Monte Carlo simulations were used to study the assembly of binary mixtures of hard disks with squares, where the components have size ratios that optimize their co-assembly into compositionally disordered solids. It is observed that, along with the enhanced regions of solid miscibility, a continuous-looking transition from the disk-like to the square-like behavior occurred through a novel mosaic (M) phase, which seamlessly bridges the regions of hexatic mesophase of disks and the tetratic mesophase of squares. The M phase has interspersed tetratic, hexatic, and rhombic-like locally ordered clusters.
Dynamic equations are presented for polar binary mixtures containing ions in the presence of the preferential solvation. In one-phase states, we calculate the dynamic structure factor of the composition accounting for the ion motions. Microphase separation can take place for sufficiently large solvation asymmetry of the cations and the anions. We show two-dimensional simulation results of the mesophase formation with an antagonistic salt, where the cations are hydrophilic and the anions are hydrophobic. The structure factor S(q) in the resultant mesophase has a sharp peak at an intermediate wa…
Sought-after ordered structures of mixtures of hard anisotropic nanoparticles can often be thermodynamically unfavorable due to the components' geometric incompatibility to densely pack into regular lattices. A simple compatibilization rule is identified wherein the particle sizes are chosen such that the order-disorder transition pressures of the pure components match (and the entropies of the ordered phases are similar). Using this rule with representative polyhedra from the truncated-cube family that form pure-component plastic-crystals, Monte Carlo simulations show the formation of plastic…
The mesophase behaviour of binary mixtures of bent-core and calamitic liquid crystals is presented. The nematogenic 4,6-dichloro-1,3-phenylene bis[4'-(10-undecen-1-yloxy)-1,1'-biphenyl-4-carboxylate] (I) was the banana-shaped component. As the calamitic compound ethyl 4'-(9-decen-1-yloxy)-1,1'-biphenyl-4-carboxylate (II), similar to one arm of the bent-core molecule, was used which exhibits smectic phases in a wide temperature range. A total of 6 mixtures with different compositions were prepared and studied by polarising optical microscopy, differential scanning calorimetry and X-ray diffract…
By means of a three-dimensional amphiphilic lattice-Boltzmann model with short-range interactions for the description of ternary amphiphilic fluids, we study how the phase separation kinetics of a symmetric binary immiscible fluid is altered by the presence of the amphiphilic species. We find that a gradual increase in amphiphile concentration slows down domain growth, initially from algebraic, to logarithmic temporal dependence, and, at higher concentrations, from logarithmic to stretched-exponential form. In growth-arrested stretched-exponential regimes, at late times we observe the self-ass…
We present the first simulations of the self-assembly kinetics of the gyroid cubic mesophase using a Boltzmann transport method. No macroscopic parameters are included in the model and three-dimensional hydrodynamics is emergent from the microscopic conservation laws. The self-assembly arise from local inter-particle interactions in an initially homogeneous, phase segregating binary fluid with dispersed amphiphile. The mixture evolves in discrete time according to the dynamics of a set of coupled Boltzmann-BGK equations on a lattice. We observe a transient microemulsion phase during self-assem…
We report the first results of our three-dimensional, mesoscopic, amphiphilic lattice-Boltzmann model, which has been used to simulate the dynamics of self-assembly of ordered cubic and lamellar phases in binary water-surfactant systems. Our results provide insight into the mechanism of ordering of such mesophases in terms of various molecular forces acting between water and surfactant molecules and the mechanism driving the transition from the lamellar to the cubic phase.
