Combustion, Explosion, and Shock Waves, Vol. 37, No. 4, pp. 464 469, 2001
Shock Compression of Hydrocarbons of the General Formula C5H8
M. F. Gogulya1 and I. M. Voskoboinikov1 UDC 541.124/128 532.591
Translated from Fizika Goreniya i Vzryva, Vol. 37, No. 4, pp. 109 115, July August, 2001.
Original article submitted April 17, 2000.
The paper reports results of experimental investigation of liquid hydrocarbons having
identical elemental compositions but different structures of molecules, initial densi-
ties, and heats of formation. Shock-compression temperatures are determined For
1,3-pentadiene, methylene cyclobutane, spiropentane, and a solution of benzene with
hexane and cyclohexane (which has the same ratio of C/H), and the shock adiabat
is determined for 1,3-pentadiene. The data obtained are used to refine the expres-
sions for the state parameters of the destruction products of hydrocarbons behind a
shock-wave front.
To understand the physicochemical aspects of be- (4C6H6 + 3C6H14 + 3C6H10 = 12C5H8), which has the
havior of hydrocarbons under dynamic loads, it is of same ratio of C/H. Some characteristics of the exam-
interest to study compounds having identical elemental ined liquids are presented in Table 1. For individual hy-
0
compositions but different molecular structures, initial drocarbons, the heats of formation ("Hf298) are taken
densities, and heats of formation. This interest is mo- from [1], and for the solution, they are obtained from
tivated by the fact that under high dynamic pressures the additivity of components.
and temperatures, hydrocarbons undergo transforma- Shock waves were produced by two methods: im-
tions behind the shock-wave front. The end products of pact of a plate accelerated by detonation products of a
the transformation are determined by elemental com- high-explosive (HE) charge along the bottom of a cell
position, and intermediate products can also depend on with a liquid sample or detonation of a HE charge which
the initial structure of the molecule. The pressures at was in contact with the cell. Charges with 40 mm di-
the beginning and end of the transformation also de- ameter and 60 mm height were initiated by a flat-front
pend on the initial molecular structure. Usually, these generator. The cells in which the examined liquids were
pressures are obtained from the form of the relation placed were made of an aluminum alloy. The particle
between the shock-wave velocity D and the particle ve- velocities in the shield (uAl) were determined in prelim-
locity u. However, with small change in specific volume inary experiments with an accuracy of H"4%.
during transformation, the curve of D(u) can lack qual- The shock-front temperature was measured by a
itative features, and to determine the beginning or end two-channel optical pyrometer in the blue ( = 420 nm)
of the transformation, one need additional information and red ( = 720 or 627 nm) spectral regions. In record-
on the state parameters of hydrocarbons at high pres- ing the radiation intensity by OK-33 and S1-74 oscillo-
sures. For liquid hydrocarbons, such a parameter can graphs, the time resolutions were 80 and 30 nsec, respec-
be the shock-compression temperature (TH). The goal tively. In the range of 1400 3500, brightness tempera-
of the present paper is to determine the effect of molec- tures were measured with an a priori error of H"3.5%. In
ular structure on shock-compression temperatures for measurements at various wavelengths, the experimental
hydrocarbons with identical elemental compositions. deviations of results did not exceed 70 K. That is, the ra-
The objects of investigation were the liquid hydro- diation of the shock-wave front in the examined liquids
carbons: 1,3-pentadiene, methylene cyclobutane, and is similar to gray radiation, and the emission factor is
spiropentane of the same empirical formula C5H8 and close to unity. Generally, shock-front temperatures can
a solution of benzene with hexane and cyclohexane differ from temperatures behind the front, but for 1,3-
pentadiene, they coincide [2]. For 1,3-pentadiene, along
1
Semenov Institute of Chemical Physics,
with temperature, we measured pressure (by manganin
Russian Academy of Sciences, Moscow 117977.
