Theoretical Equation of State of Dense Nonconformal Fluids from Effective Potentials. 1. Applications to Model Systems

A new model approach for the near-critical point region: 1. Construction of the generalized van der Waals equation of state

To date, it has been considered that all classical equations of state (EOS) have failed to describe the properties of fluids near the critical region, where the density fluctuations have a significant influence on fluid properties. In this paper, we suggest a newly constructed equation for fluid states, the generalized van der Waals (GvdW) EOS with the highly simplified Dieterici's form P = [RT/(V - b)] - a(b/V)c by a new model potential construction describing intermolecular interactions. On the basis of the model potential construction, it is shown that the a, b, and c parameters have physical interpretations as an internal pressure, a void volume, and a dimensionless value that represents an inharmonic intermolecular cell potential, respectively. As an illustration of our model approach, we initially apply it to near the critical point (cp) region, where all classical EOS descriptions have been incorporated with experimental thermodynamic data, and we obtain a table of three parameters for 12 pure normal fluids, which precisely describes thermodynamic critical values. On the basis of the basic relations between pressure and volume at the critical point, we express the corresponding EOS in terms of the c parameter, and by this means, we also obtain a theoretical vapor-liquid equilibrium (VLE) line, which closely coincides with the experimental data for several pure normal fluids near the critical region. As a result, we show that thermodynamic properties near the critical region can be described analytically by only three parameters. In addition, to validate our EOS for the temperature-differential derivatives, we show that the calculated isochoric heat capacity (Cv) of saturated argon closely coincides with the experimental data. Moreover, the possibility of a precise description with respect to the entire fluid region is also argued, in terms of the physical cases from the triple point to the ideal gas region.

Exchange frequency in replica exchange molecular dynamics

The effect of the exchange-attempt frequency on sampling efficiency is studied in replica exchange molecular dynamics (REMD). We show that sampling efficiency increases with increasing exchange-attempt frequency. This conclusion is contrary to a commonly expressed view in REMD. Five peptides (1-21 residues long) are studied with a spectrum of exchange-attempt rates. Convergence rates are gauged by comparing ensemble properties between fixed length test REMD simulations and longer reference simulations. To show the fundamental correlation between exchange frequency and convergence time, a simple model is designed and studied, displaying the same basic behavior of much more complex systems.

Liquid-vapor equilibrium and surface tension of nonconformal molecular fluids

Molecular dynamics simulations at constant temperature have been performed on the liquid-vapor interface for fluids characterized by a recently introduced three-parameter potential. This potential is a modification of the well-known spherical Kihara interaction and is termed approximate nonconformal (ANC). It has been used successfully to describe many real molecules in the gaseous phase. Besides the usual molecular energy and size, the ANC potential introduces a third parameter s, called softness, to measure the form of the potential profile. Study of these systems shows that their critical and interfacial properties follow very closely those of four selected substances: argon, methane, propane, and hexane. Deviations of the properties predicted from the experimental values are analyzed and their probable causes are determined. The critical properties of ANC fluids and their dependence on s are also obtained via first-order perturbation theory in the form of an augmented van der Waals model. Analysis of the results shows that ANC potential functions can be used as reliable effective interactions for real dense fluids.

Nonconformal Interaction Models and Thermodynamics of Polar Fluids

In this work, we develop a simple potential model for polar molecules which represents effectively and accurately the thermodynamics of dilute gases. This potential models dipolar interactions whose nonpolar part is either spherical, as in Stockmayer (SM) molecules, or diatomic, as for 2-center Lennard-Jones molecules (2CLJ). Predictions of the second virial coefficient for SM and polar 2CLJ fluids for various dipole moments and elongations agree very well with results of recent numerical calculations by C. Vega and co-workers (Phys. Chem. Chem Phys. 2002, 4, 3000). The model is used to predict the critical temperature of Stockmayer fluids for variable dipole moment and is applied to HCl as an example of a real polar molecule.