Relation between the N-NO2 bond length and stability of the secondary nitramines

Article abstract of DOI:10.1134/S107036321306011X

The fact of the constancy of activation entropy of N-NO₂ bond homolysis in a series of secondary nitramines was utilized for correction of the experimental values of activation energy E of this process proceeding from the reliable data for the rate constants of the nitramines decomposition in solutions. When comparing the refined values of E (kJ mol^-1) with the N-N bond length d _N-N (A) the following correlations were obtained: for cyclic and framework nitramines E = 663 - 356d _N-N, and for the aromatic nitramines E = 1810 - 1227d _N-N. A linear relationship between E and d is observed in the series of similar compounds. It depends on the electronic and steric effects of substituents.

Full text of DOI:10.1134/S107036321306011X

ISSN 1070-3632, Russian Journal of General Chemistry, 2013, Vol. 83, No. 6, pp. 1071–1076. © Pleiades Publishing, Ltd., 2013.
Original Russian Text © G.M. Nazin, V.G. Prokudin, V.V. Dubikhin, Z.G. Aliev, V.L. Zbarskii, N.V. Yudin, A.V. Shastin, 2013, published in Zhurnal
Obshchei Khimii, 2013, Vol. 83, No. 6, pp. 940–945.
Relation Between the N–NO2 Bond Length
and Stability of the Secondary Nitramines
G. M. Nazina, V. G. Prokudina, V. V. Dubikhina, Z. G. Alieva,
V. L. Zbarskiib, N. V. Yudina, and A. V. Shastina
a Institute of Problems of Chemical Physics, Russian Academy of Sciences,
Chernogolovka, Moscow Oblast, 142432 Russia
e-mail: prokud@icp.ac.ru
b Mendeleev Russian Chemical-Technological University, Moscow, Russia
Received May 15, 2012
Abstract―The fact of the constancy of activation entropy of N–NO2 bond homolysis in a series of secondary
nitramines was utilized for correction of the experimental values of activation energy E of this process
proceeding from the reliable data for the rate constants of the nitramines decomposition in solutions. When
comparing the refined values of E (kJ mol–1) with the N–N bond length dN–N (Å) the following correlations
were obtained: for cyclic and framework nitramines E = 663 – 356dN–N, and for the aromatic nitramines E =
1810 – 1227dN–N. A linear relationship between E and d is observed in the series of similar compounds. It
depends on the electronic and steric effects of substituents.
DOI: 10.1134/S107036321306011X
The purpose of this study was to determine the
relationship between the stability of secondary
aliphatic and aromatic nitramines and the N–N bond
length dN–N. The reason for such a study is the fact that
the dependence of the stability of the secondary
nitramines on their structure is determined mainly by
the changing activation energy E of the N–N bond
homolysis, which is directly related to the dissociation
energy of bond and its length. The preexponential
factor A, as first noted in [1], relatively weakly
depends on the structure of secondary nitramines. For
example, for a series of aliphatic compounds, the most
data obtained both for the liquid phase or solution
satisfy the equality log A = 14.5±0.5 [1]. Thus, in
terms of correlation analysis, the decay of secondary
nitramines is an isentropic series. The constancy of A
opens a possibility to correlate dN–N not only with the
activation energy, but also with the rate constants of
decomposition k, measured at the same temperature,
and also allows finding the E values from the relation
E = (log k–log A)RT at A = Const. The E values
calculated in this way can be used to refine the
experimental data and to quickly find the E in the new
conditions of the reaction. Due to the high melting
temperatures and high rates of decomposition at the
temperatures above the melting point, the data on the
decomposition of secondary nitramines in the liquid
phase are rather limited. The basic research has been
carried most often in solutions in the nonvolatile
solvent inert with respect to the secondary nitramines,
e.g., dinitrobenzene, trinitrobenzene, dicyclohexyl
phthalate, and dibutyl phthalate. However, in these
relatively viscous solvents, as well as in the liquid
phase, the kinetic influence of cage effect is observed,
and therefore the apparent decay rate is lower than in
the lighter solvents such as isooctane or benzene [2, 3].
The influence of the solvent and the possibility to
recalculate the data on the rate at changing solvent was
described in [2]. In solvents like toluene containing the
C–H bonds of lower strength, the decomposition of
secondary nitramines results in the development of the
chain processes accelerating the decay. The experi-
ments in these solvents should be excluded from consi-
deration. Apparently, the rate of thermal decom-
position of nitramines by the pathway of the N–NO2
bond homolysis the least distorted by side effects can
be obtained using benzene as a solvent.
Attempting to establish a direct correlation of
experimental E values with dN–N failed [4], possibly
1071

