Arrhenius description

Fig. 4.10 a Characteristic relaxation times determined from dielectric measurements [137] (diamonds), and from NSE spectra at (triangles) for triol (open symbols) and PU (solid symbols). The full lines correspond to Vogel-Fulcher and the dotted lines to Arrhenius descriptions, b Relaxation times from NSE spectra have been arbitrarily multiplied by a factor 6 for triol and 40 for PU to build a normalized relaxation map. (Reprinted with permission from [127]. Copyright 2002 Elsevier)... 

Systems defined by the Arrhenius description, solvent system, Lux-Flood and proton acid-base definitions... 

There are available from experiment, for such reactions, measurements of rates and the familiar Arrhenius parameters and, much more rarely, the temperature coefficients of the latter. The theories which we use, to relate structure to the ability to take part in reactions, provide static models of reactants or transition states which quite neglect thermal energy. Enthalpies of activation at zero temperature would evidently be the quantities in terms of which to discuss these descriptions, but they are unknown and we must enquire which of the experimentally available quantities is most appropriately used for this purpose. 

Following the general trend of looldng for a molecular description of the properties of matter, self-diffusion in liquids has become a key quantity for interpretation and modeling of transport in liquids [5]. Self-diffusion coefficients can be combined with other data, such as viscosities, electrical conductivities, densities, etc., in order to evaluate and improve solvodynamic models such as the Stokes-Einstein type [6-9]. From temperature-dependent measurements, activation energies can be calculated by the Arrhenius or the Vogel-Tamman-Fulcher equation (VTF), in order to evaluate models that treat the diffusion process similarly to diffusion in the solid state with jump or hole models [1, 2, 7]. 

This theory was a milestone in the development of acid-base concepts it was the first to define acids and bases in terms other than that of a reaction between them and the first to give quantitative descriptions. However, the theory of Arrhenius is far more narrow than both its predecessors and its successors and, indeed, it is the most restrictive of all acid-base theories. 

As has been described in Ref. 70, this approach can reasonably account for membrane electroporation, reversible and irreversible. On the other hand, a theory of the processes leading to formation of the initial (hydrophobic) pores has not yet been developed. Existing approaches to the description of the probability of pore formation, in addition to the barrier parameters F, y, and some others (accounting, e.g., for the possible dependence of r on r), also involve parameters such as the diffusion constant in r-space, Dp, or the attempt rate density, Vq. These parameters are hard to establish from first principles. For instance, the rate of critical pore appearance, v, is described in Ref. 75 through an Arrhenius equation ... 

It can not be described by means of a single Debye process, but more complicated relaxation functions involving distributions of relaxation times (like the Cole-Cole function [117]) or distributions of energy barriers (like log-normal functions [118]) have to be used for its description. Usually a narrowing of the relaxation function with increasing temperature is observed. The Arrhenius temperature dependence of the associated characteristic time is ... 

The evolution of emulsions through coalescence can be characterized by a kinetic parameter, >, describing the number of coalescence events per unit time and per unit surface area of the drops. Following the mean field description of Arrhenius,... 

The regime governed by coalescence was examined in more detail. The process of film rupture is initiated by the spontaneous formation of a small hole. The nucleation frequency. A, of a hole that reaches a critical size, above which it becomes unstable and grows, determines the lifetime of the films with respect to coalescence. A mean field description [19] predicts that A varies with temperature T according to an Arrhenius law ... 

The first description of gadolinite was published by Bengt Reinhold Geijer (1758-1815) in Ctell s Annalen in 1788. I am now sending you, said he, a specimen of a heavy stone which one of my friends, Hr. Lieut. Arrhenius, found. It was discovered at Ytterby, three miles from Stock-... 

In general, all ILs show a significant decrease in viscosity as the temperature increases. A systematic study of a possible description covering ILs by the Arrhenius or VTF equations was made by Okoturo and Van der Noot [44]. 

Equations (1.194) and (1.195) can be accepted, within reason, because both the chemical equilibrium constants and the hole mobility for semiconductors have an Arrhenius-type temperature dependence. It has been shown, by a least-square fitting of the electrical conductivity data of Maruenda et al. to eqn (1.193), that 85 per cent of the data points are within 1.5 per cent of the calculated values, as shown in Fig. 1.58. This indicates that the model proposed here gives an accurate description of the data. The fitting parameters are listed in Table 1.5. 

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