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A simple method to predict melting points of non-aromatic energetic compounds
Fluid Phase Equilibria 292 (2010) 1–6
Contents lists available at ScienceDirect
Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid
A simple method to predict melting points of non-aromatic energetic compounds Reza Fareghi Alamdari, Mohammad Hossein Keshavarz ∗ Department of Chemistry, Malek-ashtar University of Technology, Shahin-shahr P.O. Box 83145/115, Islamic Republic of Iran
a r t i c l e
i n f o
Article history: Received 2 August 2009 Received in revised form 18 January 2010 Accepted 21 January 2010 Available online 1 February 2010 Keywords: Melting point Non-aromatic Energetic compound Correlation Safety
a b s t r a c t This work presents a new simple method to estimate the melting points of non-aromatic energetic compounds, which contain energetic functional groups C–NO2 , C–ONO2 and N–NO2 . This method can allow the reliable prediction of melting points of non-aromatic energetic materials through a new general correlation. Elemental composition and some specific parameters of non-aromatic energetic compounds are important factors. The predicted results for various non-aromatic energetic compounds show that the present method gives reliable predictions of melting points with respect to previous works. This method has been tested for different newly synthesized explosives with complex molecular structures and energetic compounds with several energetic functional groups. © 2010 Elsevier B.V. All rights reserved.
1. Introduction The developments of high-energy materials with increased performance, reduced sensitivity to external stimuli as well as desirable physical and thermodynamic properties are major challenges to the chemical industry. There has been reasonable progress in the synthesis and development of new energetic compounds in recent years because of their possible use in formulations of propellants and explosives [1]. The risks and hazards associated with the research investigations of energetic materials can be reduced by the development of novel predictive methods. Some new simple predictive methods have recently been developed for desk calculations of various thermo-physical properties of energetic compounds such as condensed phase heat of formation [2–5] and standard enthalpy of melting [6,7]. The knowledge of physical and thermodynamic properties of energetic compounds is of special importance to the scientists and engineers. It is difficult to find the experimental values of desired properties for energetic compounds of interest in the open literature. Moreover, it can be dangerous or not practical to synthesize and measure the interested properties. Thus, estimation methods are very attractive to use for energetic materials. For the estimation of thermo-physical properties of pure organic compounds, group contribution methods have been widely used. Group additivity methods are not reliable procedures to predict melting points
∗ Corresponding author. Tel.: +98 0312 522 5071; fax: +98 0312 522 5068. E-mail addresses: [email protected], [email protected] (M.H. Keshavarz). 0378-3812/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2010.01.017
[8,9]. For example, it has been shown that the predicted melting points using group contribution method of Joback and Reid [10] have an average deviation of 37.6% for 60 carbocyclic nitroaromatic compounds [11]. A simple method has been recently introduced to estimate the melting points of nitramines, nitrate esters, nitrate salts and nitroaliphatics [12]. This paper presents a significant improvement and extension of applicability of previous work [12] for energetic compounds containing the functional groups C–NO2 , C–ONO2 and N–NO2 . Only elemental composition and increasing or decreasing effects of some specific structural parameters are used in the new method. The present method is applied to different wellknown and new non-aromatic energetic compounds. The predicted results are also compared with experimental values, Joback and Reid method [10] as well as with previous work [12]. 2. Theory Group contribution methods and quantitative structure– property/activity relationships (QSPR/QSAR) are two primary approaches, which can be used to predict physicochemical properties based on the structure of an organic compound. The group contribution methods are primarily based on the numbers and types of molecular groups in the organic compounds [8,13]. Since the first order group contribution methods fail to distinguish between the isomers that contain the same numbers and types of groups, the second order group contribution methods can be applied to incorporate interactions between next nearest neighbors. Additivity methods are broadly useful in chemistry in which the properties of molecules can be derived from the properties of the atoms or functional groups. For the property estimation of an
2
R.F. Alamdari, M.H. Keshavarz / Fluid Phase Equilibria 292 (2010) 1–6
Table 1 Comparison of the predicted melting points (K) of non-aromatic compounds by new method, previous work [12] as well as Joback and Reid (J–R) method [10] with experimental data. No. 1 2 3 4
Energetic compound CH3 CH2 ONO2 CH3 CH(ONO2 )CH3 O2 NCH2 CH2 OCH2 CH2 ONO2 O2 NOCH2 CH2 CH2 CH2 ONO2
5 6
CH3 CH(ONO2 )CH2 CH2 ONO2
7 8 9
O2 NOCH2 CH(ONO2 )CH2 ONO2 (O2 NOCH2 )4 C
10 11 12 13
Exp.
