Arrhenius approach

The acid dissociation constant has the same form m Brpnsted-Lowry as m the Arrhenius approach but is expressed m the concentration of H30" rather than The concentration terms [H30" ] and [H" ] are considered equivalent quantities m equilibrium constant expressions... 

The Br0nsted-Lowry approach to acids and bases is more generally use ful than the Arrhenius approach... 

The inherent weakness of the Arrhenius approach is in the assumptions which are made. The relation describes a simple chemical reaction whereas in practice the reactions are likely to be complex. It is assumed that the reactions at the service temperature are the same as those at the testing temperatures, that the activation energy is independent of temperature and that the chemical changes relate directly to the physical properties measured. If any of these are not true the relation will be invalid. 

The acid dissociation constant K.A has the same form in Br0nsted-Lowry as in the Arrhenius approach, but is expressed in the concentration of H30+ rather than H+. The concentration terms [H30+] and [H+] are considered equivalent quantities in equilibrium constant expressions. 

During conversion of the solid fuel, the rate of homogeneous and heterogeneous reactions which take place in the particle is calculated by a standard Arrhenius approach... 

Besides the universally accepted kinetic description of a process based on a proper analysis of the shape of vaporization curves (see Sect. 2.4), the Arrhenius approach has been widely used to probe the mechanism of decomposition at the level of elementary processes in solids, which are associated with rearrangement of the crystal lattice. These studies rest on two fundamental branches of the physical chemistry of solids, namely, the theory of disorder and the theory of transport, whose foundations had been laid in the 1920s-1930s by the outstanding Russian physicist, FYenkel, and the well-known German physical chemists, Wagner and Schottky. 

The Langmuir vaporization equations thus open up broader possibilities for description of decomposition processes than the Arrhenius approach. First, the key physical quantity entering all vaporization equations is the equilibrium pressure of products, which is directly related to the thermodynamic parameters of the process. As a result, the A and E parameters of the Arrhenius equation receive a straightforward physical interpretation. 

The apparent inapplicability of the method to measurements (by the Arrhenius approach) of rate constants k, which at first glance are not related to the absolute value of equilibrium pressure of the primary product Pgqp-However, none of the above reasons can account for the fact that this method is ignored in measurements of the vaporization rate from a free surface (after Langmuir), while it is employed widely in effusion studies (after Knudsen). 

All the predictions in these examples showed the same trend as in natural exposure but tended to overestimate the rate of change. Considering the uncertainty in actual temperature on natural exposure, the WLF predictions could be said to be good for both compounds, in spite of the shapes of the property-time curves for compound B. With selective use of the data, good predictions were obtained for both compounds by the Arrhenius approach. 

The Arrhenius approach also overestimates the degree of change, or rather underestimates the time for the change, in most cases. For materials C, D and P the predictions overestimate the time for change at 23 °C. For compound E the predicted time at 23 °C is remarkably accurate. For compounds S and X the times for change are overestimated for both 23 °C and 40 °C. 

It is interesting that the Arrhenius approach has in a few cases underpredicted the time at 40 °C but overpredicted the time at 23 °C. In this context, it should be noted that for both the WLF and Arrhenius approach the hot dry climate of the natural exposures has been approximated as 40 °C whereas in fact it was probably less than this. The temperate climate was very close to 23 °C. 

For the new compounds predictions were obtained using both the WLF and Arrhenius approaches in all cases except one no prediction was obtained for compound P2 using the... 

The WLF approach relies on the validity of the time-temperature superposition principle whilst the Arrhenius approach is dependent on the validity of the assumption that increasing temperature merely increases the rates of change and does not introduce new types of change. Neither of these is likely to be completely true in all cases, primarily because there will be different reactions taking place at different temperatures. 

The WTF approach provides a master curve that encapsulates the whole of the accumulated data and therefore potentially provides the greatest information. The Arrhenius approach on the other hand usually disregards the bulk of the data gathered being limited to a specific end point, which may have been arbitrarily chosen. If it is possible to use all the data at each temperature to obtain a reaction rate then this disadvantage of the Arrhenius approach would disappear. 

Although the Arrhenius approach is mathematically simpler, with computer help the WLF approach is practically easier to use because of there being no need to specify a measure of reaction rate nor to make any assumptions when interpolating between points. 

The WLF approach is also more versatile in that it is relatively easy to produce predictions in terms of time to reach an end point and as change in a given time. With the Arrhenius approach this necessitates re-doing the calculation completely with a different measure of reaction rate. 

The problems arrive when the change of property with time is complex, for example if it first falls and then rises. It was seen several times in this work that the WLF approach in taking all the data may produce a prediction which is dominated by one part of the ageing curves. Sometimes intuition suggests that this is giving an invalid prediction. With the Arrhenius approach it is necessary to make a choice of which part of the curve will be used and the validity of the prediction will then be dependent on whether that choice was correct. 

Both methods will indicate if results at one temperature are out of line with the others (for example because of a different reaction taking place). With Arrhenius the plot will be curved for the Arrhenius approach and using the WLF approach the poor fit to the master curve will be obvious. 

One conclusion is that more time should be spent than was possible for this report on studying the data in each case and that several analyses should be made, using all and parts of the data. Alternatively, if you are certain that all the data is relevant and valid then the WLF approach is usually the better choice, whereas if it is believed that part of the data is more valid than the rest then the Arrhenius approach is more appropriate. 

The activation energy of PHAs is calculated using Hoffman-Arrhenius approach (Hoffman, 1982). The Hoffman s Arrhenius-like model is described as ... 

Combining these results with Eq. (6.8) and using the proper model, for example, the Arrhenius approach, yields an equation that connects the measured quantities

kinetic parameters n, A, and Tact- Such an equation can only be solved numerically. Nowadays powerful sofiware is available that does the job of determining the kinetic parameters from the measured heat flow rate function. But to get reliable results, the proper kinetic model must be selected first. The theory behind it is not simple, and a lot of experience is necessary to handle the rather complex kinetic software. 

Bilz, M., Grattan, D. W. (1996). The aging of parylene difficulties with the Arrhenius approach. In J. Bridgland (Ed.), ICOM Committee for Conservation 11th triennial meeting, Edinburgh, 1-6 September 1996 Preprints (pp. 925-929). James James. 

Here, the limitations of the time-temperature shift have to be considered when using the Arrhenius approach. These limits are mainly dictated by the following facts ... 

The time-temperature shift principle using the Arrhenius approach (Eq. 1.36) means that a service time t at temperature T can be converted to a correspondingly shorter reference time fref at increased reference temperature T f, so that varying temperature profiles can be treated at constant load. This approach represents an engineering evaluation on a logarithmic time scale. Here it should be noted that absolute temperatures are to be used [104]. 

In practice, applying this time-temperature shift following the Arrhenius approach means that changes in characteristic material and component properties are measured at various temperatures over time. The recorded diagrams are called service... 

This prerequisite, however, will apply only for the rarest of applications. The Arrhenius approach has to be carefully considered, in particular when loads are superimposed and temporally non-stationary [104]. 

Every exposure causes a change in the material that can be evaluated by the Arrhenius approach using the time-temperature shift principle. 

When the time-temperature shift is applied in the Arrhenius approach, changes or shifts in the aging mechanisms present the problem that extrapolations using a change in activation factor have to be performed. Figure 1.50 [104]. 

If the reaction rate constant is expressed as an extended Arrhenius approach, see Equation (5.26),... 

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