-3-”
M . A . COOK,R. T. KEYES,W. S. PARTRIDGE A N D W. 0. URSENBACII
hindered skeletal internal rotations for these activated complexes. Finally the excellent agreement between theory and experiment for reaction 9 between Br and H? and the 100,000 fold discrepancy between calculated and observed factors for reaction 10 (CH3)LH
+ Br +(CH3),C + H B r
require special comment. We make an unqualified prediction that the observed value is wrong; in particular, we believe a reinvestigation of this reaction over a wide range of reactant pressure, degree of reaction, and pressure of additives will reveal that the over-all reaction (CH3)aCH Br? + (CH,),CBr HBr does not follow the bromination mechanism assumed for it.’d Evaluation.-Kinetic data are often so uncertain that order-of-magnitude estimates of pre-exponential factors are all that one can obtain from experiment. There are many empirical rules and approximation methods in the field of molecular structure and molecular spectroscopy which, though
+
+
[CONTRIBUTIOX FROM
THE
Vol. 79
not good enough for many purposes in their own field, are more than adequate for purposes of kinetics. The rules used here for bond tlist a n c e ~ ,for ~ , ~stretching force coiistants,‘j” and for moments of inertia for internal rotation-‘appear to be cases of this type. However, we kineticists must await developments for comparable rules for barriers to internal rotation and for either a Badger’s rule for bending force constants or, more likely, an adequate empirical classification of bending frcquencies. IVith such rules, kinetic pre-exponential factors should be calculable within a factor of four or so, without undue labor, even for complicated reactant molecules. Xt present these calculations appear t o be valid within, perhaps, a factor of about -10. It might be remarked that for practical purposes this situation is a considerable iniproveinwt over the case as stated recently by Trotinan-Dickensonll relative to reaction 10. (11) A . 17. Trotman-Dickenson, “(;as Kinetics,” .\c.iilcinic Press, Inc., S e w York, S . Y . , 1956. p . 194, line 13.
STASFORD, c.4~.
EXPLOSIVES RESEARCH GROUP,UXIVERSITY OF UTAHJ
Velocity-Diameter Curves, Velocity Transients and Reaction Rates in PETN, RDX, EDNA and Tetryl1 BY M E L V I N il. COOK,ROBERT T. KEYES,WILLIAMS.PARTRIDGE AND W. 0 . URSENBACII RECEIVED JUSE 11, 1956 \‘elucity-dianieter 3 : d j curves for cap initiated, low density P E T N (Pentaerythratol Tetranitrate), RL)S (Cyclotriinetliy!ctie triiiitrainine), E D X A (Ethylene diriitramine) and Tetryl (Trinitrophenylmethylnitramine) are presented. A.liinlysis o f these curves by the theories extant of chemical reaction rates in detonation gave total reactioti times ( 7 = McRg) expressed by average values of 8.0 X 7.5 X 1.5 X and 2.5 X sec./cm. for P E T N , RDX, tetryl and E I ) S A i respectively; , and c values of 1.0, -0.1, and -0.04 for the geometrical model, nozzle theory and curved front theory, respectively. (EKis the average grain radius.) Low-order detonation was observed in both tetryl and EDNA in the “noti-ideal” detonation rcgion and slightly into the “ideal” region for charge lengths less than 2 to 5 cm. and diameters less than 3 to 5 cm. -it the end of this low-order regime detonation changed over abruptly t o normal high-order detonation in d l except the smallest diameter charges of coarse tetryl where the high and low-order detonation curves could not be resolved
Xside from their practical value, velocity-dianieter or D ( d ) curves have theoretical value in providing (by curve fitting) the parameter T (total reaction time], or a0 (reaction zone length), occurring in the various theoretical models bf reaction rates in detonation, namely, the “nozzle” theory,? the “curved front”3 theory and the “geometrical” i n ~ c l e l . ~Moreover, comparisons of the theoretical and observed D ( d ) curves are helpful in evaluating these theories. Previous such applications have been carried out in this Laboratory for TNT,4a D?;T,5 -INin the pure state and in T N T and Composition B,6 sodium nitrate in TNTi7 and for bar( 1 ) ’lhis iiii.estigatlon was supported by Office of S a v a l Research, Contract S o . S7-onr-43107, Project No. 357239. 12) €1. Jones, Proc. R o y . Soc. (Londorz), 1898, 415 (1947). (:i) H . Eyring, R. E. Powell, G. H. Duffey a n d R. B. Parlin, C h i n .
