Transfer mechanism Langmuir

The simplest case results when a non-localised adsorption is assumed (Baret 1968a, b), so that jjd C(, and r. As the result we obtain Eq. (4.31), where are k j and kj are the rate constants of adsorption and desorption, and c is the bulk concentration of the adsorbing species. On the basis of a localised adsorption the Langmuir mechanism Eq. (4.32) results. Further transfer mechanisms used to describe the kinetics of adsorption are given in Section 4.4, Eqs (4.31) - (4.34). To use these so-called transfer mechanisms for model of dynamic adsorption layers they have to be coupled with the transport process in the bulk. Baret (1969) suggested replacing c by the so-called subsurface or sublayer concentration. This is per definition the bulk concentration adjacent to the adsorption layer c(0,t) localised at x = 0. The following two flux balance equations for the molecular transfer results. 

There are two different ways of deriving the Langmuir adsorption isotherm. One of the derivations is based on kinetic transfer mechanisms of adsorption/desorption of adsorbing molecules. The second, thermodynamic derivation starts from the equivalence of the chemical potentials of adsorbing molecules in the bulk phase and in the adsorbed state. Frumkin (1925) introduced additional interaction forces between adsorbed molecules into the Langmuir adsorption isotherm. 

Further models of adsorption kinetics were discussed in the literature by many authors. These models consider a specific mechanism of molecule transfer from the subsurface to the interface, and in the case of desorption in the opposite direction ((Doss 1939, Ross 1945, Blair 1948, Hansen Wallace 1959, Baret 1968a, b, 1969, Miller Kretzschmar 1980, Adamczyk 1987, Ravera et al. 1994). If only the transfer mechanism is assumed to be the rate limiting process these models are called kinetic-controlled. More advanced models consider the transport by diffusion in the bulk and the transfer of molecules from the solute to the adsorbed state and vice versa. Such mixed adsorption models are ceilled diffusion-kinetic-controlled The mostly advanced transfer models, combined with a diffusional transport in the bulk, were derived by Baret (1969). These dififiision-kinetic controlled adsorption models combine Eq. (4.1) with a transfer mechanism of any kind. Probably the most frequently used transfer mechanism is the rate equation of the Langmuir mechanism, which reads in its general form (cf. Section 2.5.),... 

The most frequently used transfer mechanism is the type Langmuir rate equation, which reads in its general form. 

Following Baret [9] the coupling of transfer mechanisms with the diffusion equation (4.12) can be arranged by replacing the bulk concentration c by the subsurface concentration c(0, t) which for the Langmuir mechanism (4.13) leads to... 

The fluorescence for adsorbed molecules was apparently quenched due to the reduced lifetime of the excited state in a molecule adsorbed at the metal surface as discussed earlier. Quenching due to the energy transfer to the metal can also be observed in molecules that are desorbed but reside in the electrolyte layer near the electrode surface. According to the so-called Forster energy transfer mechanism, observed in the membrane studies [35,40] and in Langmuir-Blodgett films [41], the change of the fluorescence intensity with separation of the fluorescent molecule from the quencher (metal) is described by the formula... 

The effect of on constant pattern profiles for the Langmuir isotherm systems are examined from Eqs. (7-42) and (7-43) and is illustrated in Fig. 7.7 for r = 0.2 and 0.5. Naturally, difference of dominant mass transfer mechanisms is more pronounced at smaller r. 

When chemisorption is involved, or when some additional surface chemical reaction occurs, the process is more complicated. The most common combinations of surface mechanisms have been expressed in the Langmuir-Hinshelwood relationships 36). Since the adsorption process results in the net transfer of molecules from the gas to the adsorbed phase, it is accompanied by a bulk flow of fluid which keeps the total pressure constant. The effect is small and usually neglected. As adsorption proceeds, diffusing molecules may be denied access to parts of the internal surface because the pore system becomes blocked at critical points with condensate. Complex as the situation may be in theory,... 

The diffusion of the electroactive ions is both physical and due to electron transfer reactions.45 The occurrence of either or both mechanisms is a function of the electroactive species present. It has been observed that the detailed electrochemical behaviour of the electroactive species often deviates from the ideal thin film behaviour. For example, for an ideal nemstian reaction under Langmuir isotherm conditions there should be no splitting between the anodic and cathodic peaks in the cyclic voltammogram further, for a one-electron charge at 25 °C the width at half peak height should be 90.6 mV.4 In practice a difference between anodic and cathodic potentials may be finite even at slow scan rates. This arises from kinetic effects of phase formation and of interconversion between different forms of the polymer-confined electroactive molecules with different standard potentials.46... 

Qince the discovery (6) of supported chromium oxide catalysts for polymerization and copolymerization of olefins, many fundamental studies of these systems have been reported. Early studies by Topchiev et al. (18) deal with the effects of catalyst and reaction variables on the over-all kinetics. More recent studies stress the nature of the catalytically active species (1, 2, 9,13, 14,16, 19). Using ESR techniques, evidence is developed which indicates that the active species are Cr ions in tetrahedral environment. Other recent work presents a more detailed look at the reaction kinetics. For example, Yermakov and co-workers (12) provide evidence which suggests that chain termination in the polymerization of ethylene on the catalyst surface takes place predominantly by transfer with monomer, and Clark and Bailey (3, 4) give evidence that chain growth occurs through a Langmuir-Hinshelwood mechanism. 

Langmuir-Blodgett (LB) transfer of a monolayer of an amphiphilic molecule (compressed in a Langmuir trough to fixed area and constant film pressure controlled by mechanical barriers, shown in projection) from the air-water interface onto a solid substrate (glass microscope slide) with a hydrophilic surface hydrophilic end of molecule onto hydrophilic surface. 

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