- Email: [email protected]
A simplified prediction of entropy of melting for energetic compounds
Fluid Phase Equilibria 303 (2011) 10–14
Contents lists available at ScienceDirect
Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid
A simplified prediction of entropy of melting for energetic compounds Daniel C. Evans ∗ , Samuel H. Yalkowsky Department of Pharmaceutical Science, University of Arizona, College of Pharmacy, PO Box 210207, 1703 E. Mabel Street, Tucson, AZ 85721, USA
a r t i c l e
i n f o
Article history: Received 2 September 2010 Received in revised form 4 December 2010 Accepted 11 December 2010 Available online 22 December 2010
a b s t r a c t A new widely applicable model for the prediction of the entropy of melting of organic compounds is presented. The use of three simple geometry based parameters: rotational symmetry, flexibility, and eccentricity enables the simple and accurate prediction of this important property. This paper demonstrates the use of the model for energetic compounds. © 2010 Elsevier B.V. All rights reserved.
Keywords: Entropy Melting Prediction Nitro-aromatic Energetic
1. Introduction The melting point of a compound is a major determinant of a variety of bio-relevant physical properties, including solubility and volatility. Its value is important for the design of new compounds with desired physical properties. Due to its usefulness and ease of determination, the melting point is the most widely reported property of organic compounds. Just about every compilation of physical properties of molecules contains melting point data. Unfortunately, in spite of a tremendous database of readily available melting point data, there are few guidelines for its estimation. Keshavarz and Pouretedal [1] proposed a method for predicting the entropy of melting by studying the experimental data for 61 nitro-aromatic compounds. The entropy of melting of a compound is an important determinant of its melting point.
At the melting temperature the Gibbs free energy of transition is equal to zero giving the following relationship between the Kelvin melting point temperature, Tm , the enthalpy of melting, Hm (kJ mol−1 ), and entropy of melting, Sm (J K−1 mol−1 ): Hm Sm
∗ Corresponding author. Tel.: +1 520 626 4309; fax: +1 520 626 2466. E-mail address: [email protected] (D.C. Evans). 0378-3812/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2010.12.007
2.1. Entropy of melting The entropy of melting is defined as the entropy of the liquid minus the entropy of the crystal at the melting point. Sm = S liquid − S crystal
(2)
According to Bondi [5], a compound’s entropy of melting is the sum of its rotational, conformational, and translational components: rot conf trans + Sm + Sm Sm = Sm
2. Background
Tm =
Any effective scheme for the estimation of melting point must consider the effect of chemical structure on both the enthalpy and entropy of melting. The enthalpy of melting can be predicted, with reasonable accuracy, by a number of group contribution models [2–4]. However, the prediction of the entropy of melting must account for geometric factors that are not additive-constitutive.
(3)
Thus, to predict the entropy of melting we need relationships between a compound’s molecular structure and each of the above terms. The proposed model evaluates the roles of rotational, conformational, and translational entropy in terms of the molecular symmetry number, , molecular flexibility number, , and molecular eccentricity, ε, respectively.
(1) 2.2. Rotational entropy The idea of a rotational component of entropy was introduced by Carnelley [6] when he noticed a relationship between symmetry and melting point. Later Dannenfelser et al. [7] proposed that the
D.C. Evans, S.H. Yalkowsky / Fluid Phase Equilibria 303 (2011) 10–14
11
Table 1 Values of rotational symmetry, flexibility, and eccentricity. No.
Compound name
CAS #
ε
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
Nitrobenzene 4-Nitrophenol 3-Nitroaniline 1,3-Dinitrobenzene 3-Nitrophenol 1-4-Chloro-4-nitrobenzene 2-Nitroaniline 1,4-Dinitrobenzene N-methyl-N-2,4,6-tetranitrobenzamine 2,4-Dinitrophenol 2,4,6-Trinitrophenol 4-Nitrobenzoic acid 2-Nitrobenzoic acid 1,3-Dihydroxy-2,4,6-trinitrobenzene 2,6-Dintitrophenol 2,3,4,5,6-Pentafluoro-nitrobenzene 4,4 -Dinitrodiphenyl ether 3,4-Dinitrophenol 2-Nitrophenol 2,4-Dinitrotoluene 1,3,5-Trinitrobenzene 1,2-Dintrobenzene 4-Nitroaniline Benzenamine, N-ethyl-N,2,4,6-tetranitroBenzenamine, N-methyl-N,2,4,6-tetranitro2,5-Dintrophenol 2,4-Dichloro-4 -nitrodiphenyl ether 2,3-Dintrophenol 1,3-Benzenediamine, 2,4,6-trinitro1,3,5-Benzenetriamine, 2,4,6-trinitro1,8-Dinitronaphthalene 3-Nitrotoluene 3-Nitrophthalic anhydride 2-Sec-butyl-4,6-dinitrophenol 2,4,6-Trinitrotoluene Phenol, 2-methyl-4,6-dinitro3-Methyl-2,4,6-trinitro-phenol Benzene, 2-chloro-1,3,5-trinitro2-Methoxy-1,3,5-trinitro-benzene 2,4-Dinitrotoluene Benzene, 1,3,5-trimethyl-2,4,6-trinitro2,6-Dichloro-4-nitroaniline 4-Nitrophthalic anhydride 3,4-Dintitrotoluene Hexanitrobiphenyl Hexanitrobibenzyl 2,4,6,2 ,4 ,6 -Hexanitrodiphenylsulfone 4-Nitrotoluene 2,4,6-Trinitromethaxylene 2,6-Dintitrotoluene Phenol, 2-methyl-4,6-dinitro2,3-Dintrotoluene 3-Methyl-2,4,6-trinitro-phenol Benzenamine, 2,4,6-trinitro1,4,5-Trinitronaphthalene 2,4,6,2 ,4 ,6 -Hexanitrodiphenylamine 2,2 ,4,4 ,6,6 -Hexanitrostilbene 2,4,6,2 ,4 ,6 -Hexanitrodiphenylsulfide Benzene, 1-fluoro-3-nitroBenzene, 1-fluoro-2-nitro5-Hydroxy-2-nitrobenzotrifluoride
