Temperature Dependence of T

Currently, the dependence of t on temperature is deduced from viscosity-temperature measurements. At T < T, the temperature dependence of T obeys an Arrhenius law, but this dependence is much more complex at T > T. In the latter case it is referred to an empirical Vogel-Tamman-Fulcher (VTF) law (Vogel, 1921 Tamman and Hesse, 1926 Fulcher, 1925). 

Unfortunately, reliable experimental estimates of the configurational entropy are unavailable to enable explicit application of the AG model for polymer fluids. Instead, the temperature dependence of t in polymer melts is often analyzed in terms of the empirical Vogel-Fulcher-Tammann-Hesse (VFTH) equation [103],... 

The temperature dependence of T in the high temperature regime (Z > Zt) is often modeled by an alternative VFTH equation. 

Equation (9) shows that for a1 independent of T, measurement of the emission rate as a function of temperature yields the trap energy. The temperature dependence of > (oc T1/2) and Nc(cc T3/2) can be taken into account either by determining the slope of ln(e, /T2) as a function of 1/T or by subtracting 2kTm from the slope of In e versus 1/T, where Tm is the average temperature over which the slope of In e was measured (Miller et ai, 1977). However, a is often temperature dependent. For instance, Henry and Lang (1977) show that it frequently can be represented by... 

The temperature dependence of prepared crystals slowly increases with decreasing temperature, with passing through a maximum at about 250 K.122 The conductivity falls to its room temperature value at about 200 K and then falls rapidly with decreasing temperature. Below 100 K the behaviour is that of a semiconductor with activation energy of about 34 meV. 

It is generally found that the constant , in contrast to co, depends on temperature. If the temperature dependence of (T) is represented by the standard Arrhenius equation, then the apparent activation energy appears to be on the order of 10 kJ/mol, which is close to the activation energy of most fluid diffusion processes. 

All these t /2 results are confirmed by the temperature dependence of T p (13C), leading to the same conclusion. 

Fig. 40 ImP(E) = 0 the intensity of the resonances on the central narrow band is strongly dependent on Jo/ujc and ksT (not shown). Temperature dependence of t E) with full inclusion of P(E) (middle panel) and corresponding current (lower panel) for N = 20, Jo/tcc = 5, t /t = 0.5, Tl/rAh = 0.2. The pseudo-gap increases with temperature.

A positive temperature dependence of t] is a remarkable peculiarity of solar cells, which is not observed for any kind of inorganic solar cell [157]. It is important to note that heating the cells to such elevated temperatures as Tmax may be achieved merely by the absorption of solar radiation, i.e., without any additional heating. 

Measurements of the temperature dependence of t yielded an activation energy consistent with this picture. Thus, the time t required for the appearance of fogging corresponds to the time necessary to saturate the growth tube s surface with carbon. 

Mixtures of hydrophilic Aerosil with the oligomer have been studied by H T and T2 relaxation experiments in a wide temperature range [9]. A two-phase model was used to describe the relaxation of ODMS molecules at the surface of Aerosil. According to this model [29], molecules at the surface of a solid co-exist in adsorbed and non-adsorbed states. In a certain period of time, molecules perform jumps between these two phases. The lifetime of a molecule in adsorbed and desorbed states is detected from peculiarities of the temperature dependence of T and T2 NMR relaxation times [29]. It was shown that, already at 240 K, the lifetime of ODMS molecules in the adsorbed state is about 50 ps, i.e., the frequency of adsorption-desorption at this temperature is close to 3 kHz [9]. At about 500 K, nearly all ODMS molecules are desorbed. 

The activalion energy for r, from the slope of an Arrhenius plot of In r against l/r, (Eq. 7-74), will be equal to —RT Inri). Similar expressions hold for r2 and the product r r2- The absolute value of the logarithm of a number is a minimum when this number equals unity, and so a strong temperature dependence of t will be expected only if either r, I or r, I ... 

The temperature dependence of T o is mainly included in the fnction coefficient (relation 5-22). Therefore, qo can be expressed by ... 

The entire data set, p E, T), can be summarized by the intercept, p 0, T), and slope, S T), as functions of temperature. A typical temperature dependence of T) is illustrated in Figure 31. While the data may be described qualitatively as activated , p exponential in T, the dependence is actually somewhat stronger, p exponential in T as if there were a temperature-dependent activation energy. Whenever the data permit one to judge between and T, an exponential dependence on is usually the better description. This dependence can be characterized by its T — 00 limit, //q (a hypothetical mobility at infinite temperature), and a slope (where To may be viewed as a characteristic temperature) (Eq. (5)). 

Fig. 32. Temperature dependence of [t]) and ln)/lr l for solutions of cellulose carbanilate in dioxane )...

Fig. 11. Temperature dependence of /T for Ce Cu2 + vSi2- Above 1 K, T in Ceo,97sCu2Si2 is determined by a single component. Below 1 K, short (Tis) and long (Til) components of /T are shown.

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