Decomposition of HMX in solid and liquid states under nanoconfinement

Journal Pre-proof Decomposition of HMX in Solid and Liquid States under Nanoconfinement Rozana Bari, Yung P. Koh, Gregory B. McKenna, Sindee L. Simon

PII:

S0040-6031(19)30972-4

DOI:

https://doi.org/10.1016/j.tca.2020.178542

Reference:

TCA 178542

To appear in:

Thermochimica Acta

Received Date:

31 October 2019

Revised Date:

28 January 2020

Accepted Date:

3 February 2020

Please cite this article as: Bari R, Koh YP, McKenna GB, Simon SL, Decomposition of HMX in Solid and Liquid States under Nanoconfinement, Thermochimica Acta (2020), doi: https://doi.org/10.1016/j.tca.2020.178542

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Decomposition of HMX in Solid and Liquid States under Nanoconfinement Rozana Bari, Yung P. Koh, Gregory B. McKenna, and Sindee L. Simon Department of Chemical Engineering, Texas Tech University, Lubbock, Texas 79409, USA *Corresponding authors: [email protected]; [email protected]

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Highlights for “Decomposition of HMX in Solid and Liquid States under Nanoconfinement,” by R. Bari, Y.P. Koh, G.B. McKenna and S.L. Simon. HMX decomposition occurs in solid state and liquid state

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Confinement in nanoporous media (12 and 50 nm) accelerates the decomposition of HMX

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Decomposition is described by a phase-dependent first-order autocatalytic model

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Rate constant increases with decreasing pore size in both liquid and solid states

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Activation energy increases in the smallest pore sizes (12 nm)

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Abstract The thermal properties of bulk and nanoconfined HMX were studied using differential scanning calorimetry in dynamic scanning mode at rates ranging from 0.3 to 100 °C/min. At the

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slowest heating rates, decomposition occurs in the solid phase; at intermediate heating rates, it starts in the solid phase, melts, and finishes with a faster rate of reaction in the liquid state; and at the highest heating rates, the decomposition is entirely in the liquid phase. The activation energy decreases with conversion and is highest for 12 nm-diameter pores. The decomposition reaction

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is accelerated for nanoconfined HMX compared to the bulk with the onset of decomposition decreased by 1 to 5 °C in 50 nm-diameter pores and by 4 to 11 °C in 12 nm-diameter pores. The kinetics of decomposition is well described by a first-order autocatalytic reaction model with the reaction rate constants increasing with nanoconfinement. In addition, the reaction rate constant is one order of magnitude higher in the melt state than in the solid state.

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Key Words: HMX, nanoconfinement, solid state, melting, decomposition kinetics

Introduction HMX is a nitamine-based secondary explosive, which is also known as octogen. It has a

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molecular composition of octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (C4H8N8O8), as shown in Figure 1. The decomposition of HMX has been studied by a number of researchers.1-21 The

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reaction is reported to be first-order6,10,11 and to also have autocatalytic character.17,19,20 HMX is

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known to melt at 279 °C1,15 14,18 and consequently at slower heating rates the decomposition occurs in the solid state, whereas at higher heating rates, the decomposition occurs in the liquid

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phase after the material goes through melting.1,2,19 For dynamic heating scans, the activation

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energy has been found to change with temperature1,2 and conversion.8 Nanoconfinement is known to influence thermal properties and reaction rates. For example, we have recently found that the decomposition of another explosive, CL-20 is

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accelerated under nanoconfinement.22 In contrast, some materials show the opposite behavior, with decomposition shifted to higher temperatures under nanoconfinement, including poly(ethylene oxide)23 and the pharmaceutical material nifedipine;24 and in some materials

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and/or in large enough confinement sizes, decomposition is unchanged, such as for the explosive RDX (hexogen) under confinement of 100 to 1000 nm.25 In this work, we explore the effect of nanoconfinement on the kinetics of decomposition of HMX in both solid and liquid phases. In particular, we use differential scanning calorimetry (DSC) as a function of heating rate and examine the changes upon nanoconfinement in the onset of decomposition, total heat of

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decomposition, activation energy, and reaction rate constants. We find that the behavior for bulk and nanoconfined materials can be described using a first-order autocatalytic reaction model. Methodology Materials HMX (purity = 99 % by high performance liquid chromatography, HPLC) was provided by Picatinny Arsenal and used without further purification. Nanoconfinement of HMX was performed in nanoporous borosilicate controlled pore glasses (CPG, Sigma-Aldrich), having 50

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nm- and 12 nm-diameter pores with pore volumes of 0.68 and 1.1 cm3/g, respectively, with pore

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size distribution of ± 3.7 % and ± 10 % for the 50 nm- and 12 nm-diameter pores, respectively. The CPGs were cleaned by immersing in nitric acid at 110 °C for 10 hours, followed by rinsing

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deionized water until the pH became neutral, and then by drying at 100 °C in a vacuum oven

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overnight. The CPGs were stored under desiccant until further use.

