Electrical migration, diffuse double-layer

When neither an external fluid flow nor an electrical field is imposed, the diffuse double layer is at equilibrium and the net ion fluxes due to the electrical migration and Brownian diffusion should vanish. Thus, the ions have Boltzmann distributions,... 

B.6 MISCELLANEOUS DIGITAL SIMULATIONS B.6.1 Electrical Migration and Diffuse Double-Layer Effects... 

Electrokinetic phenomenon arises when the mobile portion of the diffuse double layer and an external electric field interact in the viscous shear layer near the charged surface. If an electric field is applied tangentially along a charged surface, then the electric field exerts a force on the charge in the diffuse layer. This layer is part of the electrolyte solution, and migration of the mobile ions will carry the solvent with them and cause it to flow. On the other hand, an electric field is created if the charged surface and diffuse part of the double layer are made to move relative to each other. The four electrokinetic phenomena broadly classified are... 

The physical separation of charge represented allows externally apphed electric field forces to act on the solution in the diffuse layer. There are two phenomena associated with the electric double layer that are relevant electrophoresis when a particle is moved by an electric field relative to the bulk and electroosmosis, sometimes called electroendosmosis, when bulk fluid migrates with respect to an immobilized charged surface. 

In the presence of EOF, the observed velocity is due to the contribution of electrophoretic and electroosmotic migration, which can be represented by vectors directed either in the same or in opposite direction, depending on the sign of the charge of the analytes and on the direction of EOF, which depends on the sign of the zeta potential at the plane of share between the immobilized and the diffuse region of the electric double layer at the interface between the capillary wall and the electrolyte solution. Consequently, is expressed as... 

Ah already stated the liquid junction potential results from the different mobility of ions. Consequently no diffusion potential can result at the junction of the electrolyte solution the ions of which migrate with the same velocity. It is just this principle on which the salt bridge, filled by solutions of those salts the ions of which have approximately the same mobilities, is based (the equivalent conductivities of ions Kf and Cl- at infinite dilution at 25 °C are 73.5 and 70.3 respectively and the conductivities of ions NH+ and NOg are 73.4 and 71.4 respectively). Because ions of these salts have approximately the same tendency to transfer their charge to the more diluted solution during diffusion, practically no electric double layer is formed and thus no diffusion potential either. The effect of the salt bridge on t he suppression of the diffusion potential will be better, the more concentrated the salt solution is with which it is filled because the ions of the salt are considerably in excess at the solution boundary and carry, therefore, almost exclusively the eleotric current across this boundary. 

The resulting potential difference across the double layer is known as the zela potential. When an electric field is applied to the ends of the capillary, those ions in the diffuse part of the double layer migrate along the length of the capillary and drag the bulk solution with them. 

If the two electrode systems that compose a cell involve electrolytic solutions of different composition, there will be a potential difference across the boundary between the two solutions. This potential difference is called the liquid junction potential, or the diffusion potential. To illustrate how such a potential difference arises, consider two silver-silver chloride electrodes, one in contact with a concentrated HCl solution, activity = the other in contact with a dilute HCl solution, activity = Fig. 17.7(a). If the boundary between the two solutions is open, the and Cl ions in the more concentrated solution diffuse into the more dilute solution. The ion diffuses much more rapidly than does the Cl ion (Fig. 17.7b). As the ion begins to outdistance the Cl ion, an electrical double layer develops at the interface between the two solutions (Fig. 17.7c). The potential difference across the double layer produces an electrical field that slows the faster moving ion and speeds the slower moving ion. A steady state is established in which the two ions migrate at the same speed the ion that moved faster initially leads the march. 

First models have been derived by Dukhin et al. [27, 28, 30, 101], and Borwankar and Wasan [102]. They used a quasi-equilibrium model by assuming that the characteristic diffusion time is much greater than the relaxation time of the electrical double layer, and thus, the complicated electro-diffusion problem is reduced to a simply transport problem. Datwani and Stebe [103] analysed this model and performed extensive numerical calculations, however, they did not include the electro-migration term into the diffusion equation so that the results are not relevant for further discussions. 

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