Computing absolute free energies of disordered structures by molecular simulation

We present a Monte Carlo simulation technique by which the free energy of disordered systems can be computed directly. It is based on thermodynamic integration. The central idea is to construct an analytically solvable reference system from a configuration which is representative for the state of interest. The method can be applied to lattice models (e.g., the Ising model) as well as off-lattice molecular models. We focus mainly on the more challenging off-lattice case. We propose a Monte Carlo algorithm, by which the thermodynamic integration path can be sampled efficiently. At the examples of the hard sphere liquid and a hard disk solid with a defect, we discuss several properties of the …

Polymer-induced phase separation in suspensions of bacteria

We study phase separation in suspensions of two unrelated species of rod-like bacteria, Escherichia coli and Sinorhizobium meliloti, induced by the addition of two different anionic polyelectrolytes, sodium polystyrene sulfonate or succinoglycan, the former being synthetic and the latter of natural origin. Comparison with the known behaviour of synthetic colloid-polymer mixtures and with simulations show that "depletion" (or, equivalently, "macromolecular crowding") is the dominant mechanism: exclusion of the non-adsorbing polymer from the region between two neighbouring bacteria creates an unbalanced osmotic force pushing them together. The implications of our results for understanding phe…

Polymer-induced phase separation in Escherichia coli suspensions

We studied aggregation and phase separation in suspensions of de-flagellated Escherichia coli (AB1157) in phosphate buffer induced by the anionic polyelectrolyte sodium polystyrene sulfonate. We also performed Monte Carlo simulations of this system based on the Asakura–Oosawa model of colloid–polymer mixtures. The results of these simulations, as well as comparison with previous work on synthetic colloid–polymer mixtures, demonstrate that the role of the polymer is to cause a depletion attraction between the E. coli cells. The implication of these results for understanding the role of (predominantly anionic) extracellular polymeric substances (EPS) secreted by bacteria in various natural ph…

Depletion induced isotropic-isotropic phase separation in suspensions of rod-like colloids

When non-adsorbing polymers are added to an isotropic suspension of rod-like colloids, the colloids effectively attract each other via depletion forces. We performed Monte Carlo simulations to study the phase diagram of such rod-polymer mixture. The colloidal rods were modeled as hard spherocylinders; the polymers were described as spheres of the same diameter as the rods. The polymers may overlap with no energy cost, while the overlap of polymers and rods is forbidden. Large amounts of depletant cause phase separation of the mixture. We estimated the phase boundaries of isotropic-isotropic coexistence both in the bulk and in confinement. To determine the phase boundaries we applied the gra…

Erratum: “Computing absolute free energies of disordered structures by molecular simulation” [J. Chem. Phys. 131, 231102 (2009)]

Depletion-induced percolation in networks of nanorods.

Above a certain density threshold, suspensions of rod-like colloidal particles form system-spanning networks. Using Monte Carlo simulations, we investigate how the depletion forces caused by spherical particles affect these networks in isotropic suspensions of rods. Although the depletion forces are strongly anisotropic and favor alignment of the rods, the percolation threshold of the rods decreases significantly. The relative size of the effect increases with the aspect ratio of the rods. The structural changes induced in the suspension by the depletant are characterized in detail and the system is compared to an ideal fluid of freely interpenetrable rods.

Free energies, vacancy concentrations, and density distribution anisotropies in hard-sphere crystals: A combined density functional and simulation study

We perform a comparative study of the free energies and the density distributions in hard sphere crystals using Monte Carlo simulations and density functional theory (employing Fundamental Measure functionals). Using a recently introduced technique (Schilling and Schmid, J. Chem. Phys 131, 231102 (2009)) we obtain crystal free energies to a high precision. The free energies from Fundamental Measure theory are in good agreement with the simulation results and demonstrate the applicability of these functionals to the treatment of other problems involving crystallization. The agreement between FMT and simulations on the level of the free energies is also reflected in the density distributions …

Description of hard-sphere crystals and crystal-fluid interfaces: a comparison between density functional approaches and a phase-field crystal model.

In materials science the phase field crystal approach has become popular to model crystallization processes. Phase field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic description of the system in question. We present a study on classical density functional theory in three stages of approximation leading to a specific phase field crystal model, and we discuss the limits of applicability of the models that result from these approximations. As a test system we have chosen the three--dimensional suspension of monodisperse hard spheres. The levels of density functional theory that we discuss are fundamental measure theory, a …

Controlling electrical percolation in multicomponent carbon nanotube dispersions

Carbon nanotube reinforced polymeric composites can have favourable electrical properties, which make them useful for applications such as flat-panel displays and photovoltaic devices. However, using aqueous dispersions to fabricate composites with specific physical properties requires that the processing of the nanotube dispersion be understood and controlled while in the liquid phase. Here, using a combination of experiment and theory, we study the electrical percolation of carbon nanotubes introduced into a polymer matrix, and show that the percolation threshold can be substantially lowered by adding small quantities of a conductive polymer latex. Mixing colloidal particles of different …

Computer simulation study of a liquid crystal confined to a spherical cavity.

