The β–δ phase transition in the energetic nitramine octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine: Thermodynamics

Abstract

In this and the accompanying paper [L. Smilowitz et al., J. Chem. Phys. 117, 3789, 2002] we present a theoretical treatment and experimental study, respectively, of the β–δ solid state phase transition in the organic nitramine molecule octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX). The transition is thermodynamically first order with a measured latent heat, occurs via nucleation and growth, and exhibits a thermally activated rate of transformation. We construct a two state kinetic model of the system consisting of equilibrium terms first order in the β or δ mole fraction simulating nucleation, and second order in β and δ simulating growth. The model has four rate constants, the temperature dependence of which is described by eight parameters. We use the transition state formulation of the rate constants and apply a thermodynamic model of the activated state that associates the difference in activated state free energy in forward and reverse directions with the equilibrium transition free energy, and identifies the activated state of the growth process with a metastable melt. By associating components of the activated state free energy with independently measured thermodynamic energies we reduce the degrees of freedom to three, which we fix initially by comparison with previously published kinetic data. We apply the model to both the β–δ and δ–β transformations over a temperature range from 300 to 700 K in order to assess the theoretical validity of the model. The model reproduces the half time of the transition over this entire range, spanning conversion times from 106 to 10−4 s. In the accompanying paper we present an experimental study of the kinetics and mechanism of the phase transition based on second harmonic generation spectroscopy. We use second harmonic generation to verify the nucleation and growth mechanism of the transition and measure the mole fraction change with time over a wide range of temperatures. We use the set of parameters established by theoretical considerations in this paper as an initial parameter set and determine an optimized set by comparison with these data.

Coefficient of Thermal Expansion of the Beta and Delta Polymorphs of HMX

“…Smilowitz et al [19] discussed how controlled cooling of HMX could be used to kinetically trap the δ-phase nitramine. Both Henson et al [26] and Both the TMA and DSC results reported here are consistent with earlier work.…”

“…The agreement is very good. The measurements are also qualitatively consistent with kinetic model of Henson et al [26].…”

Kinetics of Polymorphic Transitions in Energetic Compounds

“…The integral equations for the rate obtained, based on this model, describe sigmoidal temporal dependences both for the direct and reverse PTs, which contradicts the experimental data published by the same authors in [6]. A kinetic model for the growth of a new phase constructed in [7] involves an activated transition state which is thermodynamically equivalent to the melt.…”

“…In this process the consumption of δ-HMX follows the first-order kinetic law. A theoretical interpretation of these data is given in [7]. The kinetic model suggested in this work is based on the assumptions that the PT is reversible, the nucleation stage follows the first-order kinetic law and the growth stage of a new phase follows the second-order kinetic law.…”

Data Analysis, Pre-Ignition Assessment, and Post-Ignition Modeling of the Large-Scale Annular Cookoff Tests

“…However, our present knowledge about the chemical kinetics of thermal decomposition in PBX-9501 requires that we make several simplifying assumptions about the thermophysical and thermochemical properties of the intermediate constituents and reduce the number of kinetic steps. Despite the complexity of thermal decomposition of energetic materials, firm steps have in fact been taken toward understanding the kinetics, and several simplified schemes have been proposed and applied to specific problems with some success (McGuire and Tarver 1981;Brill and Karpowicz 1982;Thynell et al 1996;Henson et al 1999;Dickson et al 2000;Henson et al 2002;a-b, Behrens 2002Tarver and Tran 2004). Recently, there has also been considerable effort to experimentally quantify the behavior of PBX-9501 when subjected to a wide range of thermal and shear-rate conditions (Tappan et al 2002;Thompson et al 2002;Kaneshige et al 2002;Asay et al 2003;Kaneshige et al 2003;Smilowitz et al 2003;Kaneshige et al 2004;Maienschein et al 2000;Maienschein et al 2004…”