Insight into the Thermodynamic Properties of Promising Energetic HNTO·AN Co-Crystal: Heat Capacity, Combustion Energy, and Formation Enthalpy

Abstract

A novel energetic co-crystal composed of hydrazinium 3-nitro-1,2,4-triazol-5-one (HNTO) and ammonium nitrate (AN), as a composite solid propellant oxidizer, was recently developed to substitute either pure ammonium perchlorate (AP) or nitrate. Unfortunately, the thermodynamic properties of this co-crystal or even the pure HNTO are not available in the open literature. Therefore, in this work, the low-temperature heat capacities of HNTO and HNTO·AN co-crystal were measured in the temperature range from 213.15 K to 378.15 K using differential scanning calorimetry. By fitting the heat capacity data, the thermodynamic functions ΔH₂₉₈._15K, ΔG₂₉₈._15K, and ΔS₂₉₈._15K were derived. In addition, the standard molar energies of combustion Δ_cU° of HNTO and HNTO·AN co-crystal were determined, and from the combustion results, the standard molar enthalpies of combustion ${\Delta }_{\mathrm{c}}{H}_{\mathrm{m}}^{\mathrm{o}}$ and formation ${\Delta }_{\mathrm{f}}{H}_{\mathrm{m}}^{\mathrm{o}}$ of these energetic compounds were derived at T = 298.15 K. The set of thermochemical data has been proposed in this work for the first time and will be undoubtedly indispensable information for the development of energetic materials based on HNTO and HNTO·AN co-crystal.

1. Introduction

Energetic materials (EMs) are defined as a class of chemical compounds that store an important extent of energy within their molecular structures, which can be released under some stimuli, such as impact, shock, or a thermal effect [1,2,3,4,5,6]. The research domain of EMs is still fertile, and its community is continuously looking for novel materials with improved performances. The main concern with EMs is the ability to obtain a satisfactory balance between thermal stability, sensitivity, density, oxygen balance (OB), and combustion/detonation parameters [7,8]. However, the synthesis of novel energetic molecules that encompasses the latter metrics is relatively complex [9]. The scientific community has therefore developed alternative strategies for the design of optimized EMs that are able to fulfill the previous criteria [10,11,12,13,14].

Among these numerous and promising alternatives, the co-crystallization process is an advanced methodology of crystal engineering that permits ordering and combining multiple molecules, among which at least one molecule is energetic, through weak interactions (hydrogen bonds, π-π stacking, and van der Waals forces), without affecting the molecular structure of the co-formers [15,16]. The co-crystallization process allows obtaining novel EMs with adjustable features, such as sensitivity, thermal stability, OB, and density, by just a correct selection of the energetic co-formers [17,18,19].

The ongoing development of EMs introduced the design of novel energetic co-crystals with promising performance, employing nitrogen-rich molecules, such as ethylene dinitramine (EDNA) [20], 5,5′-dinitro-2H,2H′-3,3′-bi1,2,4-triazole (DNBT) [21], 3,6-dinitropyrazolo[4,3-c]pyrazole [22], etc. Among these emergent nitrogen-rich molecules, hydrazine 3-nitro-1,2,4-triazol-5-one (HNTO) is an energetic salt that has recently been developed and acquires very attractive features, such as high-density ρ = 1.82 g·cm⁻³, good thermal stability, low sensitivity, and a higher energy content [23,24,25]. However, this compound suffers from a fairly low OB (−38%). For that reason, a recent study from our research group [26,27] has been conducted in order to overcome the latter issue by combining HNTO with an energetic oxidizer, namely, ammonium nitrate using a co-crystallization process, and thus increasing the overall oxygen balance of the co-crystal. The choice of AN as a co-former to HNTO has been motivated by its highly positive OB (20%), green decomposition products (chlorine-free), and low manufacturing cost [28]. In addition, the co-crystallization of HNTO with AN helped in eliminating the major disadvantage of AN, namely, the polymorphic transition (Phase IV to Phase III) that occurs near room temperature 32 °C [29], which can cause a volume change in AN-based energetic formulations, resulting in damaging and cracking accompanied by a degradation in the mechanical strength [30]. On the other hand, although AP is considered the workhorse oxidizer and the principal choice in composite solid propellants, it displays many drawbacks and hence requires its substitution with environmentally friendly and effective substances for the next generation of solid propellants [31,32].

