Saturation capacity constant

EFFECT OF SATURATION CAPACITY CONSTANTS AND OPERATING PARAMETERS... 

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... 

Type I isotherms [3] are char8u terized by an as)onptotic approach to a saturation cap8u ity with increasing pressure. This class of isotherms is most commonly observed for gases or vapors (water is an exception) adsorbed in zeolites or activated carbon. A t3rpical set of Type 1 adsorption isotherms is shown in Fig. 1. Several questions may be asked about sets of isotherms like these. How is the saturation capacity measured Is the saturation capau i1y a constant or does it decrease with temperature as suggested by Fig. 1 ... 

The high pressure adsorption of single gases and mixtures can be predicted from the low pressure (sub-atmospheric) data for the same systems. The optimum temperature for measuring the aulsorption of single gases is near their critical temperature where both the Henry s constant auid the absolute saturation capacity can be determined accurately. 

Adsorption equilibrium was represented by extended Langmuir isotherm with the same saturation capacity (qs) for both adsorbates and constants (bj) following Arrhenius temperature dependence ... 

Figure 2. Effect ofNaCi on saturation capacity (q ) and equilibrium constant (K).

Knowledge of the association constants between the template and the monomer in solution may thus be used to predict suitable starting concentrations of monomer and template, leading to a larger fraction of high affinity sites. The latter parameter is of particular importance when the template is available only in small amounts, when it is poorly soluble in the common diluents or for analytical applications, when only a limited saturation capacity is required. In such cases it has proven possible to reduce the template coneentration by more than a factor of 10 without significant loss of the recognition properties of the material [106]. 

Equation (5) is an equation-of-state for the adsorption of a pure gas as a function of temperature and pressure. The constants of this equation are the Henry constant, the saturation capacity, and the virial coefficients at a reference temperature. The temperature variable is incorporated in Equation (5) by the virial coefficients for the differential enthalpy. This equation-of-state for adsorption of single gases provides an accurate basis for predicting the thermodynamic properties and phase equilibria for adsorption from gaseous mixtures. 

Here a is the equilibrium or Henry constant at infinite dilution, a is also equal to the initial slope of the adsorption isotherm. The coefficient b is the equilibrium constant per unit of surface area, and hence this coefficient is related to the adsorption energy. C is the mobile phase concentration of the analyte in equilibrium with q, the concentration of the analyte in the stationary phase. The monolayer capacity, qs (qs = alb) is the upper limit of concentration in the stationary phase (sometimes called specific saturation capacity of the stationary phase). The Langmuir equation can also be written as ... 

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],... 

Modified multi-component Langmuir and multi-component Bi-Langmuir isotherms offer a maximum flexibility for adjustment to measured data if all coefficients are chosen individually. But in the same way as for multi-component Langmuir isotherms (Eq. 2.43) it is possible to use, for Eqs. 2.47 and 2.48, constant Langmuir terms (by = by, bjy = b]i , b2y = b2u) as well as constant adjustment terms (Xj = X) or equal saturation capacities (qsaUii = [Pg.37]

Figure 3.14 Equilibrium isotherms for (R)- and (S)- Propranolol on Cel-7A at increasing pH, see data in Figure 3.13. Plots of the saturation capacity (Left) of the three retention mechanisms and of their binding constants (Right) versus the pH of the mobile phase. Enantioselective interactions of S-propranolol (1) and of R-propranolol (2), and nonselec-tive interactions of either enantiomers (3). NB. In both figures, the left y-axis corresponds to lines 1 and 2 the right y-axis to line 3. Reproduced with permission from T. Fomstedt, G. Gotmar, M. Andersson, G. Guiochon, f. Am. Chem. Soc., 121 (1999) 1164 (Figs. 7 and 8). (g)1999, American Chemical Society.

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]. 

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