Process diffusion-controlled

Structure and diffusion-controlled processes in metallic systems... 

Note. Both the rearrangement In t-ButanoI) and the double bond isomerization of (114) (In Benzene) are quenched in a diffusion-controlled process by suitable triplet acceptors e.g., naphthalene or 2,5-dimethylhexa-2,4-diene). The rearrangement (114) (118) -I- (120) is also observed on irradiation in... 

If the PBR is less than unity, the oxide will be non-protective and oxidation will follow a linear rate law, governed by surface reaction kinetics. However, if the PBR is greater than unity, then a protective oxide scale may form and oxidation will follow a reaction rate law governed by the speed of transport of metal or environmental species through the scale. Then the degree of conversion of metal to oxide will be dependent upon the time for which the reaction is allowed to proceed. For a diffusion-controlled process, integration of Pick s First Law of Diffusion with respect to time yields the classic Tammann relationship commonly referred to as the Parabolic Rate Law ... 

Before any chemistry can take place the radical centers of the propagating species must conic into appropriate proximity and it is now generally accepted that the self-reaction of propagating radicals- is a diffusion-controlled process. For this reason there is no single rate constant for termination in radical polymerization. The average rate constant usually quoted is a composite term that depends on the nature of the medium and the chain lengths of the two propagating species. Diffusion mechanisms and other factors that affect the absolute rate constants for termination are discussed in Section 5.2.1.4. 

Termination by self-reaction of propagating radicals is a diffusion-controlled process even at very low conversion.1 The evidence for this includes the following ... 

The sum of all results is consistent with the formation of both the aryl cation and the aryl radical in the aqueous acid system without copper, and with the dominance of the aryl radical in the presence of copper. The product ratios are also qualitatively consistent with the hypothesis that the reactivity of aryl cations with nucleophiles is close to that of a diffusion-controlled process (see Sec. 8.3), and that aryl radicals have arylation rate constants that are about two orders of magnitude smaller than that for diffusion control (0.4-1.7 X 107 m-1s-1 Kryger et al., 1977 Scaiano and Stewart, 1983). Due to the relatively low yields of these dediazoniations in the pentyl nitrite/benzene systems, no conclusions should be drawn from the results. 

Although reaction 6 is essentially a diffusion-controlled process for all kinds of substituents, the small differences observed in the rate constants through the series alkane-, amino- and alkoxy-sulfonyl chlorides have been attributed to the increased importance of polar effects to the transition state11. 

Time-resolved optical absorption spectroscopy experiments have shown that arenesul-fonyl radicals decay with clean second-order kinetics14 the values of 2 k,/a h where s2 is the extinction coefficient at the monitoring wavelength, increased linearly with decreasing viscosity of the solvent, further indicating that reaction 16 is clearly a diffusion-controlled process. 

We have already mentioned the application of supercomputers to biochemical simulations. Internal dynamics may play an Important role In such simulations. An example would be enzyme binding-site fluctuations that modulate reactivity or the dynamics of antigen-antibody association (11). In the specific case of diffusion-controlled processes, molecular recognition may occur because of long-range sterlc effects which are hard to assess without very expensive simulations (12.)-... 

Figure 26 shows the redox potential of 40 monolayers of cytochrome P450scc on ITO glass plate in 0.1 KCl containing 10 mM phosphate buffer. It can be seen that when the cholesterol dissolved in X-triton 100 was added 50 pi at a time, the redox peaks were well distinguishable, and the cathodic peak at -90 mV was developed in addition to the anodic peak at 16 mV. When the potential was scanned from 400 to 400 mV, there could have been reaction of cholesterol. It is possible that the electrochemical process donated electrons to the cytochrome P450scc that reacted with the cholesterol. The kinetics of adsorption and the reduction process could have been the ion-diffusion-controlled process. 

In such systems the researcher can electrochemically clean and precondition the metal electrode before each run to provide an identical surface for the anodic and the cathodic half-reactions as well as for the catalytic reaction between them. Use of a rotating disk electrode/ckatalyst also allows surface- and diffusion-controlled processes to be easily distin-guished. ... 

