One of the most striking signatures of self-organization is spontaneous pattern formation. Among the morphologies observed, stripes are intrinsically fascinating and have potential for technological applications including nanolithography and nanoelectricity. Examples of materials featuring stripe patterns include Langmuir monolayers, magnetic films, lipid monolayers, liquid crystals and polymer films. Stripe formation is generally attributed to the competition between short-range attractive forces and long-range repulsion arising from dipole interactions. Here we show that stripe phases may result from a different mechanism based on a purely repulsive isotropic short-range pair potential with two characteristic length scales. We consider a two-dimensional (2D) assembly of particles consisting of a hard core surrounded by a soft corona and find that at densities where the hard-and-soft core radii compete with each other, decreasing the temperature induces a transition from a disordered state to an orientationally ordered phase characterized by stripe patterns.

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 (a value appropriate to approximate the shape of the Lennard-Jones potential) to lambda=9 (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 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 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.

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 free energy of the solid and fluid phases of the Girifalco C60 model are determined through extensive Monte Carlo simulations. In this model the molecules interact through a spherical pair potential, characterized by a narrow and attractive well, adjacent to a harshly repulsive core. We have used the Widom test particle method and a mapping from an Einstein crystal, in order to estimate the absolute free energy in the fluid and solid phases, respectively; we have then determined the free energy along several isotherms, and the whole phase diagram, by means of standard thermodynamic integrations. The dependence of the simulation's results on the size of the sample is also monitored in a number of cases.We highlight how the interplay between the liquid-vapor and the liquid-solid coexistence conditions determines the existence of a narrow liquid pocket in the phase diagram, whose stability is assessed and confirmed in agreement with previous studies. In particular, the critical temperature follows closely an extended corresponding-states rule recently outlined by Noro and Frenkel [J. Chem. Phys. 113, 2941 (2000)].We discuss the emerging "energetic" properties of the system, which drive the phase behavior in systems interacting through short-range forces [A. A. Louis, Phil. Trans. R. Soc. A 359, 939 (2001)], in order to explain the discrepancy between the predictions of several structural indicators and the results of full free energy calculations, to locate the fluid phase boundaries.More generally, we aim to provide extended reference data for calculations of the free energy of the C60 fullerite in the low temperature regime, as for the determination of the phase diagram of higher order Cn>60 fullerenes and other fullerene-related materials, whose description is based on the same model adopted in this work.

Recent studies have confirmed that model C60 has a stable liquid phase confined to a rather narrow temperature range; in this letter we determine the phase diagram of model C70 and show that also this fullerene possesses a liquid phase whose existence range is wider than that of C60. A "corresponding state" behaviour of C60 and C70, emerging from a description in terms of reduced quantities of both the interaction potential and the phase diagrams' parameters, is then extended to higher-order fullerenes. Critical-and triple-point densities and temperatures of C76, C84 and C92 are thereby predicted. The decreasing accuracy of such a representation of Cn>70 phase behaviour with increasing n is discussed in relation to the model potential features.