crystals
Article
Electrostatic Potentials, Intralattice Attractive Forces
and Crystal Densities of Nitrogen-Rich C,H,N,O Salts
Peter Politzer 1,2, *, Pat Lane 1 and Jane S. Murray 1,2
Received: 9 December 2015; Accepted: 30 December 2015; Published: 4 January 2016
Academic Editor: Gerhard Laus
1
2
*
Department of Chemistry, University of New Orleans, New Orleans, LA 70148, USA; [email protected] (P.L.);
[email protected] (J.S.M.)
CleveProp, 1951 W. 26th Street, Cleveland, OH 44113, USA
Correspondence: [email protected]
Abstract: The computed electrostatic potentials on C,H,N,O molecular solids and nitrogen-rich
C,H,N,O salts are used in analyzing and comparing intralattice attractive forces and crystal densities
in these two categories of compounds. Nitrogen-rich C,H,N,O salts are not an assured path to high
densities. To increase the likelihood of high densities, small cations and large anions are suggested.
Caution is recommended in predicting benefits of nitrogen-richness for explosive compounds.
Keywords: nitrogen-rich; electrostatic potentials; C,H,N,O molecular and ionic compounds;
crystal densities
1. Why “Nitrogen-Rich?”
In the detonation of an explosive compound, an initial stimulus (input of energy) is followed by
a series of steps culminating in self-sustaining highly exothermal chemical decomposition releasing
large amounts of energy and gaseous products. This results in a high pressure, supersonic shock wave
propagating through the system (detonation) [1–5]. Many explosives are composed of appropriate
numbers of carbon, hydrogen, nitrogen and oxygen atoms. Their final decomposition products, apart
from some solid carbon, are usually mainly large quantities of low molecular mass, very stable gases,
e.g., N2 , CO2 , CO, H2 O [6–9]. Due to their low masses, large amounts can be produced per gram of
explosive, while their stabilities mean that a great deal of energy is liberated.
An important point is that many C,H,N,O compounds have relatively high densities compared to
other organic compounds, in the range 1.50 g/cm3 to 2.00 g/cm3 [10–12]. This allows more explosive
to be packed into the available volume. The density is in fact one of the primary factors affecting
detonation performance [6,9].
During the past two decades, there has been a tendency to focus upon the design and synthesis of
“nitrogen-rich” explosive compounds, whether molecular or ionic [13–16], [17] and references therein.
While the term is somewhat ambiguous, basically it means replacing some C–H units in a molecular
or ionic framework by nitrogens. This is expected to increase the compound’s heat of formation (its
energy content) and possibly also its density, both of which would be desirable.
An increased density is plausible, because a nitrogen atom has a greater mass but smaller
volume than a C–H unit [18]. An increased (more positive) heat of formation is expected because the
hypothetical “formation reaction” requires breaking the very strong N”N bond in N2 and creating
much weaker C–N, C=N, N–N and/or N=N bonds in the explosive [19]. A high heat of formation
suggests that the compound has a greater intrinsic energy content, which may result in a larger heat
release during detonation.
It should be noted, however, that the effects of increasing the framework nitrogen content may
not all be beneficial, as has recently been pointed out [19]. The overall heat release depends upon the
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It should be noted, however, that the effects of increasing the framework nitrogen content may
not
all
be beneficial,
as has recently
been
pointed
out [19]. The
overall heat
release depends
upon
the
compound’s
stoichiometry
as well as
its heat
of formation;
furthermore,
a capability
for a very
large
compound’s
as well as its
of formation;
furthermore,
a capability
for adetonation).
very large
heat
release isstoichiometry
likely to be accompanied
byheat
excessive
sensitivity
(vulnerability
to accidental
heat
release
is
likely
to
be
accompanied
by
excessive
sensitivity
(vulnerability
to
accidental
Another consideration is that diminishing the number of hydrogens adversely affects the number
of
detonation).
Another
consideration
is
that
diminishing
the
number
of
hydrogens
adversely
affects
moles of gaseous products per gram of explosive, since more of the heavier N2 and less of the lighter
the
number of moles of gaseous products per gram of explosive, since more of the heavier N2 and
H
2 O are being formed. These issues will be further discussed in a later section.
less of
thepresent
lighterobjectives
H2O are being
issuesand
willionic
be further
discussed
a laterofsection.
Our
are toformed.
compareThese
molecular
C,H,N,O
solids ininterms
intralattice
Our
present objectives
compare
molecular
and ionic
C,H,N,O
solids the
in effects
terms of
of
forces,
electrostatic
potentials are
and to
crystal
densities.
At the same
time we
will consider
intralattice
forces,
electrostatic
potentials
and
crystal
densities.
At
the
same
time
we
will
consider
the
nitrogen richness upon the ionic compounds.
effects of nitrogen richness upon the ionic compounds.
2. Molecular vs. Ionic Crystal Lattices
2. Molecular vs. Ionic Crystal Lattices
The discussion in Section 1 applied to both molecular and ionic crystalline C,H,N,O explosives.
The discussion
Section
1 appliedintothe
bothnature
molecular
and
ionic crystalline
explosives.
However
there is ainmajor
difference
of the
intralattice
forces C,H,N,O
that stabilize
these
However
thereofissolids.
a major
difference
in the of
nature
of thecompounds
intralattice are
forces
that
stabilize
two
two
categories
The
crystal lattices
molecular
held
together
by these
relatively
categories
of solids.
The crystal
lattices of
molecular
compounds
areneutral,
held together
by relatively
weak
weak
Coulombic
attractions
between
molecules
that
are overall
although
having locally
Coulombic
between
molecules that
are overall
neutral,
locally
positive
positive
andattractions
negative regions
of electrostatic
potential.
Figures
1 andalthough
2 are the having
computed
electrostatic
and negative
regions
of electrostatic
Figures
1 and 2 are
the 3-nitro-1,2,4-triazole
computed electrostatic
potentials
on the
molecular
“surfaces” ofpotential.
the molecules
5-nitrotetrazole
(1) and
(2);
potentials
on
the
molecular
“surfaces”
of
the
molecules
5-nitrotetrazole
(1)
and
3-nitro-1,2,4-triazole
(2);
the surfaces are taken to be the 0.001 au contours of the molecules’ electronic densities, as proposed
theBader
surfaces
are[20].
takenSuch
to besurfaces
the 0.001encompass
au contours
of the molecules’
as proposed
by
et al.
roughly
97% of theelectronic
electronicdensities,
charge and
have the
by Bader etthat
al. [20].
roughly
of the and
electronic
and have
the
advantage
they Such
reflectsurfaces
featuresencompass
such as lone
pairs, 97%
π electrons
atomiccharge
anisotropy
that are
advantage
thatparticular
they reflect
featuresFigures
such as1 lone
electrons
and atomic
anisotropy
that are
specific
to the
molecules.
and 2pairs,
showπregions
of positive
electrostatic
potential
to
specific
to thewith
particular
molecules.