%Dev
Previous work
%Dev
J–R method
%Dev
169.1 173.9 290.8 256.7
−5.3 −8.9 5.7 −9.9
187.7 187.7 317.0 257.9
5.1 −1.7 15.2 −9.5
277.6 273.9 615.5 466.0
55.4 43.5 123.7 63.5
364.15 [26]
418.0
14.8
475.6
30.6
940.6
158.3
253.4 [25]
256.7
1.3
257.9
1.8
451.0
78.0
324.45 [26]
340.4
4.9
342.0
5.4
642.1
97.9
308.0 329.6
7.7 −20.2
293.7 398.3
2.7 −3.6
605.6 811.4
111.7 96.5
1224.1
254.7
286 [25] 413 [25]
345.15 [26] (C6 H5 )4 NNO3 [CH3 (CH2 )6 ]4 NNO3 [CH3 (CH2 )3 ]4 NNO3
New method
178.6 [25] 190.81 [25] 275.15 [26] 285 [25]
387.2 [25] 345 [25] 392.2 [25]
367.7
6.5
632.2
83.2
359.4 383.5 340.1
−7.2 11.2 −13.3
355.3 355.3 355.3
−8.3 3.0 −9.4
14
334.65 [26]
324.7
−3.0
398.3
19.0
767.7
129.4
15
478.5 [25]
466.4
−2.5
472.8
−1.2
673.5
40.8
16
449.35 [26]
449.3
0.0
303.1
−32.5
504.3
12.2
345.45 [25]
358.3
3.7
304.6
−11.8
287.9
−16.7
267.65 [25]
279.3
4.4
304.6
13.8
336.8
25.8
381.8 398.8
−10.0 −5.1
418.5 424.4
−1.3 1.0
402.0 978.3
−5.2 132.9
449.35 [26]
441.7
−1.7
307.4
−31.6
562.1
25.1
292 [25] 298.65 [25]
328.2 298.8
12.4 0.0
253.7 300.3
−13.1 0.5
516.4 280.4
76.8 −6.1
17
(CH3 )2 NNO2
18 19 20
CH3 C(CH2 OH)2 NO2 (O2 N)3 CC(NO2 )3
21 22 23
(O2 N)3 CH (CH3 )3 CNO2
424 [25] 420 [25]
R.F. Alamdari, M.H. Keshavarz / Fluid Phase Equilibria 292 (2010) 1–6
3
Table 1 (Continued ) No.
Energetic compound
24 25 26 27 28
New method
CH3 CH2 CH2 NO2 (CH3 )2 CHNO2
32
%Dev
Previous work
%Dev
J–R method
%Dev
−7.0
607.4
57.7
1091.9
183.5
271.8 218.2 188.7 183.8
8.0 −10.8 −3.9 8.7
242.7 231.6 197.2 197.2
−3.6 −5.3 0.5 16.6
399.0 244.1 263.0 266.7
58.5 −0.2 34.0 57.7
505.15 [26] 464.4
−8.1
365.0
−27.7
191.82 [25] 188.7 181.83 [25] 183.8
−1.6 1.1
197.2 197.2
2.8 8.5
278.0 251.7
44.9 38.4
347.15 [26] 387.2
11.5
423.1
21.9
871.9
151.2
385.15 [26] 358.3 O2 NCH2 CH2 CH2 NO2 CH3 NO2 (CH3 )2 CHCH2 NO2 CH3 CH2 CH2 NO2
29 30 31
Exp.
251.8 [25] 244.6 [25] 196.3 [25] 169.16 [25]
Average deviation
organic compound, group contribution methods have been widely used. The physical and thermochemical properties of an organic compound are calculated as a function of structurally dependent parameters, which can be determined by summing the number frequency of each group multiplied by its contribution. Group contribution methods can be used to estimate different properties such as normal boiling point, critical temperature, critical pressure, critical volume, standard enthalpy of formation, standard enthalpy of vaporization, standard Gibbs energy, normal melting point and standard enthalpy of fusion [8]. Group contribution methods have the advantage of supplying quick estimates, but are often of questionable and unknown reliability. Moreover, properties of large, complex and polyfunctional organic compounds cannot be accurately estimated by these methods. Normal melting points of organic compounds, in contrast to the other physicochemical properties, are not very well estimated by group contribution methods [8]. The QSPR/QSARs connect physical or chemical properties to a set of molecular descriptors. An extensive body of research in this area has focused on development of these relationships for use in different fields [8,13]. The molecular descriptors may be constitutional, geometric, electrostatic, or quantum-chemical [8,13]. The development of QSPR/QSARs is the identification of the appropriate set of descriptors that allow the desired attribute of the compound to be adequately predicted. The use of QSPR/QSARs has a key limitation because the set of organic compounds used to develop the relationship should be similar to those compounds for which predictions are desired. Complicated quantum mechanical methods can be used for simulating solid to liquid phase transitions in energetic materials [14–16]. Thompson and coauthors [14–16] have used molecular dynamic simulations to study the solid and liquid properties and to predict the melting points of several energetic compounds. Simple empirical methods have been developed for the estimation of melting point of simple organic molecules and/or homologous series, which are based on physical and structural parameters [17–19].
6.9
14.1
75.8
Some attempts have been recently introduced to predict the melting points of selected classes of energetic compounds [9,11,12]. The predicted results for nitramines, nitrate esters, nitrate salts and nitroaliphatics are relatively good with respect to experimental data [12]. For energetic compounds with polyfunctional energetic groups, deviations of the predicted results from the measured values become large. A new correlation that can be used for the reliable prediction of melting points of non-aromatic energetic compounds is described below. 3. Results and discussion In a homologous series of compounds, the addition of a substituent that leads to an increase in internal cohesive forces also leads to an increase in densities, boiling points, heats of vaporization, refractive indices and surface tensions. In contrast, internal cohesive forces do not correlate with the behavior of melting points because there are outstanding exceptions [20]. It can be shown that many outstanding puzzles exceptions are due to molecular symmetry [21,22]. There are actually different effects at work when a group is added to a molecule. The added group contributes more electrons to parent molecule to increase the polarizability of the molecule. There is an increase the London dispersion forces in this case and possibly also a change in the dipole moment. If there are strong polar groups in adjacent positions, the added group can redistribute electrons among various groups. The added groups may increase or decrease internal strains, including the bond lengths, the bond angles, the bond torsion angles and the degree of van der Waals crowding of intermolecular groups. They can also change molecular symmetry. The study of molecular structures of various non-aromatic energetic compounds with general formula Ca Hb Nc Od has shown that it is possible to get a suitable general correlation for predicting normal melting points of these compounds. It was found that for suitable combinations of elemental composition, Tm can be modeled from the melting temperature core (Tcore )
4
R.F. Alamdari, M.H. Keshavarz / Fluid Phase Equilibria 292 (2010) 1–6
Table 2 Comparison of the predicted melting points for some further non-aromatic compounds including new explosives by new method, previous work [12] as well as Joback and Reid (J–R) method [10] with experimental data. No. 1 2 3 4 5
Energetic compound CH3 ONO2 O2 NOCH2 CH2 CH2 CH2 CH2 ONO2 CH3 CH(ONO2 )CH2 CH(ONO2 )CH3 CH3 (C O)NH3 NO3 [CH3 (CH2 )5 ]4 NNO3
Exp.
