Partial and complete wetting of droplets of active Brownian particles.

We study wetting droplets formed of active Brownian particles in contact with a repulsive potential barrier, in a wedge geometry. Our numerical results demonstrate a transition between partially wet and completely wet states, as a function of the barrier height, analogous to the corresponding surface phase transition in passive fluids. We analyse partially wet configurations characterised by a nonzero contact angle θ between the droplet surface and the barrier including the average density profile and its fluctuations. These findings are compared with two equilibrium systems: a Lennard-Jones fluid and a simple contour model for a liquid-vapour interface. We locate the wetting transition where cos(θ) = 1, and the neutral state where cos(θ) = 0. We discuss the implications of these results for possible definitions of surface tensions in active fluids.

Sensitivity of solid phase stability to the interparticle potential range: studies of a new Lennard-Jones like model.

In a recent article, Wang et al. (Phys. Chem. Chem. Phys., 2020, 22, 10624) introduced a new class of interparticle potential for molecular simulations. The potential is defined by a single range parameter, eliminating the need to decide how to truncate truly long-range interactions like the Lennard-Jones (LJ) potential. The authors explored the phase diagram for a particular value of the range parameter for which their potential is similar in shape to the LJ 12-6 potential. We have reevaluated the solid phase behaviour of this model using both Lattice Switch Monte Carlo and thermodynamic integration. In addition to finding that the boundary between hexagonal close packed (hcp) and face centred cubic (fcc) phases presented by Wang et al. was calculated incorrectly, we show that owing to its finite range, the new potential exhibits several reentrant transitions between hcp and fcc phases. These phases, which do not occur in the full (untruncated) LJ system, are also found for typically adopted forms of the truncated and shifted LJ potential. However, whilst in the latter case one can systematically investigate and correct for the effects of the finite range on the calculated phase behaviour (a correction beyond the standard long-range mean field tail correction being required), this is not possible for the new potential because the choice of range parameter affects the entire potential shape. Our results highlight that potentials with finite range may fail to represent the crystalline phase behavior of systems with long-range dispersion interactions, even qualitatively.

What is the best simulation approach for measuring local density fluctuations near solvo-/hydrophobes?

Measurements of local density fluctuations are crucial to characterizing the interfacial properties of equilibrium fluids. A specific case that has been well-explored involves the heightened compressibility of water near hydrophobic entities. Commonly, a spatial profile of local fluctuation strength is constructed from the measurements of the mean and variance of solvent particle number fluctuations in a set of contiguous subvolumes of the system adjacent to the solvo-/hydrophobe. An alternative measure proposed by Evans and Stewart [J. Phys.: Condens. Matter 27, 194111 (2015)] defines a local compressibility profile in terms of the chemical potential derivative of the spatial number density profile. Using Grand canonical Monte Carlo simulation, we compare and contrast the efficacy of these two approaches for a Lennard-Jones solvent at spherical and planar solvophobic interfaces and SPC/E water at a hydrophobic spherical solute. Our principal findings are as follows: (i) the local compressibility profile χ(r) of Evans and Stewart is considerably more sensitive to variations in the strength of local density fluctuations than the spatial fluctuation profile F(r) and can resolve much more detailed structure; and (ii) while the local compressibility profile is essentially independent of the choice of spatial discretization used to construct the profile, the spatial fluctuation profile exhibits a strong systematic dependence on the size of the subvolumes on which the profile is defined. We clarify the origin and nature of this finite-size effect.

Understanding the physics of hydrophobic solvation.

Simulations of water near extended hydrophobic spherical solutes have revealed the presence of a region of depleted density and accompanying enhanced density fluctuations. The physical origin of both phenomena has remained somewhat obscure. We investigate these effects employing a mesoscopic binding potential analysis, classical density functional theory (DFT) calculations for a simple Lennard-Jones solvent, and Grand Canonical Monte Carlo (GCMC) simulations of a monatomic water (mw) model. We argue that the density depletion and enhanced fluctuations are near-critical phenomena. Specifically, we show that they can be viewed as remnants of the critical drying surface phase transition that occurs at bulk liquid-vapor coexistence in the macroscopic planar limit, i.e., as the solute radius Rs → ∞. Focusing on the radial density profile ρ(r) and a sensitive spatial measure of fluctuations, the local compressibility profile χ(r), our binding potential analysis provides explicit predictions for the manner in which the key features of ρ(r) and χ(r) scale with Rs, the strength of solute-water attraction ɛsf, and the deviation from liquid-vapor coexistence of the chemical potential, δµ. These scaling predictions are confirmed by our DFT calculations and GCMC simulations. As such, our theory provides a firm basis for understanding the physics of hydrophobic solvation.

