The behavior of a two-dimensional system of particles interacting through a potential consisting of a hard core surrounded by a soft repulsive corona is investigated at several densities and temperatures. We find that the competition between hard and soft repulsions gives origin to the spontaneous formation of spatial patterns resembling stripe textures. The effect of varying the hard and soft core radii ratio as well as that of adding an attractive component to the interparticle interaction is studied. The model investigated is relevant for macromolecular topologies possessing two intrinsic length scales.

The self-consistent Ornstein-Zernike approximation (SCOZA), the generalized mean spherical approximation (GMSA), the modified hypernetted chain (MHNC) approximation, and the hierarchical reference theory (HRT) are applied to the determination of thermodynamic and structural properties, and the phase diagram of the hard-core Yukawa fluid (HCYF). We investigate different Yukawa-tail screening lengths $\lambda ,$ ranging from $\lambda =1.8\mathrm{}$ (a value appropriate to approximate the shape of the Lennard-Jones potential) to $\lambda =9\mathrm{}$ (suitable for a simple one-body modelization of complex fluids like colloidal suspensions and globular protein solutions). The comparison of the results obtained with computer simulation data shows that at relatively low $\lambda$’s all the theories are fairly accurate in the prediction of thermodynamic and structural properties; as far as the phase diagram is concerned, the SCOZA and HRT are able to predict the binodal line and the critical parameters in a quantitative manner. At $\lambda =4\mathrm{}$ some discrepancies begin to emerge in the performances of the different theoretical approaches: the MHNC remains, on the whole, reasonably accurate in predicting the energy and the contact value of the radial distribution function; the SCOZA predicts well the equation of state up to the highest $\lambda$ values investigated. The GMSA and the MHNC underestimate and overestimate, respectively, the liquid coexisting density, while the SCOZA and HRT yield liquid branches that fall between the two former theoretical predictions, although both appear to overestimate the critical temperature somewhat. At higher $\lambda$’s the GMSA and MHNC binodals further worsen, while the SCOZA appears to remain usefully predictive. In general, the predictions of all the theories tend to slightly worsen at low temperatures and high density. The determination of the freezing line, performed by means of a one-phase “freezing criterion” (due to other authors) is not particularly satisfactory within either the SCOZA or the MHNC; the GMSA prediction for the freezing line at $\lambda =7\mathrm{}$ and 9 is instead able to follow in a qualitative manner the pattern of the solid-vapor coexistence line as determined through computer simulation studies. The necessity of further assessments of the freezing predictions is also discussed. Finally, versions of the GMSA, SCOZA, and HRT that can be expected to be more accurate for interactions with extremely short-ranged attractions are identified.