Despite HNTO·AN co-crystal possessing very interesting energetic properties for application in energetic formulations, it has not been widely acknowledged and the publications reporting such compound are very scarce. In particular, no available thermodynamic properties have been reported for either HNTO·AN co-crystal or pure HNTO in the existing literature. Therefore, the aim of the present study is focused on the determination of the formation enthalpies and the heat capacities of HNTO and HNTO·AN co-crystal through calorimetric measurements. The latter missing or inadequate thermodynamic information will unfortunately limit the uses of HNTO and HNTO·AN and will create a research gap for a better understanding of the structure–property relationship of these energetic compounds that constitute important key parameters in order to help predict their physical properties, such as enthalpies of formation in the gas state [33,34,35], lattice energies [36], intermolecular forces [37,38], energetic combustion and detonation performances [39,40]. Finally, the newly presented thermodynamic data in the present study will undoubtedly offer indispensable resources for the development of novel propellant formulations, with optimized performances based on HNTO and HNTO·AN as oxidizers.

2. Experimental Section

2.1. Materials and Cocrystal Preparation

AN, with a purity of greater than 99.9%, was purchased from VWR-Prolabo. HNTO was synthesized in our laboratory using a solution of hydrazine hydrate and a solution of 3-nitro-2,4-dihydro-3H-1,2,4-triazol-5-one (NTO) according to the procedure reported elsewhere [26]. The co-crystal of HNTO·AN (see Figure 1) at a molar ratio of 1:3 was prepared through a solvent (methanol) evaporation method for which the details can be found in our previous publication [26,27].

Before being able to use such compounds for further measurements, they were initially subjected to vacuum evaporation at 333 K and 10⁻² mbar for more than 24 h to reduce possible traces of solvents and moisture.

2.2. Apparatus and Methods

2.2.1. Heat Capacity Measurements

Conventional differential scanning calorimetry (DSC, PYRIS, PerkinElmer, Waltham, MA, USA) was used to measure the specific heat capacity of the HNTO and the HNTO·AN cocrystal in the solid state. Samples of 2–3 mg, placed in aluminum crucibles, were heated from −70 °C to 120 °C at a heating rate of 10 K·min⁻¹ and then cooled at the same heating rate. Each measurement was repeated twice. Heat capacity and temperature calibrations were carried out with sapphire and indium, respectively, using the same experimental conditions [41]. Both sample and sapphire heat capacities were corrected for the empty pan contribution.

2.2.2. Heat of Combustion Determination

The thermochemical measurements were performed on an isoperibol oxygen bomb calorimeter Parr 6200, by Parr Instrument Company, Moline, IL, USA. The samples were placed in a crucible and ignited with a cotton thread on a platinum wire (0.05 mm in diameter and of 99.99% purity) strained between the electrodes.

The energy equivalent of the calorimeter ε_calor was determined with a standard reference sample of benzoic acid (BA), according to the recommended procedure of Parr instrument. A series of 10 standardization tests have been carried out and all the obtained values were compared to the NIST [42], Standard Reference Material^®39j 26434 ± 3 J·g⁻¹ (6317.8778 ± 0.7165 cal·g⁻¹) measured at 298.15 K. As the molecules investigated in this work contain a high nitrogen content, the released N₂ is expected to react with water to form nitric acid [42]. Thus, correction for nitric acid formation has been performed via titration with 0.1 M sodium hydroxide, which leads to a corrected Δ_cU_corr using Equation (1):

$$\mathbf{\Delta }{\mathit{U}}_{\mathbf{corr}}=\mathbf{\Delta }\mathit{U}-\left({\mathbf{\Delta }}_{\mathbf{f}}{\mathit{H}}_{\mathit{H}\mathit{N}{\mathit{O}}_3}^{\mathbf{o}}\mathbf{·}{\mathit{V}}_{\mathbf{N}\mathbf{a}\mathbf{O}\mathbf{H}}\mathbf{·}{\mathit{c}}_{\mathbf{N}\mathbf{a}\mathbf{O}\mathbf{H}}\right)$$

(1)

The atomic weights used were those recommended by the IUPAC Commission.

3. Results and Discussion

3.1. The Specific Heat Capacity and Thermodynamic Function of HNTO and HNTO·AN Cocrystal

The temperature-dependent heat capacities of HNTO and HNTO·AN cocrystal samples are determined from the measured DSC heat flow rate, using a symmetry line correction to account for the heat losses that occur during the heating and cooling scans. For this correction, it is assumed that the heat losses are only temperature dependent [43]. The heat capacity of pure AN has been previously measured using adiabatic calorimetry and reported in the literature [44]. The resulting heat capacities of HNTO and HNTO·AN cocrystal together with the heat capacity of AN taken from [44] are shown in Figure 2.