New method
%Dev
Previous work
−1.7 0.5 22.2 1.2 13.9
J–R method
548 [25]
510.9
−6.8
556.9
5.3
857.3
−66.2
361.7 [25] 326 [25] 183.63 [25] 287.05 [25]
391.7 315.9 179.0 350.1
8.3 −3.1 −2.5 22.0
393.7 311.3 197.2 333.5
3.0 1.6 8.9 −4.5
341.2 412.7 255.4 677.4
−64.6 56.4 −5.7 26.6
11
376.15 [26]
387.6
3.0
459.8
7.4
12
324.15 [26]
322.4
−0.5
293.7
16.2
13
488.15 [26]
516.6
5.8
555.9
−9.4
14
432.15 [26]
436.8
1.1
359.6
−16.8
430.0
−0.5
15
374.15 [1]
379.6
1.5
395.5
5.7
628.2
67.9
16
469.15 [1]
475.8
1.4
527.8
12.5
875.2
86.6
17
498.15 [1]
581.1
16.7
666.9
33.9
1260.8
153.1
18
475.15 [1]
504.6
6.2
333.5
−29.8
951.1
100.2
19
623.15 [1]
465.9
−25.2
333.5
−46.5
918.1
47.3
HOCH2 C(CH3 )2 NO2 (CH3 )2 C(NO2 )2 CH3 CH2 CH2 NO2 C(NO2 )4
266.4 477.3 447.3
%Dev
9.2 1.9 2.7 8.0 9.8
7 8 9 10
187.7 257.9 257.9 380.0 355.3
%Dev
208.3 261.6 261.6 389.8 378.7
6
190.81 [25] 256.6 [25] 254.7 [25] 361 [25] 345 [25]
39.6 86.0 −67.6
R.F. Alamdari, M.H. Keshavarz / Fluid Phase Equilibria 292 (2010) 1–6
5
Table 2 (Continued ) No.
Energetic compound
20
21 22
NH4 NO3
Exp.
New method
%Dev
397.15 [1]
384.4
397.15 [26]
415.5
4.6
440.5
10.9
397.15 [26]
366.0
−7.8
355.3
−10.6
−3.2
Average deviation
6.9
as well as positive (T+ ) and negative (T− ) contributions of correcting terms are important factors, which can be given as follows: Tm = z1 + z2 Tcore + z3 T + + z4 T −
(1)
where Tm is the melting point of desired non-aromatic energetic compound, and z1 –z4 are the adjustable parameters, which can be found from experimental data given in Table 1. A multiple linear regression method [23] has been used to evaluate the adjustable parameters. Since the equation set is overdetermined, the leftdivision method for solving linear equations uses the least squares method [23]. It should be mentioned that an overdetermined system is a set of equations that has more independent equations than unknowns. The matrix inverse method and Cramer’s method will not work [23] in this situation. Thus, the left-division method can be used. The left-division method is based on Gauss elimination for which it uses fewer internal multiplications and divisions than the matrix method inversion. The results give the following optimized correlation: Tm (/K) = 281.7 + 28.97Tcore + 102.92T + − 110.11T −
(2a)
Tcore = a − 0.417b + 1.027c − 0.344d
(2b)
The correlation coefficient, R-squared, of Eqs. (2a) and (2b) is 0.93 [23]. The values of T+ and T− depend on some functional groups and structural parameters that can be specified as:
Previous work
438.3
%Dev
10.3
J–R method
586.4
12.4
%Dev
47.7
64.4
3.2. The energetic compounds with –N–NO2 , –NH–NO2 and –NHNO3 groups (1) The presence –N–NO2 groups: The ratio of the number of –N–NO2 to –CH2 or 3 groups has different effects: (i) If the ratio (nNNO2 /nCH2 or 3 ) ≥ 0.5, then T+ = 0.5; (ii) If the ratio (nNNO2 /nCH2 or 3 ) ≤ 0.2, then T− = 0.6. For the other ratios of nNNO2 /nCH2 or 3 , T+ and T− are zero. Unlike other physicochemical properties such as boiling point, which can be predicted quite easily by simply using additive constitutive properties, melting point is difficult to estimate. In general, according to Carnelley’s rule [21,22] it is known that the more symmetrical organic isomer has the higher melting point. Melting point is dependent upon the enthalpy and entropy of melting, i.e. Tm = Hm /Sm . The difference in melting points for different isomers in this case is due to the fact that the melting temperatures are affected not only by Hm but also by Sm . The sum of all the solid–solid phase change enthalpies behave in a more additive fashion but the fusion enthalpy by itself is not additive. In fact, the total phase change entropy is a function that behaves in additive fashion [24]. (2) The presence of –NH–NO2 and –NHNO3 groups: The value of T+ is equal to 1.0 in this situation.
