Heterogeneous energy barrier

The catalytic effect of solid particles (as ia heterogeneous nucleation) is to reduce the energy barrier to formation of a new phase. This, in effect, can reduce the interfacial energy O significantly. 

Figure 1.2. Potential energy diagram of a heterogeneous catalytic reaction, with gaseous reactants and products and a solid catalyst. Note that the uncatalyzed reaction has to overcome a substantial energy barrier, whereas the barriers in the catalytic route are much lower.

Human body fluid and SBF contain calcium and phosphate ions that are already supersaturated with respect to hydroxyapatite [20]. However, these fluids do not spontaneously deposit hydroxyapatite under normal conditions. This is because the activation energy barrier for hydroxyapatite nudeation is very high. Therefore, the ability of substrates to induce heterogeneous nudeation of hydroxyapatite and the degree of supersaturation of SBF with respect to hydroxyapatite are important factors for hydroxyapatite formation on materials in the body fluid and SBF. 

Surface energetics and thermodynamic driving force thus define the energy barrier for nucleation as shown in Fig. 2.13b. For heterogeneous nucleation,... 

Heterogeneous nucleation, however, is in many cases the predominant formation process for crystals in natural waters. In a similar way as catalysts reduces the activation energy of chemical reaction, foreign solids may catalyze the nucleation process by reducing the energy barrier. Qualitatively, if the surface of the solid substrate matches well with the crystal, the interfacial energy between the two solids is smaller than the interfacial energy between the crystal and the solution, and nucleation may take place at a lower saturation ratio on a solid substrate surface than in solution. 

It results that in the absence of any fragmentation of the original frame, the process [Pt(C6Cl5)4]-/0 is in principle quasireversible. The large peak-to-peak separation (A/sp = 1.9 V, at 0.2 V s-J) evidently reflects the high energy barrier required to pass from square planar tetracoordinate-Pt(III) to octahedral hexacoordinate-Pt(IV), which slows down the rate of the heterogeneous electron transfer. 

A further question raised by the electrochemical preannihilative emission process is what is the oxidant that oxidizes the anion or the reductant that reduces the cation before the potential at which the counterion is produced. Only two explanations are available ( ) impurities, and (2) heterogeneous electron transfer at the electrode.2 The difficulties involved in invoking an impurity mechanism for a phenomenon observed in both oxidation and reduction processes in a wide variety of solvents have been mentioned before. Unfortunately, if the emission is ascribed to heterogeneous electron transfer at the electrode, the problems are also severe. Marcus83 has shown that theoretically unless the formation of the excited state of an ion by electron transfer to or from the electrode involves a very small free energy barrier, it should not compete with the process which results in formation of the ground state of the ion and an excited state of the electrode. He has suggested... 

It is far more likely that heterogeneous nucleation plays the governing role in nucleation of voids. The effect of a particle or substrate is to lower the free energy barrier AF. Thus, Equations 6.1 and 6.3 remain unchanged, and Equation 6.2 takes on the new form... 

At this stage, it is still difficult to determine whether the conclusion is appropriate for the fundamental part of the multicomponent bismuth molybdate catalyst. Unfortunately, we have no available information on the number of active reaction sites on the catalyst system. In the heterogeneous catalysis, apparent activation energy does not necessarily correspond to the real energy barrier of the elementary slow step of the reaction. Multicomponent bismuth molybdate catalyst has been established industrially, whereas only parts of the fundamental structure and working mechanism have been elucidated. In addition, important roles of alkali metals and other additives such as lanthanides remain unknown. Apparently, further investigations should be done to clarify the complete working mechanism of the multicomponent bismuth molybdate catalyst. 

Fig. 1.13 Influence of the applied potential E on the energy barrier of the heterogeneous electron transfer process ...

The effect of exogenous solid matter (as in heterogeneous nucleation) in the supersaturated solution is equivalent to that of a catalyst in a reactive mixture. Namely, it is to reduce the energy barrier to the formation of a new phase. In effect, the solid matter reduces the interfacial energy esurf by what may amount to several orders of magnitude. 

Figure 7. Calculated two-dimensional energy surfaces for heterogeneous non-Franck-Condon transition of the three-dimensional 6-oscillator trikisoctahedral Inner Shells of 3+ and 2+ ions at (A) equal potential energies after ground state energy correction (B) at equal ground state free energies. Barrier height in B +22.9kT at 298 K (+56.9 kJ/mole, +0.59 eV, experimentally +0.59 eV177).

A heterogeneous catalytic reaction involves adsorption of reactants from a fluid phase onto a solid surface, surface reaction of adsorbed species, and desorption of products into the fluid phase. Clearly, the presence of a catalyst provides an alternative sequence of elementary steps to accomplish the desired chemical reaction from that in its absence. If the energy barriers of the catalytic path are much lower than the barrier(s) of the noncatalytic path, significant enhancements in the reaction rate can be realized by use of a catalyst. This concept has already been introduced in the previous chapter with regard to the Cl catalyzed decomposition of ozone (Figure 4.1.2) and enzyme-catalyzed conversion of substrate (Figure 4.2.4). A similar reaction profile can be constructed with a heterogeneous catalytic reaction. 

Homogeneous nucleation, however, rarely occurs under commercially important conditions. In practice, nucleation is usually dominated by a heterogeneous mechanism, where a foreign surface serves to reduce the energy barrier to nucleation. 

For the initial formation of a solid phase on a substrate surface from vapor precursors through heterogeneous nucleation, as is schematically illustrated in Figure 20.2, the critical nucleus size, r, and the corresponding energy barrier, AG, are given by the following equations ... 

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