CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
MOLECULAR DYNAMICS AND EXPERIMENTAL STUDY OF
SHOCK POLARIZATION OF NITROMETHANE
Laurent Soulard
CEA-DAM/Ile-de-France, BP12, 91680 Bruy£res-le-Chatel, France
Abstract. We present a complete study of shock electrical polarization of a dipolar molecule : the
nitromethane. From molecular dynamics simulations, we show that this effect is due to the anisotropy
of the nitromethane near the shock front : a partial and very short-lived orientation of molecules
along the shock axis propagation is observed. The evolution of the amplitude and time relaxation
of the polarization with the shock intensity is extracted from simulations, and theses results can be
compared, via an appropriate hydrodynamic description, to specific but very simple experiments. A
good agreement is found at the beginning of shock propagation but rapidly the experimental results
diverge from the theoretical signals because of chemical reactions.
INTRODUCTION
ing of an electrical dipole near the shock front. It
is the shock polarization phenomenon. An electrical
dipole implies inevitably a local anisotropy behind
the shock. We propose first in this paper an analysis
by non-equilibrium molecular dynamics (NEMD) of
the shock induced anisotropy in a simple polar liquid, the nitromethane. In a second part, we connect the NEMD results to experimental results via
the Allison's model. In the last part, we present
some shock polarization experiments which permit
to validate the NEMD calculations and the theoretical model.
The propagation of a shock wave is associated
with a strong gradient of thermodynamic properties
as the pressure or the density. In the liquid case,
molecular dynamics studies have shown that this non
equilibrium step is very transient. Thus, thermodynamic equilibrium is restored about 10~12s after
the beginning of the compression. Nevertheless, it
is this strong gradient which make specificity of a
shock wave in comparison with a static compression.
A possible specificity of the shock compression on
a particular property as chemical reactivity must be
found in this non-equilibrium zone. Unfortunately,
due to the very small thickness of this zone, the in
situ observations of relaxation mechanisms which
occur behind a shock are unreachable by any experiments and only a global effect can be measured. We
are interested in this work to the possible electrical
signal due to the non-equilibrium zone. The corresponding experimental setup is shown figure 2. For
polar liquid, many works [1, 2, 3, 4] have shown that
electrical response can be associated with the creat-
MOLECULAR DYNAMICS
The shock propagation along the x axis is due
to an appropriate choice of initial and limit conditions. The used potential functions are described in
[5] and permit a reliable calculation of the Hugoniot of nitromethane. The initial configuration is a
100 x 40 x 40 simple cubic mesh. The shock is
loaded in the system after relaxation and thermalisation of the system in the liquid phase. In slices Tn
347
Table 1: Molecular dynamics results.
u
(m/s)
910
1224
1500
P
(GPa)
(s) 1 2
3,13
4,98 0,9xl(r12
6,95 0,3xl(r12
1,5 x lo- '
TJV ,max
0,056
0,062
0,082
perpendicular to the x axis, we define by Yj^(£)
the average carbon/nitrogen bound orientation along
the i axis :
E
COS
(1)
Figure 1: Average carbon/nitrogen bound orientation along the
i = x,y,z axis from NEMD simulations
HI is a unit vector of the i axis and 7VTri the number of molecules in the slice Tn. Three shocks were
simulated corresponding to a particle velocity jump
u of 910m/s, 1224m/5 and 1500ra/s. The results
(figure 1) show that only the T^(£) curves exhibit
a narrow asymmetric peak for which maximum is
immediately after the shock front. The time rise is
very short (« 3 x 10~13s). The relaxation is approximatively exponential (table 1) :
dQ(t) , Q(t) r ( t f - u ) t , (L-Ut)
dt
X2)
• + Xi).
L
P 5 (x)rfx
(3)
Xi(t)
U is the shock velocity, S the surface of each electrode, L the initial distance between the two electrodes, xi and X2 the electrical succeptibility ahead
and behind the shock, Xi(t) the position of the left
electrode at time t, xs(t) the position of the shock
and PS(X) thepolarization at point x. From NEMD
results (see equation 2), PS can be written as :
(2)
THEORETICAL ANALYSIS
The NEMD results show that a local and transient
dipolar moment is produced by the shock immediately behind the front. This observation corresponds
to Allison's hypothesis [2]. If the sample is taken
inside two metallic plates, the shock must induce
an electrical tension between the plates. Now, we
suppose that the two electrode are connected by a
resistor R. In this condition we can show that the
time evolution of the electrical charge Q (t) is given
by the following equation :
PS(x,t)
=
With T^ = TO (1 - ti/^)
. exp<
and
(4)
-Pmox =
IJL is the molecular dipolar moment, m the molecular
weight and p the density behind the shock. We have
then for Q(t) the following equation :
348
Q
(*) = &2 exp
(5)
A
(02,01,*) =
(6)
copper
Teflon
sample
with Q(0) = 0, ki = \ (^- + ^-} and
^
_
UTQPrnaXS ^
gy
su5stjtutmg
me
error
f UnC _
tions of the equation 6 by the relation erf(2) =
order :
opposite sign when the reflected shock propagates in
the sample.