3.1. Nitroaliphatics and nitrate esters (1) Cn H2n+1 (NO2 or ONO2 )m=1 or 2 : For mononitro- or mononitratealkanes, the values of T− depend on the number of carbon atoms in the alkyl group: (i) If n = 1, then T− = 1.0; (ii) If n ≥ 2, then T− = 0.6. For m = 2, the value of T− depends on the molecular structure of the energetic compound. The value of T− is 0.40 in this case except if two nitro groups are attached to one carbon in which T− = 0.0. For m = 1 or 2, there are low melting points in these compounds with respect to polynitro- or polynitrate-alkanes because the contributions of polar –NO2 and –ONO2 groups to the internal cohesive forces are small. However, it can be expected that the contribution of T− in m = 2 is lower than m = 1. (2) The presence of an –OH group: For the existence of hydroxyl group, T+ is equal to 1.0. It has long been known that the presence of hydrogen bonding has a special impact on the physical and chemical properties. The attractive forces in the crystal lattice are high owing to the existence of strong hydrogen bonding.
The existence of these polar groups in the molecular structure gives a significant contribution of T+ to the melting points. This phenomenon is due to the ability of the energetic compounds of this category to form strong hydrogen bonding. The constants T+ and T− are zero if the conditions for giving them various values are not met. It is to be noted that Eqs. (2a) and (2b) can only predict melting points of nitroaliphatics, nitrate esters and nitramines and cannot be applied for polynitroaromatic compounds. The predicted results of Joback–Reid method [10] and previously reported work [12] are given in Table 1. Since experimental data of Table 1 were used to get the new correlations, the predicted results for some well-known and new energetic compounds are also given in Table 2 and compared with measured data as well as with previous work [12] and the Joback–Reid method [10]. The latest reported values in the NIST Chemistry Web Book [25] in Tables 1 and 2 were taken to compare the above method with experimental data. The error percent in melting points, [(predictedmeasured)/measured] × 100, are also given in Tables 1 and 2. As pointed out in Tables 1 and 2, the reliability of the present method is better than two available simple methods.
6
R.F. Alamdari, M.H. Keshavarz / Fluid Phase Equilibria 292 (2010) 1–6
4. Conclusions
References
A novel improved method has been introduced for the simple and reliable prediction of melting points of non-aromatic energetic compounds including nitroaliphatics, nitrate esters and nitramines. This model is based on a melting core temperature as well as positive (T+ ) and negative (T− ) contributions of correction terms. The predicted results for various compounds, where experimental data were available in open literature, were compared with the experimental data and the previous work [12] and the Joback–Reid method [10]. Comparison of the predicted results with experimental data as well as the outputs of previous work [12] and Joback–Reid method [10] may be taken as appropriate validation of the new method. The present method provides an improved accuracy and applicability compared to the best available simple methods for non-aromatic energetic compounds.
[1] J.P. Agrawal, R.D. Hodgson, Organic Chemistry of Explosives, John Wiley & Sons, 2007. [2] M.H. Keshavarz, J. Hazard. Mater. A 136 (2006) 145–150. [3] M.H. Keshavarz, J. Hazard. Mater. A 136 (2006) 425–431. [4] M.H. Keshavarz, J. Hazard. Mater. 169 (2009) 890–900. [5] M.H. Keshavarz, H. Sadeghi, J. Hazard. Mater. 171 (2009) 140–146. [6] M.H. Keshavarz, Indian J. Eng. Mater. Sci. 14 (2007) 386–390. [7] M.H. Keshavarz, J. Hazard. Mater. 151 (2008) 387–393. [8] E. Poling, J.M. Prausnitz, J.P. O’Connell, The Properties of Gases and Liquids, fifth ed., McGraw-Hill, 2001. [9] M.H. Keshavarz, J. Hazard. Mater. 171 (2009) 786–796. [10] K.G. Joback, R.C. Reid, Chem. Eng. Commun. 57 (1987) 233–243. [11] M.H. Keshavarz, H.R. Pouretedal, J. Hazard. Mater. A 148 (2007) 592– 598. [12] M.H. Keshavarz, J. Hazard. Mater. A 138 (2006) 448–451. [13] R. Wang, J. Jiang, Y. Pan, H. Cao, Y. Cui, J. Hazard. Mater. 166 (2009) 155– 186. [14] L. Zheng, B.M. Rice, D.L. Thompson, J. Phys. Chem. B 111 (2007) 2891– 2895. [15] P.M. Agrawal, B.M. Rice, L. Zheng, G.F. Velardez, D.L. Thompson, J. Phys. Chem. B 110 (2006) 5721–5726. [16] A. Siavosh-Haghighi, D.L. Thompson, J. Phys. Chem. C 111 (2007) 7980– 7985. [17] J.S. Chickos, G. Nichols, J. Chem. Eng. Data 46 (2001) 562–573. [18] A. Jain, G. Yang, S.H. Yalkowsky, Ind. Eng. Chem. Res. 43 (2004) 7618–7621. [19] P. Simamora, S.H. Yalkowsky, Ind. Eng. Chem. Res. 33 (1994) 1405–1409. [20] J. Wei, Ind. Eng. Chem. Res. 38 (1999) 5019–5027. [21] R.J.C. Brown, R.F.C. Brown, J. Chem. Ed. 77 (2000) 724–731. [22] T. Carnelley, Philos. Mag. 13 (1882) 112–130. [23] W.J. Palm III, Introduction to Matlab for Engineers, McGraw-Hill, 2005, p. 328 and p. 394. [24] J.S. Chickos, W.E. Acree, Thermochim. Acta 395 (2003) 59–113. [25] NIST Standard Reference Data Base Number 69, which can be accessed electronically through the NIST Chemistry Web Book (http://webbook. nist.gov/chemistry/), references for individual molecules are given therein. [26] R. Meyer, J. Köhler, A. Homburg, Explosives, sixth ed., Wiley-VCH, 2007.
List of symbols Tcore melting temperature core T+ positive contribution of correcting term for melting temperature core negative contribution of correcting term for melting temT− perature core Tm melting point of desired non-aromatic energetic compound Hm enthalpy of melting entropy of melting Sm Acknowledgement We would like to thank the Research Committee of Malek-ashtar University of Technology (MUT) for supporting this work.
