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

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.