Onsager theory Brownian motion

The fundamental theory of electron escape, owing to Onsager (1938), follows Smoluchowski s (1906) equation of Brownian motion in the presence of a field F. Using the Nemst-Einstein relation p = eD/kRT between the mobility and the diffusion coefficient, Onsager writes the diffusion equation as... 

The theory of geminate recombination reduces to the problem of Brownian motion in the presence of Coulomb attraction. Onsager s relationship for the probability p(r,0, E) that an ion pair (thermalized with an initial separation r and at an angle 6 with the applied field direction) will escape recombination is given by 9 ... 

In the first derivation of the relaxation effect the random Brownian motion of the ions in the solution was ignored, but Onsager modified the theory to take this into account. 

The work of Debye and Erich Hiickel (1896-1880), published in 1923, led to a theory of ionic solutions that explained a number of anomalies concerning conductivities of electrolytic solutions. In 1926, Lars Onsager (1903-76) added the treatment of Brownian motion toward understanding the transport properties of ions in melts, aqueous, and... 

Onsager, Lars (1903-76) Norwegian-born American chemist. Onsager made several important contributions to theoretical chemistry and physics. In 1926 he improved on the Debye-Hiickel theory of electrolytes by taking the Brownian motion of ions into account. He subsequently investigated the dielectric constants of matter that contains polar molecules. In 1931 he published fundamental work on nonequilibrium thermodynamics. He was awarded the 1968 Nobel Prize for chemistry for this work. 

The Onsager theory of ionic escape is widely used for the analysis of photo- and radiation-induced ionization in nonpolar liquids. Here an electron is trying to escape from its positive parent ion. Application of the model of Brownian motion requires the mean free path of the Brownian particle to be small compared to the characteristic... 

QSM theory provides a firm statistical mechanical basis for the phenomenological theory of irreversible processes as formulated by Onsager and the version of classical Brownian motion discussed in Section 5.2. Moreover, it gives a number of formulas that can be employed in the investigation of the role of microscopic interactions in a diversity of nonequilibrium phenomena. 

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... 

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