Dino Costa

Framing the glass formation within standard statistical mechanics is an outstanding problem of condensed matter theory. To add insight, we investigate the structural properties of the Lennard-Jones fluid in the very-low temperature regime by using a replicated version of the refined HMSA theory of the liquid state combined with an appropriate split of the pair potential [Bomont and Bretonnet, J. Chem. Phys. 114, 4141 (2001)0021-960610.1063/1.1344610]. Our scheme allows one to reach an unprecedented low-temperature domain within both the supercooled liquid and the ideal-glass phase. Therein, a density-dependent temperature is identified, whereupon the radial distribution function experiences clear-cut structural changes, insofar as an additional peak develops in between the main and the second peaks. Such a structural feature points to a local structure of the Lennard-Jones ideal glass with an fcc-like short-range order, in the absence of any long-range order.

We investigate the phase diagram of a model hard-sphere mixture consisting of two species of equal diameter, featuring a square-well cross attraction. The study is carried out using density-functional theory (DFT) in the mean-field approximation and extends to arbitrary species concentrations a former DFT study at equimolar composition [Prestipino et al., J. Chem. Phys. 159, 204902 (2023)]. In addition to the stripe phases found in the equimolar case, cylinder and cluster phases are also observed. While at high temperatures, the inhomogeneous domains can be accessed only from the high-density liquid; at low temperatures, these phases coexist with the low-density vapor, resulting in a notably rich phase diagram. The predictions of an analytic implementation of the theory—based on the Landau expansion of the free energy in powers of the density modulation amplitude—are compared with numerical DFT minimization. The Landau approach shows qualitative agreement, although it overestimates the extent of the stripe region at high density, where local concentration values may exceed their physical bounds. Differences and similarities between DFT and simulation results for narrow attractive wells are briefly discussed.

We investigate a binary mixture of identical hard spheres, interacting through a square-well cross attraction. Recently, we have shown that the equimolar mixture exhibits stripe order (i.e., a regular alternation of layers filled with particles of mostly one species) in both solid and liquid phases [Prestipino et al., J. Chem. Phys. 159, 204902 (2023)0021-960610.1063/5.0177209]. Here, we extend our study to nonequimolar conditions. Using Monte Carlo simulations, we find a rich self-assembly behavior with several forms of compositional order, depending on the departure from equimolarity and the range of attraction. While stripes are still seen in the solid phase of the 30%/70% mixture, for a larger concentration asymmetry we rather observe fcc ordering of the minority species, provided that the range of attraction is long enough. Due to the possibility to adjust the concentration in the two phases, compositional order is generally richer at solid-vapor coexistence than in the bulk solid: we observe solid droplets with stripes, displaying either square or triangular in-plane order, as well as droplets with bcc structure and honeycomblike order of the minority species in the matrix of the other species. Finally, at sufficiently low temperature the increased concentration of minority particles in the solid droplet makes the cohesive energy at coexistence systematically larger than in the bulk solid.

We study by molecular dynamics simulations the absorption of polypropylene (PP) chains within a dipalmitoylphosphatidylcholine (DPPC) lipid membrane in aqueous solvent. DPPC represents the most abundant phospholipid in biological membranes, while PP is one of the most common synthetic polymers diffused in the anthropic environment. By following in detail the absorption process, and the corresponding structural modification undergone by the membrane, we show how the initial configuration and the PP molecular weight determine the overall behavior of the system. Specifically, if PP chains initially lie on the DPPC surface, they are fully absorbed; likewise, polymers initially included within the membrane cannot escape from. On the other hand, if polymers are placed sufficiently apart from the membrane, they have time to join together and coalesce into a few nanoparticles. At contact, such nanoparticles may completely dissolve (for low molecular weight) and then be absorbed. For high molecular weight, not all of them dissolve, and therefore the system attains a condition in which some of the chains are absorbed, while others form a residual nanoparticle staying outside (but in contact with) the membrane. Such a state─albeit energetically unfavorable with respect to a condition in which all PP chains are absorbed─remains stable, at the least over a substantial simulation time, extending in our study up to 1.6 μs. The tendency for polymers to spontaneously form aggregates, which then prefer to stay in contact with the membrane, is further corroborated by calculation of the DPPC-nanoparticle potential of mean force.

We present the first systematic application of the integral equation implementation of the replica method to the study of arrested states in fluids with microscopic competing interactions (short-range attractive and long-range repulsive, SALR), as exemplified by the prototype Lennard-Jones–Yukawa model. Using a wide set of potential parameters, we provide as many as 11 different phase diagrams on the density (ρ)–temperature (T) plane, embodying both the cluster-phase boundary, TC(ρ), and the locus below which arrest takes place, TD(ρ). We describe how the interplay between TC and TD—with the former falling on top of the other, or the other way around, depending on thermodynamic conditions and potential parameters—gives rise to a rich variety of non-ergodic states interspersed with ergodic ones, of which both the building blocks are clusters or single particles. In a few cases, we find that the TD locus does not extend all over the density range subtended by the TC envelope; under these conditions, the λ-line is within reach of the cluster fluid, with the ensuing possibility to develop ordered microphases. Whenever a comparison is possible, our predictions favorably agree with previous numerical results. Thereby, we demonstrate the reliability and effectiveness of our scheme to provide a unified theoretical framework for the study of arrested states in SALR fluids, irrespective of their nature.

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.

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.

Introducing a flat and sufficiently long-ranged cross attraction in an equimolar mixture of identical hard spheres induces the spontaneous formation of stripes, the longer the attraction range, the thicker the stripes.

Equilibrium configurations upon increasing the range of the square-well cross attraction in comparison with the size of particles.