Predicting Temperature-Dependent Solid Vapor Pressures of

Figure 5 shows results for TATB, RDX, and HMX, all military explosives with very low volatility. Results for all three compounds are substantially imp...
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Predicting Temperature-Dependent Solid Vapor Pressures of Explosives and Related Compounds Using a Quantum Mechanical Continuum Solvation Model Sufian Alnemrat and Joseph P. Hooper* Department of Physics, Naval Postgraduate School, Monterey, California 93943, United States S Supporting Information *

ABSTRACT: Temperature-dependent vapor pressures of solid explosives and their byproducts are calculated to an accuracy of 0.32 log units using a modified form of the conductor-like screening model for real solvents (COSMO-RS). Accurate predictions for solids within COSMO-RS require correction for the free energy of fusion as well as other effects such as van der Waals interactions. Limited experimental data on explosives is available to determine these corrections, and thus we have extended the COSMO-RS model by introducing a quantitative structure−property relationship to estimate a lumped correction factor using only information from standard quantum chemistry calculations. This modification improves the COSMO-RS estimate of ambient vapor pressure by more than 1 order of magnitude for a range of nitrogen-rich explosives and their derivatives, bringing the theoretical predictions to within typical experimental error bars for vapor pressure measurements. The estimated temperature dependence of these vapor pressures also agrees well with available experimental data, which is particularly important for estimating environmental transport and gas evolution for buried explosives or environmentally contaminated locations. This technique is then used to predict vapor pressures for a number of explosives and degradation products for which experimental data is not readily available.

1. INTRODUCTION Nitroaromatic and nitramine compounds such as 2,4,6trinitrotoluene (TNT) and cyclotrimethylene-trinitramine (RDX) are widely used as explosive materials.1−6 The chemical decomposition and environmental transport of these explosives is critical for understanding their toxicological properties as well as for detection of landmines and roadside bombs. While certain compounds such as TNT and composition B (a meltcast mixture of TNT and RDX) have received considerable attention, for many explosives and their byproducts there are still large gaps in known environmental properties.7−18 Vapor pressure in particular is important for a variety of applications, ranging from understanding gas evolution around buried unexploded ordnance to remote detection of improvised explosive devices. The vapor pressure is typically quite low for most explosives, and frequently only parts per billion or trillion of a vapor-phase species may be found around a device.19−36 The variation in vapor pressure with temperature is thus important to consider as well, as relatively small changes in concentration can have important consequences for trace detection. In addition, explosives in the environment undergo a range of complex decomposition processes that affect environmental transport and detection algorithms. A common example is TNT, where the impurity 2,4-dinitrotoluene is often easier to detect due to its high vapor pressure, despite being only a small impurity in the bulk explosive.37−39 © 2013 American Chemical Society

In this work we consider a computational method for accurate prediction of temperature-dependent solid vapor pressures of explosives and similar compounds. Theoretical solvation models are now widely used to estimate physical, chemical, and thermodynamic properties of solutions and mixtures as a function of temperature and pressure. Group additivity methods such as UNIFAC provide accurate results for many environmentally relevant compounds based on large empirical databases but have questionable validity when treating new compounds such as homemade explosives and their degradation products.40−45 Although these models provide successful predictions of many transport properties, their treatment of the electrostatic interactions between solutes and solvents can result in large inaccuracies for polar compounds (including many explosives). Accurate calculations of polarizabilites and dispersion forces in solute−solvent mixtures are very important in order to provide accurate thermodynamic descriptions of these systems. Another limitation of these models that can lead to poor descriptor properties is the inability to handle the dynamic nature of solute−solvent mixtures. Many dynamic properties such as diffusion and some properties such as density are poorly predicted.46,47 Received: January 6, 2013 Revised: February 8, 2013 Published: February 11, 2013 2035

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charges to then construct a statistical thermodynamics theory of interacting screening surface charges between solute and solvent molecules in a liquid. The solute screening cavity is broken into discrete segments, each with their own specific surface area and a screening charge σ. Liquids are treated by considering an ensemble of these closely packed molecular screening surfaces. Each piece of the molecular surface with surface charge σ is in close contact with another of surface charge σ′. The electrostatic interaction between these two surface charge densities, referred to as the misfit energy, is given by α Emisfit = (σ + σ ′)2 (1) 2

