Electronic Thermal Conductivity during Combustion-Wave Propagation from Hot Spots in Detonating TATB

Abstract

A model for the electronic thermal conductivity of shock-compressed TATB is developed using experimental data on the growth kinetics of its electrical conductivity. It is shown that electronic thermal conduction can be the main mechanism of energy transfer from hot spots in detonating explosives.It is well known that during shock-induced detonations of heterogeneous condensed explosives (HEs), chemical reactions start at so-called hot spots -combustion microcenters which arise from a local temperature rise during shock-wave propagation through heterogeneities in the HE. The volume fraction of the microcenters is small; therefore, most of the HE reacts during combustion-wave propagation from the microcenters and the wave velocity determines the macrokinetics of HE decomposition and energy release (see, for example, [1]).At the macrolevel, the time of chemical-energy release in a detonating heterogeneous HE can be estimated as ∆τ ≈ δ/D, where D is the velocity of combustion-wave propagation from hot spots, δ is the average distance between the hot spots (on the order of the HE microcrystal size). For the characteristic values δ ≈ 10 µm and ∆τ ≈ 0.1-1 µsec, the velocity of combustion-wave propagation from the hot spots is estimated as D ≈ 10-100 m/sec. However, in shock-compressed and heated triaminotrinitrobenzene (TATB), the calculated combustion-wave velocity turned out to be smaller -D ≈ 0.1-1 m/sec [2], indicating the need for a more detailed analysis of the physical processes determining the velocity of combustionwave propagation in shock-compressed HEs.In this connection, it should be noted that the parameters of the calculation model of [2] were chosen so as to describe the measured ignition times of HEs at rather low temperatures at the boundary (up to 700 K) and low pressures (up to 1.5 GPa). The adequacy of this model for the range of much higher pressures and temperatures (10-20 GPa and 2000-3000 K), characteristic of the shock initiation of TATB, is questionable because the chemical-reaction kinetics is known to depend greatly on temperature and pressure.Another possible source of errors in calculations of the combustion of compressed-shock HEs is the great uncertainty in modeling heat transfer from hot spots to the crystalline HE. Experimental data on the thermal conductivity of shock-compressed HEs are not available. Moreover, the thermal conductivity mechanism in this case is not understood. The model of [2] considers only the lattice (phonon) thermal conductivity of HEs. However, phonon thermal conduction is a rather slow process characterized by a relaxation time of about 100 psec (see, for example, [3]). Thus, it is possible that the phonon mechanism of energy transfer from hot spots is ineffective at times of the picosecond scale characteristic of the reaction of HEs in combustion waves [4].The present paper gives calculation results for combustion-wave propagation from hot spots obtained under the assumption [4-6] that energy transfer from hot spots occurs by electronic thermal conduction.

Comparative analysis of physical mechanisms of detonation initiation in HMX and in a low-sensitive explosive (TATB)

“…(14) and (16) that the dependence of the combustion-wave velocity on pressure can be presented in the form [4] D ∼ exp(α p p). (17) This expression reveals the physical meaning of the widely used empirical models of the macrokinetics, where the reaction rate in detonating heterogeneous HEs is presented as a function of pressure. As is shown above, the main argument of the macrokinetics is the EP temperature in hot spots, which, in turn, is related to pressure.…”

“…Thus, the velocity of combustion-wave propagation in crystalline HEs under conditions of high pressures can be measured [16] or calculated by various models [13,17,18]; the density of hot spots can be estimated [19] on the basis of experimental information on the concentration and size of pores; the geometric factor can be obtained by solving a model problem [10], which implies that two other factors are constant. Such an approach offers a theoretical possibility of estimating the three basic factors and, hence, the macrokinetics as a whole by calculations based on the fundamental physical laws or on the data of special (non-detonation) experiments.…”

Physical model for shock-wave initiation of detonation of plastic-bounded TATB-based explosive

“…Thus, in [14] similar calculations were performed under the assumption of an electronic mechanism of energy transfer from hot spots and fairly high values for the combustion wave velocity were obtained. The calculated dependence of the burning rate D on the temperature of the shock-compressed unreacted HE outside hot spots turned out to be nearly exponential, and the value of the derivative A = d ln D/dT estimated from the results of these calculations was about 0.01 K −1 .…”

“…4. The latter function was chosen from calculation results for the temperature dependence of the combustion wave velocity [14] and then was adjusted to fit the results of detonation initiation experiments. We note that this function is nearly linear and its derivative varies in the range…”

Physical model of low-velocity detonation in plasticized HMX

“…It was shown [17] that the dependence of the HMX reaction rate on temperature in wide ranges of pressures and temperatures can be described by the Arrhenius law with an activation energy E a = 36 kcal/mole or 18,000 K. Concerning the parameter ε a , its value for HMX can be estimated as 1.5-2.0 eV or ≈20,000 K. This estimate is obtained from the known value of the HMX forbidden band width, which is ≈3 eV under standard conditions (see [18]), and from the fact that the activation energy of conduction electrons in molecular crystals of organic substances is normally 1.5-2 times smaller than the forbidden band width (see the analysis of experimental data in [19]). …”