Some general features of mesophase formation in hard-core plus tail potentials

Abstract

The formation of mesophases in fluids with hard-core plus tail interactions is investigated and compared with the occurrence of cluster crystals in ultra-soft repulsive potentials by using a simple variational expression for the Helmholtz free energy. The purpose of this study is mostly qualitative, i.e., to explain the origin of the different behavior of these systems, and the reason why, in the hard-core case, interactions which are apparently quite different display a common pattern for the phase diagram, featuring spheres, cylinders, lamellae, inverted cylinders, and inverted spheres as the density is increased. In the limit of zero temperature, our approach also yields some simple predictions for the densities at which the transitions between different mesophases are expected to take place, as well as for the size of their clusters at the transitions. We find that these results compare favorably with those obtained in a former study of a model fluid with competing attractive and repulsive interactions by density-functional theory with numerical minimization.

Like aggregation from unlike attraction: stripes in symmetric mixtures of cross-attracting hard spheres

“…30 and 31, are often responsible in one-component systems for self-assembling behaviours of various types, including stripes. [38][39][40][41] However, ref. 31 suggests that the cross interaction too plays a role in the stabilization of stripes, as the latter are only present when the SW range is long enough.…”

Clustering in Mixtures of SALR Particles and Hard Spheres with Cross Attraction

“… 18 , 19 , 24 , 25 Using density-functional theory, it has been shown that, for sufficiently low temperatures, SALR particles give rise to periodic microphases exhibiting (in increasing order of density) clusters, cylinders, lamellae, inverted cylinders, and inverted clusters, just to name the simplest structures. 26 − 29 The equilibrium phase diagram of a cluster-forming fluid has been also reconstructed by a thermodynamic model and assessed by computer simulation. 30 The broad interest in the physics of SALR fluids is witnessed by four recent reviews on this subject.…”

“…Generally speaking, the knowledge of this dependence can be exploited to steer the process of self-assembling toward the formation of the desired structure. For example, for moderately low values of T , one expects to see clusters in the dilute fluid, giving way to a percolated fluid at higher densities. ,,, Using density-functional theory, it has been shown that, for sufficiently low temperatures, SALR particles give rise to periodic microphases exhibiting (in increasing order of density) clusters, cylinders, lamellae, inverted cylinders, and inverted clusters, just to name the simplest structures. − The equilibrium phase diagram of a cluster-forming fluid has been also reconstructed by a thermodynamic model and assessed by computer simulation . The broad interest in the physics of SALR fluids is witnessed by four recent reviews on this subject. − …”