Hysteresis exotherm

Fig. 23. Hysteresis in an irreversible exothermic reaction in a continuous stirred tank reactor.

The stationary-state response curves, or bifurcation diagrams shown in Figs 1.13(b) and 1.12(f), represent two of the simplest possible patterns monotonic variation and a single hysteresis loop respectively. These are the only qualitatively different responses possible for the cubic autocatalytic step on its own. They are also found for a first-order exothermic reaction in an adiabatic flow reactor (see chapter 6). With only slightly more complex chemical mechanisms a whole array of extra exotic patterns can be found, such as those displayed in Fig. 1.14. The origins of these shapes will be determined in chapter 4. 

It cuts. the axis at 0ad = 4 as 1/tn tends to zero (adiabatic limit). We have already seen that this is the condition for transition from multiple stationary states (hysteresis loop) to unique solutions for adiabatic reactors, so the line is the continuation of this condition to non-adiabatic systems. Above this line the stationary-state locus has a hysteresis loop this loop opens out as the line is crossed and does not exist below it. Thus, as heat loss becomes more significant (l/iN increases), the requirement on the exothermicity of the reaction for the hysteresis loop to exist increases. 

We now consider the dependence of the stationary-state solution on the parameter d. To represent a given stationary-state solution we can take the dimensionless temperature excess at the middle of the slab, 0ss(p = 0) or 60,ss-With the above boundary conditions, two different qualitative forms for the stationary-state locus 0O,SS — <5 are possible. If y and a are sufficiently small (generally both significantly less than i), multiplicity is a feature of the system, with ignition on increasing <5 and extinction at low <5. For larger values of a or y, corresponding to weakly exothermic processes or those with low temperature sensitivity, the hysteresis loop becomes unfolded to provide... 

If some other parameter of the system, such as the adiabatic temperature excess ad is varied, so the shape of the steady-state locus may deform. For low values of B a in this model, corresponding to weakly exothermic processes, then the hysteresis loop is unfolded, as indicated in Fig. 5.6(c, d), and a simple smooth variation of the steady-state temperature excess with the residence time is observed. Thus, systems can lose criticality as other experimental parameters are changed. 

Instability in a non-flow system—that might be an exothermic batch reaction or a pile of oily rags subject to autoxidation—is apt to escalate into a conflagration or thermal explosion (see Figure 14.1, left diagram). However, instability might be confined to a narrow region close to equilibrium, and the reaction then runs out of reactants before the temperature rise can become catastrophic. Flow systems may also admit multiple steady states and hysteresis. 

Figure 7.3. Codimension-1 singular points for a reactive flash undergoing an exothermic isomerization. Nomenclature H hysteresis variety T turning point loci. Systems features Da=0.10 z=l p=l 00=0.13 physical properties of the system are listed in table 7.3 governing expressions are given in table 7.2.

As stated above, the hysteresis of ELPs in the course of the ITT transition results from the overlap of two kinetically different processes a fast endothermic process, which corresponds to the destruction of the ordered hydrophobic hydration, and a second exothermic process arising from the P-spiral chain folding. 

Almost all endothermic peaks have corresponding exothermic peaks at lower temperatures, indicating a temperature hysteresis. The exceptions are a small en-dothoinic peak for CTADeS and a transition below for CTADDS i.e., they do not have corresponding exotherms in the cooling cycle. 

Figure 2.22. DSC curves showing glass transitions of amorphous polymers with (a) an endothermic hysteresis peak on high-temperature side of glass transition (endotherm down) and (b) an exothermic hysteresis peak on low-temperature side of glass transition (endotherm down). The heat capacity of the glass is extrapolated to higher temperatures to make the broad exothermic peak more visible.

It was mentioned before that endothermic or exothermic hysteresis peaks are common in the DSC curves of the glass transition. How can the presence... 

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