The COSMO-RS model, introduced by Klamt and since expanded significantly, takes a rather different approach to the prediction of solvent and mixture properties such as vapor pressure, Henry’s constant, and partition coefficients.44,45,48−57 The method, discussed in more detail below, has been successfully applied to many liquid/liquid and vapor/liquid systems in chemical equilibrium with reasonable accuracy. For liquid vapor pressures, it requires molecular-specific information from a standard quantum chemistry calculation as well as a series of fit parameters that are kept fixed for all chemical compounds, such as van der Waals (vdW) coefficients and a dielectric scaling factor. Prediction of solid vapor pressures, the key quantity for most applications, is complicated by the need to account for the free energy of fusion (ΔGfus) of solid compounds as well as other discrepancies such as nonideal effects in the gas phase. These corrections can alter the COSMO-RS predictions by several orders of magnitude, and sufficient experimental data to estimate these individual terms is not generally available for explosives. Previous work by Kholod et al. used the COSMO-RS method to predict the water solubility of several explosive compounds at room temperature and addressed these issues by incorporating a quantitative structure−property relationship (QSPR) correction for ΔGfus.58 COSMO-RS is already quite accurate for solubility calculations, and we found that incorporating their corrections did not provide appropriate results for solid vapor pressures; further discussion on this point is given below. Qasim et al. examined the vapor pressure of TNT and a few related compounds at ambient temperature using COSMO-RS; they showed a promising improvement in the vapor pressure predictions by adding a QSPR-based correction term ΔGfus but gave no details of how this correction was calculated.13 Several other empirical and semiempirical methods have been developed to estimate solid vapor pressures, including corresponding state theory, a variety of group additivity methods, solvation free energy models, and quantitative structure−property relationships.59−63 Due to experimental difficulties in measuring explosives and related compounds, it is highly desirable to have a method that can predict solid vapor pressures using only information from quantum mechanical simulations. In this work we use known solid vapor pressures for explosives at ambient temperature to develop a QSPR for the free energy of fusion correction. The QSPR requires only quantities derived from quantum chemistry calculations and the structural topology of the explosive or byproduct molecule. These corrections bring COSMO-RS predictions of solid explosive vapor pressure to an accuracy of 0.32 log units (LU), comparable to the experimental uncertainty in many vapor pressure measurements. In addition, the estimated temperature dependence of the vapor pressure shows good agreement with available experimental data for several high explosives. Finally, we use this technique to estimate the vapor pressures of a number of explosives and byproducts which, to our knowledge, have not been experimentally measured.

where α is an adjustable parameter and includes a scaling function to account for the finite dielectric constant of the medium. This scaling function is kept constant for all chemical systems and may introduce some error for solvents with low dielectric constant.64 Hydrogen bonding (HB) is also included within the model and can also be described by an interaction between adjacent surface charges. When polar pieces of surfaces with opposite charges are in contact, the HB energy is given by 2 E HB(σ , σ ′) = aeff C hb min(σσ ′ + σhb , 0)

(2)

where σhb and Chb are adjustable parameters. The final contribution to the total interaction energy of two adjacent segments is the vdW interaction energy which is given by E VdW (x , x′) = aeff (τ(x) + τ′(x′))

(3)

where x and x′ stand for atom types and τ and τ′ are adjustable element-specific parameters proportional to the energy of the vdW surface of each element. All interaction energies in the COSMO-RS model consist of local pairwise interactions between screening surface segments, and the extension from the molecular level to macroscopic liquid properties is made by considering an ensemble of these interacting surface pieces. A probability distribution of the surface charge densities pX(σ), referred to as a “σ-profile”, is introduced for all compounds Xi in a liquid mixture. The pseudochemical potential of a solute X in solvent S is given as a statistical average over this distribution μSX =

