Langmuir term

At A <5C 2RT the two terms become the same. In intermediate ranges, although invariably smaller than the Langmuir term, the second term may be important enough not be to neglected. In that case, even if divided by T, it remains dependent on the temperature. This means that the distribution of the adsorbed gas over the various subsurfaces at a certain over-all 6 depends on the temperature. This makes the procedure for obtaining isosteric heats virtually meaningless. 

The permeation of a gas through a porous polymer is generally described by equations based on the kinetic theory of gases. The sorption isotherm described by Eq. 1 is concave to the pressure axis and is commonly observed for a penetrant gas in a glassy polymer. It is composed of Henry s law and Langmuir-terms [20] ... 

Figure 4.6. The term cq accounts for Henry s law, while Ch is the Langmuir term with b being the hole affinity constant (bar )...

Equation 2.41 represents an additive extension of the modified Langmuir isotherm. The second Langmuir term covers the adsorption of the solute molecules on a second, completely independent group of adsorption sites of the adsorbent. Those... 

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 15.7 Comparison between experimental and calculated band profiles of 2-phenylethanol in gradient elution. Experimental conditions mobile phase flow rate 1 mL/min. initial mobile phase composition 10% ACN in water column temperature 40°C column dead volume Vq = 2.71 mL. Concentration of the sample solution Cq = 132.5 mmol/L. Gradient, 2% ACN/min. Experimental band profiles (square symbols) and profiles calculated using a composite isotherm (linear plus Langmuir terms), taking into account (solid line) or not (dotted line) the adsorption of ACN on the stationary phase, (a) Injection volume, Vj = 4 mL sample size, 0.53 mmol, loading ratio, 29 molecule per 100 bonded groups, (b) Injection volume, Vj = 6 mL sample size, 0.80 mmol, loading ratio, 43 molecule per 100 bonded groups. Reproduced with permission from M.Z. El Fallah and G. Guiochon, Anal. Chem., 63 (1991) 2244 (Fig. 8). ( 1991, American Chemical Society.

Bi-Langmuir isotherm An isotherm model which is the sum of two Langmuir terms (Eq. 3.53). 

It is therefore not surprising that equation 31 fits a variety of curve shapes since) with the Langmuir term expsinded to n = 2 (i.e. equation 32), the relation in fact contains the ratio of two quadratics. Nevertheless, and particularly in view of the successful quantitative interpretation of the Langmuir forms of isotherm equations in the instances of the BET model (equations 7, et seq.) and retentions with blended stationary phases in gas chromatography (equations 14, et seq.), the LC relations cannot be dismissed as entirely empirical since, in any event, although such a connection has yet to be established, whatever interpretations are placed on the fitting constants must presumably involve at least the solute activity coefficients in the mobile and stationary phaises (see below) and, most likely, the (finite-concentration) activity coefficients pertinent to the mobile- and stationary-phase components as well. 

The solubility in glassy polymers is usually described by the so-called dual-mode model, which implies that there is a need for a more detailed definition of the sorption, c, in the flux Equation 7.1. The following Equations 7.20 and 7.21 illustrate this and can be referred to Figure 7.6. The term Cg accounts for Henry s law, while Cu is the Langmuir term with b being the hole affinity constant (bar ) and is the saturation constant (cm [STP]/cm ) ... 

In this equation, rt and q are the adsorbed and the mobile phase concentrations, X is a dimensionless coefficient, and is the equilibrium constant the upper limit of rt is given by N . The linear term describes the interaction of achiral carrier particles with the analyte, while the Langmuir term describes the saturation behavior of the chiral selector. This behavior can be understood by inspection of Fig. 5, which shows in an idealized form the adsorption isotherms of two enantiomers. 

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