Calculation of high-order virial coefficients for the square-well potential

Abstract

A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription.For more information, please contact eprints@nottingham.ac.uk AbstractAccurate virial coefficients B N (λ,ε ) (where ε is the well depth) for the threedimensional square-well and square-step potentials are calculated for orders N = 5 -9 and well widths λ = 1.1− 2.0 using a recursive method that is much faster than any previously used methods. The efficiency of the algorithm is enhanced significantly by exploiting permutation symmetry and by storing integrands for re-use during the calculation. For N = 9 the storage requirements become sufficiently large that a parallel algorithm is developed. The methodology is general and is applicable to other discrete potentials. The computed coefficients are precise even near the critical temperature, and thus open up possibilities for analysis of criticality of the system, which is currently not accessible by any other means.2

Equation of state for all regimes of a fluid: From gas to liquid

“…At the moment, there is no realistic statistical model (which includes intermolecular attraction as well as repulsion) with the completely known set of cluster integrals. Some truncated sets of irreducible integrals (virial coefficients) have been calculated for widely used interaction models (such as the Lennard-Jones model [20,24], its modifications [21,22], Morse [23] and square-well [27] potentials, etc.). There are also a number of approximations for infinite virial sets [14,23,28].…”

Evidence for a first-order phase transition at the divergence region of activity expansions

“…Recent studies of Mayer's cluster expansion [9] for the partition function of realistic interaction models (i.e., the models that include intermolecular attraction as well as repulsion: the Lennard-Jones model [10,11] and its modifications [12,13], square-well [14], Morse [15], Yukawa [16] potentials, etc.) have renewed interest to the problem.…”

Properties of supercritical N2, O2, CO2, and NH3 mixtures from the virial equation of state

“…Rather than direct evaluation of the sum as suggested in Equation ), a more efficient recursive algorithm due to Wheatley 15 is available to compute the integrand, f B . This algorithm can be modified to evaluate temperature derivatives of virial coefficients in the same Mayer‐sampling calculation 5 .…”