∫ μs(σ )pX (σ ) dσ + μsize

(4)

where μsize is a size correction term that depends on the size of solute and solvent molecules. The term μs(σ) is called the σpotential and can be calculated as ⎧ ⎪ μs (σ ) = −RT ln⎨ ⎪ ⎩

∫

⎫ ⎪ ⎬ dσ ′⎪ ⎭

⎡⎛ μ (σ ′) − E(σ , σ ′) ⎞⎤ ⎟⎥ ps (σ ′) exp⎢⎜ s ⎢⎣⎝ RT ⎠⎦⎥

(5)

The term E(σ, σ′) is the sum of misfit and hydrogen-bonding energies. Figure 1 below shows example σ-profiles for tetranitromethane (TNM), TNT, and RDX. TNT and RDX both have dominant features at positive and negative values; note that charges on the molecule will result in screening charges with the opposite sign. The peaks at positive σ correspond to the electronegative nitro groups (a red color in the σ-profile), while peaks at negative σ (blue colors) correspond to ring carbons or the electron-donating methyl

2. THEORETICAL METHODOLOGY 2.1. COSMO-RS Method. In this section we briefly discuss the COSMO-RS model and the modified vapor pressure calculations for solid explosives. The COSMO-RS method extends the COSMO continuum solvation model, which places a solute molecule inside a screening cavity and embeds this within an ideal conductor representing the solvent. COSMORS uses the same molecular cavity and its ideal screening 2036

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COSMO surface parameters were computed at the same level of theory using optimized geometries of explosives and their byproducts. The COSMOtherm program (version C30_1201) was used to calculate chemical potentials and interaction energies from the quantum chemistry results. 2.2. Vapor Pressures. COSMO-RS is properly a theory for liquids, and, for temperatures below a compound’s melting point, it computes the properties of a supercooled disordered liquid. COSMO-RS allows for the estimation of pure compound vapor pressures by calculating the chemical potentials and energies in the gas and liquid phases. The vapor pressure can then be computed from these chemical potentials using the relation ⎛ μ liquid − μgas − max(0, ΔGfus) ⎞ ⎟ Pv(T ) = P0 exp⎜ RT ⎠ ⎝ Figure 1. σ-profiles of TNM (dash-dot blue line), RDX (solid black line), and TNT (dotted red line).

(6)

where P0 is 1 mbar. Both chemical potentials are also temperature-dependent, and the resulting vapor pressure is in mbars. The liquid chemical potential is given by eq 5, and the gas-phase chemical potential is given as68

group. The σ-profile for TNM differs from those of TNT and RDX and is dominated by the strong positive σ-feature from the four nitro groups. The σ-potential can be directly calculated from standard quantum chemistry simulations and serves as the basis for estimating a wide range of thermodynamic properties of liquids and mixtures. All calculations in this work were performed using Turbomole with the Becke−Perdew (BP) functional65,66 and triple-ζ valence and polarization (TZVP) basis sets for all atoms.67 The ideal screening charge densities (σ) and the

X μgas = −ΔX −

∑ γkAkX − ωNRX − ηRT

(7)

k

where ΔX is the ideal electrostatic screening energy of solute X, the index k refers to different elements in solute X, Ak is the surface area of each element k in molecule X, and NR is the number of ring atoms in ring molecule X. A complete

Table 1. Correction Factors (ΔGfus), Vapor Pressures Computed Using Unmodified COSMO-RS, Modified Vapor Pressures with ΔGfus, and Experimental Vapor Pressures of Explosive Compounds at 25 °Ca explosive 2,4-DNT 2,6-DNT NB(l) DNB TNB β-HMX

chemical name

NQ TATP

2,4-dinitrotoluene 2,6-dinitrotoluene nitrobenzene dinitrobenzene 1,3,5-trinitrobenzene cyclotetramethylenetetranitramine cyclotrimethylenetrinitramine 1,3,5-triamino- 2,4,6trinitrobenzene 2-nitrotoluene 3-nitrotoluene 4-nitrotoluene 2,4,6-trinitroaniline 2,4,6-trinitrotoluene 2,4,6-trinitrophenylmethylnitramine pentaerythritol tetranitrate nitroguanidine triacetone triperoxide

DADP EGDN(l) NG(l)

diacetone diperoxide ethyleneglycol dinitrate nitroglycerin

RDX TATB 2-NT(l) 3-NT(l) 4-NT TNA TNT Tetryl PETN

CAS no.

