Langmuir-type sites

Ch = solubility in the Langmuir type sites Ch = hole saturation constant b = hole affinity constant... 

While the permeability of most rubbery polymers to most gases is pressure independent, the permeability of glassy polymers usually is observed to decline with increasing pressure. This is accounted for by the dual sorption theory if one assumes that both the Henry and Langmuir type sites contribute to per-... 

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 instance, the time course of SPE demonstrates that the solvent phase surfactant concentration steadily decreases (Fig. 3) [58]. The w/o-ME solution s water content decreases at the same rate as the surfactant [58]. The protein concentration at first increases, presumably due to the occurrence of Steps 2 and 3 above, but then decreases due to the adsorption of filled w/o-MEs by the solid phase (Fig. 3) [58]. Additional evidence supporting the mechanism given above is the occurrence of a single Langmuir-type isotherm describing surfactant adsorption in the solid phase for several SPE experiments employing a given protein type (Fig. 4) [58]. Here, solid-phase protein molecules can be considered as surfactant adsorption sites. Similar adsorption isotherms occurred also for water adsorption [58]. 

The model based on formal kinetics was used to model the TPD curves of adsorbed CO molecules, based on the model previously reported [4], The desorption is strongly affected by the fast readsorption of CO on unoccupied Cu+ ions, thus, a quasiequilibrium state is a suitable approximation for the description of adsorption. A Langmuir type of adsorption isotherm was assumed for the CO adsorption on the Cu+ sites in zeolite, without considering lateral interactions among adsorbed molecules. 

Several investigators [7,123] suggested the use of a Langmuir-type saturation model in addition to the electrostatic model to account for saturation effects. The Langmuir model implies that there are a finite number of localised sorption sites [15] ... 

The conditions for the validity of a Langmuir type adsorption equilibrium are i) thermal equilibrium up to the formation of a monolayer, 0 = 1 ii) the energy of adsorption is independent of 0, (i.e., equal activity of all surface sites). There is no difference between a surface complex formation constant and a Langmuir adsorption... 

Kinetic models proposed for sorption/desorption mechanisms including first-order, multiple first-order, Langmuir-type second-order, and various diffusion rate laws are shown in Sects. 3.2 and 3.4. All except the diffusion models conceptualize specific sites to or from which molecules may sorb or desorb in a first-order fashion. The following points should be taken into consideration [ 181,198] ... 

Fig. 20. Schematic adsorption isotherms with a constant surface site concentration ([A]s in Fig. 12 is here constant), but with adsorption time as a variable. At very short times, adsorption is diffusion controlled. At short times, the protein has insufficient time to conformationally adjust to the interface, thus adsorption can be reversible and of the Langmuir type. At longer times, conformational adjustments begin leading to the commonly observed semi- orir-reversible behavior of protein adsorption. Other nomenclature same as Fig. 12...

Co-adsorption and mutual interactions between the reactants on the surface form the basis for understanding the microscopic steps of the reaction. Since product formation takes place rather rapidly above room temperature, this information mainly became available from low-temperature studies. As a result, these processes are much more complicated than can be described by a Langmuir-type adsorption model (i.e., simple competition for free adsorption sites) and, moreover, an asymmetric behavior is found which means that pre-adsorbed CO inhibits the adsorption of oxygen, whereas the reverse is not the case. At very low surface concentrations of CO and Oad these will be randomly distributed over the surface as illustrated schematically by Fig. 32a (88). 

The Langmuir isotherm is based on the simplest model that involves the following assumptions (1) the adsorption energy of all sites is the same and is unaffected by adsorption on neighboring sites, (2) the adsorption is immobile, (3) each site accommodates only one adsorbed particle, and (4) adsorbed atoms (molecules) do not interact with each other. Figure 10.2a shows that the Langmuir-type isotherm for... 

Model II This is a model first given by Halsey and Taylor (41). It assumes a heterogeneous surface made up of a continuous set of homogeneous surfaces. The adsorption on these surfaces is of the Langmuir type i.e., there is no repulsion between adsorbed atoms, and on each surface the adsorption is completely random. The heat of adsorption varies continuously from a maximum value Afu to a minimum value Aht. The density of the sites with the same heat is constant between the two limits... 

A two-site model has been used (18) to model cesium transport in soils. In this model a Langmuir-type model, Equation 3,was used to represent surface sorption and a first-order model, Equation 1, was used to approximate interparticle diffusion. Extraction with CaC was used to verify the exchangeable site inventory. 

The adsorption of cumene and inhibitors on active cracking sites follows a Langmuir type of isotherm. This means that there is little or no interaction among the chemisorbed molecules on the surface. This might be expected to be the case as studies of the chemisorption of the inhibitor quinoline by similar catalyst (14) show that the surface is sparsely covered with active sites (<5% of internal surface area covered with chemisorbed quinoline at 315°C.). In addition, the active sites are homogeneous with respect to adsorption energies. 

Researchers and field practitioners often employ two-site models to describe Langmuir-type behavior. The expression is as follows ... 

If we pursue the model of the catalytic surface as a collection of a fixed number of sites S capable of forming chemical bonds with adsorbed species, then we may expect to find that substances which can compete for the catalytic sites may inhibit the reaction. Furthermore, the effectiveness of the inhibition will depend on the relative pressures of the two adsorbates as well as their sorption constants on the surface. Let us consider as an example the simple Langmuir-type sorption of two sorbates A and B on a surface of S° sites ... 

If there are A max binding sites on the particle surface and we assume 1 1 binding of the Langmuir type, then Sc is given by... 

The mathematical representation of the bilangmuir isotherm in Eq. (7.5) represents interactions on two different types of sites, each of which is described by Langmuir-type interactions. 

Our studies (19) indicated that proteins were readily adsorbed from aqueous solution onto hydrophobic polymer surfaces with Langmuir type adsorption and that the rate of adsorption toward a plateau surface concentration depends on the polymer nature. In the study of competitive adsorption from a protein mixture solution (20), fibrinogen and y-globulin adsorb onto FEP very rapidly compared with PEUU and SR. Therefore, the FEP surface in contact with blood has more acceptor sites for platelet adhesion than does the PEUU or SR surface. 

In obtaining the Langmuir isotherm equations, several aspects of the adsorption system were presupposed in the derivations. The most important of these,and the one that has been subject to the greatest doubt, is that a uniform surface is assumed. In other words, any active site has the same attraction for an impinging molecule as does any other site. Isotherms different from the Langmuir types may be derived based on various assumptions concerning the adsorption system, including different types of nommiform smfaces. 

As we have seen previously, the separation mechanism in pervaporation is explained by an adsorption-diffusion process. In this way, the selective adsorption of the components in the zeolite will be responsible for the selectivity in the separation. Adsorption is an exothermic nonactivated process. In general, the isotherm of adsorption on zeohtes follows a single site Langmuir-type isotherm [74]. 

The transport flux of ethanol for membranes loaded with alcohol dehydrogenase apoenzyme (apo-ADH) is found to be greater than nine times from those obtained for phenol. The flux vs. feed concentration curves for ethanol showed Langmuir-type isotherm. These observations clearly indicate that apo-ADH acted as molecular-recognition sites for ethanol, and it facilitates the transport of ethanol through the membranes. 

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