Diffusion typical timescale

However, there is another operative timescale in solution. This is that timescale for reaction with other photolytically generated species or with added reactants. This reaction cannot take place faster than the diffusion-limited reaction rate which is concentration dependent (59). Typical diffusion-controlled reaction rate constants are 109-1010 dm3 mol"1 second-1. By comparison, a typical gas-kinetic rate con-... 

To integrate the equations of motion in a stable and reliable way, it is necessary that the fundamental time step is shorter than the shortest relevant timescale in the problem. The shortest events involving whole atoms are C-H vibrations, and therefore a typical value of the time step is 2fs (10-15s). This means that there are up to one million time steps necessary to reach (real-time) simulation times in the nanosecond range. The ns range is sufficient for conformational transitions of the lipid molecules. It is also sufficient to allow some lateral diffusion of molecules in the box. As an iteration time step is rather expensive, even a supercomputer will need of the order of 106 s (a week) of CPU time to reach the ns domain. 

Typical values for the dimensions of the various layers are included in Figure 1 of Chapter 1. Diffusion layer thicknesses depend on the timescale and hydro-dynamic conditions they will be dealt with in detail in Sections 3 and 4. 

While experiments involving solution-phase reactants have provided deep insights into the dynamics of heterogeneous electron transfer, the magnitude of the diffusion-controlled currents over short timescales ultimately limits the maximum rate constant that can be measured. For diffusive species, the thickness of the diffusion layer, S, is defined as S = (nDt)1/2, where D is the solution-phase diffusion coefficient and t is the polarization time. Therefore, the depletion layer thickness is proportional to the square root of the polarization time. One can estimate that the diffusion layer thickness is approximately 50 A if the diffusion coefficient is 1 x 10-5 cm2 s-1 and the polarization time is 10 ns. Given a typical bulk concentration of the electroactive species of 1 mM, this analysis reveals that only 10 000 molecules or so would be oxidized or reduced at a 1 pm radius microdisk under these conditions The average current for this experiment is only 170 nA, which is too small to be detected with high temporal resolution. 

This review has attempted to put hydrodynamic modulation methods for electroanalysis and for the study of electrochemical reactions into context with other electrochemical techniques. HM is particularly useful for the extension of detection limits in analysis and for the detection of heterogeneity on electrode surfaces. The timescale addressable using HM methodology is limited by the time taken for diffusion across the concentration boundary layer, typically >0.1 s for conventional RDE and channel electrode geometries. This has meant a restriction on the application of HM to deduce fast reaction mechanisms. New methodologies, employing smaller electrodes and thin layer geometries look to lift this restraint. 

We have thus far considered coherent processes that take place in RPs (which in some cases been have been modulated by stochastic motion). However, the common spin-lattice and spin-spin relaxation processes familiar from magnetic resonance also come to bear on the dynamics of RPs. Typical values of Ti and T2 for small organic radicals in homogeneous solution are on the microsecond timescale and as such are rather slow relative to coherent mixing and RP diffusion. Thus, for the most part, effects of incoherent spin relaxation are not manifest in such reactions. However, for reactions in which the RP lifetime is substantially extended, for instance, by constraining the RP inside a microreactor such as a micelle (many examples in Ref. 14), relaxation effects become significant. 

In radiolysis, one of the most important reactions of solvated electrons is recombination with positive ions and radicals that are simultaneously produced in close proximity inside small volumes called spurs. These spurs are formed through further ionization and excitation of the solvent molecules. Thus, in competition with diffusion into the bulk, leading to a homogeneous solution, the solvated electron may react within the spurs. Geminate recombinations and spur reactions have been widely studied in water, both experimentally and theoretically, ° and also in a few other solvents. " Typically, recombinations occur on a timescale of tens to hundreds of picoseconds. In general, the primary cation undergoes a fast proton transfer reaction with a solvent molecule to produce the stable solvated proton and the free radical. Consequently, the... 

Interestingly, the diffusional behavior of membrane proteins measured experimentally by FRAP, FCS, or single particle tracking in cells is more complex than predicted by this model. This technique is described best for the case of cell surface proteins, as assessed by FRAP. Such measurements indicate that diffusion is typically much slower than one would expect based on membrane viscosity. In cell membranes, typical values of D for transmembrane proteins are approximately 0.05 pm /s or less, which is much slower than observed in artificial membranes composed of purified lipids. In addition, a significant fraction of proteins is often immobile over the timescale of diffusion experiments (4, 5). Furthermore, diffusional mobilities vary among proteins, and sometimes they differ for the same protein expressed in different cell lines (4, 5). Deviations from pure diffusion are more readily apparent when the trajectories... 

Another kind of cell, made by Graham and Curran, was based on an internal reflection crystal [80]. A gold minigrid was mounted directly on a prism (9 x 9 x 45 mm) and on top of this was a zinc selenide prism. The distance (observation) between the minigrid and the prism is typically 13-15 pm, which results in a very short response time. For a potential-step experiment, maximum absorbance is achieved within a couple of seconds. The cell is especially well-suited for potential-scan experiments because the intermediate generated at the electrode will rapidly fill out most of the observation distance even when moderately fast sweep rates (50 mV s ) are applied. Some memory effect is, however, present, because the diffusion layer will not be completely evolved on this timescale. At smaller sweep rates (2 mV s ) all of the observation layer behaves like a thin layer, where the concentrations are in equilibrium with the electrode surface concentrations. The cell has been used to study the reduction process of Fe(CO)s by CV, where it was pos-... 

Two timescales can be distinguished in the adsorption process of ionic species. The first timescale is characterized by the diffusion relaxation time of the EDL, = 1 / (D,k /) see Equations 5.32 and 5.34 above. It accounts for the interplay of electrostatic interactions and diffusion. The second scale is provided by the characteristic time of the used experimental method, tgxp, that is, the minimum interfacial age that can be achieved with the given method typically,... 

SSAR is observed when the binary diffusion couples listed in Table 2.4 are heated to an appropriate reaction temperature, TR. Examples of typical values of JR are given in Table 2.4. It is well known that amorphous metallic alloys tend to crystallize in laboratory timescales upon heating to temperatures close to their glass-transition temperature, T% [2.16]. For a typical practical timescale (e.g., minutes), one can define crystallization temperature as the temperature at which a significant fraction of an amorphous sample undergoes crystallization in the specified time. The time required for an amorphous phase to crystallize can be identified with t 2 of Fig. 2.6 (see discussion in Sect 2.1.3). In the low temperature regime (well below Tg), atomic diffusion in amorphous alloys is... 

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