Anomalous diffusion effective temperature

Ga,Mn)N film prepared by post growth Mn doping using solid state diffusion shows ferromagnetic behavior at room temperature, which is confirmed by the observation of an anomalous Hall effect (Reed et al. 2001). 

Experimentally, the effective temperature of a colloidal glass can be determined by studying the anomalous drift and diffusion properties of an immersed probe particle. More precisely, one measures, at the same age of the medium, on the one hand, the particle mean-square displacement as a function of time, and, on the other hand, its frequency-dependent mobility. This program has recently been achieved for a micrometric bead immersed in a glassy colloidal suspension of Laponite. As a result, both Ax2(t) and p(co) are found to display power-law behaviors in the experimental range of measurements [12]. 

In this chapter, we have showed that a particle undergoing normal or anomalous diffusion constitutes a system conveniently allowing one to illustrate and to discuss the concepts of FDT violation and effective temperature. Our study was carried out using the Caldeira-Leggett dissipation model. Actually this model, which is sufficiently versatile to give rise to various normal or anomalous diffusion behaviors, constitutes an appropriate framework for such a study, in quantum as well as in classical situations. 

For a particle evolving in a thermal bath, we focused our interest on the particle displacement, a dynamic variable which does not equilibrate with the bath, even at large times. As far as this variable is concerned, the equilibrium FDT does not hold. We showed how one can instead write a modified FDT relating the displacement response and correlation functions, provided that one introduces an effective temperature, associated with this dynamical variable. Except in the classical limit, the effective temperature is not simply proportional to the bath temperature, so that the FDT violation cannot be reduced to a simple rescaling of the latter. In the classical limit and at large times, the fluctuation-dissipation ratio T/Teff, which is equal to 1 /2 for standard Brownian motion, is a self-similar function of the ratio of the observation time to the waiting time when the diffusion is anomalous. 

It is shown that the applicability of fractal model of anomalous diffusion for quantitative description of thermogravimetric analysis results in case of high density polyethylene modified by high disperse mixture Fe/FeO (Z). It is shown the influence of diffusion type on the value of sample 5%-th mass loss temperature and was offered structural analysis of this effect. The critical content Z it is determined, at which degradation will be elapse so, as in inert gas atmosphere. 

Our purpose in this text is principally to present temperature scanning methods. These generally involve multiple rampings as one seeks to delineate the kinetics of a system over a wide range of conditions. However, there is a well known and established technique for the semi-quantitative study of desorption phenomena, the Temperature Programmed Desorption (TPD) method. The equations developed below are also applicable to results that can be obtained using some of the versions of the traditional TPD apparata. In such cases they can be used to quantify the TPD results to yield the kinetics of the process and/or to check for extraneous influences that can result in anomalous results, effects such as mass diffusion, heat diffusion, or purely kinetic effects. 

Chapter 4(71) focuses on the characterization of sorption kinetics in several glassy polymers for a broad spectrum of penetrants ranging from the fixed gases to organic vapors. The sorption kinetics and equilibria of these diverse penetrants are rationalized in terms of the polymer-penetrant interaction parameter and the effective glass transition of the polymer relative to the temperature of measurement. The kinetic response is shown to transition systematically from concentration independent diffusion, to concentration dependent diffusion, and finally to complex nonFickian responses. The nonFickian behavior involves so-called "Case II" and other anomalous situations in which a coupling exists between the diffusion process and mechanical property relaxations in the polymer that are induced by the invasion of the penetrant (72-78). ... 

There are several practical difficulties in translating incremental outgassing data into diffusion coefficients (Farley 2000). The most commonly used computational models require that the distribution of diffusant be uniform within the diffusion domain. This assumption is violated in many samples by the a-ejection effect and by He diffusion in nature, both of which act to round the concentration profile at the grain surface. As a consequence, the initial rate of He release from a sample is anomalously retarded relative to later release. Fortunately this effect can be identified and greatly reduced by incremental outgassing schedules that involve cycling from low to high temperatures and back (Farley 2000). 

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