Surface diffusivity

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. 

Protein adsorption has been studied with a variety of techniques such as ellipsome-try [107,108], ESCA [109], surface forces measurements [102], total internal reflection fluorescence (TIRE) [103,110], electron microscopy [111], and electrokinetic measurement of latex particles [112,113] and capillaries [114], The TIRE technique has recently been adapted to observe surface diffusion [106] and orientation [IIS] in adsorbed layers. These experiments point toward the significant influence of the protein-surface interaction on the adsorption characteristics [105,108,110]. A very important interaction is due to the hydrophobic interaction between parts of the protein and polymeric surfaces [18], although often electrostatic interactions are also influential [ 116]. Protein desorption can be affected by altering the pH [117] or by the introduction of a complexing agent [118]. 

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. 

One might expect the frequency factor A for desorption to be around 10 sec (note Eq. XVII-2). Much smaller values are sometimes found, as in the case of the desorption of Cs from Ni surfaces [133], for which the adsorption lifetime obeyed the equation r = 1.7x 10 exp(3300// r) sec R in calories per mole per degree Kelvin). A suggested explanation was that surface diffusion must occur to desorption sites for desorption to occur. Conversely, A factors in the range of lO sec have been observed and can be accounted for in terms of strong surface orientational forces [134]. 

Mobility of this second kind is illustrated in Fig. XVIII-14, which shows NO molecules diffusing around on terraces with intervals of being trapped at steps. Surface diffusion can be seen in field emission microscopy (FEM) and can be measured by observing the growth rate of patches or fluctuations in emission from a small area [136,138] (see Section V111-2C), field ion microscopy [138], Auger and work function measurements, and laser-induced desorption... 

The sequence of events in a surface-catalyzed reaction comprises (1) diffusion of reactants to the surface (usually considered to be fast) (2) adsorption of the reactants on the surface (slow if activated) (3) surface diffusion of reactants to active sites (if the adsorption is mobile) (4) reaction of the adsorbed species (often rate-determining) (5) desorption of the reaction products (often slow) and (6) diffusion of the products away from the surface. Processes 1 and 6 may be rate-determining where one is dealing with a porous catalyst [197]. The situation is illustrated in Fig. XVIII-22 (see also Ref. 198 notice in the figure the variety of processes that may be present). 

Linderoth T R, Florsch S, Laesgaard E, Stensgaard i and Besenbacher F 1997 Surface diffusion of Pt on Pt(110) Arrhenius behavior of iong ]umps Phys. Rev. Lett. 78 4978... 

Dunphy J C, Sautet P, Ogietree D F, Dabbousi O and Saimeron M B 1993 Scanning-tunneiing-microscopy study of the surface diffusion of suifur on Re(OOOI) Phys. Rev. B 47 2320... 

George S M, DeSantoio A M and Haii R B 1985 Surface diffusion of hydrogen on Ni(IOO) studied using iaser-induced thermai desorption Surf. Sol. 159 L425... 

Schultz K A and Seebauer E G 1992 Surface diffusion of Sb on Ge(111) monitored quantitatively with optical second harmonic microscopy J. Chem. Phys. 97 6958-67... 

Zhu X D, Rasing T H and Shen Y R 1988 Surface diffusion of CO on Ni(111) studied by diffraction of optical second-harmonic generation off a monolayer grating Phys. Rev. Lett. 61 2883-5... 

Jaklevic R C and Elie L 1988 Scanning-tunnelling-microscope observation of surface diffusion on an atomic scale Au on Au(111) Rhys. Rev. Lett. 60 120... 

Figure C2.11.6. The classic two-particle sintering model illustrating material transport and neck growtli at tire particle contacts resulting in coarsening (left) and densification (right) during sintering. Surface diffusion (a), evaporation-condensation (b), and volume diffusion (c) contribute to coarsening, while volume diffusion (d), grain boundary diffusion (e), solution-precipitation (f), and dislocation motion (g) contribute to densification.

The incorporation of surface diffusion into a model of transport in a porous medium is quite straightforward, since the surface diffusion fluxes simply combine additively with the diffusion fluxes in the gaseous phase. 

It is therefore reasonable to go ahead with the construction of models for the gaseous phase diffusion without considering surface diffusion, though of course it must be incorporated before the models are used predictively. 

The literature of surface diffusion is now quite extensive. A review of the basic ideas, with reference to many of the earlier papers, is given by Dacey [44], and a good selection of references including more recent work can be found in Aris [45]... 

The flux N (a,w) is the Sum of contributions from a gaseous phase flux and a flux due to surface diffusion. The surface diffusion contribution is given by equation (7.7) or, more generally, by the corresponding relation which follows from equation (7.5). For the gaseous phase contribution Feng and Stewart assume flux relations of the dusty gas form, (5.1)- ... 

The disposable parameters in these equations are the permeability 0, the surface diffusion factor y, the tortuosity function . (a) (which also... 

Since the void fraction distribution is independently measurable, the only remaining adjustable parameters are the A, so when surface diffusion is negligible equations (8.23) provide a completely predictive flux model. Unfortunately the assumption that (a) is independent of a is unlikely to be realistic, since the proportion of dead end pores will usually increase rapidly with decreasing pore radius. 

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