among the most accurate and versatile of them. Later, this theory was refined to accormt for the dependence of the activity coefficients of solutes in solution on their concentrations, leading to the real adsorption solution (RAS) theory. In most cases, however, the equations resulting from IAS and the RAS theories must be solved iteratively, which makes it inconvenient to incorporate those equations into the numerical calculations of column dynamics and in the prediction of elution band profiles. 

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