Figures
1 and portions
2 show regions
of positive and
electrostatic
to
be
associated
the hydrogens
and
the central
of the molecules,
negativepotential
regions by
be associated
withand
the hydrogens
and(All
the central
portions
of the molecules,
and negative
regions by
the
ring nitrogens
nitro oxygens.
electrostatic
potentials
being discussed
were computed
at
ring nitrogens
andB3PW91/6-31G**
nitro oxygens. (All
electrostatic potentials being discussed were computed at
the density
functional
level).
the density functional B3PW91/6-31G** level).
Figure 1. Computed electrostatic potential on 0.001 au molecular surface of 5-nitrotetrazole (1). Color
Figure 1. Computed electrostatic potential on 0.001 au molecular surface of 5-nitrotetrazole (1). Color
ranges, in kcal/mol, are: red, greater than 30; yellow, between 30 and 15; green, between 15 and 0;
ranges, in kcal/mol, are: red, greater than 30; yellow, between 30 and 15; green, between 15 and 0;
blue, negative (less than 0). Circles show positions of atoms; NO2 group is on the left. Most positive
blue, negative (less than 0). Circles show positions of atoms; NO2 group is on the left. Most positive
potential is 73 kcal/mol by the hydrogen; most negative are −29 kcal/mol by the ring nitrogen at the
potential is 73 kcal/mol by the hydrogen; most negative are ´29 kcal/mol by the ring nitrogen at the
bottom right.
bottom right.
2
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Figure
2. Computed
electrostatic potential
Figure
potentialon
on 0.001
0.001 au
au molecular
molecularsurface
surfaceof
of3-nitro-1,2,4-triazole
3-nitro-1,2,4-triazole(2).
(2).
Figure 2.
2. Computed
Computed electrostatic
electrostatic potential
on
0.001
au
molecular
surface
of
3-nitro-1,2,4-triazole
(2).
Figure
2. Computed
electrostatic
potential
on 0.001
au molecular
surface
of
3-nitro-1,2,4-triazole
(2).
Color
ranges,
in
kcal/mol,
are:
red,
greater
than
30;
yellow,
between
30
and
15;
green,
between
15 and
Color
ranges,
in
kcal/mol,
are:
red,
greater
than
30;
yellow,
between
30
and
15;
green,
between
15
Color ranges, in kcal/mol, are: red, greater than 30; yellow, between 30 and 15; green, between 15 and
Color
ranges,
in (less
kcal/mol,
are:
red, greater
than
30; yellow,
between
30 andis15;
between
and
0;
blue,
negative
than
0).
Circles
showshow
positions
of atoms;
NO2 group
ongreen,
the
lower
right.15
Most
and
0;
blue,
negative
(less
than
0).
Circles
positions
of
atoms;
NO
group
is
on
the
lower
right.
2 is on the lower right. Most
0; blue, negative (less than 0). Circles show positions of atoms; NO2 group
0; blue,
negative
(less
Circles
positions
of most
atoms;
NO2negative
group
isare
on
the
positive
potential
is 71than
kcal/mol
by theshow
N-H
hydrogen;
negative
are −33
to´33
−39lower
kcal/mol
byMost
the
Most
positive
potential
is 710).kcal/mol
the
N-H hydrogen;
´39right.
kcal/mol
positive
potential
is 71 kcal/mol
by theby
N-H
hydrogen;
most most
negative
are −33
to −39tokcal/mol
by the
positive
potential
71NO
kcal/mol
the N-H hydrogen; most negative are −33 to −39 kcal/mol by the
2 oxygens.
ring
nitrogens
and is
the
by
ring
nitrogens
NOby
2 oxygens.
2 oxygens.
ringthe
nitrogens
and theand
NOthe
ring nitrogens and the NO2 oxygens.
The crystal lattices of ionic solids are also held together by Coulombic attractions, but they are
The crystal lattices of ionic solids are also held together by Coulombic attractions, but they are
crystal
lattices the
of ionic
solids
are also
held together
by Coulombic
but theythe
are
quite The
strong,
involving
overall
integral
positive
or negative
charges on attractions,
the ions. Consider
quite strong,
positive
or or
negative
charges
on the
Consider
the salts
strong,involving
involvingthe
theoverall
overallintegral
integral
positive
negative
charges
on ions.
the ions.
Consider
the
quite
strong,
involving
the
overall
integral
positive
or
negative
charges
on
the
ions.
Consider
the
salts resulting from the interactions of 1 and 2 with a base such as NH3:
resulting
from from
the interactions
of 1 and
with2 awith
basea such
NHas3 :NH3:
salts resulting
the interactions
of 12and
base as
such
salts resulting from the interactions of 1 and 2 with a base such as NH3:
Figures 3 and 4 display the electrostatic potentials on the 0.001 au surfaces of the resulting
on the 0.001 au surfaces of the resulting
Figures
44 display
the electrostatic
Figures 33 and
and
display
electrostatic potentials
potentials
on(4).
the 0.001 au surfaces of the resulting
5-nitrotetrazolate
anion
(3) andthe
3-nitro-1,2,4-triazolate
anion
3-nitro-1,2,4-triazolate anion
anion (4).
(4).
5-nitrotetrazolate
anion
(3)
and
3-nitro-1,2,4-triazolate
5-nitrotetrazolate anion (3) and 3-nitro-1,2,4-triazolate anion (4).
Figure 3. Computed electrostatic potential on 0.001 au anionic surface of 5-nitrotetrazolate anion (3).
Figure 3. Computed electrostatic potential on 0.001 au anionic surface
surface of
of 5-nitrotetrazolate
5-nitrotetrazolate anion
anion (3).
(3).
Figure
3. Computed
electrostatic
potential
on 0.001
au anionic
surface
of 5-nitrotetrazolate
anion
(3).
Color
ranges,
in kcal/mol,
are: yellow,
between
−60 and
−80; green,
between
−80 and −100; blue,
more
Color ranges,
ranges, in
in kcal/mol,
kcal/mol,are:
are:yellow,
yellow,between
between
´60
and
´80;
green,
between
´80
and
´100;
blue,
−60 and −80; green, between −80 and −100; blue, more
Color ranges,
kcal/mol,
are:show
yellow,
betweenof−60
and −80;
between
−80 and
more
negative
than in
−100.
