DMAZ conformation search
The molecular formula of DMAZ is C4N4H10, and the geometric conformation is shown in Fig. 1.
First, 216 conformations were obtained by rotating the three single bonds N1-C10, C10-C13, and C13-N16 of DMAZ by 60°. Then at the theoretical level of PM7 and B3LYP/6-311 + + G(d,p), 5 conformers were selected from 216 conformers. The vibration analysis of the five conformations was carried out to obtain the free energy correction amount, and the high-precision single-point energy calculation at the theoretical level of B2PLYP/ma-TZVP was performed at the same time. The free energy was calculated by summing the free energy correction amount and the single point energy, and the Boltzmann distribution of the five conformations at 298.15 K was finally obtained, as shown in Table 1.
Table 2
Selected bond angles and dihedral angles of DMAZ
Bond angle/Dihedral angle/ °
|
18-17-16
|
18-17-16-13
|
17-16-13-10
|
16-13-10-1
|
13-10-1-2
|
10-1-2
|
2-1-6
|
Calculated
|
171.777
|
167.565
|
76.118
|
-63.296
|
156.871
|
112.452
|
111.434
|
Literature value7
|
171.7
|
169.1
|
80.6
|
-66.7
|
154.6
|
112.6
|
111.3
|
It can be seen from Table 1 that conformation 1 had the largest distribution ratio, which was 63.29%. The results show that conformation 1 is the most stable conformation of DMAZ molecule. At the same time, the structural properties of the most stable conformation were analyzed and compared with the literature values. Selected bond angle and dihedral angle data are shown in Table 2.
It can be seen from Table 2 that the calculated values are in good agreement with the literature values. The results show that the method of rotating single bonds is eligible in conformational search and can be applied to complex molecules.
Calculation of hydrogen extraction in gas phase
The molecular formula of DMAZ is C4N4H10, and it has 10 H atoms that can participate in the reaction. According to the site where DMAZ reacts with NO2, the enthalpy of the substance in the hydrogen extraction in the gas phase was calculated, as shown in Table 3. TS (1 ~ 10) represents TS1, TS2, ..., TS10. The calculation formula of the hydrogen extraction barrier is the enthalpy value of the transition state TS minus the enthalpy value of the reactant R. The geometrical configuration of the transition state during the hydrogen extraction is shown in Fig. 2.
It can be seen from Table 3 that the hydrogen extraction barrier of DMAZ is in the range of 25 ~ 70 kJ·mol-1. Compared with the hydrogen extraction barrier of hydrazine fuels, which is in the range of 5 ~ 25 kJ·mol-1, the hydrogen extraction barrier is large, which is in line with its long ignition delay period. When NO2 attacks the H atoms connected to C2, C6, and C10 atoms of DMAZ, the hydrogen extraction barrier is in the range of 25 ~ 40 kJ·mol-1. When it attacks the H atom connected to the C13 atom, the hydrogen extraction barrier is about 70 kJ·mol-1. The reason is that the C2, C6, and C10 atoms, benefiting from the lone electron pair of the amine N atom, have higher reactivity and lower potential barriers in the hydrogen extraction. The C13 atom is adjacent to the azide group, which is less reactive than the amine N atom, resulting in a higher potential barrier in the hydrogen abstraction. Paths 1, 5, and 7 have lower hydrogen extraction barriers, so the main reaction path of DMAZ and NO2 is that NO2 attacks H3 of C2 atom, H8 of C6 atom, and H11 atom of C10 atom to generate cis-HONO.
