Mechanism surface diffusion

The speed of provision of the feed molecules to the adsorption/catalytic sites must be balanced with engineering issues such as pressure drop in a reactor/ adsorber, so the parhcle size and pore structure of engineered forms must be optimized for each appHcation. A hierarchy of diffusion mechanisms interplays in processes using formed zeoHtes. Micropore, molecular, Knudsen and surface diffusion mechanisms are all more or less operative, and the rate Hmifing diffusion mechanism in each case is directly affected by synthesis and post-synthesis manufacturing processes. Additional details are provided in Chapter 9. 

Membranes made from zeolite materials provide separahon properties mainly based on molecular sieving and/or surface diffusion mechanism. Separation with large pore zeolite membranes is mainly based on surface diffusion when their pore sizes are much larger than the molecules to be separated. Separation with small pore zeolite membranes is mainly based on molecular sieving when the pore sizes are smaller or similar to one molecule but are larger than other molecules in a mixture to be separated. 

Fig. 11.1. Competing surface diffusion mechanisms on an fee (001) surface (adapted from Feibel-man (1990)) (a) intuitive mechanism in which adatom moves from one fourfold site to another by passing across bridge site, and (b) exchange mechanism in which diffusion occurs by concerted motion both of adatom and its subsurface partner.

Force-field calculations could be simple energy minimization or advanced monte-carlo and molecular dynamics calculations. The major assumption here is the transferability of force-field parameters among the related materials. These calculations can provide wealth of information such as the relative ordering of adsorption sites on surface, diffusion mechanism of molecules particularly inside zeolites, energy barrier for difihision, diffusion coefficients, heats of adsorption and more importantly, the effect of temperature on all these properties. 

The influence of local surface structure on the values of the Arrhenius parameters for the surface diffusivity within a particular surface patch has been studied in previous work " At the molecular scale, the surface diffusion mechanism can be modelled as a random walk, where the steps in the walk consist of hops between adsorption sites. The strong temperature dependence of the surface diffusivity that is generally observed in the literature, is consistent with the above mechanism and frequently exhibits an Arrhenius form. Thus the surface diffusivity, Ds, is given by ... 

Chen, K. and Vekilov, P. G. 2002. Evidence for the surface-diffusion mechanism of solution crystallization from molecular-level observations with ferritin, Phys Rev E Stat Nonlin Soft Matter Phys 66,021606. 

Another complication in comparing data from different techniques may arise from the possibility that several surface diffusion mechanisms may be operative. Evidence for different surface diffusion mechanisms may be revealed by large differences in measured activation energies and by large differences in absolute values of measured surface diffusion coefficients at the same temperature. Hence experimental data, especially if they originate from different techniques, need to be be compared systematically in order to decide whether the effective rates of diffusion (at the same or at different temperatures) may be indicative of different diffusion mechanisms. 

If the mechanism of transport into the porous medium is the parallel pore and surface diffusion mechanism, the flux equation can be written in terms of the two individual concentration gradients as follows ... 

The surface diffusion mechanism, in which only the less noble element (zinc in copper-zinc alloys) dissolves and the remaining more noble metal is rearranged by diffusion on the surface and nucleation of islands of almost pure metal [23]. 

The percolation model of selective dissolution, an extension of the surface diffusion mechanism, based on preexisting interconnected paths of like elements in the binary alloy and effects of curvature on dissolution potential [24, 25]. 

Fig. 8.19b). The results for the surface diffusion mechanism are in agreement with those of Nicholls and Mullins. The circle approximation used in the analytical models differs from the contours found by the numaical simulation approach which predicts undercutting and a continuous change in the curvature of the neck surface. The region of the neck surface influenced by mattCT transport also extends far beyond that given by the circle approximation, but the extension is less pronounced when surface diffusion and grain boundary diffusion occur simultaneously. 

In our MC scheme, each single MCS does not correspond to elementary atomic jump and may include a combination of different surface diffusion mechanisms. 

In Knudsen diffusion (Fig. 11.9a), the pore size forces the penetrant molecules to collide more frequently with the pore wall than with other incisive species [26]. Except for some special applications as membrane reactors, Knudsen-selective membranes are not commercially attractive because of their low selectivity [27]. In surface diffusion mechanism (Fig. 11.9 b), the pervasive molecules adsorb on the surface of the pores so move from one... 

