Temperature dependence transition estimation

These spectra, taken at variable temperatures and a small polarizing applied magnetic field, show a temperature-dependent transition for spinach ferredoxin. As the temperature is lowered, the effects of an internal magnetic field on the Mossbauer spectra become more distinct until they result at around 30 °K, in a spectrum which is characteristic of the low temperature data of the plant-type ferredoxins (Fig. 11). We attribute this transition in the spectra to spin-lattice relaxation effects. This conclusion is preferred over a spin-spin mechanism as the transition was identical for both the lyophilized and 10 mM aqueous solution samples. Thus, the variable temperature data for reduced spinach ferredoxin indicate that the electron-spin relaxation time is around 10-7 seconds at 50 °K. The temperature at which this transition in the Mossbauer spectra is half-complete is estimated to be the following spinach ferredoxin, 50 K parsley ferredoxin, 60 °K adrenodoxin, putidaredoxin, Clostridium. and Axotobacter iron-sulfur proteins, 100 °K. 

A more interesting possibility, one that has attracted much attention, is that the activation parameters may be temperature dependent. In Chapter 5 we saw that theoiy predicts that the preexponential factor contains the quantity T", where n = 5 according to collision theory, and n = 1 according to the transition state theory. In view of the uncertainty associated with estimation of the preexponential factor, it is not possible to distinguish between these theories on the basis of the observed temperature dependence, yet we have the possibility of a source of curvature. Nevertheless, the exponential term in the Arrhenius equation dominates the temperature behavior. From Eq. (6-4), we may examine this in terms either of or A//. By analogy with equilibrium thermodynamics, we write... 

The above-mentioned type of solvent effects has been incorporated into the theory of helix-coil transition by a number of authors (7,24,36 38), with various types of reactions being assumed. These theories explain why AH becomes temperature-dependent in inverse helix-coil transitions and also permit an estimate of AH in pure helicogenic solvents. Their details are surveyed in our companion review article (11). 

Fig. 31. Temperature dependence for equilibrated volumes of NIPA gel including the Con A-DDS complex (DSS-gel, open circles), MP (MP-gel, filled circles), and free of both DSS and MP squares). The latter was prepared as a control sample. Hysteresis was observed in the volume changes of DSS-gel and the free-Con A gel on heating and cooling, indicating a discontinuous phase transition. The diameter of each gel in the collapsed state, determined at 50 °C, was do = 0.074 mm the volume of this gel is denoted by V0. The concentration of dry matter in the collapsed state was estimated from the preparation recipe to be 90wt%.

It is not possible to evaluate k directly, for it appears with the entropy of activation in the temperature-independent part of the rate constant. An estimate of k requires an extrathermodynamic assumption. In two cases of iron(II) spin equilibria examined by ultrasonic relaxation the temperature dependence of the rates was precisely determined. If the assumption is made that all of the entropy of activation is due to a small value of k, minimum values of 10-3 and 10-4 are obtained. Because there is an increase in entropy in the transition from the low-spin to the high-spin states, this assumption is equivalent to assuming that the transition state resembles the high-spin state. There is now evidence that this is not the case. Volumes of activation indicate that the transition state lies about midway between the two spin states. This is a more chemically reasonable and likely situation than the limiting assumption used to evaluate k. In this case the observed entropy of activation includes some chemical contributions which arise from increased solvation and decreased vibrational partition functions as the high-spin state is compressed to the transition state. Consequently, the minimum value of k is increased and is unlikely to be less than about 10 2. 

Finally, the data published by Gee (30) permit one to evaluate the sharpness of a transition involving floor temperature. Gee studied the temperature dependence of the viscosity of liquid sulfur and observed its sudden, steep increase at a critical temperature followed by its decrease at still higher temperatures. He developed the first, relatively complete theory of equilibrium polymerization of liquid sulfur (30) from which he estimated the chain length of the polymeric sulfur at various temperatures. His results have been recently confirmed by experimental measurements of magnetic susceptibility of the liquid sulphur (50) and its electron spin resonance (57). 

As described in Sect. 2.3.4, the transition temperature, Tu, corresponding to the occurrence of SDZs, can be quantitatively estimated from the temperature dependence of the yield stress, ay, the plastic flow stress, critical stress for CSC, crcsc- However, the absolute value of the latter requires quantities difficult to determine experimentally. To overcome this difficulty, when comparing materials of similar chemical structure, one can take one of them as a reference, using its experimental T f value for deriving the T 2 values for the other i polymers of the considered series. 

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