Circles
positions
atoms;
NOgreen,
2 group
is on the
left. −100;
Mostblue,
negative
more
negative
Circles
positions
of atoms;
theleft.
left. Most
Most negative
negative
than than
−100.´100.
Circles
showshow
positions
of atoms;
NONO
2 group
is isononthe
2 group
negative than
−100.
Circlesbyshow
positions
of closest
atoms; to
NO
2 carbon
group
is
on the
negative
group.
potentials
are −126
kcal/mol
the ring
nitrogens
the
bearing
theleft.
NO2Most
potentials are ´126
kcal/molby
bythe
thering
ringnitrogens
nitrogensclosest
closesttotothe
thecarbon
carbonbearing
bearingthe
theNO
NO2 2group.
group.
−126 kcal/mol
potentials are −126 kcal/mol by the ring nitrogens closest to the carbon bearing the NO2 group.
3
3
3
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Figure
4. Computed
anionic surface
surface of
of 3-nitro-1,2,4-triazolate
3-nitro-1,2,4-triazolate
Figure 4.
Computed electrostatic
electrostatic potential
potential on
on 0.001
0.001 au
au anionic
anion
(4).
Color
ranges,
in
kcal/mol,
are:
red,
less
negative
than
−60;
yellow,
between ´60
−60 and
and ´80;
−80;
anion (4). Color ranges, in kcal/mol, are: red, less negative than ´60; yellow, between
green,
between
−80
and
−100;
blue,
more
negative
than
−100.
Circles
show
positions
of
atoms;
NO
green, between ´80 and ´100; blue, more negative than ´100. Circles show positions of atoms; NO222
group isisononthethe
lower
right.
negative
potentials
areand
−133
and
−136 kcal/mol
by nitrogens
the ring
group
lower
right.
MostMost
negative
potentials
are ´133
´136
kcal/mol
by the ring
nitrogens
closest
to the
carbon
bearing
the NO22 group.
closest to the
carbon
bearing
the
NO group.
2
The
completely negative,
negative, although
The surfaces
surfaces of
of 33 and
and 44 are
are completely
although with
with some
some local
local variation,
variation, which
which will
will
be discussed later; the surface of the cation NH44+++ is completely positive (Figure 5), again with some
be discussed later; the surface of the cation NH4 is completely positive (Figure 5), again with some
variation. The
The magnitudes
magnitudesof
ofthe
theelectrostatic
electrostaticpotentials
potentialsononthe
the
anions
3 and
4 (Figures
3 and
4) and
variation.
anions
3 and
4 (Figures
3 and
4) and
on
+
on
NH
44+ (Figure 5) are considerably greater than those on the neutral molecules 1 and 2 (Figures 1
+
NH4 (Figure 5) are considerably greater than those on the neutral molecules 1 and 2 (Figures 1 and 2)
and 2) and on the ammonia molecule (on which they vary from −40 to +24 kcal/mol [21]). It follows
and on the ammonia molecule (on which they vary from ´40 to +24 kcal/mol [21]). It follows that
that
the Coulombic
attractions
between
the ions
in two
the two
be much
stronger
between
the Coulombic
attractions
between
the ions
in the
saltssalts
will will
be much
stronger
thanthan
between
the
the
neutral
molecules
in
the
molecular
solids
1
and
2.
neutral molecules in the molecular solids 1 and 2.
+ cation. Color ranges,
Figure 5.
Figure
5. Computed
Computed electrostatic
electrostatic potential
potential on
on 0.001
0.001 au
au cationic
cationic surface
surface of
of NH
NH444++ cation.
Color ranges,
in kcal/mol,
between
178178
andand
174;174;
green,
between
174 and
in
kcal/mol, are:
are: red,
red, greater
greaterthan
than178;
178;yellow,
yellow,
between
green,
between
174 168;
and blue,
168;
less
Circles
show positions
of atoms.ofMost
positive
are 181 kcal/mol
hydrogens.
blue,than
less168.
than
168. Circles
show positions
atoms.
Mostpotentials
positive potentials
are 181bykcal/mol
by
hydrogens.
The differences in the strengths of the intralattice attractive forces in molecular and ionic solids
are reflected
in the energies
required
them.
The heat
of aionic
molecular
The differences
in the strengths
of to
theovercome
intralattice
attractive
forcesofinsublimation
molecular and
solids
solid
is the enthalpy
for therequired
transition
the crystal
to separate
gas phase
molecules.solid
For
are
reflected
in the energies
to from
overcome
them. lattice
The heat
of sublimation
of a molecular
is
the
enthalpy
for
the
transition
from
the
crystal
lattice
to
separate
gas
phase
molecules.
For
C,H,N,O molecular explosives, the magnitudes of the heats of sublimation are mainly between 20 and
30 kcal/mol
[22]. Forexplosives,
ionic compounds,
the analogue
of heats
the heat
sublimation
the lattice
enthalpy,
C,H,N,O
molecular
the magnitudes
of the
of of
sublimation
areis mainly
between
20
and 30iskcal/mol
[22]. required
For ionictocompounds,
analogue
of gas
the phase
heat ofions.
sublimation
is the lattice
which
the enthalpy
separate thethe
lattice
into free
Lattice enthalpies
are
generally much
heats required
of sublimation
[23]. For
C,H,N,O
ionicfree
explosives
in which
ions
enthalpy,
whichgreater
is the than
enthalpy
to separate
the
lattice into
gas phase
ions.the
Lattice
have +1 andare
´1generally
charges, the
estimated
enthalpies
are between
100For
andC,H,N,O
200 kcal/mol
for +1
enthalpies
much
greaterlattice
than heats
of sublimation
[23].
ionic [24];
explosives
in which the ions have +1 and −1 charges, the estimated lattice enthalpies are between 100 and 200
4
Crystals 2016, 6, 7
5 of 14
and ´2 they are roughly twice as large, and approach 400 kcal/mol for +2 and ´2. The ionic charges
are clearly a major factor.
Another interesting manifestation of the effects of overall ionic charges is evident in estimating
“effective” molecular or formula unit volumes, Veff . These are defined for any molecular or ionic
solid as,
Veff “ M{ρ
(1)
where M is the molecular or formula unit mass and ρ is the crystal density. Veff is the hypothetical
volume per molecule or per formula unit (in the case of an ionic compound) that would correspond to
the unit cell of the lattice being completely filled. (In reality, there is of course always some free space.)
Veff can also be determined by dividing the volume of the unit cell by the number of molecules or
formula units that it contains.