It can be seen from Figure 2a,b that the solid-state specific heat capacity C_p(cr) of HNTO and HNTO·AN cocrystal shows a smooth increase with the temperature from 213.15 K to 378.15 K. On the other hand, the pure AN observes an abrupt change in its heat capacity when heating from 213.15 K to 378.15 K, and such an apparent discontinuity is due to the solid–solid transition of AN that undergoes two visible transitions from tetragonal (V) to orthorhombic (IV) crystal structure at T = 255 K and a subsequent transition from orthorhombic (IV) to orthorhombic (III) structure at T = 305 K [29,44].

It is possible to denote that even though AN observes solid–solid transitions, the HNTO·AN cocrystal is stable and does not display any shift in the heat capacity and no thermal anomalies could be observed in the entire experimental temperature range. Thus, the latter finding highlights the aptitude of the co-crystallization process of AN with HNTO to suppress the latter solid–solid transition, hence stabilizing the AN crystal structure. This phase-stabilized ammonium nitrate (PSAN) exhibits a very interesting behavior since PSAN overcomes the major drawbacks of AN by avoiding the volume change (approximately 3.8% volume change) and density change caused by the solid–solid transition of AN at a low temperature of 32 °C that induces a porous structure and poor mechanical strength [30]. In addition, it is possible to denote that the heat capacity of the solid cocrystal is found to be higher than that of HNTO within the entire studied temperature range (see Figure 2c). However, the heat capacity of the cocrystal is lower than pure AN heat capacity when the crystalline phase of AN is tetragonal (V) and orthorhombic (IV), while it becomes higher when the crystalline phase of AN shifts to orthorhombic (III) at approximately T = 305K (see Figure 2c).

To further evaluate the thermodynamic functions of pure HNTO and HNTO·AN co-crystal samples, their experimental specific heat capacities measured with the two DSC runs were fitted using a linear model of two parameters α and β within a temperature range temperature from 213.15 K to 378.15 K as follow:

$${\mathit{C}}_{\mathbf{p}}\left(\mathit{T}\right) \mathbf{/}\mathbf{J}·{\mathbf{g}}^{-1}\text{·}{\mathbf{K}}^{-1}=\mathit{\alpha } \left(\mathit{T} / \mathit{K}\right)+\mathit{\beta }$$

(2)

The fitting parameters α and β, the regression coefficients r² with the relative mean square error (RMSE) of the linear fitting curves and the heat capacity for HNTO and HNTO·AN at 298.15 K are summarized in

Table 1. Fitting parameters α and β, regression coefficients r² of the linear fitting curves, and the heat capacity for HNTO and HNTO·AN cocrystal at 298.15 K.

Compound	Fitting Parameters		Cp (cr, 298.15 K)/J·g−1·K−1	r2	RMSE
HNTO	α	0.27562 ± 0.00468	1.1790 ± 0.0093	0.9982	0.00623
	β	0.00303 ± 1.56263 × 10−5
HNTO·AN	α	0.12112 ± 0.00353	1.5105 ± 0.0070	0.9996	0.00469
	β	0.00466 ± 1.17659 × 10−5

.

It can be noticed from Table 1 that the fitting C_p(T) curves represent a good linear approximation over the studied experimental temperature range with r² values exceeding 0.99. In addition, the evaluated RMSE (see Table 1) of the fitting curves is clearly within the uncertainties of the calorimetric measurements (±3%) which supports the fact that the linear fitting can properly simulate the measured heat capacity data of HNTO and HNTO·AN. Despite the studied experimental temperature range being from 213.15 K to 378.15 K, the fitting C_p function is stable and continuous, thus serving as a benchmark function for the application of HNTO and HNTO·AN co-crystal within this temperature range.

By exploiting the heat capacity data (see Figure 2 and Table 1), the thermodynamic functions of the enthalpy change, the entropy change, and the Gibbs free energy change of HNTO and HNTO·AN were evaluated within 213.15 K to 378.15 K using Equations (3)–(5) by taking T₀ = 298.15 K as a reference temperature and the results are listed in

Table 2. The heat capacity C_p, enthalpy change (${\mathit{H}}_{\mathit{T}}-{\mathit{H}}_{{\mathit{T}}_0}$), entropy change (${\mathit{S}}_{\mathit{T}}-{\mathit{S}}_{{\mathit{T}}_0}$), and Gibbs free energy change (${\mathit{G}}_{\mathit{T}}-{\mathit{G}}_{{\mathit{T}}_0}$) data at T₀ = 298.15 K of pure HNTO and HNTO·AN cocrystal.

