Onsager expression

In the intermediate regime, this may be recognized as the Green-Kubo expression for the thermal conductivity [84], which in turn is equivalent to the Onsager expression for the transport coefficients [2]. 

One characteristic feature of theories that incorporate DD interactions is a density-dependent dielectric constant s(p ) > Ss, induced by a varying concentration of dipolar ion pairs. Friedman [3] suggested such a variation of the dielectric constant to be responsible for phase separation. As a byproduct, WS theory provides a generalization of the well-known Onsager expression for the dielectric permittivity of dipolar Quids to a system comprising free ions [221],... 

Fig. 3. Circles, squares, triangles and crosses are the QE of supply as a function of electric field for PVK films of different thickness. The solid line is the Onsager expression for <2>0 = 0.11 and...

A similar mechanism has been proposed15 to explain photogeneration data in the 1 1 charge transfer complex of PVK and 2,4,7-trinitro-9-fluorenone (TNF). The data points in Fig. 4 show the measured photogeneration efficiency and the solid line is calculated from the Onsager expression with 4>0 = 0.23 and r0= 35 A0. For a... 

The Onsager expression that a thermalized electron-hole pair will escape recombination, Q(r,0, ), is... 

Furthermore, the relative permittivity (or dielectric constant) ofthe liquid is an important parameter. The probability P of an electron (ef) which is thermalised at a distance r metres from its geminate positive ion (M +) escaping recombination with it is exp(-r/r) where is the distance at which the Coulomb potential between e and M is equal to thermal energy kT and is given by the Onsager expression where e is the elementary... 

The Onsager expression (Ref. 33, Chap. 1) for calculating the relative permittivity of polar liquids, and which takes into account the local electric reaction field acting on the individual polar molecules, has the form... 

The decreases in permittivity when ions are added to a polar solvent were traditionally interpreted in terms of saturation or solvation of local ionic environments (76) until Hubbard and Onsager (77) (78) worked out a continuum theory of the kinetic depolarization effect. This arises from the fact that part of the electric field solvent dipoles near an ion is from the moving ion and similarly for the ion in the field of reorienting dipoles with the consequences that both responses are delayed in proportion to the relaxation time of the solvent polarization. The remarkably simple Hubbard-Onsager expression for the resulting decrement of static (or better limiting low frequency) permittivity can be written... 

To investigate the transport properties in a binary mixture near a plait point, the Onsager expressions for the diffusion current Jj and the heat current Jq are considered (Landau Lifshitz 1987)... 

The Onsager expression for the packing entropy is valid at very low densities and the theory can be applied directly to dilute solutions of rigid particles like tobacco mosaic virus or helical synthetic polypeptides. At the same time typical thermotropic nematics are composed of molecules with an axial ratio of the order of 3 or 4 and the packing fraction is of the order of 1. Thus, the... 

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