Surface-barrier model

Analytical equations for adsorbate uptake and radial adsorbent temperature profiles during a differential kinetic test are derived. The model assumes that the mass transfer into the adsorbent can be described by a linear driving force model or the surface barrier model. Heat transfer by Fourier conduction inside the adsorbent mass in conjunction with external film resistance is considered. 

Comparisons of estimated diffusivity values on zeolites from sorption uptake measurements and those obtained from direct measurements by nuclear magnetic resonance field gradient techniques have indicated large discrepancies between the two for many systems [10]. In addition, the former method has often resulted in an adsorbate diffusivity directly proportional to the adsorbent crystal size [11]. This led some researchers to believe that the resistance to mass transfer may be confined in a skin at the surface of the adsorbent crystal or pellet (surface barrier) [10,11]. The isothermal surface barrier model, however, failed to describe experimental uptake data quantitatively [10,12]. 

Diffusion with Surface-Resistance or Surface-Barrier Model. 247... 

Surface Barrier Model (Langmuir Kinetics Model). 294... 

Recently, different approaches to describe the kinetics of oxygen and nitrogen sorption in carbon molecular sieves have been presented. It has been shown that they can lead, as particular cases, to the two above mentioned mechanisms. Srinivasan et al. [18] proposed a surface barrier model of diffusion under a chemical potential gradient, while Trifonov and Golden [19] presented a theoretical approach based on a hopping mechanism, in which the molecules jump from occupied to free adsorption sites. Seaton et al. [20] carried out molecular dynamics simulation of diffusion in individual pores and in pore networks. The experimental selectivity can be reproduced both at the level of individual pores, as well as with pore networks having a wide range of pore sizes. 

Koresh J, Soffer A (1981) Molecular sieve carbons. Part 3. Adsorpton kinetics according to a surface barrier model. J Chem Soc Faraday Trans 177 (12) 3005-3018 Koresh JE, Soffer A(1983) Molecular sieve carbon permselective membrane. Part I. Presentation of a new device for gas mixture separation. Sep Sci Technol 18 (8) 723-734 Koresh JE, Soffer A(1986) Mechanism of permeation through molecular-sieve carbon membrane. Part 1. The effect of adsorption and the dependence on pressure. J Chem Soc Faraday Trans 1 82 (7) 2057-2063... 

In conduction models of semiconductor gas sensors, surface barriers of intergranular contacts dominate the resistance. Electrons must overcome this energy barrier, eV., in order to cross from one grain to another. For these... 

The interfacial barrier theory is illustrated in Fig. 15A. Since transport does not control the dissolution rate, the solute concentration falls precipitously from the surface value, cs, to the bulk value, cb, over an infinitesimal distance. The interfacial barrier model is probably applicable when the dissolution rate is limited by a condensed film absorbed at the solid-liquid interface this gives rise to a high activation energy barrier to the surface reaction, so that kR kj. Reaction-controlled dissolution is somewhat rare for organic compounds. Examples include the dissolution of gallstones, which consist mostly of cholesterol,... 

If the space charge in the semiconductor arises from the ionization of impurities only, as in the model we have used, the surface barrier is termed a Schottky barrier. The barrier region near the surface of the crystal is sometimes called the exhaustion region, as the mobile electrons have been removed from this region (16). 

Weisz (22) derives quantitative expressions for the heat of adsorption, the rate of adsorption, and the amount of adsorption, for a simple model. The model used involves a simple surface barrier of the type in Fig. 5, with adsorption traps as the only surface traps, and where, if the system reaches equilibrium, adsorption occurs until the adsorption traps are at the energy of the Fermi level. Weisz shows that the surface cannot become... 

The above discussion of the band model and its application to a description of equilibrium chemisorption has been brief and incomplete. It is not the principal purpose in this paper to discuss surface barrier effects in equilibrium chemisorption, but rather surface barrier effects in the irreversible region of chemisorption. However, before we begin the consideration of these latter effects, we will digress and examine the basic properties of zinc oxide, which material will be used both as motivation and as illustration in the following text. 

Considering the method of preparation of these ZnO samples, these results correspond to what one would expect on the basis of the adsorption model. The samples were sintered or evaporated at some high temperature, and then cooled to room temperature in air. As discussed in Section IV, 1, adsorption will occur until the rate of electrons crossing the surface barrier is pinched off to zero at room temperature. If the temperature is now lowered below room temperature, no electron transfer will be possible between the surface level and the bulk of the solid due to this high surface barrier. Thus the surface levels will be isolated and unable to affect the conductivity, which will therefore reflect bulk properties of the zinc oxide. 