Density Depletion and Enhanced Fluctuations in Water near Hydrophobic Solutes: Identifying the Underlying Physics.

We investigate the origin of the density depletion and enhanced density fluctuations that occur in water in the vicinity of an extended hydrophobic solute. We argue that both phenomena are remnants of the critical drying surface phase transition that occurs at liquid-vapor coexistence in the macroscopic planar limit, i.e., as the solute radius R_{s}→∞. Focusing on the density profile ρ(r) and a sensitive spatial measure of fluctuations, the local compressibility profile χ(r), we develop a scaling theory which expresses the extent of the density depletion and enhancement in compressibility in terms of R_{s}, the strength of solute-water attraction ϵ_{s}, and the deviation from liquid-vapor coexistence δµ. Testing the predictions against results of classical density functional theory for a simple solvent and grand canonical Monte Carlo simulations of a popular water model, we find that the theory provides a firm physical basis for understanding how water behaves at a hydrophobe.

The coexistence curve and surface tension of a monatomic water model.

We study the monatomic water model of Molinero and Moore the grand canonical ensemble Monte Carlo simulation. Measurements of the probability distribution of the number density obtained via multicanonical sampling and histogram reweighting provide accurate estimates of the temperature dependence of both the liquid-vapor coexistence densities and the surface tension. Using finite-size scaling methods, we locate the liquid-vapor critical point at Tc = 917.6 K, ρc = 0.311 g cm-3. When plotted in scaled variables, in order to test the law of corresponding states, the coexistence curve of monatomic water is close to that of real water. In this respect, it performs better than extended simple point charge (SPC/E), TIP4P, and TIP4P/2005 water.

Multilevel simulation of hard-sphere mixtures.

We present a multilevel Monte Carlo simulation method for analyzing multi-scale physical systems via a hierarchy of coarse-grained representations, to obtain numerically exact results, at the most detailed level. We apply the method to a mixture of size-asymmetric hard spheres, in the grand canonical ensemble. A three-level version of the method is compared with a previously studied two-level version. The extra level interpolates between the full mixture and a coarse-grained description where only the large particles are present-this is achieved by restricting the small particles to regions close to the large ones. The three-level method improves the performance of the estimator, at fixed computational cost. We analyze the asymptotic variance of the estimator and discuss the mechanisms for the improved performance.

A unified description of hydrophilic and superhydrophobic surfaces in terms of the wetting and drying transitions of liquids.

Clarifying the factors that control the contact angle of a liquid on a solid substrate is a long-standing scientific problem pertinent across physics, chemistry, and materials science. Progress has been hampered by the lack of a comprehensive and unified understanding of the physics of wetting and drying phase transitions. Using various theoretical and simulational techniques applied to realistic fluid models, we elucidate how the character of these transitions depends sensitively on both the range of fluid-fluid and substrate-fluid interactions and the temperature. Our calculations uncover previously unrecognized classes of surface phase diagram which differ from that established for simple lattice models and often assumed to be universal. The differences relate both to the topology of the phase diagram and to the nature of the transitions, with a remarkable feature being a difference between drying and wetting transitions which persists even in the approach to the bulk critical point. Most experimental and simulational studies of liquids at a substrate belong to one of these previously unrecognized classes. We predict that while there appears to be nothing particularly special about water with regard to its wetting and drying behavior, superhydrophobic behavior should be more readily observable in experiments conducted at high temperatures than at room temperature.

Phase Separation and Multibody Effects in Three-Dimensional Active Brownian Particles.

Simulation studies of the phase diagram of repulsive active Brownian particles in three dimensions reveal that the region of motility-induced phase separation between a high and low density phase is enclosed by a region of gas-crystal phase separation. Near-critical loci and structural crossovers can additionally be identified in analogy with simple fluids. Motivated by the striking similarity to the behavior of equilibrium fluids with short-ranged pairwise attractions, we show that a direct mapping to pair potentials in the dilute limit implies interactions that are insufficiently attractive to engender phase separation. Instead, this is driven by the emergence of multibody effects associated with particle caging that occurs at sufficiently high number density. We quantify these effects via information-theoretical measures of n-body effective interactions extracted from the configurational structure.

Wetting Transition of Active Brownian Particles on a Thin Membrane.

