The induction period

We have seen in Sec. III.9 that the kinetics of reactions which involve two or more consecutive intermediates is capable of a simplified treatment if the intermediate concentrations are small compared to both reactants and products. In such cases we can make the assumption that the rate of change of the concentrations of the intermediates with time is zero, a procedure which then permits us to solve the kinetic equations for the stationary concentrations of the intermediates and then eliminate them algebraically from the system of differential equations.  

However, the solutions given for the systems in Sec. III.7 indicate that the total induction time is roughly 4 to 10 times as long. In other words, if the stationary concentration of Mi is 1 per cent of Ao, then about 4 to 10 per cent of Ao will have disappeared before Mi reaches 99 per cent of the stationary concentration (Figs. III.2 to III.4). A more detailed analy- 

When the reaction involves a chain such as occurs in the reaction of H2 and CI2 

SO that the initial intermediate is reproduced, it is possible for a large amount of product—here HCl—to be built up before the intermediates— H and Cl—reach their low stationary values. It can be shown that in such cases the induction period will be negligibly small only when the rate of the slowest step in the chain, k or is very small compared to the rate of destruction of the intermediates by other processes.  

In analyzing all such reactions it is sometimes convenient to discuss the mean lifetime of an intermediate passing through a reaction step, which may be defined as the reciprocal of the rate constant (or its product with some concentration). Thus in the above scheme the mean time of Cl in step 1 is n = [ i X (H2)] and for II in step 2, t2 = [A2 X (Cyi h The mean time of chain cycle is then Tc = ri + t2. If Td is the mean lifetime for the destruction of intermediates, then the above criteria imply that Td Tc in order for the induction period to be small.  

Having identified the kinetic relation applicable to the data for a particular reaction by the general techniques outlined in the preceding paragraph, it is necessary to confirm linearity of the appropriate plot of the function f(a) against time. The special problems which relate to the induction period, the acceleratory and the deceleratory regions are conveniently considered separately. 

The delay, t0, preceding the onset of the main reaction may include contributions from (i) the time required for the sample to attain reaction temperature, h, (ii) additions to fh resulting from changes within the reaction sample, e.g. water removal (endothermic) from a hydrate, td, phase transitions, etc. and (iii) slow processes preceeding establishment of the main reaction, which are to be regarded as the true induction period, The effective values of th, td and may show different temperature coefficients so that the magnitude of t0(=th + ta + i) may vary with temperature in a complex manner, perhaps differently from that of the subsequent rate process. 

The magnitude of t0 can be measured from the intercept of a f(a)—time plot. The existence of the induction period can introduce uncertainty into a reduced time analysis if the temperature coefficient of t0 differs from that later applicable, and it is necessary to plot (t — t0)/(tb — t0) against a where tb is the time at which the selected common value of a is attained. The occurrence of a slow initial process can be reflected in deviations from linearity in the f(a) time plot, though in favourable systems the contribution may be subtracted before analysis [40]. 

---

Finally, the determination of the induction period (NF M 07-012) also reveals the potential of gum formation during storage. The fuei sampie is contained in a bomb filled with oxygen at 100°C, under a pressure of 7 bar and the oxygen pressure is monitored with time. The time corresponding to the first drop in pressure is noted, symptomatic of incipient oxidation. If no further events take place, the test is stopped after 960 minutes. This time corresponds thus to the maximum induction period. 

The Landolt reaction (iodate + reductant) is prototypical of an autocatalytic clock reaction. During the induction period, the absence of the feedback species (Irere iodide ion, assumed to have virtually zero initial concentration and fomred from the reactant iodate only via very slow initiation steps) causes the reaction mixture to become kinetically frozen . There is reaction, but the intemiediate species evolve on concentration scales many orders of magnitude less than those of the reactant. The induction period depends on the initial concentrations of the major reactants in a maimer predicted by integrating the overall rate cubic autocatalytic rate law, given in section A3.14.1.1. 

