Journal of Chemistry

Volume 2015, Article ID 158794, 12 pages

http://dx.doi.org/10.1155/2015/158794

## Significance of Theoretical Decomposition Enthalpies for Predicting Thermal Hazards

CEA, DAM, Le Ripault, 37260 Monts, France

Received 24 March 2015; Accepted 21 May 2015

Academic Editor: Robert Zaleśny

Copyright © 2015 Didier Mathieu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Much effort is currently put into the development of models for predicting decomposition enthalpies measured using differential scanning calorimetry (DSC). As an alternative to the purely empirical schemes reported so far, this work relies on theoretical values obtained on the basis of simple assumptions. For nitroaromatic compounds (NACs) studied in sealed sample cells, our approach proves clearly superior to previous ones. In contrast, it correlates poorly with data measured in pin-hole sample cells. Progress might be obtained through a combination of the present approach with the usual Quantitative Structure-Property Relationships (QSPR) methodologies. This work emphasizes the significance of the theoretical decomposition enthalpy as a fundamental descriptor for the prediction of DSC values. In fact, the theoretical value provides a valuable criterion to characterize thermal hazards, as a complement to experimental decomposition temperatures.

#### 1. Introduction

In view of the increasingly large number of compounds to be considered in process design or in the context of recent regulatory frameworks, there is currently much interest in the numerical estimation of thermal hazards prior to any experiment [1]. Such hazards are classified and predicted on the basis of several criteria [2], including exothermic onset temperatures () and decomposition enthalpies derived from differential scanning calorimetry (DSC) experiments [3–5]. The latter property, hereafter denoted by and defined as positive, is a preliminary to any assessment of thermal risks. It is a relatively simple property which may be loosely defined as the opposite of the enthalpy change associated with the decomposition of the compound studied into products. Assuming that this process yields the most stable products consistent with the stoichiometry of the system, we obtain an ideal value that can be identified with the energy content of the material.

The difference between and is determined by highly complex processes, including multiple reaction pathways, secondary reactions possibly involving the surroundings of the sample, and heat and mass transport processes within the cell. A first-principles approach to this difference is therefore out of reach, considering the computational cost inherent to ab initio molecular dynamics and the fact that reactive potentials, which could provide a more efficient alternative, are still in their infancy [6]. Therefore, some empiricism is unavoidable when it comes to predicting DSC data, and Quantitative Structure-Property Relationships (QSPR) methodologies appear as a natural approach to estimate in this context.

Although they do rely on such techniques, presently published models apply them directly to the evaluation of in terms of standard descriptors [7–15]. As a result, they do not take advantage of the availability of simple rules to estimate decomposition products and corresponding values [16]. While QSPR approaches prove extremely useful in the lack of quantitative theories, especially for complex properties in the fields of pharmaceutical chemistry, toxicology, or risk assessment, they are some reasons to believe that their direct application to is unlikely to provide the most reliable predictive tools.

First, QSPR descriptors are calculated on the unreacted compound, while also depends on the decomposition products and possibly on some features of the reaction pathways. Secondly, obviously depends on the formation enthalpy of the compound studied. Since a reliable evaluation of this property for arbitrary compounds requires quantum chemical computations, QSPR models are unlikely to provide accurate values for a wide range of compounds.

Finally, an even more significant obstacle to the application of QSPR techniques to estimate is the lack of consistent data. The routine application of DSC to thermal hazard evaluation yields decomposition enthalpies with experimental uncertainties around 10% [4]. However, a more significant variability is observed in practice due to the details of the experimental setup, including the temperature scanning rate, the materials of the device, or the kind of sample cell. For instance, on going from a sealed [3] to a pin-hole [4] sample cell, the measured decomposition enthalpies decrease from 345 to 123 kJ/mol for 2-nitrophenol, from 284 to 130 kJ/mol for 1-methyl-3-nitrobenzene, and from 339 to 161 kJ/mol for nitrobenzene. The relative scarsity of homogeneous data sets makes the parametrization and validation of QSPR models very difficult and prevents the introduction of many empirical parameters that might be necessary for reliable predictions of along such lines.

In fact, a growing body of work demonstrates the interest of more physically grounded and/or less empirical strategies to estimate the physical properties of organic substances [17–25], including complex properties characterizing reactive hazards such as flash point temperatures [23], flammability limit temperatures [24], or mechanical sensitivities of explosives [25]. Taking advantage of theoretical values, the present work investigates a semiempirical approach to the evaluation of for nitroaromatic compounds (NACs), as an alternative to the straightforward application of QSPR techniques. More specifically, two predictive equations are put forward. The first one simply assumes that can be reasonably approximated as a constant fraction of the energy content , while the second one attempts to describe how this fraction depends on the reactivity of the compound.

