Activation energy temperature dependence

The CH3S -h allene reaction was studied directly and found to exhibit complex non-Arrhenius behavior [92]. Based on the observed dual-activation-energy temperature dependence, Balia et al. [92] proposed that the reaction mechanism consists of two reaction pathways, one involving CH3S addition to an allene double bond to form an adduct, and another involving H atom abstraction from allene. 

Hence, the apparent activation energy is half the value we would obtain if there were no transport limitations. Obviously it is important to be aware of these pitfalls when testing a catalyst. Indeed, apparent activation energies generally depend on the conditions employed (as discussed in Chapter 2), and diffusion limitation may further cause them to change with temperature. 

One must recognize that TST is much simpler conceptually than VTST. Thus, there is one transition state in TST and that is located at the maximum energy on the MEP (the saddle point). In VTST the dividing surface is temperature dependent since the partition functions and consequently the free energy of activation are temperature dependent. 

On the Energy of Activation. The temperature dependence of many processes, such as diffusion, permeability, and partition coefficients, has been represented often in terms of the Arrhenius plots (52). It would appear that ki in Equation 14 also could be treated in this manner by defining... 

The diffusion activation energy ED depends on the temperature, the size of the gas molecule d, and the glass transition temperature of the polymer. This relationship is well represented in Fig. 2.61 [62] with the size of nitrogen molecules, d 2 as a reference. Table 2.17 contains values of the effective cross section size of important gas molecules. 

Analogous to the triplet DR-spectra the quintet DC-spectra are thermally activated. The temperature dependence of the individual quintet ESR intensities I(T) could be fitted with a singlet S = 0 ground state and an activated quintet state. The corresponding dependencies are given by I(T)ax/(5 -I- e ) with x = Eq/LT - . The activation energies Eg of the quintet states (obtained from the optimal fit of the curves) are different for the individual quintet states and are extremely low in energy. As shown in Fig. 20 > they lie between about 30 peV and about 10 meV. The quintet ESR intensities are reversible only below 80 K. 

Organic field effect transistors were fabricated based on C60 layers. The temperature dependence of juFE was investigated for different VG. pfe is found to be thermally activated with activation energies strongly dependent on the applied VG. Upon extrapolation of the data in the Arrhenius plot to infinite temperature in the Meyer-Neldel formalism, 7 r = 480 K and pm-i = 2.45 cm2V s 1 can be extracted. The observed temperature dependence of uEE can be explained by empirical MNR, which is based on the assumption of an exponential density of states distribution. 

A process is said to be spontaneous if it occurs without outside intervention. Spontaneous processes may be fast or slow. As we will see in this chapter, thermodynamics can tell us the direction in which a process will occur but can say nothing about the speed of the process. As we saw in Chapter 12, the rate of a reaction depends on many factors, such as activation energy, temperature, concentration, and catalysts, and we were able to explain these effects using a simple collision model. In describing a chemical reaction, the discipline of chemical kinetics focuses on the pathway between reactants and products thermodynamics considers only the initial and final states... 

In this section we shall show that, if the apparent energy of activation is temperature-dependent, the same must be true for the pre-exponential factor. We shall then consider some results of the transition state theory, and describe two mathematical forms in which the temperature-dependence of In k and of Ea can conveniently be expressed. 

The volume of activation thus plays the same part in the pressure dependence of the rate constant as the energy of activation in temperature dependence. Thus, in analogy to Equation (20-59), from the equation for the overall rate of polymerization (20-52) we obtain... 

Fig. 3.40 Ions diffusion activation eneigy temperature dependence for severai nanopaiticies sizes R (nm) 1,200 (1) 100 (2) 30 (3) 20 (4) 10 (5). Inset the activation energy dependence on mean particles size for several temperatures T (K) 100 (1) 800 (2) 1,000 (3) [143]...

The reaction rate expressed through the rate constant k strongly depends on temperature and on the activation energy. This dependence is expressed in the equation given by Svante Arrhenius and Henricus Jacobus van t Hoff ... 

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