ARRHENIUS’S LAW

In this chapter we discuss the origin of Arrhenius s Law and its application to diffusion. In the next, we examine how it is that the rate of diffusion determines that of creep. 

There are two mechanisms of creep dislocation creep (which gives power-law behaviour) and diffusiona creep (which gives linear-viscous creep). The rate of both is usually limited by diffusion, so both follow Arrhenius s Law. Creep fracture, too, depends on diffusion. Diffusion becomes appreciable at about 0.37 - that is why materials start to creep above this temperature. 

Fig 21.3. Oxidation rates increase with temperature according to Arrhenius s Law. 

Oxidation rates follow Arrhenius s Law (Chapter 18), that is, the kinetic constants k[ and kp increase exponentially with temperature ... 

If temp, product > Tg Lyo, the WLF (Williams, Landel, and Ferry) law applies [25,34]. For a similar increase in temperature, this latter law reveals a much more important decrease in the values of the physicochemical parameters than does Arrhenius s law [25]. 

For instance, if a freeze-dried vaccine with a vitreous transition temperature equal to 25°C is submitted to accelarated storage tests at temperatures lower than 25°C, Arrhenius s law is applicable. On the other hand, for temperatures above 25°C, there exists a potential risk of error in the prediction. The implementation of the accelarated storage test is thus submitted to the level of the Tg Lyo. 

Note that equation [13.8] imposes both a deviation in Arrhenius s law (for a large temperature range) and a dependence on the activation energy, Ea, on the logarithm of molecular mass (i.e. a variation by a factor of 2-3 is expected in the range 100-1 000 g-mol ) ... 

Calculation by present authors from original work (assuming that data fit Arrhenius s law). 

Calculation by present authors from original work (assuming that data fit Arrhenius s law). ) D° estimated by present authors to calculate grfi (assumed a v = lO s and X = 0.3 nm). 

Chemical reactions are governed by Arrhenius s Law which states that the rate of reaction (fe) is proportional to an exponential function of absolute temperature. 

Steps 3-5 are (physico-)chemical processes and depend nearly exponentially on temperature according to Arrhenius s law [Eq. (4.3.4)], typically with activation... 

If we want to compare the temperature dependence of a chemical reaction with that of diffusion, we have to reinterpret the influence of temperature on the diffusion coefficient in terms of Arrhenius s law with an apparent activation energy... 

As already shown in Example 4.5.2, the apparent activation energy is then determined simply by the relatively small influence of temperature on the diffusion coefficient and in terms of the Arrhenius s law we get an apparent activation energy in the range of about 5 to 20 kj mol (Figure 4.5.25). 

In comparison to the strong influence of temperature on according to Arrhenius s law, we may neglect the small change in concentrations with temperature, and Eq. (4.11.29) simplifies to ... 

The number of parameters to be identified is small energy and activation volume of the viscoplastic flow law based on Arrhenius s law (stress-assisted thermally activated slip). The experimental curves used during parameter adjustment are tensile curves, obtained at different rates. Unlike the Taylor or Sachs models, the previous mean-field homogenization models naturally predict a limited number of systems activated at low amplitude and a large number at high amplitude. Even at equal cumulated... 

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