Liquid-vapor coexistence for nanoparticles of various size.

We present molecular dynamics simulations of the liquid-vapor phase coexistence of pure nanoparticle systems with three different model nanoparticle interactions. Our simulations show that the form of the interaction potential between nanoparticles strongly influences their coexistence behavior. For nanoparticles interacting with an integrated Lennard-Jones potential, the critical temperature and critical density increase with increasing particle size. In contrast, nanoparticles interacting via a Lennard-Jones potential shifted to the surface of the nanoparticle do not exhibit the expected size dependence of the phase diagram. For this model, the critical temperature decreases with increasing nanoparticle size. Similar results were observed for composite nanoparticles, with the interactions truncated at a finite distance.

Local ordering of polymer-tethered nanospheres and nanorods and the stabilization of the double gyroid phase.

We present results of Brownian dynamics simulations of tethered nanospheres and tethered nanorods. Immiscibility between tether and nanoparticle facilitates microphase separation into the bicontinuous, double gyroid structure (first reported by Iacovella et al. [Phys. Rev. E 75, 040801(R) (2007)] and Horsch et al. [J. Chem. Phys. 125, 184903 (2006)], respectively). We demonstrate the ability of these nanoparticles to adopt distinct, minimal energy local packings, in which nanospheres form icosahedral-like clusters and nanorods form splayed hexagonal bundles. These local structures reduce packing frustration within the nodes of the double gyroid. We argue that the ability to locally order into stable structures is key to the formation of the double gyroid phase in these systems.

Icosahedral packing of polymer-tethered nanospheres and stabilization of the gyroid phase.

We present results of simulations that predict the phases formed by the self-assembly of model nanospheres functionalized with a single polymer "tether," including double gyroid, perforated lamella, and crystalline bilayer phases. We show that microphase separation of the immiscible tethers and nanospheres causes confinement of the nanoparticles, which promotes local icosahedral packing that in turn stabilizes the gyroid. We present a new metric for determining the local arrangement of particles based on spherical harmonic "fingerprints," which we use to quantify the extent of icosahedral ordering.

Entropy-mediated patterning of surfactant-coated nanoparticles and surfaces.

We perform atomistic and mesoscale simulations to explain the origin of experimentally observed stripelike patterns formed by immiscible ligands coadsorbed on the surfaces of gold and silver nanoparticles. We show that when the conformational entropy gained via this morphology is sufficient, microphase-separated stripelike patterns form. When the entropic gain is not sufficient, we instead predict bulk phase-separated Janus particles. We also show corroborating experimental results that confirm our simulational predictions that stripes form on flat surfaces as well as on curved nanoparticle surfaces.

Simulation studies of self-assembly of end-tethered nanorods in solution and role of rod aspect ratio and tether length.

We present temperature versus concentration phase diagrams for "shape amphiphiles" comprised of tethered moderate and low aspect ratio rods. Simulations of moderate aspect ratio rods (first reported by Horsch et al. [Phys. Rev. Lett. 95, 056105 (2005)]) predict their self-assembly into spherical micelles with bcc order, long micelles with nematic order, a racemic mixture of hexagonally ordered chiral cylinders, two perforated phases: one with tetragonal order and one with hexagonal order, and a smectic C lamellar phase. In contrast, we predict here that small aspect ratio tethered rods self-assemble into bcc ordered spherical micelles, hexagonally ordered cylinders, and a smectic C lamellar phase. We compare and contrast the phases obtained for the two aspect ratios and examine in further detail several unusual phases. Our simulations also reveal that for moderate aspect ratio rods there is a tendency toward phases with decreasing interfacial curvature with decreasing coil size, including a double gyroid phase. In addition, we investigate the role of tether length on the assembled structures. Our results are applicable to short rod-coil block copolymers and rodlike nanoparticles with polymer tethers, and to colloidal building blocks comprised of a flexible string of colloids tethered to a rigid string of colloids, with the interactions scaled appropriately.

Self-assembly of laterally-tethered nanorods.

We report results from a computational study of laterally tethered nanorod "shape amphiphiles". Our simulations predict that the model nanorods self-assemble into stepped-ribbon-like micelles, a centered rectangular stepped-ribbon phase, and two structurally different liquid crystalline bilayer phases: one in which the bilayers have C(mm) symmetry and another in which they have P(2) symmetry. We provide a possible explanation for the transition between the two C(mm) and P(2) liquid crystalline phases.

Phase diagrams of self-assembled mono-tethered nanospheres from molecular simulation and comparison to surfactants.

We perform Brownian dynamics simulations on model 3-D systems of mono-tethered nanospheres (TNS) to study the equilibrium morphologies formed by their self-assembly in a selective solvent. We predict that in contrast to flexible amphiphiles the nanospheres are locally ordered and there is an increase in the local order with an increase in concentration or relative nanoparticle diameter. We present the temperature vs concentration phase diagram for a system of TNS and propose a dimensionless scaling factor F(v) (headgroup volume/tether volume) that allows a comparison between the morphologies formed from TNS and traditional surfactants.

Self-assembly of polymer-tethered nanorods.

We present results of molecular simulations that predict the phases formed by self-assembly of nanorods functionalized by a polymer "tether." Microphase separation of the immiscible tethers and rods coupled with the liquid crystal ordering of the rods induces the formation of a cubic phase, a smectic C phase, a tetragonally perforated lamellar phase, and a honeycomb phase; the latter two have been observed experimentally but have not been predicted. We also predict a new phase--a racemic mixture of hexagonally ordered chiral cylinders that self-assemble from these achiral building blocks.

Hydrodynamics and microphase ordering in block copolymers: are hydrodynamics required for ordered phases with periodicity in more than one dimension?

We use Brownian dynamics (BD), molecular dynamics, and dissipative particle dynamics to study the phase behavior of diblock copolymer melts and to determine if hydrodynamics is required in the formation of phases with greater than one-dimensional periodicity. We present a phase diagram for diblock copolymers predicted by BD and provide a relationship between the inverse dimensionless temperature epsilon/k(B)T and the Flory-Huggins chi parameter, allowing for a quantitative comparison between methods and to mean field predictions. Our results concerning phase behavior are in good qualitative agreement with the theoretical predictions of Matsen and Bates [M. W. Matsen and F. S. Bates, Macromolecules 29, 1091 (1996)]; however, fluctuation effects arising from finite polymer lengths substantially alter the phase boundaries. Our results pertaining to the hydrodynamics are in contrast to earlier work by Groot et al. [R. D. Groot, T. J. Madden, and D. J. Tildesley, J. Chem. Phys. 110, 9739 (1999); D. Frenkel and B. Smit, Understanding Molecular Simulation, 2nd ed. (Academic, New York, 2001)]. In particular, we obtain the hexagonal ordered cylinder phase with BD, a method that does not include hydrodynamics.