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In a binary mixture, stripes refer to a one-dimensional periodicity of the composition, namely, a regular alternation of layers filled with particles of mostly one species. We have recently introduced [Munaò et al., Phys. Chem. Chem. Phys. 25, 16227 (2023)] a model that possibly provides the simplest binary mixture endowed with stripe order. The model consists of two species of identical hard spheres with equal concentration, which mutually interact through a square-well potential. In that paper, we have numerically shown that stripes are present in both liquid and solid phases when the attraction range is rather long. Here, we study the phase behavior of the model in terms of a density functional theory capable to account for the existence of stripes in the dense mixture. Our theory is accurate in reproducing the phases of the model, at least insofar as the composition inhomogeneities occur on length scales quite larger than the particle size. Then, using Monte Carlo simulations, we prove the existence of solid stripes even when the square well is much thinner than the particle diameter, making our model more similar to a real colloidal mixture. Finally, when the width of the attractive well is equal to the particle diameter, we observe a different and more complex form of compositional order in the solid, where each species of particle forms a regular porous matrix holding in its holes the other species, witnessing a surprising variety of emergent behaviors for a very basic model of interaction. [ABSTRACT FROM AUTHOR]

The formation of aggregates is commonly observed in soft matter such as globular protein solutions and colloidal suspensions. A lively debated issue concerns the possibility to discriminate between a generic intermediate-range order taking place in the fluid, as contrasted with the more specific presence of a clustered state. Recently, we have predicted by Monte Carlo simulations of a standard colloidal model — spherical particles interacting via a short-range attraction followed by a screened electrostatic repulsion at larger distances — the existence of a tiny structural change occurring in the pair structure. This change consists in a reversal of trend affecting a portion of the local density as the attractive strength increases, that is shown to take place precisely at the clustering threshold. Here, we address the same issue by refined thermodynamically self-consistent integral equation theories of the liquid state. We document how such theoretical schemes positively account for the observed phenomenology, highlighting their accuracy to finely describe the aggregation processes in model fluids with microscopic competing interactions. [ABSTRACT FROM AUTHOR]

Standard Monte Carlo simulations are carried out to assess the accuracy of theoretical predictions for the structural properties of a model fluid interacting through a hard-core two-Yukawa potential composed of a short-range attractive well next to a hard repulsive core, followed by a smooth, long-range repulsive tail. Theoretical calculations are performed in the framework provided by the Ornstein-Zernike equation, solved either analytically with the mean spherical approximation (MSA) or iteratively with the hypernetted-chain (HNC) closure. Our analysis shows that both theories are generally accurate in a thermodynamic region corresponding to a dense vapor phase around the critical point. For a suitable choice of potential parameters, namely, when the attractive well is deep and/or large enough, the static structure factor displays a secondary low-Q peak. In this case HNC predictions closely follow the simulation results, whereas MSA results progressively worsen the more pronounced this low-Q peak is. We discuss the appearance of such a peak, also experimentally observed in colloidal suspensions and protein solutions, in terms of the formation of equilibrium clusters in the homogeneous fluid. [ABSTRACT FROM AUTHOR]

We investigate by Monte Carlo simulation the structure and self-assembly of a mixture formed by asymmetric dimers and larger spherical particles. In our model, dimers and spheres interact through a monomer-specific short-range attraction, in addition to hard-core repulsion. The interaction parameters are chosen so as to mimic features of real colloidal mixtures. We find that the dilute mixture at low temperature is characterized by the onset of aggregates of spheres held together by dimers. In particular, when the sphere concentration is sufficiently high, the system stays homogeneous; at intermediate concentrations, very small clusters of spheres coexist with a few lamellar aggregates; finally, for even lower concentrations a single droplet eventually forms. Upon increasing the density, a sponge-like structure emerges for not too high concentrations. If the attraction between dimers and spheres is switched off, leaving only depletion forces to act, neither phase separation nor demixing are found. [ABSTRACT FROM AUTHOR]

