Jacobs-Cowperthwaite-Zwisler's equation of state

The Jacobs-Cowperthwaite-Zwisler-3 equation of state results from a pair potential of the form:

${\ displaystyle \ phi (r) = \ epsilon \ cdot \ left [\ left ({\ frac {6} {\ eta -6}} \ right) \ cdot \ exp \ left [\ eta \ cdot \ left (1 -r / r ^ {*} \ right) \ right] - \ left ({\ frac {\ eta} {\ eta -6}} \ right) \ cdot \ left ({\ frac {r ^ {*}} {r}} \ right) ^ {6} \ right]}$

to describe the interaction between molecules , which is known as EXP6 potential . It describes the pair potentials much more realistically than the Lennard-Jones potential , which is much too hard for small molecular distances. All product species are characterized by , the radius of the pair potential minimum, and , the depth of the potential wall normalized with the Boltzmann constant . The equation of state is based on a similar relationship to the Mie-Grüneisen equation of state : ${\ displaystyle r ^ {*}}$ ${\ displaystyle \ epsilon / k}$

${\ displaystyle p = {\ frac {R \ cdot T} {\ nu}} \ cdot G (\ nu, T) + p_ {0} (\ nu)}$

The explicit dependence of the green iron function and the internal pressure on the EXP6 potential function is not trivial (see Cowperthwaite et al.). ${\ displaystyle G (\ nu, T)}$ ${\ displaystyle p_ {0} (\ nu)}$ ${\ displaystyle \ phi (r)}$

The JCZ3 equation of state is an intermolecular equation of state which does not contain any adjustable parameters. It was the first successful model based on a couple potential that was used to describe detonations . The equation of state results from Monte Carlo simulations by adapting an analytical functional form. It is suitable for describing the detonation products at the very high temperatures and pressures that result from a detonation. The JCZ equation of state describes the effect of explosives more precisely than the BKW or the JWL equation of state.

literature

M.Cowperthwaite, WKZwisler: The JCZ Equations of State for Detonation Products and Their Incorporation into the TIGER Codes , Sixth Symposium (International) on detonation ACR-221, Office of Naval Research, Naval Surface Weapons Center, 162 (1976)