The linear compressibility of two-dimensional fatty acid mesophases has determined by grazing incidence x-ray diffraction. Surface pressure vs molecular area isotherms were reconstructed from these measurements, and the linear compressibility (relative distortion along a given direction for isotropic applied stress) was determined both in the sample plane and in a plane normal to the aliphatic chain director (transverse plane). The linear compressibilities range over two orders of magnitude from 0.1 to 10 m/N and are distributed depending on their magnitude in 4 different sets which we are abl…
Phase transition is observed between one-phase disordered phase and an ordered phase with multi-lamellar (onion) structures in an off-critical mixture of D$_2$O and 3-methylpyridine (3MP) containing a salt at 85mM. The salt consists of hydrophilic cations and hydrophobic anions, which interact asymmetrically with the solvent composition fluctuations inducing mesophases. The structure factor of the composition distribution obtained from small-angle neutron scattering has a peak at an intermediate wave number in the disordered phase and multiple peaks in the ordered phase. Lamellar layers formin…
Density Profiles and Direct Correlation Functions from Density Functional Theory in Binary Hard-Sphere Crystals: Substitutional Solid and Interstitial Solid Solution
Institute of Applied Physics, University of Tübingen（蒂宾根大学应用物理研究所）
The pretransitional behavior of dodecylcyanobiphenyl (12CB) (isotropic-smectic-A-solid mesomorphism) with $d = 50$ nm $BaTiO_3$ nanoparticles (NPs) linked the cubic phase was monitored via temperature studies of dielectric constant. Tests were carried out in the isotropic, liquid crystal mesomorphic and solid phases. For each phase transition the same value of the critical exponent $α=0.5$ was obtained, including nanocolloids. All phase transitions show the weakly discontinuous nature. The temperature metric of the discontinuity dT notably decreases when adding nanoparticles. The addition of n…
In a recent letter, Buhot proposes that entropy driven phase-separation in hard-core binary mixtures is directly related to a bond-percolation transition. However, at least for binary hard-sphere mixtures, calculations based on an accurate approximation to g_{ll}(r) demonstrate that n_b varies widely along the phase-boundaries calculated directly by simulations, implying that bond-percolation is unrelated to the phase-separation in these systems.
The properties of crystals consisting of several components can be widely tuned. Often solid solutions are produced, where substitutional or interstitional disorder determines the crystal thermodynamic and mechanical properties. The chemical and structural disorder impedes the study of the elasticity of such solid solutions, since standard procedures like potential expansions cannot be applied. We present a generalization of a density-functional based approach recently developed for one-component crystals to multi-component crystals. It yields expressions for the elastic constants valid in sol…
We present the results of molecular dynamics (MD) studies of hexane physisorbed onto graphite for eight coverages in the range $0.875 \le ρ\le 1.05$ (in units of monolayers). At low temperatures the adsorbate molecules form a uniaxially incommensurate herringbone (UI-HB) solid. At high coverages the solid consists of adsorbate molecules that are primarily rolled on their side perpen-dicular to the surface of the substrate. As the coverage is decreased, the amount of molecular rolling diminishes until $ρ$ = 0.933 where it disappears (molecules become primarily parallel to the surface). If the d…
We provide an exact mapping between the density functional of a binary mixture and that of the effective one-component fluid in the limit of infinite asymmetry. The fluid of parallel hard cubes is thus mapped onto that of parallel adhesive hard cubes. Its phase behaviour reveals that demixing of a very asymmetric mixture can only occur between a solvent-rich fluid and a permeated large particle solid or between two large particle solids with different packing fractions. Comparing with hard spheres mixtures we conclude that the phase behaviour of very asymmetric hard-particle mixtures can be de…
We use numerical simulations to study the phase behavior of a system of purely repulsive soft dumbbells as a function of size ratio of the two components and their relative degree of deformability. We find a plethora of different phases which includes most of the mesophases observed in self-assembly of block copolymers, but also crystalline structures formed by asymmetric, hard binary mixtures. Our results detail the phenomenological behavior of these systems when softness is introduced in terms of two different classes of inter-particle interactions: (a) the elastic Hertz potential, that has …
A previously developed fundamental measure fucntional [J. Chem. Phys. vol.107, 6379 (1997)] is used to study the phase behavior of a system of parallel hard cubes. The single-component fluid exhibits a continuous transition to a solid with an anomalously large density of vacancies. The binary mixture has a demixing transition for edge-length ratios below 0.1. Freezing in this mixture reveals that at least the phase rich in large cubes lies in the region where the uniform fluid is unstable, hence suggesting a fluid-solid phase separation. A method is develop to study very asymmetric binary mixt…
We calculate for the first time the full phase-diagram of an asymmetric non-additive hard-sphere mixture. The non-additivity strongly affects the crystallization and the fluid-fluid phase-separation. The global topology of the phase-diagram is controlled by an effective size-ratio y_{eff}, while the fluid-solid coexistence scales with the depth of the effective potential well.