The frozen in photoconductivity, as was concluded by Melnick, will arise from effects of the surface barrier layer or, of course, would arise similarly from any other rate-limiting process in the adsorption of oxygen. For our model in this discussion we shall use electron transfer over the surface barrier as the rate-limiting reaction. In this case, the rate at which adsorption occurs is proportional to exp ( —Ei/kT), where E2 is the barrier height. Thus if we measure the decay in photoconductivity (the chemisorption of oxygen) at room temperature, and then suddenly quench the sample to 130°K, it is obvious that the rate of decay in photoconductivity will decrease considerably. The change in the rate will be dependent on Ei and the temperature to which the sample is quenched. 

The results in sections 2 and 3 describe the adsorption isotherms and diffusivities of Xe in A1P04-31 based on atomistic descriptions of the adsorbates and pores. The final step in our modeling effort is to combine these results with the macroscopic formulation of the steady state flux through an A1P04-31 crystal, Eq. (1). We make the standard assumption that the pore concentrations at the crystal s boundaries are in equilibrium with the bulk gas phase [2-4]. This assumption cannot be exactly correct when there is a net flux through the membrane [18], but no accurate models exist for the barriers to mass transfer at the crystal boundaries. We are currently developing techniques to account for these so-called surface barriers using atomistic simulations. 

The LDF model is a realistic representation of the system with a surface barrier. Otherwise, k can be treated as an apparent mass transfer coefficient irrespective of the true transport mechanism which can be directly used in the design and optimization of adsorbers. This concept has been successfully used to analyze column breakthrough data for practical non-isothermal systems [18-20]. It substantially... 

The same term is sometimes used to describe the potential-distance relations in semiconductors with a low concentration of surface states (hence the term Schottky barrier model ). However, as can be understood by a reconsideration of the mechanism there (see Figs. 10.6 and 10.7), the so-called barrier is either used for the acceleration of electrons in p-type cathodes or the electrodiffusion of holes to the surface in n-type anodes. Nevertheless, the term barrier is still applied. 

The first step was the evolution away from the Schottky barrier model of photoelectrochemistry caused by the evidence from the late 1970s onward that the rate of photoelectrochemical reactions was heavily dependent on surface effects (Uosaki, 1981 Szklarczyk, 1983). This was followed by the use of both a photocathode and a photoanode in the same cell (Ohashi, 1977). Then the use of nonactive thin protective passive layers of oxides and sulfides allowed photoanodes to operate in potential regions in which they would otherwise have dissolved (Bockris and Uosaki, 1977). The final step was the introduction of electrocatalysis of both hydrogen and oxygen evolution by means of metal islets of appropriate catalytic power (Bockris and Szklarczyk, 1983). 

The overreliance on the Schottky barrier model for reactions involving adsorbed intermediates must be revised to take into account the high surface state concentration to which they often give rise. This position is emphasized in that the most obvious environmental use of photoelectrochemistry is in splitting water to produce clean hydrogen. 

Although the Schottky barrier model (negligible surface states) is applicable for some electrochemical reactions involving redox species and electrode reactions with no surface bonding of intermediate radicals, most practical, useful photoelectrochemical reactions involve significant numbers of surface states. Draw the potential-distance relations for the corresponding Helmholtz approximation (a) for a photocathode and (b) for a photoanode. (Bockris)... 

Figure 1 Schematic energy diagram for the DIET process due to the MGR model illustrating the relaxation and desorption processes. Electronic excitation due to laser irradiation occurs via the Franck-Condon transition. After a residue time t at the intermediate excited state, relaxation occurs with an excess energy ZA surpassing the surface barrier for desorption. The value of depends strongly on t, and no desorption occurs when t is shorter than the critical residence time tc. The Absicissa is the adsorbate-substrate distance.

In this model,110 it was assumed that all C 2H bonds perform thermally activated rotational jumps within energy landscapes on the surface of a cone. Specifically, six basins were supposed to be separated by six energy barriers at positions 0, 60,..., 300° around the axis of the cone. For each cone, the barriers were drawn anew from the distribution of activation energies determined for TOL in DS.12,19 Further, it was assumed that all positions on the surface of the cone, except for the barriers, have the same energy, i.e., a random-barrier model was considered. The thermally activated jumps lead to a random new position in one of the two neighboring basins. This means that several back-and-forth jumps occur over relatively low energy barriers until relatively high barriers are crossed. In other words, many... 

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