98-95-3 100-02-7 99-09-2 99-65-0 554-84-7 100-00-5 88-74-4 100-25-4 479-45-8 51-28-5 88-89-1 62-23-7 552-16-9 82-71-3 573-56-8 880-78-4 101-63-3 577-71-9 88-75-5 121-14-2 99-35-4 528-29-0 100-01-6 6052-13-7 43072-20-4 329-71-5 1836-75-5 66-56-8 1630-08-6 3058-38-6 602-38-0 99-08-1 641-70-3 88-85-7 118-96-7 534-52-1 602-99-3 88-88-0 606-35-9 121-14-2 602-96-0 99-30-9 5466-84-2 610-39-9 4433-16-3 n/a n/a 99-99-0 632-92-8 606-20-2 534-52-1 602-01-7 602-99-3 489-98-5 2243-95-0 131-73-7 n/a 2217-06-3 402-67-5 1493-27-2 88-30-2
2 2 1 2 1 2 1 4 1 1 2 2 1 2 2 2 1 1 1 1 6 2 2 1 1 1 1 1 2 6 2 1 1 1 2 2 1 2 1 1 6 2 1 1 4 1 2 2 2 2 2 1 1 1 1 1 2 1 1 1 1
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 1.5 0.5 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 1.5 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 1.0 0.0 0.0 0.5
2.33 2.67 2.67 2.67 2.67 2.67 2.67 2.67 3.33 3.00 3.33 2.67 2.67 3.67 3.00 4.00 2.67 3.00 2.67 3.00 3.00 3.00 2.67 3.33 3.67 3.00 3.00 3.00 3.67 4.00 4.00 2.67 4.00 2.67 3.33 3.33 3.67 3.33 3.33 3.00 4.00 3.33 4.00 3.00 6.00 3.33 3.33 2.67 3.67 3.00 3.33 3.00 3.67 3.33 4.33 3.33 6.67 3.33 2.67 2.67 3.00
molecular external rotational symmetry number, , determines the probability of a molecule being in the proper orientation for incorporation into the crystal. They define as the maximum number of positions into which a molecule can be rotated and still maintain its reference image. For example 1,4-dinitrobenzene has a symmetry number of 4 while 1,3-dinitrobenzene has a symmetry number of 2. The calculation of the symmetry number assumes that: (1) CH3 , NH2 , and OH are freely rotating and thus behave as if they are radially symmetrical, (2) aromatic NO2 and COOH groups act as single entities that are coplanar with the ring and bilaterally symmetrical. More recently Jain and Yalkowksy [8] combined a modified
Walden’s rule and the Boltzmann equation to obtain the following equation for the estimation of the rotational entropy of melting for rigid molecules: rot Sm = 50 − R ln
(4)
2.3. Conformational entropy Dannenfelser and Yalkowsky [9] also described the effect of the flexibility of a molecule on its entropy of melting by the Boltzmann
12
D.C. Evans, S.H. Yalkowsky / Fluid Phase Equilibria 303 (2011) 10–14
Table 2 Experimental and predicted molar entropies of fusion (J K−1 mol−1 ). No.
Compound name
1 Nitrobenzene 2 4-Nitrophenol 3 3-Nitroaniline 4 1,3-Dinitrobenzene 5 3-Nitrophenol 6 1-4-Chloro-4-nitrobenzene 7 2-Nitroaniline 8 1,4-Dinitrobenzene 9 N-methyl-N-2,4,6-tetranitrobenzamine 10 2,4-Dinitrophenol 11 2,4,6-Trinitrophenol 12 4-Nitrobenzoic acid 13 2-Nitrobenzoic acid 14 1,3-Dihydroxy-2,4,6-trinitrobenzene 15 2,6-Dintitrophenol 16 2,3,4,5,6-Pentafluoro-nitrobenzene 17 4,4 -Dinitrodiphenyl ether 18 3,4-Dinitrophenol 19 2-Nitrophenol 20 2,4-Dinitrotoluene 21 1,3,5-Trinitrobenzene 22 1,2-Dintrobenzene 23 4-Nitroaniline 24 Benzenamine, N-ethyl-N,2,4,6-tetranitro25 Benzenamine, N-methyl-N,2,4,6-tetranitro26 2,5-Dintrophenol 27 2,4-Dichloro-4 -nitrodiphenyl ether 28 2,3-Dintrophenol 29 1,3-Benzenediamine, 2,4,6-trinitro30 1,3,5-Benzenetriamine, 2,4,6-trinitro31 1,8-Dinitronaphthalene 32 3-Nitrotoluene 33 3-Nitrophthalic anhydride 34 2-Sec-butyl-4,6-dinitrophenol 35 2,4,6-Trinitrotoluene 36 Phenol, 2-methyl-4,6-dinitro37 3-Methyl-2,4,6-trinitro-phenol 38 Benzene, 2-chloro-1,3,5-trinitro39 2-Methoxy-1,3,5-trinitro-benzene 40 2,4-Dinitrotoluene 41 Benzene, 1,3,5-trimethyl-2,4,6-trinitro42 2,6-Dichloro-4-nitroaniline 43 4-Nitrophthalic anhydride 44 3,4-Dintitrotoluene 45 Hexanitrobiphenyl 46 Hexanitrobibenzyl 47 2,4,6,2 ,4 ,6 -Hexanitrodiphenylsulfone 48 4-Nitrotoluene 49 2,4,6-Trinitromethaxylene 50 2,6-Dintitrotoluene 51 Phenol, 2-methyl-4,6-dinitro52 2,3-Dintrotoluene 53 3-Methyl-2,4,6-trinitro-phenol 54 Benzenamine, 2,4,6-trinitro55 1,4,5-Trinitronaphthalene 56 2,4,6,2 ,4 ,6 -Hexanitrodiphenylamine 57 2,2 ,4,4 ,6,6 -Hexanitrostilbene 58 2,4,6,2 ,4 ,6 -Hexanitrodiphenylsulfide 59 Benzene, 1-fluoro-3-nitro60 Benzene, 1-fluoro-2-nitro61 5-Hydroxy-2-nitrobenzotrifluoride rms deviation (J K−1 mol−1 )-all 61 compounds rms deviation (J K−1 mol−1 )-38 L-B [16] recommended values a b c d
SM (exp)
43.5 48.6 61.1 47.7 55.7 39.7 46.8 62.9 60.8 62.3 86.2 71.0 66.8 73.6 58.3 47.1 24.6 62.4 55.7 61.9 38.9 58.4 50.2 63.7 51.5 62.3 66.9 62.9 63.1 90.8a 79.5 47.5b 42.1 68.9 64.8 55.6 68.4 51.0 57.6 61.9 61.2 66.5 44.2 57.2 69.8 89.3a 69.6a 51.8 89.8 47.5c 55.6 53.3 70.3 61.0 70.8 72.8 68.0a 74.9 51.2d 53.1d 62.4d
Eq. (14)
K–P method
SM
Error
SM
Error
51.3 52.4 58.1 52.4 58.1 52.4 58.1 46.6 63.7 59.1 54.2 52.4 58.1 55.0 53.4 55.7 65.5 59.1 58.1 59.1 44.3 53.4 52.4 71.1 64.5 59.1 66.5 59.1 55.0 46.6 55.7 58.1 61.5 69.2 54.2 54.2 60.8 54.2 63.7 59.1 46.6 54.2 61.5 59.1 53.4 74.8 54.2 52.4 55.0 53.4 54.2 59.1 60.8 60.0 62.2 67.4 60.0 67.4 58.1 58.1 62.8