	HNTO				HNTO·AN
T / K	Cp / J·g−1·K−1	ΔH298.15K / J·g−1	ΔS298.15K / J·g−1·K−1	ΔG298.15K / J·g−1	Cp / J·g−1·K−1	ΔH298.15K / J·g−1	ΔS298.15K / J·g−1·K−1	ΔG298.15K / J·g−1
213.15	0.9212	−155.1	−0.35	−80.5	1.1149	−212.8	−0.44	−119.7
218.15	0.9363	−147.2	−0.33	−75.5	1.1382	−202.2	−0.41	−112.6
228.15	0.9666	−130.9	−0.29	−65.7	1.1849	−180.2	−0.36	−98.3
238.15	0.9969	−114.0	−0.24	−56.0	1.2315	−157.2	−0.31	−84.1
248.15	1.0272	−96.5	−0.20	−46.4	1.2782	−133.3	−0.26	−70.0
258.15	1.0575	−78.4	−0.16	−36.9	1.3248	−108.5	−0.20	−55.9
268.15	1.0877	−59.7	−0.12	−27.5	1.3714	−82.8	−0.15	−41.9
278.15	1.1180	−40.4	−0.08	−18.3	1.4181	−56.1	−0.10	−27.9
288.15	1.1483	−20.5	−0.04	−9.1	1.4647	−28.5	−0.05	−13.9
298.15	1.1786	0.0	0.00	0.0	1.5114	0.0	0.00	0.0
308.15	1.2089	21.1	0.04	9.0	1.5580	29.5	0.05	13.9
318.15	1.2392	42.9	0.08	17.9	1.6046	59.9	0.10	27.7
328.15	1.2695	65.2	0.12	26.7	1.6513	91.2	0.15	41.5
338.15	1.2998	88.1	0.16	35.4	1.6979	123.5	0.20	55.3
348.15	1.3300	111.7	0.19	44.1	1.7446	156.6	0.25	69.0
358.15	1.3603	135.9	0.23	52.6	1.7912	190.8	0.30	82.7
368.15	1.3906	160.6	0.27	61.1	1.8378	225.8	0.35	96.3
378.15	1.4209	186.0	0.31	69.5	1.8845	261.8	0.40	110.0

. Obviously, the values of ${\mathit{H}}_{\mathit{T}}-{\mathit{H}}_{{\mathit{T}}_0}$, ${\mathit{S}}_{\mathit{T}}-{\mathit{S}}_{{\mathit{T}}_0}$, and ${\mathit{G}}_{\mathit{T}}-{\mathit{G}}_{{\mathit{T}}_0}$, present an increasing trend within the studied experimental temperature range. In addition, the values of ${\mathit{H}}_{\mathit{T}}-{\mathit{H}}_{{\mathit{T}}_0}$, ${\mathit{S}}_{\mathit{T}}-{\mathit{S}}_{{\mathit{T}}_0}$, and ${\mathit{G}}_{\mathit{T}}-{\mathit{G}}_{{\mathit{T}}_0}$ are all negative when the temperature is below 298.15 K and change sign above 298.15 K.

$${\mathit{H}}_{\mathit{T}}-{\mathit{H}}_{{\mathit{T}}_0}={{\displaystyle \int }}_{{\mathit{T}}_0}^{\mathit{T}}{\mathit{C}}_{\mathbf{p}}\mathbf{d}\mathit{T}$$

(3)

$${\mathit{S}}_{\mathit{T}}-{\mathit{S}}_{{\mathit{T}}_0}={{\displaystyle \int }}_{{\mathit{T}}_0}^{\mathit{T}}\frac{{\mathit{C}}_{\mathbf{p}}}{\mathit{T}}\mathbf{d}\mathit{T}$$

(4)

$${\mathit{G}}_{\mathit{T}}-{\mathit{G}}_{{\mathit{T}}_0}={{\displaystyle \int }}_{{\mathit{T}}_0}^{\mathit{T}}{\mathit{C}}_{\mathbf{p}}\mathbf{d}\mathit{T}-\mathit{T}{{\displaystyle \int }}_{{\mathit{T}}_0}^{\mathit{T}}\frac{{\mathit{C}}_{\mathbf{p}}}{\mathit{T}}\mathbf{d}\mathit{T}$$

(5)

3.2. The Standard Molar Enthalpies of Formation of HNTO and HNTO·AN

The enthalpy of formation ${\Delta }_{\mathrm{f}}{H}_{\mathrm{m}}^{\mathrm{o}}\left(\mathrm{cr}\right)$ of HNTO and HNTO·AN derived from combustion experiments are referred to as the crystalline state of the two compounds at a reference temperature T = 298.15 K. The values of the standard molar combustion energies ${\Delta }_{\mathrm{c}}{U}_{\mathrm{m}}^{\mathrm{o}}\left(\mathrm{cr}\right)$ correspond to the idealized combustion reactions of the solid energetic crystals.

