Theoretical Prediction of Properties of Aliphatic Polynitrates - The

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Theoretical Prediction of Properties of Aliphatic Polynitrates Gui-xiang Wang,* Xue-dong Gong, Hong-chen Du, Yan Liu, and He-ming Xiao* Computation Institute for Molecules and Materials, Department of Chemistry, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China ABSTRACT: Aliphatic polynitrates are studied using the density functional theory B3LYP method with basis set 6-31G*. The assigned infrared spectrum is obtained and is used to compute the thermodynamic properties based on the frequencies scaled by 0.96 and the principle of statistic thermodynamics. On comparison of the theoretical densities with the experimental ones, the reliability of this theoretical method is tested. Detonation properties are evaluated using the modified Kamlet-Jacobs equations based on the calculated densities and heats of formation. According to the largest exothermic principle, the relative specific impulse (Is) is investigated by calculating the enthalpy of combustion (ΔHcomb) and the total heat capacity (Cp,gases). It is found that the introduction of methylene nitrate group could decrease the specific impulses on whole. Moreover, in combination with the energetic properties, xylitol pentanitrate, mannitol hexanitrate, volemitol heptanitrate, and 1,2,3,4,5,6,7,8-octanitrate n-octane are potential candidates for high energy density compounds.

1. INTRODUCTION A solid propellant refers to a type of high energy composite material with particular characteristics, including oxidant, adhesive, plasticizer, metal incendiary agent, high energy additive, etc. It is the power source of various engines of rockets, missiles, and space craft, and its performance plays an important role in the survival capacity and combat efficiency of the missile and the development of aerospace industry. Combined with the development history of the solid propellants at home and abroad, improving the energetic level of the solid propellant becomes the main research orientations and the key points of technology for the future, i.e., seeking high energy density compound/material (HEDC/HEDM) is still our long-term focus. Certainly, exploration of a high energy plasticizer component will also be of great importance. At present, a very good way to obtain a high energy plasticizer is to substitute a compound or polymer chain with high energetic groups so as to increase energy and to improve oxygen balance, such as nitro (-NO2), nitrate (-ONO2), nitramine (-NNO2), azido (-N3), and difluoramino (-NF2) groups.1-3 Nitrate esters, such as MN, EGDN, NG, etc., as a kind of multifunctional material, have been receiving considerable attention and a lot of investigations.4,5-24 Their structures, heats of formation, pyrolysis mechanism, etc., have been studied by semiempirical MO methods, ab initio MO methods, density functional theory, etc.7-11,13-18,20-24 However, previous studies mainly focused on several mono- and bis-nitrate esters, few reports involve polynitrate esters. Therefore, in this paper, several aliphatic polynitrates (see Figure 1), i.e., methyl nitrate (MN), ethylene glycol dinitrate (EGDN), nitroglycerine (NG), erytritol tetranitrate (ETN), xylitol pentanitrate (XPN), mannitol hexanitrate (MHN), volemitol heptanitrate (VHN), and 1,2,3,4,5,6,7,8-octanitrate n-octane (ONO), are selected and r 2011 American Chemical Society

fully optimized at the DFT-B3LYP/6-31G* level to obtain the molecular geometries, spectra, thermodynamic properties, molecular volume (V), theoretical density (F), detonation velocity (D), detonation pressure (P), and the specific impulse (Is). In the past decade, quantitative criteria considering both energy (including F, D, and P) and stability (BDE of the trigger bond) requirements, i.e., F ≈ 1.9 g/cm3, D ≈ 9.0 km/s, P ≈ 40.0 GPa, and BDE ≈ 80-120 kJ/mol, are expediently employed to design and filtrate potential HEDCs,25 which is of great practical value in the formulation design of composite explosives. However, the quantitative criteria for HEDCs is not applicable for propellant which requires HEDCs possessing not only high density but also high specific impulse(Is),1-3 which has been rarely considered in previous theoretical research. Since it is quite difficult to experimentally measure the Is of propellants and impossible for unsynthesized compounds, in solid propellant research, it is of great significance and urgency to theoretically predict Is and seek HEDC candidates with the most desirable Is parameter.