464 0010-5082/01/3704-0464 $25.00 © 2001 Plenum Publishing Corporation
Shock Compression of Hydrocarbons with the General Formula C5H8 465
TABLE 1
Initial 0
Substance Structural formula "Hf298, kcal/mole
density, g/cm3
H2C C C C CH3
1,3-pentadiene 0.683 11.56
H H H
CH2 C CH2
Methylene cyclobutane 0.740 22.43
CH2 CH2
H2 C C H2
Spiropentane 0.755 37.67
C
H2 C C H2
Solution  0.783 -10.29 (calculation)
gauges) and shock-wave velocities (from the duration of from this dependence is 0.035 km/sec. At p = 11.2
shock-front glow in layers of known thickness). Mea- GPa, the change in the slope of the curve of D(u) for
surement results are presented in Table 2 and in Figs. 1 1,3-pentadiene does not lead to a marked spread of
and 2. points in the coordinates TH - uAl (see Fig. 2). For
Ignoring the transformation of 1,3-pentadiene un- 1,3-pentadiene, methylene cyclobutane, and spiropen-
der shock loading, we can describe its shock adiabat by tane, the measured temperatures are adequately de-
the generalized dependence [3] scribed by linear dependences on the particle velocity
in the aluminum shield (TH = c + duAl). Values of the
D = c0 + 2u - 0.1u2/c0,
coefficients are presented in Table 3 along with the re-
where c0 is the velocity of sound in the initial state,
gions of application and standard deviations of points
which is calculated by the Rao rule [4] to be 1.1 km/sec.
from the approximating dependences.
As is evident from Fig. 1, only the lower experimental
With the same state in the aluminum shield, the
point lies on this curve. At a pressure of p H" 7.3 GPa,
shock-compression temperature increases in the follow-
1,3-pentadiene undergoes a transformation which pro-
ing order: the solution, 1,3-pentadiene, and spiropen-
ceeds with decrease in specific volume. At p > 11.2 GPa
tane, and the values of TH for 1,3-pentadiene and
(u > 2.9 km/sec), the shock adiabat of 1,3-pentadiene
can be written as D = a + bu, where a = 1.43 km/sec
and b = 1.46. The standard deviation of points
Fig. 2. Shock-loading temperature versus particle
Fig. 1. Curves of D(u) for 1,3-pentadiene: points 1 velocity in an aluminum shield for 1,3-pentadiene,
refer to the experiment, curve 2 refers to calculation methylene cyclobutane, spiropentane, and the solu-
using the generalized dependence, curve 3 refers to tion: the curves are obtained by processing of exper-
linear approximation of experimental data, and curve imental data (the dashed curve refers to methylene
4 refers to calculation by the scheme of [5]. cyclobutane).
466 Gogulya and Voskoboinikov
Shock Compression of Hydrocarbons with the General Formula C5H8 467
TABLE 3
Matter c, K d, (K · sec)/km uAl, km/sec Inaccuracy, K
1,3-pentadiene 277.6 889.6 1.29 3.07 40
Methylene cyclobutane 196.0 932.7 1.29 3.07 65
Spiropentane 378.4 923.6 1.51 3.07 44
methylene cyclobutane practically coincide. The heat The calculated curve of shock-wave velocity versus
of formation of these substances increases in the same particle velocity for 1,3-pentadiene is given in Fig. 1
order. The smallest values of TH are observed for the (curve 4). There is good agreement between the calcu-
solution in the region of uAl < 2.4 km/sec. lated and experimental data at u > 2.9 km/sec.
For 1,3-pentadiene, the shock-compression temper- For compounds having the same empirical for-
ature can also be presented as a linear dependence on mula as 1,3-pentadiene but different initial specific vol-
pressure: TH = T0 + kp. Over the entire measurement umes (V0i) and internal energies (E0i), the shock adia-
region, TH = 938 + 79p (Ä…73 K), and with division bats were calculated as follows. By analogy with (1),
into two segments, TH = 700 + 99p (Ä…27 K) up to
Å‚ V0i Å‚ V0i
pHi 1 - - 1 = pH 1 - - 1
p = 11.5 GPa and TH = 1154 + 68p (Ä…21 K) at higher
2 V 2 V
pressures.
