The Giant SALR Cluster Fluid: A Review

Temperature-driven self-assembly in a hexagonal mesophase-forming model: a dynamic and structural study

We investigate the self-assembly and phase transitions of a binary-particle system that forms a hexagonal mesophase, modeled via isotropic Stillinger-Weber interactions and studied with molecular dynamics simulations. Two characteristic temperatures emerge: the order-disorder transition TOD, marking the onset of hexagonal order, and a higher temperature Tx where wormlike clustering of the minority component first appears in the isotropic phase. Using three complementary methods-(i) angular characterization, (ii) dynamic correlation analysis, and (iii) neighbor permanence time-we show how wormlike aggregates evolve below Tx and eventually align into the ordered mesophase at TOD. These results clarify the interplay among clustering, dynamic organization, and structural signals in driving mesophase formation, offering insights into the fundamental mechanisms governing self-assembly in complex materials.

On the build-up of effective hyperuniformity from large globular colloidal aggregates

A simple three-dimensional model of a fluid whose constituent particles interact via a short range attractive and long range repulsive potential is used to model the aggregation into large spherical-like clusters made up of hundreds of particles. The model can be thought of as a straightforward rendition of colloid flocculation into large spherical aggregates. We illustrate how temperature and particle density influence the cluster size distribution and affect inter- and intra-cluster dynamics. The system is shown to exhibit two well separated length and time scales, which can be tuned by the balance between repulsive and attractive forces. Interestingly, cluster aggregates at moderate/low temperatures approach a cluster glassy phase, whereas cluster particles retain a local liquid-like structure. These states present a strong suppression of density fluctuations for a significant range of relatively large wavelengths, meeting the criterion of effective disordered hyperuniform materials as far as the intercluster structure is concerned.

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.

On the thermal response of multiscale nanodomains formed in trans-anethol/ethanol/water surfactant-free microemulsion

HYPOTHESIS

Surfactant-free microemulsion (SFME), an emerging phenomenology that occurs in the monophasic zone of a broad category of ternary mixtures 'hydrophobe/hydrotrope/water', has attracted extensive interests due to their unique physicochemical properties. The potential of this kind of ternary fluid for solubilization and drug delivery make them promising candidates in many industrial scenarios.

EXPERIMENTS

Here the thermodynamic behavior of these multiscale nanodomains formed in the ternary trans-anethol/ethanol/water system over a wide range of temperatures is explored. The macroscopic physical properties of the ternary solutions are characterized, with revealing the temperature dependence of refractive index and dynamic viscosity.

FINDINGS

With increasing temperature, the ternary system shows extended areas in the monophasic zone. We demonstrate that the phase behavior and the multiscale nanodomains formed in the monophasic zone can be precisely and reversibly tuned by altering the temperature. Increasing temperature can destroy the stability of the multiscale nanodomains in equilibrium, with an exponential decay in the scattering light intensity. Nevertheless, molecular-scale aggregates and mesoscopic droplets exhibit significantly different response behaviors to temperature stimuli. The temperature-sensitive nature of the ternary SFME system provides a crucial step forward exploring and industrializing its stability.

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.

Phase Transitions of Associative Biomacromolecules

Multivalent proteins and nucleic acids, collectively referred to as multivalent associative biomacromolecules, provide the driving forces for the formation and compositional regulation of biomolecular condensates. Here, we review the key concepts of phase transitions of aqueous solutions of associative biomacromolecules, specifically proteins that include folded domains and intrinsically disordered regions. The phase transitions of these systems come under the rubric of coupled associative and segregative transitions. The concepts underlying these processes are presented, and their relevance to biomolecular condensates is discussed.

Molecular Dynamics Investigation of Giant Clustering in Small-Molecule Solutions: The Case of Aqueous PEHA

The importance of the formation of giant clusters in solution, in nature and industry, is increasingly recognized. However, relatively little attention has been paid to the formation of giant clusters in solutions of small, relatively soluble but nonamphiphilic molecules. In this work, we present a general methodology based on molecular dynamics that can be used to investigate such systems. As a case study, we focus on the formation of apparently stable clusters of pentaethylenehexamine (PEHA) in water. These clusters have been used as templates for the construction of bioinspired silica nanoparticles. To better understand clustering in this system, we study the effect of PEHA protonation state (neutral, +1, and +2) and counterion type (chloride or acetate) on PEHA clustering in dilute aqueous solutions (200 and 400 mM) using large-scale classical molecular dynamics. We find that large stable clusters are formed by singly charged PEHA with chloride or acetate as the counterion, although it is not clear for the case with acetate whether bulk phase separation, that might lead to precipitation, would eventually occur. Large clusters also appear to be stable for doubly charged PEHA with acetate, the less soluble counterion. We attribute this behavior to a form of complex coacervation, observed here for relatively small and highly soluble molecules (PEHA + counterion) rather than the large polyions usually found to form such coacervates. We discuss whether this behavior might also be described by an effective SALR (short-range attraction, long-range repulsion) interaction. This work might help future studies of additives for the design of novel bioinspired templated nanomaterials and of giant clustering in small-molecule solutions more generally.