The interplay of surface ordering and elasticity can be studied on the example of a liquid crystal confined to a cavity. We present a computer simulation study of a liquid of hard spherocylinders in a hard spherical cavity. With increasing density, first a uniaxial surface film forms and then a biaxial surface film, which eventually fills the entire cavity. We studied how the surface order, the adsorption, and the shape of the director field depend on the curvature of the wall. We find that orientational ordering at a curved wall is stronger than at a flat wall, while adsorption is weaker. For densities above the isotropic-nematic transition, we always find bipolar configurations.

Simple monoclinic crystal phase in suspensions of hard ellipsoids

We present a computer simulation study on the crystalline phases of hard ellipsoids of revolution. For aspect ratios $\ensuremath{\geqslant}3$ the previously suggested stretched-fcc phase [Frenkel and Mulder, Mol. Phys. 55, 1171 (1985)] is replaced by a different crystalline phase. Its unit cell contains two ellipsoids with unequal orientations. The lattice is simple monoclinic. The angle of inclination of the lattice, $\ensuremath{\beta}$, is a very soft degree of freedom, while the two right angles are stiff. For one particular value of $\ensuremath{\beta}$, the close-packed version of this crystal is a specimen of the family of superdense packings recently reported [Donev et al., Phys. R…

Solvent hydrodynamics speed up crystal nucleation in suspensions of hard spheres

We present a computer simulation study on the crystal nucleation process in suspensions of hard spheres, fully taking into account the solvent hydrodynamics. If the dynamics of collodial crystallization were purely diffusive, the crystal nucleation rate densities would drop as the inverse of the solvent viscosity. However, we observe that the nucleation rate densities do not scale in this way, but are enhanced at high viscosities. This effect might explain the large discrepancy between the nuclation rate densities obtained by simulation and experiment that have reported in the literature so far.

Crystallization in suspensions of hard spheres: a Monte Carlo and molecular dynamics simulation study

The crystallization of a metastable melt is one of the most important non-equilibrium phenomena in condensed matter physics, and hard sphere colloidal model systems have been used for several decades to investigate this process by experimental observation and computer simulation. Nevertheless, there is still an unexplained discrepancy between the simulation data and experimental nucleation rate densities. In this paper we examine the nucleation process in hard spheres using molecular dynamics and Monte Carlo simulation. We show that the crystallization process is mediated by precursors of low orientational bond-order and that our simulation data fairly match the experimental data sets.

Osmotic compression of droplets of hard rods: a computer simulation study

By means of computer simulations, we study how droplets of hard, rodlike particles optimize their shape and internal structure under the influence of the osmotic compression caused by the presence of spherical particles that act as depletion agents. At sufficiently high osmotic pressures, the rods that make up the drops spontaneously align to turn them into uniaxial nematic liquid-crystalline droplets. The nematic droplets or "tactoids" that are formed this way are not spherical but elongated, resulting from the competition between the anisotropic surface tension and the elastic deformation of the director field. In agreement with recent theoretical predictions, we find that sufficiently sm…

Hard-sphere fluids in annular wedges: density distributions and depletion potentials.

We analyze the density distribution and the adsorption of solvent hard spheres in an annular slit formed by two large solute spheres or a large solute and a wall at close distances by means of fundamental measure density functional theory, anisotropic integral equations and simulations. We find that the main features of the density distribution in the slit are described by an effective, two--dimensional system of disks in the vicinity of a central obstacle. For large solute--solvent size ratios, the resulting depletion force has a straightforward geometrical interpretation which gives a precise "colloidal" limit for the depletion interaction. For intermediate size ratios 5...10 and high sol…

Fluctuating Interfaces in Liquid Crystals

We review and compare recent work on the properties of fluctuating interfaces between nematic and isotropic liquid-crystalline phases. Molecular dynamics and Monte Carlo simulations have been carried out for systems of ellipsoids and hard rods with aspect ratio 15:1, and the fluctuation spectrum of interface positions (the capillary wave spectrum) has been analyzed. In addition, the capillary wave spectrum has been calculated analytically within the Landau-de Gennes theory. The theory predicts that the interfacial fluctuations can be described in terms of a wave vector dependent interfacial tension, which is anisotropic at small wavelengths (stiff director regime) and becomes isotropic at l…