Å‚
We considered the possibility of calculating shock-
+ (E0i - E0). (2)
V
compression parameters for 1,3-pentadiene using the
Mie Grüneisen equation of state under the assumption
Subtracting (1) from this expression and taking into
that the transformation products are carbon in the di-
account that the values of PH are identical, we obtain
amond phase and hydrogen in a condensed molecular
Å‚ V01 Å‚
phase [5]. The shock adiabat of the end products has pHi = pH1 1 - - 1 + (E0i - E01)
2 V V
the form
V
Å‚ V0i
Å‚ Å‚
1 - - 1 , (3)
pH = pc(V ) + pc(V ) dV 1 - (V0 - V ) ,
2 V
V 2V
V0 where (E0i -E01) is the difference in internal energy be-
tween the initial states, which is equal to the difference
where pc(V ) is the cold pressure component, Å‚ is the
in enthalpy of formation between the substance consid-
Grüneisen coefficient, and V0 and V are the initial and
ered and 1,3-pentadiene. The reliability of the results
final specific volumes.
obtained by expression (3) for methylene cyclobutane,
The values of V and Å‚ were determined from the
spiropentane, and the solution can be checked using
expressions [5]:
shock-compression temperatures measured with varia-
C H
V (pc) = xV (pc) + (1 - x)V (pc),
tion in particle velocity in the shield. For this, it is nec-
C H
V "E V V essary to calculate shock-compression temperatures and
a" = x + (1 - x) = const.
shock adiabats and then dependences TH(uAl). Gener-
Å‚ "p V Å‚ Å‚
ally, to calculate the temperatures, one need to know
Here x is the mass fraction of carbon in a molecule and
the temperature dependence of the specific heat cv.
E is the internal energy; subscripts C and H refer to
This dependence is identical for the hydrocarbons con-
carbon and hydrogen, respectively.
sidered, which have the same composition of transfor-
The initial specific volumes of the decomposition
mation products. The expression for the heat capacity
products (V0) and 1,3-pentadiene (V01) differ. There-
within the framework of the Mie Grüneisen equation of
fore, the shock adiabat pH1 issuing from V01 has the
state has the form [6]
form
Å‚ V0 Å‚
"E "T Å‚
pH1 = pH 1 - - 1 + (E01 - E0)
cv = + p + TH ,
2 V V
"V H "V H V
Å‚ V01
where the parameters (pressure, specific volume, inter-
1 - - 1 , (1)
2 V nal energy, and temperature) are determined by the
where (E01 - E0) is the difference in internal energy shock adiabat. Using the measured dynamic compress-
between the two initial states, which was ignored in the ibility and temperature for 1,3-pentadiene in the region
calculations. where the transformation is already completed, we have
468 Gogulya and Voskoboinikov
T
Å‚ Å‚
pH1(V, T )-pc(V ) = [EH1(V, T )-Ec(V )]= cv dT
V V
0
or
T
V
[pH1(V, T ) - pc(V )] = EH1(T ) = cv dT
Å‚
0
Ti-1 Ti-1
Ti
= cv dT + cv dT = cv dT +Żv(Ti-Ti-1). (5)
c
0 Ti-1 0
From the last expression, we obtained the average value
of cv in the temperature range of Ti-1 Ti. From the de-
pendence of pc(V ) with a step of 0.5 GPa, the change
in temperature is H"100 K. Estimates of cv in the tem-
Fig. 3. Heat capacity of transformation products
perature range of 1900 3500 K are presented in Fig. 3
of 1,3-pentadiene versus temperature calculated by
(curve 4). The value of cv increases with rise in temper-
Eq. (4): Å‚/V = 2.45 (1), 1.54 (2), 1 (3), 0.5 g/cm3
(5), and 0 (6); curve 4 is obtained using Eq. (5).
ature, but in the region T H" 2700 K there is a stepped
transition to higher values. This is due to the differ-
ent forms of equations describing variation in the cold-
1 a(a + 2bu)(V01 - V )
pressure component of molecular hydrogen at pressures
cv = p -
2 (V01 - b(V01 - V ))2
lower and higher than 9 GPa [5]. Hence, the form of
the equations used to describe the product components
influences the value of cv.
