Electron diffusion coefficient typical values

Let us use the obtained values of the diffusion coefficients D in water-alkaline glasses to estimate the contribution of diffusion to the decay of etr by reaction with acceptors at low temperatures. Let us estimate, for example, the temperature at which, for a typical concentration of acceptor additive N = 10 2M and for a maximal time of observation t = 106s, the condition 4nRDDNt = 0.01 [or, which is the same thing, exp( —4nRDDNt) = 0.99] will be fulfilled, i.e. the decay of et by the diffusion channel will amount to 1%. Taking into account the abnormally high mobility of solvated electrons [114] it is reasonable to assume that the main contribution to D is made by the diffusion of elr rather than by that of the acceptor. In this case, all the values of D obtained above must be related to the same process, the diffusion of e. ... 

Johnson and Willson interpreted the main feature of the observations on solid polyethylene doped with aromatic solutes in terms of an ionic mechanism it was analogous to that proposed for irradiated frozen glassy-alkane-systems in which ionization occurred with G = 3 — 4 [96], The produced charged species, electron and positive hole, were both mobile as indicated by the radiation-induced conductivity. The production of excited states of aromatic solutes was caused mainly by ion-electron neutralization. The ion-ion recombination was relatively slow but it might contribute to the delayed fluorescence observed. On the basis of Debye-Simoluchovski equation, they evaluated the diffusion coefficients of the radical anion of naphthalene and pyrene as approximately 4 x 10 12 and 1 x 10 12 m2 s 1 respectively the values were about three orders of magnitude less than those found in typical liquid systems. 

In an instantaneous-pulse experiment, the electrode material is radioactive and hence detectable by a Geiger counter. As the pulse is realized with an electronic device generating a current of 10 A on a 0.1 -cm electrode for 0.1 s, with a Geiger counter placed 1 cm from the electrode, register the trace of the radioactive univalent ion at 450. 5 after the pulse. Calculate the limiting sensitivity of the instrument. Suppose the diffusion coefficient of the ion is the typical value of 10" m s . (Xu)... 

In membranes, the motional anisotropies in the lateral plane of the membrane are sufficiently different from diffusion in the transverse plane that the two are separately measured and reported [4b, 20d,e]. Membrane ffip-ffop and transmembrane diffusion of molecules and ions across the bilayer were considered in a previous section. The lateral motion of surfactants and additives inserted into the lipid bilayer can be characterized by the two-dimensional diffusion coefficient (/)/). Lateral diffusion of molecules in the bilayer membrane is often an obligatory step in membrane electron-transfer reactions, e.g., when both reactants are adsorbed at the interface, that can be rate-limiting [41]. Values of D/ have been determined for surfactant monomers and probe molecules dissolved in the membrane bilayer typical values are given in Table 2. In general, lateral diffusion coefficients of molecules in vesicle... 

In the Fritsch-Faulkner model, it is assumed that redox centers are immobilized. This of course rules out electron transfer via physical diffusion of the center. The model is based on the notion of extended electron transfer. It is also assumed that the concentration, and therefore the spatial distribution of redox sites, affects the diffusion coefficient D. A notable feature of the analysis is the explicit consideration of the finite volume of the redox center, which for simplicity is assumed to be a rigid sphere. Excluded volume effects are important when the redox site concentration is high (recall that a typical value is in the range of 0.1-1 M). 

A discussion of the chronoamperometric feedback response is valuable, as potential step measurements have been used to obtain homogeneous kinetic parameters. Calculations of the chronoamperometric response also provide valuable information on the time taken to reach a true steady state, which is particularly important for approach curve measurements. It has been demonstrated that values of t in excess of 100 may be necessary to achieve steady-state conditions (within a few percent). For typical tip disk electrode radii of 12.5 and 2.5 pm, and a typical diffusion coefficient of 1X10 cm s , this corresponds to real times that are greater than 15 and 0.6 s, respectively. For the larger disk size, the time is longer than required for many other steady-state measurements with SECM. Furthermore, it is important to point out that this analysis is for the situation where A and B have the same diffusion coefficient. It has been demonstrated comprehensively that unequal diffusion coefficients of A and B greatly increase the time to true steady state even for simple electron transfer without homogeneous kinetics. ... 

Because Qcoii is a direct measure of the charge present in the layer at a delay time fd, the recombination dynamics can be determined via an iterative procedure [171]. For the data shown in Fig. 20, this analysis yields y = 3.5xl0 m s and y= 1.2 X 10 m s for the chloroform as-cast and the annealed P3HT PCBM layer, respectively. The value for the annealed sample agrees very well with the bimolecular recombination coefficient measured by TAS at carrier densities typical for steady-state AMI.5 illumination (see, e.g., [189, 195]). To compare these values to the Langevin limit, the mobilities of the electrons and the holes in the blend must be known. Information on these quantities can be gained from drift-diffusion simulations of the photocurrent transients with different collection biases (see Fig. 20b). This yields mobilities of 1.2 x 10" m and... 

From Eq. (6.45), if = —0.17, then operation on neat methanol with only product water back-fed to the anode can be theoretically achieved. Each DAFC will have a different value for this coefficient, depending on the number of electrons exchanged in the fuel oxidation. This condition must be achieved with a capillary or gas-phase pressure difference, since the electro-osmotic drag and diffusion are always toward the cathode in the DMFC. Practically, methanol crossover reduces performance, so that some methanol dilution is typical, as described in the next section. 

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