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Leveraging the anisotropic shape of DNA-functionalized nanoparticles holds potential for shape-directed crystallization of a wide collection of superlattice structures. Using coarse-grained molecular dynamics simulations, we study the self-assembly of a binary mixture of cubic gold nanoparticles, which are functionalized by complementary DNA strands. We observe the spontaneous self-assembly of simple cubic (SC), plastic body-centered tetragonal (pBCT), and compositionally disordered plastic body-centered tetragonal (d-pBCT) phases due to hybridization of the DNA strands. We systematically investigate the effect of length, grafting density, as well as rigidity of the DNA strands on the self-assembly behavior of cubic nanoparticles. We measure the potential of mean force between DNA-functionalized nanocubes for varying rigidity of the DNA strands and DNA lengths. Using free-energy calculations, we find that longer and flexible DNA strands can lead to a phase transformation from SC to the pBCT phase due to a gain in entropy arising from the orientational degrees of freedom of the nanocubes in the pBCT phase. Our results may serve as a guide for self-assembly experiments on DNA-functionalized cubic nanoparticles.

In continuation of our work in [A.P. Gantapara et al., Phys. Rev. Lett. 111, 015501 (2013)], we investigate here the thermodynamic phase behavior of a family of truncated hard cubes, for which the shape evolves smoothly from a cube via a cuboctahedron to an octahedron. We used Monte Carlo simulations and free-energy calculations to establish the full phase diagram. This phase diagram exhibits a remarkable richness in crystal and mesophase structures, depending sensitively on the precise particle shape. In addition, we examined in detail the nature of the plastic crystal (rotator) phases that appear for intermediate densities and levels of truncation. Our results allow us to probe the relation between phase behavior and building-block shape and to further the understanding of rotator phases. Furthermore, the phase diagram presented here should prove instrumental for guiding future experimental studies on similarly-haped nanoparticles and the creation of new materials., Comment: 19 pages, 12 figures

We study the effective interactions, structure, and the isothermal compressibility of a binary mixture interacting with pairwise additive pair potentials. By integrating out the degrees of freedom of species 2 in the partition sum we first show that a binary mixture can be mapped formally onto an effective one-component system with an effective Hamiltonian consisting of a structure-independent term, which contributes to the total pressure and chemical potential of the system, but does not affect the phase behavior, and a structure-dependent potential of mean force, which contains pair–, triplet–, and higher–body interactions. We then show that the 1-1 structure factor and pair correlation function, and the total isothermal compressibility of the mixture are equal to those of the effective one-component system, provided the mapping is exact. We illustrate and confirm these results by calculating the structure factors and pair correlation functions of the binary Asakura–Oosawa model, which is a simple model for colloid–polymer mixtures, and those of the corresponding one-component system for a size ratio such that the mapping onto an effective one-component Hamiltonian with a strictly pairwise potential of mean force is exact. The distinction between the osmotic and total compressibility of the mixture is emphasized.

We report computer simulations in the Grand canonical ensemble of a system of several alkanes between two solid surfaces. We computed the solvation force exerted by the fluid on the plates. The solvation force for linear decane oscillates with distance with a periodicity close to the width of the molecules. The branched alkanes ~2-methylundecane and 2-methylheptane! show a similar oscillatory behavior, however the oscillations are decreased and are shifted to the attractive regime. In addition, we computed the liquid-vapour equilibria by using Gibbs ensemble Monte-Carlo simulations of n-pentane confined in a slit of 9, 13, 17 Å. The critical temperature of the liquid-vapour coexistence shifts to lower temperatures upon confining. At a plate separation of 5 Å, no liquid-vapour equilibrium is found.

We use computer simulations to investigate the crystallization dynamics of sedimenting hard spheres in large systems (hundreds of thousands of particles). We show that slow sedimentation results primarily in face-centered cubic (fcc) stacked crystals, instead of random hexagonal close packed or hexagonal close packed (hcp) crystals. We also find slanted stacking faults, in the fcc regions. However, we attribute the formation of fcc to the free energy difference between fcc and hcp and not to the presence of these slanted stacking faults. Although the free energy difference between hcp and fcc per particle is small (only 10(-3) times the thermal energy), it can become considerable, when multiplied by the number of particles in each domain. The ratio of fcc to hcp obtained from dynamic simulations is in excellent agreement with well-equilibrated Monte Carlo simulations, in which no slanted stacking faults were found. Our results explain a range of experiments on colloids, in which the amount of fcc increases upon lowering the sedimentation rate or decreasing the initial volume fraction.

