Relaxation time Arrhenius temperature

This expression is of the same shape as that of stress relaxation of viscoelastic materials (Chap. 13). By analogy 1/k is called the "relaxation time" (t). Since chemical reactions normally satisfy an Arrhenius type of equation in their temperature dependence, the variation of relaxation time with temperature may be expressed as follows ... 

All the examples described above show that confinement in different cases may be responsible for nonmonotonic relaxation kinetics and can lead to a saddle-like dependence of relaxation time versus temperature. However, this is not the only possible reason for nonmonotonic kinetics. For instance, work [258] devoted to the dielectric study of an antiferromagnetic crystal discusses a model based on the idea of screening particles. Starting from the Arrhenius equation and implying that the Arrhenius activation energy has a linear dependence on the concentration of screening charge carriers, the authors of Ref. 258 also obtained an expression that can lead to nonmonotonic relaxation kinetics under certain conditions. However, the experimental data discussed in that work does not show clear saddle-like behavior of relaxation time temperature dependence. The authors of Ref. 258 do not even discuss such a possibility. 

The variation of the maximum relaxation time with temperature indicates that the rate constant for the second mechanism is of the Arrhenius type. This is particularly pronounced in the sulfur case. 

Figure 3. Reduced Arrhenius plot of ar (ratio of the relaxation time at temperature T and Tc) for the thermal cis-trans isomerization of azoaromatic chromophores...

The magnitude of w.r determines the response of a dielectric. to study this response either w or r may be varied. A wide variation of w means, experimentally, that different apparatuses have to be used, t, however, is easily and widely varied by varying the temperature. In polymers often more than one type of relaxation mechanism is encountered. Bach has a specific average relaxation time, distribution of relaxation times and temperature susceptibility. The temperature susceptibility can often be described by an Arrhenius factor [1] so that ... 

Relaxation Times (High Temperature Limits for Samples with Non-Arrhenius Behavior). 

Very sparse dielectric studies of polysiloxane scLCPs below the glassy transition show evidence of only one relaxation process, similar to the -process in polyacrylates, with a very broad distribution of relaxation times.The temperature dependence is Arrhenius and the activation energy of 51 kJ mol matches that of the jSi-process in poly acrylates (see above). Measurements performed on the oriented smectic glass show that... 

A method is described for fitting the Cole-Cole phenomenological equation to isochronal mechanical relaxation scans. The basic parameters in the equation are the unrelaxed and relaxed moduli, a width parameter and the central relaxation time. The first three are given linear temperature coefficients and the latter can have WLF or Arrhenius behavior. A set of these parameters is determined for each relaxation in the specimen by means of nonlinear least squares optimization of the fit of the equation to the data. An interactive front-end is present in the fitting routine to aid in initial parameter estimation for the iterative fitting process. The use of the determined parameters in assisting in the interpretation of relaxation processes is discussed. 

This equation gives linear dependence of a on T at high temperature (with slope a ) but a constant aQ is approached at low temperature (see Figure 3). The constant, k, controls the smoothing between the asymptotes. The central relaxation time is given WLF dependence (or Arrhenius with T = 0),... 

In real systems, a distribution in the characteristic time may lead to a stretched exponential decay. In the thermally activated regime where the relaxation of the magnetization is due to the Orbach mechanism, the temperature dependence of the relaxation time may be described by an Arrhenius law of the form ... 

Figure 10.2 Arrhenius plot of the natural logarithm of the relaxation time extracted from the ac susceptibility data as a function of the inverse temperature for 1 at different external fields as indicated. (Reprinted from Ref. [6]. Copyright (2009) American Chemical Society.)...

Figure 20 Temperature dependence of the a-relaxation time scale for PB. The time is defined as the time it takes for the incoherent (circles) or coherent (squares) intermediate scattering function at a momentum transfer given by the position of the amorphous halo (q — 1.4A-1) to decay to a value of 0.3. The full line is a fit using a VF law with the Vogel-Fulcher temperature T0 fixed to a value obtained from the temperature dependence of the dielectric a relaxation in PB. The dashed line is a superposition of two Arrhenius laws (see text).

The dispersion of this waiting time distribution, i.e., its second central moment, is a measure that we can use to define a homogenization time scale on which the dispersion is equal to that of a homogeneous (Poisson) system on a time scale given by the torsional autocorrelation time. The homogenization time scale shows a clear non-Arrhenius temperature dependence and is comparable with the time scale for dielectric relaxation at low temperatures.156... 

The answer to our question at the beginning of this summary therefore has to be as follows. When you want to locate the glass transition of a polymer melt, find the temperature at which a change in dynamics occurs. You will be able to observe a developing time-scale separation between short-time, vibrational dynamics and structural relaxation in the vicinity of this temperature. Below this crossover temperature, one will find that the temperature dependence of relaxation times assumes an Arrhenius law. Whether MCT is the final answer to describe this process in complex liquids like polymers may be a point of debate, but this crossover temperature is the temperature at which the glass transition occurs. 

The non-Arrhenius temperature-dependence of the relaxation time. It shows a dramatic increase when the glass transition temperature region is approached. This temperature dependence is usually well described in terms of the so called Vogel-Fulcher temperature dependence [114,115] ... 

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