Kinetic Arrhenius

Chan, H. S., and Dill, K. A. (1998). Protein folding in the landscape perspective Chevron plots and non-Arrhenius kinetics. Proteins Struct. Fund. Genet. 30, 2-33. 

ASTM E-698, "Test Method for Arrhenius Kinetic Constants for Thermally Unstable Materials," revised 1988, American Society for Testing and Materials, Philadelphia, PA. 

Arrhenius kinetics controls the process. Thus the temperature to be used in the above expression is 7 and one rewrites Eq. (4.26) as... 

Since Arrhenius kinetics dominate, it is apparent that 7 is very close to Tf, so the last expression is rewritten as... 

Shown in Fig. 7.2 is the relationship between qr and qL for various initial pressures, a value of the heat transfer coefficient h, and a constant wall temperature of In Eq. (7.8) qr takes the usual exponential shape due to the Arrhenius kinetic rate term and cp is obviously a linear function of the mixture temperature T. The qt line intersects the qr curve for an initial pressure l at two points, a and b. 

It is also possible to use microcalorimetry to obtain useful information about the kinetic processes of the instability (i.e., aggregation, proteolysis) when thermal irreversibility prevails. Scan rates will often distort the onset behavior of the melting transition that can necessarily impose a shift in the Tm, as discussed further in the following text. The scan rate dependence of the Tm may then be used to determine the activation energy of the instability, provided an Arrhenius kinetic model describes the behavior. 

The chemical stability of an amorphous formulation is usually also a function of its storage temperatme relative to Tg. The enhanced molecular mobility achieved near the glass transition translates into an increase in translational diffusion-dependent degradation pathways, such as aggregation in proteins. It should be noted that the reaction kinetics near the Tg do not obey Arrhenius kinetics, and that extrapolation of the accelerated stability data generated near the Tg to stability at the storage temperature should be viewed with extreme caution. Amorphous materials must be stored well below the glass transition (at least 10°C, and typically 40 to 50°C below Tg) to maintain their physical and chemical stability. 

The actual linking of chemical (Arrhenius) kinetics and thermodynamics was done as follows (Ref 2) ... 

The induction time t is of particular interest, since it can be compared to the induction time computed for an adiabatic thermal explosion (See Ref 6, pp 173—74 or Eq 6 of Article on Hot Spots, p H172-R) to provide a check on the correctness of the supposition that the input shock"generates a thermal explosion (at the shock entry face). Unfortunately, an exact quantitative treatment of the induction times of shock-generated thermal explosions suffers from a) uncertainty of the shockgenerated temperature in the LE and b) uncertainty in the Arrhenius kinetic parameters (activation energy and pre-exponential factor) (See Kinetics in this Vol)... 

Kapila, A. K., Matkowsky, B. J., and Vega, J. (1980). Reactive-diffusive systems with Arrhenius kinetics the Robin problem. SIAM J. Appl. Math., 38, 391-401. 

Interestingly, similar non-Arrhenius kinetics is found in computer simulations of simple models that do not consider interactions with solvent. At high temperature, the model polymer is highly random and has a high configurational entropy... 

Nitrocellulose filters 205 Non-Arrhenius kinetics 555, 598 Nonbonded interactions 325-332 Nondisruptive deletion 426, 560 Nonequilibrium dialysis 202 Nonproductive binding 114-118, 371-372... 

Table 1 Rates of Degradation (Relative to 25°C) Assuming Arrhenius Kinetics and Energies of Activation ( /) of 12, 15, and 20kcal/mol...

It can be difficult to translate oxidative stress-testing results into accurate predictions of the susceptibility of a compound to oxidation. This is partially because oxidative mechanisms can be quite diverse and complex and oxidative degradation often does not follow typical Arrhenius kinetic models. For a more indepth discussion of this subject, see Chapter 7. 

When several temperature-dependent rate constants have been determined or at least estimated, the adherence of the decay in the system to Arrhenius behavior can be easily determined. If a plot of these rate constants vs. reciprocal temperature (1/7) produces a linear correlation, the system is adhering to the well-studied Arrhenius kinetic model and some prediction of the rate of decay at any temperature can be made. As detailed in Figure 17, Carstensen s adaptation of data, originally described by Tardif (99), demonstrates the pseudo-first-order decay behavior of the decomposition of ascorbic acid in solid dosage forms at temperatures of 50° C, 60°C, and 70°C (100). Further analysis of the data confirmed that the system adhered closely to Arrhenius behavior as the plot of the rate constants with respect to reciprocal temperature (1/7) showed linearity (Fig. 18). Carsten-sen suggests that it is not always necessary to determine the mechanism of decay if some relevant property of the degradation can be explained as a function of time, and therefore logically quantified and rationally predicted. 

Review of compatibility data in this manner is important and useful in many cases. If Arrhenius treatment fits the decay observed in the compatibility samples, data obtained under relatively short-term accelerated stress conditions can efficiently be used to extrapolate the amount of decay expected at realistic long-term storage conditions. The adherence of decay to Arrhenius kinetics provides the formulator with a powerful tool for prediction and understanding of degradation. This decay model is the basis for the International Committee on Harmonization (ICH) quality guidelines... 

Table 1 Arrhenius, kinetic, and surface roughness parameters of 1,3 butadiene hydrogenation over Pd/Si02 thin film catalyst. ( ref 16, T=3Q0K, Ph2 = 0.7 kPa and Pc4H6 = 0.2 kPa) / denotes the surface-roughness-to-scan-area ratio.

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