For HNTO, the idealized combustion reaction is represented by the following equation:

$${\mathbf{C}}_2{\mathbf{H}}_6{\mathbf{O}}_3{\mathbf{N}}_{6\left(\mathbf{s}\right)}+2{\mathbf{O}}_{2\left(\mathbf{g}\right)}\to 2\mathbf{C}{\mathbf{O}}_{2\left(\mathbf{g}\right)}+3{\mathbf{H}}_2{\mathbf{O}}_{\left(\mathbf{l}\right)}+3{\mathbf{N}}_{2\left(\mathbf{g}\right)}$$

(6)

The specific combustion energy measured for HNTO is found to be −8716.6 ± 6.1 J·g⁻¹ after correction from the nitric acid contribution (see Section 2.2), and the reported value is the average of three separate measurements. Using the experimental energy of combustion of HNTO, the standard specific enthalpy of combustion of HNTO can be calculated through the following equations:

$${\mathbf{\Delta }}_{\mathbf{c}}\mathit{H}={\mathbf{\Delta }}_{\mathbf{c}}\mathit{U}+\mathbf{\Delta }{\mathit{n}}_{\mathbf{g}}\mathit{R}\mathit{T}$$

(7)

$${\mathbf{\Delta }}_{\mathbf{c}}{\mathit{H}}_{\mathbf{m}}^{\mathbf{o}}={\displaystyle \sum }{\mathbf{\Delta }}_{\mathbf{f}}{\mathit{H}}_{\mathbf{m}}^{\mathbf{o}}\left(\mathbf{products}\right)-{\displaystyle \sum }{\mathbf{\Delta }}_{\mathbf{f}}{\mathit{H}}_{\mathbf{m}}^{\mathbf{o}}\left(\mathbf{reactants}\right)$$

(8)

Thus, by applying Hess thermodynamical cycle to the idealized combustion reaction of HNTO, it was possible to compute the standard molar enthalpy of formation of HNTO at 298.15 K. By considering the heat of formation of the combustion products (carbon dioxide ${\Delta }_{\mathrm{f}}{H}_{\mathrm{m}}^{\mathrm{o}}\left({\mathrm{CO}}_2,\mathrm{g}\right)$ = (−393.5 ± 0.13) kJ·mol⁻¹ [33] and water ${\Delta }_{\mathrm{f}}{H}_{\mathrm{m}}^{\mathrm{o}}\left({\mathrm{H}}_2\mathrm{O},\mathrm{l}\right)$ = (−285.83 ± 0.04) kJ·mol⁻¹ [33], the formation enthalpy of HNTO, ${\Delta }_{\mathrm{f}}{H}_{\mathrm{m}}^{\mathrm{o}}\left(\mathrm{HNTO},\mathrm{cr}\right)$ = (−231.4 ± 1.4) kJ·mol⁻¹ was obtained. Despite the high nitrogen content in the molecular structure of HNTO, the obtained negative heat of formation of this compound demonstrates an exothermic contribution during its formation, indicating the non-negligible chemical stability of HNTO.

An analogous strategy is therefore applied to calculate the heat of formation of HNTO·AN co-crystal using the bomb calorimeter. For that reason, it is necessary to determine the equilibrium composition of the combustion reaction products of the HNTO·AN co-crystal in order to apply the Hess thermodynamic cycle. The studied HNTO·AN co-crystal is assumed to be a composite explosive formed by the association of an organic HNTO molecule and an inorganic ammonium nitrate molecule. The HNTO thermal decomposition is assumed ideal (CO₂, H₂O, and N₂ as combustion products) under an excess of oxygen in the bomb calorimeter but on the other hand, the decomposition path of AN can be difficult to assume because of its physical and chemical complexity that leads to many reaction paths [45,46] (see

Table 3. Single-step decomposition reactions of AN (positive values of heat of reaction indicate endothermic reactions, negative values exothermic). The reaction heat, Δ_rh, is expressed at T = 298.15 K [46]. “Reprinted/adapted with permission from Ref. [46]. 2022, John Wiley”.

