Arrhenius rate expression, degradation

Rate constants at 190, 160, 130, and 100 °C for the LO and DO degradation reactions were used to estimate the rate constants at 20 °C. The Arrhenius rate expression was applied with the plot of Ink versus 1000/T(K 1). A linear relationship was obtained with a correlation coefficient > 0.999 in Figure 17 in which LO and DO are represented. 

The rate expressions and values, mechanisms, and the activation energies for the condensation reactions forming polymers are similar to those of small molecule reactions. Reaction rate increases with temperature in accordance with the Arrhenius equation. Average DP also increases as the reaction temperature increases to the ceiling temperature where polymer degradation occurs. Long chains are only formed at the conclusion of classical polycondensation processes. 

To those beginning work in this field, the study reported by Zhou and Notari on the kinetics of ceftazidime degradation in aqueous solutions may be used as a study design template. First-order rate constants were determined for the hydrolysis of this compound at several pH values and at several temperatures. The kinetics were separated into buffer-independent and buffer-dependent contributions, and the temperature dependence in these was used to calculate the activation energy of the degradation via the Arrhenius equation. Ceftazidime hydrolysis rate constants were calculated as a function of pH, temperature, and buffer by combining the pH-rate expression with the buffer contributions calculated from the buffer catalytic constants and the temperature dependencies. These equations and their parameter values were able to calculate over 90% of the 104 experimentally determined rate constants with errors less than 10%. 

It is seen in Figure 5.5, that the tensile strength of test bars decreased with increase in exposure time for the bars at all temperatures and as expected degradation was more severe for specimens in solutions at higher temperatures. Because the basic steps of this procedure would apply to many polymer lifetime studies they are discussed next in some detail. In the Arrhenius relationship, the degradation rate is expressed as [83] ... 

As discussed in Chapter 1 (Sections III and TV), the kinetics of drug degradation has been the topic of numerous books and articles. The Arrhenius relationship is probably the most commonly used expression for evaluating the relationship between rates of reaction and temperature for a given order of reaction (For a more thorough treatment of the Arrhenius equation and prediction of chemical stability, see Ref. 13). If the decomposition of a drug obeys the Arrhenius relationship [i.e., k = A exp(—Ea/RT), where k is the degree of rate constant, A is the pre-exponential factor ... 

On the other hand, the effective collision concept can explain the Arrhenius term on the basis of the fraction of molecules having sufficient kinetic energy to destroy one or more chemical bonds of the reactant. More accurately, the formation of an activated complex (i.e., of an unstable reaction intermediate that rapidly degrades to products) can be assumed. Theoretical expressions are available to compute the rate of reaction from thermodynamic properties of the activated complex nevertheless, these expression are of no practical use because the detailed structure of the activated complexes is unknown in most cases. Thus, in general the kinetic parameters (rate constants, activation energies, orders of reaction) must be considered as unknown parameters, whose values must be adjusted on the basis of the experimental data. 

Assuming that the degradation pattern follows a first-order reaction as described in Eq. 17, the Arrhenius equation (Eq. 19) can be used to predict the degradation rate at the recommended storage temperature. First, an acceleration factor. A, is calculated as the ratio of the degradation rate at elevated temperature to the degradation rate at storage temperature. This ratio, which can be worked out easily from Eq. 17, can be expressed as ... 

Most studies of thermal degradation of polymers are carried out under conditions where the rate is fast enough to give measurable reaction in times from seconds to hours. Whatever the mechanism, the rate constant for any elementary reaction can be expressed as a function of temperature in terms of the Arrhenius relation ... 

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