−7.8 −3.8 3.0 −4.7 −2.4 −12.7 −11.3 16.3 −2.9 3.2 32.0 18.6 8.7 18.6 4.9 −8.6 −40.9 3.3 −2.4 2.8 −5.4 5.0 −2.2 −7.4 −13.0 3.2 0.4 3.8 8.0 44.2 23.8 −10.6 −19.4 −0.3 10.6 1.4 7.6 −3.3 −6.1 2.8 14.5 12.3 −17.3 −1.9 16.5 14.5 15.3 −0.6 34.8 −5.9 1.4 −5.8 9.6 1.1 8.7 5.5 8.0 7.6 −6.9 −5.0 −0.4 13.4 9.6
41.6 75.2 58.9 43.3 61.8 63.9 52.2 56.6 56.5 63.4 65.1 72.2 58.8 71.9 63.4 41.6 23.3 63.4 61.8 56.0 45.0 56.7 65.6 55.9 55.9 63.4 12.6 63.4 59.4 90.1 80.5 54.3 46.8 70.5 57.7 62.8 64.4 53.8 64.4 56.0 56.3 56.6 46.8 56.0 76.8 75.4 90.3 54.3 57.0 56.0 62.8 56.0 64.4 62.9 82.2 74.0 66.4 76.8 50.5 50.5 61.1
1.9 −26.6 2.2 4.4 −6.1 −24.2 −5.4 6.4 4.3 −1.1 21.1 −1.2 8.0 1.7 −5.1 5.5 1.3 −1.0 −6.1 5.9 −6.1 1.7 −15.4 7.8 −4.4 −1.1 54.3 −0.5 3.7 0.7 −1.0 −6.8 −4.7 −1.6 7.1 −7.2 4.0 −2.9 −6.9 5.9 4.9 10.0 −2.7 1.2 −7.0 13.8 −20.7 −2.5 32.8 −8.5 −7.2 −2.7 5.9 −1.8 −11.3 −1.1 1.6 −1.8 0.7 2.6 1.3 11.4 12.4
Values for compounds 30, 46, 47, and 57 were predicted by Zeman et al. [12–14]. Melting point was taken from CRC Handbook of Chemistry and Physics [17] and the NIST online database [18]. Value was observed after annealing [16]. Values for compounds 59–61 were predicted by Semnani and Keshavarz [15].
D.C. Evans, S.H. Yalkowsky / Fluid Phase Equilibria 303 (2011) 10–14
equation: conf Sm
= R ln
(5)
Yalkowksy and Khan [10] define the molecular flexibility number ϕ by: ϕ=
1
(6)
F
where F is the probability of each flexible molecular segment in the liquid being in the proper conformation for incorporation into the crystal. If we assume that the only torsional angles of a molecule are 60, 180, and 300 the value of F would be 0.333. By assuming the trans conformation has a lower energy than the gauche conformations, Yalkowksy and Khan [10] estimate the F value to be about 0.4. Combining Eqs. (5) and (6) gives: conf Sm = 7.4
(7)
To calculate the probability of a molecule being in an acceptable conformation for incorporation into the crystal, Jain and Yalkowsky [8] defined the effective number of rotatable bonds () by: = SP3 + 0.5SP2 + 0.5(RING) − 1 where SP3 = and SP2 =
and RING =
(8)
Nonring sp3 atoms :
CH2 , CH, C, NH, N, O, S
Nonring sp2 atoms :
CH, C, N, C O
rigid ring systems
(9)
(10)
(11)
2.4. Translational entropy In order for a molecule in a close packed crystal lattice to gain enough translational freedom to become disordered it must undergo expansion. It follows that a nearly spherical molecule would require less expansion for rotational disorder than a molecule that is more elongated or flat. To account for the less spherical molecule’s higher entropy of melting, Johnson and Yalkowsky [11] introduced the molecular eccentricity (ε) as a parameter for the prediction of the translational component to the total melting entropy. trans Sm = R ln ε
(12)
To calculate ε, Yalkowksy and Khan [10] define the eccentricity as the number of atoms restricted to a single plane divided by three. ε=
# of atoms in plane 3
(13)
Dividing by three gives us a reference point based on the fact that a molecule with 3 or more atoms must contain at least three atoms that are coplanar. This method, as stated in Section 2.2, treats aromatic NO2 and COOH groups as single entities that are coplanar with the ring. For example 1,4-dinitrobenzene would have an eccentricity of 2.67 while 3,5-dinitro benzoic acid would have an eccentricity of 3. Incorporating Eqs. (4), (7) and (12) into Eq. (3) gives: Sm = 50 − 19.1 log10 + 7.4 + 19.1 log10 ε
13
the chemical structure. The flexibilities and eccentricities were calculated by Eqs. (7) and (13), respectively. The experimental values of the entropy of melting for the compounds compiled by K–P [1] are listed in Table 2. (Note that some of these values are calculated rather than experimentally determined [12–15].) This table also contains their predictions and the predictions of Eq. (14), along with the errors associated with both calculations. Landolt-Bornstein [16] compiled reported experimentally determined values for 38 of these compounds and provided recommended values based on procedures listed in Section 3.3 of Ref. [16]. When available, the more recently and objectively recommended values of Landolt-Bornstein [16] (shown in boldface type) have been used in place of those used by K–P [1]. Table 3, which is located in supplementary material section, contains all of the values for enthalpy of fusion and melting point listed in Landolt-Bornstein [16] for the 38 available compounds as well as the values used by (K–P) [1] for the additional 23 compounds. Table 4, which is also located in the supplementary material, compares the results of Eq. (14) to that of earlier work done by Dannenfelser and Yalkowsky [9]. 