Since HMX decomposes rapidly after melting, melt imbibement into the nanopores is not

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possible. Hence, the loading of HMX into the CPGs was carried out using a solution evaporation method developed in our prior work on CL-20 in nanoconfinement.22 First, the HMX is

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dissolved in HPLC-grade acetone (Sigma-Aldrich) and then a specified amount of the solution is placed on top of pre-weighed CPGs (adding less solution than the CPG pore volume). Then the CPG is dried. The procedure is performed several times to get the desired amount of HMX into the pores. Samples were made for 50 nm-diameter pores with pore fullness of 30 % and 40 %

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and for 12 nm-diameter pores with pore fullness of 25 % and 60 %. In prior work results for decomposition of nanoconfined CL-20,22 consistent results were found when pores were filled to 25 % or greater presumably because the material fills the pores as plugs. DSC measurements A Mettler-Toledo differential scanning calorimeter DSC1 with an ethylene glycol cooling system was used to perform calorimetric measurements under nitrogen purge. Experiments were 3

run in 20 μL PerkinElmer hermetic pans with a perforated hole in the lid. The mass of HMX per sample ranged from 0.14 to 0.35 mg to prevent thermal runaway.1,15 In the case of HMX nanoconfined in 50 nm- and 12 nm-diameter pores, the sample mass of HMX was also in this range, with the total sample mass of HMX plus CPG ranging from 0.45 to 1.15 mg. The results which follow are normalized and reported per gram of HMX. Dynamic temperature scans were performed from 180 to 320 °C at rates ranging from 0.3 to 100 °C/min in order to study the

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decomposition reaction; in addition, scans were made from 40 to 300 °C at 30 °C/min in order to

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study the polymorphic transformation. The calibration of the DSC temperature was performed using indium for all heating rates.

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Decomposition Kinetics DSC thermograms with complete decomposition for each dynamic scan were used to

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obtain the integral of the heat flow as a function of temperature, which gives the conversion x as

𝑥=

𝑇 ∫𝑇 𝑄̇ 𝑑𝑇 𝑜

𝛽𝛥𝐻𝑇

(1)

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a function of temperature, using the following equation:

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where 𝑄̇ is the heat flow for the decomposition reaction, β is the heating rate, ∆HT is the total heat of reaction for the decomposition for a given scan, and To is a temperature prior to the reaction exotherm. The apparent activation energy, Ea for the decomposition kinetics was obtained using the model-free isoconversional method of Kissinger, Akahira, and Sunose (KAS), which was modified by Vyazovkin et al.27:

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𝛽

𝐸

𝑙𝑛 (𝑇 2 ) = − 𝑅𝑇𝑎 + 𝐶2 𝑥

𝑥

(2)

where Tx indicates the temperature to reach a specific conversion x at each heating rate β, and C2 is a constant. The apparent activation energy, Ea is obtained from the slope of the linear fit of ln(β/Tx2 ) versus inverse Tx at various x by using the data before melting. The isoconversion 4

method cannot be applied to the decomposition data after melting because although the mechanism is unchanged if all data are obtained in the liquid state, the assumption that the onset temperature of the reaction reflects the rate of the reaction is not met since the onset is dictated by the value of the Tm; in other words, given the rate constant and activation energy in the liquid state, the reaction would occur at lower temperatures if Tm were lower. Thus, application of equation 2 above Tm is incorrect and yields an apparent activation energy that is higher than the

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actual value.

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In order to describe the conversion as a function of temperature, the kinetics of the

decomposition process were analyzed. The decomposition of the HMX is assumed to follow a

𝑑𝑇

=

𝑘𝑖 𝛽

(1 − 𝑥)(𝑥 + 𝑏) 𝐸𝑎 𝑅

1

(𝑇 − 𝑇

1 𝑟𝑒𝑓

)]

(4)

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𝑘𝑖 = 𝑘𝑖𝑜 𝑒𝑥𝑝 [−

(3)

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𝑑𝑥

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first-order autocatalytic reaction:

where kio are the Arrhenius reaction rate constants at a reference temperature Tref (= 573.2 K), Ea

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is the activation energy of the reactions, and R is the gas constant. The constant b is assumed to be related to the concentration of species which initially catalyzes the decomposition reaction. The rate of reaction increases dramatically at melting and we capture this by allowing the rate constant to change at the midpoint of the melting transition: 𝛽∆𝑡𝑚

𝑘𝑖𝑜 = 𝑘2𝑜 for 𝑇 > 𝑇𝑚 +

𝛽∆𝑡𝑚

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𝑘𝑖𝑜 = 𝑘1𝑜 for 𝑇 ≤ 𝑇𝑚 +

2

2

(5)

(6)

where ∆tm is the time to melt the HMX sample, and k1o and k2o are the Arrhenius reaction rate constants before and after melting. The time to melt will depend on the thickness of the sample, its thermal diffusivity, and the resistance to heat transfer between the sample pan and furnace and 5

between the sample pan and the sample. We find that within our sample size range the data can be fit using a single value of ∆tm (2.40 s) for the bulk samples, a slightly higher value for the nanoconfined samples in the 50 nm-diameter pores (4.41 s), and a slightly smaller value for the nanoconfined samples in the 12 nm-diameter pores (1.83 s). A more in-depth analysis would model the time to melt for each sample and heating rate using the thermal diffusion equation and accounting for the heat of melting and the thermal diffusivity of the HMX-imbibed CPG;

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however, that analysis is beyond the scope of this work.