We study nonequilibrium analogues of surface phase transitions in a minimal model of active particles in contact with a purely repulsive potential barrier that mimics a thin porous membrane. Under conditions of bulk motility-induced phase separation, the interaction strength ϵ_{w} of the barrier controls the affinity of the dense phase for the barrier region. We uncover clear signatures of a wetting phase transition as ϵ_{w} is varied. In common with its equilibrium counterpart, the character of this transition depends on the system dimensionality: a continuous transition with large density fluctuations and gas bubbles is uncovered in 2D while 3D systems exhibit a sharp transition absent of large correlations.

Correction of coarse-graining errors by a two-level method: Application to the Asakura-Oosawa model.

We present a method that exploits self-consistent simulation of coarse-grained and fine-grained models in order to analyze properties of physical systems. The method uses the coarse-grained model to obtain a first estimate of the quantity of interest, before computing a correction by analyzing properties of the fine system. We illustrate the method by applying it to the Asakura-Oosawa model of colloid-polymer mixtures. We show that the liquid-vapor critical point in that system is affected by three-body interactions which are neglected in the corresponding coarse-grained model. We analyze the size of this effect and the nature of the three-body interactions. We also analyze the accuracy of the method as a function of the associated computational effort.

Composition inversion in mixtures of binary colloids and polymer.

Understanding the phase behaviour of mixtures continues to pose challenges, even for systems that might be considered "simple." Here, we consider a very simple mixture of two colloidal and one non-adsorbing polymer species, which can be simplified even further to a size-asymmetrical binary mixture, in which the effective colloid-colloid interactions depend on the polymer concentration. We show that this basic system exhibits surprisingly rich phase behaviour. In particular, we enquire whether such a system features only a liquid-vapor phase separation (as in one-component colloid-polymer mixtures) or whether, additionally, liquid-liquid demixing of two colloidal phases can occur. Particle-resolved experiments show demixing-like behaviour, but when combined with bespoke Monte Carlo simulations, this proves illusory, and we reveal that only a single liquid-vapor transition occurs. Progressive migration of the small particles to the liquid phase as the polymer concentration increases gives rise to composition inversion-a maximum in the large particle concentration in the liquid phase. Close to criticality, the density fluctuations are found to be dominated by the larger colloids.

Disappearance of the Hexatic Phase in a Binary Mixture of Hard Disks.

Recent studies of melting in hard disks have confirmed the existence of a hexatic phase occurring in a narrow window of density which is separated from the isotropic liquid phase by a first-order transition, and from the solid phase by a continuous transition. However, little is known concerning the melting scenario in mixtures of hard disks. Here we employ tailored Monte Carlo simulations to elucidate the phase behavior of a system of large (l) and small (s) disks with diameter ratio σ_{l}/σ_{s}=1.4. We find that as small disks are introduced to a system of large ones, the stability window of the hexatic phase shrinks progressively until the line of continuous transitions terminates at an end point beyond which melting becomes a first-order liquid-solid transition. This occurs at surprisingly low concentrations of the small disks, c≲1%, emphasizing the fragility of the hexatic phase. We speculate that the change to the melting scenario is a consequence of strong fractionation effects, the nature of which we elucidate.

Drying and wetting transitions of a Lennard-Jones fluid: Simulations and density functional theory.

We report a theoretical and simulation study of the drying and wetting phase transitions of a truncated Lennard-Jones fluid at a flat structureless wall. Binding potential calculations predict that the nature of these transitions depends on whether the wall-fluid attraction has a long ranged (LR) power law decay or is instead truncated, rendering it short ranged (SR). Using grand canonical Monte Carlo simulation and classical density functional theory, we examine both cases in detail. We find that for the LR case wetting is first order, while drying is continuous (critical) and occurs exactly at zero attractive wall strength, i.e., in the limit of a hard wall. In the SR case, drying is also critical but the order of the wetting transition depends on the truncation range of the wall-fluid potential. We characterize the approach to critical drying and wetting in terms of the density and local compressibility profiles and via the finite-size scaling properties of the probability distribution of the overall density. For the LR case, where the drying point is known exactly, this analysis allows us to estimate the exponent ν∥, which controls the parallel correlation length, i.e., the extent of vapor bubbles at the wall. Surprisingly, the value we obtain is over twice that predicted by mean field and renormalization group calculations, despite the fact that our three dimensional system is at the upper critical dimension where mean field theory for critical exponents is expected to hold. Possible reasons for this discrepancy are discussed in the light of fresh insights into the nature of near critical finite-size effects.