Contents lists available at ScienceDirect
Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid
A simple method to predict melting points of non-aromatic energetic compounds Reza Fareghi Alamdari, Mohammad Hossein Keshavarz ∗ Department of Chemistry, Malek-ashtar University of Technology, Shahin-shahr P.O. Box 83145/115, Islamic Republic of Iran
a r t i c l e
i n f o
Article history: Received 2 August 2009 Received in revised form 18 January 2010 Accepted 21 January 2010 Available online 1 February 2010 Keywords: Melting point Non-aromatic Energetic compound Correlation Safety
a b s t r a c t This work presents a new simple method to estimate the melting points of non-aromatic energetic compounds, which contain energetic functional groups C–NO2 , C–ONO2 and N–NO2 . This method can allow the reliable prediction of melting points of non-aromatic energetic materials through a new general correlation. Elemental composition and some specific parameters of non-aromatic energetic compounds are important factors. The predicted results for various non-aromatic energetic compounds show that the present method gives reliable predictions of melting points with respect to previous works. This method has been tested for different newly synthesized explosives with complex molecular structures and energetic compounds with several energetic functional groups. © 2010 Elsevier B.V. All rights reserved.
1. Introduction The developments of high-energy materials with increased performance, reduced sensitivity to external stimuli as well as desirable physical and thermodynamic properties are major challenges to the chemical industry. There has been reasonable progress in the synthesis and development of new energetic compounds in recent years because of their possible use in formulations of propellants and explosives [1]. The risks and hazards associated with the research investigations of energetic materials can be reduced by the development of novel predictive methods. Some new simple predictive methods have recently been developed for desk calculations of various thermo-physical properties of energetic compounds such as condensed phase heat of formation [2–5] and standard enthalpy of melting [6,7]. The knowledge of physical and thermodynamic properties of energetic compounds is of special importance to the scientists and engineers. It is difficult to find the experimental values of desired properties for energetic compounds of interest in the open literature. Moreover, it can be dangerous or not practical to synthesize and measure the interested properties. Thus, estimation methods are very attractive to use for energetic materials. For the estimation of thermo-physical properties of pure organic compounds, group contribution methods have been widely used. Group additivity methods are not reliable procedures to predict melting points
∗ Corresponding author. Tel.: +98 0312 522 5071; fax: +98 0312 522 5068. E-mail addresses: [email protected], [email protected] (M.H. Keshavarz). 0378-3812/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2010.01.017
[8,9]. For example, it has been shown that the predicted melting points using group contribution method of Joback and Reid [10] have an average deviation of 37.6% for 60 carbocyclic nitroaromatic compounds [11]. A simple method has been recently introduced to estimate the melting points of nitramines, nitrate esters, nitrate salts and nitroaliphatics [12]. This paper presents a significant improvement and extension of applicability of previous work [12] for energetic compounds containing the functional groups C–NO2 , C–ONO2 and N–NO2 . Only elemental composition and increasing or decreasing effects of some specific structural parameters are used in the new method. The present method is applied to different wellknown and new non-aromatic energetic compounds. The predicted results are also compared with experimental values, Joback and Reid method [10] as well as with previous work [12]. 2. Theory Group contribution methods and quantitative structure– property/activity relationships (QSPR/QSAR) are two primary approaches, which can be used to predict physicochemical properties based on the structure of an organic compound. The group contribution methods are primarily based on the numbers and types of molecular groups in the organic compounds [8,13]. Since the first order group contribution methods fail to distinguish between the isomers that contain the same numbers and types of groups, the second order group contribution methods can be applied to incorporate interactions between next nearest neighbors. Additivity methods are broadly useful in chemistry in which the properties of molecules can be derived from the properties of the atoms or functional groups. For the property estimation of an
2
R.F. Alamdari, M.H. Keshavarz / Fluid Phase Equilibria 292 (2010) 1–6
Table 1 Comparison of the predicted melting points (K) of non-aromatic compounds by new method, previous work [12] as well as Joback and Reid (J–R) method [10] with experimental data. No. 1 2 3 4
Energetic compound CH3 CH2 ONO2 CH3 CH(ONO2 )CH3 O2 NCH2 CH2 OCH2 CH2 ONO2 O2 NOCH2 CH2 CH2 CH2 ONO2
5 6
CH3 CH(ONO2 )CH2 CH2 ONO2
7 8 9
O2 NOCH2 CH(ONO2 )CH2 ONO2 (O2 NOCH2 )4 C
10 11 12 13
Exp.