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Results

Dynamic heating scans at 0.3 to 100 °C/min for bulk and nanoconfined HMX in 50 nm-

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and 12 nm-diameter pores are shown in Figure 2, where normalization of the heat flow 𝑄̇ was

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performed by multiplying with β/βref, where βref = 10 °C/min and the units of 𝑄̇ are per gram HMX. The reaction exotherms shift to higher temperatures with increasing heating rate, as

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expected, due to shorter exposure times at a given temperature as heating rates increases. The onset of the reaction is 55 °C lower at 0.3 °C/min compared to 100 °C/min. The decomposition

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reaction of bulk HMX (Figure 2a) takes place in the solid phase at the lowest rates from 0.3 to 1.0 °C/min before the sample reaches the melting temperature. At intermediate heating rates, from 1.8 ≤ β ≤ 10 °C/min, the exothermic reaction starts in the solid phase, and then the rate increases by a factor of approximately three at melting. This sharp increase of the decomposition

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rate is not attributed to the heat of melting, which is endothermic and only 0.11 kJ/g15, but rather it is attributed to the increase in reaction rate in the liquid state compared to the solid state. The change in shape of the exotherms in the vicinity of melting are similar to that observed by others.1,2 Similar results were observed by Rogers10 for cupferron tosylate with onset of melting at 139 °C, that undergoes simultaneous melt and decomposition. At the highest rates, for β ≥ 30

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°C/min, a melting endotherm is first observed followed by decomposition and the breadth of the melting endotherm increases with increasing heating rate since the temperature change over which time the sample melts increases with increasing rate. The DSC heating scans for the HMX confined in 50 nm-diameter pores (Figure 2b) and 12 nm-diameter pores (Figure 2c), are qualitatively similar to the bulk. However, the onset of the decomposition reaction decreases by 1 to 5 °C in the 50 nm-diameter pores and by 4 to 11 °C in

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the 12 nm-diameter pores compared to the bulk. The average onset temperature of decomposition

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for three repeat scans are reported in Table 1 for all samples at all heating rates. The dramatic increase in rate observed at intermediate heating rates for the bulk, is also observed for HMX

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confined in the 50 nm-diameter pores, but this effect is less apparent in the 12 nm-diameter

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pores.

The average total heat for the decomposition reaction for three repeat scans was obtained

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by integrating the area under the heat flow curve for the reaction exotherms at different heating rates; values are reported in Table 2. The total heat of reaction generally increases with heating

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rate from 0.78 ± 0.07 to 1.24 ± 0.15 kJ/g for 0.3 °C/min to 100 °C/min rates, respectively. The total heat of decomposition depends on the reaction products formed during the decomposition, and these will vary depending on the rate of heating and the state of the reactant i.e., before and after melting. A similar trend is observed for HMX confined in the 50 and 12 nm-diameter pores

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with similar heats of decomposition for bulk and confined systems. Values are consistent with the heat of reaction in the bulk reported in the literature by Lee et al. (1.1-1.3 kJ/g at 5 to 20 °C/min),3 whereas they are somewhat lower than those reported by Gong et al. (1.6-1.7 kJ/g at 10 °C/min). 4

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The onset of melting for HMX in the bulk was found to be at 279 °C, similar to what is reported by others in the literature.1,15 In 50 nm-diameter pores, the endotherm is weaker than the bulk and it is depressed by 2 °C. Although no endotherm is observed in the 12 nm-diameter pores, the appearance of a change in slope at ~270 °C at heating rates of 10 to 60 °C/min is an indication of the phase change of HMX from solid to liquid. The depression of melting for nanoconfined HMX in 12 nm-diameter pores can be estimated using the Gibbs28-Thomson29

(7)

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∆𝑇𝑚 = 𝑇𝑚 − 𝑇𝑚 (𝑑) = 4𝜎𝑠𝑙 𝑇𝑚 ⁄(𝑑∆𝐻𝑓 𝜌𝑠 )

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equation:

where Tm is the melting temperature in the bulk, d is the crystal size, Tm(d) is the melting

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temperature of crystal size of d, σsl is the surface energy of the solid-liquid interface, ∆Hf is the

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enthalpy of fusion in the bulk, and ρs is the solid phase density. Based on the Tm depression in the 50 nm-diameter pores, we find that 4σslTm/∆Hfρs = 100 K-nm from a linear fit of ∆Tm vs.

