Energy heterogeneous

Photocatalytic Conversion of Solar Energy. Heterogeneous, Homogeneous and Molecular Structurally-Organized Systems. K. I. Zamaraev and V. N. Parmon (Eds.), Nauka, Novosibirsk (1991) (in Russian). 

So far in this discussion, the contribution of an electric moment interaction with an ionic field has been neglected. This is justifiable on the basis of the observed results, but Kington and Macleod (11) recently found a correlation between a heat of adsorption term and the permanent quadrupole moment of the gas involved, and from this correlation they concluded that a major part of the energy heterogeneity in adsorption may be laid to the interaction between the quadrupole and the position-dependent field gradient in the solid. It is therefore necessary to examine this idea in the present context. 

Thus there are compelling reasons for regarding the initiation step (la) as a low activation energy heterogeneous process at low temperatures. In any case from estimates of ki (homogeneous) for acetaldehyde and propionaldehyde made by Baldwin et al. [21, 22] a value for ja for 40 kcal. mole" was calculated. Although this may represent an upper limit (see also Sect. 4.4), it is obvious that the rate of (la) in the gas phase below 200 °C is far too low to allow the oxidation to get started. 

It seems we have matured to the realization that any influential effects must imply involvement through some sort of force fields between catalyst and reaction partners we acknowledge these forces to be electronic and therefore chemical in nature, and thus we imply the existence of at least temporary chemical complex or bond formation with the catalyst. Clearly then, the n-body problem of chemistry (e.g., of A and B) becomes at least an (2n- - l)-body problem (A, B X AX, BX) of catalytic chemistry (even before we worry about such strictly additional problems as energy heterogeneity of sites, polyfunctional catalysis, side reactions, etc.). 

The adsorption of long chain ionic amphiphiles can be described by a model which accounts for potential energies, entropic terms in the adsorbed layer and surface energy heterogeneity of the adsorbent in the case of localized adsorption [10-12]. This is limited to the case where the adsorbate can form precipitates with the ions in equilibrium with... 

Formation of such droplets must then be an activated process whose rate is proportional to exp [—AF /(A 7 ]. We can estimate this rate using equation (4.2.6) for the interfacial energy y, and the result is that the rate of homogeneous nucleation we should expect for polymer systems is vanishingly small. In practice nucleation is usually aided by the presence of other interfaces, for example impurity particles such as dust or the container walls may well be able to nucleate critical droplets with much lower activation energies (heterogeneous nucleation) or indeed with no activation energy at all. We will return to this subject in section 5.3 when we discuss the effects of surfaces on phase separation. 

Many researchers [124-128] recognized the role of the micropore size distribution (MPSD) in the study of adsorption equilibria on activated carbon, The MPSD model [126] is based on the idea that adsorption energy heterogeneity is induced by structural heterogeneity, which can be characterized by the size distribution of the slit-shaped micropores. The MPSD is an intrinsic property of activated carbon, and in physical adsorption it dictates the adsorption equilibria through the dispersive interaction between adsorbate and the microporous network of activated carbon. 

Heterogeneous nucleation occurs on the surface of impurities. These may exist in arty system or special additives can be added to facilitate heterogeneous nucleation. Any interface with another material has potential importance for nucleation. Examples include a free surface, the wall of a container, embedded particle, an interphase boundary in a liquid or solid, and a grain or domain boundary in a solid. All such interfaces have positive free energies. Heterogeneous nucleation faces much smaller barrier towards phase transi-... 

Steepness of the isotherm beyond the monolayer region, that is, point B or where the knee is located, is a direct reflection of the surface energy heterogeneity. Mathematically, the factor s in the Unilam (i.e., uniform Langmuir) isotherm is an indicator of the steepness of this portion of the isotherm, and is hence referred to as the heterogeneity parameter. The Unilam isotherm has been discussed by Valenzuela and Myers (1989) and by Do (1998). It is given by ... 

Sikavitsas, V.I., and Yang. R.T., Predicting multicomponent diffusivities for diffusion on surfaces and in molecular sieves with energy heterogeneity, Chem. Eng. Sci.. 50( 19), 3057-3066 (1995). 

This difficulty can be removed by ascribing the DR behaviour on non-porous surfaces to their intrinsic energy heterogeneity, and modifying the original expression according to the suggestions inferred from this assumption. 

The heat capacity is generally beheved to be related to an energy heterogeneity of the sample with a known local law. 

The adsorption-desorption kinetics are sometimes assumed to be related to energy heterogeneity however, not only are the local kinetics unknown (although in a certain family) but also the basic assumptions are uncertain. 

Dubinin-Radushkevich [10] also developed a theory based on the assumption that the surface energy of adsorption varies. Thus, de Dubinin-Radushkevich indicated that the adsorption occurs at low pressures, yet underestimated. The de Dubinin-Radushkevich equation introduces a new relative parameter accounting the energy heterogeneity of the surface. 

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