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Iacovella CR, Horsch MA, Glotzer SC
Local ordering of polymer-tethered nanospheres and nanorods
JOURNAL OF CHEMICAL PHYSICS 129, 044902
[x]
View Abstract
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.
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Keys AS and Glotzer SC
How Do Quasicrystals Grow?
Phys. Rev. Lett. 99, 235503
[x]
View Abstract
Using molecular simulations, we show that the aperiodic growth of quasicrystals is controlled by the
ability of the growing quasicrystal nucleus to incorporate kinetically trapped atoms into the solid phase with minimal rearrangement. In the system under investigation, which forms a dodecagonal quasicrystal, we show that this process occurs through the assimilation of stable icosahedral clusters by the growing quasicrystal. Our results demonstrate how local atomic interactions give rise to the long-range aperiodicity of quasicrystals.
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Vanipalli SA, Iacovella CR, Sung KE, Mukhija D, Millunchick JM, Burns MA, Glotzer SC and Solomon MJ
Fluidic Assembly and Packing of Microspheres in Confined Channels
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We study fluidic assembly and packing of spherical particles in rectilinear microchannels that are terminated by a flow constriction. First, we introduce a method for active assembly of particles in the confined microchannels by triggering a local constriction in the fluid channel using a partially closed membrane valve. This microfluidic valve allows active, on-demand particle assembly as opposed to previous passive assembly methods based on terminal channels and weirs. Second, we study the three-dimensional assembly and packing of particles against a weir in confined rectilinear microchannels. The packings result in achiral particle chains with alternating (zigzag) structure. This structure is characterized by a single, repeated bond angle whose components projected into the frame of the channel are quantified by confocal microscopy and image processing. Brownian dynamics simulation of the packing comprehensively delineates the range of bond angles possible in narrow, rectilinear microchannels as well as the complex dependence of these angles on the relative dimensions of the channel and particles. The simulations of the three-dimensional packings are accurately modeled by a compact theory based on trigonometric relationships. The experimentally measured bond angles show excellent agreement with the simulations, thereby validating the functional dependence of the achiral packing bond angles on channel dimensions. This functional relationship is immediately useful for the design of anisotropic particles by microfluidic synthesis.
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Carney RP, DeVries GA, Dubois C, Kim H, Kim JY, Singh C, Ghorai PK, Tracy JB, Stiles RL, Murray RW, Glotzer SC, Stellacci F
Size Limitations for the Formation of Ordered Striped Nanoparticles
Journal of American Chemical Society (In Press)
[x]
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Iacovella CR, Horsch MA, Glotzer SC
Local ordering of polymer-tethered nanospheres and nanorods
JOURNAL OF CHEMICAL PHYSICS 129, 044902
[x]
View Abstract
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.
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Vanipalli SA, Iacovella CR, Sung KE, Mukhija D, Millunchick JM, Burns MA, Glotzer SC and Solomon MJ
Fluidic Assembly and Packing of Microspheres in Confined Channels
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View Abstract
We study fluidic assembly and packing of spherical particles in rectilinear microchannels that are terminated by a flow constriction. First, we introduce a method for active assembly of particles in the confined microchannels by triggering a local constriction in the fluid channel using a partially closed membrane valve. This microfluidic valve allows active, on-demand particle assembly as opposed to previous passive assembly methods based on terminal channels and weirs. Second, we study the three-dimensional assembly and packing of particles against a weir in confined rectilinear microchannels. The packings result in achiral particle chains with alternating (zigzag) structure. This structure is characterized by a single, repeated bond angle whose components projected into the frame of the channel are quantified by confocal microscopy and image processing. Brownian dynamics simulation of the packing comprehensively delineates the range of bond angles possible in narrow, rectilinear microchannels as well as the complex dependence of these angles on the relative dimensions of the channel and particles. The simulations of the three-dimensional packings are accurately modeled by a compact theory based on trigonometric relationships. The experimentally measured bond angles show excellent agreement with the simulations, thereby validating the functional dependence of the achiral packing bond angles on channel dimensions. This functional relationship is immediately useful for the design of anisotropic particles by microfluidic synthesis.
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Carney RP, DeVries GA, Dubois C, Kim H, Kim JY, Singh C, Ghorai PK, Tracy JB, Stiles RL, Murray RW, Glotzer SC, Stellacci F
Size Limitations for the Formation of Ordered Striped Nanoparticles
Journal of American Chemical Society (In Press)
[x]
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Keys AS and Glotzer SC
How Do Quasicrystals Grow?
Phys. Rev. Lett. 99, 235503
[x]
View Abstract
Using molecular simulations, we show that the aperiodic growth of quasicrystals is controlled by the
ability of the growing quasicrystal nucleus to incorporate kinetically trapped atoms into the solid phase with minimal rearrangement. In the system under investigation, which forms a dodecagonal quasicrystal, we show that this process occurs through the assimilation of stable icosahedral clusters by the growing quasicrystal. Our results demonstrate how local atomic interactions give rise to the long-range aperiodicity of quasicrystals.
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Singh C, Ghorai PK, Horsch MA, Jackson AM, Larson RG, Stellacci F, Glotzer SC
Entropy-Mediated Patterning of Surfactant-Coated Nanoparticles and Surfaces
Physical Review Letters 99, 226106 (2007)
[x]
View Abstract
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 nano-
particles. 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.
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Ghorai, PK and Glotzer, SC
Molecular Dynamics Simulation Study of Self-Assembled Monolayers of Alkanethiol Surfactants on Spherical Gold Nanoparticles
J. Phys. Chem. C, 111, 15857-15862, 2007
[x]
View Abstract
Atomistic molecular dynamics (MD) simulations of self-assembled alkanethiol monolayers are performed to
investigate the ligand shell organization of homoligand surfactants on spherical gold nanoparticle surfaces as
a function of temperature, nanoparticle size, and ligand tail length. At high temperature, we show that the
ligands orient randomly with respect to the surface normal with a small tilt angle. As the temperature decreases,
the molecules order and adopt a larger tilt angle. The effects of alkanethiol tail length and nanoparticle size
on the tilt structure are also significant. At low temperature, we find the equilibrium conformation of alkanethiols
obeys the crystallographic model, whereas at high temperature the continuous model is valid. The dependence
of tilt angle on different parameters and comparison with self-assembled monolayers on flat surfaces are also
discussed.
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Striolo, A, McCabe, CM, Cummings, PT, Chan, ER and Glotzer, SC
Aggregation of POSS Monomers in Liquid Hexane: A Molecular Simulation Study
J. Phys. Chem. B, 111(42); 12248-12256 (2007)
[x]
View Abstract
Polyhedral oligomeric silsesquioxanes (POSS) are multifunctional molecules that can be employed as building
blocks to develop nanocomposite materials whose mechanical properties often improve upon those of traditional
polymeric materials. We report here molecular simulation results for the effective potential of mean force
between octamethyl POSS monomers and between POSS monomers in which one methyl group has been
substituted by a linear alkane chain of nine carbon atoms in liquid normal hexane at 300 and 400 K. The
results are discussed and compared to available data for the effective interactions between octamethyl POSS
monomers in normal hexadecane. Our results show that the effective short-ranged POSS-POSS attraction is
significantly weaker in hexane than it is in hexadecane, perhaps explaining why normal hexane is often the
solvent of choice for the preparation of POSS-containing materials. Additionally, we provide results for the
radial distribution functions between selected sites in the POSS monomers that can be used both to understand
the association between POSS monomers in solution and to parametrize coarse-grained simulation models.
Such models will be used to study the formation of POSS-containing supramolecular structures such as lamellae
or micelles that are currently not accessible by atomistic simulation and can be compared to experimental
observations.
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Glotzer SC and Solomon MJ
Anisotropy of building blocks and their assembly into complex structures
Nature Materials 6 (8): 557-562 AUG 2007
[x]
View Abstract
A revolution in novel nanoparticles and colloidal building blocks has been enabled by recent breakthroughs in particle synthesis. These new particles are poised to become the ‘atoms’ and ‘molecules’ of tomorrow’s materials if they can be successfully assembled into useful structures. Here, we discuss the recent progress made in the synthesis of nanocrystals and colloidal particles and draw analogies between these new particulate building blocks and better-studied molecules and supramolecular objects. We argue for a conceptual framework for these new building blocks based on anisotropy attributes and discuss the prognosis for future progress in exploiting anisotropy for materials design and assembly.
