Rate-limiting steps film diffusion

The rate of hydrolysis of sarin on Dowex-50 cation exchange resin is insensitive to the stirring rate. However, with a more active catalyst (Amberlite-IRA 400), the rate constant at 20°C was 5.3, 7.5, and 8.5 h at 60,800 and 1000 revolutions/min , respectively, suggesting that film diffusion was the rate-limiting. step. Thus, the mechanism of the rate-limiting step depends on the nature of the catalyst [34]. 

Equations 4.31 and 4.32 also suggest another important fact regarding NEMCA on noble metal surfaces The rate limiting step for the backspillover of ions from the solid electrolyte over the entire gas exposed catalyst surface is not their surface diffusion, in which case the surfacediffusivity Ds would appear in Eq. 4.32, but rather their creation at the three-phase-boundaries (tpb). Since the surface diffusion length, L, in typical NEMCA catalyst-electrode film is of the order of 2 pm and the observed NEMCA time constants x are typically of the order of 1000 s, this suggests surface diffusivity values, Ds, of at least L2/t, i.e. of at least 4 10 11 cm2/s. Such values are reasonable, in view of the surface science literature for O on Pt(l 11).1314 For example this is exactly the value computed for the surface diffusivity of O on Pt(lll) and Pt(100) at 400°C from the experimental results of Lewis and Gomer14 which they described by the equation ... 

Zogorski et al. [125] indicate that external transport is the rate-limiting step in systems having poor mixing, dilute concentration of adsorbate, small particle sizes of adsorbent, and a high affinity of adsorbate for adsorbent. Some experiments conducted at low concentrations have shown that film diffusion solely controls the adsorption kinetics of low molecular weight substances [81,85]. 

Also, in the late 1950s and 1960s some particularly seminal papers on ion exchange kinetics appeared by Helfferich (1962b, 1963, 1965) that are classics in the field. In this research it was definitively shown that the rate-limiting steps in ion exchange phenomena were film diffusion (FD) and/ or particle diffusion (PD). Additionally, the Nernst-Planck theories were explored and applied to an array of adsorbents (Chapter 5). 

The theories proposed to explain the formation of passivation film are salt-film mechanism and acceptor mechanism [21]. In the salt-film mechanism, the assumption is that during the active dissolution regime, the concentration of metal ions (in this case, copper) in solution exceeds the solubility limit and this results in the precipitation of a salt film on the surface of copper. The formation of the salt film drives the reaction forward, where copper ions diffuse through the salt film into electrolyte solution and the removal rate is determined by the transport rate of ions away from the surface. As the salt-film thickness increases, the removal rate decreases. In the acceptor mechanism, it is assumed that the metal-ion products remain adsorbed onto the electrode surface until they are complexed by an acceptor species like water or anions. The rate-limiting step is therefore the mass transfer of the acceptor to the surface. Recent studies confirmed that water may act as an acceptor species for dissolving copper ions [22]. 

Aqueous Boundury (Diffusion) Luyer. The aqueous boundary layer (often referred to as the stagnant, unstirred, or aqueous diffusion layer) is an important hydrodynamic barrier that a drug must traverse before reaching the surface of the mucosal membrane. " Before a molecule in the intestinal lumen passes through the membrane, it must first cross the aqueous boundary layer located at the intestinal lumen and membrane interface (Fig. 2). The liquid in this layer, in reality, is not static, as the term unstirred implies, but represents a film at the surface where diffuse and natural convective mixing occurs. This unstirred layer can be a rate-limiting step for the absorption of hydro-phobic molecules. However, hydrophilic molecules such... 

Two different techniques have been employed for the precipitation of membranes from a polymer casting solution. In the first method, the precipitant is introduced from the vapor phase. In this case the precipitation is slow, and a more or less homogeneous structure is obtained without a dense skin on the top or bottom side of the polymer film. This structure can be understood when the concentration profiles of the polymer, the precipitant and the solvent during the precipitation process are considered. The significant feature in the vapor-phase precipitation process is the fact that the rate-limiting step for precipitant transport into the cast polymer solution is the slow diffusion in the vapor phase adjacent to the film surface. This leads to uniform and flat concentration profiles in the film. The concentration profiles of the precipitant at various times in the polymer film are shown schematically in Figure 13. 

The third and fourth models are based on the assumption of an immobile-water phase. This phase can be caused by the existence of crevices or pits on the grain surfaces and by dead-end pores created by tight packing of the grains. In this article, we did not consider an immobile-water film that could cover entire grain surfaces. Diffusion of Mo(VI) into the immobile-water phase retards transport because of the capacitance of this phase and also provides a rate-limiting step for sorption on the solid matrix adjacent to the immobile-water phase. For these models, transport of Mo(VI) from the flowing phase can occur by sorption to the solid phase or by diffusion to the immobile-water phase which then is followed by sorption to the solid phase. The sorption from either phase is assumed to be at local equilibrium with the adjacent fluid phase. An additional balance equation for the solid phase adjacent to the immobile-water phase is as follows ... 

Hansen (57) pointed out that evaporation of a solvent from a polymer solution faced two barriers when cast on an impermeable substrate resistance to solvent loss at the air-liquid interface and diffusion from within the film to the air interface. Evaporation of neat solvents as well as moderately dilute solutions is limited by resistance at the air interface, but as solvent concentration becomes low (5-10-15%), the rate-controlling step is diffusion through the film. Hansen pointed out that at the point when solvent loss changes to a diffusion-limited process, the concentration of solvent is sufficient to reduce the glass transition temperature, Tg, of the polymer to the film temperature. 

Ellis (60) pointed out that high-solids polyester coatings typically contain so little solvent that the Tg of the resin-solvent combination is above the temperature of the deposited film. Therefore, evaporation of solvent occurs very slowly solely by diffusion as the rate-limiting step therefore, the film sags and runs before sufficient solvent evaporates to provide "set-up" of the film. A precise method was provided for determination of the "transition point" of a given resin-solvent combination. This point is the resin concentration at which solvent evaporation changes from surface-controlled to a diffusion-controlled process. 

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