For molecular C,H,N,O solids, Veff can be approximated quite well as the volume V(0.001) that is
enclosed within the molecule’s 0.001 au surface [25–27]:
Veff pmolecular solidq « Vp0.001q
(2)
This is surprising given that V(0.001) is computed for a single isolated molecule, with no
consideration of intermolecular interactions within the crystal.
For an ionic C,H,N,O compound, the analogous procedure would be to compute V(0.001) for the
positive and negative ions separately and then to estimate Veff for the formula unit by,
Veff pionic solidq « aVp0.001qcation ` bVp0.001qanion
(3)
In Equation (3), a and b are the numbers of cations and anions, respectively, in one formula unit.
However Equation (3) is not nearly as good an approximation to the actual Veff for ionic C,H,N,O
compounds as Equation (2) is for molecular ones. The Veff obtained by Equation (3) are almost always
too large [28,29], often quite significantly so.
Equation (2) is a reasonably good approximation for molecular C,H,N,O solids because the
attractive forces between the molecules are relatively weak, and using the volume within the 0.001 au
surface of the isolated molecule is therefore acceptable. However Equation (3) is a rather poor
approximation for ionic C,H,N,O solids because the attractive forces between the oppositely-charged
ions are quite strong, and bring the ions closer together than their 0.001 au volumes would predict.
For both types of solids, the Veff can be improved by taking explicit account of the electrostatic
potentials on the molecular or ionic surfaces [24–26]. The corrected Veff can then be used to make
reasonably good estimates of crystal densities via Equation (1).
3. Electrostatic Potentials on Ionic Surfaces
On the 0.001 au surface of an ion, the electrostatic potential is everywhere positive or everywhere
negative, in accordance with the overall integral charge on the ion (Figures 3–6). However, it should
be recognized that for polyatomic ions these surface potentials are frequently far from isotropic. To
some extent, they may exhibit patterns that are qualitatively similar to those of the corresponding
neutral molecules. (It should be kept in mind that the colors on the surfaces of the neutral molecules,
the anions and the cations correspond to different ranges of potentials).
Consider the 5-nitrotetrazolate (3) and 3-nitro-1,2,4-triazolate (4) anions, Figures 3 and 4. In the
parent neutral molecules 1 and 2, the most positive features are the N-H hydrogens, with maximum
potentials of about 70 kcal/mol (Figures 1 and 2). These hydrogens are not present in the anions.
However the other positive regions in the neutral molecules—above the rings and the C–NO2 bonds,
as well as the C-H hydrogen in 2—are still in evidence, as being now the least negative regions in the
anions. The most negative potentials in the anions (as in the neutral molecules) are associated with the
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nitrogens of the rings and the oxygens of the NO2 groups, reaching magnitudes in the neighborhood
of ´130 kcal/mol, roughly 100 kcal/mol more negative than in the neutral molecules.
In2016,
Figure
Crystals
Crystals
2016,
6, 76, 7 6 is the electrostatic potential on the 0.001 au surface of the positive 5-nitrotetrazolium
cation, 5, formed by protonating one of the ring nitrogens in 1. Now there are two N–H hydrogens, and
and
they
have
the
most
positive
potentials,
174
kcal/mol.
The
regions
above
the
ring
and
C–NO
they
have
thethe
most
positive
potentials,
174174
kcal/mol.
TheThe
regions
above
the the
ring
and
the
C–NO
and
they
have
most
positive
potentials,
kcal/mol.
regions
above
ring
and
thethe
C–NO
2 2
2 bond
bond
also
strongly
positive,
with
maxima
about
152
kcal/mol.
The
most
negative
(i.e.
least
are
also
strongly
positive,
with maxima
of about
152
kcal/mol.
The most
negative
(i.e., least
positive)
bond
areare
also
strongly
positive,
with
maxima
of of
about
152
kcal/mol.
The
most
negative
(i.e.
least
positive)
regions
are
by
the
non-protonated
ring
nitrogens
and
the
NO
2
oxygens.
All
of
this
is
regions
are
by
the
non-protonated
ring
nitrogens
and
the
NO
oxygens.
All
of
this
is
analogous
positive) regions are by the non-protonated ring nitrogens and
2 the NO2 oxygens. All of this isto
analogous
is
seen
potential
of
parent
molecule
Figure
1 (except
course
what
is seen
inwhat
theispotential
ofthe
the
parent of
molecule
in Figure
1 (except
of course
that the
values
ofthat
the
analogous
to to
what
seen
in in
the
potential
thethe
parent
molecule
in in
Figure
1 (except
of of
course
that
the
values
the
electrostatic
potential
now
positive).
electrostatic
potential
are now
all positive).
the
values
of of
the
electrostatic
potential
areare
now
allall
positive).
HH
NN
O 2O
N2N
NN
CC
+N+N N N
HH
5 5
Figures 3–6show
showthat
thatit itwould
would bemisleading
misleadingto tofocus
focusonly
onlyupon
uponthetheoverall
overallcharges
chargesonon
Figures
Figures3–6
3–6 show that
it would be be
misleading to focus
only upon
the overall
charges on
polyatomic
polyatomic
ions,
ignoring
variations
electrostatic
potentials
their
surfaces.
What also
polyatomic
ions,
ignoring
thethe
variations
in in
thethe
electrostatic
onon
their
surfaces.
ions, ignoring
the
variations
in the electrostatic
potentials potentials
on their surfaces.
What
alsoWhat
needsalso
to be
needs
to
be
taken
into
account
are
the
polarizing
effects
of
the
ions
upon
each
other.
The
influence
needs
to
be
taken
into
account
are
the
polarizing
effects
of
the
ions
upon
each
other.
The
influence
of of
taken into account are the polarizing effects of the ions upon each other. The influence of these factors
these
factors
upon
crystal
densities
will
be
discussed
in
the
next
section.
these
factors
upon
crystal
densities
will beindiscussed
in the next section.
upon
crystal
densities
will
be discussed
the next section.
Figure
Computed
electrostatic
potential
onon
0.001
auau
cationic
surface
of
cation
(5).
Figure
6.
Computed
electrostatic
potential
0.001
cationic
surface
of
5-nitrotetrazolium
cation
Figure
6. 6.
Computed
electrostatic
potential
on
0.001
au
cationic
surface
of 5-nitrotetrazolium
5-nitrotetrazolium
cation
ranges,
ininkcal/mol,
are:
red,
greater
than
150;
yellow,
between
150
and
120;
green,
between
120
(5).
Color
ranges,
in
kcal/mol,
are:
red,
greater
than
150;
yellow,
between
and
120;
green,
between
(5).Color
Color
ranges,
kcal/mol,
are:
red,
greater
than
150;
yellow,
between
150150
and
120;
green,
between
and
90;
blue,
less than
90.