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Chan ER, Striolo A, McCabe C, Cummings PT, Glotzer SC
Coarse-grained force field for simulating polymer-tethered silsesquioxane self-assembly in solution
J. Chem. Phys. 127, 114102 (2007)
[x]
View Abstract
A coarse-grained model has been developed for simulating the self-assembly of nonyl-tethered polyhedral oligomeric silsesquioxane (POSS) nanoparticles in solution. A mapping scheme for groups of atoms in the atomistic molecule onto beads in the coarse-grained model was established. The coarse-grained force field consists of solvent-mediated effective interaction potentials that were derived via a structural-based coarse-graining numerical iteration scheme. The force field was obtained from initial guesses that were refined through two different iteration algorithms. The coarse-graining scheme was validated by comparing the aggregation of POSS molecules observed in simulations of the coarse-grained model to that observed in all-atom simulations containing explicit solvent. At 300 K the effective coarse-grained potentials obtained from different initial guesses are comparable to each other. At 400 K the differences between the force fields obtained from different initial guesses, although small, are noticeable. The use of a different iteration algorithm employing identical initial guesses resulted in the same overall effective potentials for bare cube corner bead sites. In both the coarse-grained and all-atom simulations, small aggregates of POSS molecules were observed with similar local packings of the silsesquioxane cages and tether conformations. The coarse-grained model afforded a savings in computing time of roughly two orders of magnitude. Further comparisons were made between the coarse-grained monotethered POSS model developed here and a minimal model developed in earlier work. The results suggest that the interactions between POSS cages are long ranged and are captured by the coarse-grained model developed here. The minimal model is suitable for capturing the local intermolecular packing of POSS cubes at short separation distances.
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Zhang ZL, Tang ZY, Kotov NA, Glotzer SC
Simulations and analysis of self-assembly of CdTe nanoparticles into wires and sheets
NANO LETTERS 7 (6): 1670-1675 JUN 2007
[x]
View Abstract
Recent experiments have reported the self-assembly of TGA- and DMAET-stabilized CdTe nanoparticles (NPs) into wires and sheets, respectively, depending upon the stabilizer used. We develop a mesoscale model based on quantum mechanical calculations and perform Monte Carlo simulations of these NPs to elucidate the conditions under which these two structures will form. We show that consideration of NP shape, directional attraction, and electrostatic interactions is key to determining the anisotropy of the NP-NP interaction and final self-assembled structures.
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Chen T, Glotzer SC
Simulation studies of a phenomenological model for elongated virus capsid formation
PHYSICAL REVIEW E 75 (5): Art. No. 051504 Part 1, MAY 2007
[x]
View Abstract
We study a phenomenological model in which the simulated packing of hard, attractive spheres on a prolate spheroid surface with convexity constraints produces structures identical to those of prolate virus capsid structures. Our simulation approach combines the traditional Monte Carlo method with a modified method of random sampling on an ellipsoidal surface and a convex hull searching algorithm. Using this approach we identify the minimum physical requirements for nonicosahedral, elongated virus capsids, such as two aberrant flock house virus particles and the prolate prohead of bacteriophage phi 29, and discuss the implication of our simulation results in the context of recent experimental findings. Our predicted structures may also be experimentally realized by the evaporation-driven assembly of colloidal spheres under appropriate conditions.
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Chen T, Zhang Z-L, Glotzer SC
Simulation studies of the self-assembly of cone-shaped particles
LANGMUIR 23 (12): 6598-6605 JUN 5 2007
[x]
View Abstract
We investigate the self-assembly of anisotropic cone-shaped particles decorated by ringlike attractive "patches". In a recent paper, we demonstrated that the self-assembled clusters, which arise due to the conical particle's anisotropic shape combined with directional attractive interactions, are precise for certain cluster sizes, resulting in a precise packing sequence of clusters of increasing sizes with decreasing cone angles (Chen et al. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 717-722). Here we explore the dependence of cluster packing on the cone angle and cooling rate and discuss the "stability" and "metastability" of the resulting structures as well as polymorphism of non-"magic-number" clusters. We investigate large clusters of cones and discuss the implication of our simulation results in the context of the Israelachvili packing rule for surfactants and a recent geometrical packing analysis on hard cones in the limit of large numbers of cones.
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Iacovella CR, Keys AS, Horsch MA, Glotzer SC
Icosahedral packing of polymer-tethered nanospheres and stabilization of the gyroid phase
PHYSICAL REVIEW E 75 (4): Art. No. 040801 Part 1, APR 2007
[x]
View Abstract
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.
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Keys AS, Abate AR, Glotzer SC, Durian DJ
Measurement of growing dynamical length scales and prediction of the jamming transition in a granular material
NATURE PHYSICS 3 (4): 260-264 APR 2007
[x]
View Abstract
Supercooled liquids and dense colloidal suspensions exhibit anomalous behaviour known as 'spatially heterogeneous dynamics' (SHD), which becomes increasingly pronounced as the system approaches the glass transition(1-3). Recently, the observation of SHD in confined granular packings under slow shear near the onset of jamming has bolstered speculation that the two transitions are related(4-6). Here, we report measurements of SHD in a system of air-driven granular beads, as a function of both density and effective temperature. On approach to jamming, the dynamics becomes progressively slower and more spatially heterogeneous. The rapid growth of timescales and dynamical length scales characterizing the heterogeneities can be described both by mode-coupling theory(7) and the Vogel - Tammann Fulcher (VTF) equation(8), such as in glass-forming liquids. The value of the control variable at the VTF transition coincides with point J (refs 9,10), the random close-packed jamming density at which all motion ceases, in analogy to a zero-temperature ideal glass transition. Our findings demonstrate further universality of the jamming concept and provide a significant step forward in the quest for a unified theory of jamming in disparate systems.
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Zhang X, Zhang Z-L, Glotzer SC
Simulation study of cyclic-tethered nanocube self-assemblies: effect of tethered nanocube architectures
NANOTECHNOLOGY 18 (11): Art. No. 115706 MAR 21 2007
[x]
View Abstract
Self-assembly of functionalized nano building blocks (NBBs) is a promising avenue for 'bottom-up' nanomaterials design. Experimental studies on functionalized polyhedral oligomeric silsesquioxane (POSS) nanocubes have revealed a wide variety of nanostructures from their assemblies. Our previous simulation studies have reproduced some of these nanostructures and predicted unusual phase behaviours imparted by the unique geometry of the nanocubes and their close packing patterns. Recent experiments further inspire us to explore the effects of tether topologies on functionalized nanocube self-assemblies. We use a simplified model and perform stochastic molecular dynamics simulations to map the morphological phase diagrams of cyclic tethered nanocubes with varying tether topology, tether number, and tether placement. Our results illustrate that the steric influence of the tethers can be manipulated to confer precise control over the self-assembled nanostructures and the phase behaviour. The novel controlling factors investigated in our study suggest new opportunities in controlling functionalized NBB self-assemblies.
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Zhang X, Zhang Z-L, Glotzer SC
Simulation study of dipole-induced self-assembly of nanocubes
JOURNAL OF PHYSICAL CHEMISTRY C 111 (11): 4132-4137 MAR 22 2007
[x]
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ecent experiments have demonstrated that nanoparticles with dipoles can self-assemble into interesting one-dimensional and two-dimensional nanostructures. In particular, nanocubes with dipoles are found to form straight nanowires and nanorings with potential applications for nanodevices. In this paper, we use a minimal model to study dipole-induced self-assembly of nanocubes with varying dipole directions, dipole strengths and both with and without face-face attractions arising from dispersive or solvophobic interactions. We reproduce the structures observed in experiments and illustrate that the self-assembled morphologies are dictated by the head-to-tail alignment of the dipoles, the orientation of the dipoles within the cubes, and the face-to-face packing of the nanocubes. Our results show how the self-assembly of dipolar nanocubes differs from that of dipolar spheres in which the only anisotropy is the dipole itself and how system parameters can be manipulated to control the assembled morphologies and the phase behavior. Our simulation model, which uses the plane separating algorithm for efficient detection of nanoparticle overlaps, can be utilized to investigate the self-assembly of other smooth, convex polyhedral-shaped nanoparticles to facilitate novel nanomaterials design.
