Thermal expln

The exponential dependence of the evolution of heat upon temp, besides rendering eq (1) nonlinear and hence difficult to solve, accounts for the existence of concepts such as ignition, ignition temp, induction period, limits of inflammability and, indeed, of the concept of "explosion itself, which. can be defined no more rigorously than by the requirement that the reaction rate become sufficiently high. This fundamental point is implied in every theoretical treatment of thermal expln, but it has been brought out explicitly in Russian scientific literature (Refs 5, 6, 9, 11 14). 

Belyaev (I960), 49-56 (Thermal explosion in gases) 56-61 (Thermal expln in solids)... 

M,A.Cook et al, JChemPhys 24, 191-201 (1956) (Rate of reaction of TNT in detonation by direct pressure measurements) 22)Dunkle s Syllabus (1957-1958) (See Vol 4 of Encycl, p XLIX) p 126 (Reaction front in detonation) 135-42 (Thermal decomposition of solids) 23)M.A.Cook, "The Science of High Explosives , Reinhold NY(1958), pp 123-42 (Reaction rate in detonation) 174-87 (Thermal decomposition of soli ds) 386-89 (Thermochemistry of detonation and expltr) 24)F.A.Baum, K.P.Sranyukovich B.I.Shekhter "Fizika Vzryva , Moscow (1959), pp 81-108 (Thermochemistry of explosives) 25)K.K.An-dreev A. F. Belyaev, " Teoria Vzryvcha-rykh Veshchestv Moscow(1960), p 49-56 (Thermal expln in gases) p 56—61 (Thermal explosion in solids) 26) Encycl of Expls PATR 2700, Vol 1 (I960), p A501 (Atomic expins, chain reactions in) 27)F.M.Turner,... 

Edit and others "The Condensed Chemical Dictionary , Re inhold, NY (1961), p 246 (Chain reactions) 28)E.Teli, JChemPhys 36, 901-03 (1962) (On the speed of reaction at high pressure) 29)Encycl of Expls, PATR 2700, Vol 2(1962), p C146-L (chain reactions) 30)Yu.N.Denisov Ya.K.Troshin, "On the Mechanism of Detonative Combustion , 8th SympCombstn (1962), pp 600-10 31)A.M.Gri shin D-M.Todes, DoklAkad N 151 (2), 366-68 (1963) CA 59, 12585 (1963) (Thermal expln with heat transfer by conversion and conduction)... 

JACS 76, 1997-99(1954) 8s CA 48, 8543(1954) (Thermal expln of Diborane-oxygen mixts)... 

Adiabatic Explosion. Since an expln takes place in an extremely short time, it may be considered to be adiabatic. Assuming that an explosive is heated by the decompn of part of the sample and that the rate of decompn increases with increasing temp, R. B.Parlin et al(Ref) derived the equation for the time-temp relationship in a purely thermal expln. A discussion of this equation would require undue space here Ref R.B.Parlin et al, OSRD Report 20 26 (1943)(Uncl assified)... 

The thermal expln of gaseous azomethane (Ref 3) occurs in accordance with the Semenov theory of thermal explosions as described in Ref 2. This process was studied also by Taylor Jahn (Ref 4)... 

Conductive and convective heat transfer, thermal expln by 3 C496—C497... 

The classical view of the mechanism of shock initiation of homogenous expls, ably presented in Ref 3, has been discussed in some detail in Vol 7 under Liquid Explosives, L31-L to L32-R. Briefly stated this mechanism involves a thermal expln at or near the shock entry face... 

The data of Fig 1 can be depicted as material temp vs time plots. This is done in Fig 3. Note that, as expected, Ti reaches asymptotic values for T0 208°> whereas T increases in an expl fashion for T0 > 208°. Also note that the times at which Tx starts to increase rapidly decrease as T0 increases. The righthand ordinate of Fig 3 depicts the decompn rate of the reacting material. Note that this rate is quite low. Indeed for reactions that are relatively exothermic and have a fairly high energy of activation (see Vol 7 article on Kinetics ), most materials rarely undergo more than a few percent decompn before they expkT. It is also noteworthy (and indeed characteristic of most thermal explns) that the inflection points (the temp at which the curves pause before the rapid rise in temp) are quite close to the critical temp... 