Circles
shownshown
positions
of atoms;
NO2 group
isgroup
on theisleft.
Most
positive
120
and
90;
blue,
less
than
90.
Circles
positions
of
atoms;
NO
2
on
the
left.
Most
120 and 90; blue, less than 90. Circles shown positions of atoms; NO2 group is on the left. Most
potentials
are 174 kcal/mol
by hydrogens.
positive
potentials
kcal/mol
hydrogens.
positive
potentials
areare
174174
kcal/mol
byby
hydrogens.
Crystal
Densities
and
Electrostatic
Potentials
Crystal
Densities
and
Electrostatic
Potentials
4. 4.
Crystal
Densities
and
Electrostatic
Potentials
has
already
been
pointed
out
that
replacing
C-H
units
molecular
ionic
frameworks
has
already
been
pointed
out
that
replacing
C-H
units
in
molecular
or
ionic
frameworks
It It
has
already
been
pointed
out
that
replacing
C-H
units
inin
molecular
oror
ionic
frameworks
byby
nitrogen
atoms
could
reasonably
be
expected
to
increase
the
crystal
densities.
The
strongly
attractive
nitrogen
atoms
could
reasonably
be
expected
to
increase
the
crystal
densities.
nitrogen atoms could reasonably be expected to increase the crystal densities. The strongly attractive
forces
between
oppositely-charged
ions
might
beanticipated
anticipated
to
have
a similar
effect.
What
isfact
in
oppositely-charged
ions
might
have
a similar
effect.
What
forces
between
oppositely-charged
ions
might
bebe
anticipated
to to
have
a similar
effect.
What
is is
in in
fact
fact
observed?
observed?
observed?
2007,
Rice
et
a database
of experimental
crystal
densities
of 180 C,H,N,O
molecular
In2007,
2007,Rice
Rice
et
al.compiled
compiled
database
experimental
crystaldensities
densities
180C,H,N,O
C,H,N,O
InIn
et al.
al.compiled
a adatabase
of ofexperimental
crystal
of of180
solids
[26].
They
were
mainly
nitroaromatics,
nitroaliphatics,
nitramines
and
nitrate
esters.
Many
molecularsolids
solids[26].
[26].They
Theywere
weremainly
mainlynitroaromatics,
nitroaromatics,nitroaliphatics,
nitroaliphatics,nitramines
nitraminesand
andnitrate
nitrate
molecular
of
them
had all-carbon
frameworks.
In frameworks.
2011,
Gao andIn
Shreeve
tabulated
the
experimental
densities
esters.
Many
themhad
hadall-carbon
all-carbon
frameworks.
In2011,
2011,
Gaoand
and
Shreeve
tabulated
esters.
Many
of ofthem
Gao
Shreeve
tabulated
thethe
of
more
than
230
C,H,N,O
salts
[15],
in
which
one
or
both
ions
were
usually
tetrazole
or
triazole
experimental
densities
of
more
than
230
C,H,N,O
salts
[15],
in
which
one
or
both
ions
were
usually
experimental densities of more than 230 C,H,N,O salts [15], in which one or both ions were usually
tetrazole
triazole
derivatives,
with
a few
being
derivatives
imidazole
pyrazole.
Thus
these
tetrazole
oror
triazole
derivatives,
with
a few
being
derivatives
of of
imidazole
oror
pyrazole.
Thus
these
can
be
viewed
as
largely
nitrogen-rich
salts.
can be viewed as largely nitrogen-rich salts.
Figure7 7compares
comparesthethedistributions
distributionsof ofdensities,
densities,onona apercentage
percentagebasis,
basis,within
withinthese
thesetwo
two
Figure
categories
compounds.
The
comparison
shows
clearly
that
nitrogen-rich
salts
represent
categories
of of
compounds.
The
comparison
shows
clearly
that
nitrogen-rich
salts
dodo
notnot
represent
anan
3 is “an
3
assured
path
to
high
densities.
It
has
been
suggested
that
a
density
greater
than
1.80
g/cm
assured path to high densities. It has been suggested that a density greater than 1.80 g/cm is “an
Crystals 2016, 6, 7
7 of 14
derivatives, with a few being derivatives of imidazole or pyrazole. Thus these can be viewed as largely
nitrogen-rich salts.
Figure 7 compares the distributions of densities, on a percentage basis, within these two categories
Crystals 2016, 6, 7
of compounds. The comparison shows clearly that nitrogen-rich salts do not represent an assured
path to high densities. It has been suggested that a density greater than 1.80 g/cm3 is “an essential
essential requirement for advanced energetic materials” [30]. This criterion is satisfied by about 22%
requirement for advanced energetic materials” [30]. This criterion is satisfied by about 22% of the
of the molecular compounds in Figure 7 but only about 6% of the ionic ones, even though the latter
molecular compounds in Figure 7 but only about 6% of the ionic ones, even though the latter were
were predominantly nitrogen-rich while many of the former were not.
predominantly nitrogen-rich while many of the former were not.
Figure
Figure 7.
7. Crystal
Crystal density
density distributions
distributions of
of C,H,N,O
C,H,N,O molecular
molecular compounds
compounds (purple)
(purple) and
and nitrogen-rich
nitrogen-rich
C,H,N,O
ionic
compounds
(green).
Vertical
axes
are
percentages.
C,H,N,O ionic compounds (green). Vertical axes are percentages.
As Zhang et al. have pointed out [30], the interactions between polyatomic ions are directional,
reflecting the nonisotropic natures of the electrostatic potentials on their surfaces (Figures
(Figures 3–6).
3–6).
Zhang
et
al.
argued
that
closer
packing
and
higher
densities
could
be
promoted
by
taking
advantage
of
Zhang et al. argued that closer packing and higher densities could be promoted by taking advantage
+,
interactions
suchsuch
as hydrogen
bonding,
and drew
to the hydroxylammonium
ion, H3 N-OH
of interactions
as hydrogen
bonding,
andattention
drew attention
to the hydroxylammonium
ion,
+, as being
as
foreffective
this purpose.
H3being
N-OHeffective
for this purpose.
It must be noted that Dunitz et al. found no general relationship between density and hydrogen
bonding for aa database
database of
of hydrocarbon,
hydrocarbon, C,H,O
C,H,O and
and C,H,N
C,H,N molecular
molecular solids
solids [31].
[31]. However that
conclusion may not be
relevant
to
the
present
systems
of
functionalized
C,H,N,O
be relevant to the present systems of functionalized C,H,N,Osalts.
salts.
