Surface diffusion rate controlled proces

The second type of polarization, concentration polarization, results from the depletion of ions at the electrode surface as the reaction proceeds. A concentration gradient builds up between the electrode surface and the bulk solution, and the reaction rate is controlled by the rate of diffusion of ions from the bulk to the electrode surface. Hence, the limiting current under concentration polarization, ii, is proportional to the diffusion coefficient for the reacting ion, D (see Section 4.0 and 4.3 for more information on the diffusion coefficient) ... 

Adsorption of molecules proceeds by successive steps (1) penetration inside a particle (2) diffusion inside the particle (3) adsorption (4) desorption and (5) diffusion out of the particle. In general, the rates of adsorption and desorption in porous adsorbents are controlled by the rate of transport within the pore network rather than by the intrinsic kinetics of sorption at the surface of the adsorbent. Pore diffusion may take place through several different mechanisms that usually coexist. The rates of these mechanisms depend on the pore size, the pore tortuosity and constriction, the cormectivity of the pore network, the solute concentration, and other conditions. Four main, distinct mechanisms have been identified molecular diffusion, Knudsen diffusion, Poiseiulle flow, and surface diffusion. The effective pore diffusivity measured experimentally often includes contributions for more than one mechanism. It is often difficult to predict accurately the effective diffusivity since it depends so strongly on the details of the pore structure. 

This model is applicable to the reactions of nonporous pellets and to porous pellets when the global rate is controlled by pore diffusion. Reaction is limited to a surface separating the solid reactant at the core of the pellet surrounded by a porous layer of solid product. It occurs initially on the external surface of the pellet, and the thickness of the product layer increases as the reaction proceeds, as illustrated in Fig. 1. The global reaction rate is determined by three resistances— mass transfer from bulk gas to particle surface, diffusion... 

Oxygen may dissolve in rubber in two ways. Physical solution can be followed by chemical reaction. Chemical reaction occurs autocatalytioally(59), and as resinification proceeds the rubber becomes first tacky, and ultimately hard and brittle. When the surface area is small the rate of reaction with oxygen may depend upon the extent of the surface, but as the surface is increased diffusion becomes no longer a rate controlling step, and the reaction velocity is independent of the surface area. 

Constant-rate Period In the constant-rate period moisture movement within the sohd is rapid enough to maintain a saturated condition at the surface, and the rate of diying is controlled by the rate of heat transferred to the evaporating surface. Drying proceeds by diffusion of vapor from the saturated surface of the material across a... 

The isothermal pyrolysis in the presence of air proceeds at a much faster rate and higher weight losses are obtained as compared to vacuum pyrolysis at the same temperature. The first order rate constant obtained is linearly related to the expression [%LOR + o-(% crystallinity)]//o with a degree of correlation r = 0.923, where a is the accessible surface fraction of the crystalline regions according to Tyler and Wooding [501], and / is the orientation factor. No correlation could be found with DP due to very rapid depolymerization. The fact that the rate is inversely proportional to the orientation and that it decreases with the increase in the thickness of the fibers indicates that the rate of the diffusion of the oxygen into the fibers controls the kinetics and that oxidation is the predominant process in air pyrolysis. 

The continued oxidation of the metal substrate beneath the protective oxide layer must become a diffusion-controlled process for thick enough oxide films in which either metal atoms or oxygen atoms diffuse through the metal oxide layer to the appropriate interface where reaction proceeds. Let us assume a thick enough oxide layer on a plane metal surface where a steady state has been achieved. Then we can write for the rate of formation of metal oxide, MO, per unit area (assuming metal ion diffusion) ... 

One of the most important parameters in the S-E theory is the rate coefficient for radical entry. When a water-soluble initiator such as potassium persulfate (KPS) is used in emulsion polymerization, the initiating free radicals are generated entirely in the aqueous phase. Since the polymerization proceeds exclusively inside the polymer particles, the free radical activity must be transferred from the aqueous phase into the interiors of the polymer particles, which are the major loci of polymerization. Radical entry is defined as the transfer of free radical activity from the aqueous phase into the interiors of the polymer particles, whatever the mechanism is. It is beheved that the radical entry event consists of several chemical and physical steps. In order for an initiator-derived radical to enter a particle, it must first become hydrophobic by the addition of several monomer units in the aqueous phase. The hydrophobic ohgomer radical produced in this way arrives at the surface of a polymer particle by molecular diffusion. It can then diffuse (enter) into the polymer particle, or its radical activity can be transferred into the polymer particle via a propagation reaction at its penetrated active site with monomer in the particle surface layer, while it stays adsorbed on the particle surface. A number of entry models have been proposed (1) the surfactant displacement model (2) the colhsional model (3) the diffusion-controlled model (4) the colloidal entry model, and (5) the propagation-controlled model. The dependence of each entry model on particle diameter is shown in Table 1 [12]. 

The second model (Fig. 20c) assumes that upon melting of reactant A, a layer of initial product forms on the solid reactant surface. The reaction proceeds by diffusion of reactant B through this layer, whose thickness is assumed to remain constant during the reaction (Aleksandrov et al., 1987 Aleksandrov and Korchagin, 1988). The final product crystallizes (C) in the volume of the melt after saturation. Based on this model, Kanury (1992) has developed a kinetic expression for the diffusion-controlled rate. Using this rate equation, an analytical expression for the combustion wave velocity has been reported (Cao and Varma, 1994)... 

Electroless deposition of Au in KAu(CN)2 -I- HF can be controlled by both the kinetic process and the diffusion process. The deposition is a two-step process, with initial diffusion-limited deposition of the intermediate species, followed by surface-limited reduction of this species. For electroless deposition of Pt, it has been reported that the rate-determining step is the deposition on n-Si, whereas it is the dissolution of silicon on p-Si. Electroless copper deposition does not occur on Si02-covered silicon surface due to the lack of anodic dissolution of silicon In a non-HF solution, the deposition of copper on a bare silicon surface results in the formation of oxide aroimd the metal particles. In HF solutions, the deposition of copper proceeds very slowly in the dark on both p-Si and n-Si samples due to the lack of carriers. The... 

Mechanism of Adsorption. The mechanism of the sulfur dioxide adsorption and oxidation on carbon shows that the sulfur dioxide pick-up can be divided into three subsequent phases in which phase change is a function of time. In phase one, the adsorption rate is controlled by the rate of sulfur dioxide diffusion into the inner surface of the adsorbent. As the adsorption proceeds, the number of locations available for adsorp-... 

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