Ionic atmosphere asymmetric

Debye and Falkenhagen predicted that the ionic atmosphere would not be able to adopt an asymmetric configuration corresponding to a moving central ion if the ion were oscillating in response to an applied electrical field and if the frequency of the applied field were comparable to the reciprocal of the relaxation time of the ionic atmosphere. This was found to be the case at frequencies over 5 MHz where the molar conductivity approaches a value somewhat higher than A0. This increase of conductivity is caused by the disappearance of the time-of-relaxation effect, while the electrophoretic effect remains in full force. 

An asymmetric effect. Because of ion movement the ionic atmosphere becomes distorted such that it is compressed in front of the ion in the direction of movement and extended behind it (Fig. 2.5). 

In Section 12.1 it was shown that when the central reference ion moves under the influence of an external field there is an excess of negative charge behind the cation and a deficit of negative charge in front of it. If the external field is removed, the asymmetric ionic atmosphere relaxes back to the symmetric distribution. This process can be pictured as if some negative charge... 

However, for very high frequencies of the external field, such as 10 Hz, the time for one oscillation is 10 s and this is comparable to or even smaller than the relaxation time. Under these conditions the ion is impelled backwards and forwards so rapidly that the build up of the ionic atmosphere to the asymmetric state cannot occur fast enough, and the asymmetric ionic atmosphere will not be fiiUy set up. At even higher frequencies the ionic atmosphere never has time to reach the asymmetric state and the relaxation effect totally disappears. The retarding effect of the asymmetry on the movement of the ions under the influence of the external field is removed. In consequence, the velocity of the ions and their individual ionic molar conductivities are significantly higher than for ordinary frequencies and are much nearer what would they would be expected to be if there were no retarding effect of the ionic atmosphere. 

The early conductance theories given by Debye and Hiickel in 1926, Onsager in 1927 and Fuoss and Onsager in 1932 used a model which assumed all the postulates of the Debye-Hiickel theory (see Section 10.3). The factors which have to be considered in addition are the effects of the asymmetric ionic atmosphere, i.e. relaxation and electrophoresis, and viscous drag due to the frictional effects of the solvent on the movement of an ion under an applied external field. These effects result in a decreased ionic velocity and decreased ionic molar conductivity and become greater as the concentration increases. 

Electrophoresis and relaxation were taken to be totally independent phenomena, whereas they are not. As a result the derivation neglected, (i) the effect of the asymmetry of the ionic atmosphere on the electrophoretic effect, and (ii) the effect of electrophoresis on the movement of the ion in an asymmetrical ionic distribution. These are cross terms described below. 

Cross term due to (ii) The central ion of the asymmetric distribution is affected by the movement of the solvent around it due to the electrophoretic effect. Since any ion in the ionic atmosphere can be considered to be a central reference ion, the electrophoretic effect will affect all the ions. Because there are interactions between the ions and the solvent molecules, this will alter the asymmetry of the ionic atmosphere which would be set up due to relaxation in the absence of the electrophoretic effect. This has the consequence of an added perturbation on the asymmetry. For a calculation of the relaxation effect this extra... 

The differences between Pitts (P) and Fuoss-Onsager (F-O) are first, the above mentioned omission by F-O of the effect of asymmetric potential on the local velocities of the solvent near the ions second, the use of the more usual boundary conditions 5.2.28b by F-O compared to the P assumption that perturbations cease to be important at r = a. Pitts, Tabor and Daly, who have analysed in detail both treatments, concluded that the discrepancy due to the different boundary conditions is small but has the effect of reducing ionic interactions in the P treatment with respect to the F-O. This is confirmed by the analysis of data with both theories. Usually P requires a smaller value of the a parameter than F-O. The third discrepancy between the theoretical treatments is in the expression of Vj, in eqn. 5.2.5, for which F-O add a term which involves the effect of the asymmetry of the ionic atmosphere upon the central ion surrounded by such atmosphere. The last difference lies in the hydrodynamic approaches and the corresponding boundary conditions. P imposes the condition that the velocity of the smoothed... 

It is expected that a similar physical picture also holds for interacting PE stars. At distances between core domains 2d > 2R, the star coronae would start to contract due to the overlap of ionic atmospheres. As a result, the stars would become asymmetric and remain separated by a water layer in a range of distances 2d < 2R. The long-range interactions due to the overlap of ionic atmospheres are essential for PE stars with a moderate number of arms (typical for experimental systems), and at low ionic strength in the solution [27],... 

Relaxation Time Effect On the way to the electrode, the central ion leaves the ionic atmosphere behind. As a result, the originally symmetric atmosphere becomes asymmetric. It exerts an electrostatic drag on the ion, thereby reducing its velocity in the direction of the field. 

Particles dispersed in an aqueous medium invariably carry an electric charge. Thus they are surrounded by an electrical double-layer whose thickness k depends on the ionic strength of the solution. Flow causes a distortion of the local ionic atmosphere from spherical symmetry, but the Maxwell stress generated from the asymmetric electric field tends to restore the equilibrium symmetry of the double-layer. This leads to enhanced energy dissipation and hence an increased viscosity. This phenomenon was first described by Smoluchowski, and is now known as the primary electroviscous effect. For a dispersion of charged hard spheres of radius a at a concentration low enough for double-layers not to overlap (d> 8a ic ), the intrinsic viscosity defined by eqn. (5.2) increases... 

There are several eomprehensive reports [7, 74-79] devoted to mixed ionic-electronic conducting ceramic membranes for gas separation and selective catalytic reactions. The requirements to membrane materials differ fixrm those to SOFC cathodes. For membranes, the most promising concept is based upon supported asymmetric functionally graded design combining a dense permselective l er and l ers with different porosity. Cathode materials may be not dense, they operate in air and m be unstable in a reducing atmosphere. On the other hand, cathode materials should be chemically inert towards other SOFC components and keep their characteristics under the working conditions. 

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