4. Results and discussion Table 2 shows that the estimations of the K–P method [1] (which are based on regression generated parameters) have a root mean squared deviation of 11.4 J K−1 mol−1 . The prediction using Eq. (14) (which is based on three derived parameters) has a root mean squared deviation of 13.4 J K−1 mol−1 . If we restrict the analysis to the 38 values that are recommended by Landolt-Bornstein [16] the error of the K–P method [1] increases to 12.4 J K−1 mol−1 , while the error of the prediction based on Eq. (14) drops to 9.6 J K−1 mol−1 . Table 4 compares the results of Eq. (14), which includes the improved eccentricity parameter, to those obtained through application of earlier work done by Dannenfelser and Yalkowsky [9]. The table clearly shows that by including this intuitive estimation of the translational component of total entropy, Eq. (14) (root mean squared deviation of 13.4 J K−1 mol−1 ) gives a more accurate prediction of the entropy of fusion than the earlier work (root mean squared deviation of 18.4 J K−1 mol−1 ). Both methods provide a reasonable estimation for the entropy of melting for energetic compounds. The method proposed in this paper is shown to be intuitive and easy to use. Furthermore it contains no fitted parameters and thus it can be applied to a wide range of organic molecules. The application to energetic and nitro-aromatic compounds provides more insight on their unique phase transition behavior. By adding the eccentricity to earlier work [9] and characterizing all three components for different nitrogen containing groups (e.g., nitro, NH3 ) we are better able to predict entropy of melting. Furthermore, since it does not require regression, this method is applicable to a larger pool of entropy of melting data. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.fluid.2010.12.007. References
(14)
3. Data Table 1 shows symmetry, flexibility, and eccentricity values for the 61 energetic compounds studied by Keshavarz and Pouretedal (K–P) [1]. The symmetry was determined by visual inspection of
[1] M.H. Keshavarz, H.R. Pouretedal, A new simple approach to predict entropy of fusion of nitroaromatic compounds, Fluid Phase Equilibria 298 (2010) 24–32. [2] A.-J. Briard, M. Bouroukba, D. Petitjean, M. Dirand, Models for estimation of pure n-alkanes’ thermodynamic properties as a function of carbon chain length, Journal of Chemical & Engineering Data 48 (2003) 1508–1516. [3] L. Zhao, S.H. Yalkowsky, A combined group contribution and molecular geometry approach for predicting melting points of aliphatic compounds, Industrial & Engineering Chemistry Research 38 (1999) 3581–3584.
14
D.C. Evans, S.H. Yalkowsky / Fluid Phase Equilibria 303 (2011) 10–14
[4] A.S. Gilbert, Entropy–enthalpy compensation in the fusion of organic molecules: implications for Walden’s rule and molecular freedom in the liquid state, Thermochimica Acta 339 (1999) 131–142. [5] A.A. Bondi, Physical Properties of Molecular Crystals, Liquids, and Glasses, first ed., John Wiley and Sons, Inc., New York, 1968. [6] T. Carnelley, Chemical symmetry, or the influence of atomic arrangement on the physical properties of compounds, Philosophical Magazine-5th Series 8 (1882) 112–193. [7] R.M. Dannenfelser, N. Surendran, S.H. Yalkowsky, Molecular symmetry and related properties, SAR & QSAR in Environmental Research, 1 (1993) 273–292. [8] A. Jain, S.H. Yalkowsky, Comparison of two methods for estimation of melting points of organic compounds, Industrial & Engineering Chemistry Research 46 (2007) 2589–2592. [9] R.-M. Dannenfelser, S.H. Yalkowsky, Estimation of entropy of melting from molecular structure: a non-group contribution method, Industrial & Engineering Chemistry Research 35 (1996) 1483–1486. [10] S.H. Yalkowksy, A. Khan, Prediction of pure component properties of hydrocarbons, in: 2009 AAPS Annual Meeting and Exposition American Association of Pharmaceutical Scientists, Los Angeles, CA, 2009 (Abstract Number 3674).
[11] J.L.H. Johnson, S.H. Yalkowsky, Two new parameters for predicting the entropy of melting: eccentricity (ε) and spirality (), Industrial & Engineering Chemistry Research 44 (2005) 7559–7566. [12] S. Zeman, M. Krupka, New aspects of impact reactivity of polynitro compounds. Part II. Impact sensitivity as “the First Reaction” of polynitro arenes, Propellants, Explosives, Pyrotechnics 28 (2003) 249–255. [13] S. Zeman, M. Krupka, New aspects of impact reactivity of polynitro compounds. Part III. Impact sensitivity as a function of the intermolecular interactions, Propellants, Explosives, Pyrotechnics 28 (2003) 301–307. [14] S. Zeman, Calculated lattice energies of energetic materials in a prediction of their heats of fusion and sublimation, HanNeng CaiLiao 10 (2002) 27–33. [15] A. Semnani, M.H. Keshavarz, Using molecular structure for reliable predicting enthalpy of melting of nitroaromatic energetic compounds, Journal of Hazardous Materials 178 (2010) 264–272. [16] M.F.Z.-Y. Zhang, K.N. Marsh, R.C. Wilhoit, Landolt-Bornstein New Series, Springer-Verlag, Berlin (Heidelberg/New York), 1995. [17] CRC Handbook of Chemistry and Physics, 2009−2010, 90th ed, Journal of the American Chemical Society 131 (2009) 12862–12862. [18] E.P.J. Linstrom, W.G. Mallard, NIST Chemistry WebBook, NIST Standard Reference Database in, National Institute of Standards and Technology, August 31, 2010.
