# Chemistry of Detonations - Kamlet M.J.

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It has been mentioned that an 80-point fit of all the experimental data of Table I to Eq. (2) led to K= 15.52 and a —2.039 with an average absolute deviation of

0.02203 (5.5%). The standard deviation a} for comparison, was 0.03050 ( 7.2%).

It is instructive also to try Eq. (2) with individual segments of the experimental data. For example, fitting only the 23 data points for TNT leads to K = 15.74, a= 1.995, and <r=» 0.04550 (11.0%). Although the high

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<7 reflects the fact that systematic variations are particularly large for this material, the result (without the potential complication of changing ôàãü) appears to confirm that P is proportional to the square of the initial density. Similarly, the 11 data points for RDX and HMX lead to Ê =15.28, à = 2.Þ5, and a —0.02394 (5.7%), which reinforces this conclusion.

The least-squares treatment also allows an evaluation of the systematic variations between laboratories mentioned in the text. Taking the data from NOL (excluding EDNA),26 the earlier LASL data, the results

of Petrone’s reinterpretation of later LASL data, the later Russian data and the BRL measurements, a 47-point least-squares fit leads to Ê =14.90, a = 2,067 and a=0.02067 (4.9%). On the other hand, the later LASL and earlier Russian data (31 points) lead to K= 15.76, a = 2.090 and <r = 0.03400 (8.1%).

Such treatment also seems to show that the relationship proposed in the present series of papers might have been masked by the inherent inaccuracies in measurement if only segments of the experimental data from the individual laboratories had been considered, e.g.,

NOL 22 data points A" = 16.79 « = 1.836 cr = 0.02538

I NOL, excluding EDNA 20 13.72 2.206 0.01938

jj’ earlier LASL 15 10.13 2.790 0.02075

| later LASL 15 18.02 1.833 0.02990

[ all LASL 30 17.87 1.795 0.03033

] earlier Russian 16 13.99 2.336 0.01898

i all Russian 21 14.68 2.214 0.02453.

THE JOURNAL OF CHEMICAL PHYSICS VOLUME 48, NUMBER 1 1 JANUARY 1968

Percus-Yevick Equation Applied to a Lennard-Jones Fluid*

R. O. Watts

Diffusion Research Unit, Research School of Physical Sciences > The Australian National University, Canberra, Australia

(Received 12 June 1967)

An efficient method of solving the Percus-Yevick and related equations is described. The method is applied to a Lennard-Jones fluid, and the solutions obtained are discussed. It is shown that the Percus-Yevick equation predicts a phase change with critical density close to 0.27 and with a critical temperature which is dependent upon the range at which the Lennard-Jones potential is truncated. At the phase change the compressibility becomes infinite although the virial equation of state does not show this behavior.

Outside the critical region the PY equation is at least two-valued for all densities in the range (0, 0.6).

I. INTRODUCTION

A number of approximate integral equations for the radial distribution function g(r) of fluids have been proposed in recent years. Two particularly useful approximations are the Percus-Yevick (PY)1-2 and the Convolution Hypernetted Chain (CHNC)3-4 equations. In this paper an efficient numerical method of solving these equations is described and the results obtained by applying the method to the PY equation are discussed. A later paper will describe the behavior of the

* The work was carried out during the tenure of an Australian National University postgraduate scholarship.

1 J. K. Percus and G. J. Yevick, Phys. Rev. 110, 1 (1958).

2 J. K. Percus, Phys. Rev. Letters 8, 462 (1962).

.8 J. M. J. Van Leeuwan, J. Groeneveld, and J. de Boer, Physica 25, 792 (1959).

4 T. Morita and K. Hiroike, Progr. Theoret. Phys. (Kyoto) 23,

1003 (1960).

CHNC equation and compare the solutions and thermodynamic functions from the two equations.

The equation will be solved under the assumption that the particles in the fluid are interacting through a truncated Lennard-Jones 12-6 potential. The Lennard-Jones potential has been used by several workers, including Khan and Broyles,5 Throop and Bearman,6 and Levesque.7 These workers studied the PY equation above the reduced critical temperature T*c in considerable detail. Their results in that region provided a good check on the accuracy of the method described here.

Tf it is assumed that the fluid is uniform, the PY

6 A. A. Khan, Phys. Rev. 134, A367 (1964); 136, A1260 (1964); A. A. Khan and A. A. Broyles, J. Chem. Hiys. 43, 43 (1965); A. A. Broyles, J. Chem. Phys. 35, 493 (1961); A. A. Broyles, S. U. Chung, and H. L. Sahlin, J. Chem. Phys. 37, 2462 (1962).

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