Fluid-solid Coexistence Research Articles

Molecular dynamics simulations of binary sphere mixtures.

Explicit simulations of fluid mixtures of highly size-dispersed particles are constrained by numerical challenges associated with identifying pair-interaction neighbors. Recent algorithmic developments have ameliorated these difficulties to an extent, permitting more efficient simulations of systems with many large and small particles of disperse sizes. We leverage these capabilities to perform molecular dynamics simulations of binary sphere mixtures with elastically stiff particles approaching the hard sphere limit and particle size ratios of up to 50, approaching the colloidal limit. The systems considered consist of 500 large particles and up to nearly 3.6×10^{6} small particles with total particle volume fractions up to 0.51. Our simulations confirm qualitative predictions for correlations between large particles previously obtained analytically and for simulations employing effective depletion interactions, but also reveal additional insights into the near-contact structure that result from the explicit treatment of the small particle solvent. No spontaneous crystal nucleation was observed during the simulations, suggesting that nucleation rates in the fluid-solid coexistence region are too small to observe crystal nucleation for feasible simulation system sizes and timescales.

Tests of a generalized Barker-Henderson perturbation theory for the phase coexistence diagram of an anisotropic potential

The Barker-Henderson perturbation theory is used frequently to compute fluid-fluid and solid-fluid phase coexistence diagrams (PCD). A generalization of this theory for anisotropic pair potentials has been suggested recently (J. Chem. Phys. 129 , 085102 (2008)). We test the accuracy of its predictions, through comparison with the results of high statistics Gibbs Ensemble Monte Carlo simulations, for a minimal model that we introduce for anisotropic pair potential without fore-aft symmetry. Agreement is found to be less close than in previous applications of this generalized Barker-Henderson theory. We also show that our minimal model captures some essential aspects of the experimental PCDs of many simple fluids and some globular proteins. In particular the flatness of the scaled PCD around the critical point can be enhanced by increasing the value of the anisotropy parameter of our model. Quantitative predictions regarding this are compared with experimental data for lysozyme and γ IIIa-crystallin.

Spontaneous Crystallization in Systems of Binary Hard Sphere Colloids.

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 simulations with and without swap moves that speed up diffusion. The crystallization process transitions from nucleation and growth to spinodal decomposition already deep within the fluid-solid coexistence regime. Finally, we present packing fraction-size ratio state diagrams in the vicinity of the stability regions of three binary crystals.

Mean force kinetic theory applied to self-diffusion in supercritical Lennard-Jones fluids.

A new kinetic-theory-based calculation of the self-diffusion coefficient for dense supercritical Lennard-Jones fluids is presented. The mean force kinetic theory, which was recently developed for transport in dense plasmas, is applied for the calculation of diffusion in dense neutral fluids. The calculation only requires the pair distribution function, a quantity that is readily calculable from equilibrium statistical mechanics for many systems, including the Lennard-Jones fluid. The self-diffusion coefficients are compared with calculations from molecular dynamics simulations, and good agreement at high density is demonstrated, even in the vicinity of the solid-fluid coexistence line. A comparison of different kinetic models with molecular dynamics simulations demonstrates that the transport coefficients have important contributions due to particle interaction via a potential of mean force and local correlations, which increase the collision rate. The new calculations compare well to those from free-volume theory and overcome a limitation of this theory that prevents its use in systems that interact via long range monotonic potentials. It is expected that this approach will also apply to other systems, including neutral-plasma and neutral-electrolyte mixtures.