It was demonstrated quite some time ago that hydrogen bonding ability can be related to the
magnitude
potential
onon
thethe
hydrogen
[32,33].
In Table
1 are1listed
the most
magnitude of
ofthe
thepositive
positiveelectrostatic
electrostatic
potential
hydrogen
[32,33].
In Table
are listed
the
positive
calculated
ionic
surface
potentials
associated
with
the
hydrogens
in
a
series
of
monopositive
most positive calculated ionic surface potentials associated with the hydrogens in a series of
cations
that arecations
commonly
in C,H,N,O
salts.in
The
hydroxylammonium
ion clearly stands out;
monopositive
that found
are commonly
found
C,H,N,O
salts. The hydroxylammonium
ion
it
has the
single
most
positive
potential,
190 kcal/mol
near190
thekcal/mol
hydroxylnear
hydrogen,
plus three
more
clearly
stands
out;
it has
the single
most positive
potential,
the hydroxyl
hydrogen,
of
about
181
kcal/mol
by the
hydrogens.
Therehydrogens.
is in fact a There
continuous
verya strongly
positive
plus
three
more
of about
181 other
kcal/mol
by the other
is in fact
continuous
very
region
encompassing
all of
the hydrogens,
in magnitude
from 177
to 190 kcal/mol
(Figure
8).
strongly
positive region
encompassing
all ranging
of the hydrogens,
ranging
in magnitude
from 177
to 190
+ , which has four hydrogen
+
The
next
most
positive
ion
in
Table
1
is
the
ammonium
ion,
NH
maxima
kcal/mol (Figure 8). The next most positive ion in Table 1 is the ammonium
ion, NH4 , which has four
4
of
181 kcal/mol,
but
are separated
by distinctly
less positive
regions
hydrogen
maxima
ofthey
181 kcal/mol,
but they
are separated
by distinctly
less(Figure
positive5).
regions (Figure 5).
The presence of
shows it
it to be a likely candidate for
of several
several highly
highly positive
positive sites
sites on
on H
H33N-OH++ shows
strongly attractive
would be the next most
attractive directional
directional interactions
interactions with
with polyatomic
polyatomic anions;
anions; NH
NH44++ would
likely in Table
Table 1.
1. Does
Does this
this translate
translate into
into higher
higher densities?
densities? Dunitz et al. found no general relationship
between density and lattice energies for their database of hydrocarbon, C,H,O and C,H,N molecular
solids
butbut
again
this this
may may
not benot
relevant
to the present
C,H,N,O
solids [31],
[31],mentioned
mentionedabove,
above,
again
be relevant
to the functionalized
present functionalized
ionic
solids.
C,H,N,O
ionic solids.
We have surveyed 87 nitrogen-rich C,H,N,O salts that have been synthesized during the past
five years [16,30,34–46]. (Only anhydrous salts were considered.) 41 of them, or 47%, have crystal
densities ≥1.80 g/cm3. This is a remarkable increase over the 6% in the earlier work that is
represented in Figure 7; some reasons for this will be proposed later.
In twelve of these 87 compounds, the cation is H3N-OH+. All twelve have densities ≥1.80 g/cm3.
3
Crystals 2016, 6, 7
8 of 14
We have surveyed 87 nitrogen-rich C,H,N,O salts that have been synthesized during the past
five years [16,30,34–46]. (Only anhydrous salts were considered.) 41 of them, or 47%, have crystal
densities ě1.80 g/cm3 . This is a remarkable increase over the 6% in the earlier work that is represented
in Figure 7; some reasons for this will be proposed later.
Crystals
6, 7 of these 87 compounds, the cation is H3 N-OH+ . All twelve have densities ě1.80 g/cm3 .
In2016,
twelve
In four of them, the density is 1.90 g/cm3 or more. Thus, the hydroxylammonium ion does promote
high
high densities
densities in
in C,H,N,O
C,H,N,O salts,
salts, as
as is
is suggested
suggested by
by the
the electrostatic
electrostatic potential
potential on
on its
its surface
surface (Figure
(Figure 8)
8)
+
+
and
as
was
argued
by
Zhang
et
al.
[30].
NH
4 is
the
cation
in
nine
of
the
compounds
surveyed,
and
six
and as was argued by Zhang et al. [30]. NH4 is the cation in nine of the compounds surveyed, and
3, 3
3
+
+
of
have
densities
with
sixthem
of them
have
densities≥1.80
ě1.80g/cm
g/cm
, withone
onebeing
being1.90
1.90 g/cm
g/cm.3 .The
The H
H33N–OH
N–OH+ and
and NH
NH44 + cations
cations
clearly
C,H,N,O salt
salt having
having aa high
high density.
density.
clearly increase
increase the
the likelihood
likelihood of
of a
a C,H,N,O
+
Figure 8.
Computed electrostatic
electrostatic potential
Color
Figure
8. Computed
potential on
on 0.001
0.001 au
au cationic
cationic surface
surfaceof
ofNH
NH3 3OH
OH + cation.
cation. Color
ranges,
in
kcal/mol,
are:
red,
greater
than
165;
yellow,
between
165
and
140;
green,
between
140
ranges, in kcal/mol, are: red, greater than 165; yellow, between 165 and 140; green, between 140 and
and
110;
blue,
less
than
110.
Circles
show
positions
of
atoms;
OH
group
is
on
the
left.
Most
positive
110; blue, less than 110. Circles show positions of atoms; OH group is on the left. Most positive
potential is 190 kcal/mol by the OH hydrogen.
potential is 190 kcal/mol by the OH hydrogen.
Table 1.
Most positive
positive electrostatic
electrostatic potentials
potentials on
on the
the 0.001
0.001 au
au surfaces
surfaces of
of some
some C,H,N,O
C,H,N,O
Table
1. Most
monopositive
cations.
monopositive cations.