Rxn N°	Decomposition Reactions	${\mathbf{\Delta }}_{\mathbf{r}}{\mathit{H}}_{\mathbf{m}}^{\mathbf{o}}$(AN)/kJ·mol−1
1	NH4NO3 ⇄ HNO3 + NH3	+179.9
2	NH4NO3 → N2O + 2 H2O	−42.3
3	4 NH4NO3 → 3 N2 + N2O4 + 8 H2O	−121.1
4	NH4NO3 → N2 + 2H2O + ½ O2	−123.9
5	NH4NO3 → NO + ½ N2 + 2 H2O	−32.6
6	3 NH4NO3 → 2N2 + N2O3 + 6 H2O	−95.0
7	5 NH4NO3 → 2 HNO3 + 4 N2 + 9 H2O	−129.1
8	8 NH4NO3 → 16 H2O + 2 NO2 + 4 NO + 5 N2	−70.0
9	4 NH4NO3 → 3 N2 + 2 NO2 + 8 H2O	−377.1
10	4 NH4NO3 → 2 NH3 + 3 NO2 + NO +N2 + 5 H2O	+82.2

). Consequently, according to the latter challenges, assuming an ideal combustion reaction of HNTO·AN co-crystal would not be consistent.

Therefore, we have attempted to realize thermal decomposition tests of AN in the bomb calorimeter, in order to gain a better understanding of its thermal decomposition mechanism in the working experimental conditions of the bomb calorimeter. However, performing an ignition of AN by itself cannot be achieved under an excess of oxygen in the bomb, and the presence of an additional fuel is necessary in order to initiate its decomposition reaction. Thus, the solid AN sample has been mixed with BA powder at different mass ratios for ignition aid purposes. Solid composites consisting of different weight fractions of BA (30 wt.% to 70 wt.%) and ammonium nitrate have been tested in the bomb calorimeter and the reaction energies ${\mathbf{\Delta }}_{\mathbf{r}}\mathit{U}$ have been recorded and their variation with BA weight fraction is presented in Figure 3a.

It is possible to denote from Figure 3a, that the variation of the measured reaction energy ${\mathbf{\Delta }}_{\mathbf{r}}{\mathit{U}}^{\mathbf{o}}$ of the BA-AN composite follow a linear evolution with the BA weight fraction. The fitting parameters a and b, the regression coefficients r² of the linear fitting curves (${\mathbf{\Delta }}_{\mathbf{r}}{\mathit{U}}^{\mathbf{o}}=\mathit{a}{\mathit{x}}_{\mathbf{BA}}+\mathit{b}$) are summarized in

Table 4. Linear fitting parameters a, b, and regression coefficients r² of the combustion energy of (AN-BA) and (HNTO·AN-BA) composites vs. the weight fraction of BA.

Compound	Fitting Parameters		r2
AN-BA	a	−0.24933 ± 0.00217	0.9998
	b	−1.62282 ± 0.09694
HNTO·AN-BA	a	−0.19858 ± 6.15467 × 10−4	0.9999
	b	−6.4836 ± 0.03198

. The regression coefficient value r² surpasses 0.999, which indicates that the measured energy is perfectly fitted with a straight line.

The decomposition energy of pure AN in the bomb calorimeter could be extracted from Figure 3a by an extrapolation of the linear fitting curve to x_BA = 0 (absence of BA) and the obtained thermal decomposition energy of AN is found to be ${\mathbf{\Delta }}_{\mathbf{r}}{\mathit{U}}_{\mathbf{m},\mathbf{exp}}^{\mathbf{o}}\left(\mathbf{AN}\right)$ = (−130 ± 8) kJ·mol⁻¹.

By considering the experimental decomposition energy of AN measured previously, it becomes possible to compare it to the energy ${\mathbf{\Delta }}_{\mathbf{r}}{\mathit{U}}_{\mathbf{m}}^{\mathbf{o}}\left(\mathbf{AN}\right)$ released from the decomposition reaction of the AN, according to the multiple reaction pathways presented in Table 3. The values of the decomposition energy ${\mathbf{\Delta }}_{\mathbf{r}}{\mathit{U}}_{\mathbf{m}}^{\mathbf{o}}\left(\mathbf{AN}\right)$ (see Figure 3b) were derived from the heat of the reaction ${\mathbf{\Delta }}_{\mathbf{r}}{\mathit{H}}_{\mathbf{m}}^{\mathbf{o}}\left(\mathbf{AN}\right)$ data shown in Table 3, and their deviation from the measured experimental value ${\mathbf{\Delta }}_{\mathbf{r}}{\mathit{U}}_{\mathbf{m},\mathbf{exp}}^{\mathbf{o}}\left(\mathbf{AN}\right)$ was calculated using Equation (9) for which the results are shown in Figure 3b as well.

