Analytic Solution to Integral Equations of Liquid State Theories for Potentials with a Hard Core at Low Densities

We present in this paper a general analytical solution to the integral equations of liquid state theories (Born-Green-Yvon, hyper-netted-chain, and Percus-Yevick Equations) at low-density limit for potentials with a hard core. For the specific case of the Lennard-Jones potential with a hard core, we have derived an analytical function for the radial distribution function at high temperature and low density. We have noted that this function has two humps which is the characteristic feature of the radial distribution function at low densities. In addition, this function has been used to calculate the third virial coefficient for such a fluid exactly. We see that for the especial case of Lennard-Jones fluid with a hard core, which its radial distribution function has explicitly been calculated at high temperatures, the correct behavior of the third virial coefficient with temperature is obtained. The magnitude of hard-core diameter has significant effect on the thermodynamic properties of fluid: for instance, when the diameter changes only by a few percent the third virial coefficient may change more than 100%. The hard-core diameter decreases when temperature increases. The reduction is less than 20%. For the supercritical fluid, the calculated compression factor and internal energy are in good agreement with those obtained from the simulation for the Lennard-Jones fluid

Deriving Analytical Expressions for the Ideal Curves and Using the Curves to Obtain the Temperature Dependence of Equation-of-State Parameters Analytical Expressions for Ideal Curves 1565

Different equations of state (EOSs) have been used to obtain analytical expressions for the ideal curves, namely, the Joule-Thomson inversion curve (JTIC), Boyle curve (BC), and Joule inversion curve (JIC). The selected EOSs are the Redlich-Kwong (RK), Soave-Redlich-Kwong (SRK), Deiters, linear isotherm regularity (LIR), modified LIR (MLIR), dense system equation of state (DSEOS), and van der Waals (vdW). Analytical expressions have been obtained for the JTIC and BC only by using the LIR, MLIR, and vdW equations of state. The expression obtained using the LIR is the simplest. The experimental data for the JTIC and the calculated points from the empirical EOSs for the BC are well fitted into the derived expression from the LIR, in such a way that the fitting on this expression is better than those on the empirical expressions given by Gunn et al. and Miller. No experimental data have been reported for the BC and JIC; therefore, the calculated curves from different EOSs have been compared with those calculated from the empirical equations. On the basis of the JTIC, an approach is given for obtaining the temperature dependence of an EOS parameter(s). Such an approach has been used to determine the temperature dependences of A 2 of the LIR, a and b parameters of the vdW, and the cohesion function of the RK. Such temperature dependences, obtained on the basis of the JTIC, have been found to be appropriate for other ideal curves as well

Monte Carlo Simulation of the (100) Surface of the fcc Lattice of Platinum and Gold

In this work, the (100) surface of Au and Pts face centered cubic lattice, has been simulated in Monte-Carlo method, using a 486-DX2 computer. The potential equation that was used for the interaction among atoms in the metal surfaces is called Sutton and Chen potential. This potential is introduced for the interaction of floating nuclei in the electron sea, and attractive term is a many body potential.   Surface atoms are allowed to move to their adjacent unoccupied sites. These movements occur when temperature increases by which surface configuration, coordination number and the solid surface will be changed. In primary movements, we have large flactuations for the energy, but when the number of movements become large enough (order of hunders of thouands), we may ignore the small energy flactuation and therefore stable configuration can obtained.   In this calculation, we have taken into account the interaction between any particle with its first and second neighbouring atoms. Probability of acceptance of any movement is equal to the Boltzman factor. Finally, an equation, that is temperature dependency of surface magnitude, was abtained

Selected thermophysical properties of dense fluids using a general regularity

A simple equation of state is used to calculate the bulk modulus, Joule-Thomson inversion temperature, and isobaric expansivity of dense fluids (with density greater than the Boyle density). The EOS predicts the following regularities: (i) the linearity of the bulk modulus versus pressure for each isotherm of a dense fluid for a range of about 100 MPa for subcritical fluids and about 1000 MPa for supercritical fluids, (ii) the linearity of bulk modulus with respect to temperature for each isochore, and (iii) the linearity of inverse isobaric expansivity with pressure for each isochore. The regularities have been found to be consistent with experimental observations. The calculated Joule-Thomson inversion temperature shows good agreement with experimental data in the range of validity of the EOS.NRC publication: N