Diffusion coefficient for charge

When the characteristic time for charge diffusion is lower than the experiment timescale, not all the redox sites in the film can be oxidized/reduced. From experiments performed under these conditions, an apparent diffusion coefficient for charge propagation, 13app> can be obtained. In early work choroamperometry and chronocoulometry were used to measure D pp for both electrostatically [131,225] and covalently bound ]132,133] redox couples. Laviron showed that similar information can be obtained from cyclic voltammetry experiments by recording the peak potential and current as a function of the potential scan rate [134, 135]. Electrochemical impedance spectroscopy (EIS) has also been employed to probe charge transport in polymer and polyelectrolyte-modified electrodes [71, 73,131,136-138]. The methods... 

Chambers JQ (1980) Chronocoulometric determination of effective diffusion-coefficients for charge-transfer through thin electroactive polymer- films. J Electroanal Chem 130 381... 

The diffusion of U and Th within a solid is, in general, very slow due to their large size and charge (Van Orman et al. 1998). Even at mantle temperatures, it is expected that a solid will not fully equilibrate with the surrounding phases (fluid, melt or other solid phases) if solid diffusion controls the equilibration. As yet, there have been no direct determinations of diffusion coefficients for any other decay chain element. 

Although these examples demonstrate the feasibility of using calculated values as estimates, several constraints and assumptions must be kept in mind. First, the diffusant molecules are assumed to be in the dilute range where Henry s law applies. Thus, the diffusant molecules are presumed to be in the unassociated form. Furthermore, it is assumed that other materials, such as surfactants, are not present. Self-association or interaction with other molecules will tend to lower the diffusion coefficient. There may be differences in the diffusion coefficient for molecules in the neutral or charged state, which these equations do not account for. Finally, these equations only relate diffusion to the bulk viscosity. Therefore, they do not apply to polymer solutions where microenvironmental viscosity plays a role in diffusion. 

The aqueous diffusivities of charged permeants are equivalent to those of uncharged species in a medium of sufficiently high ionic strength. The product DF(r/R) is the effective diffusion coefficient for the pore. It is implicit in k that adsorption of the cations does not occur, so that the fixed surface charges on the wall of the pore are not neutralized. Adsorption is more likely to occur with multivalent cations than with univalent ones. 

The diffusion coefficients for eh, H30+, OHa, H, OH, and H202, in units of 10-5 cm2s-1, are taken respectively as 4.5, 9.0, 5.0, 7.0, 2.8, and 2.2. Of these, the first three are for charged species taken from experiment. D0h is taken the same as for self-diffusion of water. Dh2o2 is derived from self-diffusion of water using Stokes law to correct for the size effect. DQh is obtained from the diffusion of He. 

Compounds differing in charge, shape, or molecular weight may have markedly different diffusion coefficients. For example, D values in CH3CN for the metal sandwich complexes ferrocene and (C6Me6)2Ru2+ are reported as 2 x 10 5 cm2/s and 0.7 x 10 5 cm2/s, respectively [7],... 

The dramatic increase of water density at a charged surface was observed by Toney et al. in their in situ X-ray scattering experiments, which has not yet been confirmed by simulation results.58,70 In another MD simulation work, Kiselev et al. found that selfdiffusion coefficient strongly decreases with increasing electric field.27 However, no difference between the self-diffusion coefficients for motion parallel and perpendicular to the external field was observed. 

Macromolecules often have a number of sites for interactions and binding of the solute or ligand molecules. For example, hemoglobin in the blood binds oxygen at certain sites. Surface charges on the molecules also affect the diffusion. Therefore, the presence of macromolecules and small solute molecules in solutions may affect Fickian-type diffusion. Most of the experimental data on protein diffusivities have been extrapolated to very dilute or zero concentration since the diffusivity is often a function of concentration. Table 6.4 shows diffusivities of some proteins and small solutes in aqueous solutions. The diffusion coefficients for the macromolecules of proteins are on the order of magnitude of 5 X 10 11 m2/s. For small solute molecules, the diffusivities are around 1 X 10 9 m2/s. Thus, macromolecules diffuse about 20 times slower then small molecules. 

II) Transition Stern-diffuse layer. All electrostatic equations (sec. 3.6c, flg. 3.20) remain unaltered after changing all charges and potentials Into their respective stationary values. The current passing from the Stem to the diffuse layer is determined by the diffusion coefficient for normal transport, x As argued In sec. 2.2c, Is probably lower than D(bulk) but of the same order. However, special cases are possible, say systems with a very high Stem layer... 

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