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inverse diameter.30 Thus, the melting of HMX in the 12 nm-diameter confinement can be estimated to be 270.7 °C, yielding a melting point depression Tm of 8.3 °C.

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The heat flow data for the HMX obtained from Figure 2 is converted to conversion x as a function of temperature using equation 1, and the results are plotted for the bulk material in Figure 3a, for the HMX confined in 50 nm-diameter pores in Figure 3b, and for HMX confined in 12 nm-diameter pores in Figure 3c. As mentioned, for HMX in the bulk, at lower heating

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rates, the decomposition reaction takes place in the solid phase. At higher heating rates, a change in the shape of the curve is observed due to melting and then the conversion occurs at a faster rate. At the highest three rates, the decomposition reaction occurs in the liquid phase; hence, no change in the shape of the curves is observed. The HMX confined in 50 nm- and 12 nm-diameter

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pores also follows a similar pattern of conversion as a function of temperature although the reaction onset and the melting point are shifted to lower temperatures. In order to model the reaction, we need the activation energy, and to this end we have applied the isoconversional KAS method.26 The resulting activation energy values for bulk and for the HMX confined in 50 nm- and 12 nm-diameter pores as a function of conversion are shown in Figure 4 as obtained from the slope of the plot of ln(β/Tx2 ) versus reciprocal

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temperature. We note that the isoconversional KAS method26 was only applied for the HMX

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before melting and cannot be applied after melting because of the change in rate at Tm as

discussed earlier. Interestingly, Ea decreases dramatically as conversion increases, presumably

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because the intermediate products catalyze the decomposition reaction.17-19 Although the Ea

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values are similar in the bulk and in the 50 nm-diameter pores, Ea in the 12 nm-diameter pores is some 25 kJ/mol higher at low conversions and decreases to the bulk value for x ≥ 0.7. The linear

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fits of Ea as a function of x are: Ea = -47x + 146 for bulk HMX

(8)

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Ea = -48x + 146 for nanoconfined HMX in 50 nm-diameter pores (9) Ea = -76x + 171 kJ/mol for nanoconfined HMX in 12 nm-diameter pores

(10)

Our results for the bulk HMX are consistent with the results of Vyazovkin and Wight who reported Ea values generally ranging from 120 to 165 kJ/mol using various reaction-based

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models, a value of 131 using a model-free method, and values ranging from 110 to 200 kJ/mol using the isoconversion model-free method.21,31These authors also showed that Ea depends the method that is used to obtain it and use of, for example, an incorrect model will yield poor results. Our Ea values are also consistent, albeit somewhat lower, than reports in the literature for the solid-state reaction, with values ranging from 159 to 294 kJ/mol,2,3,5,6,8-11,14 as well as

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consistent with values for the liquid-state reaction obtained from isothermal data of approximately 220 kJ/mol.6,10,11 On the other hand, the Ea values obtained using dynamic scans in the liquid state are distinctly higher, ranging from 394 to 572 kJ/mol,2,3,14 due to the incorrect application of the isoconversion method in this regime as previously discussed. The conversion data as a function of temperature for bulk and nanoconfined HMX in 50 nm- and 12 nm- diameter pores were fit with a first-order autocatalytic model using equations 3

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to 6, with the conversion-dependent activation energy given in equations 8 to 10. The model well

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describes the results as shown in Figure 3 where the lines are the model and the points the data. The value of b used in the model is 0.04, and it was obtained from fitting the bulk HMX data.

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The values of the initial rates of the reaction at 280 °C (553.2 K), as given by the fitting

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parameters ko1b and ko2b in the solid and liquid state, respectively, as well as the value of ∆tm, are summarized in Table 3.

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For the bulk HMX decomposition, the initial rate of reaction (dx/dt) is ko1b = 3.8 × 10−4 s-1 and ko2b = 4.1 × 10−3 s-1 at the reference temperature of 280 °C in the solid and liquid states,

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respectively, as shown in Table 3. These values are compared to the reaction rate constants at 280°C obtained by us from the model parameters reported in the literature in Table 4. The literature values are higher, ranging from 2.8 × 10−3 to 7.3× 10−3 s-1 in the solid state1,5,9,14 and from 9.7 × 10−3 to 7.6 × 10−2 s-1 in the liquid state.6,10,14 Differences in the values of

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reaction rate constant in this work and others are presumably due to (i) differences in the model and in the fitting procedures, and (ii) a broader range of heating rates used here with different Ea values, which influence the value of kob. The reaction rate constants k1o and k2o at 280 °C before and after melting for the bulk and nanoconfined HMX are plotted in Figure 5, showing that the reaction rate constants are

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approximately one order of magnitude higher in the liquid state than in the solid state, and they increase with decreasing confinement size (i.e., with increasing confinement). The decomposition reaction is accelerated by 1.4 and 1.6 times before and after melting for the HMX confined in 50 nm-diameter pores relative to the bulk, and the corresponding accelerations are 2.5 and 1.7 times in the 12 nm-diameter pores. A final comparison of the conversion of bulk and nanoconfined HMX as a function of

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temperature at 3 and 30 °C/min is shown in Figure 6a and Figure 6b, respectively where

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experimental data are plotted as symbols and model fits are plotted as lines for comparison. The figures clearly show that the onset of decomposition of the HMX in 12 nm-diameter pores begins

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at 6 and 9 °C earlier than the bulk at 3 and 30 °C/min, respectively.