Cation Cation
Most Positive
kcal/mol
Most Potentials,
Positive Potentials,
kcal/mol
hydroxylammonium
190, 181, 181,
hydroxylammonium
190, 180
181, 181, 180
ammonium
181, 181, 181,
ammonium
181, 181
181, 181, 181
5-nitrotetrazolium
174, 152
174, 153, 152
5-nitrotetrazolium
174, 174, 153,
hydrazinium
173, 173, 172
hydrazinium
173, 173, 172
3,3-dinitroazetidinium
172, 172
3,3-dinitroazetidinium
172, 172 172, 172
5-aminotetrazolium
5-aminotetrazolium
172, 172 169, 169, 169
methylammonium
1,1-dimethylhydrazinium
164, 164, 156
methylammonium
169, 169, 169
azidoformadinium
165, 157, 143
1,1-dimethylhydrazinium
164, 164, 156
t-butylhydrazinium
161, 158, 154
azidoformadinium
165, 157, 143
1,5-diaminotetrazolium
164, 141, 130, 130
t-butylhydrazinium
1-isopropyl-3,3-dinitroazetidinium161, 158, 154
158, 158, 143
hydroxyguanidinium
157, 130
152, 143, 136
1,5-diaminotetrazolium
164, 141, 130,
guanidinium
154,
154,
154
1-isopropyl-3,3-dinitroazetidinium
158, 158, 143
aminoguanidinium
154, 151
hydroxyguanidinium
157, 152, 143, 136
1,5-diamino-4-methyltetrazolium
149, 137
guanidinium
154, 154, 154
N,N,N-trimethylhydrazinium
142, 142, 130
aminoguanidinium
154, 151 136
triaminoguanidinium
1,5-diamino-4-methyltetrazolium
149, 137
N,N,N-trimethylhydrazinium
142, 142,
In Table 2 are the most negative calculated
ionic130
surface potentials of a series of mononegative
triaminoguanidinium
136
anions often found in C,H,N,O salts. In general, their magnitudes are less than those of the most
positive potentials on the cations in Table 1. It is further notable that the smaller ions tend to have the
In Table 2 are the most negative calculated ionic surface potentials of a series of mononegative
strongest potentials, whether positive or negative. This may be in part because the overall charge of
anions often found in C,H,N,O salts. In general, their magnitudes are less than those of the most
positive potentials on the cations in Table 1. It is further notable that the smaller ions tend to have the
strongest potentials, whether positive or negative. This may be in part because the overall charge of
the ion is not as delocalized [47]; another factor of course, for a given ionic framework, is the effects
of the functional groups.
In using electrostatic potentials such as those in Figures 1–6 and 8 to interpret and predict
molecular and ionic interactions, it is important to keep in mind that these potentials are typically
Crystals 2016, 6, 7
9 of 14
the ion is not as delocalized [47]; another factor of course, for a given ionic framework, is the effects of
the functional groups.
Table 2. Most negative electrostatic potentials on the 0.001 au surfaces of some C,H,N,O
mononegative anions.
Anion
Most Negative Potentials, kcal/mol
nitrate
nitroformate
azide
5-aminotetrazolate
3-nitro-1,2,4-triazolate
4-nitro-1,2,3-triazolate
dinitramide
5-nitrotetrazolate
4,5-dinitroimidazolate
3,5-dinitropyrazolate
3,5-dinitro-1,2,4-triazolate
picrate
2,4,5-trinitroimidazolate
´151, ´151, ´151
´142, ´142, ´123, ´120, ´120
´139, ´139
´137, ´137, ´137
´136, ´133
´132, ´124, ´124, ´123
´131, ´126, ´126, ´121, ´121
´126, ´126, ´118, ´118, ´116
´125, ´125, ´119
´123, ´123
´119, ´119, ´119, ´119
´119, ´119
´116, ´116, ´115, ´114
In using electrostatic potentials such as those in Figures 1–6 and 8 to interpret and predict
molecular and ionic interactions, it is important to keep in mind that these potentials are typically
computed for the ground states of the molecules or ions, prior to any interaction [48–50]. Accordingly
they do not reflect the polarizing effect that each molecule’s or ion’s electric field has upon the charge
distribution of the other. This polarization, which is stabilizing, is of course particularly significant
when resulting from the strong electric fields of ions.
The degree to which the charge distribution of a molecule, atom or ion is affected by an external
electric field is determined by its polarizability. It is well known that polarizability generally increases
with size [51–57] and in going from cations to neutral molecules to anions [58], as the outer electrons
become less tightly bound. It is therefore to be expected that the intralattice attractive interactions in
ionic compounds will be stronger when they have large polarizable anions in conjunction with cations
having several highly positive polarizing sites. Hydroxylammonium and ammonium salts with large
C,H,N,O anions fit this description, which helps to explain their frequently high densities.
Why are the recently-prepared nitrogen-rich salts more likely to have high densities than the
earlier ones represented in Figure 7? Several factors may be involved. In the newer compounds,
there is a greater emphasis upon small cations and large anions. This results in strong intralattice
attractions due to the highly-positive potentials of small cations (Table 1) and the high polarizabilities
of large anions, and evidently promotes higher densities. In contrast, a significant number of the salts
represented in Figure 7 involved large cations, which have low polarizabilities and weaker positive
potentials, and often large anions, which have weaker negative potentials (Table 2). Furthermore,
even when these compounds did have a large anion and small cation, the latter was very rarely the
hydroxylammonium while the anion was often relatively poor in oxygens or even just C,H,N in
composition; all of this diminishes the opportunities for strong hydrogen bonding.
While C,H,N,O salts with large cations are less likely to have high densities, it is not precluded, as
can be seen from the examples in Table 3. Note that the negative ion in three of the four compounds is
NO3 ´ , which has the most negative potentials in Table 2.
Crystals 2016,
2016, 6,
6, 777
Crystals
Crystals
2016,
6,
5. Discussion and Summary
Is nitrogen
beneficial? For unsubstituted molecules, replacing a C–H unit by a nitrogen
Crystals
2016, 6, richness
7
10 of 14
does tend to increase the density (Table 4). When functional groups are present, however, it is less
straightforward; for example, 1,3,5-trinitrobenzene (6) and 2,4,6-trinitropyridine (7) have essentially
3. Some
C,H,N,O
with
largerespectively.
cations and small
that have experimental
333 [59],
the sameTable
densities,
1.76
g/cm333 nitrogen-rich
[2] and 1.751salts
g/cm
Riceanions
et al. compiled
the densities
densities greater than 1.80 g/cm3 .
of 38 “high-nitrogen” C,H,N,O molecular solids [26]; only four had densities greater than 1.80 g/cm333.
Salt
Density, g/cm3
Reference
oxalhydrazinium dinitrate
1-amino-3-nitroguanidinium nitrate
oxalhydrazinium nitrate
5-aminotetrazolium dinitramide 1.833
1.945
1.91
1.840
1.833
44
38
44
29
5. Discussion and Summary
Is nitrogen richness beneficial? For unsubstituted molecules, replacing a C–H unit by a nitrogen
does
to increase
density
(Table
4). When
functional
groups
are present,
it is less
For tend
C,H,N,O
salts asthe
well,
nitrogen
richness
is not
sufficient
to make
likely ahowever,
density ≥1.80
3
straightforward;
for
example,
1,3,5-trinitrobenzene
(6)
and
2,4,6-trinitropyridine
(7)
have
essentially
3
g/cm 3. This is shown by Figure 7. To increase the probability of a high density, the salt should also
3 [2] and 1.751 g/cm3 [59],+ respectively.
same anion
densities,
g/cm
Rice et al. compiled the densities
havethe
a large
and1.76
a small
cation,
preferably H333N-OH++ or NH444+++.
of 38 “high-nitrogen” C,H,N,O molecular solids [26]; only four had densities greater than 1.80 g/cm3 .