1072
NAZIN et al.
because of the strong scatter of experimental data. At
the same time, the use of rate constants measured in
the same solvent at the same temperature allowed us
obtaining a satisfactory correlation for a series of
cyclic and framework nitramines in dibutyl phthalate
[5] and benzene [6]. It seems useful to summarize
these data, to adjust E values in correspondence with
the rate constants, and to find a correlation of E in
benzene, the most informative quantity for the
estimation of the stability at different temperatures and
in different environments.
compounds require further structural and kinetic
measurements.
A series of nitramines whose data are available on
the kinetics of decomposition and the structure of the
molecule consists of the following compounds: 1,3-
dinitro-1,3-diazacyclopentane (I), N,N'-dinitropi-
perazine (II), hexogen (III), octogen (IV), CL-20 (V),
ketohexogen (VI), 4,8,10,12-tetranitro-2,6-dioxa-4,8,10,12-
tetraazatetracyclo(5.5.003,11.05,9)dodecane (VII), 4,6,10,12-
tetranitro-2,8-dioxa-4,6,10,12-tetraazatetracyclo-
(5.5.003,11.05,9)dodecane (VIII), cis-2,4,6,8-tetranitro-
1H,5H-2,4,6,8-tetraazabicyclo(3.3.0)octane (IX), 4,10-
dinitro-2,6,8,12-tetraoxa-4,10-diazatetracyclo-
(5.5.003,11.05,9)dodecane (X), tetryl (XI), N-nitro-N-
ethyl-2,4,6-trinitroaniline (XII), and N-nitro-N-methyl-
4-nitroaniline (XIII).
In addition to cyclic and framework nitramines, we
included in the review the aromatic nitramines, analogs
of tetryl. While for the compounds of the first two
types there are quite complete literature data and only
processing of the latter is necessary, aromatic
NO2
O2N
O2N
NO2
N
N
N
NO2
O2N
N
N
NO2
N
N
O2N
N
N
N
O2N
O
NO2
NO2
III
I
II
IV
NO2
O2N
O2N
NO2
O2NN
O2NN
NNO2
N
O
N
N
N
N
O2N
N
O
O2N
N
O
NO2
NNO2
N
O
O2NN
N
N
N
N
NO2
NO2
NO2
O2N
O2N
V
VII
VIII
VI
NO2
NO2
O2N
N
NO2
NO2
O
O
CH3
C2H5
NO2
N
N
O
O
N
N
O2N
O2N
N
NO2
NO2
ХI
NO2
NO2
N
O2N
N
NO2
O2N
ХII
Х
IХ
N
O2N
CH3
ХIII
All data on these compounds and references to original
publications are collected in [3, 5, 6], which we used to
obtain the necessary information. Most of the results
on the measurement of reaction rates is given in the
literature as the kinetic parameters E and A. Therefore,
the desired values of the activation energy in benzene
Ebz were found as follows. For the average temperature
Tav of the temperature range in which the value of E
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 83 No. 6 2013

