Langmuir binding isotherms

Figure 2.7 One-site Langmuir binding isotherms of propranolol to MIP and CP beads (0 25-50 pm). Data points are the mean values of three replicates and standard deviations are indicated with error bars (data...

The Langmuir adsorption isotherm for radioligand binding [A ] to a receptor to form a radioligand-receptor complex [A R] can be rewritten in terms of one where it is not assumed that receptor binding produces a negligible effect on the free concentration of ligand ([A free]) ... 

Figure 5 also shows the effect of the ionophore concentration of the Langmuir type binding isotherm. The slope of the isotherm fora membrane with 10 mM of ionophore 1 was roughly three times larger than that with 30 mM of the same ionophore. The binding constant, K, which is inversely proportional to the slope [Eq. (3)], was estimated to be 4.2 and 11.5M for the membranes with 10 mM and 30 mM ionophore 1, respectively. This result supports the validity of the present Langmuir analysis because the binding constant, K, should reflect the availability of the surface sites, the number of which should be proportional to the ionophore concentration, if the ionophore is not surface active itself In addition, the intercept of the isotherm for a membrane with 10 mM of ionophore 1 was nearly equal to that of a membrane with 30 mM ionophore 1 (see Fig. 5). This suggests the formation of a closest-packed surface molecular layer of the SHG active Li -ionophore 1 cation complex, whose surface concentration is nearly equal at both ionophore concentrations. On the other hand, a totally different intercept and very small slope of the isotherm was obtained for a membrane containing only 3 mM of ionophore 1. This indicates an incomplete formation of the closest-packed surface layer of the cation complexes due to a lack of free ionophores at the membrane surface, leading to a kinetic limitation. In this case, the potentiometric response of the membrane toward Li+ was also found to be very weak vide infra).

For the Langmuir adsorption isotherm it is assumed that this reaction (Eq. 1) has a fixed free energy of adsorption equal to AG°, which is not dependent on the extent of adsorption and not affected by interaction among sites. In addition, each site is assumed to be capable of binding at most one molecule of adsorbate. If Q is the maximum number of moles of a pollutant adsorbed per mass adsorbent when the surface sites are saturated with an adsorbate (i.e., a full monolayer), and q is the number of moles of adsorbate per mass adsorbent at equilibrium, then according to the law of mass action Eq. (2) follows ... 

CI2 evolution reaction, 38 56 electrochemical desorption, 38 53-54 electrode kinetics, 38 55-56 factors that determine, 38 55 ketone reduction, 38 56-57 Langmuir adsorption isotherm, 38 52 recombination desorption, 38 53 surface reaction-order factor, 38 52 Temkin and Frumkin isotherm, 38 53 real-area factor, 38 57-58 regular heterogeneous catalysis, 38 10-16 anodic oxidation of ammonia, 38 13 binding energy quantification, 38 15-16 Haber-Bosch atrunonia synthesis, 38 12-13... 

We extend the model of the previous section. Instead of one regulatory site we now have two sites, say R and / 2, which are identical and bind the effector R (Fig. 8.9). We still have one active site A, hence in the absence of the effector the binding isotherm 0 (Q, Cg = 0) is a simple Langmuir curve. 

The binding energy in field adsorption can be derived from consideration of the kinetics of field adsorption. Specifically, it can be determined from a temperature dependence of the probability of field adsorption on an adsorption site, or the degree of coverage of field adsorption on a plane. As will be shown, a consideration of the probability of field adsorption based on adsorption time and desorption time leads to an equation equivalent to the Langmuir adsorption isotherm, but specific to the problem of field adsorption.112115 Let us focus on one surface atom. The average time it takes to have an image gas atom field adsorbed on the surface atom, ra, is... 

Furthermore, in 3.3 we turn to reactive binary ion-exchange. An equilibrium binding reaction (adsorption) with a Langmuir-type isotherm is considered. Formation of sharp propagating concentration fronts is studied via an unconventional asymptotic procedure [1]. 

The binding energy of one CH2 group in apolar chains can also be determined by using the constantsand A from the Langmuir and Temkin isotherm, resp. In the case of the Langmuir adsorption isotherm we obtain the following equation for two different n ... 

The concentration-dependent binding of Ru(dcb)-based sensitizers is well described by the Langmuir adsorption isotherm model from which adduct formation constants of 10 have typically been abstracted [123, 132]. While it is often stated that monolayer coverage of the sensitizers is achieved, this is difficult to prove. The colloidal nature of the films makes absolute surface area determinations almost impossible. There is no evidence for multilayer formation, so the surface coverage is at most monolayer and probably sub-monolayer in most cases. The surface coverage for sensitzers in a 1 cm geometric area is typically 10 mol, where 10 mol cm would be expected for a close-packed monolayer of 14 A diameter sensitizers on a flat surface. 

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