Polymer Nanowires

Nucleation in suspensions of anisotropic colloids

We report Monte Carlo studies of liquid crystal nucleation in two types of anisotropic colloidal systems: hard rods and hard ellipsoids. In both cases we find that nucleation pathways differ strongly from the pathways in systems of spherical particles. Short hard rods show an effect of self-poisoning. This part of the article is based on a previous publication [T. Schilling, D. Frenkel, Self-poisoning of crystal nuclei in hard-rod liquids, Phys. Rev. Lett. 92 (2004) 085505]. When a crystallite forms, its surfaces are covered preferentially by rods which align perpendicular to the surface. Therefore subsequent growth is stunted. Hard, almost spherical ellipsoids can be compressed to very hig…

Monte Carlo Study of the Isotropic-Nematic Interface in Suspensions of Spherocylinders

The isotropic to nematic transition in suspensions of anisotropic colloids is studied by means of grand canonical Monte Carlo simulation. From measurements of the grand canonical probability distribution of the particle density, the coexistence densities of the isotropic and the nematic phase are determined, as well as the interfacial tension.

Suspensions of rod-like colloids and a depleting agent under confinement

We present a computer simulation study of suspensions of rod-like colloids and a depletant in confinement to a slit-pore. Mixtures of hard spherocylinders and ideal spheres were studied by means of Monte Carlo simulations in the grand canonical ensemble. By use of finite size scaling analysis we determined the critical behaviour. In order to overcome large barriers in the free energy we applied the successive umbrella sampling method (Virnau and Muller 2004 J. Chem. Phys. 120 10925). We find that, under confinement, the critical point of gas–liquid demixing shifts to higher concentrations of rods and smaller concentrations of spheres due to the formation of an orientationally ordered surfac…

Indium-Gallium Segregation inCuInxGa1−xSe2: AnAb Initio–Based Monte Carlo Study

Thin-film solar cells with ${\mathrm{CuIn}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Se}}_{2}$ (CIGS) absorber are still far below their efficiency limit, although lab cells already reach 20.1%. One important aspect is the homogeneity of the alloy. Large-scale simulations combining Monte Carlo and density functional calculations show that two phases coexist in thermal equilibrium below room temperature. Only at higher temperatures, CIGS becomes more and more a homogeneous alloy. A larger degree of inhomogeneity for Ga-rich CIGS persists over a wide temperature range, which contributes to the observed low efficiency of Ga-rich CIGS solar cells.

Glassy dynamics in monodisperse hard ellipsoids

We present evidence from computer simulations for glassy dynamics in suspensions of monodisperse hard ellipsoids. In equilibrium, almost spherical ellipsoids show a first order transition from an isotropic phase to a rotator phase. When overcompressing the isotropic phase into the rotator regime, we observe super-Arrhenius slowing down of diffusion and relaxation, accompanied by two-step relaxation in positional and orientational correlators. The effects are strong enough for asymptotic laws of mode-coupling theory to apply. Glassy dynamics are unusual in monodisperse systems. Typically, polydispersity in size or a mixture of particle species is prerequisite to prevent crystallization. Here…

Isotropic-nematic interface in suspensions of hard rods: Mean-field properties and capillary waves

We present a study of the isotropic-nematic interface in a system of hard spherocylinders. First we compare results from Monte Carlo simulations and Onsager density functional theory for the interfacial profiles of the orientational order parameter and the density. Those interfacial properties that are not affected by capillary waves are in good agreement, despite the fact that Onsager theory overestimates the coexistence densities. Then we show results of a Monte Carlo study of the capillary waves of the interface. In agreement with recent theoretical investigations (Eur.Phys.J. E {\bf 18} 407 (2005)) we find a strongly anistropic capillary wave spectrum. For the wave-numbers accessed in o…

Isotropic-nematic interfacial tension of hard and soft rods: Application of advanced grand canonical biased-sampling techniques

Coexistence between the isotropic and the nematic phase in suspensions of rods is studied using grand canonical Monte Carlo simulations with a bias on the nematic order parameter. The biasing scheme makes it possible to estimate the interfacial tension gamma in systems of hard and soft rods. For hard rods with L/D=15, we obtain gamma ~ 1.4 kB T/L^2, with L the rod length, D the rod diameter, T the temperature, and kB the Boltzmann constant. This estimate is in good agreement with theoretical predictions, and the order of magnitude is consistent with experiments.