In this paper we examine the phase behavior of the Weeks–Chandler–Andersen (WCA) potential with β� = 40. Crystal nucleation in this model system was recently studied by Kawasaki and Tanaka [Proc. Natl. Acad. Sci. U.S.A. 107, 14036 (2010)], who argued that the computed nucleation rates agree well with experiment, a finding that contradicted earlier simulation results. Here we report an extensive numerical study of crystallization in the WCA model, using three totally different techniques (Brownian dynamics, umbrella sampling, and forward flux sampling). We find that all simulations yield essentially the same nucleation rates. However, these rates differ significantly from the values reported by Kawasaki and Tanaka and hence we argue that the huge discrepancy in nucleation rates between simulation and experiment persists. When we map the WCA model onto a hard-sphere system, we find good agreement between the present simulation results and those that had been obtained for hard spheres [L. Filion, M. Hermes, R. Ni, and M. Dijkstra, J. Chem. Phys. 133, 244115 (2010); S. Auer and D. Frenkel, Nature 409, 1020 (2001)]. © 2011 American Institute of Physics.

We study by computer simulations the stability of various crystal structures in a binary mixture of large and small spheres interacting either with a hard sphere or a screened-Coulomb potential. In the case of hard-core systems, we consider structures that have atomic prototypes CrB, gammaCuTi, alphaIrV, HgBr2, AuTe2, Ag2Se and the Laves phases (MgCu2, MgNi2, and MgZn2) as well as a structure with space group symmetry 74. By utilizing Monte Carlo simulations to calculate Gibbs free energies, we determine composition versus pressure and constant volume phase diagrams for diameter ratios of q=0.74, 0.76, 0.8, 0.82, 0.84, and 0.85 for the small and large spheres. For diameter ratios 0.76or = qor = 0.84, we find the Laves phases to be stable with respect to the other crystal structures that we considered and the fluid mixture. By extrapolating to the thermodynamic limit, we show that the MgZn2 structure is the most stable one of the Laves structures. We also calculate phase diagrams for equally and oppositely charged spheres for size ratio of 0.73 taking into consideration the Laves phases and CsCl. In the case of equally charged spheres, we find a pocket of stable Laves phases, while in the case of oppositely charged spheres, Laves phases are found to be metastable with respect to the CsCl and fluid phases.

We study the phase behavior and the interfacial tension of the screened Coulomb (Yukawa) restricted primitive model (YRPM) of oppositely charged hard spheres with diameter s using Monte Carlo simulations. We determine the gas-liquid and gas-solid phase transition using free energy calculations and grand-canonical Monte Carlo simulations for varying inverse Debye screening length k. We find that the gas-liquid phase separation is stable for k s, 17 pages, 6 Figures, accepted for publication in J. Chem. Phys

We studied the phase behavior of charged and sterically stabilized colloids using confocal microscopy in a less polar solvent (dielectric constant 5.4). Upon increasing the colloid volume fraction we found a transition from a fluid to a body centered cubic crystal at 0.0415+/-0.0005, followed by re-entrant melting at 0.1165+/-0.0015. A second crystal of different symmetry, random hexagonal close-packed, was formed at a volume fraction around 0.5, similar to that of hard spheres. We attribute the intriguing phase behavior to particle interactions that depend strongly on volume fraction, mainly due to changes in the colloid charge. In this low polarity system the colloids acquire charge through ion adsorption. The low ionic strength leads to fewer ions per colloid at elevated volume fractions and consequently a density-dependent colloid charge., Comment: 25 pages, 5 figures 1 table