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.

Molecular Dynamics Investigation of Clustering in Aqueous Glycine Solutions

Recent experiments with undersaturated aqueous glycine solutions have repeatedly exhibited the presence of giant liquid-like clusters or nanodroplets around 100 nm in diameter. These nanodroplets re-appear even after careful efforts for their removal and purification of the glycine solution. The composition of these clusters is not clear, although it has been suggested that they are mainly composed of glycine, a small and very soluble amino acid. To gain insights into this phenomenon, we study the aggregation of glycine in aqueous solutions at concentrations below the experimental solubility limit using large-scale molecular dynamics simulations under ambient conditions. Three protonation states of glycine (zwitterion = GLZ, anion = GLA, and cation = GLC) are simulated using molecular force fields based on the 1.14*CM1A partial charge scheme, which incorporates the OPLS all-atom force field and TIP3P water. When initiated from dispersed states, we find that giant clusters do not form in our simulations unless salt impurities are present. Moreover, if simulations are initiated from giant cluster states, we find that they tend to dissolve in the absence of salt impurities. Therefore, the simulation results provide little support for the possibility that the giant clusters seen in experiments are composed purely of glycine (and water). Considering that strenuous efforts are made in experiments to remove impurities such as salt, we propose that the giant clusters observed might instead result from the aggregation of reaction products of aqueous glycine, such as diketopiperazine or other oligoglycines which may be difficult to separate from glycine using conventional methods, or their co-aggregation with glycine.

Dual nature of magnetic nanoparticle dispersions enables control over short-range attraction and long-range repulsion interactions

Competition between attractive and repulsive interactions drives the formation of complex phases in colloidal suspensions. A major experimental challenge lies in decoupling independent roles of attractive and repulsive forces in governing the equilibrium morphology and long-range spatial distribution of assemblies. Here, we uncover the 'dual nature' of magnetic nanoparticle dispersions, particulate and continuous, enabling control of the short-range attraction and long-range repulsion (SALR) between suspended microparticles. We show that non-magnetic microparticles suspended in an aqueous magnetic nanoparticle dispersion simultaneously experience a short-range depletion attraction due to the particulate nature of the fluid in competition with an in situ tunable long-range magnetic dipolar repulsion attributed to the continuous nature of the fluid. The study presents an experimental platform for achieving in situ control over SALR between colloids leading to the formation of reconfigurable structures of unusual morphologies, which are not obtained using external fields or depletion interactions alone.

Ionic liquids in conducting nanoslits: how important is the range of the screened electrostatic interactions?

Analytical models for capacitive energy storage in nanopores attract growing interest as they can provide in-depth analytical insights into charging mechanisms. So far, such approaches have been limited to models with nearest-neighbor interactions. This assumption is seemingly justified due to a strong screening of inter-ionic interactions in narrow conducting pores. However, how important is the extent of these interactions? Does it affect the energy storage and phase behavior of confined ionic liquids? Herein, we address these questions using a two-dimensional lattice model with next-nearest and further neighbor interactions developed to describe ionic liquids in conducting slit confinements. With simulations and analytical calculations, we find that next-nearest interactions enhance capacitance and stored energy densities and may considerably affect the phase behavior. In particular, in some range of voltages, we reveal the emergence of large-scale mesophases that have not been reported before but may play an important role in energy storage.

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

Self-assembling complex fluids are often modeled as particles with effective competing isotropic interactions, combining a short-range attraction (SA) followed by a longer-range repulsion (LR). For moderately low temperatures and densities, SALR particles form clusters in equilibrium, at least provided that the potential parameters are appropriate. Here we inquire into the possibility that cluster formation in SALR fluids might be pushed by a foreign species even under thermodynamic conditions that would not allow for clusterization of the pure system. To this aim, we study by Monte Carlo simulations a mixture of hard-sphere two-Yukawa particles and hard spheres, with a cross interaction modeled by a square-well attraction, and we investigate the conditions of clustering in terms of strength of attraction and relative concentration of the two species. We find that clusters can occur in the mixture for the same temperature and density where the pure SALR fluid is almost structureless. In particular, we single out a cross attraction such that clusters are formed with a SALR concentration as low as 5%. We also find a situation where nearly pure droplets of hard spheres are held together by a shell of SALR particles. Conversely, we show that clustering can be undermined in the mixture under conditions for which this process takes place in the parent SALR fluid. Using a simple criterion, based on the second virial coefficients of the attractive part of interaction potentials (the so-called "reference attractive fluids"), we are able to predict accurately whether clustering is favored (or hindered) in the mixture, as compared to the pure SALR fluid.

