Diffuse double-layer effects, electrical

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

The experiments demonstrate the development of a streaming potential in consolidated bentonite clay when flushed by a NaCl-solution of either low or high concentration. The streaming potential measured in our experiments is at least 5 to 10 times larger than values reported for bentonite in the literature. Apparently this is caused by a very low electric conductivity of the bentonite samples studied. This low conductivity might be ascribed to overlapping diffuse double layers on the clay particles, caused by the high compaction and the presence of monovalent ions in the equilibrium solution. The bentonite, thus compacted, will be a very effective medium for active application of electroosmosis. Compared with electrically shorted conditions, chemical osmosis will be reduced when the clay is not short-circuited. 

Oklejas, V., Sjostrom, C., and Harris, J.M. (2003) Surface-enhanced Raman scattering based vibrational stark effects as a spatial probe of interfacial electric fields in the diffuse double layer. Journal of Physical Chemistry E, 107, 7788-7794. 

Little is known about the effects of pressure on the electrical double layer [63], but compaction of the diffuse double layer by the high concentrations of supporting electrolytes used in our experiments means that double-layer contributions to AVgf can be expected to be small. In any event, the close equivalence between AV ] and AV jl, regardless of the medium, indicates that double layer effects in aqueous systems can be empirically neglected as far as pressure effects are concerned. 

As a consequence of the selective adsorption of ions with a higher affinity for the stationary phase than their counterions electrostatic theories assume the formation of a surface potential between the bulk mobile phase and stationary phase. The adsorbed ions constitute a charged surface, to which is attracted a diffuse double layer of strongly and weakly bound oppositely charged ions equivalent in number to the adsorbed surface charges to maintain electrical neutrality. Because of repulsion effects the adsorbed ions are expected to be spaced evenly over the stationary phase surface and at a concentration that leaves the properties of the stationary phase largely unaltered except for its electrostatic potential. The transfer of solutes from the bulk mobile phase to the... 

A further complication arises when attention is focussed on the electron density distribution within the semiconductor solid. This, in contrast to the metal case, now is able to vary from a low to a high concentration level as electrons in a conduction band or as holes in a valence band. The electric field on the solid side of the electrical double layer now has spatial extent - a diffuse double layer character exists within the solid. The conventional electric field effects previously associated with ion motion and ion distributions in the electrolyte have a counterpart within the solid phase. 

By adding an indifferent salt, the diffuse double layer is compressed, with the result that the repulsion between the ionised groups is diminished so that the additional expansion factor of electrical nature is greatly lessened. The swollen particle must thus expell part of the water it contains until a new equilibrium is reached at a lower total volume. The electroviscous effect and its removal by added salts are thus seen in the first place as volume changes of the expanded particles. 

This chapter is concerned with the mechanisms of formation of the electrical double layer at a dielectric solid/electrolytic solution interface. When such a contact occurs, the solid s surface acquires a certain charge due to the dissociation of surface ionizable groups and adsorption of ions from solution. Since the whole system is assumed to be electroneutral, the solution has to bear an equal charge of opposite sign. This charge is effectively confined to a thin layer near the dividing surface, termed the diffuse double layer. Its thickness is characterized by the reciprocal Debye length. 

For the film thickness, as a first approximation, one can take that Lf = K. Another simplifying assumption is that the viscosity changes abruptly at the boundary between the film and the solution. Estimation of the viscosity of the film as a function of potential is very difficult, since electro-neutrality is not maintained in the diffuse double layer, and it is difficult to take into account the influence of the electric field in the double layer on the viscosity of the film. Instead, the viscosity of the film, tjf, can be taken as a parameter, to fit the theoretical curve to the experimental results. To do this one substracts from the observed frequency shift the contribution of the mass effect caused by electrostatic adsorption of ions [Eq. (56)]. 

Extending out into solution from the electrical double layer (or the compact double layer, as it is sometimes known) is a continuous repetition of the layering effect, but with diminishing magnitude. This extension of the compact double layer toward the bulk solution is known as the Gouy-Chapman diffuse double layer. Its effect on electrode kinetics and the concentration of electroactive species at the electrode surface is manifest when supporting electrolyte concentrations are low or zero. 

Consider a simple experiment in which a clean solid surface (free of adsorbed liquid and vapour impurities) is immersed in an excess of pure liquid (Path 1 in Fig. 6.5). If thermal effects arising from absorption, solubility, and swelling of a solid may be eliminated, the whole enthalpy change on immersion is ascribed only to the interface. Sometimes the immersion of a solid in a liquid is accompanied by the formation of an electrical double layer. For mineral oxide-water systems [51, 52], the double-layer effects (i.e., generation of surface charge by protonation or deprotonation of some surface hydroxyl groups, and adsorption of counterions in the Stern or/and diffuse layers) are clearly secondary in comparison with the basic wetting (this contribution is 10-15 % of the total heat effect, at the most). 

The effect is dependent on the electrical double layer (q.v.) at the interface, and if a plane surface can be assumed (i.e. if the curvature is negligible compared with the thickness of the diffuse double layer), the interface can be treated as a parallel plate capacitor. For steady conditions, the electrical force applied must balance the frictional force. Now the viscosity of the liquid rj is the force per unit area per unit velocity gradient. The velocity of the liquid is zero at the surface of shear and the velocity gradient can be written as u/k where is... 

This is not immediately applicable to electrophoresis, however. The solid particle with its fixed double layer (net charge Q) is moving relative to a solution in which the diffuse double layer is distributed (see electrical double layer). The latter is equivalent to a charge -Q spread out on a concentric sphere of radius where this is the thickness of the ionic atmosphere. The presence of this atmosphere reduces the mobility, and the potential at the surface of the particle, by the factor 1/(1+ Kr) so that in place of equation (E.16) the zeta-potential (see electrokinetic effects) is given by... 

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