Pair correlation function and freezing transitions in a two-dimensional system of model ultrasoft colloids

Density functional theory (DFT) of freezing has been used to investigate the freezing transitions in a system of colloidal particles confined to a two-dimensional plane. The particles interact via a model Hertzian type potential of varying softness. The pair-correlation functions (PCFs) needed as input structural information in DFT are calculated by solving hypernetted chain (HNC) integral equation theory. The PCFs thus obtained have been compared with those obtained through experiment and simulations and are found to be in good qualitative agreement. We found that the PCFs are sensitive to the softness of the potential: showing splitting of pair-correlation peak in the harder case and anomalous non-monotonic density dependence in the softer case. Using the common tangent construction method, we have also proposed the fluid-triangular solid phase diagrams in the temperature-density plane. We found that the phase diagram exhibit solid-fluid coexistence region whose thickness decreases with the increasing temperature as well as with increasing softness of the potential. In the temperature and density range of our calculation, DFT fails to produce any reentrance in the phase diagram.

Thermodynamics and dynamics of two-dimensional systems with dipolelike repulsive interactions.

Thermodynamics and dynamics of a classical two-dimensional system with dipolelike isotropic repulsive interactions are studied systematically using extensive molecular dynamics (MD) simulations supplemented by appropriate theoretical approximations. This interaction potential, which decays as an inverse cube of the interparticle distance, belongs to the class of very soft long-ranged interactions. As a result, the investigated system exhibits certain universal properties that are also shared by other related soft-interacting particle systems (like, for instance, the one-component plasma and weakly screened Coulomb systems). These universalities are explored in this article to construct a simple and reliable description of the system thermodynamics. In particular, Helmholtz free energies of the fluid and solid phases are derived, from which the location of the fluid-solid coexistence is determined. The quasicrystalline approximation is applied to the description of collective modes in dipole fluids. Its simplification, previously validated on strongly coupled plasma fluids, is used to derive explicit analytic dispersion relations for the longitudinal and transverse wave modes, which compare satisfactory with those obtained from direct MD simulations in the long-wavelength regime. Sound velocities of the dipole fluids and solids are derived and analyzed.

Premelting, solid-fluid equilibria, and thermodynamic properties in the high density region based on the Lennard-Jones potential.

The Lennard-Jones potential is used to study the high density fluid and face centered cubic solid state region, including solid-fluid equilibria. Numerous thermodynamic properties are considered, elucidating the behavior of matter in this poorly studied region. The present molecular simulation results are extensively compared to the latest and most accurate equation of state models for fluid and solid phases. It is shown that current models do not cover the thermodynamics of the system adequately near the solid-fluid phase transition. Furthermore, thermodynamic stability is analyzed, indicating that published solid-fluid coexistence data may not be correct at high temperatures. Particular attention is paid to the premelting zone, a range of states close to the melting line, which is characterized by strong variations of several thermodynamic properties. Because the underlying microscopic mechanisms are not yet fully understood, it is hoped that these data may contribute to the development of a theoretical framework for describing premelting effects.

Collective modes in simple melts: Transition from soft spheres to the hard sphere limit

We study collective modes in a classical system of particles with repulsive inverse-power-law (IPL) interactions in the fluid phase, near the fluid-solid coexistence (IPL melts). The IPL exponent is varied from n = 10 to n = 100 to mimic the transition from moderately soft to hard-sphere-like interactions. We compare the longitudinal dispersion relations obtained using molecular dynamic (MD) simulations with those calculated using the quasi-crystalline approximation (QCA) and find that this simple theoretical approach becomes grossly inaccurate for n,gtrsim 20. Similarly, conventional expressions for high-frequency (instantaneous) elastic moduli, predicting their divergence as n increases, are meaningless in this regime. Relations of the longitudinal and transverse elastic velocities of the QCA model to the adiabatic sound velocity, measured in MD simulations, are discussed for the regime where QCA is applicable. Two potentially useful freezing indicators for classical particle systems with steep repulsive interactions are discussed.

