Statistical entropy and clustering in absence of attractive terms in the interparticle potential

Recently a new intriguing class of systems has been introduced, the so-called generalized exponential models, which exhibit clustering phenomena even if the attractive term is missing in their interaction potential. This model is characterized by a index n which tunes the repulsive penetrability of the potential. This family of potentials can represent the effective interactions for a large number of soft matter systems. In this paper we study the structural and thermodynamic properties in the fluid regime of the generalized exponential model with a value of index n suggested by Mladek et al. [B. M. Mladek, G. Kahl, and C. N. Likos, Phys. Rev. Lett. (2008)] to fit the effective potential of a typical amphiphilic dendrimers. We use the conventional approach of the liquid state theory based on the hypernetted chain closure of the Ornstein-Zernike equation together with some Monte Carlo numerical simulations. Moreover, we try to detect qualitatively the freezing line exploiting the predictive properties of a one-phase rule based on the expansion of the statistical entropy