Separate adsorption isotherm

The separate adsorption isotherms for gases A and B on a certain solid obey the Langmuir equation, and it may be assumed that the mixed or competitive adsorption obeys the corresponding form of the equation. 

Based on capacity factor measurements, a pH of 5.0 was chosen for the separations. Adsorption isotherms were measured and found to exhibit almost ideal Langmuirian behavior for the proteins and for the displacer. In agreement with capacity factor measurements, a displacement performed at pH 5.0 produced an excellent separation of the two proteins (Figure 11.4). 

Until relatively recently, the fact that an experimental isotherm necessarily contained composite information concerning the adsorption of the two components of a binary solution was considered to be a major problem. For a rigorous interpretation it was felt necessary to process the data to obtain the so-called individual adsorption isotherm or separate adsorption isotherm of each component. However, this is not at all straightforward and requires the introduction of a number of assumptions relating to the structure of the adsorbed layer. The main problem is of course to know the composition of the adsorbed layer. One assumption often used in the case of volatile components is that introduced by Williams (1913) the solid will adsorb the same amount of each component from the vapour in equilibrium with the solution as from the solution itself. This of course implies that the adsorbed layer has the same composition at the liquid-solid and gas-solid interfaces and it requires numerous gravimetric measurements from the vapour... 

A somewhat subtle point of difficulty is the following. Adsorption isotherms are quite often entirely reversible in that adsorption and desorption curves are identical. On the other hand, the solid will not generally be an equilibrium crystal and, in fact, will often have quite a heterogeneous surface. The quantities ys and ysv are therefore not very well defined as separate quantities. It seems preferable to regard t, which is well defined in the case of reversible adsorption, as simply the change in interfacial free energy and to leave its further identification to treatments accepted as modelistic. 

Fig. XI-11. Relation of adsorption from binary liquid mixtures to the separate vapor pressure adsorption isotherms, system ethanol-benzene-charcoal (n) separate mixed-vapor isotherms (b) calculated and observed adsorption from liquid mixtures. (From Ref. 143.)...

Some representative plots of entropies of adsorption are shown in Fig. XVII-23, in general, T AS2 is comparable to Ah2, so that the entropy contribution to the free energy of adsorption is important. Notice in Figs. XVII-23 i and b how nearly the entropy plot is a mirror image of the enthalpy plot. As a consequence, the maxima and minima in the separate plots tend to cancel to give a smoothly varying free energy plot, that is, adsorption isotherm. 

One application of the grand canonical Monte Carlo simulation method is in the study ol adsorption and transport of fluids through porous solids. Mixtures of gases or liquids ca separated by the selective adsorption of one component in an appropriate porous mate The efficacy of the separation depends to a large extent upon the ability of the materit adsorb one component in the mixture much more strongly than the other component, separation may be performed over a range of temperatures and so it is useful to be to predict the adsorption isotherms of the mixtures. 

The treatment here is restricted to the Langmuir or constant separation factor isotherm, single-component adsorption, dilute systems, isothermal behavior, and mass-transfer resistances acting alone. References to extensions are given below. Different isotherms have been considered, and the theory is well understood for general isotherms. 

When the adsorption equihbrium is nonlinear, skewed peaks are obtained, even when N is large. For a constant separation-factor isotherm with R < 1 (favorable), the leading edge of the chromatographic peak is steeper than the trailing edge. Wmen R > 1 (unfavorable), the opposite is true. 

For nonlinear systems, however, the evaluation of the flow rates is not straightforward. Morbidelli and co-workers developed a complete design of the binary separation by SMB chromatography in the frame of Equilibrium Theory for various adsorption equilibrium isotherms the constant selectivity stoichiometric model [21, 22], the constant selectivity Langmuir adsorption isotherm [23], the variable selectivity modified Langmuir isotherm [24], and the bi-Langmuir isotherm [25]. The region for complete separation was defined in terms of the flow rate ratios in the four sections of the equivalent TMB unit ... 

Fig. 9-7. Region for complete separation under Equilibrium Theory. Linear adsorption isotherms.

The competitive adsorption isotherms were determined experimentally for the separation of chiral epoxide enantiomers at 25 °C by the adsorption-desorption method [37]. A mass balance allows the knowledge of the concentration of each component retained in the particle, q, in equilibrium with the feed concentration, < In fact includes both the adsorbed phase concentration and the concentration in the fluid inside pores. This overall retained concentration is used to be consistent with the models presented for the SMB simulations based on homogeneous particles. The bed porosity was taken as = 0.4 since the total porosity was measured as Ej = 0.67 and the particle porosity of microcrystalline cellulose triacetate is p = 0.45 [38]. This procedure provides one point of the adsorption isotherm for each component (Cp q. The determination of the complete isotherm will require a set of experiments using different feed concentrations. To support the measured isotherms, a dynamic method of frontal chromatography is implemented based on the analysis of the response curves to a step change in feed concentration (adsorption) followed by the desorption of the column with pure eluent. It is well known that often the selectivity factor decreases with the increase of the concentration of chiral species and therefore the linear -i- Langmuir competitive isotherm was used ... 