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Chen T, Zhang Z-L, Glotzer SC
A precise packing sequence for self-assembled convex structures
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 104 (3): 717-722 JAN 16 2007
[x]
View Abstract
Molecular simulations of the self-assembly of cone-shaped particles with specific, attractive interactions are performed. Upon cooling from random initial conditions, we find that the cones self-assemble into clusters and that clusters comprised of particular numbers of cones (e.g., 4-17, 20, 27, 32, and 42) have a unique and precisely packed structure that is robust over a range of cone angles. These precise clusters form a sequence of structures at specific cluster sizes (a "precise packing sequence") that for small sizes is identical to that observed in evaporation-driven assembly of colloidal spheres. We further show that this sequence is reproduced and extended in simulations of two simple models of spheres self-assembling from random initial conditions subject to convexity constraints, including an initial spherical convexity constraint for moderate- and large-sized clusters. This sequence contains six of the most common virus capsid structures obtained in vivo, including large chiral clusters and a cluster that may correspond to several nonicosahedral, spherical virus capsids obtained in vivo. Our findings suggest that this precise packing sequence results from free energy minimization subject to convexity constraints and is applicable to a broad range of assembly processes.
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Brick CM, Chan ER, Glotzer SC, Marchal JC, Martin DC
Self-lubricating nano-ball-bearings
ADVANCED MATERIALS 19 (1): 82- JAN 8 2007
[x]
View Abstract
Friedel-Crafts alkylation of octaphenyl-octasilsesquioxane (OPS) introduces a hydrocarbon layer around the rigid OPS core (see figure). Although periodic order is maintained even in the melt, as determined from X-ray diffraction measurements, this layer provides access to low-melting solids for butyl, hexyl, octyl, and decyl substituents. Because the alkyl groups interdigitate, the butyl and hexyl melts are stable to temperatures of ca. 400 degrees C, which is ca. 100 degrees C higher than the octyl and decyl compounds.
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Horsch MA, Zhang ZL, Glotzer SC
Simulation studies of self-assembly of end-tethered nanorods in solution and role of rod aspect ratio and tether length
JOURNAL OF CHEMICAL PHYSICS 125 (18): Art. No. 184903 NOV 14 2006
[x]
View Abstract
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 [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.
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Horsch MA, Zhang ZL, Glotzer SC
Self-assembly of laterally-tethered nanorods
NANO LETTERS 6 (11): 2406-2413 NOV 8 2006
[x]
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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.
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Tang ZY, Zhang Z-L, Wang Y, Glotzer SC, Kotov NA
Self-assembly of CdTe nanocrystals into free-floating sheets
SCIENCE 314 (5797): 274-278 OCT 13 2006
[x]
View Abstract
In their physical dimensions, surface chemistry, and degree of anisotropic interactions in solution, CdTe nanoparticles are similar to proteins. We experimentally observed their spontaneous, template-free organization into free-floating particulate sheets, which resemble the assembly of surface layer (S-layer) proteins. Computer simulation and concurrent experiments demonstrated that the dipole moment, small positive charge, and directional hydrophobic attraction are the driving forces for the self-organization process. The data presented here highlight the analogy of the solution behavior of the two vastly different classes of chemical structures.
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Chan ER, Ho LC, Glotzer SC
Computer simulations of block copolymer tethered nanoparticle self-assembly
JOURNAL OF CHEMICAL PHYSICS 125 (6): Art. No. 064905 AUG 14 2006
[x]
View Abstract
We perform molecular simulations to study the self-assembly of block copolymer tethered cubic nanoparticles. Minimal models of the tethered nanoscale building blocks (NBBs) are utilized to explore the structures arising from self-assembly. We demonstrate that attaching a rigid nanocube to a diblock copolymer affects the typical equilibrium morphologies exhibited by the pure copolymer. Lamellar and cylindrical phases are observed in both systems but not at the corresponding relative copolymer tether block fractions. The effect of nanoparticle geometry on phase behavior is investigated by comparing the self-assembled structures formed by the tethered NBBs with those of their linear ABC triblock copolymer counterparts. The tethered nanocubes exhibit the conventional triblock copolymer lamellar and cylindrical phases when the repulsive interactions between different blocks are symmetric. The rigid and bulky nature of the cube induces interfacial curvature in the tethered NBB phases compared to their linear ABC triblock copolymer counterparts. We compare our results with those structures obtained from ABC diblock copolymer tethered nanospheres to further elucidate the role of cubic nanoparticle geometry on self-assembly.
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Glotzer SC, Horsch MA, Iacovella CR, Zhang ZL, Chan ER, Zhang X
Self-assembly of anisotropic tethered nanoparticle shape amphiphiles
CURRENT OPINION IN COLLOID = INTERFACE SCIENCE 10 (5-6): 287-295 DEC 2005
[x]
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The varied and exotic shapes of new nanoscale organic and inorganic building blocks provide new opportunities to engineer materials possessing specific functionality and physical properties dictated by the unique packings of these particles. We briefly review some of the current strategies for inducing the self-assembly of these building blocks focusing on one strategy in particular-the attachment of tethers to the building blocks at precise locations to create tethered nanoparticle "shape amphiphiles". We use Computer simulation to demonstrate that the resulting anisotropy imparted to nanocrystals or nanocolloids by the tethers can be used to encode simple design rules into the building blocks that ultimately result in a unique self-assembled structure. We present a general classification scheme for tethered nanoparticles wherein the anisotropy of a shape amphiphile is described by a vector comprised of one or more axes each describing a measure of anisotropy. (c) 2005 Elsevier Ltd. All rights reserved.
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Zhang ZL, Keys AS, Chen T, Glotzer SC
Self-assembly of patchy particles into diamond structures through molecular mimicry
LANGMUIR 21 (25): 11547-11551 DEC 6 2005
[x]
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Fabrication of diamond structures by self-assembly is a fundamental challenge in making three-dimensional photonic crystals. We simulate a system of model hard particles with attractive patches and show that they can self-assemble into a diamond structure from an initially disordered state. We quantify the extent to which the formation of the diamond structure can be facilitated by "seeding" the system with small diamond crystallites or by introducing a rotation interaction to mimic a carbon-carbon antibonding interaction. Cur results suggest patchy particles may serve as colloidal "atoms" and "molecules" for the bottom-up self-assembly of three-dimensional crystals.
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Zhang X, Chan ER, Glotzer SC
Self-assembled morphologies of monotethered polyhedral oligomeric silsesquioxane nanocubes from computer simulation
JOURNAL OF CHEMICAL PHYSICS 123 (18): Art. No. 184718 NOV 8 2005
[x]
View Abstract
Self-assembly of functionalized nanoscale building blocks is a promising strategy for "bottom-up" materials design. Recent experiments have demonstrated that the self-assembly of polyhedral oligomeric silsesquioxane (POSS) "nanocubes" functionalized with organic tethers can be utilized to synthesize novel materials with highly ordered, complex nanostructures. We have performed molecular simulations for a simplified model of monotethered POSS nanocubes to investigate systematically how the parameters that control the assembly process and the resulting equilibrium structures, including concentration, temperature, tether lengths, and solvent conditions, can be manipulated to achieve useful structures via self-assembly. We report conventional lamellar and cylindrical structures that are typically found in block copolymer and surfactant systems, including a thermotropic order-order transition, but with interesting stabilization of the lamellar phase caused by the bulkiness and cubic geometry of the POSS nanocubes.
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Iacovella CR, Horsch MA, Zhang Z, Glotzer SC
Phase diagrams of self-assembled mono-tethered nanospheres from molecular simulation and comparison to surfactants
LANGMUIR 21 (21): 9488-9494 OCT 11 2005
[x]
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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.
