Temperature dependence conclusions

Forbes M D E, Closs G L, Calle P and Gautam P 1993 The temperature dependence of the exchange coupling in polymethylene biradicals. Conclusions regarding the mechanism of the coupling J. Phys. Chem. 97 3384-9... 

For 1 = 6 the contribution of AH° is unfavorable and that of AS° is favorable. The specific values make T = 298 K very close to the equilibrium temperature. This implies that the reaction is shifted to favor polymer at higher temperatures and to favor the cyclic monomer at lower temperatures. Since the difference between AH° and T AS° is so small, the temperature dependence of AH° and AS° could alter this conclusion. 

Such considerations appear to be very relevant to the deformation of polymethylmethacrylate (PMMA) in the glassy state. At first sight, the development of P200 with draw ratio appears to follow the pseudo-affine deformation scheme rather than the rubber network model. It is, however, not possible to reconcile this conclusion with the temperature dependence of the behaviour where the development of orientation reduces in absolute magnitude with increasing temperature of deformation. It was proposed by Raha and Bowden 25) that an alternative deformation scheme, which fits the data well, is to assume that the deformation is akin to a rubber network, where the number of cross-links systematically reduces as the draw ratio is increased. It is assumed that the reduction in the number of cross-links per unit volume N i.e. molecular entanglements is proportional to the degree of deformation. 

The important fact is that the number of collisions Zr increases with temperature. It may be attributed to the effect of attraction forces. They accelerate the molecule motion along the classical trajectories favouring more effective R-T relaxation. This effect becomes relatively weaker with increase of temperature. As a result the effective cross-section decreases monotonically [199], as was predicted for the quantum J-diffusion model in [186] (solid line) but by classical trajectory calculations (dotted and broken lines) as well. At temperatures above 300 K both theoretical approaches are in satisfactory mutual agreement whereas some other approaches used in [224, 225] as well as SCS with attraction forces neglected [191] were shown to have the opposite temperature dependence for Zr [191]. Thus SCS results with a... 

The validity of the above conclusions rests on the reliability of theoretical predictions on excited state barriers as low as 1-2 kcal mol . Of course, this required as accurate an experimental check as possible with reference to both the solvent viscosity effects, completely disregarded by theory, and the dielectric solvent effects. As for the photoisomerization dynamics, the needed information was derived from measurements of fluorescence lifetimes (x) and quantum yields (dielectric constant, where extensive formation of ion pairs may occur [60], the observed photophysical properties are confidently referable to the unperturbed BMPC cation. Figure 6 shows the temperature dependence of the... 

The conclusion regarding the fact that constant current conductivity involves not all microcrystals of the sample is proved by results of measurements of electric conductivity in sintered ZnO films in case of alternating current (Fig. 2.10). The availability of barrier-free ohmic pathways is proved by a low value of initial resistivity in sintered samples ( 1 - 5 kOhm) in addition to exponential dependence of electric conductivity plotted as a function of inverse temperature having activation energy 0.03 - 0.5 eV, which coincides with ionization energy of shallow dope levels. The same value is obtained from measurements of the temperature dependence of the Hall constant [46]. 

Works [40, 91] surveyed y versus temperature for deactivation of 02( Aj ) on quartz at 350- 900 K. The obtained temperature dependencies were in the Arrhenius form with the activation energy of 18.5kJ/mole. A conclusion was drawn up about the chemisorption mechanism of singlet oxygen deactivation on quartz surface. A similar inference was arrived at by the authors of work [92] relative to 02( A ) deactivation (on a surface of oxygen-annealed gold). 

The quantum yield for the formation of the cycloaddition product has been found to be temperature dependent, increasing by a factor of approximately three as the temperature is lowered from 65 ( = 0.24) to 5°C ( = 0.69). Photolysis of mixtures of the olefin and f/my-stilbene in the presence of sensitizers yielded no cycloaddition product (42) but rather only m-stilbene. This suggests that the cycloadduct is produced via a singlet reaction. This conclusion is supported by the fact that tetramethylethylene quenches fluorescence from the /rans-stilbene singlet. A plot of l/ (42) vs. 1/[TME] (TME = tetramethylethylene) is linear. The slope of this plot yields rate constants for cycloadduct formation which show a negative temperature dependence. To account for this fact, a reversibly formed exciplex leading to (42) was proposed in the following mechanism<82) ... 

So, if one will compare the temperature dependence of the experimentally obtained escape times of some unknown system with the temperature dependence of Kramers time presented in Table I, one can make conclusions about potential profile that describes the system. 

H2 to Fe(C0)4 from (1.97 + 0.15) x 10 14cm3molecule 4s 1 to (2.47 + 0.49) x 10 14 cm3 molecule 1 s 1 was measured upon increasing the temperature from 296.5 K to 315 K (55). Although the experimental error bars preclude reaching quantitative conclusions about the activation energy based on these two results, it is remarkable that the ratio of these values, 1.25, is very close to the ratio of the calculated app values at these temperatures, 1.32. Additional measurements of the temperature dependence could provide a more stringent test of these theoretical predictions. 

It appears that the rate constant for most of the boards has a smaller temperature dependence than the initial maximum rate, the corresponding "activation energy" E3 being around or less than 5 kcal/mol. An important conclusion is that the rate is diffusion limited. This has to be compared to a mean activation energy around 20 kcal/mole for the initial maximum rate of heat release for the commercial boards. As a consequence thereof the total heat release extrapolated over infinite time does increase to a significant extent with temperature from 150 to 230°C. 

These results are similar to those in the previous section, with n — 1 replacing n, and similar conclusions about temperature dependence can be drawn, except that for a first-order reaction, ea = eAp and A = A,. The relationships of these differing Arrhenius parameters for a third-order reaction are explored in problem 4-12. 

The l3C NMR spectrum of the C4H7+ cation in superacid solution shows a single peak for the three methylene carbon atoms (72) This equivalence can be explained by a nonclassical single symmetric (three-fold) structure. However, studies on the solvolysis of labeled cyclopropylcarbinyl derivatives suggest a degenerate equilibrium among carbocations with lower symmetry, instead of the three-fold symmetrical species (13). A small temperature dependence of the l3C chemical shifts indicated the presence of two carbocations, one of them in small amounts but still in equilibrium with the major species (13). This conclusion was supported by isotope perturbation experiments performed by Saunders and Siehl (14). The classical cyclopropylcarbinyl cation and the nonclassical bicyclobutonium cation were considered as the most likely species participating in this equilibrium. 

Coming back to aromatic anion radicals, a more accurate comparison between the experimental reaction kinetics and the predictions of the dissociative electron transfer theory revealed that the agreement is good when steric hindrance is maximal (tertiary carbon acceptors) and that the reaction is faster and faster than predicted as steric hindrance decreases, as discussed in detail in Section 3.2.2 (see, particularly, Figure 3.1). These results were interpreted as indicating an increase in the ET character of the reaction as steric hindrance increases. Similar conclusions were drawn from the temperature dependence of the kinetics, showing that the entropy of activation increases with steric hindrance, paralleling the increase in the ET character of the reaction. 

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