Hot spots theory

Some of the quantitative consequences of hot spot theory were presented in Ref 19. A qualitative discussion of heat flow in a compressed gas bubble hot spot was also presented in Ref 19. The necessity of having enough, but not too much, liquid or solid spray or foam within a compressed gas bubble (in order to have sufficient heat flow from the bubble to the surrounding condensed explosive) provides another hard-to-control variable in impact testing and thus increases the variability of test results... 

Phung (Ref 201) attempted to apply the thermal hot-spot theory to pulsed-electron... 

According to the hot-spot theory (Neppiras Noltingk 1950), the homogeneous ultrasound reaction takes place in the collapsing cavitation bubble and in the superheated (ca. 2,000 K) liquid shell around it. Species with sufficient vapor pressure diffuse into the cavity, where they undergo the effect of adiabatic collapse. 

The generally accepted explanation for the origin of sonochemistry and sonoluminescence is the hot-spot theory, in which the potential energy given to the bubble as it expands to maximum size is concentrated into a heated gas core as the bubble implodes. The oscillations of a gas bubble driven by an acoustic field are well described by the Rayleigh-Plesset equation.7... 

The hot-spot theory, expounded by Bowden and Yoffe in their earlier work [2], is the foundation for most of their interpretations of initiation experiments. Heat (certainly), shock, friction, and intense electron beams were aU described as causing localized heating, such that if the region grows beyond a critical size the rate of heat generation exceeds the rate of heat loss and explosion occurs. 

Behind the alternatives there lay uncertainties about the identity of the processes being initiated. Nevertheless, the validity of the hot-spot theory, at least with respect to carefully circumscribed situations, was confirmed by several ingenious experiments which proved to have a striking relevance to many practi-... 

Studies of slow thermal decomposition, when combined with the hot-spot theory, proved to have particularly interesting consequences for understanding the sensitivity of the azides and their troublesome and seemingly temperamental response to some stimuli. 

Thus, within the thermal or hot-spot theory, there existed a rationale for describing not only how azides respond to various stimuli, but considering the many possible parameters involved in the energy transfer from an external stimulus to the molecules of a crystal, a basis for the erratic behavior of samples. 

In addition, unlike most solids to which the heat transfer equation has been applied, the azides are sensitive to shocks of such low intensity that the average temperature rise generated is of the order of tens of degrees (not large enough to initiate a fast reaction). Some alternative mechanism for localizing the energy must therefore be found if the hot spot theory is to apply. 

The nature of the extreme conditions which produce radicals in sonicated media is still a matter of debate in spite of numerous cases of "compelling" evidence. From the historical and scientific points of view, SL was studied because of the possible correlation of the appearance phase of SL flashes with bubble dynamics.6,136 It is generally thought that recombination of radicals is responsible for SL. However, it is not firmly established that SL exclusively arises from such a process. A survey of the literature also reveals that for multi-bubble fields, SL and sonochemistry (SC) are not necessarily coupled. Therefore, SL should not be systematically used as a tool for an estimation of the extreme conditions at the root of sonochemistry. Three kinds of hypotheses might explain radical formation, i.e., the hot-spot theory, 2 the shock-wave model, and the electrical theories.1 8/1 9... 

Carbon tetrafluoride has a low y value and should be less effective than argon. An interpretation based only on the "hot-spot" theory seems unsatisfactory, and the mechanism can be more complex than a simple pyrolysis. On the other hand, CF4 is an effective energy carrier in plasma chemistry, giving support to the existence of electrical phenomena. It can be suggested that a reaction takes place between species derived from the gas molecule (an excited state, a radical ion ) and the alkyl halide, which cleaves in a second step, in analogy with chlorocarbon radiolysis. However, the question is open for future investigations. 

It is surprising to see the apparent parsimonious interest of sonochemists in the Diels-Alder addition. This reaction with a large negative activation volume is frequently carried out in heated sealed tubes. Then, from the sonochemist s viewpoint, the high pressures and temperatures produced by the cavitational collapses should activate the reaction, provided the reactants are able to penetrate into the bubble. Non-volatile reagents should not be activated since the pressures and temperatures decrease sharply outside the bubble. Thus, the hot-spot theory predicts that the sonochemical Diels-Alder reactivity should more or less be related to the volatility of the partners. 

Another important aspect is the question of the reaction mechanisms. Since the sonochemical activation of Diels-Alder systems seems to have no direct link with the volatility of the substrates, the reactions should not take place in the "microreactor" bubble, and a purely thermal interpretation based on the hot-spot theory then seems inadequate. Alternative explanations could be based on a redox reaction between the two partners, or an ionization of one reactant. The existence of intermediate charge transfer complexes in Diels-Alder chemistry has been postulated for a long time, but most authors consider that no complete electron exchange is actually involved. l With the strong electron-accepting tetracyano-ethylene, a partial transfer occurs, but not at all with acrylic compounds. 

The last point which can be evoked here is conceptually linked to the hot-spot theory. If the limit liquid layers around a bubble are in direct contact with the heated and pressurized bubble content, far above the critical point of the liquid, these layers should be in a supercritical state. 23 This attractive hypothesis (see p. 61) was used by Hoffmann et al to rationalize the sonolysis of nitrophenyl derivatives. Supercritical fluids are characterized by a very high flexibility of important parameters (density, dielectric constant, solubilizing power) as a function of pressure. Experts in the field distinguish gas-like and liquid-like media, in which the kinetics of a reaction can vary over a broad range. For instance, the conjugate addition of piperidine to methyl propiolate was studied in supercritical ethane or fluoroform (Fig. 5). ... 

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