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Gebremichael Y, Vogel M, Bergroth MNJ, Starr FW, Glotzer SC
Spatially heterogeneous dynamics and the Adam-Gibbs relation in the Dzugutov liquid
JOURNAL OF PHYSICAL CHEMISTRY B 109 (31): 15068-15079 AUG 11 2005
[x]
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We perform molecular dynamics simulations of a one-component glass-forming liquid and use the inherent structure formalism to test the predictions of the Adam-Gibbs (AG) theory and to explore the possible connection between these predictions and spatially heterogeneous dynamics. We calculate the temperature dependence of the average potential energy of the equilibrium liquid and show that it obeys the Rosenfeld-Tarazona T-3/5 law for low temperature T, while the average inherent structure energy is found to be inversely proportional to temperature at low T, consistent with a Gaussian distribution of potential energy minima. We investigate the shape of the basins around the local minima in configuration space via the average basin vibrational frequency and show that the basins become slightly broader upon cooling. We evaluate the configurational entropy S-conf, a measure of the multiplicity of potential energy minima sampled by the system, and test the validity of the AG relation between S-conf and the bulk dynamics. We quantify the dynamically heterogeneous motion by analyzing the motion of particles that are mobile on short and intermediate time scales relative to the characteristic bulk relaxation time. These mobile particles move in one-dimensional "strings", and these strings form clusters with a well-defined average cluster size. The AG approach predicts that the minimum size of cooperatively rearranging regions (CRR) of molecules is inversely proportional to Sconf, and recently (Phys. Rev. Lett. 2003, 90, 085506) it has been shown that the mobile-particle clusters are consistent with the CRR envisaged by Adam and Gibbs. We test the possibility that the mobile-particle strings, rather than clusters, may describe the CRR of the Adam-Gibbs approach. We find that the strings also follow a nearly inverse relation with S-conf. We further show that the logarithm of the time when the strings and clusters are maximum, which occurs in the late-beta-relaxation regime of the intermediate scattering function, follows a linear relationship with 1/TSconf, in agreement with the AG prediction for the relationship between the configurational entropy and the characteristic time for the liquid to undergo a transition to a new configuration. Since strings are the basic elements of the clusters, we propose that strings are a more appropriate measure of the minimum size of a CRR that leads to configurational transitions. That the cluster size also has an inverse relationship with S-conf may be a consequence of the fact that the clusters are composed of strings.
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Horsch MA, Zhang ZL, Glotzer SC
Self-assembly of polymer-tethered nanorods
PHYSICAL REVIEW LETTERS 95 (5): Art. No. 056105 JUL 29 2005
[x]
View Abstract
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.
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Chan ER, Zhang X, Lee CY, Neurock M, Glotzer SC
Simulations of tetra-tethered organic/inorganic nanocube-polymer assemblies
MACROMOLECULES 38 (14): 6168-6180 JUL 12 2005
[x]
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We perform molecular simulations to study the self-assembly of tetratethered nanoparticles with a cubic geometry. We develop a minimal model of the tethered nanoscale building block (NBB) to represent a polyhedral oligomeric silsesquioxane (POSS) molecule with polymeric functionalities based on information about the molecular structure and interactions obtained from ab initio density functional theory calculations. Using this model, we explore the rich nanostructures formed from self-assembly of the NBBs and make analogies with the morphologies observed in block copolymer, surfactant, and liquid crystalline systems. On the basis of the assembled structures produced and determination of the location and nature of the order-disorder transitions in the system, we propose phase diagrams to describe the behavior of these molecules. We find that qualitative similarities exist between the phase diagrams for the tetratethered NBBs and those for block copolymer and surfactant systems.
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Bergroth MNJ, Vogel M, Glotzer SC
Examination of dynamic facilitation in molecular dynamics simulations of glass-forming liquids
JOURNAL OF PHYSICAL CHEMISTRY B 109 (14): 6748-6753 APR 14 2005
[x]
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Using data from molecular dynamics computer simulations of the one-component Dzugutov liquid and of BKS silica in metastable equilibrium supercooled states, we examine ideas introduced by Garrahan and Chandler (GC) in their dynamic facilitation (DF) model of the glass transition. Utilizing a recently introduced measure of DF, we find that DF is important for particle motion in both the supercooled Dzugutov liquid and in the BKS silica melt, that mobility propagates continuously, and that this effect becomes increasingly pronounced with decreasing T. We show that, in both systems, dynamic facilitation is strongest on the time scale of the late-beta relaxation, where clusters of highly mobile neighboring particles escaping from their cages are largest and, except for the silicon atoms in BKS silica, stringlike motion is most prominent. By comparing the two systems, we show that the temperature dependence of one measure of DF as the mode-coupling temperature is approached from high temperature is similar, once the temperature dependence of the structural relaxation time in each system is scaled out.
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Horsch MA, Iacovella CR, Zhang ZL, Glotzer SC
Self-organization of nanoscopic building blocks into ordered assemblies
Mat. Res. Soc. Symp. Proc. Vol. 818, 2004
[x]
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Glotzer SC, Horsch MA, Lamm MH, Iacovella CR, Zhang Z-L
Teaching Computational Materials Science for Nanoscale Science and Engineering
Mat. Res. Soc. Symp. Proc. Vol. 827E, 2004
[x]
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Horsch MA, Zhang ZL, Glotzer SC
Tethered Nanoparticles: A New Class of “Macromolecule” for Bio-inspired Materials
Mat. Res. Soc. Symp. Proc. Vol. EXS-1, 2004
[x]
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Vogel M, Glotzer SC
Temperature dependence of spatially heterogeneous dynamics in a model of viscous silica
PHYSICAL REVIEW E 70 (6): Art. No. 061504 Part 1, DEC 2004
[x]
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Molecular dynamics simulations are performed to study spatially heterogeneous dynamics in a model of viscous silica above and below the critical temperature of the mode coupling theory, T-MCT. Specifically, we follow the evolution of the dynamic heterogeneity as the temperature dependence of the transport coefficients shows a crossover from non-Arrhenius to Arrhenius behavior when the melt is cooled. It is demonstrated that, on intermediate time scales, a small fraction of oxygen and silicon atoms are more mobile than expected from a Gaussian approximation. These highly mobile particles form transient clusters larger than that resulting from random statistics, indicating that the dynamics are spatially heterogeneous. An analysis of the clusters reveals that the mean cluster size is maximum at times intermediate between ballistic and diffusive motion, and the maximum size increases with decreasing temperature. In particular, the growth of the clusters continues into the crossover to Arrhenius behavior for the transport coefficients. These findings imply that the structural relaxation in silica cannot be understood as a statistical bond breaking process. Although the mean cluster sizes for silica are at the lower end of the spectrum of values reported in the literature for other model liquids, we find that spatially heterogeneous dynamics in models of strong and fragile glass formers are similar on a qualitative level. However, unlike the results for fragile liquids, we show that correlated particle motion along quasi-one-dimensional, stringlike paths is of little importance for the structural relaxation in this model of silica, suggesting that stringlike motion is suppressed by the presence of a network structure. To study transient clusters of localized particles, we calculate a generalized susceptibility corresponding to the self-part of a four-point time dependent density correlation function. We find that this generalized susceptibility is maximum on the time scale of the structural relaxation, where a strong increase of the peak height indicates a growing length of spatial correlations between localized particles upon cooling. Characterizing the local structural environments of the most mobile and the most immobile particles, respectively, we show that high particle mobility is facilitated by, but not limited to, the vicinity of defects in the network structure.
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Lacevic N, Glotzer SC
Dynamical heterogeneity and jamming in glass-forming liquids
JOURNAL OF PHYSICAL CHEMISTRY B 108 (51): 19623-19633 DEC 23 2004
[x]
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The relationship between spatially heterogeneous dynamics (SHD) and jamming is studied in a glass-forming binary Lennard-Jones system via molecular dynamics simulations. It has been suggested [Phys. Rev. Lett. 2001, 86, 111](1) that the probability distribution of interparticle forces P(F) develops a peak at the glass transition temperature T-g and that the large force inhomogeneities, responsible for structural arrest in granular materials, are related to dynamical heterogeneities in supercooled liquids that form glasses. It has been further suggested that "force chains" present in granular materials may exist in supercooled liquids and may provide an order parameter for the glass transition. Our goal is to investigate the extent to which the forces experienced by particles in a glass-forming liquid are related to SHD and compare these forces to those observed in granular materials and other glass-forming systems. Our results are summarized as follows. We calculate P(F) for positive (repulsive) instantaneous forces and find no peak in P(F) at any temperature in our system, even below T-g. We also find that particles that have been localized for a long time are less likely to experience high relative force and that mobile particles experience higher relative forces at shorter time scales, indicating a correlation between pairwise forces and particle mobility. We construct force chains based on the magnitude of pairwise positive instantaneous forces. We find that force chains constructed in this manner are composed of both localized and mobile particles; therefore there is no one-to-one correspondence between force chains as defined here and locally mobile or immobile regions of the liquid. We also find that force chains do not play the same role as force chains in granular materials but may indicate a difference in the evolution of the local environment of particles with different mobility. We also discuss a possible relationship between force chains found here and the development of stringlike motion found in this and other glass-forming liquids [Phys. Rev. Lett. 1998, 80, 2338; J. Chem. Phys. 2004, 120, 4415].