The bromate-ferroin reaction has a quadratic autocatalytic sequence, but in this case the induction period is detennined primarily by the time required for the concentration of the hiliibitor bromide ion to fall to a critical low value tlirough the reactions... 

Clock-type induction periods occur in the spontaneous ignition of hydrocarbon-oxygen mixtures [2], in the setting of concrete and the curing of polymers [3]. A related phenomenon is the induction period exhibited... 

Experimental results are in general conformity with the Avrami equation, but the interpretation of various observations is still complicated in many instances. One intriguing observation is that the induction period for nucleation is inversely proportional to the length of time the liquid is held in the liquid state after previous melting. This dependence on prior history may be qualitatively understood... 

However, reaction 7 suffers other shortcomings, eg, entropy problems. Other proposals range from trace peroxidic contaminants to ionic mechanisms for generating peroxides (1) to cosmic rays (17). In any event, the initiating reactions are significant only during the induction period (18). 

In the absence of zinc oxide, cross-linking proceeds through an accelerator polysulfide. With TBSI (14) and other sulfenamides, the accelerator decomposes upon heating during the induction period (before cross-linking) as shown in Figure 2 (13). 

Fig. 5. Cure characteristics of accelerators A, thiuram B, dithiocarbamate C, sulfenamide D, thiazole and E, guanidine. The induction period represents...

Thermal Decomposition of GIO2. Chloiine dioxide decomposition in the gas phase is chaiacteiized by a slow induction period followed by a rapid autocatalytic phase that may be explosive if the initial concentration is above a partial pressure of 10.1 kPa (76 mm Hg) (27). Mechanistic investigations indicate that the intermediates formed include the unstable chlorine oxide, CI2O2. The presence of water vapor tends to extend the duration of the induction period, presumably by reaction with this intermediate. When water vapor concentration and temperature are both high, the decomposition of chlorine dioxide can proceed smoothly rather than explosively. Apparently under these conditions, all decomposition takes place in the induction period, and water vapor inhibits the autocatalytic phase altogether. The products of chlorine dioxide decomposition in the gas phase include chlorine, oxygen, HCl, HCIO, and HCIO. The ratios of products formed during decomposition depend on the concentration of water vapor and temperature (27). 

Fig. 10. Free2e drying profiles for A, whole milk, and B, nonfat milk. Heat was transmitted by radiation from heated wires above the fro2en milk which rested in a transparent plastic tray. (-----------------------) is the induction period. Total pressure was 33 Pa (0.25 mm Hg).

Antioxidants may be assessed in a variety of ways. For screening and for fundamental studies the induction period and rate of oxidation of petroleum fractions with and without antioxidants present provide useful model systems. Since the effect of oxidation differs from polymer to polymer it is important to evaluate the efficacy of the antioxidant with respect to some property seriously affected by oxidation. Thus for polyethylene it is common to study changes in flow properties and in power factor in polypropylene, flow properties and tendency to embrittlement in natural rubber vulcanisates, changes in tensile strength and tear strength. 

Figure 3-8 is a plot of Ca, Cb, Cq, and Cd for a hypothetical system of the Scheme X type. An interesting feature is the time delay after the start of the reaction before the final product, D, appears in significant concentrations. This delay in product appearance is called an induction period or lagtime. In order to observe an induction period it is only necessary that the system include several relatively stable intermediates, so that the bulk of the material balance is temporarily stored in these prior forms. An experimental measurement of the induction period requires an arbitrary definition of its length. 

The dependence of reaction rates on pH and on the relative and absolute concentrations of reacting species, coupled with the possibility of autocatalysis and induction periods, has led to the discovery of some spectacular kinetic effects such as H. Landolt s chemical clock (1885) an acidified solution of Na2S03 is reacted with an excess of iodic acid solution in the presence of starch indicator — the induction period before the appearance of the deep-blue starch-iodine colour can be increased systematically from seconds to minutes by appropriate dilution of the solutions before mixing. With an excess of sulfite, free iodine may appear and then disappear as a single pulse due to the following sequence of reactions ... 

