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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. [ABSTRACT FROM AUTHOR]

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]

We study the transient behavior of a model fluid composed by soft repulsive spheres subjected to a planar uniform shear. To this aim, we use a dynamical non-equilibrium molecular dynamics method originally developed by Ciccotti and Jacucci [Phys. Rev. Lett. 35, 789 (1975)] and recently applied to the study of the transient regimes in various fluid systems. We show that the dynamical method allows one to study the transient behavior of the viscous time-dependent response over a wide range of applied shear rates, provided that a temperature control is enforced on the system. In this study, we adopt in particular the configurational thermostat of Braga and Travis [J. Chem. Phys. 123, 134101 (2005)]. The initial behavior of the dynamical response to a θ-like perturbation is characterized by a rapid increase, culminating in a pronounced peak, later relaxing to a plateau value. The latter positively reproduces the values of the viscosity observed in standard steady-state non-equilibrium molecular dynamics. [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]

We apply RISM (reference interaction site model) and PRISM (polymer-RISM) theories to calculate the site–site pair structure and the osmotic equation of state of suspensions of circular or hexagonal platelets (lamellar colloids) over a range of ratios of the particle diameter over thickness D s. Despite the neglect of edge effects, the simpler PRISM theory yields results in good agreement with the more elaborate RISM calculations, provided the correct form factor, characterizing the intramolecular structure of the platelets, is used. The RISM equation of state is sensitive to the number n of sites used to model the platelets, but saturates when the hard spheres, associated with the interaction sites, nearly touch; the limiting equation of state agrees reasonably well with available simulation data for all densities up to the isotropic–nematic transition. When properly scaled with the second virial coefficient, the equations of state of platelets with different aspect ratios D s nearly collapse on a single master curve. [ABSTRACT FROM AUTHOR]

We study theoretically a prototype hard-sphere two-Yukawa model with competing interactions, under thermodynamic conditions associated with the formation of clusters. We adopt the analytically solvable random phase approximation and show that this theory predicts reasonably well the structure of the fluid—in comparison with exact Monte Carlo results—within a unique parameterization of the direct correlation function inside the hard core of particles. In particular, the theory follows correctly the development, in the structure factor, of a local peak at low wavevectors, as peculiarly associated with the onset of aggregation. We then model the direct correlation function in the same wavevector regime by a Gaussian function, so as to systematically investigate, in a "reverse" scheme, how varying the properties of the local peak modifies the original underlying competing interaction. We show that large variations in the height of the peak are generally associated with comparatively smaller variations in the height of the microscopic repulsive barrier; moreover, the shrinking and shifting towards lower wavevectors of the peak may be interpreted in terms of the displacement of the barrier, producing a substantial enlargement of the range of both the attractive and repulsive contributions to the interaction potential. Finally, we document the way the repulsive barrier tends to vanish as the two-Yukawa fluid approaches a "simple fluid" behavior, heralding the onset of a liquid-vapor phase separation. [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 study the structure and phase behavior of a model fluid with competing short-range attraction and long-range repulsion, constituted by hard spheres interacting by means of two opposite Kac potentials. We use, to this purpose, a thermodynamically self-consistent integral equation approach developed by one of the authors [J.-M. Bomont and J.-L. Bretonnet, J. Chem. Phys. 119, 2188 (2003)], which proven accurate in predicting the properties of other competing fluids. We choose the potential parameters in such a way that, upon appropriate thermodynamic conditions, the fluid displays microphase separation terminating, at sufficiently low temperatures, with a phase transition into an ordered-pattern fluid. The propensity toward the pattern formation is indicated by long-wavelength, slowly decaying oscillations in the pair correlation function, and by the presence of a sharp peak in the structure factor S(q) at a small but finite wavevector qc. The limits of stability of the micro-separated phase are identified by a drastic, diverging-like, increase of S(qc) as the temperature drops. The behavior of S(q) in the disordered-pattern phase suggests that different morphologies of the ordered patterns should be expected, depending on the ratio between the strengths of competing interactions. The structural predictions are confirmed, at the thermodynamic level, by the change of sign observed in the 'residual multi-particle entropy,' according to the one-phase ordering criterion developed by Giaquinta and Giunta [Physica A 187, 145 (1992)], and by the trend shown by the chemical potential. Our self-consistent approach succeeds in describing the thermodynamic regime where the phase transition occurs, whereas, as reported in the literature, other sophisticated schemes within the same theoretical framework generally fail; reasons of this outcome and putative remedies are discussed. [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]