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Glotzer SC, Solomon MJ, Kotov NA
Self-assembly: From nanoscale to microscale colloids
AICHE JOURNAL 50 (12): 2978-2985 DEC 2004
[x]
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Horsch MA, Zhang ZL, Iacovella CR, Glotzer SC
Hydrodynamics and microphase ordering in block copolymers: Are hydrodynamics required for ordered phases with periodicity in more than one dimension?
JOURNAL OF CHEMICAL PHYSICS 121 (22): 11455-11462 DEC 8 2004
[x]
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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 [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.
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Glotzer SC
Some assembly required
SCIENCE 306 (5695): 419-420 OCT 15 2004
[x]
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Materials science has traditionally involved the study of the self-assembly of atoms or molecules into bulk thermodynamic phases. In her Perspective, Glotzer predicts that this field will be revolutionized by new materials made from larger, more complex building blocks designed to assemble in specific ways. These building blocks allow potentially much greater control over a material's properties, enabling the design rather than the selection of materials for specific uses.
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Albano F, Lacevic N, Falk ML, Glotzer SC
Relating metallic glass mechanical properties to liquid structure
MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING 375: 671-674 Sp. Iss. SI, JUL 15 2004
[x]
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Molecular dynamics simulations indicate that the mechanical properties of a model metallic glass depend critically on the degree of supercooling attained in the liquid prior to vitrification. A well-characterized binary glass-forming system roughly analogous to ZrTi was quenched instantaneously from a series of liquid temperatures. These temperatures ranged from approximately twice that of the onset of supercooled liquid behaviour down to just above the mode-coupling temperature (T-MCT). The low-temperature mechanical properties of these glass samples is studied in simple shear at constant strain rate while the density of the system is held constant. All the glasses exhibit an initial linear response at small strain and approached a steady-state flow regime at large strain. However, glasses obtained by quenching from supercooled liquids just above T-MCT, which we will refer to as T-MCT glasses, exhibit higher shear strength and modulus than glasses obtained by quenching from higher temperature liquids. The T-MCT glasses also exhibit pronounced shear softening. The change in pressure during shear is markedly different in these glasses, and indicates that the T-MCT glasses retain aspects of the quenched-in structure out to as much as 25 train. The changes in pressure also indicate significant structural changes occur even during nearly linear stress-strain response.
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Zhang ZL, Glotzer SC
Self-assembly of patchy particles
NANO LETTERS 4 (8): 1407-1413 AUG 2004
[x]
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Molecular simulations are performed to study the self-assembly of particles with discrete, attractive interaction sites - "patches" - at prescribed locations on the particle surface. Chains, sheets, rings, icosahedra, square pyramids, tetrahedra, and twisted and staircase structures are obtained through suitable design of the surface pattern of patches'. Our simulations predict that the spontaneous formation of two-dimensional sheets and icosahedra occurs via a first-order transition while the formation of chains occurs via a continuous disorder-to-order transition as in equilibrium polymerization. Our results show how precise arrangements of patches combined with patch "recognition" or selectivity may be used to control the relative position of particles and the overall structure of particle assemblies. In this context, patchy particles represent a new class of building block for the fabrication of precise structures.
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Chen T, Lamm MH, Glotzer SC
Biomolecule-directed assembly of nanoscale building blocks studied via lattice Monte Carlo simulation
JOURNAL OF CHEMICAL PHYSICS 121 (8): 3919-3929 AUG 22 2004
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We perform lattice Monte Carlo simulations to study the self-assembly of functionalized inorganic nanoscale building blocks using recognitive biomolecule linkers. We develop a minimal coarse-grained lattice model for the nanoscale building block (NBB) and the recognitive linkers. Using this model, we explore the influence of the size ratio of linker length to NBB diameter on the assembly process and the structural properties of the resulting aggregates, including the spatial distribution of NBBs and aggregate topology. We find the constant-kernel Smoluchowski theory of diffusion-limited cluster-cluster aggregation describes the aggregation kinetics for certain size ratios.
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Vogel M, Glotzer SC
Spatially heterogeneous dynamics and dynamic facilitation in a model of viscous silica
PHYSICAL REVIEW LETTERS 92 (25): Art. No. 255901 JUN 25 2004
[x]
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We perform molecular dynamics simulations to study the structural relaxation dynamics of a model of viscous silica, the prototype of a strong glass former. We find that the melt dynamics are spatially heterogeneous regardless of whether the bulk relaxation is non-Arrhenius or Arrhenius, and cannot be understood as a statistical bondbreaking process. Further, we show that stringlike motion is suppressed by the covalent bondings, yet high particle mobility propagates continuously, supporting the concept of dynamic facilitation emphasized in recent theoretical work.
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Gebremichael Y, Vogel M, Glotzer SC
Formation of transient clusters on nanoscopic length scales in a simulated one-component supercooled liquid
MOLECULAR SIMULATION 30 (5): 281-287 APR 2004
[x]
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Dense liquids above their glass transition exhibit spatially heterogeneous dynamics in which regions within the liquid exhibit enhanced or diminished mobility relative to the average on some time scale. Substantial evidence suggests that these regions are confined to nanoscopic sizes at temperatures close to the mode coupling temperature T MCT , and reach well beyond the characteristic length scale over which the two-point static structure of the liquid is correlated. In this paper, we investigate the formation of clusters of mobile particles in a dynamically heterogeneous model liquid. We find that clusters are formed as a result of mobility propagation that begins from distributed locations confined within a nanoscopic local structure. This mobility is facilitated through the development of quasi-one dimensional string-like rearrangements within the nanoscopic region.
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Aichele M, Gebremichael Y, Starr FW, Baschnagel J, Glotzer SC
Polymer-specific effects of bulk relaxation and stringlike correlated motion in the dynamics of a supercooled polymer melt (vol 119, pg 5290, 2003)
JOURNAL OF CHEMICAL PHYSICS 120 (14): 6798-6798 APR 8 2004
[x]
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Particle rearrangements during transitions between local minima of the potential energy landscape of a binary Lennard-Jones liquid
Vogel M, Doliwa B, Heuer A, Glotzer SC
JOURNAL OF CHEMICAL PHYSICS 120 (9): 4404-4414 MAR 1 2004
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The potential energy landscape (PEL) of binary Lennard-Jones (BLJ) mixtures exhibits local minima, or inherent structures (IS), which are organized into metabasins (MBs). We study the particle rearrangements related to transitions between both successive IS and successive MB for a small 80:20 BLJ system near the mode-coupling temperature T-MCT. The analysis includes the displacements of individual particles, the localization of the rearrangements, and the relevance of string-like motion. We find that the particle rearrangements during IS and MB transitions do not change significantly at T-MCT. In particular, an onset of single particle hopping on the length scale of the interparticle distance is not observed. Further, it is demonstrated that IS and MB dynamics are spatially heterogeneous and facilitated by string-like motion. To investigate the mechanism of string-like motion, we follow the particle rearrangements during suitable sequences of IS transitions. We find that most strings observed after a series of transitions do not move coherently during a single transition, but subunits of different sizes are active at different times. Several findings suggest that, though string-like motion is of comparable relevance when the system explores a MB and when it moves from one MB to another, the occurrence of a successful string enables the system to exit a MB. Moreover, we show that the particle rearrangements during two consecutive MB transitions are basically uncorrelated. In particular, different groups of particles are highly mobile. We further find the positions of strings during successive MB transitions weakly but positively correlated, supporting the idea of dynamic facilitation. Finally, the relation between the features of the potential energy landscape and the relaxation processes in supercooled liquids is discussed.