Table 3
Enthalpy of substances during the reaction of DMAZ with NO2 in the gas phase
C atom
|
H atom
|
R
|
TS (1 ~ 10)
|
IM
|
P
|
C2
|
H3
|
0
|
25.44
|
24.66
|
65.96
|
H4
|
0
|
41.045
|
34.84
|
65.95
|
H5
|
0
|
36.18
|
25.97
|
63.99
|
C6
|
H7
|
0
|
30.50
|
29.45
|
64.03
|
H8
|
0
|
25.49
|
25.65
|
65.55
|
H9
|
0
|
27.37
|
26.76
|
63.34
|
C10
|
H11
|
0
|
26.51
|
24.29
|
56.78
|
H12
|
0
|
32.31
|
27.99
|
60.17
|
C13
|
H14
|
0
|
69.88
|
47.65
|
57.84
|
H15
|
0
|
68.15
|
46.42
|
57.84
|
Table 4
C-H and O-H spacings in transition states of the reaction in the gas phase
Spacing / Å
|
C-H
|
O-H
|
TS1
|
1.403
|
1.236
|
TS2
|
1.368
|
1.254
|
TS3
|
1.376
|
1.243
|
TS4
|
1.389
|
1.238
|
TS5
|
1.402
|
1.23
|
TS6
|
1.4
|
1.228
|
TS7
|
1.396
|
1.238
|
TS8
|
1.39
|
1.235
|
TS9
|
1.366
|
1.241
|
TS10
|
1.369
|
1.232
|
At the same time, from the perspective of the enthalpy of the hydrogen extraction, the reaction enthalpy of hydrazine fuel and NO2 is within 15 ~ 25 kJ·mol-1, and that of DMAZ and NO2 is within 60 ~ 65 kJ·mol-1 or so. Comparing the ignition delay period of hydrazine fuel and DMAZ, the results show that the reaction enthalpy of DMAZ and NO2 is larger, and the reaction proceeds slower, so the ignition delay period is longer.
The hydrogen extraction reaction between DMAZ and NO2 means that the H atom of DMAZ is captured by NO2 to generate cis-HONO. The hydrogen extraction is the process of transferring H atoms from C atoms to O atoms. Therefore, the transition state C-H spacing, O-H spacing, and extraction of hydrogen barrier relationship can be analyzed from the structural aspect. The C-H spacing and O-H spacing of the transition state during the reaction are shown in Table 4.
From the C-H spacing in Table 4, it can be seen that the value of the C-H spacing in the transition state TS9 is the smallest, which is 1.366 Å. The comparison results show that NO2 has the weakest attack on the H14 atom, which makes the attraction of NO2 to the H14 atom the smallest, which is consistent with the maximum hydrogen extraction barrier of path 9. From the O-H spacing, the values of the different transition states are roughly the same, around 1.23 Å. The larger values of TS2, TS3, and TS9 are consistent with the larger hydrogen extraction barriers of paths 2, 3, and 9.
At 258 ~ 378 K, the reaction rate constants of the hydrogen extraction between H atoms at different sites of DMAZ and NO2 in the gas phase were calculated by TST, as shown in Fig. 3. It can be seen from Fig. 3 that the reaction rate constant increased with the increase of temperature. At the temperature of 258 ~ 378 K, the reaction rate constant of route 7 was the largest; route 6 was close to it, which indicates that routes 6 and 7 are the main reaction routes. The reaction rate constants of routes 3, 4, and 5 were the second, indicating that routes 3, 4, and 5 are secondary reaction routes, and the reaction rate constants of routes 1, 2, 9, and 10 were smaller, indicating routes 1, 2, 9, and 10 almost never occur. The three-parameter Arrhenius formula was obtained by fitting the reaction rate constant of the hydrogen extraction between gas-phase DMAZ and NO2 at 258–378 K, and the results are shown in Table 5.
Table 5
Three-parameter Arrhenius formula for the reaction of DMAZ with NO2 in the gas phase
Reaction path
|
A
|
n
|
Ea / kJ·mol− 1
|
R1
|
2.63E-24
|
3.21
|
19.84
|
R2
|
4.57E-24
|
3.27
|
35.27
|
R3
|
3.56E-22
|
3.27
|
30.4
|
R4
|
2.64E-23
|
3.32
|
24.68
|
R5
|
2.16E-23
|
3.25
|
19.82
|
R6
|
6.29E-23
|
3.2
|
21.3
|
R7
|
9.67E-24
|
3.44
|
19.86
|
R8
|
6.92E-24
|
3.42
|
26.14
|
R9
|
7.68E-23
|
3.05
|
64.28
|
R10
|
1.17E-22
|
3.21
|
62.21
|
The reaction activation energies of the hydrogen extraction of routes 1, 5, and 7 were relatively small, namely 19.84, 19.82, and 19.86 kJ·mol-1, respectively. The activation energy of the hydrogen extraction of route 9 was the largest, which was 64.28 kJ·mol-1. The greater the activation energy of the reaction, the less likely the reactants cross the activation energy barrier and the less likely the reaction proceeds.
