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It should be said that only since Cowan and Fickett’s report have good experimental detonation pressure data been available for use in arriving at best-fit parameters. Abo, the covolume factors (ki) have been deliberately normalized but not set equal to molecular excluded volumes. In this normalization, rather cogent argu-
*S. R. Brinkley and E. B. Wilson, Jr., “Revised Method of Predicting the Detonation Velocities in Solid Explosives,” OSRD Rept. 905, 1942.
" E. A, Christian and H. G. Snay, "Analysis of Experimental Data on Detonation Velocities,” U.S. Naval Ordnance Laboratory Rept., Nav0rd-1508, 1951.
11C. L. Mader, "Detonation Properties of Condensed Explosives Computed Using the Âecker-Kistiakowsky-Wilson Equation of State,” Los Alamos Scientific Laboratory Rept. LA-2900, 1963.
ments were made for reducing the orientation effect of the polar molecules (H2O and NHs in particular), and thereby increasing the magnitudes of the corresponding ki& relative to those for nonpolar molecules.18 The result is an empirical equation which at this time is the best available for general detonation state calculations.
Three significant consequences in regard to detonation calculations on C-H-N-0 compositions derive from the present K-W parameters and covolume factors: the predicted detonation temperature is quite low; the predominant carbon-oxygen product is C02 rather than CO over a wide range of compositions at the higher loading densities; the detonation pressure ¦ and velocity are reasonably close to experiment where experimental data are available. Whether the result on CO* is correct or not, it has served as one point of departure for the discussion which follows.
Ï1. THE COVOLUME FACTOR-MO LECULAR-WEIGHT RELATIONSHIP
The covolume factors#nost recently used by Mader11 for HA C02j and N2 (and thus, by inference, for iso-electronic CO) were further adjusted from Cowan and Fickett’s values8 so as best to reproduce experimental Hugoniots18-14; i.e., H2O, 360—>250; C02, 670—>600; Na, 380—*380; CO, 390—>Ç 90. The A/s for the “minor” detonation species, CH<, H2, NO, and Oj, in current K-W detonation computations remain the “theoretical” values derived from calculated molecular dimensions. In the light of this fact and because HsO, C02, N2, and CO are usually considered to comprise 98+% of the detonation gases from organic C-H-N-0 explosives, it is noteworthy that Mader’s A/s for the “major” detonation species are closely proportional to their molecular weights (Table II).
This observation is of substantial interest in view of Christian and Snay’s report10 that empirical covolume
Table I. Parameters in Eq. (4).
Source Ref. a 0 ê 6
Ê is tiako w sky-W i Iso n 71
Brinkley-W llso n 9 0.25 0.3 1.0 0
Cowan-Fickett 8 0.5 0.09 11.85 400
Mader, RDX 11 0.5 0.16 10.91 400
Mader, TNT 11 0.5 0.096 12.69 400
“These are now the “geometric” covolume factors of Ref. 8. The argument for HsO and NH| is that they will not exhibit their strong polar attraction toward the nonpolar molecules which are present in much higher concentration. Consequently these species should be given effective covolume factors more like those of nonpolar molecules.
«W. Fickett, “Detonation Properties of Condensed Explosives Calculated with an Equation of State Based on Intermolecular Potentials/’ Los Alamos Sri. Laboratory Rept. LA-2712, 1962. “ Ì. H. Rice and J. M. Walsh, J. Chem. Phys. 26, 824 (1957). fcV. N. Zuberov and G. S. Telegin, Dokl. Akad. Nauk SSSR 142, 309 (1962) ^English transl.: Soviet Phye.—Doklady 7, 34 (1962)}
Table II. The covolume factor-molecular weight relationship for the major detonation species.
Species ki ki/Mi
HjO 250 13.89
N* 380 13.57
CO 390 13.93
COz 600 13.64
factors for the total gas mixtures of twenty organic explosives, chosen to give best average agreement between calculated and measured detonation velocities, were also roughly proportional (=Ü~4%) to the average molecular weights of the assumed gaseous detonation products. Taken in combination, these findings have suggested that, for most organic C-H-N-0 explosives, v.Xjki in the Kistiakowsky-Wilson equation may be replaced by the product HM, where H is the constant 13.76 and M is the average gas molecular weight. Since (M/Vt) =pK, pt being the density of the gaseous products in the detonation state, this allows transformation of Eq. (4) to
P=(RTpjM) (1+X^), Õ = êÍðËÒ+â)". (6)
We now introduce two terms which will become very important in subsequent discussions: N, the number of moles of gaseous detonation products per gram of explosive, and G, the weight fraction of explosive going over to gaseous products. From the definitions, NM=G, so that after combining constants, êÍ—A and (ÇêÍ=Â, the equation may now take the general form