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Discussion The HMX used in this was in the β polymorph and crystallization from acetone also forms the β polymorph.32 For the bulk HMX, the dynamic heating scan at 30 °C/min shows

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transformation of the β polymorph to δ polymorph at 190°C, similar to observed by Goetz and Brill at 175 °C.33 The polymorphic transformations were observed to be depressed by 4 and 13

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°C for nanoconfined HMX in 50 and 12 nm-diameter pores, respectively, with a linear dependence on inverse pore diameter. This confinement effect on the  to  polymorphic transition temperature (T is approximately twice that of the melting transition, which was 2 °C

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in the 50 nm pores and estimated to be 8 °C in the 12 nm pores from the Gibbs-Thompson (GT) equation. Application of the GT equation to the  to  polymorphic transition yields a value of 4σssT/∆Hρs = 150 K-nm, where ss is the surface energy of the solid-solid interface and H is the enthalpy of the  to  polymorphic transition. Although nanoconfinement can influence packing density and the equilibrium crystal structure,34-36 we have no indication that

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nanoconfined HMX results in changes in equilibrium phase behavior beyond the depression of the transition temperatures as described by the GT equation. Pressure is known to influence the decomposition of HMX with the decomposition rate increasing strongly with pressure at low to moderate pressures below 1 GPa and decreasing at higher pressures.37-39 For example, the solid state reaction rate increases five orders of magnitude as pressure increases from atmospheric pressure to 100 MPa.37 In addition, the

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activation energy changes in a compensatory manner with the rate, increasing as rate increases

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for pressures below 1 GPa.37,39,40 In our experiments, we perforated the top of the DSC pans in order to allow the gaseous reaction products to escape, and thus, for the bulk reaction, ambient

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conditions are maintained. However, in the nanopores, the material could be under pressure for

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two reasons: i) pressure could build up as the reaction proceeds if the gas diffusion out of the pores is not fast enough, and ii) pressure could build up on heating the confined HMX from room

P =  K (T-Ta)

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temperature because of differential thermal expansion of the HMX and the CPG41: (11)

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where  is the differential volumetric thermal expansion coefficient of HMX and CPG, which is assumed to be that of HMX (63 × 10-6 K-1)42, K is the bulk modulus of HMX (K = 15 GPa)43, Ta is room temperature where the HMX is considered to be in its stress-free state because this is the temperature where the solvent was evaporated during sample preparation, and the resulting

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pressure would be 240 MPa at the melting point. Such large pressures, however, would be expected to significantly increase both the nanoconfined polymorphic transition temperature and the melting point, and neither are observed. Furthermore, our results indicate only a modest increase in the solid-state reaction rate from 1.4 to 2.5 times faster than the bulk in 50 and 12 nm-diameter pores, respectively, and an increase in decomposition rate after melting with

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acceleration factors of 1.6 and 1.7 times that of the bulk reaction in the two pores. If the HMX were isochorically confined and/or the gaseous reaction products were unable to diffuse out of the pores, one would expect much higher decomposition rates under nanoconfinement and much higher rates in the solid state compared to the liquid state given that the isochoric constraints would be eliminated on melting and given the higher diffusivity of gases in the liquid state. Results should also not depend on pore size since the pressure arising from equation 11 will not

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depend on pore size. In addition, from the isoconversion analysis, we observe that Ea decreased

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with conversion, whereas if pressure were building up as temperature increased on heating or as gaseous products were released, one would expect an increase in the activation energy with

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conversion. Thus, our results are inconsistent with pressure increasing in the nanopores. The

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explanation may be that the material fills as small plugs in the pores, thus shortening the length scale needed for diffusion and reducing the isochoric constraint since the ends of the plugs can

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freely expand. We note that in our prior work on CL-20,22 an increase in the decomposition rate was observed under nanoconfinement and the increase was larger at lower pore fullness (7 %)

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where the diffusion length scale is shorter, which is again inconsistent with the acceleration being due to a pressure effect arising from containment of gaseous reaction products.

