Third virial coefficients and critical properties of quadrupolar two center Lennard-Jones modelsy (original) (raw)
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Third virial coefficients and critical properties of quadrupolar two center Lennard-Jones models
Physical Chemistry …, 2003
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.
Physical Chemistry Chemical Physics, 2003
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.
The second virial coefficient of quadrupolar two center Lennard-Jones models
Physical Chemistry Chemical Physics, 2001
The second virial coefficient of 2-center Lennard-Jones molecules which have an embedded point quadrupole has been determined via numerical integration. A number of models with di †erent reduced bond lengths and quadrupole moments have been considered. For each model the second virial coefficient has been determined for a range of temperatures. It is shown that the presence of the quadrupole moment signiÐcantly raises the Boyle temperature and, for a certain temperature, reduces the value of the second virial coefficient with respect to the non-polar model. Empirical Ðts for are given which reproduce the generated data. It is also shown B 2 that the inclusion of the quadrupole considerably improves the description of for real substances which B 2 have a signiÐcant quadrupole moment, as is the case for
Critical properties of molecular fluids from the virial series
The Journal of Chemical Physics, 2003
We present results for the fourth virial coefficient of quadrupolar Lennard-Jones diatomics for several quadrupole moments and elongations. The coefficients are employed to predict the critical properties from two different truncated virial series. The first one employs the exact second and third virial coefficients, calculated in our previous work. The second includes also the exact fourth virial coefficient as obtained in this work. It is found that the first method yields already fairly good predictions. The second method significantly improves on the first one, however, yielding good results for both the critical temperature and pressure. Particularly, when compared with predictions from perturbation theories available in the literature, the virial series to fourth order compares favorably for the critical temperature. The results suggest that the failure of perturbation theories to predict the critical temperature and pressure is not only related to the neglect of density fluctuations, but also to poor prediction of the virial coefficients.
Second virial coefficients for chain molecules
Industrial & Engineering Chemistry Research, 1994
The importance of having accurate second virial coefficients in phase equilibrium calculations, especially for the calculation of dew points, is discussed. The square-well potential results in a simple but inaccurate equation for the second virial coefficient for small, spherical molecules such as argon. Here, we present a new equation for the second virial coefficient of both spherical molecules and chain molecules which is written in a form similar t o that for the square-well potential. This new equation is accurate in comparison to Monte Carlo simulation data on second virial coefficients for square-well chain molecules and with second virial coefficients obtained from experiments on n-alkanes.
Journal of Molecular Liquids, 2016
The second virial coefficient and Boyle's temperature of three different anisotropic prolate models with orientational dependent potentials has been determined via numerical integration. Namely, the Gay-Berne, the Gay-Berne-Kihara and the Kihara potentials are treated, the latter used as consistence test. A prototype model with a given geometry with different multipolar anisotropies has been considered. In addition, Boyle temperatures are also evaluated with any desire accuracy. These calculations enlarge the compilation data set of molecular models owning values of the second virial coefficient.
Second virial coefficient for real gases at high temperature
We study the second virial coefficient, B(T ), for simple real gases at high temperature. Theoretical arguments imply that there exists a certain temperature, T i , for each gas, for which this coefficient is a maximum. However, the experimental data clearly exhibits this maximum only for the Helium gas. We argue that this is so because few experimental data are known in the region where these maxima should appear for other gases. We make different assumptions to estimate T i . First, we adopt an empirical formulae for B(T ). Secondly, we assume that the intermolecular potential is the Lennard-Jones one and later we interpolate the known experimental data of B(T ) for Ar, He, Kr, H 2 , N 2 , O 2 , Ne and Xe with simple polynomials of arbitrary powers, combined or not with exponentials. With this assumptions we estimate the values of T i for these gases and compare them.
Second virial coefficients of Exp-6 chains: A Monte Carlo simulation
Chemical Physics, 2012
The second virial coefficients of Exp-6 chains are calculated using the Monte Carlo method. The results are presented as the scaled second virial coefficient B 2 /(m 2 r 3 ) for various chain lengths m and repulsive-wall steepness parameters a at different scaled temperatures T ⁄ . The scaled coefficient reduces and converges to a constant value as m ? 1. Interestingly, the scaled coefficient scales as B 2 / (m 2 r 3 ) / Àa À1 , where the dependence reduces for larger m. The gyration radius increases with a, and in good solvent regime, scales like a self-avoiding chain when m ? 1. The interaction energy between two chains depends on m, T ⁄ , and a. With increasing m, the interaction becomes less repulsive. With increasing a or T ⁄ , the repulsion between chains increases, and chains behave as they are in good solvent conditions. Moreover, the h point decreases with increasing a and reducing m. Finally, the results are compared with the theoretical predictions using the PHSC model.
Understanding the phase diagrams of quadrupolar molecules
Recent research on the effect of a quadrupole moment on the phase diagram of linear molecules is reviewed. In particular the effect of the quadrupole on the vapour-liquid and solid-liquid equilibria will be discussed. It is found that the quadrupole moment increases the critical temperature, pressure and density of the fluid over the model without a quadrupole and leads to deviations from the principle of corresponding states. The effect of the quadrupole on a molecular model with a spherical repulsive core is larger than on one with a nonspherical core. The presence of the quadrupole stabilizes solid structures which are not close packed. This leads to a shrinkage of the liquid range as measured by the ratio of the triple to critical point temperature and exhibited by systems like carbon dioxide and acetylene.