2. COMPUTATIONAL METHODS Some studies18,20 have shown that the DFT-B3LYP method26,27 in combination with the 6-31G*28 basis set is able to give accurate molecular structures, infrared vibrational frequencies, and other properties. In this paper, several aliphatic polynitrates are studied at this level with the Gaussian03 Received: June 13, 2010 Revised: December 14, 2010 Published: January 7, 2011 795

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The Journal of Physical Chemistry A

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MO PM348 method are precise enough to substitute the experimental data as has been proven in the previous studies.49 In practice, F0 can only approach to but not equal Fcryst, thus the D and P calculated using Fcryst can be considered as their upper limit (maximum values). As is known to all, accurate prediction of crystal density is difficult. The “group or volume additivity” method,50,51 although simple and rapid, cannot give reliable results owing to its inherent drawbacks, while the “crystal packing” method,52,53 which is more reliable, has its limitation in routine calculation due to its extensive requirement of computer resources. Recently, an efficient and convenient way has been worked out to predict the crystalline densities of energetic materials with CHNO elements.54 Studies have indicated that,54 when the average molar volume V estimated by the Monte Carlo method based on 0.001electrons/bohr3 density space at the B3LYP/6-31G** or 6-31G* level is used, the theoretical molecular density Fmol (Fmol = M/V, M is the molecular weight) is very close to the experimental crystal density Fcryst. It is worth noting that the average volume used here should be the statistical average of at least 100 volume calculations. Furthermore, the relative specific impulse values have also been calculated using the method introduced by Politzer et al.55 The specific impulse (Is), widely used as a means of characterizing and evaluating explosives, is often expressed in terms of the absolute temperature in the combustion chamber, TC, and the number of moles of gaseous products produced per unit weight of explosive, N (N = n/M, where n is the number of moles of gaseous products produced by 1 molar explosive and M is the molecular weight of the explosive) by the simplified relationship given as eq 356

Figure 1. Illustration of the molecular structures of the title compounds.

program package.29 Since the DFT-calculated harmonic vibrational frequencies are usually larger than those observed experimentally, they are scaled using a factor of 0.96 as was done before.30 On the basis of the principle of statistical thermodynamics,31 standard molar heat capacity (C°p,m), standard molar entropy (S°m), and standard molar enthalpy (H°m) from 200 to 800 K are derived from the scaled frequencies using a selfcompiled program. Detonation velocity and pressure are the most important parameters for evaluating the detonation characteristics of energetic materials. For explosives with CHNO elements, these parameters can be calculated using the Kamlet-Jacbos (K-J) equations32,33 0:5

D ¼ ð1:011 þ 1:312F0 ÞðNM Q 0:5 Þ0:5 0:5

P ¼ 1:558F0 2 NM Q 0:5

Is TC 1=2 N 1=2

ð3Þ

This proportionality can be rationalized by kinetic theory. To apply eq 3, it is necessary to establish the identities and amounts of the various products and to determine the combustion temperature. A simple approach to obtain the approximate combustion temperature involves assuming that the heat of combustion of the explosive is used entirely to heat the product gases to the combustion temperature so that

ð1Þ

- ΔHcomb ¼ Cp;gases ðTC - T0 Þ

ð2Þ

where ΔHcomb is the enthalpy of combustion, Cp,gases represents the total heat capacity of the gaseous products, and T0 and TC are the initial and the combustion temperatures, respectively. In eq 4, it is assumed that ΔHcomb is constant over the temperature range between T0 and TC and that the pressure in the combustion chamber remains constant because of a steady-state situation; the rates of formation and discharge of gaseous products are taken to be equal. ΔHcomb can be calculated from the heats of formation of the explosive and the gaseous products as follows

where P is the detonation pressure (GPa), D is the detonation velocity (km/s), F0 is the packed density (g/cm3), N is the moles of gas produced by per gram of explosives, M is the average molar weight of detonation products, and Q is the chemical energy of detonation (kJ/g). N, M, and Q are decided according to the largest exothermic principle. Obviously, D and P of unsynthesized explosives and hypothetical compounds cannot be evaluated for lack of experimental Q and F0 values. Therefore, we have recommended and used modified K-J equations based on the calculation results of quantum chemistry.25,34-47 In detail, the loading density of the explosives F0 is replaced by the crystal theoretical density (Fcryst), while Q is calculated as the difference between the heats of formation (HOF) of products and that of reactants. From the K-J equations, it can be found that Q has much less effect than F0 on D and P. Therefore, Q and HOF estimated by the semiempirical

ΔHcomb ¼

products X

Ni ΔHf , i - NHEDC ΔHf , HEDC

ð4Þ

ð5Þ

i

The molar heats of formation for gaseous products are known, while those for explosives can be determined in a number of ways. For example, a reasonable estimate can often be obtained from standard bond enthalpies plus any strain contributions. However, Politzer55 has pointed out that the relative specific 796

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Figure 2. The calculated infrared spectra of the title compounds at the B3LYP/6-31G* level.