Summary and Conclusions The decomposition kinetics of bulk and nanoconfined HMX in solid and liquid phases

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have been studied using DSC. Dynamic heating scans show that HMX rapidly decomposes after melting, hence we adopted the solution-based method of imbibing the HMX into the nanoporous confining medium developed in our prior work on CL-20. For bulk HMX, the decomposition takes place in the solid state at the slowest heating rates; starts in the solid state, then passes through melting, and completes decomposition in the liquid states for the intermediate heating

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rates; at the highest heating rates the decomposition takes place only at the liquid state. For nanoconfined HMX, the decomposition takes place in a qualitatively similar pattern as in the bulk but the exotherm is shifted to lower temperatures. The activation energy of the bulk and nanoconfined HMX decreases as conversion increases. The reaction kinetics for bulk and nanoconfined HMX were well described by a first-order autocatalytic reaction model with the rate constant in the liquid state being approximately one order of magnitude larger than that in

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the solid state and with the rate constant increasing as pore size decreased. The decomposition

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reaction accelerated for nanoconfined HMX by 1.4 and 1.6 times in the solid state before melting in 50 nm- and 12 nm-diameter pores, respectively, and by 2.5 and 1.7 times in the liquid state in

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the 50 nm- and 12 nm-diameter pores.

Declaration of interests

Author Credit Statements.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Rozana Bari: Carried out experiments and performed data analysis. Wrote and revised manuscript. Yung P. Koh: Worked with calorimetry experiments and data analysis.

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Gregory B. McKenna: Originated project ideas, supervised and mentored the body of work. Edited the manuscript. Obtained funding for the work. Sindee L. Simon: Originated project ideas, developed calorimetry models and supervised and mentored the body of work. Reviewed and edited the manuscript. Obtained funding for the work.

Acknowledgements The authors gratefully acknowledge discussions with Dr. Victor Stepanov and thank him for supplying the HMX material. We are also grateful to the Enhanced Energetic Effects (EEE) 14

of the Office of the Secretary of Defense (OSD) program and the Advanced Propulsion and Explosives (APEX) program at Picatinny Arsenal for funding of this work through the National Armaments Consortium (NAC) via the Defense Ordnance Technology Consortium contract

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DOTC-16-01-INIT0177.

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References (1) Burnham AK, Weese RK. Thermal decomposition kinetics of HMX. USDOE Report UCRL-TR-204262. 2004; doi:10.2172/877784. (2) Pinheiro GFM, Lourenco VL, Iha K. Influence of the heating rate in the thermal decomposition of HMX. Journal of Thermal Analysis and Calorimetry. 2002;67(2):445-52. (3) Lee JS, Hsu CK, Chang CL. A study on the thermal decomposition behaviors of PETN, RDX, HNS and HMX. Thermochimica Acta. 2002 Sep 15;392:173-6. (4) Gong FY, Zhang JH, Ding L, Yang ZJ, Liu XB. Mussel-inspired coating of energetic crystals: A compact core-shell structure with highly enhanced thermal stability. Chemical Engineering Journal. 2017;309:140-50. (5) Oxley JC, Kooh AB, Szekeres R, Zheng W. Mechanisms of nitramine thermolysis. The Journal of Physical Chemistry. 1994;98(28):7004-8. (6) Robertson AJB. The thermal decomposition of explosives. Part II. Cyclotrimethylenetrinitramine and cyclotetramethylenetetranitramine. Transactions of the Faraday Society. 1949;45:85-93. (7) Behrens Jr R. Identification of octahydro‐1, 3, 5, 7‐tetranitro‐1, 3, 5, 7‐tetrazocine (HMX) pyrolysis products by simultaneous thermogravimetric modulated beam mass spectrometry and time‐of‐flight velocity‐spectra measurements. International Journal of Chemical Kinetics. 1990;22(2):135-57. (8) Kimura J, Kubota N. Thermal decomposition process of HMX. Propellants, Explosives, Pyrotechnics. 1980;5(1):1-8. (9) Hoondee W. The thermal decomposition of (Beta)-HMX. Doctoral dissertation, Monterey, California; Naval Postgraduate School. 1971. (10) Rogers RN. Differential scanning calorimetric determination of kinetics constants of systems that melt with decomposition. Thermochimica Acta. 1972;3(6):437-47. (11) Rogers RN, Daub GW. Scanning calorimetric determination of vapor-phase kinetics data. Analytical Chemistry. 1973;45(3):596-600. (12) Rogers RN, Smith LC. Estimation of preexponential factor from thermal decomposition curve of an unweighed sample. Analytical Chemistry. 1967;39(8):1024-5. (13) Maycock JN, Verneker VRP. Thermal decomposition of δ-HMX (cyclotetramethylenetetranitramine). Explosivstoffe. 1969;17:5. (14) Ordzhonikidze O, Pivkina A, Frolov Y, Muravyev N, Monogarov K. Comparative study of HMX and CL-20. Journal of Thermal Analysis and Calorimetry. 2011;105(2):529-34. (15) Bhattacharia SK, Weeks BL, Chen CC. Melting behavior and heat of fusion of compounds that undergo simultaneous melting and decomposition: An investigation with HMX. J Chem Eng Data. 2017;62(3):967-72. (16) Brill TB, Arisawa H, Brush PJ, Gongwer PE, Williams GK. Surface chemistry of burning explosives and propellants. The Journal of Physical Chemistry. 1995;99(5):1384-92. (17) Schroeder MA. Critical analysis of nitramine decomposition data: product distributions from HMX and RDX decomposition. USArmy Materiel Laboratory Technical Report BRL-TR2659. 1985. (18) Gao B, Wang DJ, Zhang J, Hu YJ, Shen JP, Wang J, Huang B, Qiao ZQ, Huang H, Nie FD, Yang GC. Facile, continuous and large-scale synthesis of CL-20/HMX nano co-crystals with high-performance by ultrasonic spray-assisted electrostatic adsorption method. Journal of Materials Chemistry A. 2014;2(47):19969-74.

