Efficiency,column

The column efficiency characterizes the dispersion of the product in the chromatographic column. A loss of efficiency will directly impact on the peak resolution and therefore on the achieved purity and/or yield for the purified product(s). 

Several physical causes could disturb the elution stream through the column, leading to a loss of efficiency. 

Temperature This criterion is often underconsidered in the operation of a preparative chromatographic process. Temperature has a direct impact on the adsorption isotherms and modifies the retention of the separated compounds. A significant loss of efficiency can be observed with a radial heterogeneity of the temperature, which will modify the retention of the products. This heterogeneity is linked to a difference between the temperature of the eluent and the temperature of the column body. This is particularly important to consider on small-scale preparative devices (5-10 cm ID columns), the wall effect is less significant for larger columns. 

A favorable effect on the column efficiency can be achieved when the column body is slightly warmer than the eluent (1-2 °C) (Dapremont et al., 1998) to correct the bed heterogeneity near the column wall. 

Viscous Fingering effect This phenomenon is observed when the viscosity of the injected sample is significantly larger than the eluent viscosity. A hydro-dynamic instability appears within the column, leading to a fingering elution of the viscous solution in the bed. This disturbance of the flow will strongly impact the obtained efficiency. A reduction of the injected concentration is efficient to correct this effect, which can appear during a process scale-up. 

Never forget that column efficiency measured as theoretical plates can be performed only with isocratic elution. Gradient elution requires determination of peak capacity as a measure for the separating capability of a column. 

Note that the analytes of high molecular mass result in reduced column efficiencies, due to lower diffusion rates, compared to smaller solutes. 

At the beginning of a chromatographic separation the solute occupies a narrow band of finite width. As the solute passes through the column, the width of its band 

In their original theoretical model of chromatography, Martin and Synge treated the chromatographic column as though it consists of discrete sections at which partitioning of the solute between the stationary and mobile phases occurs. They called each section a theoretical plate and defined column efficiency in terms of the number of theoretical plates, N, or the height of a theoretical plate, H where 

A column s efficiency improves with an increase in the number of theoretical plates or a decrease in the height of a theoretical plate. 

Assuming a Gaussian profile, the extent of band broadening is measured by the variance or standard deviation of a chromatographic peak. The height of a theoretical plate is defined as the variance per unit length of the column 

The increase in a solute s baseline width as it moves from the point of injection to the detector. 

The performance characteristics of the stationary phase, whatever its type, are important factors in achieving successful separations. The efficiency of the column will be an indicator not only of the column performance, adsorbent and packed bed characteristics but also of system performance. In considering only the contribution of the stationary phase to column performance the factors which influence the sample band as it travels through the packed bed must be considered. There are five fac- 

Reminding the plate theory model this approach also leads to the value of the height equivalent to one theoretical plate H and to the number N, of theoretical 

If these two parameters are accessible from the elution peak of the compound, just because and a are in the same ratio as that of L to cr.  

On the chromatogram, a represents the half-width of the peak at 60.6 per cent of its height and the retention time of the compound, and a should be measured in the same units (time, distances or eluted volumes if the flow is constant). If a is expressed in units of volume (using the flow), then 4cr corresponds to the volume of the peak , that contains around 95 per cent of the injected compound. By consequence of the properties of the Gaussian curve w = 4cr and Wi 2 — 2.35cr), Equation 1.9 results. However, because of the distortion of most peaks at their base, expression 1.9 is rarely used and finally Equation 1.10 is preferred. 

Af is a relative parameter, since it depends upon both the solute chosen and the operational conditions adopted. Generally a constituent is selected which appears towards the end of the chromatogram in order to get a reference value, for lack of advance knowledge of whether the column will successfully achieve a given separation. 

