Fluid-solid Coexistence Region 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.

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.

Polydispersity effects in colloid–polymer mixtures

We study phase separation and transient gelation experimentallyin a mixture consisting of polydisperse colloids (polydispersity:≈ 6%) andnon-adsorbing polymers, where the ratio of the average size of the polymer to that of the colloid is≈ 0.062.Unlike what has been reported previously for mixtures with somewhat lower colloid polydispersity (≈ 5%), the addition of polymers does not expand the fluid–solid coexistence region. Instead, wefind a region of fluid–solid coexistence which has an approximately constant width but anunexpected re-entrant shape. We detect the presence of a metastable gas–liquid binodal,which gives rise to two-stepped crystallization kinetics that can be rationalized as theeffect of fractionation. Finally, we find that the separation into multiple coexistingsolid phases at high colloid volume fractions predicted by equilibrium statisticalmechanics is kinetically suppressed before the system reaches dynamical arrest.

Generic behavior of the hydrodynamic function of charged colloidal suspensions

We discuss the generic behavior of the hydrodynamic function H(q) and diffusion function D(q) characterizing the short-time diffusion in suspensions of charge-stabilized colloidal spheres, by covering the whole fluid regime. Special focus is given to the behavior of these functions at the freezing transition specified by the Hansen-Verlet freezing rule. Results are presented in dependence on scattering wavenumber q, effective particle charge, volume fraction, salt concentration, and particle size, by considering both the low-charge and high-charge branch solutions of static structure factors. The existence of two charge branches leads to the prediction of a re-entrant melting-freezing-melting transition for increasing particle concentration at very low salinity. A universal limiting contour line is derived for the principal peak height value of H(q), independent of particle charge and diameter, and concentration and salinity, which separates the fluid from the fluid-solid coexistence region. This line is only weakly dependent on the value of the structure factor peak height entering the Hansen-Verlet rule. A dynamic freezing criterion is derived in terms of the short-time cage diffusion coefficient, a quantity easily measurable in a scattering experiment. The higher-dimensional parameter scans underlying this study make use of the fast and highly efficient deltagamma-scheme in conjunction with the analytic rescaled mean spherical approximation input for the static structure factor. Our results constitute a comprehensive database useful to researchers performing dynamic scattering experiments on charge-stabilized dispersions.

Phase diagrams of charged colloids from thermodynamic integration

We present full phase diagrams (including solid phases) of spherical charged colloids, usingMonte Carlo sampling and thermodynamic integration of the Helmholtz free energy.Colloids and their co- and counterions are described by the primitive model forionic systems that consists of hard-spheres with central point charges, while thesolvent is taken into account solely through its dielectric constant. Two systems areconsidered: (i) a size-asymmetric system of oppositely charged spheres with size ratiosq = 0.3 and 0.5 and (ii) a charge- and size-asymmetric system with colloid chargeQ = 10 and counterionsof charge −1 in the presence of monovalent added salt. In system (i), for both size ratios, the stable solidphase is equivalent to the NaCl crystal where the oppositely charged spheres take thelattice positions of Na and Cl ions. In system (ii), the phase diagram consists of gas–liquidand fluid–solid coexistence regions. We show that added salt stabilizes the fluid phase andshrinks the fluid–solid coexistence region, in agreement with experimental and theoreticalresults.

Structural precursor to freezing: An integral equation study

Recent simulation studies have drawn attention to the shoulder which forms in the second peak of the radial distribution function of hard spheres at densities close to freezing and which is associated with local crystalline ordering in the dense fluid. We address this structural precursor to freezing using an inhomogeneous integral equation theory capable of describing local packing constraints to a high level of accuracy. The addition of a short-range attractive interaction leads to a well known broadening of the fluid-solid coexistence region as a function of attraction strength. The appearance of a shoulder in our calculated radial distribution functions is found to be consistent with the broadened coexistence region for a simple model potential, thus demonstrating that the shoulder is not exclusively a high density packing effect.

Phase behavior of hard spheres with a short-range Yukawa attraction.

The phase diagram of a system consisting of hard spheres with an attractive Yukawa interaction is computed by Monte Carlo simulations. Upon decreasing the range of attraction, we find the following scenarios: (a) a stable fluid-fluid and fluid-solid transition, a triple point with fluid-fluid-solid coexistence, and a metastable isostructural solid-solid transition (b) a fluid-fluid and isostructural solid-solid transition, which are both metastable with respect to a broad fluid-solid transition, (c) a metastable fluid-fluid transition, a stable isostructural solid-solid and fluid-solid transition and a triple point with fluid-solid-solid coexistence. Our results show that a large part of the fluid-solid coexistence region is occupied by metastable fluid-fluid and/or solid-solid coexistence regions, which has repercussions on the kinetics and on the nonequilibrium behavior of the system, such as nucleation, vitrification, and gelation.

“Sticky hard spheres” model of proteins near crystallization: A test based on the osmotic compressibility of lysozyme solutions

In order to establish a simple model of protein interparticle interaction near crystallization conditions, we have measured the osmotic compressibility of the metastable fluid phase of hen egg-white lysozyme within the fluid-solid coexistence region. Light scattering measurements were performed in an extended volume fraction range at $\mathrm{pH}=4.7$ as a function of temperature. A sufficient amount of NaCl has been added in order to severely screen the electrostatic interactions. Below 0.2 M NaCl, the system can still be kept in a metastable fluid phase for a sufficiently long time before nucleation of the crystal phase takes place. The experimental compressibility up to particle volume fractions $\ensuremath{\Phi}\ensuremath{\approx}0.23$ is compared to the theoretical expression for adhesive (``sticky'') hard spheres, and the agreement is found satisfactory. We also determined the values of the Baxter \ensuremath{\tau} adhesiveness parameter, which shows an apparent linear temperature dependence within the investigated temperature range. These results suggest that the main temperature dependence of the interparticle interaction potential is simply through the Boltzmann ${k}_{B}T$ factor.

Fluorescence microscopy of phospholipid monolayer phase transitions

Over many years, a detailed picture of the phase transitions in phospholipid monolayers at the air-water interface has been constructed from extensive studies of the force-area, viscoelastic and surface potential properties of phospholipid monolayers, yet the microscopic nature of the transitions has remaned obscure. Recent investigations have focused specifically on these aspects. Through the use of fluorescence microscopy, electron diffraction and X-ray scattering experiments, in combination with data obtained by classical methods, a wealth of new information regarding the properties of monolayers undergoing phase transistions has been genrated. Direct observation of fluid-solid phase coexistence at the air-water interface has been achieved with fluorescence microscopy and on solid supports with electron miscroscopy. The fluid-solid coexistence region has been studied most thoroughly to date, but regions of gas-fluid and fluid-fluid phase coexistence have also been detected. Numerous factors govern the properties of the coexistence region; however, the promiment features can be explained in terms of a competition between forces: long-range electrostatic forces and short-range attractive forces. In this review these recent experimental findings and theoretical interpretations are summarized.