The emergence of supramolecular aggregates from simple microscopic interaction rules is a fascinating feature of complex fluids which, besides its fundamental interest, has potential applications in many areas, from biological self-assembly to smart material design. We here investigate by Monte Carlo simulation the equilibrium structure of a two-dimensional mixture of asymmetric dimers and spheres (disks). Dimers and disks are hard particles, with an additional short-range attraction between a disk and the smaller monomer of a dimer. The model parameters and thermodynamic conditions probed are typical of colloidal fluid mixtures. In spite of the minimalistic character of the interaction, we observe--upon varying the relative concentration and size of the two colloidal species--a rich inventory of mesoscale structures at low temperature, such as clusters, lamellæ (i.e., polymer-like chains), and gel-like networks. For colloidal species of similar size and near equimolar concentrations, a dilute fluid of clusters gives way to floating lamellæ upon cooling; at higher densities, the lamellæ percolate through the simulation box, giving rise to an extended network. A crystal-vapour phase-separation may occur for a mixture of dimers and much larger disks. Finally, when the fluid is brought in contact with a planar wall, further structures are obtained at the interface, from layers to branched patterns, depending on the nature of wall-particle interactions. [ABSTRACT FROM AUTHOR]

We investigate the structure of a dilute mixture of amphiphilic dimers and spherical particles, a model relevant to the problem of encapsulating globular "guest" molecules in a dispersion. Dimers and spheres are taken to be hard particles, with an additional attraction between spheres and the smaller monomers in a dimer. Using the Monte Carlo simulation, we document the low-temperature formation of aggregates of guests (clusters) held together by dimers, whose typical size and shape depend on the guest concentration X. For low X (less than 10%), most guests are isolated and coated with a layer of dimers. As X progressively increases, clusters grow in size becoming more and more elongated and polydisperse; after reaching a shallow maximum for X ≈50%, the size of clusters again reduces upon increasing X further. In one case only ( X = 50%and moderately low temperature) the mixture relaxed to a fluid of lamellae, suggesting that in this case clusters are metastable with respect to crystal-vapor separation. On heating, clusters shrink until eventually the system becomes homogeneous on all scales. On the other hand, as the mixture is made denser and denser at low temperature, clusters get increasingly larger until a percolating network is formed. [ABSTRACT FROM AUTHOR]

Specialized Monte Carlo methods are nowadays routinely employed, in combination with thermodynamic integration (TI), to locate phase boundaries of classical many-particle systems. This is especially useful for the fluid-solid transition, where a critical point does not exist and both phases may notoriously go deeply metastable. Using the Lennard-Jones model for demonstration, we hereby investigate on the alternate possibility of tracing reasonably accurate transition lines directly by integrating the pressure equation of state computed in a canonical-ensemble simulation with local moves. The recourse to this method would become a necessity when the stable crystal structure is not known. We show that, rather counterintuitively, metastability problems can be alleviated by reducing (rather than increasing) the size of the system. In particular, the location of liquid-vapor coexistence can exactly be predicted by just TI. On the contrary, TI badly fails in the solid-liquid region, where a better assessment (to within 10% accuracy) of the coexistence pressure can be made by following the expansion, until melting, of the defective solid which has previously emerged from the decay of the metastable liquid. [ABSTRACT FROM AUTHOR]

An accurate thermodynamically self-consistent integral equation theory of the liquid state is used to investigate model fluids with competing attractive interaction at short distances and long-range repulsion, focusing on thermodynamic states where the formation of clusters is expected to occur. We find a remarkable accuracy of theoretical predictions, through a detailed assessment against results of Monte Carlo simulations. The behavior of theoretical radial distribution functions and structure factors faithfully follows the onset and growth of cluster aggregates in the homogeneous dense-vapor phase. The thermodynamic properties of the system sensitively depend on the ratio between the repulsive barrier and the attraction strength. We elucidate the role of accurate theoretical tools to investigate the properties of fluids with complex phase behaviors. [ABSTRACT FROM AUTHOR]