In order to compare the performances of columns of different design for a given compound - or to compare, in gas chromatography, the performances between a capillary column and a packed column - more realistic values are obtained by replacing the total retention time which appears in expressions 1.8-1.10, by the adjusted retention time which does not take into account the hold-up time % spent by any compound in the mobile phase = tR tu) The three preceding expressions become  

K Nemst distribution coefficient Vs Volume of the stationary phase Volume of the mobile phase Cs Solute concentration in the stationary phase Cm Solute concentration in the mobile phase 

The capacity factor is independent of the equipment being used, and is a measure of the column s ability to retain a sample component. Small values of k imply that the respective component elutes near the void volume thus, the separation will be poor. High values of k, on the other hand, are tantamount to longer analysis times, peak broadening, and a decrease in sensitivity. 

The height of a theoretical plate, in which the distribution equilibrium of sample molecules between stationary and mobile phases is established, is related to the plate number via the length of the separator column, as shown in Eq. (2.8)  

Based on chromatographic data, the theoretical plate height, H, which is defined as the ratio of the peak variance and the colunm length L, can be calculated via Eq. (2.9)  

The term 8 In 2 arises from the approximation of a peak as a Gaussian curve. Using Eq. (2.8), the number of theoretical plates is shown in Eq. (2.10)  

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Column Efficiency. Under ideal conditions the profile of a solute band resembles that given by a Gaussian distribution curve (Fig. 11.1). The efficiency of a chromatographic system is expressed by the effective plate number defined from the chromatogram of a single band. 

Two methods for improving chromatographic resolution (a) Original separation showing a pair of poorly resolved solutes (b) Improvement in resolution due to an increase in column efficiency ... 

From equation 12.1 it is clear that resolution may be improved either by increasing Afr or by decreasing wa or w-q (Figure 12.9). We can increase Afr by enhancing the interaction of the solutes with the column or by increasing the column s selectivity for one of the solutes. Peak width is a kinetic effect associated with the solute s movement within and between the mobile phase and stationary phase. The effect is governed by several factors that are collectively called column efficiency. Each of these factors is considered in more detail in the following sections. 

A quantitative means of evaluating column efficiency that treats the column as though it consists of a series of small zones, or plates, in which partitioning between the mobile and stationary phases occurs. 

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... 

Equations 12.21 and 12.22 contain terms corresponding to column efficiency, column selectivity, and capacity factor. These terms can be varied, more or less independently, to obtain the desired resolution and analysis time for a pair of solutes. The first term, which is a function of the number of theoretical plates or the height of a theoretical plate, accounts for the effect of column efficiency. The second term is a function of a and accounts for the influence of column selectivity. Finally, the third term in both equations is a function of b, and accounts for the effect of solute B s capacity factor. Manipulating these parameters to improve resolution is the subject of the remainder of this section. 

To increase the number of theoretical plates without increasing the length of the column, it is necessary to decrease one or more of the terms in equation 12.27 or equation 12.28. The easiest way to accomplish this is by adjusting the velocity of the mobile phase. At a low mobile-phase velocity, column efficiency is limited by longitudinal diffusion, whereas at higher velocities efficiency is limited by the two mass transfer terms. As shown in Figure 12.15 (which is interpreted in terms of equation 12.28), the optimum mobile-phase velocity corresponds to a minimum in a plot of H as a function of u. 

To minimize the multiple path and mass transfer contributions to plate height (equations 12.23 and 12.26), the packing material should be of as small a diameter as is practical and loaded with a thin film of stationary phase (equation 12.25). Compared with capillary columns, which are discussed in the next section, packed columns can handle larger amounts of sample. Samples of 0.1-10 )J,L are routinely analyzed with a packed column. Column efficiencies are typically several hundred to 2000 plates/m, providing columns with 3000-10,000 theoretical plates. Assuming Wiax/Wiin is approximately 50, a packed column with 10,000 theoretical plates has a peak capacity (equation 12.18) of... 

Quantitative Calculations In a quantitative analysis, the height or area of an analyte s chromatographic peak is used to determine its concentration. Although peak height is easy to measure, its utility is limited by the inverse relationship between the height and width of a chromatographic peak. Unless chromatographic conditions are carefully controlled to maintain a constant column efficiency, variations in... 