Critical Drying of Liquids.

We report a detailed simulation and classical density functional theory study of the drying transition in a realistic model fluid at a smooth substrate. This transition (in which the contact angle θ→180°) is shown to be critical for both short-ranged and long-ranged substrate-fluid interaction potentials. In the latter case critical drying occurs at exactly zero attractive substrate strength. This observation permits the accurate elucidation of the character of the transition via a finite-size scaling analysis of the density probability function. We find that the critical exponent ν_{∥} that controls the parallel correlation length, i.e., the extent of vapor bubbles at the wall, is over twice as large as predicted by mean field and renormalization group calculations. We suggest a reason for the discrepancy. Our findings shed new light on fluctuation phenomena in fluids near hydrophobic and solvophobic interfaces.

Coarse-grained depletion potentials for anisotropic colloids: Application to lock-and-key systems.

When colloids are mixed with a depletant such as a non-adsorbing polymer, one observes attractive effective interactions between the colloidal particles. If these particles are anisotropic, analysis of these effective interactions is challenging in general. We present a method for inference of approximate (coarse-grained) effective interaction potentials between such anisotropic particles. Using the example of indented (lock-and-key) colloids, we show how numerical solutions can be used to integrate out the (hard sphere) depletant, leading to a depletion potential that accurately characterises the effective interactions. The accuracy of the method is based on matching of contributions to the second virial coefficient of the colloids. The simplest version of our method yields a piecewise-constant effective potential; we also show how this scheme can be generalised to other functional forms, where appropriate.

Quantifying Density Fluctuations in Water at a Hydrophobic Surface: Evidence for Critical Drying.

Employing smart Monte Carlo sampling techniques within the grand canonical ensemble, we investigate the properties of water at a model hydrophobic substrate. By reducing the strength of substrate-water attraction, we find that fluctuations in the local number density, quantified by a rigorous definition of the local compressibility χ(z), increase rapidly for distances z within one or two molecular diameters from the substrate as the degree of hydrophobicity, measured by the macroscopic contact angle θ, increases. Our simulations provide evidence for a continuous (critical) drying transition as the substrate-water interaction becomes very weak: cos(θ)→-1. We speculate that the existence of such a transition might account for earlier simulation observations of strongly enhanced density fluctuations.

Porous Liquid Phases for Indented Colloids with Depletion Interactions.

We study indented spherical colloids, interacting via depletion forces. These systems exhibit liquid-vapor phase transitions whose properties are determined by a combination of strong "lock-and-key" bonds and weaker nonspecific interactions. As the propensity for lock-and-key binding increases, the critical point moves to significantly lower density, and the coexisting phases change their structure. In particular, the liquid phase is porous, exhibiting large percolating voids. The properties of this system depend strongly on the topological structure of an underlying bond network: we comment on the implications of this fact for the assembly of equilibrium states with controlled porous structures.

Self-assembly and crystallisation of indented colloids at a planar wall.

We report experimental and simulation studies of the structure of a monolayer of indented ("lock and key") colloids, on a planar surface. On adding a non-absorbing polymer with prescribed radius and volume fraction, depletion interactions are induced between the colloids, with controlled range and strength. For spherical particles, this leads to crystallisation, but the indented colloids crystallise less easily than spheres, in both simulation and experiment. Nevertheless, simulations show that indented colloids do form plastic (rotator) crystals. We discuss the conditions under which this occurs, and the possibilities of lower-symmetry crystal states. We also comment on the kinetic accessibility of these states.

Demixing cascades in cluster crystals.

In a cluster crystal, each lattice site is occupied by multiple soft-core particles. As the number density is increased at zero temperature, a "cascade" of isostructural phase transitions can occur between states whose site occupancy differs by unity. For low but finite temperature, each of these transitions terminates in a critical point. Using tailored Monte Carlo simulation techniques, we have studied such demixing cascades in systems of soft particles interacting via potentials of the generalized exponential form u(r) = ε exp [-(r/σ)(n)]. We have estimated the critical parameters of the first few transitions in the cascade as a function of the softness parameter n. The critical temperature and pressure exhibit non-monotonic behavior as n is varied, although the critical chemical potential remains monotonic. The trends for the pressure and chemical potential are confirmed by cell model calculations at zero temperature. As n → 2(+), all the transitions that we have observed are preempted by melting although we cannot rule out that clustering transitions survive at high density.