ΔGfus (kcal/mol)

log(Pv)COSMO (mbar)

log(Pv)QSPR (mbar)

log(Pv)exp (mbar)b

error |log(Pv)QSPR − log(Pv)exp|

error |log(Pv)COSMO − log(Pv)exp|

121-14-2 606-20-2 98-95-3 99-65-0 99-35-4 2691-41-0

2.613 2.615 0.454 2.360 3.960 8.615

−2.092 −1.824 −0.082 −1.793 −2.869 −10.53

−4.034 −3.770 −0.428 −3.552 −5.804 −14.068

−3.455 −3.083 −0.485c −4.222c −5.066c −14.965

0.580 0.680 0.057 0.668 0.734 0.897

1.363 1.259 0.617 2.429 2.197 4.435

121-82-4

5.137

−3.335

−7.874

−8.356

0.516

5.022

3058-38-6

7.854

−9.390

−15.215

−14.606

0.610

5.216

88-72-2 99-08-1 99-99-0 489-98-5 118-96-7 479-45-8

0.650 0.668 0.837 4.531 4.203 6.531

−0.291 −0.525 −0.678 −4.156 −2.952 −4.887

−0.781 −1.030 −1.310 −7.520 −5.698 −9.051

−0.717 −0.714d −1.186 −7.170e −5.135 −8.061

0.064 0.316 0.124 0.350 0.563 0.990

0.426 0.189 0.508 3.014 2.183 3.174

78-11-5

6.506

−3.754

−8.566

−7.810

0.756

4.056

113-00-8 17088-37 -8 1073-91-2 628-96-6 55-63-0

5.593 1.400

−7.891 −2.786

−12.050 −1.447

−11.663 −1.208

0.387 0.240

3.772 1.578

1.031 2.284 4.098

−0.275 0.894 −0.752

−1.050 −0.790 −3.781

−0.751 −0.993 −3.193

0.299 0.203 0.588

0.476 1.887 2.441

a

Compounds denoted with (l) are liquids at ambient conditions. All logarithms are base 10. bExperimental data from critical review by Ostmark et al.69 cExperimental data from critical review by HSDB. dExperimental data from critical review by Stull72 and Aim.73 eExperimental data from critical review by Rosen et al.62,74 2037

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deviation is achieved by incorporating the vapor pressure correction, compared to 1.57 LU accuracy from direct COSMO-RS calculations (which we again note are for a supercooled liquid). The list in Table 1 covers a range of different classes of explosives, including nitroaromatics, nitramines, nitrate esters, and homemade explosives such as DADP and TATP. For several important explosives such as PETN, RDX, and HMX, there is a large improvement of approximately 4 log units for the solid-state vapor pressure. In addition to the tabulated data, we have fit all compounds discussed in this work to the Antoine equation

discussion of the gas-phase chemical potential can be found in ref 68, which uses the same notation. The final term in the numerator of eq 6, which is zero for liquids, accounts for the free energy of fusion if available. Here we develop a QSPR to estimate this term based on a comparison of the experimental vapor pressures at a specific reference pressure/temperature and the liquid-phase COSMORS value at the same conditions. The discrepancy between these is used to estimate the correction factor ΔGfus, though we note again that other corrections (such as the nonideality of the explosive gases, errors in van der Waals parameters and dielectric scaling factor, and others) may be incorporated into this term and not simply the free energy of fusion alone. As we discuss below, these other correction factors may be playing a larger role than expected in COSMO-RS predictions of explosives and their byproducts. Experimental data on solid explosive vapor pressures have often shown significant variation and disagreement between methods of collection; a recent critical review by Ostmark and co-workers discusses these complications in detail and summarizes the most reliable data.69 For our work, the temperature-dependent vapor pressures of 20 solid explosives and byproducts were drawn from a number of experimental studies and used to create a QSPR molecular descriptor based on molecular volume, molecular flexibility, and the chemical potentials of the explosive compounds in the gas and liquid state. Similar descriptors were also used by Klamt and coauthors to treat the solubility of solid-phase drugs and pesticides, though their specific parameters from these studies were found to be unsuitable for explosive materials.70,71 The general regression equation for the free energy of fusion correction factor for explosive compounds used in our work is given by ΔGfus = 19.45V + 0.34μgas + 0.34μ liquid − 0.29N