#### 2. Theory

In a first step, the present approach involves only simple thermodynamic considerations. In a second step, density functional theory (DFT) concepts are invoked in an attempt to introduce kinetic factors. Because primarily reflects the heat released as the sample decomposes, the energy content of the substance should provide a major contribution to measured DSC values. The difference between both quantities may be further decomposed into three correction terms accounting, respectively:(1)for the fact that the equilibrium products relevant to the thermodynamic conditions in the sample cell may differ from the most stable ones in standard conditions ();(2)for the fact that kinetics may affect the actual composition of the products ();(3)for energy losses associated with heat and matter transport processes ():While may be estimated on the basis of standard approximations, there is no simple way to calculate the three terms on the r.h.s. of this equation. Therefore, we follow a simpler approach, assuming in a first step that each correction represents a given fraction of . As a result,where is a constant that does not depend on the compound under consideration. An advantage of this approach is that it automatically ensures the condition .

Going one step further, we are faced with the challenge to estimate how depends on the compound under study. Among many factors that are likely to affect the value of this ratio, reactivity might be the one whose role is easiest to describe at least qualitatively. Indeed, a complete decomposition requires that the products be slowly cooled down to the ambient temperature. Such complete decomposition is especially unlikely for materials that remain chemically unaffected up to high temperatures. As temperature increases, the system can explore a larger fraction of the potential energy surface (PES) and is thus more likely to get stuck in metastable configurations during cooling. Therefore, the amount of energy eventually released in decomposition processes depends on the energy barriers .

In the lack of detailed knowledge of reaction pathways, we have to be satisfied with the features of the initial and final states to evaluate the role of . On the products side, the Bell-Evans-Polanyi principle [26] suggests that is likely to get lower as increases. This principle is frequently invoked to correlate reaction properties with a difference between reactants and products, especially in the field of high energy compounds [27]. Nevertheless, it is not sufficient to quantitatively estimate energy barriers, as reflected by the lack of correlation between decomposition enthalpies and decomposition temperatures [4].

Some improvement might be obtained by taking advantage of reactant features. In particular, bond dissociation energies (BDEs) appear to be ideal descriptors in view of evaluating [28]. However, they may be tedious to compute, requiring the optimization of complex open-shell species if large molecules are considered. An attractive alternative is provided by reactivity descriptors at the basis of conceptual DFT [29], namely, electronegativity () and chemical hardness (). In fact, an early attempt to predict DSC measurements from empirical relationships already assumed that those quantities play a primary role [8].

In the present work, the reactivity descriptors are introduced with the help of dimensionality considerations. The simplest dimensionless quantity that may be defined on the basis of and is their ratio , where is implicitly multiplied by the electron charge in atomic units. Therefore, assuming that depends on and , it should then be expandable as a power series:Since the principle of maximum hardness implies that is a measure of the stability of the system [29], is expected to decrease as increases, with the limit of large values corresponding to an increasing resistance of the molecule to changes in its electronic structure, hence to energy release. This implies that since the linear term is predominant for large values of . On the other hand, setting is required if we want the energy released to decrease to zero in the hypothetical limit of an infinitely stable system with . This suggests a possibly improved alternative to (2):In what follows, both (2) and (4) are considered to predict . Given many factors that may affect measured values, depending on the detailed experimental setup, associated with the approximate character of conceptual DFT inherent to the fact that it attempts to describe reactivity in term of features of the unreacted compound, it is not a priori obvious to decide which equation will prove most reliable.

An attractive feature of present models is the fact that they depend on a single input variable , where if a constant fraction of the energy content is assumed to contribute to measured DSC data as in (2), or if this fraction is assumed to depend linearly on as in (4). As a consequence, their performances may be straightforwardly estimated, for instance, graphically from the plot of versus , or by considering the determination coefficient between both quantities. This is especially gratifying in view of the scarcity of homogeneous data, which make it awkward to define statistically significant external test sets for multiparameters models.