On the Lennard-Jones and Devonshire theory for solid state thermodynamics

ABSTRACTThe Lennard-Jones and Devonshire theory is developed into a self-consistent scheme for essentially complete thermodynamic information. The resulting methodology is compared with molecular simulation of the Lennard-Jones system in the face-centred-cubic solid state over an excessive range of state points. The thermal and caloric equations of state are in almost perfect agreement along the entire fluid–solid coexistence lines over more than six orders of magnitude in pressure. For homogeneous densities greater than twice the solid triple point density, the theory is essentially exact for derivatives of the Helmholtz energy. However, the fluid–solid phase equilibria are in disagreement with simulation. It is shown that the theory is in error by an additive constant to the Helmholtz energy A/(NkBT). Empirical inclusion of the error term makes all fluid–solid equilibria indistinguishable from exact results. Some arguments about the origin of the error are given.

Melting upon cooling and freezing upon heating: fluid-solid phase diagram for Švejk-Hašek model of dimerizing hard spheres.

A simple model of dimerizing hard spheres with highly nontrivial fluid-solid phase behavior is proposed and studied using the recently proposed resummed thermodynamic perturbation theory for central force (RTPT-CF) associating potentials. The phase diagram has the fluid branch of the fluid-solid coexistence curve located at temperatures lower than those of the solid branch. This unusual behavior is related to the strong dependence of the system excluded volume on the temperature, which for the model at hand decreases with increasing temperature. This effect can be also seen for a wide family of fluid models with an effective interaction that combines short range attraction and repulsion at a larger distance. We expect that for sufficiently high repulsive barrier, such systems may show similar phase behavior.

Stabilizing the hexagonal close packed structure of hard spheres with polymers: Phase diagram, structure, and dynamics.

We study the phase behaviour of a binary mixture of colloidal hard spheres and freely jointed chains of beads using Monte Carlo simulations. Recently Panagiotopoulos and co-workers predicted [Nat. Commun. 5, 4472 (2014)] that the hexagonal close packed (HCP) structure of hard spheres can be stabilized in such a mixture due to the interplay between polymer and the void structure in the crystal phase. Their predictions were based on estimates of the free-energy penalty for adding a single hard polymer chain in the HCP and the competing face centered cubic (FCC) phase. Here we calculate the phase diagram using free-energy calculations of the full binary mixture and find a broad fluid-solid coexistence region and a metastable gas-liquid coexistence region. For the colloid-monomer size ratio considered in this work, we find that the HCP phase is only stable in a small window at relatively high polymer reservoir packing fractions, where the coexisting HCP phase is nearly close packed. Additionally we investigate the structure and dynamic behaviour of these mixtures.

Particle dynamics in fluids with random interactions.

We study the dynamics of particles in a multi-component 2d Lennard-Jones (LJ) fluid in the limiting case where all the particles are different (APD). The equilibrium properties of this APD system were studied in our earlier work [L. S. Shagolsem et al., J. Chem. Phys. 142, 051104 (2015).]. We use molecular dynamics simulations to investigate the statistical properties of particle trajectories in a temperature range covering both the fluid and the solid-fluid coexistence region. We calculate the mean-square displacement as well as displacement, angle, and waiting time distributions, and compare the results with those for one-component LJ fluid. As temperature is lowered, the dynamics of the APD system becomes increasingly complex, as the intrinsic difference between the particles is amplified by neighborhood identity ordering and by the inhomogeneous character of the solid-fluid coexistence region. The ramifications of our results for the analysis of protein tracking experiments in living cells are discussed.

Influences of depletion potential on vapor-liquid critical point metastability

Phase behavior of a neutral colloid dispersion is investigated based on an improved Asakura-Oosawa (AO) model. Several observations are made: (i) an increase of solvent fugacity can enlarge the fluid-solid (FS) coexistence region, and this makes fugacity become a powerful factor in tuning a vapor-liquid transition (VLT) critical point metastability. (ii) A reducing of size ratio of the solvent versus colloid particle can enlarge the FS coexistence region as well as lower the VLT critical temperature, and a combination of the two effects makes the size ratio an extremely powerful factor adjusting the VLT critical point metastability. (iii) Existence of a long-range attraction term in the effective colloid potential is not a necessary condition for occurrence of a vapor-solid transition (VST), and short-ranged oscillatory depletion potential also can induce the VST over an even broader temperature range. (iv) Sensitivity of the freezing line on the size ratio is disclosed, and one can make use of the sensitivity to prepare mono-disperse colloid of well-controlled diameter by following a fractionated crystallization scheme; moreover, broadening of the FST coexistence region by raising the solvent fugacity and/or lowering the size ratio has important implication for crystallization process.

