Abstract
Systems composed of spherical charged particles in solvents containing counterions and inducing effective short-range attraction are studied in the framework of mesoscopic eld-theor y. We limit ourselves to meaneld approximation (MF) and to weak ordering. We discuss properties of potentials consisting of strong shortrange attraction and weak long-range repulsion (SALR) in the context of formation of nonuniform distribution of particles on a mesoscopic length scale instead of macroscopic phase separation. In earlier work it was found that spherical, cylindrical and slab-like clusters of particles are formed, and for low enough temperatures the clusters form ordered, periodic bcc, hexagonal and lamellar phases. In addition, a gyroid phase was predicted in which two interwoven regular network-like clusters branching in triple junctions are formed. At properly rescaled density and temperature, the coexistence lines between different ordered phases were found to be universal in MF, with the exception of the gyroid phase. Here the phase diagram is determined for two choices of the SALR potential, one corresponding to a large range of the attractive part of the potential, and the other one to a very small range of attraction. We nd that the region of stability of the gyroid phase very weakly depends on the form of the SALR potential within the approximate theory.
Highlights
Relevant macromolecules, nanoparticles or colloids are typically charged, and repel each other
The prediction of stability of the gyroid phase is based on mean-field approximation to a mesoscopic field theory, and the results were obtained under assumption of weak ordering
In this work we address an open issue how the stability region of this gyroid phase on the phase diagram depends on the shape of the short-range attraction long-range repulsion (SALR) potential, and on the size of the equilibrium clusters at strong dilution
Summary
Relevant macromolecules, nanoparticles or colloids are typically charged, and repel each other. When separations between the particles forming the cluster are mainly within the range of attraction and the separation between clusters is larger than the range of repulsion, the energy takes low values This effect may overcompensate the entropy loss associated with cluster formation. Simulation [9, 11] and theoretical studies [17, 18] of particular examples of the SALR potential show that spherical, cylindrical and slab-like clusters are formed for an increasing density. Between the stability regions of the hexagonal phase of cylinders and lamellar phase of slabs, a thermodynamically stable gyroid phase was found [17], but its stability region is not universal, i.e., it may be different for different forms of the effective interactions In this phase particles form two interwoven networks of clusters which branch in triple junctions.
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