%Dev
Previous work
%Dev
J–R method
%Dev
169.1 173.9 290.8 256.7
−5.3 −8.9 5.7 −9.9
187.7 187.7 317.0 257.9
5.1 −1.7 15.2 −9.5
277.6 273.9 615.5 466.0
55.4 43.5 123.7 63.5
364.15 [26]
418.0
14.8
475.6
30.6
940.6
158.3
253.4 [25]
256.7
1.3
257.9
1.8
451.0
78.0
324.45 [26]
340.4
4.9
342.0
5.4
642.1
97.9
308.0 329.6
7.7 −20.2
293.7 398.3
2.7 −3.6
605.6 811.4
111.7 96.5
1224.1
254.7
286 [25] 413 [25]
345.15 [26] (C6 H5 )4 NNO3 [CH3 (CH2 )6 ]4 NNO3 [CH3 (CH2 )3 ]4 NNO3
New method
178.6 [25] 190.81 [25] 275.15 [26] 285 [25]
387.2 [25] 345 [25] 392.2 [25]
367.7
6.5
632.2
83.2
359.4 383.5 340.1
−7.2 11.2 −13.3
355.3 355.3 355.3
−8.3 3.0 −9.4
14
334.65 [26]
324.7
−3.0
398.3
19.0
767.7
129.4
15
478.5 [25]
466.4
−2.5
472.8
−1.2
673.5
40.8
16
449.35 [26]
449.3
0.0
303.1
−32.5
504.3
12.2
345.45 [25]
358.3
3.7
304.6
−11.8
287.9
−16.7
267.65 [25]
279.3
4.4
304.6
13.8
336.8
25.8
381.8 398.8
−10.0 −5.1
418.5 424.4
−1.3 1.0
402.0 978.3
−5.2 132.9
449.35 [26]
441.7
−1.7
307.4
−31.6
562.1
25.1
292 [25] 298.65 [25]
328.2 298.8
12.4 0.0
253.7 300.3
−13.1 0.5
516.4 280.4
76.8 −6.1
17
(CH3 )2 NNO2
18 19 20
CH3 C(CH2 OH)2 NO2 (O2 N)3 CC(NO2 )3
21 22 23
(O2 N)3 CH (CH3 )3 CNO2
424 [25] 420 [25]
R.F. Alamdari, M.H. Keshavarz / Fluid Phase Equilibria 292 (2010) 1–6
3
Table 1 (Continued ) No.
Energetic compound
24 25 26 27 28
New method
CH3 CH2 CH2 NO2 (CH3 )2 CHNO2
32
%Dev
Previous work
%Dev
J–R method
%Dev
−7.0
607.4
57.7
1091.9
183.5
271.8 218.2 188.7 183.8
8.0 −10.8 −3.9 8.7
242.7 231.6 197.2 197.2
−3.6 −5.3 0.5 16.6
399.0 244.1 263.0 266.7
58.5 −0.2 34.0 57.7
505.15 [26] 464.4
−8.1
365.0
−27.7
191.82 [25] 188.7 181.83 [25] 183.8
−1.6 1.1
197.2 197.2
2.8 8.5
278.0 251.7
44.9 38.4
347.15 [26] 387.2
11.5
423.1
21.9
871.9
151.2
385.15 [26] 358.3 O2 NCH2 CH2 CH2 NO2 CH3 NO2 (CH3 )2 CHCH2 NO2 CH3 CH2 CH2 NO2
29 30 31
Exp.
251.8 [25] 244.6 [25] 196.3 [25] 169.16 [25]
Average deviation
organic compound, group contribution methods have been widely used. The physical and thermochemical properties of an organic compound are calculated as a function of structurally dependent parameters, which can be determined by summing the number frequency of each group multiplied by its contribution. Group contribution methods can be used to estimate different properties such as normal boiling point, critical temperature, critical pressure, critical volume, standard enthalpy of formation, standard enthalpy of vaporization, standard Gibbs energy, normal melting point and standard enthalpy of fusion [8]. Group contribution methods have the advantage of supplying quick estimates, but are often of questionable and unknown reliability. Moreover, properties of large, complex and polyfunctional organic compounds cannot be accurately estimated by these methods. Normal melting points of organic compounds, in contrast to the other physicochemical properties, are not very well estimated by group contribution methods [8]. The QSPR/QSARs connect physical or chemical properties to a set of molecular descriptors. An extensive body of research in this area has focused on development of these relationships for use in different fields [8,13]. The molecular descriptors may be constitutional, geometric, electrostatic, or quantum-chemical [8,13]. The development of QSPR/QSARs is the identification of the appropriate set of descriptors that allow the desired attribute of the compound to be adequately predicted. The use of QSPR/QSARs has a key limitation because the set of organic compounds used to develop the relationship should be similar to those compounds for which predictions are desired. Complicated quantum mechanical methods can be used for simulating solid to liquid phase transitions in energetic materials [14–16]. Thompson and coauthors [14–16] have used molecular dynamic simulations to study the solid and liquid properties and to predict the melting points of several energetic compounds. Simple empirical methods have been developed for the estimation of melting point of simple organic molecules and/or homologous series, which are based on physical and structural parameters [17–19].
6.9
14.1
75.8
Some attempts have been recently introduced to predict the melting points of selected classes of energetic compounds [9,11,12]. The predicted results for nitramines, nitrate esters, nitrate salts and nitroaliphatics are relatively good with respect to experimental data [12]. For energetic compounds with polyfunctional energetic groups, deviations of the predicted results from the measured values become large. A new correlation that can be used for the reliable prediction of melting points of non-aromatic energetic compounds is described below. 3. Results and discussion In a homologous series of compounds, the addition of a substituent that leads to an increase in internal cohesive forces also leads to an increase in densities, boiling points, heats of vaporization, refractive indices and surface tensions. In contrast, internal cohesive forces do not correlate with the behavior of melting points because there are outstanding exceptions [20]. It can be shown that many outstanding puzzles exceptions are due to molecular symmetry [21,22]. There are actually different effects at work when a group is added to a molecule. The added group contributes more electrons to parent molecule to increase the polarizability of the molecule. There is an increase the London dispersion forces in this case and possibly also a change in the dipole moment. If there are strong polar groups in adjacent positions, the added group can redistribute electrons among various groups. The added groups may increase or decrease internal strains, including the bond lengths, the bond angles, the bond torsion angles and the degree of van der Waals crowding of intermolecular groups. They can also change molecular symmetry. The study of molecular structures of various non-aromatic energetic compounds with general formula Ca Hb Nc Od has shown that it is possible to get a suitable general correlation for predicting normal melting points of these compounds. It was found that for suitable combinations of elemental composition, Tm can be modeled from the melting temperature core (Tcore )
4
R.F. Alamdari, M.H. Keshavarz / Fluid Phase Equilibria 292 (2010) 1–6
Table 2 Comparison of the predicted melting points for some further non-aromatic compounds including new explosives by new method, previous work [12] as well as Joback and Reid (J–R) method [10] with experimental data. No. 1 2 3 4 5
Energetic compound CH3 ONO2 O2 NOCH2 CH2 CH2 CH2 CH2 ONO2 CH3 CH(ONO2 )CH2 CH(ONO2 )CH3 CH3 (C O)NH3 NO3 [CH3 (CH2 )5 ]4 NNO3
Exp.