3. RESULTS AND DISCUSSION

impulse is not highly sensitive to the method used for obtaining the heats of formation. Therefore, in our work, we compute the gas-phase heats of formation with the semiempirical MO PM3 method to predict the specific impulse. All the calculations considered here were performed on a Pentium IV personal computer using the default convergence criteria given in the programs.

3.1. Infrared Spectra. Figure 2 and Table 1 provide the calculated IR spectra of the aliphatic polynitrates obtained at the B3LYP/6-31G* level. Due to the complexity of vibrational modes, it is difficult to assign all bands. Therefore, only some typical vibrational modes were analyzed and discussed. 797



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Table 1. Key Vibrational Frequencies (in cm-1) of the Aliphatic Polynitrates Computed at the B3LYP/6-31G* Levela chemical name

ν(O-N)

ν(C-O)

νs(NO2)

νas(NO2)

MN

838.7

994.6

1294.2

1689.9

EGDN NG

817.3, 839.7 812.4, 833.6

986.5 887.5, 997.3

1269.8, 1295.7 1271.9, 1278.9

1698.8, 1702.5 1696.9-1703.2

ETN

811.3, 816.1

874.9, 944.1

1274.2-1304.4

1699.9-1716.0

XPN

793.0-813.5

997.2

1278.8-1297.2

1708.2-1726.2

MHN

780.7-839.2

1015.4

1269.8-1295.3

1704.2-1740.4

VHN

814.9-838.2

1044.2, 1052.8

1268.1-1282.3

1708.8-1734.5

ONO

790.5-824.0

987.2, 1001.5

1271.7-1312.1

1706.8-1743.4

ν(O-N), O-NO2 streching vibration; ν(C-O), C-ONO2 streching vibration; νs(NO2) and νas(NO2), symmetric and asymmetric stretch of -NO2 group. a

ranging from 200 to 800 K were obtained and are listed in Table 3. From these data, all the thermodynamic functions increase with temperature evidently. This is because the main contributions to the thermodynamic functions are from the translations and rotations of molecules when temperature is low, however, at the higher temperature, the vibrational movement is intensified and therefore makes more contributions to the thermodynamic properties, which lead to the increase in the thermodynamic functions. Taking NG (nitroglycerine) as an example, the temperature-dependent relations for C°p, m, S°m, and H°m in the range of 200-800 K can be expressed as shown in Figure 3 (where R2 is the correlation coefficient and SD is the standard deviation). As the temperature increases, the gradients of C°p,m and S°m decrease, while that of H°m increases constantly. In addition, all the thermodynamic functions increase with increasing the number of methylene nitrate (-CH(ONO2)-) groups (n1 = 1, 2, ..., 8). The correlation equations are C°p,m = 1.88 þ 71.77n1, S°m = 198.00 þ 111.74n1, and H°m = 2.08 þ 13.11n1, and the corresponding correlation coefficients are 1.0000, 0.9991, and 0.9998, respectively. Similarly, C°p,m, S°m, and H°m increase on an average by 71.77 J 3 mol-1 3 K-1, 111.74 J 3 mol-1 3 K-1, and 13.11 kJ 3 mol-1 when one more methylene nitrate group is introduced, which shows good group additivity of thermodynamic functions. 3.3. Density and Detonation Properties. Table 4 collects V, F, D, and P of the title compounds. The oxygen balances (OB100), calculated heats of formation HOF, and Q are also listed in this table. The oxygen balances (OB100) are calculated using the formula (6), which can be used to rudely predict the impact sensitivities of the explosives.59 100ð2nO - nH - 2nC - 2nCOO Þ ð6Þ OB100 ¼ M

Table 2. Partial Experimental and Calculated Frequencies of MNa wavenumber (cm-1) 560 (551.7 w),

assignment deformation of the O;NdO angle

655 (640.9 w) 757 (734.6 w)

out-of-plane deformation

853 (838.7 s) 1018 (994.6 m)

O-NO2 streching vibration C-ONO2 streching vibration

1140 (1131.3 w),

rocking vibration of -CH3 group

of nitro groups

1177 (1151.2 w) 1433 (1422.8 w)

deformation vibration of -CH3 group

1678 (1689.9 s),

symmetric and asymmetric

1290 (1294.2 s) 2860 (2957.1 w), 2950 (3038.6 w), 3006 (3056.9 w)

stretch of nitrate group C-H symmetric and asymmetric stretches

a

Calculated values are in parentheses. Key: s, m, and w represent strong, medium, and weak vibrations, respectively.