Contents lists available at ScienceDirect
Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid
A simplified prediction of entropy of melting for energetic compounds Daniel C. Evans ∗ , Samuel H. Yalkowsky Department of Pharmaceutical Science, University of Arizona, College of Pharmacy, PO Box 210207, 1703 E. Mabel Street, Tucson, AZ 85721, USA
a r t i c l e
i n f o
Article history: Received 2 September 2010 Received in revised form 4 December 2010 Accepted 11 December 2010 Available online 22 December 2010
a b s t r a c t A new widely applicable model for the prediction of the entropy of melting of organic compounds is presented. The use of three simple geometry based parameters: rotational symmetry, flexibility, and eccentricity enables the simple and accurate prediction of this important property. This paper demonstrates the use of the model for energetic compounds. © 2010 Elsevier B.V. All rights reserved.
Keywords: Entropy Melting Prediction Nitro-aromatic Energetic
1. Introduction The melting point of a compound is a major determinant of a variety of bio-relevant physical properties, including solubility and volatility. Its value is important for the design of new compounds with desired physical properties. Due to its usefulness and ease of determination, the melting point is the most widely reported property of organic compounds. Just about every compilation of physical properties of molecules contains melting point data. Unfortunately, in spite of a tremendous database of readily available melting point data, there are few guidelines for its estimation. Keshavarz and Pouretedal [1] proposed a method for predicting the entropy of melting by studying the experimental data for 61 nitro-aromatic compounds. The entropy of melting of a compound is an important determinant of its melting point.
At the melting temperature the Gibbs free energy of transition is equal to zero giving the following relationship between the Kelvin melting point temperature, Tm , the enthalpy of melting, Hm (kJ mol−1 ), and entropy of melting, Sm (J K−1 mol−1 ): Hm Sm
∗ Corresponding author. Tel.: +1 520 626 4309; fax: +1 520 626 2466. E-mail address: [email protected] (D.C. Evans). 0378-3812/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2010.12.007
2.1. Entropy of melting The entropy of melting is defined as the entropy of the liquid minus the entropy of the crystal at the melting point. Sm = S liquid − S crystal
(2)
According to Bondi [5], a compound’s entropy of melting is the sum of its rotational, conformational, and translational components: rot conf trans + Sm + Sm Sm = Sm
2. Background
Tm =
Any effective scheme for the estimation of melting point must consider the effect of chemical structure on both the enthalpy and entropy of melting. The enthalpy of melting can be predicted, with reasonable accuracy, by a number of group contribution models [2–4]. However, the prediction of the entropy of melting must account for geometric factors that are not additive-constitutive.
(3)
Thus, to predict the entropy of melting we need relationships between a compound’s molecular structure and each of the above terms. The proposed model evaluates the roles of rotational, conformational, and translational entropy in terms of the molecular symmetry number, , molecular flexibility number, , and molecular eccentricity, ε, respectively.
(1) 2.2. Rotational entropy The idea of a rotational component of entropy was introduced by Carnelley [6] when he noticed a relationship between symmetry and melting point. Later Dannenfelser et al. [7] proposed that the
D.C. Evans, S.H. Yalkowsky / Fluid Phase Equilibria 303 (2011) 10–14
11
Table 1 Values of rotational symmetry, flexibility, and eccentricity. No.
Compound name
CAS #
ε
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
Nitrobenzene 4-Nitrophenol 3-Nitroaniline 1,3-Dinitrobenzene 3-Nitrophenol 1-4-Chloro-4-nitrobenzene 2-Nitroaniline 1,4-Dinitrobenzene N-methyl-N-2,4,6-tetranitrobenzamine 2,4-Dinitrophenol 2,4,6-Trinitrophenol 4-Nitrobenzoic acid 2-Nitrobenzoic acid 1,3-Dihydroxy-2,4,6-trinitrobenzene 2,6-Dintitrophenol 2,3,4,5,6-Pentafluoro-nitrobenzene 4,4 -Dinitrodiphenyl ether 3,4-Dinitrophenol 2-Nitrophenol 2,4-Dinitrotoluene 1,3,5-Trinitrobenzene 1,2-Dintrobenzene 4-Nitroaniline Benzenamine, N-ethyl-N,2,4,6-tetranitroBenzenamine, N-methyl-N,2,4,6-tetranitro2,5-Dintrophenol 2,4-Dichloro-4 -nitrodiphenyl ether 2,3-Dintrophenol 1,3-Benzenediamine, 2,4,6-trinitro1,3,5-Benzenetriamine, 2,4,6-trinitro1,8-Dinitronaphthalene 3-Nitrotoluene 3-Nitrophthalic anhydride 2-Sec-butyl-4,6-dinitrophenol 2,4,6-Trinitrotoluene Phenol, 2-methyl-4,6-dinitro3-Methyl-2,4,6-trinitro-phenol Benzene, 2-chloro-1,3,5-trinitro2-Methoxy-1,3,5-trinitro-benzene 2,4-Dinitrotoluene Benzene, 1,3,5-trimethyl-2,4,6-trinitro2,6-Dichloro-4-nitroaniline 4-Nitrophthalic anhydride 3,4-Dintitrotoluene Hexanitrobiphenyl Hexanitrobibenzyl 2,4,6,2 ,4 ,6 -Hexanitrodiphenylsulfone 4-Nitrotoluene 2,4,6-Trinitromethaxylene 2,6-Dintitrotoluene Phenol, 2-methyl-4,6-dinitro2,3-Dintrotoluene 3-Methyl-2,4,6-trinitro-phenol Benzenamine, 2,4,6-trinitro1,4,5-Trinitronaphthalene 2,4,6,2 ,4 ,6 -Hexanitrodiphenylamine 2,2 ,4,4 ,6,6 -Hexanitrostilbene 2,4,6,2 ,4 ,6 -Hexanitrodiphenylsulfide Benzene, 1-fluoro-3-nitroBenzene, 1-fluoro-2-nitro5-Hydroxy-2-nitrobenzotrifluoride
