Quasi-homogeneous surfaces

The contradiction in Equation (1) concerning the homogeneity and heterogeneity of the surface is eliminated by accepting the theory of quasi-homogeneous surfaces developed in some detail by the author (22). A quasi-homogeneous surface is one, the two different active centers of which are characterized by a constant ratio... 

At the same time the zr are constant over the entire quasi-homogeneous surface ... 

The results obtained for quasi-homogeneous surfaces can be used for the interpretation of data derived for heterogeneous surfaces. 

This monomer concentration Ma in the formalism of the quasi-homogeneous approximation, unlike M a, refers to the whole volume of the two-phase system. The aforementioned quantities are connected by the simple relationship Ma = flM a where y01 stands for the volume fraction of the a-th phase in miniemulsion. An analogous relation, Ra = sdaR a, exists between the concentrations Ra of the a-th type active centers in the entire system and those R a in the surface layer of the a-th phase. This layer thickness da has the scale of average spatial size of the a-th type block, which hereafter is presumed to be small as compared to the average radius of miniemulsion drops. Apparently, in this case, the curvature of the interphase surface can be neg-... 

The expression for the rate of a bimolecular reaction of adsorbed particles when the latter have a rapid surface mobility can be obtained in the traditional way for chemical kinetics if the law of mass action is used for large quasi-particles. Let us consider the reaction AZ+BZ on a homogeneous surface containing three species of particles (s = 3) A, B, and Y (the real properties of the vacant sites Y are taken into account in the final expressions). Particles of A and B are at neighboring sites of a lattice and enter the c.s. of one another. 

As shown in previous subsection, the activation energy of desorption coincides with the adsorption heat if there is no lateral interaction of the activated desorption complex and its surrounding, e — 0. This is the model that Jones and Perry invoked [144,145] to describe thermal desorption in the Hg/W(100) system. They were able to reproduce the experimental data, taking K(l(d)=K() — const, and Eej(6)=Q(6) the adsorption heat Q(6) was calculated with the quasi-chemical approximation for a homogeneous surface. The calculated and experimental spectra were found to be in a... 

Notice that the homogeneity indices of these IPMS are close to those of perfectly homogeneous minimal surfaces. Clearly then, three-periodic minimal surfaces are quasi-homogenous hyperbolic surfaces, in contrast to... 

Just as for cubic phases, the rod description of the R phase is an approximation to a hyperbolic surface. The smooth surface that defines the hydrophobic-polar interfaces resembles mesh surfaces containing a hexagonal array of pores. The genesis of this phase can also be understood as a resolution of the requirement for quasi-homogeneous interface. 

Experimental results on the basis of a kinetic approach of Me UPD on quasi-homogeneous substrate surfaces using large and small signal system perturbation techniques are rather rare [3.89, 3.119, 3.214-3.216, 3.313, 3.314]. 

These controversial results on the kinetics of Me UPD processes, obtained on the basis of the simplest approach assuming quasi-homogeneous substrate surfaces, led to the development of a different kinetic model including surface inhomogeneities, gradients of Meads> and surface diffusion as discussed in the following. 

S(/) can be described by the well-known Avrami theorem [3.317], supposing multiple nucleation on a quasi-homogeneous substrate surface with a sufficient density of nuclei, statistically local distribution of nuclei, and overlapping of growing 2D islands ... 

D nucleation and growth can be excluded. This is a necessary but not sufficient criterion for a nucleation-free Meads overlayer formation process on quasi-homogeneous substrate surfaces. 

In cases where the electrode surfaces differ insignificantly and a one-to-one correspondence between them can be reached, the hydrodynamic velocity components normal to the electrode surfaces are negligibly small and the electrical field in the IEG is quasi-homogeneous (except for the near-electrode layers). In this case, the local, one-dimensional approximation method is used. 

Two edge layers included surface species chemically and kinetically described as discussed above and considered together with all other species within one quasi-homogeneous mixture. In other words, in edge layers the catalytic active sites were equally accessible to all gas species. Surface sites were not allowed to react with each other and to migrate from the edge layers. 

Figure 3 Examples of regimes found in range II (medium values of a), (a) regime dominated by purely two-dimensional overlap (of the hydrophobic coils here). Within this regime, there is no increase of the thickness of the hydrophobic layer when the surface concentration increases, with y = 3 the coils are in the excluded volume geometry. (b) regime dominated by a partial three-dimensional growth of the hydrophilic coils which form quasi-brush structures. In this regime, the contribution of the hydrophobic coils is independent of the surface concentration because they form a quasi-homogeneous layer, the value of y being 1, whatever the quality of the solvent...

Absence of cross-sectional deformations As constant as possible wall thickness Sufficiently high remaining formability Quasi homogeneous material strucmre Status of low residual stresses Minimum surface damage If one of these requirements is not fulfilled, neither a successful completion of hydroforming... 

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