Rao and Sircar [5-7] introduced nanoporous supported carbon membranes which were prepared by pyrolysis of PVDC layer coated on a macroporous graphite disk support. The diameter of the macropores of the dried polymer film was reduced to the order of nanometer as a result of a heat treatment at 1,000°C for 3 h. These membranes with mesopores could be used to separate hydrogen-hydrocarbon mixtures by the surface diffusion mechanism, in which gas molecules were selectively adsorbed on the pore wall. This transport mechanism is different from the molecular sieving mechanism. Therefore, these membranes were named as selective sitrface flow (SSF ) membranes. It consists of a thin (2-5 pm) layer of nanoporous carbon (effective pore diameter in the range of 5-6 A) supported on a mesoporous inert support such as graphite or alumina (effective pore diameter in the range of 0.3-1.0 pm). The procedures for making the selective surface flow membranes were described in [5, 7]. In particular, the requirements to produce a surface diffusion membrane were shown clearly in [7]. 

The surface diffusion mechanism is the most significant one in low temperature sintering of metal powders. Kuczynski[19] derived the following relationships between neck growth time tneck and neck radius Xneck ... 

Transport in zeolites depends on the adsorption properties and is an activated phenomenon. For the surface diffusion mechanism, the diffusion flux can be expressed as [8]... 

The clusters of attached and intergrown particles in Fig. 11 (1100°C calcine) exhibit marked development of blocky morphology as the crystallites approach crude forms, seemingly under the influence of a less orderly process than the stepwise surface diffusion mechanism indicated to be the main transport system up to 900°C. At temperatures in the vicinity of 1100°C vapor phase transport is considered likely in the calcination conditions employed. The pattern of thickness fringes in several crystallites is characteristic of development toward the cubic form. 

Surface diffusion of adsorbed molecular species along the pore wall surface. This mechanism of transport becomes dominant for micro-pores and for strongly adsorbed species. Extensions of the Maxwell-Stefan bulk diffusion model have been proposed in order to provide a realistic description of the combined bulk, Knudsen and surface diffusion mechanisms, apparently with limited success [70, 71]. 

Many events occur in the MTZ during adsorption which render the analysis complex. First, one or more adsorbates transfer from the fluid bulk by convection or diffusion across the fluid film which is external to the solid surface. Secondly, these adsorbates penetrate the particle by Maxwell, Knudsen and surface diffusion mechanisms (see Chapter 4), and adsorb onto the internal surface where the heat of adsorption is released. Heat may then be transferred to the adsorbent, to the flowing process fluid, and, via the vessel wall, to the surrounding environment. Heat and mass transfer may occur in the MTZ by bulk and diffusive flows in both the radial and axial directions. An additional complexity is that the flow through a packed bed may not be uniform across its entire cross-sectional area. This may be because of channelling of fluid at the wall or because of temperature gradients created when the heat of adsorption is released. 

The migration of K on Fe/Al203 has been studied by Auger electron spectroscopy [234]. The migration is faster in H2 than in O2, and faster in moist gas than in dry. The kinetics of surface migration was found to be consistent with a surface diffusion mechanism [234]. 

Carbon fibers also can be produced by the pyrolytic deposition of hydrocarbon gases. Many hydrocarbon gases, such as methane, naphthalene, and benzene, have been used to produce carbon fibers with deposition temperatures of 1000-1200°C. Dining the pyrolysis process, thin tubes of carbon are first formed on ultra-fine particles. The tubes then grow by a surface diffusion mechanism, and the subsequent high temperature treatment with a temperature up to 2500°C results in the formation of carbon fibers with diameters ranging from 10 run to mote than 100 /im. Carbon fibers produced from hydrocarbon gases often have central hollow cores. 

In the same fashion, for the case of a surface diffusion mechanism from equations (2.88)-(2.90) one obtains ... 

It is worth noting that the total step length per unit surface area Ls equals the reciprocal step distance both for parallel linear steps and for steps created by screw dislocations. Therefore the expressions for the growth current density retain the same mathematical form [4.49]. For instance, in the case of a surface diffusion mechanism the current will be given by equation (4.20) in which the step distance 2xo should be replaced by r i.e. ... 

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