$$\mathit{r}\mathit{e}\mathit{l}\mathit{a}\mathit{t}\mathit{i}\mathit{v}\mathit{e} \mathit{d}\mathit{e}\mathit{v}\mathit{i}\mathit{a}\mathit{t}\mathit{i}\mathbf{o}\mathit{n} / \%=100\mathbf{·}\left|\frac{{\mathbf{\Delta }}_{\mathbf{r}}{\mathit{U}}_{\mathbf{m}}^{\mathbf{o}}\left(\mathbf{AN}\right)-{\mathbf{\Delta }}_{\mathbf{r}}{\mathit{U}}_{\mathbf{m},\mathbf{exp}}^{\mathbf{o}}\left(\mathbf{AN}\right)}{{\mathbf{\Delta }}_{\mathbf{r}}{\mathit{U}}_{\mathbf{m},\mathbf{exp}}^{\mathbf{o}}\left(\mathbf{AN}\right)}\right|$$

(9)

The minimal deviation of ${\mathbf{\Delta }}_{\mathbf{r}}{\mathit{U}}_{\mathbf{m}}^{\mathbf{o}}\left(\mathbf{AN}\right)$ (calculated from Table 3) from the experimental decomposition energy ${\mathbf{\Delta }}_{\mathbf{r}}{\mathit{U}}_{\mathbf{m},\mathbf{exp}}^{\mathbf{o}}\left(\mathbf{AN}\right)$ measured by the calorimeter has been reached by the reaction path N° 2 (see Figure 3b), which was presented in Table 3 by the following reaction:

$$\mathbf{N}{\mathbf{H}}_4\mathbf{N}{\mathbf{H}}_3\to {\mathbf{N}}_2\mathbf{O}+2{\mathbf{H}}_2{\mathbf{O}}_{ }$$

(10)

Therefore, taking into account the decomposition pathways of the AN determined previously, it could be possible to adopt a certain decomposition pathway for the HNTO·AN (1:3) co-crystal as follows:

$$\{\begin{array}{c}{\mathbf{C}}_2{\mathbf{H}}_6{\mathbf{O}}_3{\mathbf{N}}_{6\left(\mathbf{s}\right)}+2{\mathbf{O}}_{2\left(\mathbf{g}\right)}\to 2\mathbf{C}{\mathbf{O}}_{2\left(\mathbf{g}\right)}+3{\mathbf{H}}_2{\mathbf{O}}_{\left(\mathbf{l}\right)}+3{\mathbf{N}}_{2\left(\mathbf{g}\right)}\\ \mathbf{N}{\mathbf{H}}_4\mathbf{N}{\mathbf{O}}_{3\left(\mathbf{s}\right)}\to {\mathbf{N}}_2{\mathbf{O}}_{\left(\mathbf{g}\right)}+2{\mathbf{H}}_2{\mathbf{O}}_{\left(\mathbf{l}\right)}\end{array}$$

(11)

$${\left[{\mathbf{C}}_2{\mathbf{H}}_6{\mathbf{O}}_3{\mathbf{N}}_6+3\mathbf{N}{\mathbf{H}}_4\mathbf{N}{\mathbf{O}}_3\right]}_{\left(\mathbf{s}\right)}+2{\mathbf{O}}_{2\left(\mathbf{g}\right)}\to 3{\mathbf{N}}_2{\mathbf{O}}_{\left(\mathbf{g}\right)}+2\mathbf{C}{\mathbf{O}}_{2\left(\mathbf{g}\right)}+9{\mathbf{H}}_2{\mathbf{O}}_{\left(\mathbf{l}\right)}+3{\mathbf{N}}_{2\left(\mathbf{g}\right)}$$

(12)

Thus, using the Hess thermodynamical cycle, it is possible to determine the formation enthalpy of the co-crystal using the reaction path of Equations (11) and (12) and the combustion energy of the co-crystal that was measured by the bomb calorimeter. However, the combustion test performed in the calorimeter showed that the HNTO·AN co-crystal observed an incomplete ignition because of the presence of AN, as explained above, which required the use of the BA as a combustion aid additive. Therefore, a similar methodology to that used to determine the decomposition energy of AN has been employed in order to obtain the energy of combustion of the HNTO·AN co-crystal. The combustion of solid composites consisting of varying weight fractions of benzoic acid (30 wt.% to 70 wt.%) and HNTO·AN co-crystal has been performed in the bomb calorimeter and the combustion energy ${\mathbf{\Delta }}_{\mathbf{c}}\mathit{U}$ has been accordingly recorded and its variation with the benzoic acid weight fraction is plotted in Figure 2a.

Comparable to the AN-BA composite, the combustion energy of the HNTO·AN-BA composite also exhibits a strong linear evolution with the weight fraction of the benzoic acid. A linear fitting of the experimental combustion energy ${\mathbf{\Delta }}_{\mathbf{c}}\mathit{U}$ data has been performed and the fitting parameters are summarized in Table 4. Thus, an extrapolation of the linear fitting curve to x_BA = 0 (absence of BA) permits to obtain the combustion energy of the HNTO·AN co-crystal ${\mathbf{\Delta }}_{\mathbf{c}}{\mathit{U}}_{\mathbf{m},\mathbf{exp}}^{\mathbf{o}}\left(\mathbf{HNTO}·\mathbf{AN}\right)$ = (−2608 ± 13) kJ·mol⁻¹.