#### 3. Computational Details

In this work, the decomposition products are obtained on the basis of a simple generalization to halogenated compounds of the well-known H_{2}O-CO_{2} arbitrary initially introduced to estimate the heats of detonation of C–H–N–O explosives [30]. More specifically, decomposition products are obtained according to the following priority order: HF > CF_{4} > H_{2}O > CO_{2} > CCl_{4} > CO > HCl. If necessary, the remaining elements are converted into graphite, H_{2}, N_{2}, S_{8}, O_{2}, F_{2}, and Cl_{2}. In practice, the last three products are never obtained for the present data set because of the relative scarcity of O, F, and Cl atoms in present NACs.

The energy content is then obtained as the difference between the formation enthalpy of the substance under study and corresponding values for the decomposition products . The latter are taken from the NIST Webbook database [31]. Because experimental values of are missing for most NACs under study, theoretical values computed using the semiempirical RM1 Hamiltonian are used. This method is chosen for its relatively good performance and computational efficiency [32].

For (4), values of and are obtained within the finite difference approach by simple difference and as an average of the ionization potential () and electronegativity ():IP and EA are derived from the energies and of the highest occupied and lowest unoccupied molecular orbitals, obtained simply as a by-product of the RM1 computations. More specifically, and [29]. All RM1 calculations are carried out using the MOPAC7 program [33].

Typical errors associated with RM1 formation enthalpies are about 20 kJ/mol [32] while experimental uncertainties may cause much larger errors (>100 kJ/mol). Therefore, no significant improvement is expected from the use of more accurate procedures. Larger theoretical uncertainties might possibly arise from the use of the RM1 orbitals to obtain the reactivity descriptors. Therefore, we have also investigated in unpublished work the use of enthalpies and orbital energies derived from PBE0/6-31+G(d,p)//AM1 calculations combined with simple atom equivalent schemes [34]. It turned out that this higher theoretical level does not provide any significant improvement with respect to RM1-based procedures. Because RM1 calculations are much easier to carry out routinely in an industrial context, only the results obtained on this basis are presented in the sequel.

Similarly, we investigated the effect of taking into account the contribution of intermolecular interactions to despite the introduction of sublimation enthalpies calculated on the basis of simple models [35, 36]. Again, this does not significantly affect the results, as expected from the relatively small magnitude of sublimation enthalpies. Moreover, this approach is not rigorous as the compounds studied typically melt before undergoing a decomposition. Therefore, it is better to ignore the intermolecular contribution to until a more satisfactory approach is developed.

On the other hand, as an alternative to the above-mentioned decomposition rules assuming a complete oxidation of hydrogen and carbon into CO_{2} whenever possible, the use of the Kistiakowsky-Wilson rules (applying the modified version for compounds with CO_{2} oxygen balance <−40%) was also considered [16]. These rules favor the formation of CO over CO_{2}. This change has a more significant impact on the individual results than going from RM1 to PBE0 electronic structures or introducing sublimation enthalpies. Nevertheless, the overall performance of the models is not significantly affected. Therefore, only the results based on the generalized H_{2}O-CO_{2} arbitrary are presented in this work. In the lack of significantly better rules, this is the most attractive option, implying that the effect of any incomplete oxidation is implicitly taken into account through the values of the empirical parameters.

#### 4. Data Sets

Recent studies aimed at predicting decomposition enthalpies of NACs as measured by DSC focus on two data sets. The first one is a set of 22 enthalpies measured using a standard aluminium sealed sample cell (SC data) [3]. The second one is a set of 77 enthalpies measured in aluminium sample cells with a pin-hole on the lid (PH data) [4]. Technical details regarding these sample cells may be found in references cited in these earlier publications [3, 4]. Most modeling studies focus on the SC data set [8–12]. Only very recent ones take advantage of the PH data set [13, 15]. Both SC and PH data sets are considered in the present work. They provide 99 experimental decomposition enthalpies for 84 compounds, because some molecules have been studied using both kinds of sample cells and are thus present in the two sets.

#### 5. Results

##### 5.1. Observed versus Theoretical Enthalpies

Figure 1 compares experimental data with theoretical values . Because the kind of sample cell is likely to influence the measured enthalpies, SC and PH data are shown using different colors. Furthermore, for the analysis of the 77 PH values at hand, the 35 compounds with substituents in ortho position with respect to nitro groups (ortho compounds) are treated separately, assuming that the associated values might prove more difficult to rationalize than corresponding data for the remaining 42 compounds deprived of ortho substituents (nonortho compounds). This assumption is motivated by the possible role of interactions between nitro groups and corresponding ortho substituents. This partition of the data set between nonortho/ortho compounds was introduced in a previous study [13].