The A term relates to a diffusion-controlled process and the B zero-order term to an erosive process. 

It is usually believed that the growth of dendritic crystals is controlled by a bulk diffusion-controlled process which is defined as a process controlled by a transportation of solute species by diffusion from the bulk of aqueous solution to the growing crystals (e.g., Strickland-Constable, 1968 Liu et al., 1976). The appearances of feather- and star-like dendritic shapes indicate that the concentrations of pertinent species (e.g., Ba +, SO ) in the solution are highest at the corners of crystals. The rectangular (orthorhombic) crystal forms are generated where the concentrations of solute species are approximately the same for all surfaces but it cannot be homogeneous when the consumption rate of solute is faster than the supply rate by diffusion (Nielsen, 1958). 

Given that, under the defined conditions, there is no interfacial kinetic barrier to transfer from phase 2 to phase 1, the concentrations immediately adjacent to each side of the interface may be considered to be in dynamic equilibrium throughout the course of a chronoamperometric measurement. For high values of Kg the target species in phase 2 is in considerable excess, so that the concentration in phase 1 at the target interface is maintained at a value close to the initial bulk value, with minimal depletion of Red in phase 2. Under these conditions, the response of the tip (Fig. 11, case (a)] is in agreement with that predicted for other SECM diffusion-controlled processes with no interfacial kinetic barrier, such as induced dissolution [12,14—16] and positive feedback [42,43]. A feature of this response is that the current rapidly attains a steady state, the value of which increases... 

The superscripts o and w denote the organic and aqueous phases, respectively. Equation (6) suggests a linear dependence off c ) on t for a diffusion-controlled process. 

This technique has been used to study the extraction kinetics of rare-earth elements from an aqueous phase into heptane by 2-ethylhexyl phosphonic acid mono-2-ethylhexyl ester (HEH/EHP) [31]. The linear dependence of f c ) on t in Fig. 5 was considered to indicate that the extraction of ErCl3 by HEH/EHP is a diffusion-controlled process. 

Since the ion transfer is a rather fast process, the faradaic impedance Zj can be replaced by the Warburg impedance Zfy corresponding to the diffusion-controlled process. Provided that the Randles equivalent circuit represents the plausible model, the real Z and the imaginary Z" components of the complex impedance Z = Z —jZ " [/ = (—1) ] are given by [60]... 

J. Lebenhaft and R. Kapral, Diffusion-controlled processes among partially absorbing stationary sinks, J. Stat. Phys. 20, 25 (1979). 

They have shown that singlet energy transfer from many donors to biacetyl takes place by a diffusion-controlled process. 

WI Higuchi, EN Heistand. Dissolution rates of finely divided drug powders I. Effect of a distribution of particle sizes in a diffusion-controlled process. J Pharm Sci 52 67-71, 1963. 

Exciplexes are complexes of the excited fluorophore molecule (which can be electron donor or acceptor) with the solvent molecule. Like many bimolecular processes, the formation of excimers and exciplexes are diffusion controlled processes. The fluorescence of these complexes is detected at relatively high concentrations of excited species, so a sufficient number of contacts should occur during the excited state lifetime and, hence, the characteristics of the dual emission depend strongly on the temperature and viscosity of solvents. A well-known example of exciplex is an excited state complex of anthracene and /V,/V-diethylaniline resulting from the transfer of an electron from an amine molecule to an excited anthracene. Molecules of anthracene in toluene fluoresce at 400 nm with contour having vibronic structure. An addition to the same solution of diethylaniline reveals quenching of anthracene accompanied by appearance of a broad, structureless fluorescence band of the exciplex near 500 nm (Fig. 2 )... 

If quenching is a diffusion-controlled process (k 3xl09L mol 1 s ), the lifetime t 3x 10-7 s coincides with the lifetime of triplet acetophenone (product of peroxyl radical disproportionation in oxidized ethylbenzene). 

---