Diffusion-limited process

Singlet-singlet excitation transfer, as discussed in Section 6.5.2, takes place at distances of 6-7 nm. Use data from Problem 9.13 and estimate the diffusion limit for this process in water. (The largest values observed are 3 X10 M sec" ) Is the process diffusion-limited ... 

Examination of oven-aged samples has demonstrated that substantial degradation is limited to the outer surface (34), ie, the oxidation process is diffusion limited. Consistent with this conclusion is the observation that oxidation rates are dependent on sample thickness (32). Impact property measurements by high speed puncture tests have shown that the critical thickness of the degraded layer at which surface fracture changes from ductile to brittle is about 0.2 mm. Removal of the degraded layer restores ductiHty (34). Effects of embrittled surface thickness on impact have been studied using ABS coated with styrene—acrylonitrile copolymer (35). 

Polymerization Processes. Free-radical polymerization is carried out in a variety of ways. One of the practical problems that must be dealt with is mnaway reactions which can result from auto acceleration, an increase in rate of polymerization caused by diffusion-limited termination (reduced... 

The former usually involves process temperature or isolation. Sohds surface characteristics are important in that they control the extent to which an operation is diffusion-limited, i.e., diffusion into and out of the pores of a given sohds particle, not through the voids among separate particles. The size of the solids parti(des, the surface-to-mass ratio, is also important in the evaluation of surface characteristics and the diffusion problem. 

The work of Thiele (1939) and Zeldovich (1939) called attention to the fact that reaction rates can be influenced by diffusion in the pores of particulate catalysts. For industrial, high-performance catalysts, where reaction rates are high, the pore diffusion limitation can reduce both productivity and selectivity. The latter problem emerges because 80% of the processes for the production of basic intermediates are oxidations and hydrogenations. In these processes the reactive intermediates are the valuable products, but because of their reactivity are subject to secondary degradations. In addition both oxidations and hydrogenation are exothermic processes and inside temperature gradients further complicate secondary processes inside the pores. 

Airstream neutralization of acid aerosols by NH3 present in the airway-lumen reduces the health risk associated with acid particles by reducing the acid concentration prior to particle deposition.- In addition, the liquid lining of the respiratory tract probably acts as a chemical buffer," further reducing the health hazard posed by inspired acid particles. Principal factors controlling airstream neutralization of acid aerosols, which is considered to be a diffusion-limited process, are particle surface area, and particle... 

Diffusion-limited A chemical or physical process that depends upon the... 

So far we have described the growth of a compact cluster. But, as we have seen in Fig. 5, some clusters show more fllamental structures under speciflc circumstances, and this type of form is called fractal. The simplest growth process leading to fractal structures is the so-called diffusion-limited... 

Actually, this is not really diffusion-XimiiQd, but rather Laplacian growth, since the macroscopic equation describing the process, apart from fluctuations, is not a diffusion equation but a Laplacian equation. There are some crucial differences, which will become clearer below. In some sense DLA is diffusion-limited aggregation in the limit of zero concentration of the concentration field at infinity. 

Film-free conditions It has been observed for many metals that the magnitude of / i, (see Section 1.4) increases with temperature and that the activation energy for dissolution is low, suggestive of a diffusion-limited anode process when the migration of corrosion products away from the surface is rate controlling. Some examples of the value of the activation energy for this process are given in Table 2.4. 

Further investigations of spinel formation reactions are to be found in the literature [1], but the above representative selection illustrates a number of typical features of these rate processes. Following migration of cations from one constituent onto the surfaces of the other, the process is limited by the rate of diffusion across a barrier layer. While obedience to a particular kinetic expression is sometimes reported, the data available are not always sufficiently precise to enable the fit found to be positively... 

It is therefore important to examine under what conditions the above criterion is met (i.e. fast ion backspillover relative to its desorption or consumption) for otherwise the promotional process will be internally diffusion limited not due to slow diffusion of the reactants but due to slow diffusion (backspillover) of the promoting species. 

Changing the equilibrium conditions by having condensate in the sample due to water in the carrier gas or the diffusion limitation of the condensate in larger particles changes the reaction speed. Although the kinetics of the reaction and the diffusion of the condensate are not the process Imitating steps they have an effect on the overall reaction rate as described above. 

In Og (Figure 8.1.5b), xmlike in the Ig case, the fuel jet momentum dispersed and the centerline velocity decayed rapidly owing to the lack of buoyancy. As a result, the fuel molecules diffused in every direction and formed a quasi-spherical flame. The slow diffusion processes (1) limited the transport rates of the fuel and oxygen into the flame zone and (2) decreased... 

Mass transport may constitute another problem. Since many catalysts are porous systems, diffusion of gases in and out of the pores may not be fast enough in comparison to the rate of reaction on the catalytic site. In such cases diffusion limits the rate of the overall process. 

Normally the activation energy for diffusion in the gas phase is much smaller than the activation energy for a catalyzed reaction, and hence, according to Eqs. (38) and (46), the overall or apparent activation energy for the diffusion-limited process is half of what it would be without transportation limitation. If we plot the rate as a function of reciprocal temperature one observes a change in slope when transport limitations starts to set in. 

The induced co-deposition concept has been successfully exemplified in the formation of metal selenides and tellurides (sulfur has a different behavior) by a chalcogen ion diffusion-limited process, carried out typically in acidic aqueous solutions of oxochalcogenide species containing quadrivalent selenium or tellurium and metal salts with the metal normally in its highest valence state. This is rather the earliest and most studied method for electrodeposition of compound semiconductors [1]. For MX deposition, a simple (4H-2)e reduction process may be considered to describe the overall reaction at the cathode, as for example in... 

Here, we find it necessary to be able to measure the progress of a solid state reaction. If we can do so, then we can determine the type of diffusion involved. If - log (In(l-x)) is plotted against In t, one obtains a value for the slope, m, of the line which allows cleissification of the most likely diffusion process. Of course, one must be sure that the solid state reaction is primarily diffusion-limited. Otherwise, the analysis does not hold. 

Zeolites have ordered micropores smaller than 2nm in diameter and are widely used as catalysts and supports in many practical reactions. Some zeolites have solid acidity and show shape-selectivity, which gives crucial effects in the processes of oil refining and petrochemistry. Metal nanoclusters and complexes can be synthesized in zeolites by the ship-in-a-bottle technique (Figure 1) [1,2], and the composite materials have also been applied to catalytic reactions. However, the decline of catalytic activity was often observed due to the diffusion-limitation of substrates or products in the micropores of zeolites. To overcome this drawback, newly developed mesoporous silicas such as FSM-16 [3,4], MCM-41 [5], and SBA-15 [6] have been used as catalyst supports, because they have large pores (2-10 nm) and high surface area (500-1000 m g ) [7,8]. The internal surface of the channels accounts for more than 90% of the surface area of mesoporous silicas. With the help of the new incredible materials, template synthesis of metal nanoclusters inside mesoporous channels is achieved and the nanoclusters give stupendous performances in various applications [9]. In this chapter, nanoclusters include nanoparticles and nanowires, and we focus on the synthesis and catalytic application of noble-metal nanoclusters in mesoporous silicas. 

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