Pseudopotential Theories of Detonation

Fickett in Detonation Properties of Condensed Explosives Calculated with an Equation of State Based on Intermole-cular Potentials , LosAlamosScientific-LabRept LA-2712(1962), pp 38-42, reports that pseudopotential theories are obtd by an approach completely different from perturbation theories. The problem of defining a system of detonation products consisting of both solid carbon in some form and a fluid mixt of the remaining product species has been formally rearranged to a single fictitious substance with an extremely complicated compn- temp-dependent potential function I , called the pseudopotential. The fictitious substance corresponding to this potential is clearly non-conformal with the components of the mixt 

The order-disorder problem reqd for calculation of the pseudopotential has been solved approx by three different methods  

1) In the moment method, the pseudopotential is expanded in a power series, the first term of which is equivalent to the one-fluid theory 

2) the pair-correlation method gives a more interesting first-order result - a complicated expression for the effective potential function, which contains both the compn temp and gives the one-fluid result only in the high temp limit 3) in the pseudo-pair-potential method, the moment method series is rearranged into a sum of pair interaction terms plus a sum of triplet interaction terms 

Fickett reports that the first order result of the moment method (one-fluid theory) is a rigorous upper bound to the Gibbs free energy, and that the pseudo-pair-potential result is a rigorous lower bound to the same quantity. Both bounds are so widely separated that they are mostly of theoretical interest. Fickett concludes that none of the pseudopotential results is simple enough to use in the complete detonation calculation 

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