Although the previous protocol suggests it is not necessary to deprotonate the sulfonamide prior to exposure to the zinc carbenoid, a experimentally simpler procedure can be envisioned wherein the alcohol and promoter are deprotonated in a single flask (Fig. 3.15). In protocol IV, the alcohol and promoter are combined in flask A and are treated with diethylzinc, thus forming the zinc alkoxide and zinc sulfonamide. In sub-protocol IVa, this solution is transferred to flask C which contains the zinc carbenoid. Sub-protocol IVb represents the reversed addition order. Sub-protocol IVa is not only found to be the superior protocol in this sub-set, it is found to out-perform all of the previous protocols Despite the persistence of the induction period, a large rate enhancement over the uncatalyzed process is observed. This considerable rate enhancement also translates to a reduction in the overall reaction time when compared to sub-protocols la and Ilia. Selectivity rises... 

Figure 4 The effect of stabilizer concentration on the induction period of polypropylene thermal oxidative breakdown (temperature 200°C P02 = 300 Tor). 1-polyamineani-line disulfide 2-polydiiminodiphenyloxide disulfide 3-polythiosemicarbazide disulfide 4-Santanox 5-hydroru-beanic polydisulfide 6-thiocarbamidepoly disulfide 7-po-lydisulfide.

The yield of product is increased to 81% (analyzed by evolution of M-butane) if 0.67 g. (0.0033 mole) of aluminum isopropoxide is added to the suspension of magnesium before addition of the halide solution. Alternatively, an equivalent amount of 2-propanol and iodine (giving 0.01 mole of CsII OMgl) may be added. These modified procedures (particularly the second) also shorten the induction periods and render unnecessary any special drying of the reagents and apparatus and the use of fresh magnesium. 

Stability refers to a measure of the extent to which a fat resists the development of oxidative rancidity, and thus it is a measure of the induction period. Stability is usually expressed as the time that elapses under specified conditions before rancidity can be detected. 

There are also methods based on the detection of aldehydic substances, for the typical odor and flavor of rancidity seem to be associated with the liberation of aldehydic materials during the oxidative deterioration. The Kreis test (18), perhaps the best known of these methods, consists of treating the fat with concentrated hydrochloric acid and a solution of phloroglucinol. The red color formed is attributed to a condensation product of epihydrin aldehyde with phloroglucinol. Historically, the chief difficulty with this method has been that fats which are not rancid will often give a positive Kreis test. It has been shown that if this test is quantitatively correlated with the induction period... 

Various tests for rancidity, such as the Kreis test, may be used in stability determinations if the intensity of reaction is plotted against time. The curves so obtained will give an indication of the length of the induction period. However, the plotting of a curve for each sample is somewhat laborious. 

When PAN block copolymers are synthesized with the help of such method the reaction is conducted during a period of time (20—30 min) shorter than the induction period of AN polymerization (45 min) in the presence of cerium ions. When the mechanism and the laws governing the reaction of AN copolymerization with PEO and PPO were studied, it was established that the initiation of the block copolymerization proceeds in accordance with the following scheme ... 

According to Demin et al. (125, 126) the steady-state polymerization of ethylene occurs at 5-70°C in the presence of Cr(7r-C3H6)3 and Zr (tt-CsHs) 4. In Ballard et al. (123) the induction period at ethylene polymerization using Zr (7r-C3H6)4 was observed the introduction of hydrogen... 

Inhibitors or retarders that give inert products are called ideal .173 The term ideal inhibitor has also been used to describe a species that stops all polymerization until such time as it is completely consumed (i.e. the induction period) and then allows polymerization to proceed at the normal rate. However, in many cases the products formed during inhibition or retardation are not inert. Four... 

---