Arrhenius relation local temperatures

Figure 13. Plots of In 1/(t)a versus 1 An Arrhenius relation between the inverse of the lifetimes ((t)a) of the four isomers and their associated local microcanonical temperatures (T ). (Reproduced from Ref. 11 with permission.)...

We analyzed the temperature dependence of 1/Ti using the semi-classical BPP model for the effect of molecular motion on 1/Ti [32]. In this model, 1/Ti can be related to the values of correlation time, Tc, which is the characteristic time between significant fluctuations in the local magnetic field experienced by a spin due to moleciflar motions or reorientations of a molecule. As usual, it is assumed that Tc follows Arrhenius-hke behavior ... 

The condition for applicability of the criterion is that it must be possible to relate the local rate of generation of heat to the temperature, over a small initial fraction of conversion, by an Arrhenius-type of kinetic expression involving the conversion of a single component. This is not a severe restriction. 

It is quite natural to try to plot log(f)fl versus 1/7 ,1, 1. Figure 13 displays a very clear numerical fact An Arrhenius-like exponential relation is observed between the local microcanonical temperature and the inverse of the average lifetime in each basin. Here we have used the numerical data studied in Refs. 8 and 19. The local microcanonical temperatures in Fig. 13 (and Fig. 14) cover the range of the total energy [— 13.5e, —11.0e]. 13.5e is close to the lowest end of the liquid-like... 

Defining the microcanonical temperature as a kinetic energy that maximizes a phase-space distribution when projected onto the potential energy coordinate, we have shown that this temperature can characterize a time scale of structural isomerization dynamics in the liquid-like phase. In particular, it has been found that the local microcanonical temperature bears an Arrhenius-like relation to the inverse of the average lifetime in isomerization of M7 clusters. Thus, with this temperature one can extract critical information hidden behind the stepwise fluctuation of the kinetic energy of a trajectory in an isomerization process [33]. We have explored a possible origin of the Arrhenius-like relation. 

Then it was possible to collect reaction rates in form of simple functions of a single parameters with Arrhenius formulas, which are quite common in literature and databases of chemical kinetics and reaction rates. The use of electron temperature as a parameter does not prevent the capability to make comparison with other existing models, since it could be related, in a one to one correspondence, with experimental informations on the streamer electric field. Indeed electron temperature is trivially connected with the mean electron energy, which is determined by the local electric field in the Boltzmann equation (Raizer, 1991). This is sufficient to make straightforward a direct comparison between this simulation and other existing ones or experimental data. In the following we considered as reference an electron temperature value of 4 eV (Kulikovsky, 1998). 

It is argued that this temperature dependence of the activation energy arises from local correlation effects and is intimately involved with the presence of cation vacancies in the elongated octahedron site. Whilst such vacancies must remain speculative in the absence of an accurate structure determination of this composition, the presence of such vacancies in the closely related phase Lii ijTii 85100.15(1 04)3 suggests that this is the most likely origin for non-Arrhenius conductivity in the Lii+, Ti2 xAl,c(P04)3 system. 

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