Falkenhagen

Falkenhagen, H. The Present State of the Theory of Electrolytic Solutions 2... 

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. 

These aspects were examined in a study [51] which employed a generalized Debye-Falkenhagen description for the ionic atmosphere dynamical friction and GH theory for the rate. It was found that, while indeed the atmosphere is almost never equilibrated during the barrier passage and to a large extent is frozen on this time scale, the atmosphere frictional derivations from the equilibrium solvation TST result... 

The first satisfactory explanation of these effects was given, in the twenties, by Debye, Hiickel, Onsager, and Falkenhagen (see, for instance, Ref. 8). Using a remarkably clever combination of microscopic and macroscopic concepts, they were able to describe the behavior of dilute electrolytes by the famous limiting laws . 

As soon as the concentration of the solute becomes finite, the coulombic forces between the ions begin to play a role and we obtain both the well-known relaxation effect and an electrophoretic effect in the expression for the conductivity. In Section V, we first briefly recall the semi-phenomenological theory of Debye-Onsager-Falkenhagen, and we then show how a combination of the ideas developed in the previous sections, namely the treatment of long-range forces as given in Section III and the Brownian model of Section IV, allows us to study various microscopic... 

After the writing of this article, the problem of limiting viscosity was also considered 16 although the potential part of the shear viscosity plays the important role, the method developed here can be applied as well the results are in agreement with the theory of Falkenhagen.8-16... 

Debye-Falkenhagen effect physchem The increase in the conductance of an electrolytic solution when the applied voltage has a very high frequency. d3 bT fal-kon,hag-on i,fekt ... 

Historically, one of the central research areas in physical chemistry has been the study of transport phenomena in electrolyte solutions. A triumph of nonequilibrium statistical mechanics has been the Debye—Hiickel—Onsager—Falkenhagen theory, where ions are treated as Brownian particles in a continuum dielectric solvent interacting through Cou-lombic forces. Because the ions are under continuous motion, the frictional force on a given ion is proportional to its velocity. The proportionality constant is the friction coefficient and has been intensely studied, both experimentally and theoretically, for almost 100... 

Numerous LC CC applications were performed by Pasch, Schulz, and Falkenhagen in Germany on (high)polymers and by Trathnigg in Austria on oligomers (for review see Ref [23]). Presently, the LC CC method is rather widely used in the separation of complex polymer systems [26-28,31-33,173-194]. 

P. Debye and M. Falkenhagen, Dispersion von Leitfdhigkeit und Dielektizitdtskonsta-nte bei Starken Elektrolyten, Phys. Zeitschrift, 29 (1928), p. 121. 

The Debye-Huckel-Onsager equation for the dependence of the ordinary diffusion conductance on concentration has been extended by Falkenhagen, Leist and Kelbg [3] to apply to more concentrated solutions and their equation for a 1 1-electrolyte may be written... 

Falkenhagen, Hans Electrolytes, R. P. Bell, Trans., Oxford University, Oxford,... 

So far, the discussion of concentrated electrolyte solutions has presumed that ionic relaxation is complete and so is a static correction. Dynamic electrolyte theories are still in their infancy and, in view of the rate of ionic relaxation compared with chemical reaction rates for dilute electrolytes (Sect. 1.6), such effects are probably not very important in concentrated electrolyte solutions containing reactants. The Debye— Falkenhagen [92] theory predicts a change in the relaxation time of electrolyte solutions with concentration, though experimental confirmation is scant [105]. At very high concentrations, small changes in the relaxation time ( 25%) of solvent relaxation can be identified (see also Lestrade et al. [106]). 

Debye and Falkenhagen [92] also predicted that the permittivity of electrolyte solutions should increase as c,/2 where c is the ionic concentration. According to Hasted [105], such an effect has not been demonstrated experimentally, probably because the high conductivity of such solutions can mask permittivity changes. On the contrary, the permittivity of electrolyte solutions decreases with concentration [106] by 25—50% at lmoldm-3. This is probably associated with the binding of dipolar solvent molecules to ions, thus reducing the solvent orientational contri-butional to the permittivity (dielectric saturation). 

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