Temperature dependence Arrhenius region

Some general features were found, namely that the P relaxation in the lower alkyl methacrylates appears to be an intramolecular process independent of the nature of the side group, and that the a process is strongly determined by the a relaxation. However, the crossover region between the a and P processes presents different profiles. The P dynamics, which follows Arrhenius-type temperature dependence below Tg, seems to change by merging with the a process, followed by a further... 

Therefore, there are different dynamics below and above the aP splitting region. This change in molecular dynamics is enhanced through the analysis proposed for glass formers by Stickel, Fischer and Richert [34] of the derivatives d/dT, d/d(l/7) and d /d7 of log is aiax that are used to linearize the different VFTH dependence laws t(7) (reducing Arrhenius-type temperature dependence to a constant). The d/d(l/7) derivative takes the form ... 

Figure 15 shows the 3D plot of s relative to neutralized chitosan, evidencing the a process in the high temperature-low frequency range whose Arrhenius-type temperature dependence of relaxation times is shown in the inset. The secondary process observed in the low-temperature region is due to local main chain motion via the glycosidic bond, influenced by the amino side group (see [149] for discussion). 

The bifurcational diagram (fig. 44) shows how the (Qo,li) plane breaks up into domains of different behavior of the instanton. In the Arrhenius region at T> classical transitions take place throughout both saddle points. When T < 7 2 the extremal trajectory is a one-dimensional instanton, which crosses the maximum barrier point, Q = q = 0. Domains (i) and (iii) are separated by domain (ii), where quantum two-dimensional motion occurs. The crossover temperatures, Tci and J c2> depend on AV. When AV Vq domain (ii) is narrow (Tci — 7 2), so that in the classical regime the transfer is stepwise, while the quantum motion is a two-proton concerted transfer. This is the case when the tunneling path differs from the classical one. The concerted transfer changes into the two-dimensional motion at the critical value of parameter That is, when... 

The measured dependence of kn(T) and T) consists of an Arrhenius region ( = 9.6 kcal/mol) going over to the low-temperature plateau below IlOK, where k 10 s . The isotope effect grows as the temperature drops, kn/ko — 20 at T = 100 K (fig. 15). Tunneling is promoted by the torsional vibrations of the OH and CH groups, as well as the oxy-group bending vibration. 

The kinetics of the CTMAB thermal decomposition has been studied by the non-parametric kinetics (NPK) method [6-8], The kinetic analysis has been performed separately for process I and process II in the appropriate a regions. The NPK method for the analysis of non-isothermal TG data is based on the usual assumption that the reaction rate can be expressed as a product of two independent functions,/ and h(T), where f(a) accounts for the kinetic model while the temperature-dependent function, h(T), is usually the Arrhenius equation h(T) = k = A exp(-Ea / RT). The reaction rates, da/dt, measured from several experiments at different heating rates, can be expressed as a three-dimensional surface determined by the temperature and the conversion degree. This is a model-free method since it yields the temperature dependence of the reaction rate without having to make any prior assumptions about the kinetic model. 

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] ... 

Conversely, at the lower temperatures, the rate constant for H-abstraction is small while, at the same time, the rate of adduct decomposition is lowered. As a result, at the lower temperatures (right side of Fig. 6.11), adduct formation predominates and a negative temperature dependence, as well as a dependence on pressure is observed for the overall rate constant. In the intermediate region, both addition and abstraction are occurring at significant rates, leading to the curved OH decay plots in Fig. 6.10 and the discontinuities in the Arrhenius plots of Fig. 6.11. 

Fig. 5.3. Locus of Hopf bifurcation points in K-fi parameter plane for thermokinetic model with the full Arrhenius temperature dependence and y = 0.21. The nature of the Hopf bifurcation point and, hence, the stability of the emerging limit cycle changes along this locus at k = 2.77 x 10 3. Supercritical bifurcations are denoted by the solid curve, subcritical bifurcations occur along the broken segment, i.e. at the upper bifurcation point for the lowest k. The stationary-state solution is unstable and surrounded by a stable limit cycle for all parameter values within the enclosed region. Oscillatory behaviour also occurs in the small shaded region below the Hopf curve, where the stable stationary state is surrounded by both an unstable and...

A few comments on (2.27), (2.29), and (1.12) are appropriate at this point. The activation energy in the Arrhenius region is independent of 17, since friction changes only the velocity at which a classical particle crosses the barrier and thus affects only the preexponential factor. However, friction reduces both kc and Tc and thereby widens the Arrhenius region. Dissipation has a noticeable effect on the temperature dependence of... 

The temperature dependence of this rate constant was measured by Al-Soufi et al. [1991], and is shown in Figure 6.17. It exhibits a low-temperature limit of rate constant kc = 8x 105 s 1 and a crossover temperature 7 C = 80K. In accordance with the discussion in Section 2.5, the crossover temperature is approximately the same for hydrogen and deuterium transfer, showing that the low-temperature limit appears when the low-frequency vibrations, whose masses are independent of tunneling mass, become quantal at Tisotope effect increases with decreasing temperature in the Arrhenius region by about two orders of magnitude and approaches a constant value kH/kD = 1.5 x 103 at T[Pg.174]

The solid-state environment prevents diffusion of radicals, so reactions are only possible with neighboring Cl2 molecules. Reaction (9.15) can therefore occur only in clusters (RH-C12) , where > 2. Products are observed only when the mole fraction of chlorine in the mixture is greater than 0.1. The k(T) dependence includes an Arrhenius region (60-90 K) in which the activation energy (2-4 kcal/mol) is 1.5-2 times larger than in the corresponding gas-phase reactions. The low-temperature plateau occurs below 40-50 K where kc is 5 x 10-3 s-1 and 2 x 10 2 s-1 for the radicals of n-butylchloride and methylcyclohexane, respectively. 

Figure 11 Arrhenius plots of the slow component of nonradiative decay times of MG in (A) PVAc, (B) PMA, and (C) PEMA as functions of temperature. Below Tg the plots show two regions of Arrhenius temperature dependence. (From Refs. 1, 12.)...

The temperature dependence of k, was investigated and reported in Ref. [266], To obtain low-temperature data, samples were prepared in a 50% glycerol-water mixture. Figure 33 presents the temperature variation of k,. One can see from this Fig. that the electron transfer rate falls smoothly from the room temperature value to a non-zero value, kt = 9 + 4 s 1, which does not vary further from 170 down to 77 K. Data in the temperature-dependent region (T > 253 K) give the value Ea 2 kcal mol 1 for the Arrhenius activation energy. 

Experimental results from studies of Arrhenius dependence of different characteristics of lysozyme are presented in Fig 4.1. (Alfimova and Likhtenshtein, 1979 Likhtenshtein, 1993 Likhtenshtein et al., 2000). The discontinuities on the curves indicate local conformational transitions and are apparently due to the appearance of a more open conformation of the protein. As can be seen from Fig. 4.1., these methods reveal conformational transitions at a temperature of about 30°C, whereas the temperature dependence of the partial heat capacity decreases monotonically in this temperature region. Recently, the presence of the conformational transition in lysozyme was confirmed independently. It was shown that the segmental motion of Trp 108 is hindered by the local cage structure at T < 30°C, although relieved from restricted motion by thermal agitation or by the formation of a ligand complex. 

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