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Gebremichael Y, Vogel M, Glotzer SC
Particle dynamics and the development of string-like motion in a simulated monoatomic supercooled liquid
JOURNAL OF CHEMICAL PHYSICS 120 (9): 4415-4427 MAR 1 2004
[x]
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The microscopic details of local particle dynamics is studied in a glass-forming one component supercooled liquid modeled by a Dzugutov potential developed for simple metallic glass formers. Our main goal is to investigate particle motion in the supercooled liquid state, and to ascertain the extent to which this motion is cooperative and occurring in quasi-one-dimesional, string-like paths. To this end we investigate in detail the mechanism by which particles move along these paths. In particular, we show that the degree of coherence-that is, simultaneous motion by consecutive particles along a string-depends on the length of the string. For short strings, the motion is highly coherent. For longer strings, the motion is highly coherent only within shorter segments of the string, which we call "microstrings." Very large strings may contain several microstrings within which particles move simultaneously, but individual microstrings within a given string are temporally uncorrelated with each other. We discuss possible underlying mechanism for this complex dynamical behavior, and examine our results in the context of recent work by Garrahan and Chandler [Phys. Rev. Lett. 89, 035704 (2002)] in which dynamic facilitation plays a central role in the glass transition.
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Glotzer SC
Nanoscale science - Complex rules for soft systems
NATURE MATERIALS 2 (11): 713-714 NOV 2003
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The nanometre scale is a brave new world for scientists — mixing materials at such small dimensions can cause all sorts of surprising effects. New studies of experimental systems on the nanoscale further our understanding of these complex phenomena.
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Zhang ZL, Horsch MA, Lamm MH, Glotzer SC
Tethered nano building blocks: Toward a conceptual framework for nanoparticle self-assembly
NANO LETTERS 3 (10): 1341-1346 OCT 2003
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We perform molecular simulations to study the self-assembly of nanoparticles functionalized with oligomeric tethers attached to specific locations on the nanoparticle surface. We demonstrate that for certain categories of tethered nano building blocks the obtained morphologies may be predicted using concepts from block copolymer microphase separation and liquid-crystal phase ordering, whereas for other categories the unique packing constraints introduced by nanoparticle geometry and by nanoparticle-tether topology lead to structures far richer than those found in conventional block copolymer, surfactant, and liquid-crystal systems. Our results suggest the potential usefulness of considering tethered nano building blocks as a new class of "macromolecule" for assembling novel materials on the nanoscale.
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Lacevic N, Starr FW, Schroder TB, Glotzer SC
Spatially heterogeneous dynamics investigated via a time-dependent four-point density correlation function
JOURNAL OF CHEMICAL PHYSICS 119 (14): 7372-7387 OCT 8 2003
[x]
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Relaxation in supercooled liquids above their glass transition and below the onset temperature of "slow" dynamics involves the correlated motion of neighboring particles. This correlated motion results in the appearance of spatially heterogeneous dynamics or "dynamical heterogeneity." Traditional two-point time-dependent density correlation functions, while providing information about the transient "caging" of particles on cooling, are unable to provide sufficiently detailed information about correlated motion and dynamical heterogeneity. Here, we study a four-point, time-dependent density correlation function g(4)(r,t) and corresponding "structure factor" S-4(q,t) which measure the spatial correlations between the local liquid density at two points in space, each at two different times, and so are sensitive to dynamical heterogeneity. We study g(4)(r,t) and S-4(q,t) via molecular dynamics simulations of a binary Lennard-Jones mixture approaching the mode coupling temperature from above. We find that the correlations between particles measured by g(4)(r,t) and S-4(q,t) become increasingly pronounced on cooling. The corresponding dynamical correlation length xi(4)(t) extracted from the small-q behavior of S-4(q,t) provides an estimate of the range of correlated particle motion. We find that xi(4)(t) has a maximum as a function of time t, and that the value of the maximum of xi(4)(t) increases steadily from less than one particle diameter to a value exceeding nine particle diameters in the temperature range approaching the mode coupling temperature from above. At the maximum, xi(4)(t) and the alpha relaxation time tau(alpha) are related by a power law. We also examine the individual contributions to g(4)(r,t), S-4(q,t), and xi(4)(t), as well as the corresponding order parameter Q(t) and generalized susceptibility chi(4)(t), arising from the self and distinct contributions to Q(t). These contributions elucidate key differences between domains of localized and delocalized particles.
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Lacevic N, Glotzer SC
Approach to the glass transition studied by higher order correlation functions
JOURNAL OF PHYSICS-CONDENSED MATTER 15 (31): S2437-S2446 AUG 13 2003
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We present a theoretical framework based on a higher order density correlation function, analogous to that used to investigate spin glasses, to describe dynamical heterogeneities in simulated glass-forming liquids. These higher order correlation functions are a four-point, time-dependent density correlation function g(4) (r,t) and a corresponding `structure factor' S-4 (q,t) which measure the spatial correlations between the local liquid density at two points in space, each at two different times. g(4) (r, t) and S-4 (q, t) were extensively studied via molecular dynamics simulations of a binary Lennard-Jones mixture approaching the mode coupling temperature from above in Franz et al (1999 Phil. Mag. B 79 1827), Donati et al (2002 J. Non-Cryst. Solids 307 215), Glotzer et al (2000 J. Client. Phys. 112 509), Lacevic et al (2002 Phys. Rev. E 66 030101), Lacevic et al (2003 J. Chem. Phys. submitted) and Lacevic (2003 Dissertation The Johns Hopkins University). Here, we examine the contribution to g(4)(r, t), S-4(q, t) and the corresponding dynamical correlation length, as well as the corresponding order parameter Q(t) and generalized susceptibility chi(4)(t), from localized particles. We show that the dynamical correlation length xi(4)(ss)(t) of localized particles has a maximum as a function of time t, and the value of the maximum of xi(4)(ss)(t) increases steadily in the temperature range approaching the mode coupling temperature from above.
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Lamm MH, Chen T, Glotzer SC
Simulated assembly of nanostructured organic/inorganic networks
NANO LETTERS 3 (8): 989-994 AUG 2003
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We perform lattice Monte Carlo simulations to study nanostructured networks formed by linking organically functionalized inorganic nanoscale building blocks. We develop a minimal lattice model of an octafunctional nanoscale building block (NBB) by representing the inorganic core with a rigid cube and the organic linkers with "bead-spring" chains. Using this model, we explore the effect of linker length on network properties including porosity, spatial distribution of NBBs, and extent of cross-linking during assembly. We compare our results with recent experimental data on networks of octafunctional polyhedral oligomeric silsesquioxane (POSS) cubes.
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Aichele M, Gebremichael Y, Starr FW, Baschnagel J, Glotzer SC
Polymer-specific effects of bulk relaxation and stringlike correlated motion in the dynamics of a supercooled polymer melt
JOURNAL OF CHEMICAL PHYSICS 119 (10): 5290-5304 SEP 8 2003
[x]
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We analyze dynamical heterogeneities in a simulated "bead-spring" model of a nonentangled, supercooled polymer melt. We explore the importance of chain connectivity on the spatially heterogeneous motion of the monomers. We find that when monomers move, they tend to follow each other in one-dimensional paths, forming strings as previously reported in atomic liquids and colloidal suspensions. The mean string length is largest at a time close to the peak time of the mean cluster size of mobile monomers. This maximum string length increases, roughly in an exponential fashion, on cooling toward the critical temperature T-MCT of the mode-coupling theory, but generally remains small, although large strings involving ten or more monomers are observed. An important contribution to this replacement comes from directly bonded neighbors in the chain. However, mobility is not concentrated along the backbone of the chains. Thus, a relaxation mechanism in which neighboring mobile monomers along the chain move predominantly along the backbone of the chains, seems unlikely for the system studied.
