Temperature dependence Arrhenius-like relation

The autocatalator model is in many ways closely related to the FONT system, which has a single first-order exothennic reaction step obeying an Arrhenius temperature dependence and for which the role of the autocatalyst is taken by the temperature of the system. An extension of this is tlie Sal nikov model which supports tliennokinetic oscillations in combustion-like systems [48]. This has the fonn ... 

Other factors that can impact these constants relate to reaction solution conditions. We have already discussed how temperature can affect the value of kCM and kcJKM according to the Arrhenius equation (vide supra). Because enzymes are composed of proteins, and proteins undergo thermal denaturation, there are limits on the range of temperature over which enzymes are stable and therefore conform to Arrhenius-like behavior. The practical aspects of the dependence of reaction velocity on temperature are discussed briefly in Chapter 4, and in greater detail in Copeland (2000). 

This paper is a continuation of a series of theoretical studies carried out at the Institute of Chemical Physics which seek to give a description of various phenomena of combustion and explosion under the simplest realistic assumptions about the kinetics of the chemical reaction. A characteristic feature of the specific rate (rate constant) of chemical combustion reactions is its strong Arrhenius-like dependence on the temperature with a large value of the activation heat, related to the large thermal effect of the combustion reaction. 

While experimental evidence for polaronic relaxation is extensive, other experiments render the polaron models problematic (i) the use of the Arrhenius relation to describe the temperature dependence of the mobility (see above) leads to pre-factor mobilities well in excess of unity, and (ii) the polaron models cannot account for the dispersive transport observed at low temperatures. In high fields the electrons moving along the fully conjugated segments of PPV may reach drift velocities well above the sound velocity in PPV.124 In this case, the lattice relaxation cannot follow the carriers, and they move as bare particles, not carrying a lattice polarization cloud with them. In the other limit, creation of an orderly system free of structural defects, like that proposed by recently developed self-assembly techniques, may lead to polaron destabilization and inorganic semiconductor-type transport of the h+,s and e s in the HOMO and LUMO bands, respectively. 

The temperature dependence of a structural relaxation process is in some cases of the Arrhenius type like in the case in 1,5-pentanediol. Very often we observe, however, a much stronger dependence especially at low temperatures. This has been succes-fully described by the Vogel-Fulcher-Tamann (VFT) equation involving an additional parameter, the T temperature, which is related to the glass temperature T °... 

It is argued that this temperature dependence of the activation energy arises from local correlation effects and is intimately involved with the presence of cation vacancies in the elongated octahedron site. Whilst such vacancies must remain speculative in the absence of an accurate structure determination of this composition, the presence of such vacancies in the closely related phase Lii ijTii 85100.15(1 04)3 suggests that this is the most likely origin for non-Arrhenius conductivity in the Lii+, Ti2 xAl,c(P04)3 system. 

The Arrhenius relation will not be observed above the temperature at which the decomposition or, as may occur for enzymes, inactivation of one or more of the reactants occurs (r ax)- Indeed, adherence to this relation at temperatures well above T ax for niost microorganisms has been used as evidence for an abiotic, rather than a biologically mediated mechanism of transformation (Wolfe and Macalady, 1992). For biotransformations, the Arrhenius equation also fails to describe the temperature dependence of reaction rates below the temperature at which biological functions are inhibited (T in), and above the temperature of maximum transformation rate (Topt). An empirical equation introduced by O Neill (1968) may be used to estimate the rates of biotransformation as a function of ambient temperature, min opt max (in this case, the lethal temperature), and the maximum biotransformation rate (p-max)- Because of the complexity of biochemical systems and the myriad of different structures encompassed by pesticide compounds, Tmiii, Topt, Tmax and p max are all likely to vary among different compounds, microbial species and geochemical settings (e.g., Gan et al., 1999, 2000). However, Vink et al. (1994) demonstrated the successful application of the O Neill function to describe the temperature dependence of biotransformation for 1,3-dichloro-propene and 2,4-D in soils (Figure 13). 

Note The success of the Arrhenius theory has often induced workers to apply it to other phenomena. Several physical properties of a system tend to depend on temperature like an Arrhenius relation, but this does not necessarily mean that we can assign an activation energy to the phenomenon. A case in point is the fluidity, i.e., the reciprocal of the viscosity, since there is no such thing as an activation energy for fluid motion (a true fluid moves if only the... 

The productivity of the SB 12 catalyst depends on polymerization conditions, mainly the monomer concentration and the polymerization temperature. The dependence on monomer concentration is of first order allowing an easy computation of the productivity level attainable in each kind of process. Like stereospeclflclty, the productivity of the SB 12 catalyst is closely related to the polymerization temperature. It can be used over a broad range of temperatures, typically from 50 to 80 C, with a broad modulation of the productivity level. In this temperature range, the activity of the catalyst can be adequately represented by an Arrhenius semi-logarithmic relation as expressed in table 4. In our laboratory conditions, the catalyst activity activation energy is found to be 33.2 kilojoule per mole of TiCl3 with a squared correlation coefficient r of 0.980. 

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