It is evident from Figure 2 and Table 1 that there are three strong characteristic regions. One in the 1689.9-1743.4 cm-1 range corresponds to the NdO asymmetric stretch of -ONO2 groups, and in this region, vibrations recorded equal those for NdO bonds. For example, XPN has five bands at 1708.2, 1710.5, 1713.2, 1719.7, and 1726.2 cm-1. In addition, its central position moves toward higher frequency as the number of nitrate groups increases. Another remarkable signal centering in 1261.51482.9 cm-1 is associated with the NdO symmetric stretch of nitrate groups. The third region at less than 1151.2 cm-1 is mainly caused by the O-NO2 streching vibration. To see the reliability of theoretical computation, the experimental and calculated vibrational frequencies of MN (methyl nitrate)6 are compared in Table 2. It is evident from Table 2 that the calculated frequencies of MN (551.7, 640.9, 838.7, 1131.3, 1294.2, 1422.8, and 1689.9 cm-1) are in good accord with the experimental values (560, 655, 853, 1140, 1290, 1433, and 1678 cm-1). All of these prove the reliability of the computational IR at the B3LYP/6-31G* level. The trivial discrepancy is perhaps due to the intermolecular interactions existing in experimental samples. 3.2. Thermodynamic Properties. On the basis of the above scaled vibrational results, the principle of statistic thermodynamics, and the self-compiled program, thermodynamic properties

where nO, nH, and nC represent the numbers of O, H, and C atoms, respectively; nCOO is the number of COO- groups, and here nCOO = 0 for the aliphatic polynitrates; M is the molecular weight. From Table 4, although the derivations between Fcalcd and Fexptl are somewhat big (such as 0.34, 0.27, 0.20, 0.28, and 0.17), there is a good correlation between them (see Figure 4). The correlation equation is ð7Þ Fcalcd ¼ 0:73 þ 0:69Fexptl with correlation coefficient (R) 0.9722, which indicates that Fcalcd at the B3LYP/6-31G* level could be used to predict the crystal 798



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Table 3. Thermodynamic Properties of the Title Compounds at Different Temperaturesa 200 °C

chemical name MN

EGDN

NG

ETN

XPN

MHN

VHN

ONO

a

C°p,m

298.15 °C

300 °C

400 °C

500 °C

600 °C

700 °C

800 °C

60.37

75.75

76.04

91.40

104.81

115.94

125.10

132.68

S°m

273.38

300.32

300.79

324.79

346.67

366.79

385.37

402.59

H°m

9.08

15.75

15.89

24.27

34.10

45.16

57.22

70.12

C°p,m

111.26

143.95

144.56

175.61

201.51

222.24

238.77

252.08

S°m

372.93

423.42

424.31

470.25

512.32

550.97

586.51

619.29

H°m

15.50

28.02

28.28

44.33

63.23

84.46

107.54

132.10

C°p,m

163.39

214.55

215.49

262.21

300.25

330.21

353.78

372.55

S°m H°m

459.49 21.88

534.31 40.44

535.64 40.84

604.22 64.79

666.98 92.99

724.48 124.57

777.22 158.82

825.73 195.17

C°p,m

220.32

287.55

288.77

349.79

399.34

438.23

468.73

492.94

S°m

551.46

652.05

653.83

745.51

829.10

905.49

975.43

1039.66 259.49

H°m

28.95

53.90

54.43

86.45

124.00

165.96

211.37

C°p,m

273.24

358.85

360.39

436.72

498.15

546.10

583.56

613.19

S°m

616.27

741.51

743.74

858.21

962.53

1057.77

1144.88

1224.81

H°m

34.98

66.05

66.72

106.69

153.56

205.87

262.43

322.32

C°p,m S°m

330.88 737.22

430.88 888.12

432.70 890.79

523.01 1028.03

595.99 1152.89

653.05 1266.81

697.63 1370.97

732.85 1466.51

H°m

43.42

80.84

81.64

129.56

185.66

248.23

315.85

387.44

C°p,m

383.15

500.68

502.81

608.70

693.98

760.49

812.33

853.23

S°m

793.96

969.02

972.13

1131.74

1277.11

1409.77

1531.06

H°m

49.30

92.71

93.64

149.38

214.69

287.55

366.30

449.65

C°p,m

441.29

575.68

578.10

697.87

794.15

869.20

927.67

973.77

S°m

880.16

1081.70

1085.27

1268.52

1435.02

1586.73

1725.29

1852.29

H°m

56.29

106.28

107.34

171.33

246.13

329.45

419.41

514.57

1642.3

Units: T, K; C°p,m, J 3 mol-1 3 K-1; ΔS°m, J 3 mol-1 3 K-1; ΔH°m, kJ 3 mol-1.