We develop an efficient simulation method to study suspensions of charged spherical colloids using the primitive model. In this model, the colloids and the co- and counterions are represented by charged hard spheres, whereas the solvent is treated as a dielectric continuum. In order to speed up the simulations, we restrict the positions of the particles to a cubic lattice, which allows precalculation of the Coulombic interactions at the beginning of the simulation. Moreover, we use multiparticle cluster moves that make the Monte Carlo sampling more efficient. The simulations are performed in the semigrand canonical ensemble, where the chemical potential of the salt is fixed. Employing our method, we study a system consisting of colloids carrying a charge of 80 elementary charges and monovalent co- and counterions. At the colloid densities of our interest, we show that lattice effects are negligible for sufficiently fine lattices. We determine the fluid-solid melting line in a packing fraction eta-inverse screening length kappa plane and compare it with the melting line of charged colloids predicted by the Yukawa potential of the Derjaguin-Landau-Verwey-Overbeek theory. We find qualitative agreement with the Yukawa results, and we do not find any effects of many-body interactions. We discuss the difficulties involved in the mapping between the primitive model and the Yukawa model at high colloid packing fractions (eta0.2).

We report a numerical study of equilibrium phase-diagrams and interfacial properties of bulk and confined colloid-polymer mixtures using grand canonical Monte Carlo simulations. Colloidal particles are treated as hard spheres, while the polymer chains are described as soft repulsive spheres. The polymer-polymer, colloid-polymer, and wall-polymer interactions are described by density-dependent potentials derived by Bolhuis and Louis [Macromolecules, 35 (2002), p.1860]. We compared our results with those of the Asakura-Oosawa-Vrij model, that treats the polymers as ideal particles. We find that the number of polymers needed to drive the demixing transition is larger for the interacting polymers, and that the gas-liquid interfacial tension is smaller. When the system is confined between two parallel hard plates, we find capillary condensation. Compared with the AOV model, we find that the excluded volume interactions between the polymers suppress capillary condensation. In order to induce capillary condensation, smaller undersaturations and smaller plate separations are needed in comparison with ideal polymers., Comment: 9 pages, 10 figures, accepted for publication in the J. Chem. Phys

We study the phase behavior of a mixture of colloidal hard rods with a length-to-diameter ratio of L/sigma(c)=5 and nonadsorbing ideal polymer. We map our binary mixture onto an effective one-component system by integrating out the degrees of freedom of the polymer coils. We derive a formal expression for the exact effective Hamiltonian of the colloidal rods, i.e., it includes all effective many-body interactions and it is related to the exact free volume available for the polymer. We determine numerically on a grid the free volume available for the ideal polymer coils "on the fly" for each colloidal rod configuration during our Monte Carlo simulations. This allows us to go beyond first-order perturbation theory, which employs the pure hard-rod system as reference state. We perform free energy calculations for the isotropic, nematic, smectic, and crystal phase using thermodynamic integration and common tangent constructions are used at fixed polymer fugacities to map out the phase diagram. The phase behavior is determined for size ratios q=sigma(p)/sigma(c)=0.15, 0.5, and 1, where sigma(p) is the diameter of the polymer coils. The phase diagrams based on the full effective Hamiltonian are compared with those obtained from first-order perturbation theory, from simulations using the effective pair potential approximation to the effective Hamiltonian, and with those based on an empiric effective depletion potential for the rods. We find that the many-body character of the effective interactions stabilizes the nematic and smectic phases for large q, while the effective pair potential description overestimates the attractive interactions and favors, hence, a broad isotropic-crystal coexistence.

The critical behavior of electrolyte mixtures was studied using grand canonical Monte Carlo simulations. Mixtures consist of large multivalent macroions and small monovalent co- and counterions. The system can be viewed as a binary mixture of macroions (with their counterions) and salt (co- and counterion pair). The primitive model description was used, in which the ions are point charges with a hard core and the solvent is treated as a uniform dielectric continuum. The grand canonical simulations are based on insertions and removals of neutral molecules: macroion with its counterions or coions and a counterion. We propose a distance biasing method that enables direct grand canonical simulations up to charge asymmetry of 10:1. We calculated the critical loci that connect the salt-free state, which consists of only macroions and counterions, with the pure salt state using mixed-field finite-size scaling with no pressure mixing. The critical parameters are determined for macroion to counterion charge asymmetries of 2:1, 3:1, and 10:1. Our results suggest that binary electrolyte mixtures are type-I mixtures, where the two components mix continuously.