We show by extensive molecular dynamics simulations that accurate predictions of liquid-vapor coexistence in molten alkali halides can be achieved in terms of a rigid ion potential description in which temperature-dependent ionic diameters are employed. The new ionic sizes result from the fitting of the experimental isothermal compressibilities, a condition whose physical implications and consequences are illustrated. The same diameters also allow us to formulate confident predictions for the compressibilities of salts in cases where the experimental data are lacking. The extension of the present approach to molten alkali-halide mixtures and to other classes of molten salts is discussed. [ABSTRACT FROM AUTHOR]

We investigate thermodynamic properties of anisotropic colloidal dumbbells in the frameworks provided by the Reference Interaction Site Model (RISM) theory and an Optimized Perturbation Theory (OPT), this latter based on a fourth-order high-temperature perturbative expansion of the free energy, recently generalized to molecular fluids. Our model is constituted by two identical tangent hard spheres surrounded by square-well attractions with same widths and progressively different depths. Gas-liquid coexistence curves are obtained by predicting pressures, free energies, and chemical potentials. In comparison with previous simulation results, RISM and OPT agree in reproducing the progressive reduction of the gas-liquid phase separation as the anisotropy of the interaction potential becomes more pronounced; in particular, the RISM theory provides reasonable predictions for all coexistence curves, bar the strong anisotropy regime, whereas OPT performs generally less well. Both theories predict a linear dependence of the critical temperature on the interaction strength, reproducing in this way the mean-field behavior observed in simulations; the critical density--that drastically drops as the anisotropy increases--turns to be less accurate. Our results appear as a robust benchmark for further theoretical studies, in support to the simulation approach, of self-assembly in model colloidal systems. [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]

Within the coexistence region between liquid and vapor the equilibrium pressure of a simulated fluid exhibits characteristic jumps and plateaus when plotted as a function of density at constant temperature. These features exclusively pertain to a finite-size sample in a periodic box, as they are washed out in the bulk limit. Below the critical density, at each pressure jump the shape of the liquid drop undergoes a morphological transition, changing from spherical to cylindrical to slablike as the density is increased. We formulate a simple theory of these shape transitions, which is adapted from a calculation originally developed by Binder and coworkers [L. G. MacDowell, P. Virnau, M. Muller, and K. Binder, J. Chem. Phys. 120. 5293 (2004)]. Our focus is on the pressure equation of state (rather than on the chemical potential, as in the original work) and includes an extension to elongated boxes. Predictions based on this theory well agree with extensive Monte Carlo data for the cut-and-shifted Lennard-Jones fluid. We further discuss the thermodynamic stability of liquid drops with shapes other than the three mentioned above, like those found deep inside the liquid-vapor region in simulations starting from scratch. Our theory classifies these more elaborate shapes as metastable. [ABSTRACT FROM AUTHOR]

Starting from a family of equations of motion for the dynamics of extended systems whose trajectories sample constant pressure and temperature ensemble distributions (Ferrario, M., 1993, in Computer Simulation in Chemical Physics , edited by M. P. Allen and D. J. Tildesley (Dordrecht: Kluwer)), explicit time reversible integration schemes are derived through a straightforward Trotter factorization of the dynamic Liouville propagator, along the lines first described by Tuckerman, M., Martyna, G. J., and Berne, B. J., 1992, J. chem. Phys., 97 , 1990. The original Andersen's constant-pressure dynamics are recovered in the limit of zero coupling with the Nose thermostat. Reversible integration schemes are derived as a generalization of the velocity Verlet algorithm, with direct handling of the velocity dependent forces in such a way that both predictions and relative iterative corrections are not required. For the sake of clarity both the equations of motion and the Trotter factorization are kept to the basic level. The proposed structure can accommodate easily, when needed, complications such as multiple timesteps and more effective thermostats (Nose-Hoover-chain). Finally, an application is made to a model molecular system subjected to holonomic constraints by means of the SHAKE algorithm. In the constant pressure case it is no longer possible to avoid using a prediction for the constraint contribution to the volume acceleration; however, recourse to a minimal iteration scheme still achieves excellent overall behaviour for the proposed integration algorithm, with no perceptible difference from the unconstrained case. [ABSTRACT FROM AUTHOR]

Convergent theoretical evidence, based on self-consistent integral equations for the pair structure and on Monte Carlo simulations, is presented for the existence of small simultaneous jump discontinuities of several thermodynamic and structural properties of systems of colloidal particles with competing short-range attractive and long-range repulsive interactions, under physical conditions close to the onset of particle clustering. The discontinuities thus provide a signature of the transition from a homogeneous fluid phase to a locally inhomogeneous cluster phase. [ABSTRACT FROM AUTHOR]