Å‚ a(a + 2bu)k
TH - , (4)
Thus, even with a rather complete set of experi-
V (V01 - b(V01 - V ))2
mental data on shock-compression characteristics, there
where a and b are the shock-adiabat coefficients and k is uncertainty in values of the specific heat. Nev-
is the slope of the curve of TH(p). The values of cv ob- ertheless, the shock-compression temperatures for the
tained from expression (4) depend appreciably on the remaining compounds C5H8 can be calculated. For
chosen value of Å‚/V . Assuming that the transforma- this, using experimental values for the temperature of
tion yields carbon in the diamond phase and molecu- 1,3-pentadiene at T > 1800 K, we obtain the tempera-
lar hydrogen, it is reasonable to take this ratio in the ture dependence of the thermal-energy component:
same form as in the calculation of the shock adiabat
T
V
(Å‚/V = 1.54 g/cm3). However, in this case, the value
EH1(T ) = cv dT = [pH1(V, T ) - pc(V )]
of cv decreases with increase in temperature (curve 2 in Å‚
0
Fig. 3). The same tendency of heat capacity variation is
2
= 0.472T + 3.832T - 5.027.
observed in the case where the Grüneisen coefficient is
estimated from the form of the experimental shock adia- The standard deviation of experimental points from this
bat [7] (Å‚ = 2b-1 = 1.92) and the specific volume is the dependence is 27 K. This expression is also valid for
initial value for a mixture of diamond with hydrogen: other compounds of the same empirical formula. There-
V0 = 0.7840 cm3/g (curve 1 in Fig. 3). More realistic fore, using expression (3) to calculate shock adiabats,
tendencies of variation of cv take place only for Å‚/V < 1 we can obtain values of EHi(T ) for any substance and
(curves 3, 5, and 6 in Fig. 3). This indicates that in- then find temperature values from the above depen-
terpolation of initial experimental data on shock-wave dence. This calculation procedure applies within the
velocities and temperatures by linear dependences does framework of the assumptions of identical transforma-
not guarantee reliable information on the heat capacity tion products, and, as a consequence, within the frame-
of the transformation products. work of identical values of the cold-pressure component
The agreement between calculated and experimen- and energy at equal specific volumes.
tal values of shock-wave velocities for 1,3-pentadiene Calculated and experimental values of shock-
and the availability of experimental values for TH gives compression temperatures versus the state in the shield
reasons for analysis of one more approach to estimat- are presented in Fig. 4, and curves of p(V ) are presented
ing cv. Within the framework of the Mie Grüneisen in Fig. 5. The experimental shock-compression temper-
equation of state, atures for methylene cyclobutane at p > 15 GPa and for
Shock Compression of Hydrocarbons with the General Formula C5H8 469
Thus, the paper reports new experimental data on
shock-compression temperature for hydrocarbons hav-
ing the empirical formula C5H8. The results obtained
are used to refine the expressions proposed in [5] for
calculation of shock-compression parameters (including
temperature) of individual hydrocarbons in the case of
their destruction behind the shock front. The calcula-
tion procedure described can also be used for other hy-
drocarbons with the same empirical formula provided
that for one of them, the shock adiabat and shock-
compression temperature are known.
This work was supported by the Russian Foun-
dation for Fundamental Research (Grant Nos. 97-03-
32000a and 00-03-32162a).
Fig. 4. Comparison of experimental (points) and cal-
REFERENCES
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Fig. 5. Calculated shock adiabats for
(eds.), Physics of High Energy Density, Academic Press,
1,3-pentadiene, methylene cyclobutane, spiropen-
tane, and the solution. New York London (1971), pp. 88 93.
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the calculated values. The indicated pressures deter-
Academic Press, New York London (1970), pp. 515
mine the lower boundaries of the region of application of
568.
the above procedure for calculating shock-compression
parameters. A different situation is observed for the
solution. The temperatures calculated for the solution
at uAl > 2.29 km/sec (p > 19 GPa) are approximately
200 K below the experimental values. Formal agreement
0
was obtained for "Hf298 = 8.13 kcal/mole. A compar-
ison of the calculated values shows that a change in
the enthalpy of formation has a significant effect on the
temperature and course of the shock adiabat in the p V
coordinates but practically does not influence its shape
in the p u coordinates (see Table 2).