Figure 3. Relationships between the thermodynamic functions (C°p,m, S°m, and H°m) of NG and the temperature (T).

theoretical and experimental D and P of NG are 8.03 km 3 s-1 and 25.92 GPa and 7.70 km 3 s-1 and 25.30 GPa, respectively. This reflects that the predicted detonation properties of the title compounds using

densities (F0 exptl. in Table 4). D and P can therefore be evaluated. Comparing the theoretical D and P with the experimental ones, we find that the differences between them are small. For example, the 799



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Table 4. Predicted Densities and Detonation Properties of the Title Compoundsa OB100

Q

HOF

V

Fcalcd

F0 exptlb

Dc

MN

1.30

1619.1

-135.99

49.54

1.56 (1.22)

1.20

7.44 (6.30)d

18.59

EGDN

2.63

1641.5

-226.32

86.83

1.75 (1.48)

1.48

8.00 (7.30)d

25.07

NG

3.08

1541.6

-320.37

126.99

1.79 (1.59)

1.54

8.03 (7.70)e

25.92 (25.30)e

ETN

3.31

1506.0

-395.90

160.49

1.88 (1.60)

1.67

8.40

29.90

XPN

3.45

1472.9

-489.85

194.37

1.94

1.75

8.61

32.32

MHN

3.54

1470.1

-547.17

237.71

1.90 (1.73)

1.70

8.42 (8.26)d

30.38

VHN

3.60

1439.4

-667.91

273.52

1.93

1.74

8.50

31.42

ONO

3.65

1438.4

-733.09

313.38

1.92

1.72

8.43

30.64

chemical name

Pc

Units: HOF/(kJ 3 mol-1), Q/(J 3 g-1), V/(cm3 3 mol-1), Fcalcd/(g 3 cm-3), D/(km 3 s-1), p/(GPa). The experimental values in parentheses (Fexptl) are taken from ref 57. b F0 exptl is the predicted experimental density. c D and P are predicted by F0 exptl according to the K-J equations. d The experimental values in parentheses are taken from ref 57. e The experimental values in parentheses are taken from ref 58. a

about the chemical bond. As a whole, the fewer Mulliken bond populations a bond has, the easier the bond breaks. Though Mulliken population analysis60 suffers from some shortcomings, such as the basis set dependence, results derived from Mulliken population analysis at the same calculation condition are still meaningful for comparing trends in the electron distribution for homologous compounds as was done here. The bond orders obtained from the Mulliken population analysis for the title compounds at the B3LYP/6-31G* level are listed in Table 5. Inspecting the data in Table 5, we can see clearly that the overlap population of the O-NO2 bond (MO-NO2) is the least in each molecule, which predicts that the O-NO2 bond with least overlap population may be the trigger bond during thermolysis initiation processes. Meanwhile, on the whole, with the number of methylene nitrate (-CH(ONO2)-) groups increasing, MO-NO2 decreases as expected (see Figure 6). This suggests that the stability of the title compounds decreases and their sensitivities increase accordingly, which confirms that the -CH(ONO2)- group has an effect on activity. 3.4.2. Kinetic Parameter. To measure the relative stabilities of the title compounds, the bond dissociation energies (BDEs) are calculated. Generally speaking, the less energy that is required to break a bond, the weaker the bond is and the more possible the bond becomes a trigger bond. BDE is the required energy in homolysis of a bond and is commonly denoted by the difference between the total energies of the product and the reactant after zero-point energy correction. The expressions for the homolysis of the A-B bond (8) and for calculating its BDE (9) are shown as follows:61

Figure 4. The relationship between Fcalcdand Fexptl.