Based on the calculation results of the hydrogen extraction barrier, reaction rate constant, and reaction activation energy, it is concluded that when the reaction of DMAZ and NO2 is carried out in the gas phase, path 7 is the main reaction path.
Calculation of hydrogen extraction in NTO liquid phase
Most chemical reactions are carried out in solutions. The solvent effect in different solutions affects the solubility of reactants, the chemical balance and changes the reaction energy barrier. Therefore, it is very important to consider the solvent effect in theoretical calculations. Tang32 reviewed the construction of reaction density functional theory and its application in aqueous and organic phase systems, successfully expounded the influence mechanism of solvents on several types of chemical reactions, and proposed the energy barriers and rates of liquid-phase reactions. Even the reaction mechanism has an important impact. In quantum chemical calculations, according to the application of solvent molecules, solvation models can be divided into explicit solvation models, implicit solvation models, and discrete-continuous combination models. At present, the implicit solvation model is widely used as a relatively mature computational model. In this section, the relatively mature SMD implicit solvation model was selected. For the NTO liquid phase, the solvent parameters were selected, the static permittivity (eps) was 2.5, and the dynamic permittivity (epsinf) was 1.9.
Next, according to the site of the reaction of DMAZ with NO2, at the theoretical level of B3LYP/6–31 + + G(d,p), the hydrogen extraction path in the NTO liquid phase was calculated.
During the calculation, it was found that the difference between the transition state enthalpy and the sum of the enthalpy of the reactants was negative. According to TST, the enthalpy of the transition state was the highest point on the potential energy surface and should be greater than the sum of the enthalpy of the reactants. The reason for this is that there is a complex IM1 between the transition state and the reactants. The reactants first undergo a complex reaction to generate complex IM1, and then with the progress of the reaction, transition state TS is generated, followed by complex IM2, and finally product P is obtained. The enthalpy values of substances during the reaction of DMAZ with NO2 in the NTO liquid phase are shown in Table 6. The calculation formula of the potential barrier is the enthalpy value of the transition state TS minus the enthalpy value of the complex IM1. The important transition state structure is shown in Fig. 4.
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)
It can be seen from Table 5 that the hydrogen extraction barrier is 59.37 kJ·mol-1 when NO2 attacks the H5 atom connected to the C2 atom; when it attacks other H atoms connected to the C2, C6, and C10 atoms of DMAZ, the hydrogen extraction barrier is within 20 ~ 30 kJ·mol-1, and the hydrogen extraction barrier of path 26 is the smallest, which is 21.58 kJ·mol-1; when attacking the H atom of the C13 atom, the hydrogen extraction barrier is 70 kJ·mol-1 or so. Therefore, in the liquid phase, the main reaction path of DMAZ and NO2 is route 26, that is, NO2 attacks the H11 atom connected to the C10 atom to generate cis-HONO.
From the perspective of the reaction enthalpy of the hydrogen extraction, in the gas phase, the reaction enthalpy between DMAZ and NO2 is about 60 ~ 65 kJ·mol-1; in the liquid phase, it is around 25 ~ 35 kJ·mol-1. The calculation results show that the reaction enthalpy of DMAZ and NO2 in the gas phase is higher than that in the NTO liquid phase, indicating that the gas phase reaction absorbs more energy and the reaction is not easy to proceed, while the NTO liquid phase reaction is easier. The combustion mechanism of DMAZ and NTO was obtained. It is speculated that under actual working conditions, DMAZ and NTO mainly undergo the liquid-phase reaction.
From the structural point of view, compared with the gas-phase reaction, during the liquid-phase reaction between DMAZ and NO2, the position of NO2 in the transition state structure is reversed. The results show that the liquid environment of NTO has a certain influence on the molecular conformation of the transition state. The C-H spacing and O-H spacing of the transition state in the reaction in the NTO liquid phase are similar, as shown in Table 7.
