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

Abstract

Self-assembling complex fluids are often modeled as particles with effective competing isotropic interactions, combining a short-range attraction (SA) followed by a longer-range repulsion (LR). For moderately low temperatures and densities, SALR particles form clusters in equilibrium, at least provided that the potential parameters are appropriate. Here we inquire into the possibility that cluster formation in SALR fluids might be pushed by a foreign species even under thermodynamic conditions that would not allow for clusterization of the pure system. To this aim, we study by Monte Carlo simulations a mixture of hard-sphere two-Yukawa particles and hard spheres, with a cross interaction modeled by a square-well attraction, and we investigate the conditions of clustering in terms of strength of attraction and relative concentration of the two species. We find that clusters can occur in the mixture for the same temperature and density where the pure SALR fluid is almost structureless. In particular, we single out a cross attraction such that clusters are formed with a SALR concentration as low as 5%. We also find a situation where nearly pure droplets of hard spheres are held together by a shell of SALR particles. Conversely, we show that clustering can be undermined in the mixture under conditions for which this process takes place in the parent SALR fluid. Using a simple criterion, based on the second virial coefficients of the attractive part of interaction potentials (the so-called “reference attractive fluids”), we are able to predict accurately whether clustering is favored (or hindered) in the mixture, as compared to the pure SALR fluid.

Competition between clustering and phase separation in binary mixtures containing SALR particles

“…This outcome indicates that it is a sufficiently extended range of 1-2 attraction, rather than its depth, that favours macrophase separation over clustering. Indeed, in our previous study, 52 where the range of attraction is kept fixed at n = 1, we have never found evidence of a macrophase separation. In that study we argued that increasing the well depth is a way to enhance the stability of clusters (thus causing them to appear at higher temperatures), without interfering much with the repulsive barrier at larger distances.…”

“…55) encompassing all particles. The need for a double check emerges from previous studies of SALR particles 37 and their mixtures, 49,50,52 where giant clusters have occasionally been observed at equilibrium. For n r 3 equilibrium is typically attained after 5 Â 10 5 MC cycles; for n = 4, as many as 2 Â 10 7 MC cycles are required to equilibrate the system.…”

“…For the same values of T and r, also the HSTY-HS mixture is homogeneous when e 12 = 0.25e 11 and n = 1 in eqn (4). 52 Upon increasing the range of the SW attraction, we may reasonably expect that the mixture will finally undergo a liquid-vapour separation; indeed, when the balance between repulsion and attraction is progressively shifted toward the latter, the formation of macroscopic droplets will eventually become preferred with respect to clustering. We start by considering the equimolar case, w = 0.5.…”

“…For instance, this model can reproduce the behaviour of soft-matter systems with a non negligible solute–solvent interaction, typically due to screened–Coulomb interactions, as occurring in solutions of biomolecules. In a previous work 52 we have shown that, upon setting a proper attraction strength between HSTY and HS particles, it is possible to induce clustering under thermodynamic conditions for which the pure HSTY fluid would be homogeneous. A similar conclusion was reached in ref.…”

“…In particular, upon tuning the size of monomers making up the dimer and using monomer-specific interactions with the second species, it is possible to obtain a large variety of selfassembling structures, including vesicles 46 and coating shells (capsules). 47,48 A second possibility would be to consider a mixture of monatomic species with various types of SALR potentials: [49][50][51][52] leveraging on the interactions, one can produce microphases exhibiting many different kinds of stable aggregates.…”