Multiple yielding processes in a colloidal gel under large amplitude oscillatory stress.

Fatigue refers to the changes in material properties caused by repeatedly applied loads. It has been widely studied for, e.g., construction materials, but much less has been done on soft materials. Here, we characterize the fatigue dynamics of a colloidal gel. Fatigue is induced by large amplitude oscillatory stress (LAOStress), and the local displacements of the gel are measured through high-frequency ultrasonic imaging. We show that fatigue eventually leads to rupture and fluidization. We evidence four successive steps associated with these dynamics: (i) the gel first remains solid, (ii) it then slides against the walls, (iii) the bulk of the sample becomes heterogeneous and displays solid-fluid coexistence, and (iv) it is finally fully fluidized. It is possible to homogeneously scale the duration of each step with respect to the stress oscillation amplitude σ0. The data are compatible with both exponential and power-law scalings with σ0, which hints at two possible interpretations of delayed yielding in terms of activated processes or of the Basquin law. Surprisingly, we find that the model parameters behave nonmonotonically as we change the oscillation frequency and/or the gel concentration.

Classical XY model with conserved angular momentum is an archetypal non-Newtonian fluid.

We find that the classical one-dimensional XY model, with angular-momentum-conserving Langevin dynamics, mimics the non-Newtonian flow regimes characteristic of soft matter when subjected to counterrotating boundaries. An elaborate steady-state phase diagram has continuous and first-order transitions between states of uniform flow, shear-banding, solid-fluid coexistence and slip planes. Results of numerical studies and a concise mean-field constitutive relation offer a paradigm for diverse nonequilibrium complex fluids.

Impact of single-particle compressibility on the fluid-solid phase transition for ionic microgel suspensions.

We study ionic microgel suspensions composed of swollen particles for various single-particle stiffnesses. We measure the osmotic pressure π of these suspensions and show that it is dominated by the contribution of free ions in solution. As this ionic osmotic pressure depends on the volume fraction of the suspension ϕ, we can determine ϕ from π, even at volume fractions so high that the microgel particles are compressed. We find that the width of the fluid-solid phase coexistence, measured using ϕ, is larger than its hard-sphere value for the stiffer microgels that we study and progressively decreases for softer microgels. For sufficiently soft microgels, the suspensions are fluidlike, irrespective of volume fraction. By calculating the dependence on ϕ of the mean volume of a microgel particle, we show that the behavior of the phase-coexistence width correlates with whether or not the microgel particles are compressed at the volume fractions corresponding to fluid-solid phase coexistence.

Scaling of Lennard–Jones liquid elastic moduli, viscoelasticity and other properties along fluid–solid coexistence

AbstractStatic and dynamical properties of the Lennard–Jones (LJ) fluid along the fluid–solid coexistence line are determined by molecular dynamics simulation. A number of properties, such as the radial distribution function, Einstein frequency, mean force, root mean square force, and normalised time correlation functions are shown to be essentially invariant or structurally isomorphic along this line when scaled by so‐called macroscopic variables (MRU). Other quantities subject to MRU such as the potential energy, pressure and infinite frequency compressional modulus are not constant along this line of states but can be reproduced using simple formulae of the form for Roskilde fluids. The elastic moduli fall within the domain of isomorphism theory. A generalised Cauchy relationship in which the infinite frequency longitudinal modulus is proportional to the longitudinal modulus of the fluid was found to be obeyed very well for the LJ fluid phase along this coexistence line.