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Starr FW, Douglas JF, Glotzer SC
Origin of particle clustering in a simulated polymer nanocomposite and its impact on rheology
JOURNAL OF CHEMICAL PHYSICS 119 (3): 1777-1788 JUL 15 2003
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Many nanoparticles have short-range interactions relative to their size, and these interactions tend to be "patchy" since the interatomic spacing is comparable to the nanoparticle size. For a dispersion of such particles, it is not a priori obvious what mechanism will control the clustering of the nanoparticles, and how the clustering will be affected by tuning various control parameters. To gain insight into these questions, we perform molecular dynamics simulations of polyhedral nanoparticles in a dense bead-spring polymer melt under both quiescent and steady shear conditions. We explore the mechanism that controls nanoparticle clustering and find that the crossover from dispersed to clustered states is consistent with the predictions for equilibrium particle association or equilibrium polymerization, and that the crossover does not appear to match the expectations for first-order phase separation typical for binary mixtures in the region of the phase diagram where we can equilibrate the system. At the same time, we cannot rule out the possibility of phase separation at a lower temperature. Utilizing the existing framework for dynamic clustering transitions offers the possibility of more rationally controlling the dispersion and properties of nanocomposite materials. Finally, we examine how nanocomposite rheology depends on the state of equilibrium clustering. We find that the shear viscosity for dispersed configurations is larger than that for clustered configurations, in contrast to expectations based on macroscopic colloidal dispersions. We explain this result by the alteration of the polymer matrix properties in the vicinity of the nanoparticles. We also show that shear tends to disperse clustered nanoparticle configurations in our system, an effect particularly important for processing.
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Glotzer SC, Gebremichael Y, Lacevic N, Schroder TB, Starr FW
Spatially heterogeneous dynamics in liquids near their glass transition
LIQUID DYNAMICS: EXPERIMENT, SIMULATION, AND THEORY ACS SYMPOSIUM SERIES 820: 214-227 2002
[x] Liquids near their glass transition are dynamically heterogeneous, and experiments and simulations have uncovered much about the rich and complex nature of this heterogeneity. This paper highlights key results from our computer simulation studies of spatially heterogeneous dynamics (SHD) in supercooled liquids near their glass transtion. We speculate on the relationship between SHD and other phenomena ubiquitous to glasses and their liquids, and outline several outstanding questions in this Field.
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Mallamace F, Glotzer SC, Malescio G, Poole PH, Salvetti G
Horizons in complex systems - In honor of Professor H. Eugene Stanley on the occasion of his 60th birthday - Preface
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 314 (1-4): XV- NOV 1 2002
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Lacevic N, Starr FW, Schroder TB, Novikov VN, Glotzer SC
Growing correlation length on cooling below the onset of caging in a simulated glass-forming liquid
PHYSICAL REVIEW E 66 (3): Art. No. 030101 Part 1, SEP 2002
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We present a calculation of a fourth-order, time-dependent density correlation function that measures higher-order spatiotemporal correlations of the density of a liquid. From molecular dynamics simulations of a glass-forming Lennard-Jones liquid, we find that the characteristic length scale of this function has a maximum as a function of time which increases steadily beyond the characteristic length of the static pair correlation function g(r) in the temperature range approaching the mode coupling temperature from above. This length scale provides a measure of the spatially heterogeneous nature of the dynamics of the liquid in the alpha-relaxation regime.
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Starr FW, Sastry S, Douglas JF, Glotzer SC
What do we learn from the local geometry of glass-forming liquids?
PHYSICAL REVIEW LETTERS 89 (12): Art. No. 125501 SEP 16 2002
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We examine the local geometry of a simulated glass-forming polymer melt. Using the Voronoi construction, we find that the distributions of Voronoi volume P(u(v)) and asphericity P(a) appear to be universal properties of dense liquids, supporting the use of packing approaches to understand liquid properties. We also calculate the average free volume [u(f)] along a path of constant density and find that [u(f)] extrapolates to zero at the same temperature T-0 that the extrapolated relaxation time diverges. We relate [u(f)] to the Debye-Waller factor, which is measurable by neutron scattering.
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Donati C, Franz S, Glotzer SC, Parisi G
Theory of non-linear susceptibility and correlation length in glasses and liquids
JOURNAL OF NON-CRYSTALLINE SOLIDS 307: 215-224 SEP 2002
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Within the framework of the effective potential theory of the structural glass transition, we calculate for the p-spin model and for a hard sphere liquid in the hypernetted chain approximation a static non-linear susceptibility related to a four-point density correlation function, and show that it diverges in mean field with exponent gamma = 1/2 as the critical temperature T-c is approached from below. When T-c is approached from above, we calculate for the p-spin model a time dependent non-linear susceptibility and show that there is a characteristic time where this susceptibility has a maximum, and that this time grows with decreasing T. This susceptibility diverges as T-c is approached from above, and has key features in common with a generalized susceptibility related to particle displacements, previously introduced to measure correlated particle motion in simulations of glass-forming liquids.
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Glotzer SC, Paul W
Molecular and mesoscale simulation methods for polymer materials
ANNUAL REVIEW OF MATERIALS RESEARCH 32: 401-436 2002
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Polymers offer a wide spectrum of possibilities for materials applications, in part because of the chemical complexity and variability of the constituent molecules, and in part because they can be blended together with other organic as well as inorganic components. The majority of applications of polymeric materials is based on their excellent mechanical properties, which arise from the long-chain nature of the constituents. Microscopically, this means that polymeric materials are able to respond to external forces in a broad frequency range, i.e., with a broad range of relaxation processes. Computer simulation methods are ideally suited to help to understand these processes and the structural properties that lead to them and to further our ability to predict materials properties and behavior. However, the broad range of timescales and underlying structure prohibits any one single simulation method from capturing all of these processes. This manuscript provides an overview of some of the more popular computational models and methods used today in the field of molecular and mesoscale simulation of polymeric materials, ranging from molecular models and methods that treat electronic degrees of freedom to mesoscopic field theoretic methods.
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Glotzer SC, Gebremichael Y, Lacevic N, Schroder TB, Starr FW
Glass-forming liquids and polymers: with a little help from computational statistical physics
COMPUTER PHYSICS COMMUNICATIONS 146 (1): 24-29 JUN 15 2002
[x]
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Starr FW, Schroder TB, Glotzer SC
Molecular dynamics simulation of a polymer melt with a nanoscopic particle
MACROMOLECULES 35 (11): 4481-4492 MAY 21 2002
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We perform molecular dynamics simulations of a bead-spring polymer melt surrounding a nanoscopic particle. We explore the effect of the polymer/nanoparticle interactions, surface-to-volume ratio, and boundary conditions on both the structure and dynamics of the polymer melt. We find that the chains near the nanoparticle surface are elongated and flattened and that this effect is independent of the interaction for the range of interactions we study. We show that the glass transition temperature T-g of the melt can be shifted to either higher or lower temperatures by tuning the interactions between polymer and nanoparticle. A gradual change of the polymer dynamics approaching the nanoparticle surface causes the change in the glass transition. The magnitude of the shift is exaggerated by increasing fraction of surface monomers in the system. These behaviors support a "many-layer"-based interpretation of the dynamics. Our findings appear applicable to systems in which surface interactions dominate, including both traditional and nanofilled polymer melts, as well as systems with markedly different geometries, such as ultrathin polymer films. In particular, we show how our results might be compared with those obtained from experimental studies of "bound" polymer.
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Glotzer SC
Colloids reinforce glass theory
PHYSICS WORLD 13 (4): 22-23 APR 2000
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Glotzer SC
Spatially heterogeneous dynamics in liquids: insights from simulation
JOURNAL OF NON-CRYSTALLINE SOLIDS 274 (1-3): 342-355 SEP 2000
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In this paper, review of recent theoretical and simulation work on dynamical heterogeneity and correlated particle motion in glass-forming liquids and polymers is presented. Evidence for increasing mobility fluctuations in these systems with decreasing temperature, and the relationship between dynamical heterogeneity and decoupling of diffusion and structural relaxation is described. The relationship between dynamical heterogeneity, string-like collective motion, the clustering of strings, and mode-coupling theory is briefly discussed. (C) 2000 Elsevier Science B.V. All rights reserved.