Computer simulations of contact melting and associated interfacial phenomena in binary eutectic systems were performed on the basis of the standard phase-field model with miscibility gap in solid state. It is shown that the model predicts the existence of equilibrium three-phase (solid-liquid-solid) states above the eutectic temperature, which suggest the explanation of the phenomenon of phase separation in liquid eutectic observed in experiments. The results of simulations provide the interpretation for the phenomena of contact melting and formation of diffusion zone observed in the experimen…
Low frequency quasi-localized modes of amorphous glasses appear to exhibit universal density of states, depending on the frequencies as $D(ω) \sim ω^4$. To date various models of glass formers with short range binary interaction, and network glasses with both binary and ternary interactions, were shown to conform with this law. In this paper we examine granular amorphous solids with long-range electrostatic interactions, and find that they exhibit the same law. To rationalize this wide universality class we return to a model proposed by Gurevich, Parshin and Schober (GPS) and analyze its predi…
The growth of multicomponent structures in simulations and experiments often results in kinetically trapped, nonequilibrium objects. In such cases we have no general theoretical framework for predicting the outcome of the growth process. Here we use computer simulations to study the growth of two-component structures within a simple lattice model. We show that kinetic trapping happens for many choices of growth rate and inter-component interaction energies, and that qualitatively distinct kinds of kinetic trapping are found in different regions of parameter space. In a region in which the low-…
Disordered multihyperuniform many-particle systems are exotic amorphous states that allow exquisite color sensing capabilities due to their anomalous suppression of density fluctuations for distinct subsets of particles, as recently evidenced in photoreceptor mosaics in avian retina. Motivated by this biological finding, we present the first statistical-mechanical model that rigorously achieves disordered multihyperuniform many-body systems by tuning interactions in binary mixtures of non-additive hard-disk plasmas. We demonstrate that multihyperuniformity competes with phase separation and st…
A new description of the binary fluid problem via the lattice Boltzmann method is presented which highlights the use of the moments in constructing two equilibrium distribution functions. This offers a number of benefits, including better isotropy, and a more natural route to the inclusion of multiple relaxation times for the binary fluid problem. In addition, the implementation of solid colloidal particles suspended in the binary mixture is addressed, which extends the solid-fluid boundary conditions for mass and momentum to include a single conserved compositional order parameter. A number o…
We perform particle resolved experimental studies on the heterogeneous crystallisation process of two compo- nent mixtures of hard spheres. The components have a size ratio of 0.39. We compared these with molecular dynamics simulations of homogenous nucleation. We find for both experiments and simulations that the final assemblies are interstitial solid solutions, where the large particles form crystalline close-packed lattices, whereas the small particles occupy random interstitial sites. This interstitial solution resembles that found at equilibrium when the size ratios are 0.3 [Filion et al…
We consider binary mixtures of soft repulsive spherical particles and calculate the depletion interaction between two big spheres mediated by the fluid of small spheres, using different theoretical and simulation methods. The validity of the theoretical approach, a virial expansion in terms of the density of the small spheres, is checked against simulation results. Attention is given to the approach toward the hard-sphere limit, and to the effect of density and temperature on the strength of the depletion potential. Our results indicate, surprisingly, that even a modest degree of softness in t…
The self-assembly of hard polyhedral particles confined to a flat interface is studied using Monte Carlo simulations. The particles are pinned to the interface by restricting their movement in the direction perpendicular to it while allowing their free rotations. The six different polyhedral shapes studied in this work are selected from a family of truncated cubes defined by a truncation parameter, s, which varies from cubes (s = 0) via cuboctahedra (s = 0.5) to octahedra (s = 1). Our results suggest that shapes with small values of s show square-like behavior whereas shapes with large values …
