Heterogeneity energetical

M. R. Baer, Thermochemica Acta, 384, 351 (2002). Modeling Heterogeneous Energetic... 

Bulnes, F., Pereyra, V., Bdccardo, J.L., and Zgrablich, G. (1999). Effects of the heterogeneous energetic topography on the collective motion of adsorbed particles. J. Chem. Phys., Ill, 1. 

Studies of typical nanomaterials (soil mineral components, adsorbents, silica gels with deposited proteins, so called smart surfaces, latexes, synthetic zeolites modified by ions, MCM-41 molecular sieves) were made earlier by the author of this chapter [11-17]. At present our research focuses on studies of surface properties (e.g. adsorption capacity), total heterogeneity (energetic and geometrical) of surface layers, as well as structures and phase transformations of... 

From the earliest days, the BET model has been subject to a number of criticisms. The model assumes all the adsorption sites on the surface to be energetically identical, but as was indicated in Section 1.5 (p. 18) homogeneous surfaces of this kind are the exception and energetically heterogeneous surfaces are the rule. Experimental evidence—e.g. in curves of the heat of adsorption as a function of the amount adsorbed (cf. Fig. 2.14)—demonstrates that the degree of heterogeneity can be very considerable. Indeed, Brunauer, Emmett and Teller adduced this nonuniformity as the reason for the failure of their equation to reproduce experimental data in the low-pressure region. 

If the surface of the adsorbent is energetically heterogeneous rather than homogeneous each step of the isotherm will be replaced by an assortment of steps, corresponding to the completion of a monolayer on the different homogeneous patches of the surface. If the steps are sufficiently numerous... 

In practice the kinetics are usually more complex than might be expected on this basis, siace the activation energy generally varies with surface coverage as a result of energetic heterogeneity and/or sorbate-sorbate iateraction. As a result, the adsorption rate is commonly given by the Elovich equation (15) ... 

At low adsorbate loadings, the differential heat of adsorption decreases with increasing adsorbate loadings. This is direct evidence that the adsorbent surface is energetically heterogeneous, ie, some adsorption sites interact more strongly with the adsorbate molecules. These sites are filled first so that adsorption of additional molecules involves progressively lower heats of adsorption. 

AH practical adsorbents have surfaces that are heterogeneous, both energetically and geometrically (not all pores are of uniform and constant dimensions). The degree of heterogeneity differs substantially from one adsorbent type to another. These heterogeneities are responsible for many nonlinearities, both in single component isotherms and in multicomponent adsorption selectivities. 

Heterogeneous Ideal Adsorbed S olution TheoTy (HIAST). This IAS theory has been extended to the case of adsorbent surface energetic heterogeneity and is shown to provide improved predictions over lAST (12). 

Jaroniec, M., Gilpin, R. K., Kaneko, K. and Choma, J., Evaluation of energetic heterogeneity and microporosity of activated carbon fibers on the basis of gas adsorption isotherms, Langmuir, 1991, 7(1 1), 2719 2722. 

Computer Simulations and Theory of Adsorption on Energetically and Geometrically Heterogeneous Surfaces... 

In addition to purely energetical heterogeneity one should also take into account some basic aspects of possible heterogeneities resulting from geometrical effects. The simplest and yet experimentally quite important geometric effects are due to the finite size of crystallites. Experimental measurements ave clearly demonstrated that the size of typical crystallites may be quite small (of the order of 50-100 A [116,132] and quite large (of the order of 10 A [61]. 

The question we ask here is whether the surface heterogeneity, either energetical or geometrical, changes the properties of the critical region and whether the transition retains its second-order character. 

Similarly to the previously considered case of the first-order transitions, the above picture applies to a specific situation in which the sample exhibits just one type of crystallites, all of the same size, and where we neglect the effects of energetical heterogeneity that are bound to be present at the crystallite boundaries. In real samples one expects to find a distribution of the crystallite sizes, and hence more complex behavior. 

Another special case of weak heterogeneity is found in the systems with stepped surfaces [97,142-145], shown schematically in Fig. 3. Assuming that each terrace has the lattice structure of the exposed crystal plane, the potential field experienced by the adsorbate atom changes periodically across the terrace but exhibits nonuniformities close to the terrace edges [146,147]. Thus, we have here another example of geometrically induced energetical heterogeneity. Adsorption on stepped surfaces has been studied experimentally [95,97,148] as well as with the help of both Monte Carlo [92-94,98,99,149-152] and molecular dynamics [153,154] computer simulation methods. 

The kinetic factor is proportional to the energetic state of the system and (for heterogeneous catalytic systems) the number of active sites per unit volume (mass) of catalyst. The driving-force group includes the influence of concentration and distance from chemical equilibrium on the reaction rate, and the hindering group describes the hindering effect of components of the reaction mixture on the reaction rate. The kinetic factor is expressed as the rate constant, possibly multiplied by an equilibrium constant(s) as will be shown later. 

At mercury electrodes the geometric and actual surface areas are identical. There is no site on the electrode that is energetically preferable to any other site (except for the deposition of heterogeneous patches). Except at rather positive potentials, the mercury electrode is usually not covered with a film of insoluble oxides or other compounds. 

Unlike solid state -stacks, however, double helical DNA is a molecular structure. Here CT processes are considered in terms of electron or hole transfer and transport, rather than in terms of material conductivity. Moreover, the 7r-stack of DNA is constructed of four distinct bases and is therefore heterogeneous and generally non-periodic. This establishes differences in redox energetics and electronic coupling along the w-stack. The intimate association of DNA with the water and counterions of its environment further defines its structure and contributes to inhomogeneity along the mole-... 

Heterogeneous catalysis is by nature a surface phenomenon. An efficient catalytic system under reactive conditions demands a delicate energetic balance. For a catalytic reaction to occur, reactant molecules must adsorb on a surface, react, and... 

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