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(19) Oyumi Y, Brill TB. Thermal decomposition of energetic materials. 3. A high-rate, in situ, FTIR study of the thermolysis of RDX and HMX with pressure and heating rate as variables. Combustion and Flame. 1985;62(3):213-24. (20) Behrens R. Thermal decomposition processes of energetic materials in the condensed phase at low and moderate temperatures. Reaction Mechanisms of Energetic Materials in the Condensed Phase: Long-term Aging, Munition Safety and Condensed-Phase Processes in Propellants and Explosives. 2005;1. (21) Vyazovkin S, Wight CA. Model-free and model-fitting approaches to kinetic analysis of isothermal and nonisothermal data. Thermochimica Acta. 1999;340:53-68. (22) Bari R, Denton AA, Fondren ZT, McKenna GB, Simon SL. Acceleration of decomposition of CL-20 explosive under nanoconfinement. Journal of Thermal Analysis and Calorimetry. 2019;1-7; doi:10.1007/s10973-019-09027-5. (23) Abudakka M, Decker DS, Sutherlin LT, Teeters D. Ceramic/polymer interpenetrating networks exhibiting increased ionic conductivity with temperature control of ion conduction for thermal runaway protection. International Journal of Hydrogen Energy. 2014;39(6):2988-96. (24) Cheng S, McKenna GB. Nanoconfinement Effects on the Glass Transition and Crystallization Behaviors of Nifedipine. Molecular Pharmaceutics. 2019;16(2):856-66. (25) Ren XN, Zhao FQ, Xiao LB, Gao HX. Investigation on Continuous Specific Heat Capacities, Thermodynamic Properties and Thermal Decomposition Kinetics of Micro-sized and Nano-sized RDX. Chinese Journal of Explosives & Propellants. 2019; 42(3): 257-261. (26) Kissinger HE. Reaction kinetics in differential thermal analysis. Analytical Chemistry. 1957;29(11):1702-6. (27) Vyazovkin S, Burnham AK, Criado JM, Perez-Maqueda LA, Popescu C, Sbirrazuoli N. ICTAC Kinetics Committee recommendations for performing kinetic computations on thermal analysis data. Thermochim Acta. 2011;520:1-19. (28) Gibbs JW. The collected works of JW Gibbs. Longmans, Green; 1928. (29) Thomson JJ. Applications of dynamics to physics and chemistry. Macmillan; 1888. (30) Xu B, Di X, McKenna GB. Melting of pentaerythritol tetranitrate (PETN) nanoconfined in controlled pore glasses (CPG). Journal of Thermal Analysis and Calorimetry. 2013;113(2):539-43. (31) Vyazovkin S, Wight CA. Isothermal and non-isothermal kinetics of thermally stimulated reactions of solids.Int. Rev. Phys. Chem. 1998;17(3):407-33. (32) Cady HH. Studies on the Polymorphs of HMX. US Atomic Energy Commission Report LAMS-2652; 1962. (33) -octahydro-1,3,5,7tetranitro-1,3,5,7-tetrazocine and their temperature dependence. Journal of Physical Chemistry. 1979;83(3):340-6. (34) Lopez E, Simon SL. Trimerization reaction kinetics and Tg depression of polycyanurate under nanoconfinement. Macromolecules. 2015;48(13):4692-701. (35) Bernstein J, Bernstein JM. Polymorphism in molecular crystals. Oxford University Press; 2002. (36) Pallaka MR, Unruh DK, Simon SL. Melting behavior of n-alkanes in anodic aluminum oxide (AAO) nanopores using Flash differential scanning calorimetry. Thermochimica Acta. 2018;663:157-64.

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(37) Glascoe EA, Zaug JM, Burnham AK. Pressure-dependent decomposition kinetics of the energetic material HMX up to 3.6 GPa. The Journal of Physical Chemistry A. 2009; 113 (48): 13548-55. (38) Burnham AK, Weese RK, Wemhoff AP, Maienschein JL, A historical and current perspective on predicting thermal cookoff behavior. J Therm Anal Calorim. 2007;89: 407-15. (39) Piermarini GJ, Block S, Miller PJ. Effects of pressure and temperature on the thermal -octahydro-1,3,5,7-tetranitro-1,3,5,7tetrazocine. Journal of Physical Chemistry. 1987;91(14):3872-8. (40) Brill TB, Gongwer PE, Williams GK, Thermal decomposition of energetic materials. 66. Kinetic compensation effects in HMX, RDX, and NTO. J Phys Chem. 1994;98:12242-7. (41) Simon SL, Park JY, McKenna GB. Enthalpy recovery of a glass-forming liquid constrained in a nanoporous matrix: Negative pressure effects. The European Physical Journal E. 2002;8(2):209-16. (42) Sewell TD, Menikoff R, Bedrov D, Smith GD. A molecular dynamics simulation study of elastic properties of HMX. J Chem Phys. 2003;119:7417-26. (43) Dobratz BM. Properties of chemical explosives and explosive simulants. USDOE Report UCRL-51319. 1972; doi:10.2172/4285272.