Early stages of aggregation in fluid mixtures of dimers and spheres: a theoretical and simulation study

We use Monte Carlo simulation and the Reference Interaction Site Model (RISM) theory of molecular fluids to investigate a simple model of colloidal mixture consisting of dimers, made up of two tangent hard monomers of different size, and hard spheres. In addition to steric repulsion, the two species interact via a square-well attraction only between small monomers and spheres. Recently, we have characterized the low-temperature regime of this mixture by Monte Carlo, reporting on the spontaneous formation of a wide spectrum of supramolecular aggregates [Prestipino et al., J. Phys. Chem. B, 2019, 123, 9272]. Here we focus on a regime of temperatures where, on cooling, the appearance of local inhomogeneties first, and the early stages of aggregation thereafter, are observed. In particular, we find signatures of aggregation in the onset of a low-wavevector peak in the structure factors of the mixture, as computed by both theory and simulation. Then, we link the structural information to the microscopic arrangement through a detailed cluster analysis of Monte Carlo configurations. In this regard, we devise a novel method to compute the maximum distance for which two spheres can be regarded as bonded together, a crucial issue in the proper identification of fluid aggregates. The RISM theory provides relatively accurate structural and thermodynamic predictions in comparison with Monte Carlo, but with slightly degrading performances as the fluid progresses inside the locally inhomogeneous phase. Our study certifies the efficacy of the RISM approach as a useful complement to numerical simulation for a reasoned analysis of aggregation properties in colloidal mixtures.

Inverse design of equilibrium cluster fluids applied to a physically informed model

Inverse design strategies have proven highly useful for the discovery of interaction potentials that prompt self-assembly of a variety of interesting structures. However, often the optimized particle interactions do not have a direct relationship to experimental systems. In this work, we show that Relative Entropy minimization is able to discover physically meaningful parameter sets for a model interaction built from depletion attraction and electrostatic repulsion that yield self-assembly of size-specific clusters. We then explore the sensitivity of the optimized interaction potentials with respect to deviations in the underlying physical quantities, showing that clustering behavior is largely preserved even as the optimized parameters are perturbed.

Debye vs. Casimir: controlling the structure of charged nanoparticles deposited on a substrate

Fine-tuning the interactions between particles can allow one to steer their collective behaviour and structure. A convenient way to achieve this is to use solvent criticality to control attraction, via critical Casimir forces, and to control repulsion via the Debye screening of electrostatic interactions. Herein, we develop a multiscale simulation framework and a method for controlled deposition of quantum dots to investigate how these interactions affect the structure of charged nanoparticles deposited on a substrate, altogether immersed in a binary liquid mixture intermixed with salt. We consider nanoparticles and substrates favouring the same component of the mixture and find that the critical Casimir interactions between the nanoparticles become drastically reduced at the substrate. In particular, the interactions can become a few k_BT weaker and their decay length a few orders of magnitude smaller than in the bulk. At off-critical compositions, the decay length increases upon approaching criticality, as expected, but the interaction strength decreases. With molecular dynamics simulations and experiments, we reveal that the nanoparticles can self-assemble into crystalline clusters which form superstructures resembling cluster fluids and spinodal morphology. The simulations additionally predict the formation of fractal-like nanoparticle gels and bicontinuous phases. Our results demonstrate that charged nanoparticles in a salty binary liquid mixture provide exciting opportunities to study the formation of complex structures experimentally and theoretically, which may lead to applications in optoelectronics and photonics.

Cluster formation in symmetric binary SALR mixtures

The equilibrium cluster fluid state of a symmetric binary mixture of particles interacting through short-ranged attractive and long-ranged repulsive interactions is investigated through Monte Carlo simulations. We find that the clustering behavior of this system is controlled by the cross-interaction between the two types of particles. For a weak cross-attraction, the system displays a behavior that is a composite of the behavior of individual components, i.e., the two components can both form giant clusters independently and the clusters distribute evenly in the system. For a strong cross-attraction, we instead find that the resulting clusters are mixtures of both components. Between these limits, both components can form relatively pure clusters, but unlike clusters can join at their surfaces to form composite clusters. These insights should help to understand the mechanisms for clustering in experimental binary mixture systems and help tailor the properties of novel nanomaterials.

Modeling Elastically Mediated Liquid-Liquid Phase Separation

We propose a continuum theory of the liquid-liquid phase separation in an elastic network, where phase-separated microscopic droplets rich in one fluid component can form as an interplay of fluids mixing, droplet nucleation, network deformation, thermodynamic fluctuation, etc. We find that the size of the phase-separated droplets decreases with the shear modulus of the elastic network in the form of ∝[modulus]^{-1/3} and the number density of the droplet increases almost linearly with the shear modulus ∝[modulus], which are verified by the experimental observations. Phase diagrams in the space of (fluid constitution, mixture interaction, network modulus) are provided, which can help to understand similar phase separations in biological cells and also to guide fabrications of synthetic cells with desired phase properties.