Relaxation time dependence on temperature

A very rough physical idea is to suppose that the dependence of ROa s.s. on temperature is given by a W.L.F. e-quation rather tiian by an Arrhenius one. The reason for such an assumption lies in tne fact that "relaxation times" depends on temperature, around Tq, according to a W.L.F. equation, and an analogy between diffusion process and relaxation processes is possible. Accordingly,... 

While all relaxation times depend on temperature and pressure, only the global motions (viscosity, terminal relaxation time, steady-state recoverable compliance) are functions of Af , (and to a lesser extent MWD). The glass transition temperature of rubbers is independent of molecular weight because chain ends for high polymers are too sparse to affect this bulk property (Figure 3.14 Bogoslovov et al., 2010). The behavior can be described by the empirical Fox-Hory equation (Fox and Flory, 1954) ... 

Glass Transition Time Magnification and Quenching. Polymers are glass-forming materials. If no crystallization occurs, this means that the spectrum of relaxation time depends on temperature via the difference T — where is the glass transition temperature. For all kinds of glasses the dependence is similar all the times of the spectrum are multiplied by the same factor a = f(T — The closer to T, ... 

Fig. 18. Experimental and theoretical curves for dependence of the transverse relaxation time Ti on temperature for protons in an aqueous solution of manganous ion at a resonance frequency of 10 Mc/sec. [Bemheim et al. (5).]...

A superstatistical equilibrium distribution is written as a superposition of Boltzmann distributions with different temperatures. We showed that the excess heat could be written as a superposition of correlation functions with different temperatures using the generalized fluctuation-dissipation theorem. When a relaxation time depends on a temperature, we can expect various behaviors for the area of the hysteresis loop from the fluctuation-dissipation theorem. 

The dependence of the reciprocal of the spin-lattice relaxation time Tf1 on temperature T for water is generally approximated [390-394] by the sum of two exponents ... 

Over small temperature ranges, a linear dependence of the transverse relaxation time T2 on temperature is observed for technical SBR samples in the vicinity of room temperature (Fig. 7.1.13(a)). The temperature coefficients depend only weakly on the filler contents... 

The F relaxation times depend on both copper(II) and F concentration. 1/Tip is linearly dependent on the enzyme concentration between pH 7.8 and pH 10. l/Tg is independent of frequency between 7 and 56 MHz and strongly influenced by the temperature, a behavior typical of slow exchange condition. IT2p is governed by the rate of chemical exchange of fluoride ions between the bulk and the binding site, whereas 1/T 1 is only partially dependent on t. ... 

The quantity rj/G represents the melt relaxation time to, the time in which shear stress decays to He (34%) of its original value. The relaxation time depends on the molecular mass and the melt temperature, factors which... 

This aspect was addressed in a model developed by Kovacs et al. [1979], which assumed that aging involves a distribution of relaxation times with multiple relaxation processes and that each relaxation time depends on the temperature and the glass structure. The model does not attempt to curve-fit the heat capacity data but, instead, uses a peak shift method [Hutchinson, 1992], which removes the need to assume a particular distribution of relaxation times. 

To study the effects of interaction of starch with silica, the broadband DRS method was applied to the starch/modified silica system at different hydration degrees. Several relaxations are observed for this system, and their temperature and frequency (i.e., relaxation time) depend on hydration of starch/silica (Figures 5.6 and 5.7). The relaxation at very low frequencies (/< 1 Hz) can be assigned to the Maxwell-Wagner-Sillars (MWS) mechanism associated with interfacial polarization and space charge polarization (which leads to diminution of 1 in Havriliak-Negami equation) or the 5 relaxation, which can be faster because of the water effect (Figures 5.8 and 5.9). 

Various phenomenological equations have heen used to describe the dependence of the characteristic relaxation time on temperature and structiu-e and sometimes pressure, including the TNM equation (120), equations derived hy Hodge (123) and Scherer (124), both based on the approach of Adam and Gibbs (125), the KAHR and similar equations (119,126), equations based on free volume, and several others (127,128). The essential idea in all of these equations is that the characteristic relaxation time depends on the instantaneous state of the material (ie, temperature, pressure, and some measure of structure— volume, 5, Tf, and/or Pf). The most widely used form is the TNM equation for isobaric structural recovery ... 

In practical terms, this involves modeling the available capacity using an SOC estimator in real time. In any case, the choice of an SOC indicator is complicated. To measure the open-circuit voltage necessitates relatively long relaxation times, depends on the temperature and is therefore difficult to apply to a vehicle. The electrical parameters obtained by impedance spectroscopy need to be sufficiently reactive to the SOC to facilitate an accurate evaluation of the SOC (on the other hand, with the SOH, the technique is more easily applicable). 

The relaxation time, t, is a measure for the exponential fade-out time of the distorted distribution function /(y) towards equilibrium, described by the Fermi distribution function fo( y)- It is important to remember that with this method only one relaxation time is considered, irrespectively what external force (electrical field, temperature gradient or magnetic field) gives rise to the distortion of the conduction-electron system. This simplification restricts the applicability of the relaxation-time method. The relaxation time, depends on the kind of scattering process. 

The experimental determination of the two latter influences on the elastic properties of a vulcanized elastomeric material is performed effectively with the aid of stress relaxation tests [242]. Relaxation effects depend on temperature and loading time. Here, a distinction must be made between physical and chemical relaxation [242]. 

In a similar way, Kovacs [9] has invoked a distribution of relaxation times to account for multiple relaxation events in the aging polymer, where each relaxation time depends on the glass structure and the temperature. The difference is that rather than trying to fit the observed heat capacity data, the movement of the enthalpy recovery peak in the DSC curves was followed, as discussed by Hutchinson [10]. This approach obviated the need to define a specific distribution of relaxation times. 

Fig. 9. Dependence of in-lattice relaxation time Tj on temperature for polystyrene 1 initial, 2 with 1,3%, 3 with 23% of aerosil, 4 and S with 49,2 and 75% of fluoroplast...

Pulsed ENDOR offers several distinct advantages over conventional CW ENDOR spectroscopy. Since there is no MW power during the observation of the ESE, klystron noise is largely eliminated. Furthemiore, there is an additional advantage in that, unlike the case in conventional CW ENDOR spectroscopy, the detection of ENDOR spin echoes does not depend on a critical balance of the RE and MW powers and the various relaxation times. Consequently, the temperature is not such a critical parameter in pulsed ENDOR spectroscopy. Additionally the pulsed teclmique pemiits a study of transient radicals. 

ESR can detect unpaired electrons. Therefore, the measurement has been often used for the studies of radicals. It is also useful to study metallic or semiconducting materials since unpaired electrons play an important role in electric conduction. The information from ESR measurements is the spin susceptibility, the spin relaxation time and other electronic states of a sample. It has been well known that the spin susceptibility of the conduction electrons in metallic or semimetallic samples does not depend on temperature (so called Pauli susceptibility), while that of the localised electrons is dependent on temperature as described by Curie law. 

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