Diffusion energy barriers

Figure 5.23 Irregular diffusion energy barrier encountered in glassy or amorphous solids.

The separation of a mixture of molecules A and B is characterized by the selectivity or ideal separation factor a/b = P(A)/P(B), i.e. the ratio of permeability of the molecule A over the permeability of the molecule B. According to Equation (5.5), it is possible to make separations by diffusivity selectivity D(A)/D(B) or solubility selectivity S(A)/S(B) [25,26]. This formalism is known in membrane science as the solution-diffusion mechanism. Since the limiting stage of the mass transfer is overcoming of the diffusion energy barrier, this mechanism implies the activated diffusion. Becanse of this, the temperature dependences of the diffusion coefficients and permeability coefficients are described by the Arrhenins equations. 

Table 5.1. DPT binding energies, E(, for CO and O [with respect to (1/2)02] at br and cus sites (Fig. 5.9a), diffusion energy barriers, to neighboring br and cus sites, and reaction energy barriers,...

The nucleation rate is dominated by two factors. One is the critical free energy barrier of nucleation. Its exponential dependence was first proposed by Volmer and Weber (1926). The other is the diffusion energy barrier for molecules crossing over the liquid-solid interfaces. Its exponential dependence was first proposed by Becker and Doring (1935). The quantitative expression of the prefactor in the kinetic equation of the nucleation rate is given by Turnbull and Fisher (1949) as... 

Following adsorbate diffusion on surfaces, the use of fast STM [43] became possible even in real time and now allows surface scientists to draw a detailed picture of adsorbate kinetics, hopping rates, and diffusion energy barriers [44, 45] as well as to explore nucleation and growth of various homoepitaxial and heteroepitaxial systems [46]. Even the dynamics of surface reactions under high pressures [47,... 

STM instruments are available that allow scanning at a rate of 20 frames [50] and in some cases, even 80 frames s [43]. Such instruments are usually operated in the constant-height mode and can be used for following adsorbate diffusion and chemical reactions in real time. This is helpful in the field of catalysis and also for fundamental aspects such as determining hopping rates and diffusion energy barriers [44]. 

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