Table 4. Some experimental densities and heats of formation, ΔHfff.
Table 4. Some experimental densities and heats of formation, ∆Hf .
Compound
Density aaa
Density
g/cm333a g/cm3
Structure
Compound
Structure
ΔHfff bbb
∆Hf b kcal/mol
kcal/mol
(cal/g) (cal/g)
H
N
1 H-imidazole
1 H-imidazole
1.0303
1.0303
11.9 (175)
11.9 (175)
N
H
N
1 H-1,2,3-triazole
1 H-1,2,3-triazole
N
1.1861
1.1861
---
N
1.4060
1.4060
56.4 (805)
56.4 (805)
0.7739
0.7739
−37.68
(−447.7)
´37.68
(´447.7)
0.8606
0.8606
´20.66
(´242.6)
−20.66
(−242.6)
—
N
H
N
1 H-tetrazole
1 H-tetrazole
N
N
cyclohexane
cyclohexane
H
H
H
N
N
N
piperidine
piperidine
aaa
a Reference [58];
b Reference [60].
Reference
[58]; bbb Reference
[60].
A greater nitrogen/carbon ratio does frequently result in a more positive heat of formation, ΔHfff
(Table 4). Thus the values for 6 and 7 are −10.4 kcal/mol (−48.8 cal/g) and 18.8 kcal/mol (88.0 cal/g),
10
5. Discussion and Summary
Is nitrogen richness beneficial? For unsubstituted molecules, replacing a C–H unit by a nitrogen
does tend to increase the density (Table 4). When functional groups are present, however, it is less
straightforward; for example, 1,3,5-trinitrobenzene (6) and 2,4,6-trinitropyridine (7) have essentially
Crystals 2016, 6, 7
11 of 14
the same densities, 1.76 g/cm3 [2] and 1.751 g/cm3 [59], respectively. Rice et al. compiled the densities
of 38 “high-nitrogen” C,H,N,O molecular solids [26]; only four had densities greater than 1.80 g/cm3.
For C,H,N,O salts as well, nitrogen richness is not sufficient to make likely a density ě1.80 g/cm3 .
For C,H,N,O salts as well, nitrogen richness is not sufficient to make likely a density ≥1.80
This is shown
by Figure 7. To increase the probability of a high density, the salt should also have a
g/cm3. This is shown by Figure 7. To increase the+ probability
of a high density, the salt should also
large anion and a small cation, preferably H3 N-OH or NH4 ++ .
have a large anion and a small cation, preferably H3N-OH or NH4+.
A greater nitrogen/carbon ratio does frequently result in a more positive heat of formation, ∆Hf
(Table 4). Thus the values
for4.6 Some
and 7experimental
are ´10.4 kcal/mol
cal/g)
and 18.8ΔH
kcal/mol
(88.0 cal/g),
Table
densities (´48.8
and heats
of formation,
f.
respectively [2]. This may (or may not) lead to a greater heat release Q upon detonation, as shall be
f b
Density aof the enthalpy
ΔHchange
seen. For an explosive X, Q is typically taken to be the negative
per gram of X
Compound
Structure
3
in the overall detonation reaction:
g/cm
kcal/mol (cal/g)
«
ff
H
1 ÿ
Q“´ N
ni ∆Hf,i ´ ∆Hf,X
(4)
MX
i
1 H-imidazole
1.0303
11.9 (175)
In Equation (4), MX is the mass of X in g/mol,
ni is the number of moles of final detonation product
N
i, having molar heat of formation ∆Hf,i , and ∆Hf,X is the molar heat of formation of the explosive X.
From Equation (4), the detonation heatHrelease Q is greater as the heat of formation ∆Hf,X of the
N of formation ∆Hf,i of the products are more negative.
compound is more positive and as the heats
1.1861
--- the amounts of the
1
H-1,2,3-triazole
N
Replacing C–H units by nitrogens is likely to increase
∆Hf,X
but it may also decrease
three common detonation products that haveNnegative heats of formation: CO2 (g), ´94.05 kcal/mol;
CO (g), ´26.42 kcal/mol; H2 O (g), ´57.80 kcal/mol [60]. Producing one less mole of CO2 would
H
negate a quite considerable increase of 94 kcal/mol
in ∆Hf,X ; two fewer moles of H2 O would cancel an
N N/C ratio means that more N2 is formed as a product,
increase of 115 kcal/mol! Of course, a larger
1.4060
56.4to(805)
H-tetrazole
which may be1viewed
as desirable since N2 isN (at the moment)
considered
be environmentally
benign; however its heat of formation is zero, so it does not contribute to the detonation heat release Q.
N
N
Increasing the N/C ratio may therefore have two opposing effects, one making Q larger and the other
making it smaller.
There are yet other factors to take into account. A larger value of Q is associated with a higher level
0.7739
−37.68 (−447.7)
cyclohexane
of detonation performance [6], but it is also linked to greater sensitivity [5,19,61,62], i.e., undesirable
vulnerability to accidental detonation caused by an unintended stimulus such as shock or impact.
Finally, if the increase in N2 is accompanied Hby a decrease in the lighter product H2 O, then the volume
of gas produced per gram of compound willN be less—adversely affecting detonation performance [6].
So, given piperidine
all these conflicting factors, our answer to0.8606
the question posed
at(−242.6)
the beginning of this
−20.66
section, “Is nitrogen richness beneficial?” is an unequivocal yes and no! Putting it more elegantly,
one should not generalize; it depends upon the particular case.
a Reference [58]; b Reference [60].
Author Contributions: P.P. and J.S.M. conceived and designed the plan for the paper and analyzed the data;
P.L. andA
J.S.M.
carried
out the calculations;
wrote
the paper.
greater
nitrogen/carbon
ratio P.P.
does
frequently
result in a more positive heat of formation, ΔHf
Conflicts
Thevalues
authors
declare
of interest.
(Table of
4).Interest:
Thus the
for
6 andno7 conflict
are −10.4
kcal/mol (−48.8 cal/g) and 18.8 kcal/mol (88.0 cal/g),
10
Crystals 2016, 6, 7
12 of 14
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