Temperature-dependent aging

Isolator Structural parameter Bound Manufacturing error (%) Temperature dependency (%) Aging deterioration (%)... 

Fig. 4.3 a Temperature dependence aging rate P at different initial vacancy concentrations (j> = 0.05 and 4> = 0.025. b Normalized aging rate / vo function of temptnatme. The figures are reprinted ftorn [61]... 

Figure 7 Relative change of electrical resistivity during isothermal aging condition with falling and rising temperatures obtained by PPM calculations [25, 33] without (a) and with (b) incorporating thermal activation process in the spin flip probability 6. The assumed temperature dependency of 6 is indicated in figure c.

The rate at which ageing occurs depends on the ageing temperature. At very low ageing temperatures, over-ageing is not observed in a realistic time... 

Do not infer from the above discussion that all the catalyst in a fixed bed ages at the same rate. This is not usually true. Instead, the time-dependent effectiveness factor will vary from point to point in the reactor. The deactivation rate constant kj) will be a function of temperature. It is usually fit to an Arrhenius temperature dependence. For chemical deactivation by chemisorption or coking, deactivation will normally be much higher at the inlet to the bed. In extreme cases, a sharp deactivation front will travel down the bed. Behind the front, the catalyst is deactivated so that there is little or no conversion. At the front, the conversion rises sharply and becomes nearly complete over a short distance. The catalyst ahead of the front does nothing, but remains active, until the front advances to it. When the front reaches the end of the bed, the entire catalyst charge is regenerated or replaced. 

The general experimental approach used in 2D correlation spectroscopy is based on the detection of dynamic variations of spectroscopic signals induced by an external perturbation (Figure 7.43). Various molecular-level excitations may be induced by electrical, thermal, magnetic, chemical, acoustic, or mechanical stimulations. The effect of perturbation-induced changes in the local molecular environment may be manifested by time-dependent fluctuations of various spectra representing the system. Such transient fluctuations of spectra are referred to as dynamic spectra of the system. Apart from time, other physical variables in a generalised 2D correlation analysis may be temperature, pressure, age, composition, or even concentration. 

The anions A2H may also be involved. The two forms of propagating centre, (III) and (IV), may well co-exist, their relative kinetic importance depending upon solvent, temperature, concentrations, age of the reaction and - in the general case - the nature of the acid. The transition states for both the reactions (iii) and (iv) can best be visualised as cyclic and 6-centred [2c, 7a, 29]. 

A unified approach to the glass transition, viscoelastic response and yield behavior of crosslinking systems is presented by extending our statistical mechanical theory of physical aging. We have (1) explained the transition of a WLF dependence to an Arrhenius temperature dependence of the relaxation time in the vicinity of Tg, (2) derived the empirical Nielson equation for Tg, and (3) determined the Chasset and Thirion exponent (m) as a function of cross-link density instead of as a constant reported by others. In addition, the effect of crosslinks on yield stress is analyzed and compared with other kinetic effects — physical aging and strain rate. 

Because the closure temperature depends on the diffusion properties of a mineral and on the isotopic systems, by determining the closure ages of several minerals (sometimes using different isotopic systems), the closure temperature can be found to be a function of closure age. Figure 1-21 shows an example. That is, with the concept of closure temperature and closure age, it is possible to reveal the full temperature-time history of a rock (thermochronology), more than simply the formation age. 

A. Garriga and F. Ritort, Mode dependent nonequilibrium temperatures in aging systems. Phys. Rev. 72, 031505 (2005). 

Digital timers of excellent quality that are based on crystal oscillators are available. The resonant frequency of such oscillators is temperature dependent and subject to aging effects, but the state of the art is highly developed. Crystal-controlled clock oscillators having a maximum error of 1 ppm at 25°C are commercially available from a number of manufacturers. Some units are tem-... 

Fig. 112 Comparison of the temperature dependence at 1 Hz of mechanical E" ( , ) and dielectric m" (thin and thick continuous lines) modulus of quenched and aged PMMA, respectively, after superposition of the low-temperature part of the /3 transition (from [75])...

Fig. 14 Temperature dependence of yield stress, cry, and plastic flow stress, crpf, for quenched and physically aged PMMA. Strain rate is 2 x 10-3 s-1 (From [32])...

It is worth pointing out that hindering of the ft-a cooperativity due to physical ageing leads to quite a different temperature dependence of nSSA, as shown in Fig. 27, compared to the case of quenched PMMA shown in Fig. 24. Instead of a plateau, a large increase of nSSA is observed in the temperature range 30-80 °C. 

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