New method
%Dev
Previous work
−1.7 0.5 22.2 1.2 13.9
J–R method
548 [25]
510.9
−6.8
556.9
5.3
857.3
−66.2
361.7 [25] 326 [25] 183.63 [25] 287.05 [25]
391.7 315.9 179.0 350.1
8.3 −3.1 −2.5 22.0
393.7 311.3 197.2 333.5
3.0 1.6 8.9 −4.5
341.2 412.7 255.4 677.4
−64.6 56.4 −5.7 26.6
11
376.15 [26]
387.6
3.0
459.8
7.4
12
324.15 [26]
322.4
−0.5
293.7
16.2
13
488.15 [26]
516.6
5.8
555.9
−9.4
14
432.15 [26]
436.8
1.1
359.6
−16.8
430.0
−0.5
15
374.15 [1]
379.6
1.5
395.5
5.7
628.2
67.9
16
469.15 [1]
475.8
1.4
527.8
12.5
875.2
86.6
17
498.15 [1]
581.1
16.7
666.9
33.9
1260.8
153.1
18
475.15 [1]
504.6
6.2
333.5
−29.8
951.1
100.2
19
623.15 [1]
465.9
−25.2
333.5
−46.5
918.1
47.3
HOCH2 C(CH3 )2 NO2 (CH3 )2 C(NO2 )2 CH3 CH2 CH2 NO2 C(NO2 )4
266.4 477.3 447.3
%Dev
9.2 1.9 2.7 8.0 9.8
7 8 9 10
187.7 257.9 257.9 380.0 355.3
%Dev
208.3 261.6 261.6 389.8 378.7
6
190.81 [25] 256.6 [25] 254.7 [25] 361 [25] 345 [25]
39.6 86.0 −67.6
R.F. Alamdari, M.H. Keshavarz / Fluid Phase Equilibria 292 (2010) 1–6
5
Table 2 (Continued ) No.
Energetic compound
20
21 22
NH4 NO3
Exp.
New method
%Dev
397.15 [1]
384.4
397.15 [26]
415.5
4.6
440.5
10.9
397.15 [26]
366.0
−7.8
355.3
−10.6
−3.2
Average deviation
6.9
as well as positive (T+ ) and negative (T− ) contributions of correcting terms are important factors, which can be given as follows: Tm = z1 + z2 Tcore + z3 T + + z4 T −
(1)
where Tm is the melting point of desired non-aromatic energetic compound, and z1 –z4 are the adjustable parameters, which can be found from experimental data given in Table 1. A multiple linear regression method [23] has been used to evaluate the adjustable parameters. Since the equation set is overdetermined, the leftdivision method for solving linear equations uses the least squares method [23]. It should be mentioned that an overdetermined system is a set of equations that has more independent equations than unknowns. The matrix inverse method and Cramer’s method will not work [23] in this situation. Thus, the left-division method can be used. The left-division method is based on Gauss elimination for which it uses fewer internal multiplications and divisions than the matrix method inversion. The results give the following optimized correlation: Tm (/K) = 281.7 + 28.97Tcore + 102.92T + − 110.11T −
(2a)
Tcore = a − 0.417b + 1.027c − 0.344d
(2b)
The correlation coefficient, R-squared, of Eqs. (2a) and (2b) is 0.93 [23]. The values of T+ and T− depend on some functional groups and structural parameters that can be specified as:
Previous work
438.3
%Dev
10.3
J–R method
586.4
12.4
%Dev
47.7
64.4
3.2. The energetic compounds with –N–NO2 , –NH–NO2 and –NHNO3 groups (1) The presence –N–NO2 groups: The ratio of the number of –N–NO2 to –CH2 or 3 groups has different effects: (i) If the ratio (nNNO2 /nCH2 or 3 ) ≥ 0.5, then T+ = 0.5; (ii) If the ratio (nNNO2 /nCH2 or 3 ) ≤ 0.2, then T− = 0.6. For the other ratios of nNNO2 /nCH2 or 3 , T+ and T− are zero. Unlike other physicochemical properties such as boiling point, which can be predicted quite easily by simply using additive constitutive properties, melting point is difficult to estimate. In general, according to Carnelley’s rule [21,22] it is known that the more symmetrical organic isomer has the higher melting point. Melting point is dependent upon the enthalpy and entropy of melting, i.e. Tm = Hm /Sm . The difference in melting points for different isomers in this case is due to the fact that the melting temperatures are affected not only by Hm but also by Sm . The sum of all the solid–solid phase change enthalpies behave in a more additive fashion but the fusion enthalpy by itself is not additive. In fact, the total phase change entropy is a function that behaves in additive fashion [24]. (2) The presence of –NH–NO2 and –NHNO3 groups: The value of T+ is equal to 1.0 in this situation.
3.1. Nitroaliphatics and nitrate esters (1) Cn H2n+1 (NO2 or ONO2 )m=1 or 2 : For mononitro- or mononitratealkanes, the values of T− depend on the number of carbon atoms in the alkyl group: (i) If n = 1, then T− = 1.0; (ii) If n ≥ 2, then T− = 0.6. For m = 2, the value of T− depends on the molecular structure of the energetic compound. The value of T− is 0.40 in this case except if two nitro groups are attached to one carbon in which T− = 0.0. For m = 1 or 2, there are low melting points in these compounds with respect to polynitro- or polynitrate-alkanes because the contributions of polar –NO2 and –ONO2 groups to the internal cohesive forces are small. However, it can be expected that the contribution of T− in m = 2 is lower than m = 1. (2) The presence of an –OH group: For the existence of hydroxyl group, T+ is equal to 1.0. It has long been known that the presence of hydrogen bonding has a special impact on the physical and chemical properties. The attractive forces in the crystal lattice are high owing to the existence of strong hydrogen bonding.
