Onsager’s theory

A proposal based on Onsager s theory was made by Landau and Lifshitz [27] for the fluctuations that should be added to the Navier-Stokes hydrodynamic equations. Fluctuating stress tensor and heat flux temis were postulated in analogy with the Onsager theory. Flowever, since this is a case where the variables are of mixed time reversal character, tlie derivation was not fiilly rigorous. This situation was remedied by tlie derivation by Fox and Ulilenbeck [13, H, 18] based on general stationary Gaussian-Markov processes [12]. The precise fomi of the Landau proposal is confimied by this approach [14]. 

Onsager s theory can also be used to detemiine the fomi of the flucUiations for the Boltzmaim equation [15]. Since hydrodynamics can be derived from the Boltzmaim equation as a contracted description, a contraction of the flucUiating Boltzmann equation detemiines fluctuations for hydrodynamics. In general, a contraction of the description creates a new description which is non-Markovian, i.e. has memory. The Markov... 

The solvent effects on charge-transfer spectra between Me3Sn-NCS and I2 was investigated. Onsager s theory of dielectrics was used to estimate the stabilisation energy of excited states257. 

The time relaxation corresponds to the change in the initial entropy state. As it has been established by one of the present authors (6), it is possible to derive generalized thermodynamic forces and fluxes in the sense of Onsager s theory and to study e.g. stability problems of tubular reactors. 

The dependence on the absolute value of the field strength is a noteworthy feature of Onsager s theory of course symmetry considerations impose always a dependence of the FDE on an even... 

An increase of the photocurrent at energies less than 2 eV was observed [151,152] unlike the previous result. This was attributed to the localized impurity ionization up to 0.8 eV below the conduction band. The crystals are considered as model systems for the one and three-dimensional versions of Onsager s theory of germinate recombination. 

The investigation of the quantum yield of the poly(diphenylacetylene) and its complex with TNF show that maximum photosensitivity was at 25% of the acceptor content [184]. This relates to the case when all the conjugated blocks form complexes with TNF. The strong dependence of the quantum yield on the electric field strength permitted the explanation of the photosensitivity in the framework of Onsager s theory with a thermalization distance of 2 nm. 

Delay et al (Ref 12) detd IR absorption spectra in the range 3 to l9u and from the intensities of the bands concluded that the sym form was more abundant in the azides of Ag, Cu, Hg Na but the reverse was true for the azides of Pb Tl. Gray Wad ding ton (Ref 18) stated th at TlNj crysts are isomor-phous with those of Na Rb azides. The elec conductivity of TIN, is 5.9 x 10 s mho at 275° (Ref 18). Brouty (Ref 10) detd the mean activity coefficient of TIN, by EMF+ measurements and calcd ionic radii of Ti Nj. Conductivity measurements by Brouty (Ref 11) did not agree with Onsager s theory deviations were found at very high dilutions. An electro-chem cell used by Suzuki (Ref 16) gave a Ap1 29S° value of 59.17 kcal/mol for... 

Again we wish to emphasize that it is the modified moments (aWtU ) and (V5(D) Moi) arising from the use of Onsager s theory of the moments in liquids that are important. With reasonable values of internal refractive index, the moments in vacuum can be reduced. Furthermore, our theory does account for values of j greater than those predicted by the Debye-Hiickel limiting law if the ions can be assumed to have dipole characteristics. 

N," Conductivity measurements by Brouty (Ref 11) did not agree with Onsager s theory deviations were found at very high dilutions. 

The general equation that relates forces and fluxes is given by Onsager s theory. For a single force X, it establishes a linear dependence between fluxes and forces that can be written as... 

The need for a local field correction in Raman spectra was first suggested by Woodward and George [39] who, however, made no attempt to present a quantitative expression for the magnitude of the effect. Starting from Onsager s theory, Pivovarov derived an expression for the ratio between polarizability derivatives in solution and in vacuo (and then Raman intensities) [34,35] ... 

Still starting from the Onsager s theory, Mirone and co-workers [29,36,38] proposed a relation for the ratio between Raman intensities in solution and in vacuo given by the following formula ... 

By analogy with the the Onsager s theory, it is assumed that the response of the molecule to an external probing field can be expressed in terms of an external dipole moment fit, sum of the molecular dipole moment and the dipole moment arising from the molecule-induced dielectric polarization. Following ref. [8] and ref. [47],... 

The definition of the cavity (shape and size) is an intricate and delicate question that may have a considerable influence on the results (even qualitatively). In the original Onsager s theory, the molecular cavity was defined as a sphere and the volume was taken equal to the partial molecular volume of the solute in the solution. In practice, this volume can be assumed to be equal to the average volume in the pure liquid. Experimental values are then easily deduced from the experimental density of the liquid at 20°C when this quantity is available. Obviously, in SCRF applications, it became rapidly necessary to achieve a theoretical definition of the cavity applicable to any molecular structure. In former works carried out by our group [28,62], it was shown that a simple linear relationship exists between the experimental volume derived from the liquid density (Onsager s recipe) and the van der Waals volume, i.e., the volume enclosed by a set of overlapping atomic spheres with Bondi radii [63], Roughly, this relationship is... 

The theoretical base of the spur process is Onsager s theory of the geminate pair recombination. Contrary to this, the blob model is most appropriate for consideration of early radiation-chemical processes in multiparticle track entities, such as blobs and ionization columns. The main distinction between the spur and blob comes from the large difference in the initial number of ion-electron pairs they contain. 

How does the cell constant k compare with the geometric value HA obtained from an approximate measurement of the dimensions of your ceU Why is the equivalent conductance Aq so large for an HCl solution How do the slopes of your A versus -Jc plots for strong electrolytes compare with literature values and the values expected from Onsager s theory Find a literature (or textbook) value for the equilibrium constant for HAc ionization. Using this value and Eq. (13), draw a dashed literature/theory line on your plot of log versus -Jm. Are the deviations of your data points from this line reasonable in view of the experimental errors expected in this work What is the limiting factor in the accuracy of your measurements ... 

Other ions in the solution. The self-energy of a dipole embedded in a dielectric sphere is the key to Onsager s theory of the dielectric constant of dipolar fluids. Equally, in any theory for, say, the surface energy of water, or adsorption of molecule, the self-energy of a molecule as a function of its distance from an interface is involved. In adsorption proper, the same selfenergy for a molecule appears in the partition function of statistical mechaiucs from which the adsorption isotherm is derived. 

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