Temperature-dependent activation energy

The presence of cross-linked phosphates may be recognized by their ready hydrolysis, which leads to a rapid drop in the viscosity of the solution and a parallel decrease in its pH. Aqueous solutions of all cross-linked phosphates are hydrolyzed after twenty hours. In contrast to the hydrolysis of normal P—O—P bonds in meta- and polyphosphates, that of the cross-linking sites is practically independent of concentration, pH, ionic strength and the nature and concentration of added salts. It does, however, follow a first-order law, as for normal P—O—P bonds, and is strongly temperature dependent. Activation energies of 18.9 and 15.4 kcal/mole have been... 

Jortner, J., 1976, Temperature dependent activation energy for electron transfer between biological molecules J. Chem. Phys. 64 486034867. 

The entire data set, p E, T), can be summarized by the intercept, p 0, T), and slope, S T), as functions of temperature. A typical temperature dependence of T) is illustrated in Figure 31. While the data may be described qualitatively as activated , p exponential in T, the dependence is actually somewhat stronger, p exponential in T as if there were a temperature-dependent activation energy. Whenever the data permit one to judge between and T, an exponential dependence on is usually the better description. This dependence can be characterized by its T — 00 limit, //q (a hypothetical mobility at infinite temperature), and a slope (where To may be viewed as a characteristic temperature) (Eq. (5)). 

Hops from deep sites to nearby, higher-energy sites contribute to the activation energy for transport. At lower and lower temperature, that contribution increases because a carrier spends most of its time in deeper and deeper sites. The apparent temperature-dependent activation energy mentioned in conjunction with Eq. (5) is easily understood on this basis. (Of course, any reorganization energy for the electron transfer process may also contribute to the temperature dependence.)... 

Almost all the known heat capacities of activation refer to reactions in solution. While most of the information has been obtained relatively recently, it is noteworthy that temperature-dependent activation energies, indicating a significant value for AO, were already reported for a number of reactions in the 1930 s when recalculation of previous data also provided a few further examples (see Moelwyn-Hughes, 1947a ... 

For materials showing WLF-like behavior, such a plot yields a curved line and thus a temperature-dependent activation energy. 

Several chemical marker compounds formed at sterilizing temperatures from precursor compounds inherently present in the foods have been reported (Kim and Taub, 1993 Kim et al, 1994). In order to apply these chemical markers to real processing conditions, where lethality accumulates under nonisothermal conditions, accurate informations about the reaction rate constants and their temperature dependence (activation energy or Z-value) are needed. The variability of the precursor concentration within the particulates and among different particulates also needs to be considered carefully. 

More generally, it can be seen that eqn (1.6) can be used to obtain an expression for a temperature-dependent activation energy (and imply a temperature-dependent pre-exponential factor), usually written as ... 

Equations 14.10 and 14.11 are two different ways of representing the temperature dependence of zero-shear viscosity. For a material that follows the WLF Equation 14.11, obtain an expression for the temperature-dependent activation energy E in Equation 14.10. 

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