Mass of Adsorbent in the Column

The mass of the packing material in the column is a largely underestimated parameter. As it was discussed in the theory chapter, the retention is proportional to the total surface area of the adsorbent in the column. External methods of the surface area measurement determine the specihc surface area (in square meters per gram of the material), and the total surface in the column is a product of the specific surface area of base material and the mass of the adsorbent in the column. 

The retention factor, according expression (2-1) from Chapter 2, is 

This shows that the retention factor is proportional to the total surface area of the adsorbent. On the other hand, the selectivity, a, is the ratio of the capacity factors and is independent on the total surface area  

TABLE 3-4. Relative Standard Deviation of Conventional and Surface-Specific Retention Factors on Different Columns 

Unfortunately, the measurement of the total surface area of the adsorbent in the column is a tedious process that involves several different experimental techniques, and unless column manufacturers choose to provide this information, it is not feasible that pharmaceutical scientist would be willing to measure it. 

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TABLE 3-5. Comparison of the Calculated and Measured Mass of Adsorbent in the Column (for Five Different Columns)... 

Here we provide a brief description of the methodology for the estimation of the mass of adsorbent in the column and total surface area. 

The estimation of the amount of adsorbent in the column is based on the comparison of the total pore volume (Vptot [niL]) of the adsorbent in the column with the specific pore volume (Vp [mL/g]) of the same adsorbent determined from the full nitrogen adsorption isotherm. The ratio of these two values will give the adsorbent mass. Total pore volume in the column is determined as the difference of the column void volume (Vo) and the interparticle volume (Vip). 

Fig. 6.3 A dissection of the frontal chromatogram [31]. The breakthrough curve is represented by the thick line. The two gray/hatched surfaces on the left side (Ai, A2) represent the mass of compound in the extra- and dead-column volumes. Area A3 represents the mass of the compound adsorbed to the stationary phase. Adapted with permission from Elsevier.

The overall rate of mass transfer of adsorbate in the bed is affected by external transport from the bulk of the gas to the external surfaces of the adsorbent particles, axial dispersion and backmixing in the gas phase, and internal transport within the pores. External transport can be correlated by equations similar to those used for mass transfer in packed absorption columns, such as the Ranz-Marshall (1952) equation ... 

The latter relationship is readily derived from a mass balance on the contaminant entering the column. This wave speed is referred to as the stoichiometric wave speed. It applies strictly only to one component. It will be recognized that manipulation of Eq. (9.11) with similar substitutions yields the wave speed result for bulk separations where the derivative of v with respect to the spatial variable does not drop out and where two or more components may adsorb. The result has a very similar form but of course depends on not one isotherm slope but on two or more and very significantly the wave speed depends on the relative mole fractions of the adsorbing species and the initial loadings in the column. 

M mass of solute to be separated N number of effective theoretical plates P pressure Q flow rate R resolution S peak capacity Sm specific heat of mobile phase Ss specific heat of adsorbent Sg specific heat of detector cell walls V volume in conventional units Vo system dead volume Vr retention volume V r corrected retention volume Vm volume of mobile phase in the column Vs volume of stationary phase in the column Ve extra column volume... 

Constant Pattern Behavior In a real system the finite resistance to mass transfer and axial mixing in the column lead to departures from the idealized response predicted by equilibrium theory. In the case of a favorable isotherm the shock wave solution is replaced by a constant pattern solution. The concentration profile spreads in the initial region until a stable situation is reached in which the mass transferrate is the same at all points along the wave front and exactly matches the shock velocity. In this situation the fluid-phase and adsorbed-phase profiles become coincident. This represents a stable situation and the profile propagates without further change in shape—hence the term constant pattern. 

Mark and Saito 31) attempted fractionating polymers by means of chromatography as early as 1936. They filtered solutions of cellulose acetate in acetone through a column with a charcoal-like adsorbent made from blood. The eluate contained the fraction of highest molar mass the rest of the sample was trapped in the column. It could be extracted by dioxane from separated portions of the packing. The largest molecules had travelled farthest. This was in contrast to expectation from Traube s rule and indicated size exclusion. 

The plug-flow model indicates that the fluid velocity profile is plug shaped, that is, is uniform at all radial positions, fact which normally involves turbulent flow conditions, such that the fluid constituents are well-mixed [99], Additionally, it is considered that the fixed-bed adsorption reactor is packed randomly with adsorbent particles that are fresh or have just been regenerated [103], Moreover, in this adsorption separation process, a rate process and a thermodynamic equilibrium take place, where individual parts of the system react so fast that for practical purposes local equilibrium can be assumed [99], Clearly, the adsorption process is supposed to be very fast relative to the convection and diffusion effects consequently, local equilibrium will exist close to the adsorbent beads [2,103], Further assumptions are that no chemical reactions takes place in the column and that only mass transfer by convection is important. 

Interpretation of the adsorption behavior of polypeptides and protein with nonporous HPLC sorbents can thus be based on Eqs. (140)—(143) in which the film mass transfer and surface interaction rates are both considered finite. Simplified cases can be derived from these two relationships for fixed-bed performance409,410,412 where the equilibrium relationship can be expressed by the Langmuir isotherm. Under these isothermal conditions, attainable adsorption capacity of the adsorbent q, which is the amount of the protein retained by the adsorbent when the column reaches saturation, can be expressed by... 

The column void volume, Vo, is dehned as the total volume of the liquid phase in the column and could be measured independently [18]. Total adsorbent surface area in the column, S, is determined as the product of the adsorbent mass and specific surface area. 

Figure 2-5. Illustration of the column shce for construction of mass balance. Mobile-phase flow F in mL/min analyte concentration c in mol/L n is the analyte accumulation in the shce dx in mol v is the mobile-phase volume in the shce dx expressed as VqIL, where L is the column length s is the adsorbent surface area in the shce dx, expressed as S/L, where S is the total adsorbent area in the column.

Other Experimental Methods. It is probably suitable to discuss here column porous structure. Porous space of a conventional packed column consists of the interparticle volume (Vip—space around particles of packing) and pore volume (Vp— space inside porous particles). The sum of those two constitutes the column void volume. The void volume marker ( unretained ) should be able to evenly distribute itself in these volumes while moving through the column. Only in this case the statistical center mass of its peak will represent the true volume of the Uquid phase in the column. In other words, its chromatographic behavior should be similar to that of the eluent molecules in a monocomponent eluent. If a chosen void volume marker compound has some preferential interaction with the stationary phase compared to that of the eluent molecules, it will show positive retention and could not be used as void marker. If on the other hand it has weaker interaction, it will be excluded from the adsorbent surface and will elute faster than the real void time, meaning that it also could not be used. For any analytical applications (when no thermodynamic dependences are not extracted from experimental data), 10% or 15% error in the determination of the void volume are acceptable. It is generally recommended to avoid elution of the component of interest with a retention factor lower than 1.5. Accurate methods for the determination of the column void volume are discussed in Chapter 2. 

Interparticle volume could be measured using GPC as the total exclusion volume of high-molecular-weight polymers, and the void volume could be accurately measured as the elution volume of deuterated acetonitrile eluted with neat acetonitrile. The example of these measurements and comparison with the adsorbent mass determined by unpacking the column and weighing the dried adsorbent are shown in Table 3-5. 

Figure 8.9b shows the movement of the active zone represented by the length d as it advances through the bed at various times. At the beginning of breakthrough, at which the lower end of d barely touches the bottom of the column, the total volume of treated water is represented by Vt. The shaded portion in the curve represents the total breakthrough mass of adsorbate before exhaustion. The total volume of wastewater treated at exhaustion is designated by Vx. 

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