We study binary mixtures of hard particles, which exclude up to their $k$th nearest neighbors ($k$NN) on the simple cubic lattice and have activities $z_k$. In the first model analyzed, point particles (0NN) are mixed with 1NN ones. The grand-canonical solution of this model on a Husimi lattice built with cubes unveils a phase diagram with a fluid and a solid phase separated by a continuous and a discontinuous transition line which meet at a tricritical point. A density anomaly, characterized by minima in isobaric curves of the total density of particles against $z_0$ (or $z_1$), is also obser…
Much work has been devoted to analysing thermodynamic models for solid dispersions with a view to identifying regions in the phase diagram where amorphous phase separation or drug recrystallization can occur. However, detailed partial differential equation non-equilibrium models that track the evolution of solid dispersions in time and space are lacking. Hence theoretical predictions for the timescale over which phase separation occurs in a solid dispersion are not available. In this paper, we address some of these deficiencies by (i) constructing a general multicomponent diffusion model for a…
Computer simulations of the fluid-to-solid phase transition in the hard sphere system were instrumental for our understanding of crystallization processes. But while colloid experiments and theory have been predicting the stability of several binary hard sphere crystals for many years, simulations were not successful to confirm this phenomenon. Here, we report the growth of binary hard sphere crystals isostructural to Laves phases, AlB$_2$, and NaZn$_{13}$ in simulation directly from the fluid. We analyze particle kinetics during Laves phase growth using event-driven molecular dynamics simulat…
Understanding the dynamics of charge exchange between a solid surface and a liquid is fundamental to various situations, ranging from nanofiltration to catalysis and electrochemistry. Charge transfer is ultimately determined by physicochemical processes (surface group dissociation, ion adsorption, etc...) occurring in the few layers of molecules at the interface between the solid and the liquid. Unfortunately, these processes remain largely uncharted due to the experimental challenges in probing interfacial charge dynamics with sufficiently high spatial and temporal resolution. Here, we resolv…
Phase transformations can be difficult to characterize at the microscopic level due to the inability to directly observe individual atomic motions. Model colloidal systems, by contrast, permit the direct observation of individual particle dynamics and of collective rearrangements, which allows for real-space characterization of phase transitions. Here, we study a quasi-two-dimensional, binary colloidal alloy that exhibits liquid-solid and solid-solid phase transitions, focusing on the kinetics of a diffusionless transformation between two crystal phases. Experiments are conducted on a monolaye…
In this paper, a novel method for the measurement of equilibrium contact angle of highly volatile binary liquids is proposed. The proposed method, which combines finite element method and energy equilibration, is able to calculate the solid-liquid contact area. The calculated solid-liquid contact area can then be used to estimate the equilibrium contact angle. Using the proposed approach, the contact angles of binary liquid droplet on a microgrooved and smooth polycarbonate substrate were calculated. The proposed method can be an efficient tool for finding the contact angle of all liquids (bot…
It was recently shown that the real part of the frequency-dependent fluidity for several glass-forming liquids of different chemistry conforms to the prediction of the random barrier model (RBM) devised for ac electrical conduction in disordered solids [S. P. Bierwirth \textit{et al.}, Phys. Rev. Lett. {\bf 119}, 248001 (2017)]. Inspired by these results we introduce a crystallization-resistant modification of the Kob-Andersen binary Lennard-Jones mixture for which the results of extensive graphics-processing unit (GPU)-based molecular-dynamics simulations are presented. We find that the low-t…
We present a phase field theory for binary crystal nucleation. In the one-component limit, quantitative agreement is achieved with computer simulations (Lennard-Jones system) and experiments (ice-water system) using model parameters evaluated from the free energy and thickness of the interface. The critical undercoolings predicted for Cu-Ni alloys accord with the measurements, and indicate homogeneous nucleation. The Kolmogorov exponents deduced for dendritic solidification and for "soft-impingement" of particles via diffusion fields are consistent with experiment.