RELATION BETWEEN THE N–NO2 BOND LENGTH
1073
The kinetic characteristics of decomposition of nitramines, and the N–NO2 bond lengths
Comp.
no.
E,
kobs (s–1)
at Тav
kbz (s–1)
at Тav
Ebz,
d(N–N),
Environment
Dinitrobenzene [3]
Trinitrobenzene [3]
Melt [3]
ΔТ, °С
170–210
120–210
135–200
log (A/s–1)
13.6
σ
2
2
2
S
2
2
2
Eа,av
kJ mol–1
kJ mol–1
Å
156.3
158.6
155.3
8.7×10–5
1.2×10–5
3.1×10–5
8.7×10–5
1.2×10–5
3.1×10–5
164.5
162.8
160.3
162.5 1.419
I
14.0
13.9
Nitrobenzene [3]
Trinitrobenzene [3]
Liquid phase [31]
Dinitrobenzene [3]
Trinitrotoluene [3]
Trinitrotoluene [3]
225–245
230–235
216–250
160–200
166–184
195–280
155.8
191.7
198.4
166.1
154.4
171.6
173.7
12.0
15.7
17.3
14.3
13.9
15.5
15.4
1.1×10–4
1.2×10–4
6.8×10–4
1.7×10–5
1.2×10–4
8.9×10–3
5.0×10–4
5.5×10–5
7.4×10–2
8.6×10–6
2.1×10–1
5.4×10–5
3.8×10–4
1.1×10–3
2.8×10–5
2.2×10–5
5.4×10–4
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
1
2
2
2
2
2
1
2
2
2
2
1
2
2
2
2
2
2
2
2
2.2×10–4
2.4×10–4
1.4×10–3
3.4×10–5
2.4×10–4
1.8×10–2
1.0×10–3
5.5×10–5
1.5×10–1
8.6×10–6
2.1×10–1
5.4×10–5
3.8×10–4
1.1×10–3
5.6×10–5
2.2×10–5
1.1×10–4
177.1
177.0
168.3
164.5
157.0
158.7
161.9
166.9
155.3
174.5
164.3
151.2
152.4
151.4
157.2
156.5
156.7
158.6
157.4
168.4
144.0
152.4
149.9
149.0
148.6
151.9
148.8
174.1 1.373
160.7 1.409
II
III
Dicyclohexyl phthalate [3] 201–280
Benzene [2]
180
Liquid phase [3]
Dinitrobenzene [3]
Liquid phase [3]
Dinitrobenzene [5]
Dibutyl phthalate [5]
Benzene [2]
213–299
171–215
271–314
150–190
160–190
180
198.8
187.9
220.6
45.3
18.5
16.0
19.7
18.6
17.98
–
169.4 1.392
151.8 1.436
IV
V
43.86
–
1.438
1.421
VI
Dibutyl phthalate [5]
Dibutyl phthalate [5]
Dinitrobenzene [5]
Dibutyl phthalate [5]
Benzene [6]
150–180
150–190
145–190
140–185
180
162.9
166.6
170.0
165.0
–
15.23
15.68
15.77
14.96
–
VII
VIII
IX
1.422
157.6 1.414
2.3×10–4
2.3×10–4
Dibutyl phthalate [5]
Liquid phase [3]
210–250
211–260
132–164
131–155
140–160
140–165
150–175
130–139
158.1
160.7
146.1
150.7
147.3
167.4
150.3
254.9
13.15
15.4
12.9
13.8
13.5
16.0
13.5
27.3
1.39
X
7.5×10–2
6.0×10–6
7.6×10–6
2.02×10–5
2.9×10–5
2.4×10–5
4.2×10–6
1.5×10–3
1.2×10–5
1.5×10–5
4.0×10–5
5.8×10–5
4.8×10–5
8.4×10–6
157.6 1.347
XI
140–150
150–175
232.3
150.3
24.5
13.5
3.0×10–5
1
1
2
2
6.0×10–5
145.9
151.2
Dinitrobenzene [3]
Dinitrobenzene [3]
2.4×10–5
4.8×10–5
144–165
140
139.4
13.9
–
7.7×10–4
1.7×10–4
1.3×10–4
1
1
1
2
1
1
1.5×10–3
1.7×10–4
1.3×10–4
137.8
140.5
134.5
139.2 1.362
1.346
XII
Benzene
Benzene
–
–
120
–
XIII
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 83 No. 6 2013

