Thermodynamics, static properties and transport behaviour of fluids with competing interactions

Discontinuous Structural Transitions in Fluids with Competing Interactions

This paper explores how competing interactions in the intermolecular potential of fluids affect their structural transitions. This study employs a versatile potential model with a hard core followed by two constant steps, representing wells or shoulders, analyzed in both one-dimensional (1D) and three-dimensional (3D) systems. Comparing these dimensionalities highlights the effect of confinement on structural transitions. Exact results are derived for 1D systems, while the rational function approximation is used for unconfined 3D fluids. Both scenarios confirm that when the steps are repulsive, the wavelength of the oscillatory decay of the total correlation function evolves with temperature either continuously or discontinuously. In the latter case, a discontinuous oscillation crossover line emerges in the temperature-density plane. For an attractive first step and a repulsive second step, a Fisher-Widom line appears. Although the 1D and 3D results share common features, dimensionality introduces differences: these behaviors occur in distinct temperature ranges, require deeper wells, or become attenuated in 3D. Certain features observed in 1D may vanish in 3D. We conclude that fluids with competing interactions exhibit a rich and intricate pattern of structural transitions, demonstrating the significant influence of dimensionality and interaction features.

Exact equilibrium properties of square-well and square-shoulder disks in single-file confinement

This study investigates the (longitudinal) thermodynamic and structural characteristics of single-file confined square-well and square-shoulder disks by employing a mapping technique that transforms the original system into a one-dimensional polydisperse mixture of nonadditive rods. Leveraging standard statistical-mechanical techniques, exact results are derived for key properties, including the equation of state, internal energy, radial distribution function, and structure factor. The asymptotic behavior of the radial distribution function is explored, revealing structural changes in the spatial correlations. Additionally, exact analytical expressions for the second virial coefficient are presented. The theoretical results for the thermodynamic and structural properties are validated by our Monte Carlo simulations.

Arrested states in colloidal fluids with competing interactions: A static replica study

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.

Modeling the structure and thermodynamics of multicomponent and polydisperse hard-sphere dispersions with continuous potentials

A model system of identical particles interacting via a hard-sphere potential is essential in condensed matter physics; it helps to understand in and out of equilibrium phenomena in complex fluids, such as colloidal dispersions. Yet, most of the fixed time-step algorithms to study the transport properties of those systems have drawbacks due to the mathematical nature of the interparticle potential. Because of this, mapping a hard-sphere potential onto a soft potential has been recently proposed [Báez et al., J. Chem. Phys. 149, 164907 (2018)]. More specifically, using the second virial coefficient criterion, one can set a route to estimate the parameters of the soft potential that accurately reproduces the thermodynamic properties of a monocomponent hard-sphere system. However, real colloidal dispersions are multicomponent or polydisperse, making it important to find an efficient way to extend the potential model for dealing with such kind of many-body systems. In this paper, we report on the extension and applicability of the second virial coefficient criterion to build a description that correctly captures the phenomenology of both multicomponent and polydisperse hard-sphere dispersions. To assess the accuracy of the continuous potentials, we compare the structure of soft polydisperse systems with their hard-core counterpart. We also contrast the structural and thermodynamic properties of soft binary mixtures with those obtained through mean-field approximations and the Ornstein-Zernike equation for the two-component hard-sphere dispersion.

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.

Aggregation behavior of nanoparticles: Revisiting the phase diagram of colloids

Surface functionalization of metal nanoparticles (NPs), e.g., using peptides and proteins, has recently attracted a considerable attention in the field of design of therapeutics and diagnostics. The possibility of diverse functionalization allows them to selectively interact with proteins, while the metal core ensures solubility, making them tunable therapeutic agents against diseases due to mis-folding or aggregation. On the other hand, their action is limited by possible self-aggregation, which could be, however, prevented based on the full understanding of their phase diagram as a function of the environmental variables (temperature, ionic strength of the solution, concentration) and intrinsic characteristics (size, charge, amount, and type of functional groups). A common modeling strategy to study the phase behavior is to represent the NPs as spheres interacting via effective potentials implicitly accounting for the solvation effects. Their size put the NPs into the class of colloids, albeit with particularly complex interactions including both attractive and repulsive features, and a consequently complex phase diagram. In this work, we review the studies exploring the phases of these systems starting from those with only attractive or repulsive interactions, displaying a simpler disperse-clustered-aggregated transitions. The phase diagram is here interpreted focusing on the universal aspects, i.e., those dependent on the general feature of the potentials, and available data are organized in a parametric phase diagram. We then consider the potentials with competing attractive short range well and average-long-range repulsive tail, better representing the NPs. Through the proper combination of the attractive only and repulsive only potentials, we are able to interpret the appearance of novel phases, characterized by aggregates with different structural characteristics. We identify the essential parameters that stabilize the disperse phase potentially useful to optimize NP therapeutic activity and indicate how to tune the phase behavior by changing environmental conditions or the NP chemical–physical properties.