Time of relaxation effect

Fig. 2.7 Time-of-relaxation effect. During the movement of the ion the ionic atmosphere is renewed in a finite time so that the position of the ion does not coincide with the centre of the ionic atmosphere... 

The mathematical theory of the time-of-relaxation effect is based on the interionic electrostatics and the hydrodynamic equation of flow continuity. It is the most involved part of the theory of strong electrolytes. Only the main conclusions will be given here. 

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. 

The influence of the interionic forces is due to two phenomena, namely, the electrophoretic effect and the time-of-relaxation effect. The net ionic atmosphere around a given ion carries the opposite charge and therefore moves in a direction opposite to the central ion. The final result is an increase in the local viscosity, and retardation of the central ion. This is called the electrophoretic effect. The time-of-relaxation effect is also related to the fact that the ionic atmosphere around a given ion is moving and therefore disrupted from its equilibrium configuration. It follows that the ionic atmosphere must constantly be re-formed from new counter ions as the ion under observation moves through the solution. The net effect is that the electrical force on each ion is reduced so that the net forward velocity is smaller. 

It is of great interest that the curves shown in Figs. 10 and 11 indicate that the equivalent conductances are approaching maxima which would be observed if the electrophoretic and time of relaxation effects were overcome by the intense electric fields. At one volt per centimeter an ion with an equivalent conductance, A, of 100 moves at a rate of about two centimeters per hour. At, for instance, 300... 

B In Huckel s and Henry s treatment of electrophoresis the reader who is familiar with the theory of the conductivity of strong electrolytes will have missed the so-cailed time-of-relaxation effect This effect, originating in the deformation of the double layer also has a retarding influence on the electrophoresis. In the applied field the charge of the double layer is displaced in a direction opposite to the movement of the particle Not only does this charge retard the electrophoresis by its movement (electrophoretic retardation see 6a), but also by the dissymmetry of the double layer resulting from this displacement a retarding potential difference is set up. 

Both methods A and B attack fundamentally the same problem, insofar as the surface conductance of the first method is a direct consequence of the presence of the double layer In the first case the counter E M F results as a stationary equilibrium between extra supply of electricity through the surface layer and a counter current originated by this E M F In the second case the extra supply of charge from the double layer is dispersed in the stationary state by conduction and by diffusion So the second method is perhaps able to describe the time-of-relaxation effect in more detail, but fundamentally there is no difference between the two methods. 

The problem of the influence of the time-of-relaxation effect on electrophoresis has been attacked by various authors They treat it in different ways and different approximations. Owing to the mathematical intricacies their results are far from satisfying. More recently Overbeek Booth and Henry independently have given new treatments of this effect. Booth and Overbeek treated the relocation effect for spherical insulating particles surrounded by a Gcuy double layer. Booth and... 

In using Overbeek s calculations on the time-of relaxation effect one must keep... 

The equivalence of electrophoresis and electro-osmosis has also been repeatedly tested It has been explained in 6b that reliable values of the ( -potential can only be calculated from electroph.oretic measurements if the time-of-relaxation effect can be neglected. If is not very small this is only realised in the case of large particles with a thin double layer. It follows from Henry s considerations (c/ 6a) that just in this case the electrophotelic velocity is equal to the velocity of electro-osmosis, both obeying the equation of Helmholtz Smoluchow ski (4, 26). This equality can be demonstrated very clearly by the ultramicroscopic method for the determination of the electrophoretic velocity. 

Although it may be that the interpretation of conductivities of colloids cannot always be as precise as wc should wish, in principle we know exactly how the interpretation should be given. In conductivity we see reflected the ruimber, specific charge and mobility of the colloidal particles and the ions constituting the sol. Moreover we find in it the influence of the interaction of these components by electrophoretic and by time-of-relaxation effects. In some cases effects of association or dissociation may play a r61e too. 

The electrophoretic velocity neglecting the time-of-relaxation effect is... 

If the conductivity is measured in a field of high frequency the oscillating movement of the particles may become so rapid that the asymmetry of the double layer has not enough time to develop to its full extent. As a consequence the time-of-relaxation effect loses part of its efficacy and a rise of conductance results. 

So Schmidt and Erkkila experimenting on congo-sols and casein-sols found a rise in conductance of 6-30% for a frequency of about 10. In fields of very high tensions (100,000 V/cm) the velocity of the particles may be so large, that the particle is drawn out of its ionic atmosphere, so that both the time-of-relaxation effect and the electrophoretic retardation disappear. An example of this effect is found in Hartley s work on paraffin-chain salts. 

A quantitative relation between the D.C. and the double layer (third effect) is very difficult to give because the increase of the D.C. rests completely upon the time-of-relaxation effect, and we know already from the electrophoresis how difficult calculations of this effect are. 

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