Microphase separation in two-dimensional systems with competing interactions

Abstract

The formation of clusters in condition of thermodynamic equilibrium can be easily observed both in two and three dimensions. In two dimensions relevant cases include pattern formation in Langmuir monolayers and ferrofluids, while in three dimensions cluster phases have been observed in colloids and in protein solutions. We have analyzed the problem within the scenario of competing interactions: typically, a short-range attractive interaction against a long-range repulsive one. This simplified approach is suggested by the fact that the forces, governing self-organization, act on a length scale which is larger than the molecular size; as a consequence many specific details of the molecules of interest are not necessary for studying the general features of microphases. We have tackled the microphase formation by simulations in bidimensional fluids, exploiting the parallel tempering scheme. In particular, we have analyzed the density range in which the particles arrange in circular domains (droplets), and the temperature range in which the system goes from microphases to the homogeneous fluid phase. As the density increases, the droplet size increases as well, but above a certain density the morphology changes and stripes are formed. Moreover at low density, we observe the formation of a liquidlike phase of disordered droplets; at higher densities, instead, the droplets tend to arrange onto a triangular superlattice. Such a change affects the features of the static structure factor, which gives well defined signatures of the microphase morphology. In each case, the specific heat exhibits a peak close to the transition from microphases to the homogeneous fluid phase, which is due to the breaking up of the clusters. The saturation of the height of the specific heat peak, with the increasing of the system size, suggests the possibility of a Kosterlitz-Thouless transition.

Competition between line tension and curvature stabilizes modulated phase patterns on the surface of giant unilamellar vesicles: A simulation study

“…Simulation studies of Fan et al showed that more complicated models, such as lipid recycling, can stabilize nonequilibrium patterns on a flat membrane [19]. Other models for the stabilization of multiple/patterned domains have also been studied including a general competing interaction model [20] and the effects of dipolar repulsion between lipids [21][22][23]. It has been shown that electrostatics are too short-range to account for the many micron length scale we observe in modulated phases [8] To begin modeling the modulated phases we first formulate an energy functional.…”

Model colloidal fluid with competing interactions: Bulk and interfacial properties

“…Similarly, in the striped phase in two dimensions the particles are arranged in parallel stripes with low-density regions in between the stripes. 2, 14,18 In three dimensions the stripes form a gel-like network of elongated clusters. 5,15,17 This behavior is most striking given that the pair interactions between the particles are spherically symmetrical and suggests that such systems could be important candidates for developing self-assembling pattern forming materials.…”

“…Theory and simulation in both two and three dimensions for model systems with competing interactions predict that such interactions can give rise to a state with undamped periodic density fluctuations, which indicates a transition to cluster or striped phases ͑microphase separation͒. [9][10][11][12][13][14][15][16][17][18] In the cluster phase the colloids are ordered in such a way that there are assemblies containing tens or hundreds of particles and large voids between the clusters containing hardly any particles. Similarly, in the striped phase in two dimensions the particles are arranged in parallel stripes with low-density regions in between the stripes.…”

Explicit spatial description of fluid inclusions in porous matrices in terms of an inhomogeneous integral equation

“…To that aim we have analyzed the behavior of a two dimensional fluid with competing interaction ranges whose particles tend to cluster at low temperatures. Our model is a soft core version of the "short-range attractive and long-range repulsive" (SALR) potential first proposed by Sear and coworkers 26 , and analyzed in detail by Imperio and Reatto 27,28 . The clustering properties under disordered confinement of this hard core model have also recently been studied by Schwanzer and Kahl 29 .…”