Q(«)
1 — kiTit
1with TO//
signal,
Figure 2: Experimental setup
at zero
' we
1
—e
EXPERIMENTS
— e
(7)
The experimental setup is shown on figure 2.
The used samples are nitromethane and cyclohexane, a non polar liquid. For cyclohexane, no signal
is detected. For nitromethane, the recorded signal is
a series of peak of current alternately positive and
negative (figure 3). Simulation of this experiment
with an ID hydrocode shows that each peak (except the first) is synchrone with the various shock
reflexion. It is interesting to note that the amplitude
of the second peak (i.e. the first shock reflexion)
is about twice the amplitude of the first peak, as
theory predicts it. The signals can be easily detected up to the fifth peak for u = 910ra/s and the
sixth peak for u = 1038m/5. The corresponding
final pressures are respectively 20GPa and 24GPa.
NEMD simulations (table 1) together with the theoretical analysis show that the time tmax is much
smaller (< 50 x 10~12s) than the time resolution of
our experiments (200 x 10~12s). Thus, the peaks of
current don't correspond necessary to the theoretical
Imax of equation 9. In an other hand, it is easily
to show that the charge Q for Imax is very small
in comparison with the final charge (i.e. when the
shock is far from the electrode). So, to compare calculations (NEMD results associated with theoretical
analysis) and experimental curves, we have choose
the Q(t) curve (figure 4). We can see that the theoretical Q(t) agrees with experimental measurement
I/TI — I/ TQ. At the beginning of
1 and the charge (equation 7) is :
t
(8)
In the simple but physical case TI = r<2 and TO <
TI, the current /(t) is maximum at time tmax
TO In (TI/TO) and the corresponding amplitude is :
TQ (U - U)
(9)
Equation 9 shows that I max don't depend of the
experimental setup geometry (i.e. S and L). Moreover, the dependance of Imax with the shock strength
is difficult to foresee because TO, U — u and PQ
don't vary in the same manner. Polarization due to
the reflection of the shock on the second electrode
can be calculate in the same manner. It is possible to
show that the shock reflexion causes a second peak
of tension with an opposite sign and a larger amplitude, resulting from the depolarization when the
shock reach the electrode, and a new polarization of
349
Figure 3: Experimental result in nitromethane for u =
910m/5.
Figure 4: Experimental and theoretical electrical charge in
nitromethane for u = 910m/ S. Electrical data for shocked
nitromethane can be found in [6]
only at the beginning of the signal. Next, the experimental charge increases linearly with time while
theoretical charge is almost constant.
The comparison of experimental and theoretical
results shows that, except on the shock front, the
shocked nitromethane don't behave like a perfect
dielectric. An reasonable hypothesis is to suppose
that chemical reactions occur behind the front, with
creation of ionic charges in the system. But, because
the hydrodynamics of the system agrees with an inert
material, only very few chemical reactions occur in
the nitromethane up to rather high pressure (24GPa).
cur behind a shock wave. Moreover, this experiment
shows that chemical reaction exist in the system even
for pressure much lower than the ignition pressure
(8GPa).
CONCLUSION
[3] G.E. Hauver. J. Appl Phys., 36(7):2113, 1965.
We have described in this work the electric response of a polar liquid in which a shock wave
propagate. NEMD shows that a very transient and
local anisotropy occurs immediately behind the front.
The corresponding amplitude and relaxation time are
consistent with experimental results. The shock polarization experiment in association with NEMD is
then and very interesting (and not complicated) tool
to examine the non-equilibrium processes which oc-
[4] M. de Icaza-Herrera, H.N. Presles, and
C. Brochet. Revue de Physique appliquee,
13(11):547, 1978.
REFERENCES
[1] RJ. Eichelberger and G.E. Hauver. In CNRS,
editor, Les ondes de detonations, page 364,
1961.
[2] RE. Allison. J. Appl Phys., 36(7):2111, 1965.
[5] L. Soulard. this proceeding.
[6] S.S. Nabatov, V.V. Yakushev, and A.N. Dremin.
Eletrical properties of nitromethane under shock
compression.
Fizika Goreniya i Vzryra,
11(2):300, 1974.
350