Using dynamical density functional theory we calculate the speed of solidification fronts advancing into a quenched two-dimensional model fluid of soft-core particles. We find that solidification fronts can advance via two different mechanisms, depending on the depth of the quench. For shallow quenches, the front propagation is via a nonlinear mechanism. For deep quenches, front propagation is governed by a linear mechanism and in this regime we are able to determine the front speed via a marginal stability analysis. We find that the density modulations generated behind the advancing front hav…
We present results from Langevin dynamics simulations of a glassy active-passive mixture of soft-repulsive binary colloidal disks. Activity on the smaller particles is applied according to the quorum sensing scheme, in which a smaller particle will be active for a persistence time if its local nearest neighbors are equal to or greater than a certain threshold value. We start with a passive glassy state of the system and apply activity to the smaller particles, which shows a nonmonotonous glassy character of the active particles with the persistence time of the active force, from its passive li…
We report on the results of a molecular dynamics simulation study of binodal glassy systems, formed in the process of isochoric rapid quenching from a high-temperature fluid phase. The transition to vitreous state occurs due to concurrent spinodal decomposition and solidification of the matter. The study is focused on topographies of the porous solid structures and their dependence on temperature and average density. To quantify the pore-size distributions, we put forth a scaling relation that provides a robust data collapse in systems with high porosity. We also find that the local density of…
Simulations are used to determine the effect of inertia on athermal shear of a two-dimensional binary Lennard-Jones glass. In the quasistatic limit, shear occurs through a series of rapid avalanches. The distribution of avalanches is analyzed using finite-size scaling with thousands to millions of particles. Inertia takes the system to a new underdamped universality class rather than driving the system away from criticality. Scaling exponents are determined for the underdamped and overdamped limits and a critical damping that separates the two regimes. Systems are in the overdamped universalit…
We show that molecular dynamics simulations can furnish useful boundary conditions at a solid surface bounding a two-component fluid. In contrast to some previous reports, convective-diffusive flow is consistent with continuum equations down to atomic scales. However, concentration gradients can produce flow without viscous dissipation that is inconsistent with the commonly used Navier slip condition. Also, differential wetting of the two components coupled to a concentration gradient can drive convective flows that could be used to make nano-pumps or motors.
We review recent work on the phase behaviour of binary charged sphere mixtures as a function of particle concentration and composition. Both size ratios and charge ratios are varied over a wide range. By contrast to hard spheres the long ranged Coulomb interaction stabilizes the crystal phase at low particle concentrations and shifts the occurrence of amorphous solids to particle concentrations considerably larger than the freezing concentration. Depending on size- and charge ratios we observe upper azeotrope, spindle, lower azeotrope and eutectic types of phase diagrams, all known well from m…
We study low-salt, binary aqueous suspensions of charged colloidal spheres of size ratio Phi = 0.57, number densities below the eutectic number density n_E, and number fractions of p = 1.00-0.40. The typical phase obtained by solidification from a homogeneous shear-melt is a substitutional alloy of body centred cubic structure. In strictly gas-tight vials, the polycrystalline solid is stable against melting and further phase transformation for extended times. For comparison, we prepare the same samples also by slow and mechanically undisturbed deionization in commercial slit cells. These cells…
In superionic compounds one component pre-melts providing high ionic conductivity to solid state electrolytes. Here, we find sublattice melting in colloidal crystals of oppositely charged particles that are highly asymmetric in size and charge in salt solutions. The small particles in ionic compounds melt when the temperature increases forming a superionic phase. These delocalized small particles in a crystal of large oppositely charged particles, in contrast to superionic phases in atomic systems, form crystals with non-electroneutral stoichiometric ratios. This generates structures with mult…
This work presents a consistent formulation of the structural phase-field-crystal model of substitutional binary alloys that allows for the description phases of unequal densities, a key feature in solidification. We further develop the dynamics of the model to be consistent with conserved Langevine dynamics in the true governing species densities. Additionally, this work expands on the ability to control pressure, so far only implemented in pure materials, to binary alloys by improving the control system that controls pressure from previous work. We study the equilibrium properties of the new…
