Surface rate limiting

The dopant was diffused into (111) single crystals, having dislocation densities of less than 500/cm2, under intrinsic vacuum sealed tube conditions. It was found that the low-concentration migration of the dopant, from the vapor phase and into the bulk, was markedly affected by a surface rate-limiting process. The diffusion data for 1100 to 1250C could be described by ... 

Interestingly, steady-state oxygen permeation measmements by Dou et al. ° provided no evidence of a surface rate limitation for CSZ tubes containing a segregated impurity phase. The order with respect to oxygen remained close to G. This second phase consisted of a... 

Process 2, the adsorption of the reactant(s), is often quite rapid for nonporous adsorbents, but not necessarily so it appears to be the rate-limiting step for the water-gas reaction, CO + HjO = CO2 + H2, on Cu(lll) [200]. On the other hand, process 4, the desorption of products, must always be activated at least by Q, the heat of adsorption, and is much more apt to be slow. In fact, because of this expectation, certain seemingly paradoxical situations have arisen. For example, the catalyzed exchange between hydrogen and deuterium on metal surfaces may be quite rapid at temperatures well below room temperature and under circumstances such that the rate of desorption of the product HD appeared to be so slow that the observed reaction should not have been able to occur To be more specific, the originally proposed mechanism, due to Bonhoeffer and Farkas [201], was that of Eq. XVIII-32. That is. 

As with the other surface reactions discussed above, the steps m a catalytic reaction (neglecting diffiision) are as follows the adsorption of reactant molecules or atoms to fomi bound surface species, the reaction of these surface species with gas phase species or other surface species and subsequent product desorption. The global reaction rate is governed by the slowest of these elementary steps, called the rate-detemiming or rate-limiting step. In many cases, it has been found that either the adsorption or desorption steps are rate detemiining. It is not surprising, then, that the surface stmcture of the catalyst, which is a variable that can influence adsorption and desorption rates, can sometimes affect the overall conversion and selectivity. 

Any one of the five basic processes may be responsible for limiting the extraction rate. The rate of transfer of solvent from the bulk solution to the soHd surface and the rate into the soHd are usually rapid and are not rate-limiting steps, and the dissolution is usually so rapid that it has only a small effect on the overall rate. However, knowledge of dissolution rates is sparse and the mechanism may be different in each soHd (1). 

The key to solving these problems is to design the vessel for a mass flow pattern. This involves consideration of both the hopper angle and surface finish, the effect of inserts used to introduce gas and control the soHds flow pattern, and sizing the outlet valve to avoid arching and discharge rate limitations. In addition, the gas or Hquid must be injected such that the soHd particles ate uniformly exposed to it, and flow instabiHties such as fluidization in localized regions are avoided. 

Acid producers. Corrosion usually is moderate and localized. Almost all significant attack is associated with anaerobic bacteria (facultative and obhgate), as aerobic acid-producing varieties usually reside near the top of deposits and corrosion products contacting oxygenated waters. Thus, the direct effect on corrosion at metal surfaces is limited. Additionally, although acidic products may be expected to increase corrosion rates, acidity cannot be pronounced in deposits to put it simply, the deposits and corrosion products would dissolve at sufficiently acidic pH. 

A furdrer complication is that in these slowly growing oxide films, tire spread of the oxide across the metal surface is limited in the early stages by nucleation and growth control. The bare patches of metal between the oxide nuclei will clearly be exposed to a higher oxygen potential and new oxide nuclei will grow at a different initial rate than on the existing nuclei. 

Since NFI3 is highly water-soluble and neutralization within the droplet occurs rapidly, " the rate-limiting step in acid neutralization is normally NH 3 transport to the air/droplet interface, which is dependent on [NH3]4 and particle surface area. At high [NH3J4, the rate of NH, uptake across the air/droplet interface is given by... 

The Environmental Protection Agency (EPA) and other federal, state and local authorities govern security of supply in relation to quantity for surface and groundwater by the granting of an abstraction license. The license limits the total daily quantity and the rate at which the waters may be abstracted, taking account of the natural resource and the needs of other abstractors. Metered water supply is subject to contract with the water companies, who may impose quantity and draw-off rate limitations. The limitations imposed by the license or contract may influence plant location. 

Acetylcholine serves as a neurotransmitter. Removal of acetylcholine within the time limits of the synaptic transmission is accomplished by acetylcholinesterase (AChE). The time required for hydrolysis of acetylcholine at the neuromuscular junction is less than a millisecond (turnover time is 150 ps) such that one molecule of AChE can hydrolyze 6 105 acetylcholine molecules per minute. The Km of AChE for acetylcholine is approximately 50-100 pM. AChE is one of the most efficient enzymes known. It works at a rate close to catalytic perfection where substrate diffusion becomes rate limiting. AChE is expressed in cholinergic neurons and muscle cells where it is found attached to the outer surface of the cell membrane. 

A and E refer to the desorption, dissociation, decomposition or other surface reactions by which the reactant or reactants represented by M are converted into products. If [M] is constant within the temperature interval studied, then the values of A and E measured refer to this process. Alternatively, if the effective magnitude of [M] varies with temperature, the apparent Arrhenius parameters do not specifically refer to the product evolution step. This is demonstrated quantitatively by the following example [36]. When E = 100 kJmole-1 andA [M] = 3.2 X 1030 molecules sec-1, then rate coefficients at 400 and 500 K are 2.4 X 1017 and 1.0 X 1020 molecules sec-1, respectively. If, however, E is again 100 kJ mole-1 and A [M] varies between 3.2 X 1030 molecules sec-1 at 500 K and z X 3.2 X 1030 molecules sec-1 at 400 K, the measured values of A and E vary significantly, as shown in Fig. 7, when z ranges from 10-3 to 103. Thus, the measured value of E is not necessarily identifiable with the rate-limiting step if a concentration of a participant is temperature-dependent. This... 

Decompositions rate-limited by a surface or desorption step comparable in some respects with heterogeneous catalytic processes... 

---