Linear case This case is met when the adsorption isotherm is considered linear, which means operation under diluted conditions. Taking into account the saturation capacities of the CSP, this behavior is usually met for concentrations around or below 1 g for separation of enantiomers. 

Current use of statistical thermodynamics implies that the adsorption system can be effectively separated into the gas phase and the adsorbed phase, which means that the partition function of motions normal to the surface can be represented with sufficient accuracy by that of oscillators confined to the surface. This becomes less valid, the shorter is the mean adsorption time of adatoms, i.e. the higher is the desorption temperature. Thus, near the end of the desorption experiment, especially with high heating rates, another treatment of equilibria should be used, dealing with the whole system as a single phase, the adsorbent being a boundary. This is the approach of the gas-surface virial expansion of adsorption isotherms (51, 53) or of some more general treatment of this kind. 

Equation (1) merely states that the general distribution law applies to the system and that the adsorption isotherm is linear. At the concentrations normally employed in liquid chromatographic separations this will be true. 

The upper curve shows the adsorption isotherm that normally occurs in liquid chromatography separations where the concentration of solute in the system is very low. The isotherm is linear and thus the distribution coefficient is constant at all concentrations of solute in either phase. It follows that as the peak velocity is inversely related to the distribution coefficient, all solute concentrations travel at the same velocity through the column and the peak is symmetrical. 

This precipitation process can be carried out rather cleverly on the surface of a reverse phase. If the protein solution is brought into contact with a reversed phase, and the protein has dispersive groups that allow dispersive interactions with the bonded phase, a layer of protein will be adsorbed onto the surface. This is similar to the adsorption of a long chain alcohol on the surface of a reverse phase according to the Langmuir Adsorption Isotherm which has been discussed in an earlier chapter. Now the surface will be covered by a relatively small amount of protein. If, however, the salt concentration is now increased, then the protein already on the surface acts as deposition or seeding sites for the rest of the protein. Removal of the reverse phase will separate the protein from the bulk matrix and the original protein can be recovered from the reverse phase by a separate procedure. 

The main difference between the chromatographic process carried out in the linear and the nonlinear range of the adsorption isotherm is the fact that in the latter case, due to the skewed shapes of the concentration profiles of the analytes involved, separation performance of a chromatographic system considerably drops, i.e., the number of theoretical plates (N) of a chromatographic system indisputably lowers. In these circumstances, all quantitative models, along with semiquantitative and nonquantitative rules, successfully applied to optimization of the linear adsorption TLC show a considerably worse applicability. 

The SH signal directly scales as the square of the surface concentration of the optically active compounds, as deduced from Eqs. (3), (4), and (9). Hence, the SHG technique can be used as a determination of the surface coverage. Unfortunately, it is very difficult to obtain an absolute calibration of the SH intensity and therefore to determine the absolute number for the surface density of molecules at the interface. This determination also entails the separate measurement of the hyperpolarizability tensor jS,-, another difficult task because of local fields effects as the coverage increases [53]. However, with a proper normalization of the SH intensity with the one obtained at full monolayer coverage, the adsorption isotherm can still be extracted through the square root of the SH intensity. Such a procedure has been followed at the polarized water-DCE interface, for example, see Fig. 3 in the case of 2-( -octadecylamino)-naphthalene-6-sulfonate (ONS) [54]. The surface coverage 6 takes the form ... 

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... 

In a separate study, Igwe and Abia46 determined the equilibrium adsorption isotherms of Cd(II), Pb(II), and Zn(II) ions and detoxification of wastewater using unmodified and ethylenediamine tetraacetic acid (EDTA)-modified maize husks as a biosorbent. This study established that maize husks are excellent adsorbents for the removal of these metal ions, with the amount of metal ions adsorbed increasing as the initial concentrations increased. The study further established that EDTA modification of maize husks enhances the adsorption capacity of maize husks, which is attributed to the chelating ability of EDTA. Therefore, this study demonstrates that maize husks, which are generally considered as biomass waste, may be used as adsorbents for heavy metal removal from wastewater streams from various industries and would therefore find application in various parts of the world where development is closely tied to affordable cost as well as environmental cleanliness.46... 

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