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Franz S, Glotzer SC, Sastry S
Special issue containing articles from the ICTP-NIS Conference on 'Unifying concepts in glass physics', - 15-18 September 1999, Trieste, Italy - Preface
JOURNAL OF PHYSICS-CONDENSED MATTER 12 (29): U3-U3 JUL 24 2000
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Glotzer SC, Jans N, Poole PH
The potential energy landscape of the /- J Ising spin glass
JOURNAL OF PHYSICS-CONDENSED MATTER 12 (29): 6675-6682 JUL 24 2000
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We calculate 'inherent structures' (configurations corresponding to local potential energy minima) in the /- J Ising spin glass over a wide range of temperature T in two and three dimensions. We find that the T-dependence of the average value of the inherent-structure energy E is strikingly similar to that shown recently for a glass-forming liquids. E decreases with T only weakly at high T, bur begins to decrease much more rapidly as the spin-glass transition temperature T-sg is approached. As in the liquid, we find that the rapid decrease of E with decreasing T occurs in the regime of T in which the relaxation of the spin autocorrelation function becomes increasingly non-exponential. In addition, we show that the inherent structures of the spin glass can be used to identify clusters of strongly correlated 'frozen' spins, and that an incipient percolating cluster of these spins appears (within numerical error) at T = T-sg.
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Schroder TB, Sastry S, Dyre JC, Glotzer SC
Crossover to potential energy landscape dominated dynamics in a model glass-forming liquid
JOURNAL OF CHEMICAL PHYSICS 112 (22): 9834-9840 JUN 8 2000
[x]
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An equilibrated model glass-forming liquid is studied by mapping successive configurations produced by molecular dynamics simulation onto a time series of inherent structures (local minima in the potential energy). Using this "inherent dynamics" approach we find direct numerical evidence for the long held view that below a crossover temperature, T-x, the liquid's dynamics can be separated into (i) vibrations around inherent structures and (ii) transitions between inherent structures [M. Goldstein, J. Chem. Phys. 51, 3728 (1969)], i.e., the dynamics become "dominated" by the potential energy landscape. In agreement with previous proposals, we find that T-x is within the vicinity of the mode-coupling critical temperature T-c. We further find that near T-x, transitions between inherent structures occur via cooperative, stringlike rearrangements of groups of particles moving distances substantially smaller than the average interparticle distance.
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Glotzer SC, Novikov VN, Schroder TB
Time-dependent, four-point density correlation function description of dynamical heterogeneity and decoupling in supercooled liquids
JOURNAL OF CHEMICAL PHYSICS 112 (2): 509-512 JAN 8 2000
[x]
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Dynamical heterogeneity and the decoupling of diffusion and relaxation in a supercooled liquid is investigated via a time-dependent, four-point density correlation function. We show that the main contribution to the corresponding generalized susceptibility chi(4)(t) in a molecular dynamics simulation of a Lennard-Jones liquid arises from spatial correlations between temporarily localized ("caged") particles. By comparing chi(4)(t) with a generalized susceptibility chi(M)(t) related to a correlation function for the squared particle displacements, we demonstrate a connection between dynamical heterogeneity and the decoupling of relaxation and diffusion.
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Franz S, Donati C, Parisi G, Glotzer SC
On dynamical correlations in supercooled liquids
PHILOSOPHICAL MAGAZINE B-PHYSICS OF CONDENSED MATTER STATISTICAL MECHANICS ELECTRONIC OPTICAL AND MAGNETIC PROPERTIES 79 (11-12): 1827-1831 NOV-DEC 1999
[x] We show how the growth of a dynamical correlation length and its associated susceptibility recently observed by the present authors and co-workers as T-c is approached can be understood in an appropriate theoretical framework. We discuss some predictions for these quantities in the region below T-c which have not yet been explored in numerical simulations.
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Allegrini P, Douglas JF, Glotzer SC
Dynamic entropy as a measure of caging and persistent particle motion in supercooled liquids
PHYSICAL REVIEW E 60 (5): 5714-5724 Part B, NOV 1999
[x]
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The length-scale dependence of the dynamic entropy is studied in a molecular dynamics simulation of a binary Lennard-Jones liquid above the mode-coupling critical temperature T-c. A number of methods exist for estimating the entropy of dynamical systems, and we utilize an approximation based on calculating the mean first-passage time (MFPT) for particle displacement because of its tractability and its accessibility in real and simulation measurements. The MFPT dynamic entropy S(epsilon) is defined as equal to the inverse of the average first-passage time for a particle to exit a sphere of radius epsilon. This measure of the degree of chaotic motion allows us to identify characteristic time and space scales and to quantify the increasingly correlated particle motion and intermittency occurring in supercooled liquids. In particular, we identify a "cage" size defining the scale at which the particles are transiently localized, and we observe persistent particle motion at intermediate length scales beyond the scale where caging occurs. Furthermore, we find that the dynamic entropy at the scale of one interparticle spacing extrapolates to zero as the mode-coupling temperature T-c is approached.
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Lee BP, Douglas JF, Glotzer SC
Filler-induced composition waves in phase-separating polymer blends
PHYSICAL REVIEW E 60 (5): 5812-5822 Part B, NOV 1999
[x]
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The influence of immobile tiller particles (spheres, fibers, platelets) on polymer-blend phase separation is investigated computationally using a generalization of the Cahn-Hilliard-Cook (CHC) model. Simulation shows that the selective affinity of one of the polymers for the filler surface leads to the development of concentration waves about the filler particles at sin early stage of phase separation in near critical composition blends. These "target" patterns are overtaken in late-stage phase separation by a growing "background" spinodal pattern characteristic of blends without filler particles. The Linearized CHC model is used to estimate the number of composition oscillations emanating from isolated filler particles. In far-off-critical composition blends, an "encapsulation layer" grows at the surface of the filler rather than a target pattern. The results of these simulations compare favorably with experiments on filled phase-separating ultrathin blend films in which the filler particles are immobilized on a solid substrate.
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Donati C, Glotzer SC, Poole PH, Kob W, Plimpton SJ
Spatial correlations of mobility and immobility in a glass-forming Lennard-Jones liquid
PHYSICAL REVIEW E 60 (3): 3107-3119 SEP 1999
[x]
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Using extensive molecular dynamics simulations of an equilibrium, glass-forming Lennard-Jones mixture, we characterize in detail the local atomic motions. We show that spatial correlations exist among particles undergoing extremely large ("mobile") or extremely small:("immobile") displacements over a suitably chosen time interval. The immobile particles form the cores of relatively compact clusters, while the mobile particles move cooperatively and form quasi-one-dimensional stringlike clusters. The strength and length scale of the correlations between mobile particles are found to grow strongly with decreasing temperature, and the mean cluster size appears to diverge near the mode-coupling critical; temperature. We show that these correlations in the particle displacements are related to equilibrium fluctuations in the local potential energy and local composition.
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Sastry S, Debenedetti PG, Stillinger FH, Schroder TB, Dyre JC, Glotzer SC
Potential energy landscape signatures of slow dynamics in glass forming liquids
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 270 (1-2): 301-308 AUG 1 1999
[x]
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We study the properties of local potential energy minima (inherent structures') sampled by liquids at low temperatures as an approach to elucidating the mechanisms of the observed dynamical slowing down observed as the glass transition temperature is approached. This onset of slow dynamics is accompanied by the sampling of progressively deeper potential energy minima. Further, evidence is found in support of a qualitative change in the inherent structures sampled in a temperature range that includes the mode coupling critical temperature T-c, such that a separation of vibrational relaxation within inherent structure basins from that due to inter-basin transitions becomes valid at temperatures T < T-c, Average inherent structure energies do not show any qualitatively significant system size dependence.
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Lapena AM, Glotzer SC, Langer SA, Liu AJ
Effect of ordering on spinodal decomposition of liquid-crystal/polymer mixtures
PHYSICAL REVIEW E 60 (1): R29-R32 JUL 1999
[x]
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Partially phase-separated liquid-crystal/polymer dispersions display highly fibrillar domain morphologies that are dramatically different from the typical structures found in isotropic mixtures. To explain this, we numerically explore the coupling between phase ordering an phase-separation kinetics in model two-dimensional fluid mixtures phase separating into a nematic phase, rich in liquid crystal, coexisting with an isotropic phase, rich in polymer. We find that phase ordering can lead to fibrillar networks of the minority polymer-rich phase.
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Donati C, Glotzer SC, Poole PH
Growing spatial correlations of particle displacements in a simulated liquid on cooling toward the glass transition
PHYSICAL REVIEW LETTERS 82 (25): 5064-5067 JUN 21 1999