Thereby, we calculated the molar formation enthalpy of the HNTO·AN co-crystal at 298.15 K, considering the heat of formation of the combustion products (carbon dioxide ${\Delta }_{\mathrm{f}}{H}_{\mathrm{m}}^{\mathrm{o}}\left({\mathrm{CO}}_2,\mathrm{g}\right)$ = (−393.5 ± 0.13) kJ·mol⁻¹, water ${\Delta }_{\mathrm{f}}{H}_{\mathrm{m}}^{\mathrm{o}}\left({\mathrm{H}}_2\mathrm{O},\mathrm{l}\right)$ = (−285.83 ± 0.04) kJ·mol⁻¹, and nitrous oxide ${\Delta }_{\mathrm{f}}{H}_{\mathrm{m}}^{\mathrm{o}}\left({\mathrm{N}}_2\mathrm{O},\mathrm{g}\right)$ = 82.05 kJ·mol⁻¹ [47], and the obtained molar formation enthalpy of HNTO·AN corresponds to ${\Delta }_{\mathrm{f}}{H}_{\mathrm{m}}^{\mathrm{o}}\left(\mathrm{HNTO}·\mathrm{AN},\mathrm{cr}\right)$ = (−505 ± 13) kJ·mol⁻¹. The approach for estimating the thermodynamic molar formation enthalpy of HNTO·AN co-crystal used in this study is dependent on the assumption that the thermal decomposition of AN follows just a single reaction mechanism and that this reaction pathway is not influenced by the co-crystallization process and remains unchanged during the decomposition of the co-crystal.

It is worth mentioning that the formation enthalpy of the HNTO·AN co-crystal is quite different from that of the solid mixture (calculated as ${\mathit{x}}_{\mathbf{AN}}{\mathbf{\Delta }}_{\mathbf{f}}{\mathit{H}}_{\mathbf{m}}^{\mathbf{o}}\left(\mathbf{AN},\mathbf{cr}\right)+{\mathit{x}}_{\mathbf{HNTO}}{\mathbf{\Delta }}_{\mathbf{f}}{\mathit{H}}_{\mathbf{m}}^{\mathbf{o}}\left(\mathbf{HNTO},\mathbf{cr}\right)$), which highlights the difference between the co-crystal and the solid mixture. In addition, the obtained formation enthalpy of the HNTO·AN co-crystal is found to be lower than that of its co-formers ${\mathbf{\Delta }}_{\mathbf{f}}{\mathit{H}}_{\mathbf{m}}^{\mathbf{o}}\left(\mathbf{AN},\mathbf{cr}\right)=$ −365.6 kJ·mol⁻¹ [46], ${\mathbf{\Delta }}_{\mathbf{f}}{\mathit{H}}_{\mathbf{m}}^{\mathbf{o}}\left(\mathbf{HNTO},\mathbf{cr}\right)$ = (−231.4 ± 1.4) kJ·mol⁻¹, revealing that the obtained co-crystal is chemically more stable than its co-formers.

4. Conclusions

In the present study, the heat capacities of energetic HNTO and its co-crystal HNTO·AN were measured using differential scanning calorimetry. The heat capacity equations of the two energetic compounds are found to be ${\mathit{C}}_{\mathbf{p}}\left(\mathit{T}\right)$/J·g⁻¹·K⁻¹ = $0.27562 \left(\mathit{T} / \mathit{K}\right)+0.00303$ and ${\mathit{C}}_{\mathbf{p}}\left(\mathit{T}\right)$/J·g⁻¹·K⁻¹ = $0.12112 \left(\mathit{T} / \mathit{K}\right)+0.00466$ for HNTO and HNTO·AN co-crystal, respectively, within a temperature range of 213.15 K to 378.15 K. Based on the heat capacity data, the enthalpy change, the entropy change and the Gibbs energy change of HNTO and HNTO·AN are also determined, taking 298.15 K as the benchmark temperature. The measurements of the combustion energies of HNTO and HNTO·AN cocrystal in conjunction with the application of the Hess thermodynamic cycle enable their heats of formation to be determined. The thermodynamic results obtained can provide valuable information for further thermochemical calculations involving these energetic materials. All the obtained results will certainly be utilized as input parameters for the prediction of the detonation and combustion parameters of HNTO and HNTO·AN and will also help to design future propellant formulations with optimized performances based on these two nitrogen-rich oxidizers.