log10(PFv) = A −

B C+T

(9)

where the vapor pressure is in mbar and the temperature T is in kelvin. These A, B, and C parameters are given in the Supporting Information and allow analytic evaluation of the QSPR-modified calculated vapor pressure curves of all explosives considered here. We next consider the temperature dependence of the vapor pressure, which is a key issue for many applications as discussed above. As we are mainly interested in vapor detection well below the melting point of most explosives, we initially consider the free energy of fusion to be temperature-independent, but we retain the temperature-dependent terms in the chemical potentials and vapor pressure equations. The temperature dependence of the free energy could in principle be estimated from the enthalpy of fusion and the melting point, but for compounds with limited experimental data this would most likely require additional QSPR-type estimates for the relevant enthalpies and melting point. As discussed below, it appears this is not necessary for temperatures of interest to explosives detection and environmental contamination; a constant ΔGfus correction in the COSMO-RS model provides a very good estimate for the temperature dependence of Pv. Figure 2 shows a detailed comparison of experimental vapor pressure calculations for 2,4,6-trinitrotoluene (TNT) against values directly from COSMO-RS and those modified with ΔGfus. A considerable number of studies have been performed on the vapor pressure of TNT, and four representative data sets

(8)

where V is the cavity volume of the solute molecule which is measured by a vdW-like surface of each element in the molecule in units of A3, the chemical potentials (in kcal/mol) are derived from COSMO-RS as discussed above and are taken at a reference temperature of 25 °C, and N is either the number of aromatic ring atoms as a measure of molecular rigidity or the number of rotatable bonds for nonaromatic systems. Rotatable bonds are defined as the number of single bonds that are noncyclic, nonterminal, and nonring bonds. Bonds attached to hydrogen or C−N amide bonds are considered nonrotatable. The above parameters in the regression equation contain the necessary information to describe explosive compounds in their crystalline phase.71

3. RESULTS AND DISCUSSION Table 1 shows experimental solid vapor pressures at ambient temperature (Pvexp) compared with the unscaled COSMO-RS values (PvCOSMO) as well as those corrected for the free energy of fusion and other factors (PvQSPR). We note that several of these compounds are liquids at ambient conditions (denoted with (l) next to the name in the table); the liquid explosives also benefit considerably from this correction factor, further evidence that much more than just the free energy of fusion is playing a role in this term. The vapor pressure calculations using the above regression equation show good agreement with experimental values at ambient temperature. An accuracy of 0.32 LU in the standard

Figure 2. Modified vapor pressure of 2,4,6-trinitrotoluene. Solid black line represents the modified vapor pressure calculations, and the dashed line represents the uncorrected COSMO-RS calculations. 2038

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are shown in this figure. The trend in the temperature dependence of the vapor pressure is predicted accurately with or without correction, but with the modification the absolute values are brought to within the experimental scatter. The maximum discrepancy is approximately 0.5 log units. Uncorrected COSMO-RS values differ from experiment by approximately 2 log units at room temperature. Figure 3 shows results for the nitrotoluenes 2-NT, 3-NT, and 4-NT, which are commonly used as taggants in explosives, as

Figure 4. Modified vapor pressure of 2,4-DNT (solid black line), 2,6DNT (dashed cyan line), and TNA (dotted green line).

