Diffusion, coefficients surface

An alternative defining equation for surface diffusion coefficient Ds is that the surface flux Js is Js = - Ds dT/dx. Show what the dimensions of Js must be. 

It was commented that surface viscosities seem to correspond to anomalously high bulk liquid viscosities. Discuss whether the same comment applies to surface diffusion coefficients. 

It is known that even condensed films must have surface diffusional mobility Rideal and Tadayon [64] found that stearic acid films transferred from one surface to another by a process that seemed to involve surface diffusion to the occasional points of contact between the solids. Such transfer, of course, is observed in actual friction experiments in that an uncoated rider quickly acquires a layer of boundary lubricant from the surface over which it is passed [46]. However, there is little quantitative information available about actual surface diffusion coefficients. One value that may be relevant is that of Ross and Good [65] for butane on Spheron 6, which, for a monolayer, was about 5 x 10 cm /sec. If the average junction is about 10 cm in size, this would also be about the average distance that a film molecule would have to migrate, and the time required would be about 10 sec. This rate of Junctions passing each other corresponds to a sliding speed of 100 cm/sec so that the usual speeds of 0.01 cm/sec should not be too fast for pressurized film formation. See Ref. 62 for a study of another mechanism for surface mobility, that of evaporative hopping. 

The state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. 

Because of the close similarity in shape of the profiles shown in Fig. 16-27 (as well as likely variations in parameters e.g., concentration-dependent surface diffusion coefficient), a contrdling mechanism cannot be rehably determined from transition shape. If rehable correlations are not available and rate parameters cannot be measured in independent experiments, then particle diameters, velocities, and other factors should be varied ana the obsei ved impacl considered in relation to the definitions of the numbers of transfer units. 

X-ray scattering studies at a renewed pc-Ag/electrolyte interface366,823 provide evidence for assuming that fast relaxation and diffu-sional processes are probable at a renewed Sn + Pb alloy surface. Investigations by secondary-ion mass spectroscopy (SIMS) of the Pb concentration profile in a thin Sn + Pb alloy surface layer show that the concentration penetration depth in the solid phase is on the order of 0.2 pm, which leads to an estimate of a surface diffusion coefficient for Pb atoms in the Sn + Pb alloy surface layer on the order of 10"13 to lCT12 cm2 s i 820 ( p,emicai analysis by electron spectroscopy for chemical analysis (ESCA) and Auger ofjust-renewed Sn + Pb alloy surfaces in a vacuum confirms that enrichment with Pb of the surface layer is probable.810... 

There are several correlations for estimating the film mass transfer coefficient, kf, in a batch system. In this work, we estimated kf from the initial concentration decay curve when the diffusion resistance does not prevail [3]. The value of kf obtained firom the initial concentration decay curve is given in Table 2. In this study, the pore diffusion coefficient. Dp, and surface diffusion coefficient, are estimated by pore diffusion model (PDM) and surface diffusion model (SDM) [4], The estimated values of kf. Dp, and A for the phenoxyacetic acids are listed in Table 2. 

These measurements showed that in-plane lateral proton diffusion was facilitated at air-water interfaces on which stearic acid monolayers were formed, with a surface diffusion coefficient that depended critically on the physical state of the monolayer, and which was at most ca. 15% of the magnitude in bulk solution. These promising initial studies... 

Fig. 3.1.7 The surface diffusion coefficient / surface of cyclohexane (squares) and acetone (circles) in porous silicon with 3.6-nm mean...

Surface diffusion considerably influences the mass transfer inside the intraparticle space of a porus adsorbent. The surface diffusion coefficient Ds can be expressed by... 

Equation 17.59 has been confirmed experimentally, suggesting that molecules move over a surface by hopping to adjacent adsorption sites. It may be assumed that this process involves a lower energy of activation than that required for complete desorption. The molecule will continue to hop until it finds a vacant adsorption site, thus explaining the increase of surface diffusion coefficient with coverage. 

These results were extended by Tilton et a/.(n8) to adsorption of eosin-labeled BSA on polymer surfaces. They also found a component that surface diffuses, with coefficients ranging from 1.2 x 10 9 to 2.6 x 10 9cm2/s, depending on surface type. In this study, intersecting TIR laser beams rather than a focused stripe were used to define the spatial intensity variation. Surface diffusion was even noted for the most irreversibly adsorbed eosin-labeled BSA components this was evident on samples rinsed for long periods with unlabeled BSA after exposure to eosin-labeled BSA. The surface diffusion coefficient of the irreversibly bound BSA was found to be a strong function of adsorbed concentration.(n9)... 

For this estimate, values for the surface diffusion coefficient (D) and the surface exchange coefficient (i) in eq 2 were obtained by linearizing Mitterdorfer s rate expressions for surface transport and adsorption/desorption (ref 84) and re-expressing in terms of the driving forces in eq 2. 

Dp and D are surface diffusion coefficients parallel and normal to steps, respectively, and e is the step interaction energy. Obviously, two simple cases arise for /= 0 and / = Jt/2, i.e. for the profile modulation parallel and perpendicular to the intrinsic steps. Since the step energ>" is in general larger than the step interaction energy [24,28] and the diffusion parallel to steps faster than normal to steps [29,30], the decay rate of such profiles is expected to be much faster when the modulation is parallel to the steps. The dependence of B, D and E on... 

On the other hand, the rates of decay for the two profiles are significantly different as seen in fig. 6. The ratio turns out to be 25 which is almost equal to the factor l/6tatf a in eq. (6). This is qualitatively consistent with theory. It follows that the ratio of surface diffusion coefficients and energies in eq.(6) is near unity at this temperature. Umavelling this ratio is not possible without additional assumptions [18]. For example, selecting a... 

The fact FIM only images a small area at the apex of the tip makes it insensitive to vibration and to thermal drift. Because of this, FIM has been used to study the motion of a single atom on a tip over a long period of time. By tracing the trajectory of a single atom, the surface diffusion coefficient and the rate of directional walk of single atoms was directly measured. 

K and <0 being constants. The reaction constant k was shown to be proportional to the surface diffusion coefficient, so the activation energy for migration was computed from the temperature coefficient of k, i.e.,... 

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