1074
NAZIN et al.
Ea, kJ mol–1
was determined we calculated the observed rate
constant kobs and then transformed it into the rate
constant in benzene according to the formula: kbz
=
II
IV
III
kobsS/σ, where S = kbz/kobs is kinetic cage effect, which
reduces the rate in a viscous solvent, and σ is a
statistical factor of the reaction, which must be
considered in the case of multifunctional nitramines.
X
I
VII
VIII
XI
IX
V
VI
The cage effect is due to the reduction of the
starting compound at the recombination of aminyl
radical R2N• and NO2 particles emerging in the first
stage of decay. The value of S, which is observed in
solvents like dinitrobenzene, takes a value within 2–
3 range [2]. In fact, it is equal to the limiting
magnitude of the cage effect, which is defined as a
ratio of the rate constants of recombination and
disproportionation (into R2NO and NO) of the primary
particles. Both the reactions proceed with low
activation energy and differ only in the probability of
aminyl radical to react with NO2 at either oxygen or
nitrogen atoms. A similar situation occurs in the
recombination of NO2 with alkyl radicals. Thus, at the
recombination of methyl radical with NO2 the yield
ratio CH3ONO/CH3NO2 is 2 [7], that is, in this case the
disproportionation is exactly 2 times faster than the
recombination. Further in the calculations of kbz, S = 2
is taken, with no great loss in accuracy at the calcula-
tion of Ebz.
XII
XIII
d(N–NO2), Å
The dependence of the activation energy of thermal decom-
position of secondary nitramines in benzene Ebz on the
N–N bond length.
reaction with the rate constant k1 [8]. For this reason,
in the case of dinitropiperazine II, which has two
groups with the same value of d(N–NO2), σ = 1.
After calculating kbz we find Ebz = (kbz – log A)RTav.
According to the most reliable published data we can
establish that log A is 14.5 and 14.0 for aliphatic and
aromatic nitramines, respectively [3]. To calculate Ebz
we used all the data obtained under isothermal
conditions. In almost all cases, the reaction kinetics
was measured by the manometric method. The table
lists the input data and results of Ebz calculation, as
well as the values of dN–N. The information on the bond
length was taken from the Cambridge Structural
Database [9]. At the inconsistence of the literature data
the dN–N values were taken from the more recent
publications. All references to primary sources,
corresponding to the selected dN–N, are given in [5, 6].
The statistical factor σ is determined from the
structural data, and, except for the case of stepwise
decay, it is equal to the number of nitramine groups
with a maximum N–NO2 bond length. Use of σ makes
it possible to eliminate the difference in the nitramines
due to the number of the nitramine groups and to
assign kbz to a single reaction group NNO2. In
determining σ, the possibility should be considered of
a stepwise mechanism of decomposition of secondary
nitramines. If the nitramine groups are separated by
one methylene group, then splitting of one of them
with a rate constant k1 leads to a rapid decomposition
of the whole molecule to the final product without the
formation of stable intermediates. In this case, the
parameter σ is equal to the number of the most reactive
groups. If the NNO2 groups are separated by two
methylene groups, at the decomposition of one of them
a stable intermediate is formed, which comprises the
second nitramine group that then decomposes at about
the same rate constant as the first one. When the decay
rate is measured by the formation of the end products
(manometric, colorimetric, and gravimetric methods),
then the stepwise mechanism results in the first order
The structure of nitramine XII was investigated by
XRD method, and it was found that the N–N bond
length in this compound is 1.362 Å. Comparison of Ebz
(kJ mol–1) with dN–N (Å) shows that the data for the
cyclic and framework nitramines are collinear (see the
figure), in correspondence with the regression equation
Ebz = (663±43) – (356±30)d(N–NO2),
r = 0.938; SEbz = 29; n = 10.
(1)
At the increase in bond length by 0.01 Å the
activation energy decreases by 3.56 kJ mol–1. The main
reason for the increase in the N–N bond length of
cyclic nitramines is, as noted in [5], the conformational
strain, which forces the nitramine group to acquire a
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 83 No. 6 2013