the modified K-J equation are reliable. In fact, many previous studies have shown the reliability of the calculation method.25 Figure 5 presents the relationships between OB100, Q, F0 exptl, HOF, V, D, P, and the number of -CH(ONO2)- groups (n1 = 1, 2, ..., 8). OB100 increases and Q decreases with the increasing number of -CH(ONO2)- groups, respectively. HOF and V exhibit linear relationships, i.e., HOF = -55.90 - 85.26n1 (R = -0.9987, SD = 11.7487) and V = 11.80 þ 37.46n1 (R = 0.9997, SD = 2.4786). F0 exptl, D, and P increase with the number of -CH(ONO2)- group on whole, revealing that the increase of substituted groups benefits the densities and detonation properties of the title compounds. When n1 = 5, the density, detonation velocity, and pressure reach the maximum values, i.e., F0 exptl = 1.75 g 3 cm-3, D = 8.61 km 3 s-1 and P = 32.32 GPa. When n1 > 5, F0 exptl, D, and P change little. However, compared with famous energetic plasticizers in some solid propellants, such as EGDN (F0 exptl = 1.48 g/cm3, D = 8.00 km/s, P = 25.07 GPa) and NG (F0 exptl = 1.54 g/cm3, D = 8.03 km/s, P = 25.92 GPa), they all have better detonation performance when the number of -CH(ONO2)- groups is not less than 4, which indicates that they are all potential energetic compounds. Therefore, in the design of an explosive molecule, we can adjust the detonation properties by changing the substituted groups. 3.4. Pyrolysis Mechanism and Identification of Stability. 3.4.1. Bond Overlap Populations. Bond overlap populations reflect the electron accumulations in the bonding region, and they can provide us with detailed information

R 1 A- BR 2 ðgÞ f R 1 A 3 ðgÞ þ R 2 B 3 ðgÞ

ð8Þ

BDEðR1A - BR2Þ ¼ ½ER1A • þ ER2B• - EðR1A - BR2Þ

ð9Þ

where R1A-BR2 stands for the neutral molecule and R1A 3 and R2B 3 for the corresponding product radicals after the bond dissociation; BDE(R1A-BR2) is the BDE of the bond R1ABR2; E (R1A-BR2), E R1A• and E R2B• are the zero-point energy corrected total energies of the molecule and the product radicals, respectively. In this paper, first, taking NG as an example, five possible initial steps in the pyrolysis route are considered by breaking the following bonds: (1) O-NO2, (2) C-C, (3) C-H, (4) C-O, and (5) H transfer reactions of C-H bond. Results are collected in Table 6. 800



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Figure 5. Correlations between OB100, Q, F0 exptl, HOF, V, D, P and the number of methylene nitrate groups (n1).

Table 5. Mulliken Bond Populations for the Title Compounds chemical name

MO-NO2

MC-O

MC-C

MC-H

MNdO

MN EGDN

0.1572 0.1459

0.1827 0.1687

0.3281

0.3722 0.3593

0.3124 0.3045

NG

0.1491

0.1704

0.2886

0.3442

0.2981

ETN

0.1407

0.1586

0.2809

0.3473

0.2836

XPN

0.1330

0.1717

0.2586

0.3472

0.2849

MHN

0.1293

0.1539

0.3085

0.3535

0.3015

VHN

0.1351

0.1612

0.2676

0.3412

0.2886

ONO

0.1270

0.1581

0.2724

0.3463

0.2892

the trigger bond during the thermolysis initiation process, which validates the conclusion drawn from the above Mulliken population analysis. Therefore, only the BDEs of the O-NO2 bonds are calculated except for NG. Comparing the BDEs of O-NO2 for all title compounds, we found they are large enough and suffice the stability request of BDE ≈ 80-120 kJ 3 mol-1 suggested previously,25 which shows the title compounds are quiet stable. 3.5. Relative Specific Impulse. Table 7 gives idealized stoichiometric decomposition reactions and some properties for the aliphatic polynitrates. To facilitate comparisons, our values are given relative to HMX, a widely used HEDM. According to the largest exothermic principle,36 all nitrogens are assumed to go to N2, carbons to CO2 (if oxygens are enough) or C, while oxygens preferentially form H2O (if hydrogens are available). We use such reactions to calculate the quantity n/M. Figure 7a presents the correlations between N, TC, and the number of methylene nitrate groups (n1), which indicates that N decreases with n1 while TC increases rapidly when n1 < 2 and slowly when n1 g 2. Is also decreases on the whole (see Figure 7b), which shows that the introduction of methylene nitrate groups decreases the specific impulse. Except for EGDN (Is = 14.52), Is values of all nitrates are less than that of HMX (Is = 14.43). Since the solid propellant requires HEDMs to possess high density and high specific impulse, combination with the energetic properties, we suggest that XPN (xylitol pentanitrate), MHN (mannitol hexanitrate), VHN (volemitol heptanitrate), and ONO (1,2,3,4,5,6,7,8octanitrate n-octane) are potential HEDCs for energetic plasticizers. Their relative specific impulses (Is, compared with HMX) and densities are 0.983 and 1.75 g 3 cm-3, 0.986

Figure 6. Correlation between MC-NO2 and the structures.