98-95-3 100-02-7 99-09-2 99-65-0 554-84-7 100-00-5 88-74-4 100-25-4 479-45-8 51-28-5 88-89-1 62-23-7 552-16-9 82-71-3 573-56-8 880-78-4 101-63-3 577-71-9 88-75-5 121-14-2 99-35-4 528-29-0 100-01-6 6052-13-7 43072-20-4 329-71-5 1836-75-5 66-56-8 1630-08-6 3058-38-6 602-38-0 99-08-1 641-70-3 88-85-7 118-96-7 534-52-1 602-99-3 88-88-0 606-35-9 121-14-2 602-96-0 99-30-9 5466-84-2 610-39-9 4433-16-3 n/a n/a 99-99-0 632-92-8 606-20-2 534-52-1 602-01-7 602-99-3 489-98-5 2243-95-0 131-73-7 n/a 2217-06-3 402-67-5 1493-27-2 88-30-2
2 2 1 2 1 2 1 4 1 1 2 2 1 2 2 2 1 1 1 1 6 2 2 1 1 1 1 1 2 6 2 1 1 1 2 2 1 2 1 1 6 2 1 1 4 1 2 2 2 2 2 1 1 1 1 1 2 1 1 1 1
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 1.5 0.5 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 1.5 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 1.0 0.0 0.0 0.5
2.33 2.67 2.67 2.67 2.67 2.67 2.67 2.67 3.33 3.00 3.33 2.67 2.67 3.67 3.00 4.00 2.67 3.00 2.67 3.00 3.00 3.00 2.67 3.33 3.67 3.00 3.00 3.00 3.67 4.00 4.00 2.67 4.00 2.67 3.33 3.33 3.67 3.33 3.33 3.00 4.00 3.33 4.00 3.00 6.00 3.33 3.33 2.67 3.67 3.00 3.33 3.00 3.67 3.33 4.33 3.33 6.67 3.33 2.67 2.67 3.00
molecular external rotational symmetry number, , determines the probability of a molecule being in the proper orientation for incorporation into the crystal. They define as the maximum number of positions into which a molecule can be rotated and still maintain its reference image. For example 1,4-dinitrobenzene has a symmetry number of 4 while 1,3-dinitrobenzene has a symmetry number of 2. The calculation of the symmetry number assumes that: (1) CH3 , NH2 , and OH are freely rotating and thus behave as if they are radially symmetrical, (2) aromatic NO2 and COOH groups act as single entities that are coplanar with the ring and bilaterally symmetrical. More recently Jain and Yalkowksy [8] combined a modified
Walden’s rule and the Boltzmann equation to obtain the following equation for the estimation of the rotational entropy of melting for rigid molecules: rot Sm = 50 − R ln
(4)
2.3. Conformational entropy Dannenfelser and Yalkowsky [9] also described the effect of the flexibility of a molecule on its entropy of melting by the Boltzmann
12
D.C. Evans, S.H. Yalkowsky / Fluid Phase Equilibria 303 (2011) 10–14
Table 2 Experimental and predicted molar entropies of fusion (J K−1 mol−1 ). No.
Compound name
1 Nitrobenzene 2 4-Nitrophenol 3 3-Nitroaniline 4 1,3-Dinitrobenzene 5 3-Nitrophenol 6 1-4-Chloro-4-nitrobenzene 7 2-Nitroaniline 8 1,4-Dinitrobenzene 9 N-methyl-N-2,4,6-tetranitrobenzamine 10 2,4-Dinitrophenol 11 2,4,6-Trinitrophenol 12 4-Nitrobenzoic acid 13 2-Nitrobenzoic acid 14 1,3-Dihydroxy-2,4,6-trinitrobenzene 15 2,6-Dintitrophenol 16 2,3,4,5,6-Pentafluoro-nitrobenzene 17 4,4 -Dinitrodiphenyl ether 18 3,4-Dinitrophenol 19 2-Nitrophenol 20 2,4-Dinitrotoluene 21 1,3,5-Trinitrobenzene 22 1,2-Dintrobenzene 23 4-Nitroaniline 24 Benzenamine, N-ethyl-N,2,4,6-tetranitro25 Benzenamine, N-methyl-N,2,4,6-tetranitro26 2,5-Dintrophenol 27 2,4-Dichloro-4 -nitrodiphenyl ether 28 2,3-Dintrophenol 29 1,3-Benzenediamine, 2,4,6-trinitro30 1,3,5-Benzenetriamine, 2,4,6-trinitro31 1,8-Dinitronaphthalene 32 3-Nitrotoluene 33 3-Nitrophthalic anhydride 34 2-Sec-butyl-4,6-dinitrophenol 35 2,4,6-Trinitrotoluene 36 Phenol, 2-methyl-4,6-dinitro37 3-Methyl-2,4,6-trinitro-phenol 38 Benzene, 2-chloro-1,3,5-trinitro39 2-Methoxy-1,3,5-trinitro-benzene 40 2,4-Dinitrotoluene 41 Benzene, 1,3,5-trimethyl-2,4,6-trinitro42 2,6-Dichloro-4-nitroaniline 43 4-Nitrophthalic anhydride 44 3,4-Dintitrotoluene 45 Hexanitrobiphenyl 46 Hexanitrobibenzyl 47 2,4,6,2 ,4 ,6 -Hexanitrodiphenylsulfone 48 4-Nitrotoluene 49 2,4,6-Trinitromethaxylene 50 2,6-Dintitrotoluene 51 Phenol, 2-methyl-4,6-dinitro52 2,3-Dintrotoluene 53 3-Methyl-2,4,6-trinitro-phenol 54 Benzenamine, 2,4,6-trinitro55 1,4,5-Trinitronaphthalene 56 2,4,6,2 ,4 ,6 -Hexanitrodiphenylamine 57 2,2 ,4,4 ,6,6 -Hexanitrostilbene 58 2,4,6,2 ,4 ,6 -Hexanitrodiphenylsulfide 59 Benzene, 1-fluoro-3-nitro60 Benzene, 1-fluoro-2-nitro61 5-Hydroxy-2-nitrobenzotrifluoride rms deviation (J K−1 mol−1 )-all 61 compounds rms deviation (J K−1 mol−1 )-38 L-B [16] recommended values a b c d
SM (exp)
43.5 48.6 61.1 47.7 55.7 39.7 46.8 62.9 60.8 62.3 86.2 71.0 66.8 73.6 58.3 47.1 24.6 62.4 55.7 61.9 38.9 58.4 50.2 63.7 51.5 62.3 66.9 62.9 63.1 90.8a 79.5 47.5b 42.1 68.9 64.8 55.6 68.4 51.0 57.6 61.9 61.2 66.5 44.2 57.2 69.8 89.3a 69.6a 51.8 89.8 47.5c 55.6 53.3 70.3 61.0 70.8 72.8 68.0a 74.9 51.2d 53.1d 62.4d
Eq. (14)
K–P method
SM
Error
SM
Error
51.3 52.4 58.1 52.4 58.1 52.4 58.1 46.6 63.7 59.1 54.2 52.4 58.1 55.0 53.4 55.7 65.5 59.1 58.1 59.1 44.3 53.4 52.4 71.1 64.5 59.1 66.5 59.1 55.0 46.6 55.7 58.1 61.5 69.2 54.2 54.2 60.8 54.2 63.7 59.1 46.6 54.2 61.5 59.1 53.4 74.8 54.2 52.4 55.0 53.4 54.2 59.1 60.8 60.0 62.2 67.4 60.0 67.4 58.1 58.1 62.8