Figure 5 shows results for TATB, RDX, and HMX, all military explosives with very low volatility. Results for all three

Figure 3. Modified vapor pressure of DADP (dash-dot green line), 2NT (solid black line), 3-NT (dot red line), and 4-NT (dash dark yellow line).

well as diacetone diperoxide (DADP), a homemade explosive. Representative experimental data are also presented. These compounds have a smaller number of strongly electronegative groups than most materials considered here, and the uncorrected liquid-phase values given by COSMO-RS are already accurate to within approximately 0.5 log units (note that 2-NT and 3-NT are in fact liquids at ambient conditions). Our correction improves the accuracy to approximately 0.12 LU in the case of 4-NT and 0.064 LU in the case of 2-NT, as shown in Figure 3 and Table 1. We note that even though the magnitude of the ΔGfus correction is small for these compounds (0.6−0.8 kcal/mol for the nitrotoluenes), it has a substantial effect on the magnitude of the predicted vapor pressure. The correction factor improves predictions for DADP compared to Damour’s data75 and Oxley’s 2009 data,34 though we note that this material and similar homemade explosives such as HMTD and TATP represent a challenge experimentally due to their low stability at ambient conditions.76,77 Measurements within the same group using different techniques have shown orders of magnitude differences in DADP vapor pressures; Ostmark discusses the experimental difficulties in more detail.12,34,69,78 Figure 4 shows the vapor pressure data for 2,4,6-trinitroaniline, 2,4-dinitrotoluene, and 2,6-dinitrotoluene. 2,4-DNT and 2,6-DNT are important impurities and degradation products of TNT that generally have much higher vapor pressures than the parent compound. Corrected results show an excellent match with Lenchitz’s data32 and a small error of the order of 0.5−0.6 LU close to room temperature compared to Freedman’s and Pella’s data.33,79 TNA vapor pressure predictions show excellent agreement with available data from Rosen and Dickinson74 compared to about 3 LU deviation with standard COSMO-RS calculations.

Figure 5. Modified vapor pressure of RDX (solid black line), βHMX(dashed red line), δ-HMX (dash-dot brown line), and TATB (dotted green line).

compounds are substantially improved, showing over 4 orders of magnitude better agreement with experimental data. However, as discussed by Ostmark, there are concerns with what phase is being measured in the experimental data for HMX, which has four different polymorphs. Rosen and Dickinson present data for β-HMX (the common phase at ambient conditions), but much of their data was taken above the β to δ phase transition temperature. Taylor made measurements on δ-HMX, but the data does not agree with that of Rosen. Our theoretical curve is in good agreement with these previous literature values, but we anticipate that further experimental work on the temperature-dependent vapor pressures of β and δ-HMX are necessary. We have also calculated δ-HMX separately and applied the same manner of correction for the vapor pressure; these results are shown in Figure 5 and are generally about 1 log unit lower than that of βHMX. 2039

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Supporting Information). We first consider five compounds that were not included for the fitting set but which do have limited experimental solid vapor pressure data. The COSMORS method with the QSPR correction does quite well in predicting Pv, with errors for AP, HP, HNS, NM, and IPN within about 0.5 log units. Included in the list of other compounds are a number of environmentally important amino transformation products of TNT such as 2-amino-4,6-dinitrotoluene (2-ADNT and 4ADNT) and nitroso derivatives of RDX such as hexahydro-1nitroso-3,5-dinitro-1,3,5-triazine (MNX, DNX, and TNX). The former are toxic and widespread at military locations as a result of a reduction reaction of a nitro group on the TNT ring, a rate-limiting step in TNT biodegradation. The latter set is a group of degradation products found when RDX is destabilized due to reduction reactions under anaerobic conditions. In the following figures we present the temperaturedependent vapor pressure for these compounds for comparison against future experimental measurements or for use in environmental modeling work. Figure 7 below shows the temperature-dependent curves of high-volatility compounds such as IPN and TNM, and Figure 8 shows vapor pressure predictions of compounds with very low volatility such as HNS and TACOT. Based on the results of the first part of this work, we would expect the absolute value of these vapor pressures to be accurate to better than 0.5 LU and the variation with temperature to be accurate within the entire plotted range. Finally, we consider the physical significance of the correction factor ΔGfus. Though this ostensibly represents the free energy of fusion, there are a number of reasons to believe

Figure 6. Modified vapor pressure of NB (square), DNB (circle), TNB (up triangle), tetryl (down triangle), PETN (cross), TATP (left triangle), EGDN (right triangle), NG (circle), and NQ (star) compounds.

