Langmuir species

Dd Diffusion coefficient of the Henry s law species (cm /sec) Dh Diffusion coefficient of the Langmuir species (cm /sec) Ratio of Langmuir and Henry s law diffusion coefficients Henry s law constant (cm gas (STP)/cm polymer-atm)... 

Petropoulos [20] and Paul and Koros [21] independently developed models where the diffusion of the gas species adsorbed in the Langmuir region is partially, or even totally, immobilized. In this case, a parameter Fa is introduced, defined either as the ratio of diffusion coefficients in the Langmuir (Du) and Henry s Law region (Do) or as the fraction of the Langmuir species that are fully mobile. In this case, the concentration of mobile species is given by ... 

Langmuir adsorption isotherm A theoretical equation, derived from the kinetic theory of gases, which relates the amount of gas adsorbed at a plane solid surface to the pressure of gas in equilibrium with the surface. In the derivation it is assumed that the adsorption is restricted to a monolayer at the surface, which is considered to be energetically uniform. It is also assumed that there is no interaction between the adsorbed species. The equation shows that at a gas pressure, p, the fraction, 0, of the surface covered by the adsorbate is given by ... 

Although still used the Langmuir equation is only of limited value since in practice surfaces are energetic inhomogeneous and interactions between adsorbed species often occur. 

Various functional forms for / have been proposed either as a result of empirical observation or in terms of specific models. A particularly important example of the latter is that known as the Langmuir adsorption equation [2]. By analogy with the derivation for gas adsorption (see Section XVII-3), the Langmuir model assumes the surface to consist of adsorption sites, each having an area a. All adsorbed species interact only with a site and not with each other, and adsorption is thus limited to a monolayer. Related lattice models reduce to the Langmuir model under these assumptions [3,4]. In the case of adsorption from solution, however, it seems more plausible to consider an alternative phrasing of the model. Adsorption is still limited to a monolayer, but this layer is now regarded as an ideal two-dimensional solution of equal-size solute and solvent molecules of area a. Thus lateral interactions, absent in the site picture, cancel out in the ideal solution however, in the first version is a properly of the solid lattice, while in the second it is a properly of the adsorbed species. Both models attribute differences in adsorption behavior entirely to differences in adsorbate-solid interactions. Both present adsorption as a competition between solute and solvent. 

Ref. 205). The two mechanisms may sometimes be distinguished on the basis of the expected rate law (see Section XVni-8) one or the other may be ruled out if unreasonable adsorption entropies are implied (see Ref. 206). Molecular beam studies, which can determine the residence time of an adsorbed species, have permitted an experimental decision as to which type of mechanism applies (Langmuir-Hinshelwood in the case of CO + O2 on Pt(lll)—note Problem XVIII-26) [207,208]. 

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

The first step consists of the molecular adsorption of CO. The second step is the dissociation of O2 to yield two adsorbed oxygen atoms. The third step is the reaction of an adsorbed CO molecule with an adsorbed oxygen atom to fonn a CO2 molecule that, at room temperature and higher, desorbs upon fomiation. To simplify matters, this desorption step is not included. This sequence of steps depicts a Langmuir-Hinshelwood mechanism, whereby reaction occurs between two adsorbed species (as opposed to an Eley-Rideal mechanism, whereby reaction occurs between one adsorbed species and one gas phase species). The role of surface science studies in fomuilating the CO oxidation mechanism was prominent. 

The main supramolecular self-assembled species involved in analytical chemistry are micelles (direct and reversed), microemulsions (oil/water and water/oil), liposomes, and vesicles, Langmuir-Blodgett films composed of diphilic surfactant molecules or ions. They can form in aqueous, nonaqueous liquid media and on the surface. The other species involved in supramolecular analytical chemistry are molecules-receptors such as calixarenes, cyclodextrins, cyclophanes, cyclopeptides, crown ethers etc. Furthermore, new supramolecular host-guest systems arise due to analytical reaction or process. 

Adsorbed molecules are more strongly held at the sites where the weakest metal-metal bonding is to be found, and these conespond to the active sites of Langmuir. A demonstration of this effect was found in smdies of the adsorption of H2S from a H2S/H2 mixture on a single crystal of copper of which die separate crystal faces had been polished and exposed to die gas. The formation of copper sulphide first occuiTed on die [100] and [110] planes at a lower H2S partial pressure dran on die more densely packed [111] face. Thus die metal atoms which are less strongly bonded to odrer metal atoms can bond more strongly to die adsorbed species from die gas phase. 

The model is intrinsically irreversible. It is assumed that both dissociation of the dimer and reaction between a pair of adjacent species of different type are instantaneous. The ZGB model basically retains the adsorption-desorption selectivity rules of the Langmuir-Hinshelwood mechanism, it has no energy parameters, and the only independent parameter is Fa. Obviously, these crude assumptions imply that, for example, diffusion of adsorbed species is neglected, desorption of the reactants is not considered, lateral interactions are ignored, adsorbate-induced reconstructions of the surface are not considered, etc. Efforts to overcome these shortcomings will be briefly discussed below. 

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 ... 

If the three-parameter Michaelis-Menten equation is divided by C i, it becomes the same as the three-parameter Langmuir-I linshelwood equation where 1/Cm = Ka. Both these rate equations can become quite complex when more than one species is competing with the reactant(s) for the enzyme or active sites on the solid catalyst. 

Its main features are given by the use of a stream of inert carrier gas which percolates through a bed of an adsorbent covered with adsorbate and heated in a defined way. The desorbed gas is carried off to a detector under conditions of no appreciable back-diffusion. This means that the actual concentration of the desorbed species in the bed is reproduced in the detector after a time lag which depends on the flow velocity and the distance. The theory of this method has been developed for a linear heating schedule, first-order desorption kinetics, no adsorbable component in the entering carrier gas (Pa = 0), and the Langmuir concept, and has already been reviewed (48, 49) so that it will not be dealt with here. An analysis of how closely the actual experimental conditions meet the idealized model is not available. 

We now examine what happens to the modified electrochemical Langmuir isotherm (Eq. 6.36) when AO is created only by the presence of the adsorbate j, i.e. in absence of any coadsorbing ionic species. Substituting equation (6.49) into equation (6.36) and expressing AO via the Helmholz equation (5.16) one obtains ... 

Examples of Hougen-Watson kinetic models, which are also called Langmuir-Hinshelwood models, can be derived for a great variety of assumed surface mechanisms. See Butt and Perry s Handbook (see Suggestions for Further reading in Chapter 5) for collections of the many possible models. The models usually have numerators that are the same as would be expected for a homogeneous reaction. The denominators reveal the heterogeneous nature of the reactions. They come in almost endless varieties, but all reflect competition for the catalytic sites by the adsorbable species. 

In Langmuir-Hinshelwood kinetics is it assumed that all species are adsorbed and accommodated (in thermal equilibrium) with the surface before they take part in any reactions. Hence, species react in the chemisorbed state on the surface. This is the prevailing situation in heterogeneous catalysis. 

In essence, we have used the Langmuir isotherms for the adsorbing and desorbing species. By substituting the coverages into the rate expression for the ratedetermining step we obtain... 

All of these rates are measured on surfaces shown to be clean by AES, and this Indicates that these processes occur on surfaces containing only submonolayer coverages of reactant species, exactly the situation required for the Langmuir-Hinshelwood model of surface reactions. 

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