The existence of these polar groups in the molecular structure gives a significant contribution of T+ to the melting points. This phenomenon is due to the ability of the energetic compounds of this category to form strong hydrogen bonding. The constants T+ and T− are zero if the conditions for giving them various values are not met. It is to be noted that Eqs. (2a) and (2b) can only predict melting points of nitroaliphatics, nitrate esters and nitramines and cannot be applied for polynitroaromatic compounds. The predicted results of Joback–Reid method [10] and previously reported work [12] are given in Table 1. Since experimental data of Table 1 were used to get the new correlations, the predicted results for some well-known and new energetic compounds are also given in Table 2 and compared with measured data as well as with previous work [12] and the Joback–Reid method [10]. The latest reported values in the NIST Chemistry Web Book [25] in Tables 1 and 2 were taken to compare the above method with experimental data. The error percent in melting points, [(predictedmeasured)/measured] × 100, are also given in Tables 1 and 2. As pointed out in Tables 1 and 2, the reliability of the present method is better than two available simple methods.
6
R.F. Alamdari, M.H. Keshavarz / Fluid Phase Equilibria 292 (2010) 1–6
4. Conclusions
References
A novel improved method has been introduced for the simple and reliable prediction of melting points of non-aromatic energetic compounds including nitroaliphatics, nitrate esters and nitramines. This model is based on a melting core temperature as well as positive (T+ ) and negative (T− ) contributions of correction terms. The predicted results for various compounds, where experimental data were available in open literature, were compared with the experimental data and the previous work [12] and the Joback–Reid method [10]. Comparison of the predicted results with experimental data as well as the outputs of previous work [12] and Joback–Reid method [10] may be taken as appropriate validation of the new method. The present method provides an improved accuracy and applicability compared to the best available simple methods for non-aromatic energetic compounds.
[1] J.P. Agrawal, R.D. Hodgson, Organic Chemistry of Explosives, John Wiley & Sons, 2007. [2] M.H. Keshavarz, J. Hazard. Mater. A 136 (2006) 145–150. [3] M.H. Keshavarz, J. Hazard. Mater. A 136 (2006) 425–431. [4] M.H. Keshavarz, J. Hazard. Mater. 169 (2009) 890–900. [5] M.H. Keshavarz, H. Sadeghi, J. Hazard. Mater. 171 (2009) 140–146. [6] M.H. Keshavarz, Indian J. Eng. Mater. Sci. 14 (2007) 386–390. [7] M.H. Keshavarz, J. Hazard. Mater. 151 (2008) 387–393. [8] E. Poling, J.M. Prausnitz, J.P. O’Connell, The Properties of Gases and Liquids, fifth ed., McGraw-Hill, 2001. [9] M.H. Keshavarz, J. Hazard. Mater. 171 (2009) 786–796. [10] K.G. Joback, R.C. Reid, Chem. Eng. Commun. 57 (1987) 233–243. [11] M.H. Keshavarz, H.R. Pouretedal, J. Hazard. Mater. A 148 (2007) 592– 598. [12] M.H. Keshavarz, J. Hazard. Mater. A 138 (2006) 448–451. [13] R. Wang, J. Jiang, Y. Pan, H. Cao, Y. Cui, J. Hazard. Mater. 166 (2009) 155– 186. [14] L. Zheng, B.M. Rice, D.L. Thompson, J. Phys. Chem. B 111 (2007) 2891– 2895. [15] P.M. Agrawal, B.M. Rice, L. Zheng, G.F. Velardez, D.L. Thompson, J. Phys. Chem. B 110 (2006) 5721–5726. [16] A. Siavosh-Haghighi, D.L. Thompson, J. Phys. Chem. C 111 (2007) 7980– 7985. [17] J.S. Chickos, G. Nichols, J. Chem. Eng. Data 46 (2001) 562–573. [18] A. Jain, G. Yang, S.H. Yalkowsky, Ind. Eng. Chem. Res. 43 (2004) 7618–7621. [19] P. Simamora, S.H. Yalkowsky, Ind. Eng. Chem. Res. 33 (1994) 1405–1409. [20] J. Wei, Ind. Eng. Chem. Res. 38 (1999) 5019–5027. [21] R.J.C. Brown, R.F.C. Brown, J. Chem. Ed. 77 (2000) 724–731. [22] T. Carnelley, Philos. Mag. 13 (1882) 112–130. [23] W.J. Palm III, Introduction to Matlab for Engineers, McGraw-Hill, 2005, p. 328 and p. 394. [24] J.S. Chickos, W.E. Acree, Thermochim. Acta 395 (2003) 59–113. [25] NIST Standard Reference Data Base Number 69, which can be accessed electronically through the NIST Chemistry Web Book (http://webbook. nist.gov/chemistry/), references for individual molecules are given therein. [26] R. Meyer, J. Köhler, A. Homburg, Explosives, sixth ed., Wiley-VCH, 2007.
List of symbols Tcore melting temperature core T+ positive contribution of correcting term for melting temperature core negative contribution of correcting term for melting temT− perature core Tm melting point of desired non-aromatic energetic compound Hm enthalpy of melting entropy of melting Sm Acknowledgement We would like to thank the Research Committee of Malek-ashtar University of Technology (MUT) for supporting this work.