Bulk homogeneous conditions

The more sophisticated potentials used in the nanowire study point to an important consideration in modeling such systems. Simple potentials are parameterized under bulk homogeneous conditions and may give poor descriptions of the inhomogeneous environment near a crack tip. In an effort to employ a classical potential that is responsive to a rapidly changing environment, Omeltchenko and coworkers ° simulated a graphite sheet modeled by more than a million particles. The authors used a reactive bond order potential developed by Brenner. In this approach, the total potential energy can be written as follows ... 

The development of the electric field in the direction perpendicular to the current is called Hall effect. At x xc, i.e. under conditions when the metallic cluster is big and well formed running through the whole sample volume, behavior of the Hall effect is similar to that in bulk, homogeneous metals [96,97]. The only difference is that the cluster volume, through which the current flows, fills only a part of the sample volume. The Hall... 

Indirect and direct electrolysis — Electrolysis is the oxidation or reduction reaction caused by the current flowing through the cell. Direct electrolysis is a -> heterogeneous process and the -> electron transfer proceeds directly from the electrode to the molecule of the substrate. In the case of indirect electrolysis the -> mediator is necessary, which is first heterogeneously reduced (oxidized) at the electrode and then the electron transfer to/from the molecule of the substrate occurs in homogeneous conditions in the bulk of the solution. The intermediate... 

In pseudo-homogeneous models it is assumed that the catalyst surface is totally exposed to the bulk fluid conditions, i.e. that there are no fluid-to-particle heat and mass transfer resistances. On the other side, heterogeneous models take conservation equations for both phases into account separately. 

This effect must not be confused with the cybotactic effects we have mentioned, nor with the hole in the solute-solvent correlation function gMs(t) (see Figure 8.5). The hole in the radial correlation function is a consequence of its definition, corresponding to a conditional property, namely that it gives the radial probability distribution of the solvent S, when the solute M is kept at the origin of the coordinate system. Cybotactic effects are related to changes in the correlation function gMs(t) (or better gMs(r> )) with respect to a reference situation. Surface proximity effects can be derived by the analysis of the gMs(r,fi) functions, or directly computed with continuum solvation methods. It must be remarked that the obtention of gMs(r) functions near the surface is more difficult than for bulk homogeneous liquids. Reliable descriptions of gMs(ri re even harder to reach. 

Fig. 5.11. Variation of the piezoelectric coupling coefficient 633 with the directional fiber fractions and V2. The values are normalized with respect to the bulk piezoelectric material and homogeneous electrostatic fields. Both substitution sequences are shown for different factors C3 the results are identical for the homogeneous conditions of C3 = 0.

To illustrate the influence exerted by the energy of adsorption of an intermediate on the rate of an electrocatalytic reaction, consider a very simple two-step reaction of the type A —> X —> B where X, the intermediate, is reversibly adsorbed on the electrode (with a degree of surface coverage 9x). For the sake of simplicity, the electrode surface will be assumed to be homogeneous (i.e., conditions of Langmuir adsorption hold), while the system lacks adsorbed species other than X. The rate, of the adsorption step (the first step) is then proportional to the bulk concentration of the starting material, c, and to the free surface part (1 - 9x) (the part not taken up by species X), while the rate of further transformation of intermediate X, which is tied to its desorption, will be proportional to the surface fraction, 9x, taken up by it ... 

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