Third virial coefficients and critical properties of quadrupolar two center Lennard-Jones models

Abstract

We report numerical results for the third virial coefficient of two center Lennard-Jones quadrupolar molecules. Calculations are performed for 35 models with different elongations and quadrupoles over a temperature range from half to twice the critical temperature. It is found that increasing the elongation at fixed quadrupole has the effect of increasing B 3 . On the other hand, at fixed elongation B 3 first decreases with increasing quadrupole at low temperatures, then increases with increasing quadrupole at higher temperatures. We estimate the temperature at which the third virial coefficient vanishes. Although both this temperature and the critical temperature increase with the quadrupole moment, their ratio remains almost constant. We predict the critical properties using two different truncated virial series. The first one employs the exact second and third virial coefficients. The second one approximates the fourth order contribution by using estimates obtained for hard diatomics. It is found that both methods yield fairly good predictions, with a somewhat better performance of the approximate fourth order expansion. The two methods are complementary, however, because they consistently bracket the exact value as determined from computer simulations.

Virial coefficients of hard-core attractive Yukawa fluids

“…Numbers in the subscript indicate the 67% confidence limits of the last digit of the reported value. associating fluids [27], and quadrupolar two center LJ fluids [24], and it increases sharply and becomes positive and goes through a maxima. The peak at which B * 3 is maximum occurs at lower temperature as increases.…”

“…On the other hand, numerical integration based method is used by Vega and co-workers [21,22,24,25] to calculate second, third and fourth virial coefficients of the two-center Lennard-Jones molecules embedded with point quadrupole and dipole moments.…”

Critical properties of molecular fluids from the virial series

“…23,22 In a second approximation ͑VSB4͒, we attempt to improve on the previous equation by considering a virial series truncated to fourth order, using the results of this work for B 4 ,…”

“…In practice, the integral must be solved using a Monte Carlo method. The procedure is essentially that described previously for the calculation of B 3 , 22 with the difference that one must further sample the five degrees of freedom specifying the position and orientation of the fourth molecule. Sampling of the fourth molecule is performed in the same way as for the third molecule in calculations of B 3 .…”

“…A detailed account of the methodology may be found elsewhere. 22 By randomly sampling the configurations as specified, the D k coefficients involved in the calculation of B 3 are given by…”