Electron diffusion coefficient

FIGURE 8.6 Evolution of the electron diffusion coefficient in LAr starting with an initial velocity 4.8 times the thermal velocity. Reproduced from Mozumder (1982). 

Schmidt KH, Flan P, Bartels DM (1995) Radiolytic yields of the hydrated electron from transient conductivity improved calculation of the hydrated electron diffusion coefficient and analysis of some diffusion-limited (e )aq reaction rates. J Phys Chem 99 10530-10539 Schoneich C, Aced A, Asmus K-D (1991) Halogenated peroxyl radicals as two-electron-transfer agents. Oxidation of organic sulfides to sulfoxides. J Am Chem Soc 113 375-376 Schuchmann Fl-P, von Sonntag C (1981) Photolysis at 185 nm of dimethyl ether in aqueous solution Involvement of the hydroxymethyl radical. J Photochem 16 289-295 Schuchmann Fl-P, von Sonntag C (1984) Methylperoxyl radicals a study ofthey-radiolysis of methane in oxygenated aqueous solutions. Z Naturforsch 39b 217-221 Schuchmann Fl-P, von Sonntag C (1997) Heteroatom peroxyl radicals. In Alfassi ZB (ed) Peroxyl radicals. Wiley, Chichester, pp 439-455... 

Figure 8.27 illustrates the theoretical electron density profiles and photocurrent transients calculated by Solbrand et al. The transients exhibit a maximum at a time fpeak = d2/6D. The inset in Fig. 8.26 shows that a plot of fpeak VS. d2 is linear as predicted (the authors use W rather than d to denote the film thickness), and the slope of the plot gives a value of 1.5 x 10-scm-2s-1 for the electron diffusion coefficient. 

Aoki, A. and Heller, A. (1993) Electron-diffusion coefficients in hydrogels formed of cross-linked redox polymers. Journal of Physical Chemistry, 97 (42), 11014-11019. 

One of the key questions that remains unanswered is the role of temporary localisation of electrons in traps in determining the rate of electron transport in porous and nanocrystalline electrodes. Dlocik et al. [90] have taken electron trapping and detrapping into account by defining effective values for the electron diffusion coefficient and lifetime as... 

The ratio of the free electron diffusion coefficient (3-86) and the electron mobility (3-70) is proportional to the average electron energy, which is known as the Einstein relation ... 

Figure 14 (a) Time-dependent behavior of eation radicals in liquid n-dodecane monitored at 790 nm. The dotted and the solid lines represent the experimental curve and the simulation curve, respectively. The parameters of the electron diffusion coefficient (Dg) = 6.4 x 10 cm /sec, the cation radical diffusion coefficient (Z)+) = 6.0 x 10 cm /sec, the relative dielectric constant e = 2.01, the reaction radius R = 0.5 nm, and the exponential function as shown in Eq. (19) with ro = 6.6 nm were used, (b) Time-dependent distribution function obtained from fitting curve of (a), r indicates the distance between the cation radical and the electron. The solid line, dashed line, and dots represent the distribution of cation radical lectron distance at 0, 30, and 100 psec after irradiation, respectively. 

Interactions and electric communication between redox centers are of importance for charge transfer. A Ru complex of poly[2-(2-pyridyl)-bisbenz-imidazole] where the redox centers are coordinated directly to a long-range 7t network has been investigated [36b]. Electron-transfer studies yielded electron diffusion coefficients of over 10 cm s" for the Ru(IIEII) state, at least one order of magnitude higher than for a non-conjugated Ru(bpy)3 type polymers. 

In the simple models, is independent of the potential because the effects of both the counterion activity and interactions of charged sites (electron-electron interactions) are neglected. However, in real systems the electrochemical potential of counterions is changed as the redox state of the film is varied, the counterion population is limited, and interactions between electrons arise. According to Chidsey andMnr-ray, the potential dependence of the electron diffusion coefficient can be expressed as follows [39] ... 

The electron diffusion coefficient D E) from the electric field in the single-walled zigzag CNT with adsorbed hydrogen atoms has a pronounced nonlinear character (Fig. 1.5). Increase of the field leads to an increase in first rate, and then to his descending to a stationary value. This phenomenon is observed for all systems with intermittent and limited electron dispersion law [17]. Electron diffusion coefficient can be considered constant in the order field amplitudes E 5x10 V/m. The maximum value of the diffusion coefficient for semiconductor CNTs observed at field strengths of the order ofE- 4.8x10 V/m. 

FIGURE 1.5 Dependence of the electron diffusion coefficient D(E) on the intensity of the external electric field E for CNT (10,0) ideal - solid line and hydrogen adatom - dashed line, x-axis is a dimensionless quantity of the external electric field E (unit corresponds to 4.7x10 V/m), they-axis is a dimensionless diffusion coefficient D(E) (unit corresponds to 3.5xl(EA/m). 

When adding the adsorbed hydrogen atoms the electron diffusion coefficient, as well as the conductivity is reduced by 0.05% (Fig. 1.5). This behavior of the diffusion coefficient in an external electric field is observed for different concentrations of hydrogen adatoms (Fig. 1.6) and semiconductor CNTs with different diameters by adding 100 adatoms (Fig. 1.7). 

The method for theoretical calcrdation of the semiconducting zigzag CNT transport properties with adsorbed hydrogen atoms developed. Analytical expressions for the conductivity and the electron diffusion coefficient in zigzag CNT with hydrogen adatoms in the presence of an electric field. 

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