i i c s s . , 4 6 , BD (1940). (4) (a) RZ. A. Cook, G. S. Horsley, W. S. Partridge and W. 0. Ursenlmch, .I. C h i n . P h y s . , 2 4 , G O (1956); (b) .\I. A. Cook and F. A . Olson, .I. . l ) i ’ . Iizs2. Clreiiz. Eng., 1, 391 (1S55). i i l 51 A. Couk and 1%’. S. Partridge, J . P k y s . Chein., 59, 673 11955). f l j ) 51. A . C o o k , 1;. LI. Mayfield and W. S. Partridge, ibid., 59, 673 (1!4.;5). 17) &I. A . Cook a n d W’. 0. Ursenbach, Paper S o . 2 5 , Second O S R aylnyosium on Detonatiun, Feb. 51-11, 1955, Washington, D. C .
ium nitrate, lead nitrate, aluminum and other ingredients in T N T and in some cases, Composition B. This paper presents velocity-diameter curves for low density PETN, RDX, tetryl, and E D S A together with the reaction rates computed by means of the three published models of reaction rates in detonation. Presented also are experimental data concerning a velocity transient observed to occur in the early stages of the detonation process in the small diameter charges of low density, cap initiated tetryl and EDNA. Another factor of importance in evaluating and applying the curved front theory aside from the D ( d ) curves is the steadystate shape of the detonation wave. Experimental wave shape results with these and other explosives were presented by Cook, et aLn Experimental Methods and Results The explosives used in this study were of the highest (service) available purity and were screened using U. S . standard Tyler screens. The screen cuts used for P E T S were -35 +48 mesh and -65 +lo0 mesh, -65 +lo0 mesh (8) hl. A . Cook, G . S. Horsley, R . T. Keyes. \V, S . Partridge ant1 \ V 0 Ursenbach, J . A p p l . P h y s . , 27, 269 (1956).
VELOCITY-DIAMETER CURVES
Jan. 5 , 1957
TABLE Ia D ( d ) DATAFOR P E T N , R D X MEASURED 7
d , cm.
0.318 ,635
,953
1.27
1.59
1.90
2.22
2.54
PI
(n./cm.9 0.914 ,914 ,964 .970
.960 ,960
,950 ,971
,961 ,921
,920 ,943
.go9 .915
.926 .941
PETN
D (mm.1
D
psec.)
k./cm.a)
(mm./ rsec.)
4.24 4.18 5.16 5.09
1.00 1.o 1.016 0.954
4.94 5.10 5.41 5.20
5.29 5.31
3.31 5.31
5.11 5.31
5.13 5.26
5.23 5.32
5.26 5.30
PI
1.017 1.002
0.991 ,960
,974 .964
.996 .989
.979
5.51 5.41
5.40 5.41
5.38 5.46
5.51 5.44
5.48
--RDX--65 100 mesh D PI (mm.1
+
(g./cm.a)
psec.)
1.25 1.26 1.21 1.21
5.69 5.50 6.37 6.40
1.17 1.16
1.22 1.22
1.19 1.17
1.15 1.15
1.16 1.16
I
.
1.14
6.68 6.60
6.72 6.72
6.70 6.51
6.58 6.56
6.49 6.53
6.47 6.42
AND
EDNA
7
-35
(mm./ (g.1m.a)
1.025 0,997 1.01 1.00 1.002 1.008 1.020 1.000 0.985 .931 1.00 1.00 0.954 ,977 1.03 1.03 0.980 .970 1.00 1.00 0.960 .979 1.00 1.01 0.976 ,976 1.00 1.01
EDNA
+D+ 40 mesh rsec.)
D
c
.. .. 3.24 3.41 c c
4.15 3.74 c c
4.40 4.25 C
c
4.61 4.45 0
c
4.82 c C
4.98
+ 100 mesh D
Pl
psec.)
(g./cm.s)
6
2.81 2.60 c
-65
(rum./
3.44 3.49 4.08 4.83 4.80 4.98 5.26 5.00 5.20 5.24 5.16 5.30 5.36 5.24 5.46 5.43 5.56 5.58 5.28 5.47 5.56 5.60 5.58 5.53 5.61 5.64
(mm.1 psec.)
