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Glossary of Capacitor Terms

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• Ionic Mobility
  

Ionic Mobility

Case 1: Infinite Dilution

Ions are susceptible to collisions with solvent molecules and other ions due to the latent thermal energy of the solution; otherwise known as Brownian motion. The mean free path between collisions is, of course, very short. Instantaneous velocities of all ions and solvent molecules may be on the order of 10⁴ cm/sec, but are randomly directed. Unpolarized, there is no net movement of ions, but in the presence of an electric field the drift is biased in a particular direction. The distribution of ions is, however, random on average.

Mobility is affected by the size, charge, and shape of an ion; and solvent composition. The effects of ion-size, -charge and -shape cumulatively define the charge density. Very small ions, regardless of charge, have an intrinsically high charge density and so are solvated to a large extent in water or other highly polar solvents. Extensive solvation effectively increases the size of small ions. Very large ions are usually limited by their physical size to slow movement. Intermediately sized ions are generally most mobile. The conductance of a given ion at infinite dilution is roughly,

lambda^o = |z| x F² / (6 x PI x N x eta^o x r)

where the superscript 'o' denotes infinite dilution, 'z' is the charge on the ion, F is the Faraday constant, N is Avogadro's number, eta^o is the medium (i.e., solvent) viscosity, and 'r' is the combined radius of the ion and its solvation sphere. This relationship is known as Stokes' law.

Interestingly the product 'LAMBDA x eta' is nearly a constant for many ions, and especially so for large particles; but itself is a function of temperature. Walden's rule states that

LAMBDA^o x eta^o = constant,

and is derivable from Stokes' law. It is not quantitative, however, as there are many exceptions to the rule.

Hence, conductivity is strongly dependent on temperature, with the changing viscosity of the medium a large factor.

Case 2: Concentrated Solutions

Ions moving through a viscous medium tend to drag along adjacent solvent molecules. This is known as the electrophoretic effect. Neighboring counter-ions must thus move against this stream, whereas ions of the same kind move with the stream. This effect is concentration dependent, becoming zero at infinite dilution. The electrophoretic effect combines with the Brownian motion drag in a composite term describing ionic motion without the effects of an electric field. No net motion of the solvent molecules occurs, however, because of other forces acting on them.

The net ionic velocity thus depends in a complicated way on concentration, ionic charge, mean ionic diameter, temperature, dielectric constant and viscosity of the solvent in addition to the electric field.

An ion in solution without the influence of external forces (e.g., an electric field) sits in a spherically symmetrical atmosphere of other ions that exerts no net force on the ion (i.e., neither attractive or repulsive so the system is at equilibrium). If the ion is moved off center, the 'ionic atmosphere' restores equilibrium by adjusting accordingly. This is known as the relaxation, or Falkenhagen effect. The conductivity of an electrolyte is therefore constant at less than radio frequencies because the atmosphere is capable of following the field. Under the influence of an electric field, relaxation becomes in effect a back, or reverse potential that resists the movement of individual ions in the field. The theory describing this effect is so involved that it will not be developed further.

In concentrated solutions, without the effects of an electric field or other external force, the distribution of ions is random on average, but short range order exists around each ion due to its attraction for counter-ions. At a high enough concentration ion pairing will occur that prevents further decreases in resistivity, and in fact results in increasing resistivity as more ions are added. The practical implications are that capacitor electrolytes have a resistivity minima that depends on the solvent dielectric constant, whether the electrolyte is weak or strong in the solvent, and the chemical natures of the electrolyte and solvent. Note that the dielectric constant of a material is temperature dependent.

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Updated: 24 March 2000

Copyright © 1996-2000 Tyra T. Buczkowski. All rights reserved.