Gravity-induced liquid crystal phase transitions of colloidal platelets.

he influence of gravity on a suspension of sterically stabilized colloidal gibbsite platelets is studied. An initially isotropic-nematic biphasic sample of such a suspension develops a columnar phase on the bottom on prolonged standing. This phenomenon is described using a simple osmotic compression model. We performed Monte Carlo simulations of cut spheres with aspect ratio L/D = 1/15 and took data from the literature to supply the equations of state required for the model. We find that the model describes the observed three-phase equilibrium quite well.

Isotropic–isotropic phase separation in mixtures of rods and spheres: Some aspects of Monte Carlo simulation in the grand canonical ensemble

Abstract In this article we consider mixtures of non-adsorbing polymers and rod-like colloids in the isotropic phase, which upon the addition of polymers show an effective attraction via depletion forces. Above a certain concentration, the depletant causes phase separation of the mixture. We performed Monte Carlo simulations to estimate the phase boundaries of isotropic–isotropic coexistence. To determine the phase boundaries we simulated in the grand canonical ensemble using successive umbrella sampling [J. Chem. Phys. 120 (2004) 10925]. The location of the critical point was estimated by a finite size scaling analysis. In order to equilibrate the system efficiently, we used a cluster move…

Isotropic-nematic interface and wetting in suspensions of colloidal platelets.

We study interfacial phenomena in a colloidal dispersion of sterically stabilized gibbsite platelets, exhibiting coexisting isotropic and nematic phases separated by a sharp horizontal interface. The nematic phase wets a vertical glass wall and polarized light micrographs reveal homeotropic surface anchoring both at the free isotropic-nematic interface and at the wall. On the basis of complete wetting of the wall by the nematic phase, as found in our density functional calculations and computer simulations, we analyze the balance between Frank elasticity and surface anchoring near the contact line. Because of weak surface anchoring, the director field in the capillary rise region is uniform…

Interfacial tension of the isotropic-nematic interface in suspensions of soft spherocylinders.

The isotropic to nematic transition in a system of soft spherocylinders is studied by means of grand canonical Monte Carlo simulations. The probability distribution of the particle density is used to determine the coexistence density of the isotropic and the nematic phases. The distributions are also used to compute the interfacial tension of the isotropic--nematic interface, including an analysis of finite size effects. Our results confirm that the Onsager limit is not recovered until for very large elongation, exceeding at least L/D=40, with L the spherocylinder length and D the diameter. For smaller elongation, we find that the interfacial tension increases with increasing L/D, in agreem…

Precursor-mediated crystallization process in suspensions of hard spheres.

We report on a large scale computer simulation study of crystal nucleation in hard spheres. Through a combined analysis of real and reciprocal space data, a picture of a two-step crystallization process is supported: First dense, amorphous clusters form which then act as precursors for the nucleation of well-ordered crystallites. This kind of crystallization process has been previously observed in systems that interact via potentials that have an attractive as well as a repulsive part, most prominently in protein solutions. In this context the effect has been attributed to the presence of metastable fluid-fluid demixing. Our simulations, however, show that a purely repulsive system (that ha…

Connectivity percolation in suspensions of hard platelets

We present a study on connectivity percolation in suspensions of hard platelets by means of Monte Carlo simulation. We interpret our results using a contact-volume argument based on an effective single--particle cell model. It is commonly assumed that the percolation threshold of anisotropic objects scales as their inverse aspect ratio. While this rule has been shown to hold for rod-like particles, we find that for hard plate-like particles the percolation threshold is non-monotonic in the aspect ratio. It exhibits a shallow minimum at intermediate aspect ratios and then saturates to a constant value. This effect is caused by the isotropic-nematic transition pre-empting the percolation tran…

Periodic unmixing of a binary metallic vapor

We report on a type of surface structuring after short pulse laser ablation of a binary alloy. We observe the emergence of a concentric ring structure with changing elemental composition. The composition changes are interpreted by condensation of the ambient ablation vapor due to stress wave excitations in the ablation spot.

Solid-solid phase transition in hard ellipsoids

We present a computer simulation study of the crystalline phases of hard ellipsoids of revolution. A previous study [P. Pfleiderer and T. Schilling, Phys. Rev. E 75, 020402 (2007)]. showed that for aspect ratios a/bor=3 the previously suggested stretched-fcc phase [D. Frenkel and B. Mulder, Mol. Phys. 55, 1171 (1985)] is unstable with respect to a simple monoclinic phase with two ellipsoids of different orientations per unit cell (SM2). In order to study the stability of these crystalline phases at different aspect ratios and as a function of density we have calculated their free energies by thermodynamic integration. The integration path was sampled by an expanded ensemble method in which …