Transition Arrhenius region

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 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] ... 

Since at the probability of transition becomes equal to m, the integral (5) is divided into two summands the second is proportional to exp (- V Kb T) and determines the constant value of the activation energy in the Arrhenius region where all transitions are the over -barrier ones. With falling temperature the contribution of transitions corresponding to the region w( ) lo increases, and apparent activation energy E, ... 

An Arrhenius plot of the rate constant, consisting of the three domains above, is schematically shown in fig. 45. Although the two-dimensional instanton at Tci < < for this particular model has not been calculated, having established the behavior of fc(r) at 7 > Tci and 7 <7 2, one is able to suggest a small apparent activation energy (shown by the dashed line) in this intermediate region. This consideration can be extended to more complex PES having a number of equivalent transition states, such as those of porphyrines. 

Several attempts have been made to superimpose creep and stress-relaxation data obtained at different temperatures on styrcne-butadiene-styrene block polymers. Shen and Kaelble (258) found that Williams-Landel-Ferry (WLF) (27) shift factors held around each of the glass transition temperatures of the polystyrene and the poly butadiene, but at intermediate temperatures a different type of shift factor had to be used to make a master curve. However, on very similar block polymers, Lim et ai. (25 )) found that a WLF shift factor held only below 15°C in the region between the glass transitions, and at higher temperatures an Arrhenius type of shift factor held. The reason for this difference in the shift factors is not known. Master curves have been made from creep and stress-relaxation data on partially miscible graft polymers of poly(ethyl acrylate) and poly(mcthyl methacrylate) (260). WLF shift factors held approximately, but the master curves covered 20 to 25 decades of time rather than the 10 to 15 decades for normal one-phase polymers. 

Existence of a time-temperature equivalence that takes a different mathematical form in the glassy state (Arrhenius) and in the glass transition and rubbery regions (WLF). 

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. 

Tunneling in potential (92) was discussed in ref 210 as the reason for deviations of the fracture rate temperature dependence from that expected in thermal fluctuation theory [216]. To the low-temperature fracture stipulated by the stressed lattice vibrations there corresponds a transition, in the 6 region, from the Arrhenius relationship to the low-temperature plateau [217]. Experimental data are explained in terms of these notions [218]. 

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