Table 7
C-H and O-H spacings in transition states of NTO liquid phase reactions
Spacing / Å
|
C-H
|
O-H
|
TS11
|
1.441
|
1.206
|
TS12
|
1.441
|
1.206
|
TS13
|
1.45
|
1.197
|
TS14
|
1.43
|
1.203
|
TS15
|
1.437
|
1.202
|
TS16
|
1.44
|
1.2
|
TS17
|
1.426
|
1.214
|
TS18
|
1.424
|
1.214
|
TS19
|
1.355
|
1.249
|
TS20
|
1.343
|
1.254
|
From the C-H spacing in Table 7, it can be seen that the values of the C-H spacing in the transition states TS19 and TS20 are smaller, 1.355 Å and 1.243 Å. The comparison results show that in the NTO liquid phase, NO2 has the weakest attack on the H14 and H15 atoms of DMAZ, which makes the attraction to the H14 and H15 atoms smaller, which is consistent with the larger hydrogen extraction barriers of paths 19 and 20. From the O-H spacing, the values of the different transition states are roughly the same, around 1.20 Å. The larger values of TS19 and TS20 are also consistent with the larger hydrogen extraction barriers of paths 19 and 20. Comparing the C-H spacing in the gas phase and the NTO liquid phase, the C-H spacing in the NTO liquid phase is larger than that in the gas phase. The comparison results show that the hydrogen extraction proceeds more effectively in the NTO liquid phase.
In the liquid NTO, since the transition state enthalpy is lower than the sum of the products, the reaction rate constant was calculated in two steps. The first step was the formation of complex IM1 between NO2 and H atoms at different sites of DMAZ, and the reaction rate constant is K1. The second step was for the transition state generated from IM1, and the reaction rate constant is K2. Because the process generating IM1 is barrier free, the reaction rate constant is large, so the rate-determining step] is the second step of the reaction, so the total reaction rate constant is approximately K2. At the temperature of 258 ~ 378 K, the reaction rate constants of the hydrogen extraction between H atoms at different sites of DMAZ and NO2 in the NTO liquid phase were calculated by TST, as shown in Fig. 5.
It can be seen from Fig. 5 that all the reaction rate constants increased with the increase of temperature. At the temperature of 258 ~ 378 K, the reaction rate constant of path 17 was the largest, indicating that path 17 is the main reaction path in the liquid phase. Paths 11, 12, 14, and 15 are the secondary reactions. Paths 13, 16, 18, 19, and 20 have small reaction rate constants, indicating that they hardly occur. The three-parameter Arrhenius formula was obtained by fitting the reaction rate constants of DMAZ and NO2 in the liquid phase at 258 ~ 378 K, and the results are shown in Table 8.
Tab. 8 Three-parameter Arrhenius formula for the reaction of DMAZ with NO2 in the NTO liquid phase
|
Reaction path
|
A
|
n
|
Ea / kJ·mol-1
|
R11
|
1.42E+10
|
0.37
|
22.44
|
R12
|
8.05E+09
|
0.45
|
22.32
|
R13
|
3.74E+10
|
0.24
|
58.98
|
R14
|
3.55E+10
|
0.55
|
22.28
|
R15
|
3.63E+10
|
0.46
|
25.46
|
R16
|
1.74E+10
|
0.68
|
30.99
|
R17
|
1.74E+10
|
0.73
|
19.88
|
R18
|
4.52E+09
|
0.57
|
26.4
|
R19
|
9.34E+10
|
0.19
|
72.77
|
R20
|
1.51E+11
|
0.34
|
67.85
|
The activation energy of route 17 is the smallest, which is 19.88 kJ·mol-1. The activation energy of hydrogen extraction via route 19 is the largest, which is 72.77 kJ·mol-1. The larger the activation energy, the less easily the reaction crosses the energy barrier and therefore the less likely the reaction proceeds.
The analysis results of hydrogen extraction barrier, reaction rate constant, and reaction activation energy are consistent. It is concluded that when the reaction of DMAZ and NTO is carried out in liquid NTO, path 17 is the main reaction path.