Microcolumns use less solvent and, because the sample is diluted to a lesser extent, produce larger signals at the detector. These columns are made from fused silica capillaries with internal diameters of 44—200 pm and lengths of up to several meters. Microcolumns packed with 3-5-pm particles have been prepared with column efficiencies of up to 250,000 theoretical plates. 

Open tubular microcolumns also have been developed, with internal diameters of 1-50 pm and lengths of approximately 1 m. These columns, which contain no packing material, may be capable of obtaining column efficiencies of up to 1 million theoretical plates.The development of open tubular columns, however, has been limited by the difficulty of preparing columns with internal diameters less than 10 pm. 

The required number of actual plates, A/p, is larger than the number of theoretical plates, because it would take an infinite contacting time at each stage to estabhsh equihbrium. The ratio is called the overall column efficiency. This parameter is difficult to predict from theoretical... 

This is the one case where the overall column efficiency can be related analytically to the Murphree plate efficiency, so that the actual number of plates is calculable by dividing the number of theoretical plates through equation 86 ... 

The simplest efficiency is the overaH column efficiency which is the number of theoretical plates in a column divided by the number of actual plates ... 

EmpiricalEfficieny Prediction Methods. Numerous empirical methods for predicting plate efficiency have been proposed. Probably the most widely used method correlates overall column efficiency as a function of feed viscosity and relative volatiHty (64). A statistical correlation of efficiency and system variables has been developed from numerous plate efficiency data (65). 

FIG. 14-7 O Connell correlation for overall column efficiency for absorption. To convert ffP/ i in pound-moles per cubic foot-centipoise to Idlogram-moles per cubic meter-pascal-second, multiply by 1.60 X 10 . [O Connell, Trans. Am. Inst. Chem. Eng., 42, 741 (1946).]... 

The designer has httle control over the first set but can deal effectively with the other two. Ultimate concern is with ovei all column efficiency ... 

FIG. 14-37 Overall column efficiency of 25-mm Oldersbaw column compared with point efficiency of 1,22-m-diameter-sieve sieve-plate column of Fractionation Research, Inc, System = cyclohexane-n-heptane, [(Fair, Null, and Bolles, Ind, Eng, Chem, Process Des, Dev, 22, 53 (i.982),]... 

Tbe best-established theoretical method for predicting E is that of tbe AlCbE [Buhhle-Tray Design Manual, American Institute of Chemical Engineers, New York, 1958). It is based on tbe sequential prediction of point efficiency, Murpbree efficiency, and overall column efficiency ... 

For sieve trays, Chan and Fair [Ind. Eng. Chem. Pioc. Des. Dev., 23, 814 (1983)] used a data bank of larger-scale distillation column efficiencies to deduce the following expression for the product kcCi ... 

Overall Column Efficiency Calculated values of E, , must be corrected for entrainment, if any, by the Colburn equation [Eq. (14-101)]. The resiJting corrected efficiency is then converted to column efficiency by the relationship of Lewis [Ind. Eng. Chem., 28, 399 (1936)] ... 

Holdup and Flooding At this point it is useful to introduce the concepts of holdup and flooding in column contactors. It is normal practice to select the phase which preferentially wets the internals of the column as the continuous phase. This then allows the dispersed phase to exist as discrete droplets within the column. If the dispersed phase were to preferentially wet the internals, this could cause the dispersion to prematurely coalesce and pass through the column as rivulets or streams which would decrease interfacial area and therefore column efficiency. 

A high number of plates and a low HETP indicate a high column efficiency. 

Equation (16-168) shows that the resolution is the result of independent effects of the separation selectivity (ot), column efficiency [Np), and capacity (k ). Generally, peaks are essentially completely resolved when R, = 1.5 (>99.5 percent separation). In practice, values of R, 1, corresponding to 98 percent separation, are often considered adequate. 

Displacement Development A complete prediction of displacement chromatography accounting for rate factors requires a numerical solution since the adsorption equilibrium is nonlinear and intrinsically competitive. When the column efficiency is high, however, useful predictious can be obtained with the local equilibrium theoiy (see Fixed Bed Transitions ). 

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