Solid surfaces diffusion

Diffusion of reactants from the bulk solution to the solid surface Diffusion of the reactants to the active catalytic centers located either on the surface or in the pores of the solid C hemical reactions at the catalytic centers... 

For very small drops 0.1 pm or so in diameter (as in a mist of HjSOJ, the target efficiency rises as the particle diameter decreases, contrary to what is predicted by impingement theory. The tiny droplets move across the streamlines by diffusion and are immobilized on the solid surfaces. Diffusion is more and more effective as the particles become smaller, and the target efficiency is correspondingly increased. 

Consider the absorption of oxygen from air in the aeration of a lake or the solid surface diffusion in the hardening of mild steel in a carburizing atmosphere. Both these processes involve diffusion in a semiinfinite medium. Assume that a semi-infinite medium has a uniform initial concentration of Cao and is subjected to a constant surface concentration of Cas- Derive the equation for the concentration profiles for a preheated piece of mild steel with an initial concentration of 0.02 wt% carbon. This mild steel is subjected to a carburizing atmosphere for 2 h, and the surface concentration of carbon is 0.7%. If the diffusivity of carbon through the steel is 1 x 10 m /s at the process temperature and pressure, estimate the carbon composition at 0.05 cm below the surface. 

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 cleaning process proceeds by one of three primary mechanisms solubilization, emulsification, and roll-up [229]. In solubilization the oily phase partitions into surfactant micelles that desorb from the solid surface and diffuse into the bulk. As mentioned above, there is a body of theoretical work on solubilization [146, 147] and numerous experimental studies by a variety of spectroscopic techniques [143-145,230]. Emulsification involves the formation and removal of an emulsion at the oil-water interface the removal step may involve hydrodynamic as well as surface chemical forces. Emulsion formation is covered in Chapter XIV. In roll-up the surfactant reduces the contact angle of the liquid soil or the surface free energy of a solid particle aiding its detachment and subsequent removal by hydrodynamic forces. Adam and Stevenson s beautiful photographs illustrate roll-up of lanoline on wood fibers [231]. In order to achieve roll-up, one requires the surface free energies for soil detachment illustrated in Fig. XIII-14 to obey... 

Though a porous medium may be described adequately under non-reactive conditions by a smooth field type of diffusion model, such as one of the Feng and Stewart models, it does not necessarily follow that this will still be the case when a chemical reaction is catalysed at the solid surface. In these circumstances the smooth field assumption may not lead to appropriate expressions for concentration gradients, particularly in the smaller pores. Though the reason for this is quite simple, it appears to have been largely overlooked,... 

Numerical values for solid diffusivities D,j in adsorbents are sparse and disperse. Moreover, they may be strongly dependent on the adsorbed phase concentration of solute. Hence, locally conducted experiments and interpretation must be used to a great extent. Summaries of available data for surface diffusivities in activated carbon and other adsorbent materials and for micropore diffusivities in zeolites are given in Ruthven, Yang, Suzuki, and Karger and Ruthven (gen. refs.). 

Adsorbents, and activated carbon in particular, are typically characterized by a highly porous structure. Adsorbents with the highest adsorption capacity for gasoline or fuel vapors have a large pore volume associated with pore diameters on the order of 50 Angstroms or less. When adsorption occurs in these pores, the process is comparable to condensation in which the pores become filled with hquid adsorbate. Fig. 5 depicts the adsorption process, including transfer of adsorbate molecules through the bulk gas phase to the surface of the solid, and diffusion onto internal surfaces of the adsorbent and into the pores. 

By way of example, Volume 26 in Group III (Crystal and Solid State Physics) is devoted to Diffusion in Solid Metals and Alloys, this volume has an editor and 14 contributors. Their task was not only to gather numerical data on such matters as self- and chemical diffusivities, pressure dependence of diffusivities, diffusion along dislocations, surface diffusion, but also to exercise their professional judgment as to the reliability of the various numerical values available. The whole volume of about 750 pages is introduced by a chapter describing diffusion mechanisms and methods of measuring diffusivities this kind of introduction is a special feature of Landolt-Bornstein . Subsequent developments in diffusion data can then be found in a specialised journal. Defect and Diffusion Forum, which is not connected with Landolt-Bdrnstein. 

Crystal growth is a diffusion and integration process, modified by the effect of the solid surfaces on which it occurs (Figure 5.3). Solute molecules/ions reach the growing faces of a crystal by diffusion through the liquid phase. At the surface, they must become organized into the space lattice through an... 

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... 

The kinetics of ion backspillover on the other hand will depend on two factors On the rate, I/nF, of their formation at the tpb and on their surface diffusivity, Ds, on the metal surface. As will be shown in Chapters 4 and 5 the rate of electrochemically controlled ion backspillover is normally limited by I/nF, i.e. the slow step is their transfer at the tpb. Surface diffusion is usually fast. Thus, as shown in Chapter 5, for the case of Pt electrodes where reliable surface O diffusivity data exist, obtained by Gomer and Lewis several years ago,76 Ds is at least 4.-10 11 cm2/s at 400°C and thus an O2 ion can move at least 1 pm per s on a Pt(lll) or Pt(110) surface. Therefore ion backspillover from solid electrolytes onto electrode surface is not only thermodynamically feasible, but can also be quite fast on the electrode surface. But does it really take place This we will see in the next Chapter. 

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