RELATION BETWEEN THE N–NO2 BOND LENGTH
1075
pyramidal structure reducing the resonance conjuga-
tion within the nitramine group.
The reactor was a glass 0.5–5.0 ml ampule equipped
with a crescent-like membrane with a pointer, placed
in a metal enclosure with a window to observe the
deflection. The pressure was measured by the
compensation method. This technique allows to
perform experiments at high temperatures in almost all
solvents, and to measure the kinetics of decomposition
at high degrees of filling the container with the
material.
In the aromatic compounds another type of
electronic interaction occurs between the nitramine
group and the substituent. As a result of conjugation of
the nitro group with the benzene ring the N–N bond
length is reduced, and simultaneously due to even
stronger conjugation with the ring of the free valence
of aminyl radical the strength of this bond decreases. A
straight line drawn through the points for compounds
XI–XII reflects a stronger dependence of E on d than
the cyclic nitramines.
X-ray diffraction study of compound XII.
Colorless bulky crystals, empirical formula C8H7N5O8,
belonging to the monoclinic type: a = 15.052(1),
b = 7.504(1), c = 10.661(1) Å, β = 93.160(10)°, V =
1202.3(2) Å3, M = 301.19, dcalc = 1.664 g cm–3, Z = 4,
space group P21/c. A set of experimental reflections
was obtained with an automatic 4-circle diffractometer
KM-4 (KUMA DIFFRACTION) with χ-geometry, by
the method of ω/2θ scanning using monochromatic
MoKα-radiation (2θ ≤ 50°).In total 2873 reflections
were measured, of which 2115 were independent
(Rint = 0.0191). No correction for extinction was applied
(μ = 0.151 mm–1). The structure was determined by the
direct method with SIR92 software [13], followed by a
series of calculations of electron density maps.
Hydrogen atoms were localized objectively from the
difference electron density synthesis and refined in an
isotropic approximation. Full-anisotropic (nonhydrogen
atoms) refinement was carried out by the mean square
method with the SHELXL-97 software [14] and
completed at R1 = 0.0367 for 1873 reflections with I ≥
2σ(I) and R1 = 0.0422 for all 2115 reflexes. The
number of refined parameters is 219, GOOF 1.041.
The maximum peak in the difference synthesis of
electron density is equal to 0.245 Å3. A CIF file con-
taining full information on the investigated structure is
deposited in Cambridge Crystallographic Data Centre,
no. 876381, and can be freely obtained on the website:
www.ccdc.cam.ac.uk/data_request/cif.
Ebz = 1810 – 1227d(N–NO2).
The point for the compound XIII drops out of this
dependence due to a decrease in the steric shielding,
which leads to increased conjugation and further
reduction of the N–N bond strength.
Thus, in the series of such compounds having the
same type of electronic and steric interactions with
substituents, there is a correlation between the activa-
tion energy of decomposition and the N–N bond length.
The existence of relation (1) allows us to estimate
approximately the thermal stability of the new
compounds from the results of the XRD studies. A
quantitative measure of thermal stability of compounds
is the rate constant for the initial stage of non-catalytic
decomposition. To find this value for each compound,
first we calculated Ebz by Eq. (1) and then kbz for any
temperature. Dividing kbz by 2 we may find the
approximate value of the rate constants of
decomposition of nitramine in the liquid state kliquid
,
and based on this value, to estimate according to
certain rules [10] the rate constant for the initial stage
of decomposition in the solid phase ksolid, which is the
ultimate goal of the forecast. The maximum error in
going from a ksolid to kliquid is no more than 5% [10].
EXPERIMENTAL
REFERENCES
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by the nitration of 4-nitro-N-methylaniline with nitric
acid in acetic anhydride, and recrystallized from
isopropanol, mp 144–145°C. Compound XIII was
prepared in a procedure similar to that described in
[12], recrystallized from hexane-ethyl acetate (2:1), mp
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RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 83 No. 6 2013

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RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 83 No. 6 2013