We next use the same modified COSMO-RS method to generate temperature-dependent vapor pressures for compounds outside the test set and several chemicals that, to our knowledge, have no systematic temperature-dependent experimental vapor pressure data. Table 2 below shows a list of these compounds’ vapor pressure calculations at room temperature (coefficients for the Antoine equation are given in the

Table 2. Free Energies of Fusion (ΔGfus), Calculated Vapor Pressures, Vapor Pressure Modified with ΔGfus, and Available Experimental Vapor Pressures of Explosive Compounds at 25 °Ca explosive compd AP HP(l) HNS NM(l) IPN TNM(l) δ-HMX 2-ADNT 4-ADNT MNX DNX TNX FOX-7 TACOT CL-20 DMNB DINA PETRIN EDNA TEGDN DDNP ONC TNCB HMTD

chemical name ammonium perchlorate hydrogen peroxide hexanitrostilbene nitromethane isopropylnitrate tetranitromethane δ-cyclotetramethylene-tetranitramine 2-amino-4,6-dinitrotoluene 4-amino-2,6-dinitrotoluene hexahydro-1-nitroso-3,5-dinitro-1,3,5-triazine hexahydro-1,3-dinitroso-5-nitro-1,3,5-triazine hexahydro-1,3,5-trinitroso-1,3,5-triazine 1,1-diamino-2,2-dinitroethylene tetranitro-2,3,5,6-dibenzo-1,3a,4,6atetraazapentalene hexanitrohexaazaisowurtzitane 2,3-dimethyl-2,3-dinitrobutane diethanolnitraminedinitrate pentaerythritoltrinitrate ethylene dinitramine triethyleneglycoldinitrate 4,6-dinitro-2-diazophenol octanitrocubane 2,4,6-trinitrochlorobenzene hexamethylene triperoxidediamine

μsolvent (kcal/mol)

μgas (kcal/mol)

ΔGfus (kcal/mol)

log(Pv)QSPR (mbar)

log(Pv)exp (mbar)b

4.910 −2.021 −0.832 −0.959 −2.978 −1.254 1.194 −2.290 −2.468 −1.136 −1.276 −1.225 −0.467 −2.342

16.572 1.001 17.763 0.621 −1.977 −3.666 19.656 8.965 8.966 7.889 7.992 8.126 8.520 19.551

8.047 0.367 9.329 1.215 0.971 0.784 7.367 3.589 3.532 3.853 3.647 3.471 4.279 6.755

−10.988 0.507 −17.485 0.949 1.553 2.587 −15.950 −8.114 −8.179 −6.794 −6.816 −6.618 −6.469 −18.016

−10.400 0.453 −17.210 1.680 1.620c

1.695 −2.910 −0.888 −1.607 −0.912 −2.875 −1.648 −1.102 −2.066 −1.448

15.286 0.772 7.753 6.176 9.771 4.841 11.355 0.363 5.836 8.766

8.322 2.434 4.660 3.965 4.412 2.768 4.706 5.298 3.487 3.751

−13.075 −1.486 −6.683 −5.946 −7.553 −4.834 −9.991 −1.961 −5.355 −7.245

a c

Compounds denoted with (l) are liquids at ambient conditions. All logarithms are base 10. bExperimental data were obtained from Ostmark et al.69 IPN experimental.80 2040

