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

Adsorption on a Spherical Colloidal Particle from a Mixture of Nanoparticles with Competing Interactions

Adsorption of nanoparticles on a spherical colloidal particle is studied by molecular dynamics simulations. We consider a generic model for a mixture of nanoparticles with energetically favored self-assembly into alternating layers of the two components. When both components are attracted to the colloidal particle, the adsorbed nanoparticles self-assemble either into alternating parallel tori and clusters at the two poles of the colloidal particle, or into alternating spirals wrapped around the spherical surface. The long-lived metastable states obtained in simulations follow from the spherical shape of the adsorbing surface and the requirement that the neighboring chains of the nanoparticles are composed of different components. A geometrical construction leading to all such patterns is presented. When the second component particles are repelled from the colloidal particle and the attraction of the first component is strong, the attracted particles form a monolayer at the surface of the colloidal particle that screens the repulsion of the second component. The subsequent adsorbed alternating spherical layers of the two components form together a thick shell. This structure leads to the adsorption that is larger than in the case of the same attraction of the two components to the colloidal particle.

Secondary nucleation in symmetric binary SALR mixtures

Monte Carlo simulation is used to study secondary nucleation, fissioning, or 'reproduction', of giant clusters in a symmetric binary model fluid with competing short-range (SA) and long-range (LR) interactions. Previous work [M. B. Sweatman, Mol. Phys., 116(15-16), 1945-1952] suggests that a pure SALR fluid can exhibit secondary nucleation if the solute concentration is slowly increased. We show this is also true for a binary symmetric SALR mixture where the cross-interactions can be tuned to generate clusters with three different kinds of structure; (i) independent clusters of each component, (ii) contact clusters of different components, and (iii) mixed clusters. In each case, the overall concentration of each component is identical. This binary model is an initial step towards using SALR fluids to model the intra-cellular space of biological cells that contain a wide range of membraneless organelles and the chemical 'soup' at the origin of life.

Spontaneous pattern formation in monolayers of binary mixtures with competing interactions

A model for a monolayer of two types of particles spontaneously forming ordered patterns is studied using a mesoscopic theory and MC simulations. We assume hard-cores of the same size a for both components. For r > a, like particles attract and repel each other at short and large distances, respectively, with the same potential u(r) for both species, and the cross-interaction is -u(r). The model is inspired by oppositely charged particles or macromolecules with preferential solubility in different components of a solvent that is close to a miscibility critical point, in particular by inclusions in biological membranes. We obtain the phase diagram in the chemical potentials and temperature variables as well as in the concentration, density and temperature variables, using the mean-field one-shell approximation. We find that the presence of the second component significantly extends the temperature range of stability of the ordered phases. We obtain three stable phases with periodic concentration: the lamellar L phase with alternating stripes of the two components for similar chemical potentials, and a hexagonal arrangement of the clusters of the minority component in the liquid of the majority component. The latter two phases, however, are stable only at relatively high temperatures. At lower temperatures, the L phase coexists with a disordered one-component fluid or with very dilute gas with mixed components. At still lower temperatures, the one-component phase coexisting with the L phase can be disordered or ordered, depending on the chemical potentials. The theoretical results are confirmed by MC simulations for selected thermodynamic states.

A density functional theory and simulation study of stripe phases in symmetric colloidal mixtures

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.

Microphase versus macrophase separation in the square-well-linear fluid: A theoretical and computational study

Due to the presence of competing interactions, the square-well-linear fluid can exhibit either liquid-vapor equilibrium (macrophase separation) or clustering (microphase separation). Here we address the issue of determining the boundary between these two regimes, i.e., the Lifshitz point, expressed in terms of a relationship between the parameters of the model. To this aim, we carry out Monte Carlo simulations to compute the structure factor of the fluid, whose behavior at low wave vectors accurately captures the tendency of the fluid to form aggregates or, alternatively, to phase separate. Specifically, for a number of different combinations of attraction and repulsion ranges, we make the system go across the Lifshitz point by increasing the strength of the repulsion. We use simulation results to benchmark the performance of two theories of fluids, namely, the hypernetted chain (HNC) equation and the analytically solvable random phase approximation (RPA); in particular, the RPA theory is applied with two different prescriptions as for the direct correlation function inside the core. Overall, the HNC theory proves to be an appropriate tool to characterize the fluid structure and the low-wave-vector behavior of the structure factor is consistent with the threshold between microphase and macrophase separation established through simulation. The structural predictions of the RPA theory turn out to be less accurate, but this theory offers the advantage of providing an analytical expression of the Lifshitz point. Compared to simulation, both RPA schemes predict a Lifshitz point that falls within the macrophase-separation region of parameters: in the best case, barriers roughly twice higher than predicted are required to attain clustering conditions.

Pattern Formation in Two-Component Monolayers of Particles with Competing Interactions

Competing interactions between charged inclusions in membranes of living organisms or charged nanoparticles in near-critical mixtures can lead to self-assembly into various patterns. Motivated by these systems, we developed a simple triangular lattice model for binary mixtures of oppositely charged particles with additional short-range attraction or repulsion between like or different particles, respectively. We determined the ground state for the system in contact with a reservoir of the particles for the whole chemical potentials plane, and the structure of self-assembled conglomerates for fixed numbers of particles. Stability of the low-temperature ordered patterns was verified by Monte Carlo simulations. In addition, we performed molecular dynamics simulations for a continuous model with interactions having similar features, but a larger range and lower strength than in the lattice model. Interactions with and without symmetry between different components were assumed. We investigated both the conglomerate formed in the center of a thin slit with repulsive walls, and the structure of a monolayer adsorbed at an attractive substrate. Both models give the same patterns for large chemical potentials or densities. For low densities, more patterns occur in the lattice model. Different phases coexist with dilute gas on the lattice and in the continuum, leading to different patterns in self-assembled conglomerates ('rafts').

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

We investigate by Monte Carlo simulations a mixture of particles with competing interactions (hard-sphere two-Yukawa, HSTY) and hard spheres (HS), with same diameters σ and a square-well (SW) cross attraction. In a recent study [G. Munaò et al., J. Phys. Chem. B, 2022, 126, 2027-2039], we have analysed situations-in terms of relative concentration and attraction strength-where HS promote the formation of clusters involving particles of both species under thermodynamic conditions that would not allow for clustering of the pure HSTY fluid. Here, we focus on the role played by the range of cross attraction in determining the equilibrium structure of the mixture, starting from a homogeneous low-density state. When the width of the well exceeds approximately σ, clustering takes place in the system, with aggregates characterised by various sizes and shapes. Only for low HSTY concentrations (less than 10%) a single big cluster appears, anticipating the behaviour observed for a wider well, around 1.2σ. In the latter case, a spherical cluster encompassing almost all particles is the stable structure at equilibrium. We interpret this outcome as a macrophase, liquid-vapour separation where the spherical cluster is just the form taken at low density by the liquid phase inside the vapour phase: indeed, when the density takes larger values, periodic boundary conditions select liquid-vapour interfaces with other non-spherical shapes, similarly as found for a finite sample of simple fluid going through the liquid-vapour coexistence region. For still higher densities we document the existence of a solid phase characterized by the alternation of bilayers filled with particles of one species and bilayers of the other species, giving the solid a peculiar wafer structure.