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Table 1. The onset temperature of decomposition of bulk and nanoconfined HMX in 50 nm- and 12 nm-diameter pores as a function of heating rates. Tonset (°C) Heating rate (°C/min) 50 nm

12 nm

293 ± 1.1

288 ± 0.1

282 ± 0.8

60

288 ± 1.2

284 ± 0.8

279 ± 0.2

30

284 ± 0.6

282 ± 0.5

275 ± 0.9

10

280 ±0.4

278 ± 0.3

269 ± 0.3

3

269 ± 0.7

268 ± 0.4

1.8

265 ± 0.2

261 ± 0.4

1

253 ± 0.2

251 ± 0.7

248 ± 0.4

0.6

245 ± 1.9

243 ± 0.7

241 ± 0.4

0.3

238 ± 0.4

233 ± 0.7

230 ± 0.8

of

100

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Bulk

263 ± 0.5

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-p

257 ± 0.3

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Table 2. Total heat of decomposition of bulk and nanoconfined HMX in 50 nm- and 12 nmdiameter pores as a function of heating rates. ∆H (kJ/g) Heating rate (°C/min) 50 nm

12 nm

1.24 ± 0.15

1.26 ± 0.03

1.39 ± 0.12

60

1.44 ± 0.04

1.15 ± 0.13

1.27 ± 0.07

30

1.29 ± 0.09

1.20 ± 0.06

1.21 ± 0.06

10

1.13 ± 0.05

1.15 ± 0.05

1.20 ± 0.04

3

0.91 ± 0.04

0.91 ± 0.08

1.8

0.86 ± 0.04

0.84 ± 0.07

1

0.88 ± 0.08

0.81 ± 0.04

0.87 ± 0.08

0.6

0.83 ± 0.07

0.85 ± 0.04

0.86 ± 0.05

0.3

0.78 ± 0.07

0.82 ± 0.12

0.78 ± 0.07

of

100

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Bulk

0.84 ± 0.08

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-p

0.88 ± 0.07

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Table 3. Fitting results for decomposition reaction kinetics of bulk and nanoconfined HMX for b = 0.04 and Tref = 280 °C (553.2 K).

50

12

∆tm (s)

2.40

4.41

1.83

ko1×b (s-1)

3.8 × 10−4

5.2 × 10−4

9.3 × 10−4

ko2×b (s-1)

4.1 × 10−3

6.4 × 10−3

7.0× 10−3

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∞

of

D (nm)

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Table 4. Initial rate of reaction for bulk HMX at 280 °C in the solid and liquid states, respectively. ko2×b (s-1)

3.8 × 10−4 [This work]

4.1 × 10−3 [This work]

5.5 × 10−3 [1]

7.6 × 10−2 [6]

3.3 × 10−3 [5]

1.1 × 10−2 [12]

7.4 × 10−3 [9]

9.7 × 10−3 [14]

of

ko1×b (s-1)

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lP

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-p

ro

2.8 × 10−3 [14]

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NO2 | N O2N-N

N-NO2 N | NO2

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Figure 1. Molecular structure of HMX

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of ro -p re lP ur na Jo Figure 2. Normalized heat flow versus temperature for heating rates as indicated for HMX in the (a) bulk state, and nanoconfined in (b) 50 nm-diameter pores, and (c) 12 nm-diameter pores. Scaling of the heat flow is performed my multiplying 𝑄̇ βref/β using βref = 10 K/min. View in color online for the best clarity.

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of ro -p re lP ur na Jo Figure 3. Conversion versus temperature for heating rates as indicated for HMX in the (a) bulk state, and nanoconfined in (b) 50 nm-diameter pores, and (c) 12 nm-diameter pores. Symbols are for three sets of experimental data at each heating rates, and the solid lines are the model fit. View in color online for the best clarity. 25

of ro

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-p

Figure 4. Activation energy Ea for bulk and nanoconfined HMX as a function of conversion x. The error in Ea are from the standard deviation in the slope from the linear fit using equation 2. View in color online for the best clarity.

26

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Figure 5. Reaction rate constant ko at 280 °C as a function of inverse pore diameter for HMX before (red circles) and after melting (blue squares).

27

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Figure 6. Conversion x as a function of temperature for bulk and nanoconfined HMX in 50 nmand 12 nm-diameter pores at (a) 3 °C/min and (b) 30 °C/min, with experimental data as symbols and the solid lines as the model fit. View in color online for the best clarity.

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