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account in COSMO-RS, there is an additional systematic error when using this solvation model for vapor pressures of explosives and similar compounds. Several sources may be contributing to this; the vapor pressure expression (eq 6) ignores nonideal effects in the gas, although this error should be small for solids with very low vapor pressures. The gas-phase chemical potential in COSMO-RS is a semiempirical term that is not based on a rigorous derivation like the liquid chemical potential in the theory. The system is also very sensitive to the van der Waals coefficients, which are a series of atom-specific parameters in COSMO-RS; we found that small changes in the vdW parameters for oxygen, for example, had a large effect on the vapor pressure of explosives. The COSMO-RS vdW energy is generally much larger for these explosive compounds than the hydrogen-bonding or misfit energies, and it is very possible that this may be the origin of this additional systematic error. Experimental data is not available to directly validate this vdW energy, however, and even comparisons with ab initio estimates would be challenging for explosives in the liquid phase. There is also the issue of the dielectric scaling factor used in the misfit energy, which contains a fit parameter that previous work has suggested is important for low-polarity solvents.64 Many of the solid explosives here (RDX, HMX, PETN, TNT, etc) have dielectric constants between 2.7 and 3.2 (ref 81), and thus a further exploration of this factor for explosives may be warranted. The previous correction factors by Kholod et al. considered only solvation in highly polar solvents and thus would likely be less affected by this issue. Thus, while a lumped correction factor is currently the best option to provide a useful way to accurately calculate solid explosive vapor pressures, further research is desirable to improve other individual terms in the COSMO-RS solvation model.

Figure 7. Modified vapor pressure predictions of high-volatility explosive compounds in Table 2.

4. CONCLUSIONS The temperature-dependent vapor pressure is a critical property for trace detection of explosives and has application in toxicological studies as well for sensing landmines and improvised explosive devices. In this work we have modified the COSMO-RS solvation model with a QSPR-based correction for the free energy of fusion and other factors. This brings the predicted ambient vapor pressure to within 0.32 log units of the most reliable experimental data, which is on the same order as the typical variation in measurements. In addition, the temperature dependence of the vapor pressure is accurately predicted over the full range of interest for detection applications. Several compounds outside the fitting set were used to validate this approach, and a range of explosives and important environmental products that lack systematic vapor pressure data were calculated using the same correction method. Though COSMO-RS must be adjusted for the free energy of fusion to treat solid compounds, our calculations suggest that other factors are also playing a prominent role in the correction. Further work to refine the COSMO-RS predictions for explosive compounds is desirable, particularly in regards to treatment of the van der Waals interactions and the dielectric scaling factor in the underlying COSMO model.

Figure 8. Modified vapor pressure predictions of low-volatility explosive compounds in Table 2.

other factors are contributing heavily (perhaps even dominating) this factor. First, we consider the previous work by Kholod et al. on water solubility of a number of explosive compounds.58 Though COSMO-RS aqueous solubility predictions were found to be quite accurate for many explosives (less than 0.1 LU), there were still errors for certain important compounds such as nitramines. To address this, the authors introduced a simplex representation of molecular structure (SiRMS) QSPR model based on 54 drugs and pesticides and 5 nitro compounds. The ΔGfus terms generated by this approach improved solubility for a number of the problematic explosive compounds, and all correction values were positive as would be required for the free energy of fusion. However, direct use of Kholod et al.’s parameters to correct COSMO-RS vapor pressures leads to very poor results; in all cases, our ΔGfus terms are 3−5 kcal/mol higher, which has a dramatic effect on the vapor pressure. Furthermore, predicted vapor pressures for liquid explosives and related compounds also benefit heavily from a (normally positive) ΔGfus correction; our correction factor for nitroglycerin, for example, is positive and relatively close to the corrections for solid RDX and TNT. This suggests that although a positive free energy of fusion should be taken into

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ASSOCIATED CONTENT

* Supporting Information S

Tables of Antoine equation coefficients for the temperaturedependent vapor pressure of all compounds discussed in this work. This material is available free of charge via the Internet at http://pubs.acs.org. 2041

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Office of Naval Research grant N00014-12-WX-20884 under the Science for Addressing Asymmetric Explosive Threats program directed by Dan Prono. The authors thank Darrel Cherf and James Hemmer for preliminary calculations on explosive compounds. This research was performed while one of the authors (S.A.) held a National Research Council Research Associateship Award at Naval Postgraduate School.

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