Diffusion surface transport

The concentration boundary layer forms because of the convective transport of solutes toward the membrane due to the viscous drag exerted by the flux. A diffusive back-transport is produced by the concentration gradient between the membranes surface and the bulk. At equiUbrium the two transport mechanisms are equal to each other. Solving the equations leads to an expression of the flux ... 

In the film-penetration model (H19), it is assumed that the reactant A penetrates through the surface element by one-dimensional unsteady-state molecular diffusion. Convective transport is assumed to be insignificant. The diffusing stream of the reactant A is depleted along the path of diffusion by its reversible reaction with the reactant B, which is an existing component of the liquid surface element. If such a reaction can be represented as... 

We now describe a relatively simple MD model of a low-index crystal surface, which was conceived for the purpose of studying the rate of mass transport (8). The effect of temperature on surface transport involves several competing processes. A rough surface structure complicates the trajectories somewhat, and the diffusion of clusters of atoms must be considered. In order to simplify the model as much as possible, but retain the essential dynamics of the mobile atoms, we will consider a model in which the atoms move on a "substrate" represented by an analytic potential energy function that is adjusted to match that of a surface of a (100) face-centered cubic crystal composed of atoms interacting with a Lennard-Jones... 

In addition to enhancing surface reactions, water can also facilitate surface transport processes. First-principles ab initio molecular dynamics simulations of the aqueous/ metal interface for Rh(l 11) [Vassilev et al., 2002] and PtRu(OOOl) alloy [Desai et al., 2003b] surfaces showed that the aqueous interface enhanced the apparent transport or diffusion of OH intermediates across the metal surface. Adsorbed OH and H2O molecules engage in fast proton transfer, such that OH appears to diffuse across the surface. The oxygen atoms, however, remained fixed at the same positions, and it is only the proton that transfers. Transport occurs via the symmetric reaction... 

At steady state, dc/dt = 0, so an expression for c can be obtained immediately. Obviously, close to the surface, transport of c is dominated by diffusion but further away from the surface convection dominates. 

Erosion is typically characterized by either occurring on the surface or in the bulk. Surface erosion is controlled by the chemical reaction and/or dissolution kinetics, while bulk erosion is controlled by diffusion and transport processes such as polymer swelling, diffusion of water through the polymer matrix, and the diffusion of degradation products from the swollen polymer matrix. The processes of surface and bulk erosion are compared schematically in Fig. 1. These two processes are idealized descriptions. In real systems, the tendency towards surface versus bulk erosion behavior is a function of the particular chemistry and device geometry (Tamada and Langer, 1993). Surface erosion may permit the... 

The convolution treatment of the linear and semi-infinite diffusion reactant transport (Section 1.3.2) leads to the following relationship between the concentrations at the electrode surface and the current ... 

Diffusion. The transport process may consist of two parts, diffusion and convection. When the liquid is stagnant and resting relative to the particle the transport is done by diffusion only. A steady state is quickly established in the solution around the particle (4 ). (Strictly it is a quasi-steady state since the particle is growing ( 5)). At the particle surface the concentration gradient becomes equal to (c-cs)/r, which leads to the growth rate... 

A plot of (Ink) vs (1/T) yields a linear relationship with the slope equal to (-EJR) and the intercept equal to (lnAf). Thus, by measuring (k) values at several temperatures, the ( a) value can be determined. Low a values (<42 kj mole) usually indicate diffusion-controlled transport processes, whereas higher Ea values indicate chemical reaction or surface-controlled processes [21,25]. 

Sorption/desorption is the key property for estimating the mobility of organic pollutants in solid phases. There is a real need to predict such mobility at different aqueous-solid phase interfaces. Solid phase sorption influences the extent of pollutant volatilization from the solid phase surface, its lateral or vertical transport, and biotic or abiotic processes (e.g., biodegradation, bioavailability, hydrolysis, and photolysis). For instance, transport through a soil phase includes several processes such as bulk flow, dispersive flow, diffusion through macropores, and molecular diffusion. The transport rate of an organic pollutant depends mainly on the partitioning between the vapor, liquid, and solid phase of an aqueous-solid phase system. 

Similar to the pure surface electrode reaction, the response of reaction (2.146) is characterized by splitting of the net peak under appropriate conditions. The splitting occurs for an electrochemically quasireversible reaction and vanishes for the pure reversible reaction. Typical regions where the splitting emerges are 3 < m < 10 and 0.1 < r < 10 for a = 0.5 and i sw = 50 mV. Contrary to the surface electrode reaction where the ratio of the split peak currents is solely sensitive to a, in the present system this ratio depends additionally on r. For instance, if a = 0.5 and r = 1 the ratio is = 1 for r = 10, > 1 and r = 0.1, < 1. Finally it is worth mentioning when experimentally possible, the electrode mechanism represented by (2.145) to (2.147) has to be simplified to a simple surface reaction (Sect. 2.5.1) in order to avoid the complexity arising from the effect of diffusion mass transport. 

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. 

In the absence of transport limitations, the processes of adsorption, surface diffusion, surface reaction, and desorption can be treated via the transition state theory (Baetzold and Somorjai, 1976 Zhdanov et al, 1988). For example, the application of the TST to a single site adsorption process,... 

The interpretation of this data on metals in terms of microscopic mechanisms of surface atom transport is not totally understood. The original papers[ 11] proposed that during surface transport the controlling process was adatom terrace diffusion between steps with the adatom concentration being that in local equilibrium with the atomic steps. This may indeed be the case, but in light of other experiments on adatom diffusion[13] and exchange processes at steps[14] the possibility of step attachment/detachment limited kinetics caimot be raled out. 

Diffusive mass transport of the byproducts away from the surface... 

Figure 24 depicts schematically the concentration profile of dissolved hydrogen in a porous catalyst particle brought about by interaction of diffusive mass transport of hydrogen into the porous catalyst particles and the consumption of hydrogen by anodic oxidation at the inner surface of the catalyst. 

A third type of internal solid state reaction (see later in Fig. 9-12) is characterized by two (solid) reactants A and B which diffuse into a crystal C from opposite sides. C acts as a solvent for A and B. If the reactants form a stable compound AB with each other (but not with the solvent crystal C), an internal solid state reaction eventually takes place. It occurs in the solvent crystal at the location of maximum supersaturation of AB by internal precipitation and subsequent growth of the AB particles. Similar reactions can be observed on a crystal surface which, in this case, plays the role of the solvent matrix C. Surface transport of the reactants leads to a product band precipitated on the surface at some distance from each of the two reactants and completely analogous to the internal reactions described before. In addition, internal reactions have also been observed if (viscous) liquids are chosen as the reaction media (C). 

Grain-boundary grooves can develop during thermal annealing by mass transport arising from vapor transport, surface diffusion, or surface-to-surface transport by means of volume diffusion. 

The fibrillar morphology of Shirakawa polyacetylene is an advantage in applications requiring a high surface area but a problem in many other cases, especially the study of diffusion and transport processes and the possible device applications where re-... 

---