1.0
Fa
0.996 1.017
4.15 3,52
0.988 ,990
5.03 5.25
,994 ,991
j.36 5.60
,971 ,981
5.48 5.52
.959 .967
5.31 5.49
,966 ,965
5.44
.98 .97
5.59 5.63
5,51
7.54
1.061 6.12 1.059 6.10 5.90 19.89 1,059 5.97 1.048 1.045 5.90 1.054 5.92 5.76 0.98 5.78 .99 a F = failed; Dt = transient or low-order velocity. Two detonation failures occurred in this diameter, but the loworder transient (or the normal wave) persisted the length of the charge in these two shots. These shots measured a t L / d > 3 before transient was observed. for RDX, -20 +28 mesh and -35 +48 mesh for tetryl, and -35 $48 and -65 +lo0 mesh for EDNA. Charges were loose-packed (vibrated for density uniformity) in plastic tubing of wall thickness l/a?‘‘ for d < 1 cm., plastic tubing of wall thickness l/16’’ for 1 d 2.5 cm., and manilapaper tubes for d > 2.5 cm. Tubes of d < 2.5 cm. were all 15 f 0.4 cm. in length and those of d > 2.5 cm. were six or more diameters in length. Densities were determined in all cases by weight-volume measurements. Velocities were measured by means of a rotating mirror (“streak”) camera of film writing speed up t o 5 mm./psec. except for the shots of d > 7.5 cm. where a “pin-oscillograph” capable of measuring times to 0.01 psec. was used. The “pin” method was considered unsatisfactory for use in very small diameter charges owing t o a possible adverse influence of pin inserts on wave propagntion in very small diameter charges. IVhile velocities were measurable by the methods used here with ail accuracy of about i O . l T o , the reproducibility of results was considerably less accurate (about i l t o 2yG) owing to the influence of unavoidable density fluctuations in the loose-packed explosives. Table I summarizes the D ( d ) data obtained in this investigation.
In order to obtain velocities a t the nearest even densities, density corrections by means of the equation
+
DP, = DP, S(Pe - PI) (1) were made, where DpI is the velocity measured a t the density P I and D , is that a t the nearest round value pe of density. The average large diameter (ideal) velocity D’ may be expressed by the linear relation D* = Di o S ( p i - 1.0) (2) with values of the parameters Dl.0 and S given in Table 11. The D ( d ) results for P E T N and R D X corrected to p1 = 0.95 g./cc. and 1.2 g./cc., respectively, are shown in Fig. 1. In both tetryl and E D N A a t diameters from the critical one (d,) t o slightly above d,,* (minimum diameter for D = D*, where D* is the “ideal” or “hydrodynamic” velocity) the wave commenced propagating a t low velocity (loworder detonation), but suddenly changed over to the normal high velocity or high-order detonation a t a point from 2 to 5 cm. from the point of initiation. The traces in each case where this dual velocity effect was observed showed two straight line sections. I n early studies, however, velocities
+
A. COOK,It. T. KEYES,W. S.PARTRIDGE AND W. 0. URSENBACII
AI.
TABLE Ib D ( d ) DATAFOR TETRYL MEASURED
_-_ -20 + 28 mesh-d cm
pi,
( g . , cm.3)
0.318 0 .635 0.033
1.27
1.905
2,222
2.54
3.18
gsec.)
,955 ,926 ,916 ,934 ,939 ,925 ,926 ,924 ,952 ,900 ,932 ,918 ,990 .91s
D
(mm., psec.:
..
... 0.90 0.952 ,952 ,961
0.905 ,988 ,916 ,927 .9Oi ,908 .961
1 .XI
Dt (mm./
1.51 1.97 1.98
I; 1.51 1.97 1.98
1.97 1.95
.. ..
2.30 2.26 2.46 2.65 2.42 2.33 2.34 2.41 2.66 2.60 2.13 2.51 1.93 2.38 2.38 2.44 ,
.
4.35 4.33 4 96 4.77 4.45
5.28
.. 5.11 4.86 5.16 5.12 4.98 5.03 5.21 5.20 5.00 5.10 5.11 4.94
3 . xo 4.39 5.04
6.30 7 .