From Table 6, it can be seen that, BDE of the homolysis of the O-NO2 bond is the least, which suggests that the O-NO2 bond is 801



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Table 6. Total Energies (hartree), the Zero-Point Energies (hartree), and BDEs (kJ/mol) for the Title Compounds (reactant) and the Related Radicals (products)a chemical name NG

MN EGDN ETN XPN MHN VHN ONO

breaking bonds

reactant energy

zero point energy

product energy (1)

zero point energy (1)

product energy (2)

zero point energy (2)

O-NO2 C-C C-H C-O H transfer O-NO2 O-NO2 O-NO2 O-NO2 O-NO2 O-NO2 O-NO2

-958.1672 -958.1672 -958.1672 -958.1672 -958.1672 -320.1894 -639.1784 -1277.1456 -1596.1348 -1915.1245 -2234.1014 -2553.0917

0.1259 0.1259 0.1259 0.1259 0.1259 0.0548 0.0907 0.1607 0.1962 0.2308 0.2659 0.3007

-753.0349 -638.5172 -957.56611 -677.8312 -958.0983 -115.0505 -434.0450 -1072.0185 -1391.0037 -1709.9981 -2028.9703 -2347.9647

0.1089 0.0758 0.1088 0.1052 0.1183 0.0368 0.0736 0.1445 0.1799 0.2150 0.2498 0.2846

-205.0722 -319.5203 -0.5003 -280.2168

0.0088 0.0391 0 0.0106

-205.0722 -205.0722 -205.0722 -205.0722 -205.0722 -205.0722 -205.0722

0.0088 0.0088 0.0088 0.0088 0.0088 0.0088 0.0088

BDE 136.77 287.17 312.68 220.70 161.58b 151.54 139.42 125.19 135.47 124.40 135.99 125.19

a BDEs are corrected by the zero-point energies. b The activation energy for the H transfer reaction obtained from the energies of transition state and reactant including zero-point energy corrections.

Table 7. Idealized Stoichiometric Decomposition Reactions and Some Properties of the Aliphatic Polynitratesa

a

molecule

idealized stoichiomitric reaction

M

n

N

ΔfH (kJ/mol)

ΔHcomb (kJ/mol)

CP,gases (J/(mol 3 K))

TC

Is

relative Is

HMX MN EGDN NG ETN XPN MHN VHN ONO

C4N8O8H8 f 4.0 H2O þ 2.0CO2 þ 4.0N2 þ 2.0C CH3NO3 f 1.5H2O þ 0.8CO2 þ 0.5N2 þ 0.2C C2H4N2O6 f 2.0H2O þ 2.0CO2 þ 1.0N2 C3H5N3O9 f 2.5H2O þ 3.0CO2 þ 0.2O2 þ 1.5N2 C4H6N4O12 f 3.0H2O þ 4.0CO2 þ 0.5O2 þ 2.0N2 C5H7N5O15 f 3.5H2O þ 5.0CO2 0.8O2 þ 2.5N2 C6H8N6O18 f 4.0H2O þ 6.0CO2 þ 1.0O2 þ 3.0N2 C7H9N7O21 f 4.5H2O þ 7.0CO2 þ 1.2O2 þ 3.5N2 C8H10N8O24 f 5.0H2O þ 8.0CO2 þ 1.5O2 þ 4.0N2

296.16 77.04 152.06 227.09 302.11 377.13 452.16 527.18 602.21

10.00 2.75 5.00 7.25 9.50 11.75 14.00 16.25 18.50

0.0338 0.0357 0.0329 0.0319 0.0314 0.0312 0.0310 0.0308 0.0307

246.06 -135.99 -226.32 -320.37 -395.90 -489.85 -547.17 -667.91 -733.09

-2000.40 -521.89 -1044.36 -1464.74 -1903.63 -2324.11 -2781.21 -3174.90 -3624.14

340.88 94.77 170.76 239.48 308.19 376.91 445.62 514.34 583.05

6166.49 5805.33 6414.10 6414.59 6474.96 6464.44 6539.36 6470.97 6513.98

14.43 14.40 14.52 14.31 14.27 14.19 14.23 14.12 14.15

1 0.998 1.006 0.992 0.989 0.983 0.986 0.979 0.981

CP (J/(mol 3 K)): H2O, 33.33; CO2, 37.65; N2, 28.86; C, 8.53. ΔfH (kJ/mol): H2O, -241.83; CO2, -393.51; N2, 0; C, 0.