Before examining various approximate solutions of Eq 4 for conditions of special interest, it is convenient to write Eq 4 in dimensionless form and to introduce some simplification. From the description of the thermal expln process given above, two reasonable approximations can be made which give rise to useful solutions. The appro xiina tions are ... 

Since chemical rate decreases drastically even for small decreases in temp, the reaction of a hot spot can be quenched by a cold front reaching the center of the hot spot. Therefore, unless a thermal expln occurs at the center of the hot spot before the cooling wave reaches that point, there will be no expln in the hot spot at all. From the curves in Fig 7, it may be seen that the maximum time available for an expln to occur is, therefore, equal to about 0.04 dimensionless time units. Hence, according to Ref 7, the criterion for expln may be expressed as... 

The obvious importance of the thermal expln of hot spots in the theoretical description of the initiation of detonation by impact or shock was presented in Vol 7, H170-175,143-55, L31-32, and in this Vol under Shock Initiation , a section under Shock Sensitivity of Explosives Conse-... 

The writer studied the initiation of Pb Azide by high-intensity light (Ref 9b). He found that the process of initiation was thermal, with thermal expln occurring in a thin layer that was heated by absorbing most of the incident light. He was able to make estimates of the kinetic parameters of Pb Azide based on observed initiation delays and thermal expln theory... 

The thermographic method which obtains critical conditions for thermal expln of reactants heated in a manner to keep temp gradients at... 

Additionally, the thermal expln of particles method was used in the range of 277—500° to obtain E = 38kcal/mole and ZQ = 1019 cal/g sec for Nitrostarch. However, under isothermal conditions (95—117°) the initial step rate constant for Nitrostarch was found to be k = 10145 exp(-36000/RT>ec 1... 

In general, with the exception of Nitrostarch, agreement is satisfactory between kinetic parame -ters obtained from thermal expln studies and isothermal measurements. However, Z values obtained by either approach for Nitrocellulose or DINA appear to be considerably higher than expected on the basis of classical kinetics... 

In a series of studies, summarized in Ref 18, Merzhanov and co-workers examined conditions under which thermal explns may be quenched. This theoretical analysis provided two characteristic dimensionless parameters which determine the conditions for quenching. These are Kcr obtained from inflection points of 0M vs k plots (0M is the max value of 6), and a quantity e = [(6m/k) (deM/dK)] =Kcr,whichisa measure of the uncertainty in the determination of the critical conditions. Both CI and are functions of 0 and 7, which (as well as k and 0) are defined as follows ... 

Machine computation was used to obtain kcx and as functions of 7 and 3. The thermographic test procedure was then employed to obtain k and e, from observed A Tmax vs T0 plots, for mixts of Tetryl and Picric Acid (claimed to be a first-order decompn reaction), and for a Tetryl/chalk mixt (claimed to be an autocatalytic decompn). Agreement between calcd and observed k s and e s was excellent All these studies are somewhat pedantic, in that they provide rigorous proof for a well-established fact, namely that quenching the thermal expln of expl materials is well-nigh impossible if 0 is sufficiently large. Merzhanov and co-workers also show that many exothermic... 

Expls and proplnts decomp exothermally at every temp above absolute zero. If the mass of the material is such that the heat produced by the decompn cannot be dissipated as rapidly as it is produced, the mass will heat itself to expln. The lowest constant surface temp above which a thermal expln is initiated is a function of the size, thermal conductance, the heat of reaction, and the reaction kinetic parameters. 

Explosive reactions) 14)D.A.Frank-Kamenetskii, ZhFizKhim 10, 365-70 (1939) 16, 357-61 (1942) 20, 729-36 (1943) (Mathematical theory of thermal expln, called 1 stationary theory of thermal expln ) 15)K.K. ndreev, KhimReferatZhur 1940, No 10-11, p 129 CA 37, 1604 (1943) (Mechanism of expl reaction) 16)M.Mucahy A.Yoffe, Australian Chemlnst Jour Proc 11, 106-20 ( 1944) (Chain reactions and gaseous explns) 17)lbid 11, 134-46 166-74 (1944) (Propagation of gaseous explns. 

B.Parlin et al(Ref) derived the equation for the time-temp relationship in a purely thermal expln. A discussion of this equation would require undue space here Ref R.B.Parlin et al, OSRD Report 20 26... 

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