Fluid-solid coexistence from two-phase simulations: Binary colloidal mixtures and square well systems

Molecular dynamics simulations are performed to clarify the reasons for the disagreement found in a previous publication [G. A. Chapela, F. del Río, and J. Alejandre, J. Chem. Phys. 138(5), 054507 (2013)] regarding the metastability of liquid-vapor coexistence on equimolar charged binary mixtures of fluids interacting with a soft Yukawa potential with κσ = 6. The fluid-solid separation obtained with the two-phase simulation method is found to be in agreement with previous works based on free energy calculations [A. Fortini, A.-P. Hynninen, and M. Dijkstra, J. Chem. Phys. 125, 094502 (2006)] only when the CsCl structure of the solid is used. It is shown that when pressure is increased at constant temperature, the solids are amorphous having different structures, densities, and the diagonal components of the pressure tensor are not equal. A stable low density fluid-solid phase separation is not observed for temperatures above the liquid-vapor critical point. In addition, Monte Carlo and discontinuous molecular dynamics simulations are performed on the square well model of range 1.15σ. A stable fluid-solid transition is observed above the vapor-liquid critical temperature only when the solid has a face centered cubic crystalline structure.

Three dimensional (temperature–tension–composition) phase map of mixed DOPC–DPPC vesicles: Two solid phases and a fluid phase coexist on three intersecting planes

Mapping the phase behavior of multicomponent phospholipid membranes has been an ongoing pursuit, motivated by interest in both fundamental physics and cell function. Prior investigations addressed temperature-composition space and the features of the associated domains. The current study additionally considers membrane tension, analogous to pressure in bulk materials. Focusing on model mixed 1,2-dioleoyl-sn-glycero-3-phosphocholine and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DOPC and DPPC respectively) membranes, we examine the thermodynamic impact of tension on fluid-solid coexistence and the nature of phase-separated domains. Reported here is the 3 dimensional composition-temperature-tension phase map containing three intersecting curved surfaces. Depending on the system’s position in this 3D space, giant unilamellar vesicles containing DOPC and DPPC may exhibit, in addition to a 2-component fluid Lα phase, two different types of solid DPPC-rich domains: tracer-excluding hexagonal patches or tracer-selective stripes. The fluid phase occurs at high temperatures. At cool temperatures striped solid DPPC-rich domains coexist with the fluid at elevated tensions. These stripes occur independent of tension, at the coolest temperatures. At low tensions and intermediate temperatures, patchy solid DPPC-rich domains coexist with the Lα fluid and may persist, if kinetically trapped, at lower temperatures. We associate the striped DPPC domains with a tilt-gel (Lβ’) morphology and the hexagonal DPPC patches with a dense corrugated ripple phase (Pβ’). These assignments, based on the reported areal densities of the corrugated and tilt solids, enabled first principles estimates of the coexistence boundaries that match the experiments well, including the tension sensitivity of coexistence curves and triple-point-like features for fixed composition.

Equilibrium and non-equilibrium cluster phases in colloids with competing interactions.

The phase behavior of colloids that interact via competing interactions - short-range attraction and long-range repulsion - is studied by computer simulation. In particular, for a fixed strength and range of repulsion, the effect of the strength of an attractive interaction (ε) on the phase behavior is investigated at various colloid densities (ρ). A thermodynamically stable equilibrium colloidal cluster phase, consisting of compact crystalline clusters, is found below the fluid-solid coexistence line in the ε-ρ parameter space. The mean cluster size is found to linearly increase with the colloid density. At large ε and low densities, and at small ε and high densities, a non-equilibrium cluster phase, consisting of elongated Bernal spiral-like clusters, is observed. Although gelation can be induced either by increasing ε at constant density or vice versa, the gelation mechanism is different in either route. While in the ρ route gelation occurs via a glass transition of compact clusters, gelation in the ε route is characterized by percolation of elongated clusters. This study both provides the location of equilibrium and non-equilibrium cluster phases with respect to the fluid-solid coexistence, and reveals the dependencies of the gelation mechanism on the preparation route.