Figure 7. Correlations between N and TC (a), Is (b), and the number of -CH(ONO2)- groups (n1) for the title compounds.

and 1.70 g 3 cm-3, 0.979 and 1.74 g 3 cm-3, and 0.981 and 1.72 g 3 cm-3, respectively.

the conclusions of this work are as follows: (1) The calculated and assigned IR spectra have three strong characteristic regions. Two of them correspond to the NdO asymmetric and symmetric stretch of nitrate group. The third, less than 1151.2 cm-1, is mainly caused by the O-NO2 streching vibration.

4. CONCLUSIONS Using the B3LYP/6-31G* method, we have theoretically studied the performance for some aliphatic polynitrates, and 802



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(2) Thermodynamic properties in the range from 200 to 800 K are obtained. The gradients of C°p,m and S°m to the temperature decrease, but that of H°m increases, as the temperature increases. (3) Except for HOF and heat of detonation, the oxygen balance, volume, density, detonation velocity, and detonation pressure increase with the number of methylene nitrate groups. (4) The relative specific impulses of the title compounds are all close to that of HMX. (5) Considering the energetic properties and the specific impulse, XPN, MHN, VHN, and ONO are potential candidates of HEDMs and may be used as energetic plasticizers.

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’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]; [email protected]. Telephone and Fax: +86-25-84303919.

’ ACKNOWLEDGMENT We gratefully thank Special Foundation of China Postdoctoral Science Foundation (No. 201003588), China Postdoctoral Science Foundation (No. 20090461122), Jiangsu Planned Projects for Postdoctoral Research Funds (No. 0901009B), Research Fund for the Doctoral Program of Higher Education of China (No. 20103219120014), NUST Research Funding (No. 2010GJPY049), and the Scientific Research Foundation of NUST for the support of this work. ’ REFERENCES (1) Peng, P. G.; Liu, P. L.; Zhang, R.; Li, Y. N.; He, N. C.; Xing, Y. M. The Properties and Principle of the Propellants; National University of Defense Technology Press, Changsha, People’s Republic of China, 1987. (2) Zheng, J.; Hou, L. F.; Yang, Z. J. Solid Rocket Technol. 2001, 24, 28. (3) Pang, A. M.; Zheng, J. J. Solid Rocket Technol. 2004, 27, 28. (4) Ji, Y. P.; Li, P. R.; Wang, W.; Lan, Y.; Ding, F. A. Chin. J. Explos. Propellants 2005, 28, 47. Brand, J. C. D.; Cawthon, T. M. J. Am. Chem. Soc. 1955, 77, 319. (5) Waring, C. E.; Krastins, G. J. Phys. Chem. 1970, 74, 999. (6) Korolevich, M. V.; Sivchik, V. V.; Zhbankov, R. G.; Lastochkina, V. A. J. Appl. Spectrosc. 1986, 45, 1275. (7) Xiao, H. M.; Wang, D. X. Acta Armamentarii 1992, 4, 41. (8) Akutsu, Y.; Che, R.; Tamura, M. J. J. Energ. Mater. 1993, 11, 195. (9) Gong, X. D.; Yu, B. H.; Wang, D. X.; Xiao, H. M. Chin. J. Org. Chem. 1994, 14, 274. (10) Xiao, H. M.; Yu, B. H. Acta Chim. Sin. 1994, 52, 750. (11) Gong, X. D.; Wang, J.; Xiao, H. M. Chem. J. Chin. Univ. 1994, 15, 1817. (12) Henderson, D. O.; Mu, R.; Tung, Y. S.; Huston, G. C. Appl. Spectrosc. 1995, 49, 444. (13) Gong, X. D.; Xiao, H. M. Acta Phys. Chim. Sin. 1997, 13, 36. (14) Gong, X. D.; Xiao, H. M.; Van de Graaf, B. J. Mol. Struct.: THEOCHEM. 1997, 393, 207. (15) Gong, X. D.; Xiao, H. M. Acta Phys. Chim. Sin. 1998, 14, 33. (16) Song, W. Y.; Gong, X. D. J. Nanjing Univ. Aeronaut. Astronaut. 1998, 30, 551. (17) Gong, X. D.; Xiao, H. M. J. Mol. Struct.: THEOCHEM. 1999, 488, 179. (18) Gong, X. D.; Xiao, H. M. J. Mol. Struct.: THEOCHEM. 2000, 498, 181. (19) Bunte, S. W.; Sun, H. J. Phys. Chem. B 2000, 104, 2477. 803



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Theoretical Prediction of Properties of Aliphatic Polynitrates - The

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