Characterization Using Zero-order Kinetics

This type of experiment can be repeated at other temperatures, determining the activation energy and the estimation of time to explosion. The concept of time to explosion or TMRad (Time to Maximum Rate under Adiabatic conditions) is extremely useful for that purpose [18]. This TMRad can be estimated by 

This expression was established for zero-order reactions, but can also be used for other reactions, if the influence of concentration on reaction rate can be neglected. This approximation is particularly valid for fast and exothermic reactions (see Section 2.4.3). 

Worked Example 12.1 TMRad from Zero-order Approximation 

To obtain a TMRad longer than 8 hours, the temperature must not exceed 65 °C, and 50 °C for a TMRad longer than 24 hours. 

it is possible to define the maximum allowable temperature by considering the acceptable induction time for the thermal explosion. This assessment of the probability of a runaway by using a zero-order reaction model may be too cautious. 

---

If there are indeed two types of sorbed molecules, as implied by Fig. 20 and Eq. 20, then it should be possible to detect the difference in retentivity as the system is evaporated from liquid-saturation to virtual dryness. We reported [146-149] that this is indeed the case, based on numerous time-studies of evaporation using acetone, chloroform or toluene as the volatile sorbed liquid. A typical example of such a time-study is recorded in Fig. 21, which shows the sequential changes in kinetics as the (in this case CHC13) liquid-saturated system is allowed to evaporate to dryness at constant temperature under conditions that prevent sample shrinkage [148], The non-adsorbed molecules are eliminated first during the interval required for a, to decrease from a0 to (, which is characterized by zero-order kinetics [146, 147] (Inset Fig. 21), i.e. ... 

Saturation kinetics are also called zero-order kinetics or Michaelis-Menten kinetics. The Michaelis-Menten equation is mainly used to characterize the interactions of enzymes and substrates, but it is also widely applied to characterize the elimination of chemical compounds from the body. The substrate concentration that produces half-maximal velocity of an enzymatic reaction, termed value or Michaelis constant, can be determined experimentally by graphing r/, as a function of substrate concentration, [S]. 

Isomerization of jS-isophorone to a-isophorone has been represented as a model reaction for the characterization of solid bases 106,107). The reaction involves the loss of a hydrogen atom from the position a to the carbonyl group, giving an allylic carbanion stabilized by conjugation, which can isomerize to a species corresponding to the carbanion of a-isophorone (Scheme 9). In this reaction, zero-order kinetics has been observed at 308 K for many bases, and consequently the initial rate of the reaction is equal to the rate constant. The rate of isomerization has been used to measure the total number of active sites on a series of solid bases. Figueras et al. (106,107) showed that the number of basic sites determined by CO2 adsorption on various calcined double-layered hydroxides was proportional to the rate constants for S-isophorone isomerization (Fig. 3), confirming that the reaction can be used as a useful tool for the determination of acid-base characteristics of oxide catalysts. 

As indicated in the previous sections, the antioxidant content in plastic material is often determined by chromatographic methods. Another widely used technique for polymer characterization is thermal analysis with differential scanning calorimetry (DSC). When the oxygen induction time (OIT) for a sample containing a phenoHc antioxidant is measured, a significant oxidative exothermic response is obtained in the DSC when all the phenolic antioxidant in a sample is consumed. The OIT is thus directly related to the antioxidant content in the material and to the stabihzing function, i.e. the antioxidant efficiency in the sample, if the consumption of phenolic antioxidants obeys zero-order kinetics at the temperature used [44]. Table 1 shows the amount of the antioxidant Irganox 1081 in polyethylene (PE) determined by HPLC and extraction by microwave assisted extraction (MAE),... 

There are quite a few situations in which rates of transformation reactions of organic compounds are accelerated by reactive species that do not appear in the overall reaction equation. Such species, generally referred to as catalysts, are continuously regenerated that is, they are not consumed during the reaction. Examples of catalysts that we will discuss in the following chapters include reactive surface sites (Chapter 13), electron transfer mediators (Chapter 14), and, particularly enzymes, in the case of microbial transformations (Chapter 17). Consequently, in these cases the reaction cannot be characterized by a simple reaction order, that is, by a simple power law as used for the reactions discussed so far. Often in such situations, reaction kinetics are found to exhibit a gradual transition from first-order behavior at low compound concentration (the compound sees a constant steady-state concentration of the catalyst) to zero-order (i.e., constant term) behavior at high compound concentration (all reactive species are saturated ) ... 

The release kinetics are characterized by an initial lag-phase, a zero release phase and a depletion phase. During the lag-phase water intrudes into the polymer matrix and activates the latent catalyst. During the zero-order release phase, an equilibrium between water intrusion and polymer erosion is established and an eroding front, (V2), that penetrates the device is established. Because thin disks were used, device geometry remains essentially constant and zero order release uncomplicated by a decrease in total surface area is observed. The depletion phase characterizes a decrease in device and depletion of the incorporated acidic excipient. 

---