−7.8 −3.8 3.0 −4.7 −2.4 −12.7 −11.3 16.3 −2.9 3.2 32.0 18.6 8.7 18.6 4.9 −8.6 −40.9 3.3 −2.4 2.8 −5.4 5.0 −2.2 −7.4 −13.0 3.2 0.4 3.8 8.0 44.2 23.8 −10.6 −19.4 −0.3 10.6 1.4 7.6 −3.3 −6.1 2.8 14.5 12.3 −17.3 −1.9 16.5 14.5 15.3 −0.6 34.8 −5.9 1.4 −5.8 9.6 1.1 8.7 5.5 8.0 7.6 −6.9 −5.0 −0.4 13.4 9.6
41.6 75.2 58.9 43.3 61.8 63.9 52.2 56.6 56.5 63.4 65.1 72.2 58.8 71.9 63.4 41.6 23.3 63.4 61.8 56.0 45.0 56.7 65.6 55.9 55.9 63.4 12.6 63.4 59.4 90.1 80.5 54.3 46.8 70.5 57.7 62.8 64.4 53.8 64.4 56.0 56.3 56.6 46.8 56.0 76.8 75.4 90.3 54.3 57.0 56.0 62.8 56.0 64.4 62.9 82.2 74.0 66.4 76.8 50.5 50.5 61.1
1.9 −26.6 2.2 4.4 −6.1 −24.2 −5.4 6.4 4.3 −1.1 21.1 −1.2 8.0 1.7 −5.1 5.5 1.3 −1.0 −6.1 5.9 −6.1 1.7 −15.4 7.8 −4.4 −1.1 54.3 −0.5 3.7 0.7 −1.0 −6.8 −4.7 −1.6 7.1 −7.2 4.0 −2.9 −6.9 5.9 4.9 10.0 −2.7 1.2 −7.0 13.8 −20.7 −2.5 32.8 −8.5 −7.2 −2.7 5.9 −1.8 −11.3 −1.1 1.6 −1.8 0.7 2.6 1.3 11.4 12.4
Values for compounds 30, 46, 47, and 57 were predicted by Zeman et al. [12–14]. Melting point was taken from CRC Handbook of Chemistry and Physics [17] and the NIST online database [18]. Value was observed after annealing [16]. Values for compounds 59–61 were predicted by Semnani and Keshavarz [15].
D.C. Evans, S.H. Yalkowsky / Fluid Phase Equilibria 303 (2011) 10–14
equation: conf Sm
= R ln
(5)
Yalkowksy and Khan [10] define the molecular flexibility number ϕ by: ϕ=
1
(6)
F
where F is the probability of each flexible molecular segment in the liquid being in the proper conformation for incorporation into the crystal. If we assume that the only torsional angles of a molecule are 60, 180, and 300 the value of F would be 0.333. By assuming the trans conformation has a lower energy than the gauche conformations, Yalkowksy and Khan [10] estimate the F value to be about 0.4. Combining Eqs. (5) and (6) gives: conf Sm = 7.4
(7)
To calculate the probability of a molecule being in an acceptable conformation for incorporation into the crystal, Jain and Yalkowsky [8] defined the effective number of rotatable bonds () by: = SP3 + 0.5SP2 + 0.5(RING) − 1 where SP3 = and SP2 =
and RING =
(8)
Nonring sp3 atoms :
CH2 , CH, C, NH, N, O, S
Nonring sp2 atoms :
CH, C, N, C O
rigid ring systems
(9)
(10)
(11)
2.4. Translational entropy In order for a molecule in a close packed crystal lattice to gain enough translational freedom to become disordered it must undergo expansion. It follows that a nearly spherical molecule would require less expansion for rotational disorder than a molecule that is more elongated or flat. To account for the less spherical molecule’s higher entropy of melting, Johnson and Yalkowsky [11] introduced the molecular eccentricity (ε) as a parameter for the prediction of the translational component to the total melting entropy. trans Sm = R ln ε
(12)
To calculate ε, Yalkowksy and Khan [10] define the eccentricity as the number of atoms restricted to a single plane divided by three. ε=
# of atoms in plane 3
(13)
Dividing by three gives us a reference point based on the fact that a molecule with 3 or more atoms must contain at least three atoms that are coplanar. This method, as stated in Section 2.2, treats aromatic NO2 and COOH groups as single entities that are coplanar with the ring. For example 1,4-dinitrobenzene would have an eccentricity of 2.67 while 3,5-dinitro benzoic acid would have an eccentricity of 3. Incorporating Eqs. (4), (7) and (12) into Eq. (3) gives: Sm = 50 − 19.1 log10 + 7.4 + 19.1 log10 ε
13
the chemical structure. The flexibilities and eccentricities were calculated by Eqs. (7) and (13), respectively. The experimental values of the entropy of melting for the compounds compiled by K–P [1] are listed in Table 2. (Note that some of these values are calculated rather than experimentally determined [12–15].) This table also contains their predictions and the predictions of Eq. (14), along with the errors associated with both calculations. Landolt-Bornstein [16] compiled reported experimentally determined values for 38 of these compounds and provided recommended values based on procedures listed in Section 3.3 of Ref. [16]. When available, the more recently and objectively recommended values of Landolt-Bornstein [16] (shown in boldface type) have been used in place of those used by K–P [1]. Table 3, which is located in supplementary material section, contains all of the values for enthalpy of fusion and melting point listed in Landolt-Bornstein [16] for the 38 available compounds as well as the values used by (K–P) [1] for the additional 23 compounds. Table 4, which is also located in the supplementary material, compares the results of Eq. (14) to that of earlier work done by Dannenfelser and Yalkowsky [9]. 