Debye-Falkenhagen theory

The polarizability of the individnal molecules is also frequency dependent, but the characteristic values are of the order of lO Vs and lO Vs for the rotational and electronic polarization, respectively. " Therefore, in the typical frequency domain for investigation of dispersions (1/s < co < 10 /s) the polarizability, e, of the material building up the particles is frequency independent. On the other hand, the disperse medium (which is usually an electrolyte solution) has a dielectric permittivity, Ej, for which the freqnency dependence can be described by the Debye-Falkenhagen theory. Besides, the characteristic relaxation time of the bulk electrolyte solutions is also given by Eqnation 5.385. ... 

One further problem which should be mentioned is of the effect of ion-ion interactions and ion atmosphere relaxation on the permittivity particularly at moderate or high concentrations. The classic Debye-Falkenhagen theory (83) for high dilutions predicting an increment in permittivity proportional to relaxing at frequencies of order f])p(GHz)... 

The jump relaxation model of Punke is a concept of wide validity [410]. In certain aspects it may be compared to the Debye-Falkenhagen theory [411] of liquid electrolytes. The interaction of the point defects expresses itself in a relatively flat defect potential , that is superimposed on the lattice potential, as shown in Fig. 6.34. 

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... 

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... 

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]). 

The concentration dependence of ionic mobility at high ion concentrations and also in the melt is still an unsolved problem. A mode coupling theory of ionic mobility has recently been derived which is applicable only to low concentrations [18]. In this latter theory, the solvent was replaced by a dielectric continuum and only the ions were explicitly considered. It was shown that one can describe ion atmosphere relaxation in terms of charge density relaxation and the elctrophoretic effect in terms of charge current density relaxation. This theory could explain not only the concentration dependence of ionic conductivity but also the frequency dependence of conductivity, such as the well-known Debye-Falkenhagen effect [18]. However, because the theory does not treat the solvent molecules explicitly, the detailed coupling between the ion and solvent molecules have not been taken into account. The limitation of this approach is most evident in the calculation of the viscosity. The MCT theory is found to be valid only to very low values of the concentration. 

See - conductance, - conductivity cell, -> conductometry, - Debye-Falkenhagen effect, -> Debye-Huckel-Onsager theory, - electrolyte, -> ion, -> Kohlrausch square root law, - mass transport. 

University in Ithaca. Nobel Prize in 1936 for contributions to the knowledge of molecular structure based on his research on dipole moments, X-ray diffraction (Debye-Scherrer method), and electrons in gases. His investigations of the interaction between ions and electric fields resulted in the - Debye-Huckel theory. See also -> Debye-Falkenhagen effect, - Debye-Huckel limiting law, - Debye-Huckel length, - Debye relaxation time. 

As the dependency does not include any specific property of the ion (in particular its chemical identity) but only its charge the explanation of this dependency invokes properties of the ionic cloud around the ion. In a similar approach the Debye-Huckel-Onsager theory attempts to explain the observed relationship of the conductivity on c1/2. It takes into account the - electrophoretic effect (interactions between ionic clouds of the oppositely moving ions) and the relaxation effect (the displacement of the central ion with respect to the center of the ionic cloud because of the slightly faster field-induced movement of the central ion, - Debye-Falkenhagen effect). The obtained equation gives the Kohlrausch constant ... 

The measurements of the Debye-Falkenhagen effect are generally made with reference to potassium chloride the results for a number of electrolytes of different valence types have been found to be in satisfactory agreement with the theoretical requirements. Increase of temperature and decrease of the dielectric constant of the solvent necessitates the use of shorter wave lengths for the dispersion of conductance to be observed these results are also in accordance with expectation from theory. 

Later, Falkenhagen and co-workers and Onsager and Fuoss established a method of calculating parameter A starting from the Debye-Huckel theory. However, the above equation is only valid for concentrations up to about 0.01 mol/L. According to the above equation the relative viscosity should always increase with concentration. However, experiments show non-monotonic behavior for several electrolytes such as most of the potassium halides, and several mbidium and cesium halides [12]. 

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... 

Refs. [i] Debye P, Falkenhagen H (1928) Phys Z 29 401 [ii] Falken-hagen H (1971) Theory der Elektrolyte. Hirzel, Leipzig, p 117... 

Falkenhagen effect, -> Debye-Huckel-Onsager theory. Refs. [i] Atkins PW (1994) Physical chemistry. Oxford University Press, Oxford, p 855 [ii] Bockris J OM, Reddy AKN (1998) Modern electrochemistry, vol. 1. Plenum Press, p 520... 

The dispersion of conductance at high frequencies was predicted by Debye and Falkenhagen, who developed the theory of the subject the phenomena were subsequently observed by Sack and others. The... 

Induced Interaction between Two Multipole Systems. Equation (58) defines in general form the classical electrostatic interaction of two electric systems having permanent multipoles and pj" , in conformity with the classical theory of Keesom. In the classical approach also, as shown by Debye and Falkenhagen, one has to take into consideration energies due to interactions between the permanent multipoles of the one system and electric multipoles induced in the other, and vice versa. Restricting the problem in a first approximation to the energy arising from the mutual interaction of dipoles, we can write ... 

In this chapter we present a simple model calculation that demonstrates how this cooperative motion affects the scattering spectrum. Our approach is based on the Debye-Onsager treatment of ion transport (see Falkenhagen, 1934 Stephen, 1971). This is our first discussion of cooperative effects in light scattering. In Chapter 13 this problem is reconsidered in the context of the general theory of nonequilibrium thermodynamics. 

Duca KA, Jordan PC (1997) Ion-water and water-water interactions in a gramicidinlike channel effects due to group polarizability and backbone flexibility. Biophys Chem 65 123-141 Falkenhagen H, Dole M (1929) Viscosity of electrolyte solutions and its significance to the Debye theory. Phys Z 30 611-622... 

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