Excluded volume in the generic van der Waals equation of state and the self-diffusion coefficient of the Lennard-Jones fluid

Abstract

In the previous papers applying the generic van der Waals equation of state the mean excluded volume was defined with the contact diameter of particles at which the potential energy is equal to zero-the size parameter in the case of the Lennard-Jones potential. This parameter appears as the upper limit of the integral for the generic van der Waals parameter B (mean excluded volume divided by the density) in the generic van der Waals equation of state. Since the choice is not unique, in this paper we reexamine the manner of defining the upper limit and propose another choice for the upper limit. We also propose an interpretation of the free volume overlap factor alpha appearing in the free volume theory of diffusion and a method of estimating it in terms of the intermolecular potential energy only. It is shown that with the so-estimated free volume overlap factor and the new choice of the upper limit of the integral for B the self-diffusion coefficient in the modified free volume theory of diffusion not only acquires a better accuracy than before, but also becomes calculable in terms of only the intermolecular interaction potential without an adjustable parameter. We also assess some of effective diameters of molecules proposed in the literature for their ability to predict the self-diffusion coefficient within the framework of the modified free volume theory of diffusion.

Thermal conductivity of the Lennard-Jones fluid: An empirical correlation

“…To compute this transport property in Lennard-Jones fluids using molecular dynamics, a large number of techniques are available. They are based on either equilibrium [15], synthetic nonequilibrium [17], or boundary driven non-equilibrium approaches [13,16,18]. Among them we have chosen a boundary nonequilibrium molecular dynamics scheme, the HEX (Heat EXchange) algorithm developed by Hafskjold et al [18], simple to handle and providing reliable results.…”

“…An example of one temperature profile is addressed in figure 2. Using these parameters, the estimated errors (using the subblocks average method [15] with subblock composed of 5.10 5 timesteps to ensure the statistical independence) lie between 1 and 9%, depending on the state, see the appendix.…”

“…The code used is homemade [26] and uses the Verlet velocity algorithm [15] to integrate the equations of motion. The Verlet neighbor list coupled with a cell list method [15] has been used to save CPU time.…”

“…The Verlet neighbor list coupled with a cell list method [15] has been used to save CPU time. The reduced time step, , ranging from 0.07 to 0.3, depending on the thermodynamic state, has been applied.…”

“…In particular, to the best of our knowledge, it only exists one work (theoretically based) [14] which provides a relation to estimate the LJ thermal conductivity. This lack of MD data on thermal conductivity of the LJ fluid is surprising as long as it exists various efficient schemes to compute this transport property: the classical equilibrium molecular dynamics (EMD) method [15] and different non-equilibrium molecular dynamics (NEMD) approaches [13,[16][17][18].…”