4. Results and discussion Table 2 shows that the estimations of the K–P method [1] (which are based on regression generated parameters) have a root mean squared deviation of 11.4 J K−1 mol−1 . The prediction using Eq. (14) (which is based on three derived parameters) has a root mean squared deviation of 13.4 J K−1 mol−1 . If we restrict the analysis to the 38 values that are recommended by Landolt-Bornstein [16] the error of the K–P method [1] increases to 12.4 J K−1 mol−1 , while the error of the prediction based on Eq. (14) drops to 9.6 J K−1 mol−1 . Table 4 compares the results of Eq. (14), which includes the improved eccentricity parameter, to those obtained through application of earlier work done by Dannenfelser and Yalkowsky [9]. The table clearly shows that by including this intuitive estimation of the translational component of total entropy, Eq. (14) (root mean squared deviation of 13.4 J K−1 mol−1 ) gives a more accurate prediction of the entropy of fusion than the earlier work (root mean squared deviation of 18.4 J K−1 mol−1 ). Both methods provide a reasonable estimation for the entropy of melting for energetic compounds. The method proposed in this paper is shown to be intuitive and easy to use. Furthermore it contains no fitted parameters and thus it can be applied to a wide range of organic molecules. The application to energetic and nitro-aromatic compounds provides more insight on their unique phase transition behavior. By adding the eccentricity to earlier work [9] and characterizing all three components for different nitrogen containing groups (e.g., nitro, NH3 ) we are better able to predict entropy of melting. Furthermore, since it does not require regression, this method is applicable to a larger pool of entropy of melting data. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.fluid.2010.12.007. References
(14)
3. Data Table 1 shows symmetry, flexibility, and eccentricity values for the 61 energetic compounds studied by Keshavarz and Pouretedal (K–P) [1]. The symmetry was determined by visual inspection of
[1] M.H. Keshavarz, H.R. Pouretedal, A new simple approach to predict entropy of fusion of nitroaromatic compounds, Fluid Phase Equilibria 298 (2010) 24–32. [2] A.-J. Briard, M. Bouroukba, D. Petitjean, M. Dirand, Models for estimation of pure n-alkanes’ thermodynamic properties as a function of carbon chain length, Journal of Chemical & Engineering Data 48 (2003) 1508–1516. [3] L. Zhao, S.H. Yalkowsky, A combined group contribution and molecular geometry approach for predicting melting points of aliphatic compounds, Industrial & Engineering Chemistry Research 38 (1999) 3581–3584.
14
D.C. Evans, S.H. Yalkowsky / Fluid Phase Equilibria 303 (2011) 10–14
[4] A.S. Gilbert, Entropy–enthalpy compensation in the fusion of organic molecules: implications for Walden’s rule and molecular freedom in the liquid state, Thermochimica Acta 339 (1999) 131–142. [5] A.A. Bondi, Physical Properties of Molecular Crystals, Liquids, and Glasses, first ed., John Wiley and Sons, Inc., New York, 1968. [6] T. Carnelley, Chemical symmetry, or the influence of atomic arrangement on the physical properties of compounds, Philosophical Magazine-5th Series 8 (1882) 112–193. [7] R.M. Dannenfelser, N. Surendran, S.H. Yalkowsky, Molecular symmetry and related properties, SAR & QSAR in Environmental Research, 1 (1993) 273–292. [8] A. Jain, S.H. Yalkowsky, Comparison of two methods for estimation of melting points of organic compounds, Industrial & Engineering Chemistry Research 46 (2007) 2589–2592. [9] R.-M. Dannenfelser, S.H. Yalkowsky, Estimation of entropy of melting from molecular structure: a non-group contribution method, Industrial & Engineering Chemistry Research 35 (1996) 1483–1486. [10] S.H. Yalkowksy, A. Khan, Prediction of pure component properties of hydrocarbons, in: 2009 AAPS Annual Meeting and Exposition American Association of Pharmaceutical Scientists, Los Angeles, CA, 2009 (Abstract Number 3674).
[11] J.L.H. Johnson, S.H. Yalkowsky, Two new parameters for predicting the entropy of melting: eccentricity (ε) and spirality (), Industrial & Engineering Chemistry Research 44 (2005) 7559–7566. [12] S. Zeman, M. Krupka, New aspects of impact reactivity of polynitro compounds. Part II. Impact sensitivity as “the First Reaction” of polynitro arenes, Propellants, Explosives, Pyrotechnics 28 (2003) 249–255. [13] S. Zeman, M. Krupka, New aspects of impact reactivity of polynitro compounds. Part III. Impact sensitivity as a function of the intermolecular interactions, Propellants, Explosives, Pyrotechnics 28 (2003) 301–307. [14] S. Zeman, Calculated lattice energies of energetic materials in a prediction of their heats of fusion and sublimation, HanNeng CaiLiao 10 (2002) 27–33. [15] A. Semnani, M.H. Keshavarz, Using molecular structure for reliable predicting enthalpy of melting of nitroaromatic energetic compounds, Journal of Hazardous Materials 178 (2010) 264–272. [16] M.F.Z.-Y. Zhang, K.N. Marsh, R.C. Wilhoit, Landolt-Bornstein New Series, Springer-Verlag, Berlin (Heidelberg/New York), 1995. [17] CRC Handbook of Chemistry and Physics, 2009−2010, 90th ed, Journal of the American Chemical Society 131 (2009) 12862–12862. [18] E.P.J. Linstrom, W.G. Mallard, NIST Chemistry WebBook, NIST Standard Reference Database in, National Institute of Standards and Technology, August 31, 2010.