Why are effective potentials 'soft'?

This paper is concerned with effective potentials W-1(R) between interacting supramolecular particles separated by a distance R. We focus on the question of why these potentials are typically 'soft', i.e., remain finite for R --> 0 and vary more weakly with R than the underlying interatomic interaction potentials. On the basis of a general expression linking W-1(R) to the free energy F of the supramolecular system we investigate the origin of the apparent 'softness' of W-1(R) by considering a number of special model systems, starting with an atom and a diatomic molecule. This simple model already yields a W-1(R) that is finite at R = 0, but W-1(R) does not exhibit the slowly varying character typical of effective potentials for realistic systems. We then show that the larger length scale is recovered when one introduces both many-body interactions and thermal fluctuations within the framework of a 'toy model', that is disc-shaped supramolecular units composed of thermalized configurations of Lennard-Jones atoms. In this case, W-1(R) varies so slowly that it can be parametrized by estimating the free energy change associated with the overlap of the discs. The resulting overlap approximation to W-1(R) behaves qualitatively like ad hoc effective potentials used in mesoscale simulations, such as dissipative particle dynamics. Indeed, on the basis of Monte Carlo simulations and a solution of a hypernetted chain integral equations, we find that fluids interacting via DPD and overlap potentials have very similar structural and thermophysical properties. Moreover, the 'overlap' fluid (like other 'effective' fluids) turns out to be so 'soft' that its properties, particularly at high densities, can be very well estimated by a mean-field treatment.