A thermodynamic discriminant for the Lennard-Jones potential

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Abstract
It is shown that for an assembly of molecules interacting with the Lennard-Jones n : 6 pair potential the classical fluctuation discriminant Δ of the configurational energy and the virial , defined by can be related exactly to configurational thermodynamic properties and the repulsion exponent n. The condition that the discriminant is essentially positive (Schwarz's inequality) provides an experimental lower bound for n. The experimental behaviour of the discriminant for argon is examined for solid, liquid and gas states. It is found that the assumption of a 12 : 6 potential leads to negative values of Δ over certain temperature and pressure ranges of the fluid. It appears that a value of n between 13 and 14 would be sufficient to satisfy the inequality for the liquid, but that a much higher value is indicated by the less reliable results for the gas at high temperatures. The theoretical behaviour of the discriminant is discussed, and it is shown that Δ should tend to zero rapidly at high temperatures and at high densities. A brief account is given of the appropriate quantal analogue of Δ which unfortunately appears to be experimentally inaccessible.

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