Carl Schreck

Biomimetic Isotropic Nanostructures for Structural Coloration

The self-assembly of films that mimic color-producing nanostructures in bird feathers is described. These structures are isotropic and have a characteristic length-scale comparable to the wavelength of visible light. Structural colors are produced when wavelength-independent scattering is suppressed by limiting the optical path length through geometry or absorption.

Assembly of Optical-Scale Dumbbells into Dense Photonic Crystals

We describe the self-assembly of nonspherical particles into crystals with novel structure and optical properties combining a partial photonic band gap with birefringence that can be modulated by an external field or quenched by solvent evaporation. Specifically, we study symmetric optical-scale polymer dumbbells with an aspect ratio of 1.58. Hard particles with this geometry have been predicted to crystallize in equilibrium at high concentrations. However, unlike spherical particles, which readily crystallize in the bulk, previous experiments have shown that these dumbbells crystallize only under strong confinement. Here, we demonstrate the use of an external electric field to align and assemble the dumbbells to make a birefringent suspension with structural color. When the electric field is turned off, the dumbbells rapidly lose their orientational order and the color and birefringence quickly go away. In this way, dumbbells combine the structural color of photonic crystals with the field addressability of liquid crystals. In addition, we find that if the solvent is removed in the presence of an electric field, the particles self-assemble into a novel, dense crystalline packing hundreds of particles thick. Analysis of the crystal structure indicates that the dumbbells have a packing fraction of 0.7862, higher than the densest known packings of spheres and ellipsoids. We perform numerical experiments to more generally demonstrate the importance of controlling the orientation of anisotropic particles during a concentration quench to achieve long-range order.

Jamming in systems composed of frictionless ellipse-shaped particles.

We study numerically frictionless ellipse packings versus the aspect ratio alpha, and find that the jamming transition is fundamentally different from that for spherical particles. The normal mode spectra possess two gaps and three distinct branches over a range of alpha. The energy from deformations along modes in the lowest-energy branch increases quartically, not quadratically. The quartic modes cause novel power-law scaling of the static shear modulus and their number matches the deviation from isostaticity. These results point to a new critical point at alpha>1 that controls jamming of aspherical particles.

Short-range Order and Near-field Effects on Optical Scattering and Structural Coloration

We have investigated wavelength-dependent light scattering in biomimetic structures with short-range order. Coherent backscattering experiments are performed to measure the transport mean free path over a wide wavelength range. Overall scattering strength is reduced significantly due to short-range order and near-field effects. Our analysis explains why single scattering of light is dominant over multiple scattering in similar biological structures and is responsible for color generation.

Photonic band gaps in three-dimensional network structures with short-range order

We show numerically a significant depletion of the density of optical states in disordered three-dimensional network structures. The pseudo photonic band gap is likely produced by short-range order and uniformity of local topology.

A comparison of jamming behavior in systems composed of dimer- and ellipse-shaped particles

We compare the structural and mechanical properties of static packings composed of frictionless convex (ellipses) and concave (rigid dimers) particles in two dimensions. We employ numerical simulations to generate static packings and measure the shear stress in response to applied simple shear strain as a function of the aspect ratio and amount of compression. We find that the behavior near jamming is significantly different for ellipses and dimers even though both shapes are roughly characterized by the aspect ratio and possess the same number of translational and rotational degrees of freedom per particle. For example, we find that ellipse packings are hypostatic (not isostatic as found for dimers), display novel power-law scaling of the static linear shear modulus and contact number with the amount of compression, and possess stress-strain relations that are qualitatively different from that for dimers. Thus, we observe that important macroscopic properties of static packings of anisotropic particles can depend on the microscale geometrical features of individual particles.

Tuning jammed frictionless disk packings from isostatic to hyperstatic.

We perform extensive computational studies of two-dimensional static bidisperse disk packings using two distinct packing-generation protocols. The first involves thermally quenching equilibrated liquid configurations to zero temperature over a range of thermal quench rates r and initial packing fractions followed by compression and decompression in small steps to reach packing fractions φ(J) at jamming onset. For the second, we seed the system with initial configurations that promote micro- and macrophase-separated packings followed by compression and decompression to φ(J). Using these protocols, we generate more than 10(4) static packings over a wide range of packing fraction, contact number, and compositional and positional order. We find that disordered, isostatic packings exist over a finite range of packing fractions in the large-system limit. In agreement with previous calculations, the most dilute mechanically stable packings with φ min ≈ 0.84 are obtained for r > r*, where r* is the rate above which φ(J) is insensitive to rate. We further compare the structural and mechanical properties of isostatic versus hyperstatic packings. The structural characterizations include the contact number, several order parameters, and mixing ratios of the large and small particles. We find that the isostatic packings are positionally and compositionally disordered (with only small changes in a number of order parameters), whereas bond-orientational and compositional order increase strongly with contact number for hyperstatic packings. In addition, we calculate the static shear modulus and normal mode frequencies (in the harmonic approximation) of the static packings to understand the extent to which the mechanical properties of disordered, isostatic packings differ from partially ordered packings. We find that the mechanical properties of the packings change continuously as the contact number increases from isostatic to hyperstatic.

Particle-scale reversibility in athermal particulate media below jamming.

We perform numerical simulations of repulsive, frictionless athermal disks in two and three spatial dimensions undergoing cyclic quasistatic simple shear to investigate particle-scale reversible motion. We identify three classes of steady-state dynamics as a function of packing fraction φ and maximum strain amplitude per cycle γ(max). Point-reversible states, where particles do not collide and exactly retrace their intracycle trajectories, occur at low φ and γ(max). Particles in loop-reversible states undergo numerous collisions and execute complex trajectories but return to their initial positions at the end of each cycle. For sufficiently large φ and γ(max), systems display irreversible dynamics with nonzero self-diffusion. Loop-reversible dynamics enables the reliable preparation of configurations with specified structural and mechanical properties over a broad range of φ.

Structural relaxation in dense liquids composed of anisotropic particles.

We perform extensive molecular dynamics simulations of dense liquids composed of bidisperse dimer- and ellipse-shaped particles in two dimensions that interact via purely repulsive contact forces. We measure the structural relaxation times obtained from the long-time α decay of the self part of the intermediate scattering function for the translational and rotational degrees of freedom (DOF) as a function of packing fraction φ, temperature T, and aspect ratio α. We are able to collapse the packing-fraction and temperature-dependent structural relaxation times for disks, and dimers and ellipses over a wide range of α, onto a universal scaling function F(±)(|φ-φ(0)|,T,α), which is similar to that employed in previous studies of dense liquids composed of purely repulsive spherical particles in three dimensions. F(±) for both the translational and rotational DOF are characterized by the α-dependent scaling exponents μ and δ and packing fraction φ(0)(α) that signals the crossover in the scaling form F(±) from hard-particle dynamics to super-Arrhenius behavior for each aspect ratio. We find that the fragility of structural relaxation at φ(0), m(φ(0)), decreases monotonically with increasing aspect ratio for both ellipses and dimers. For α>α(p), where α(p) is the location of the peak in the packing fraction φ(J) at jamming onset, the rotational DOF are strongly coupled to the translational DOF, and the dynamic scaling exponents and φ(0) are similar for the rotational and translational DOF. For 1<α<α(p), the translational DOF become frozen at higher temperatures than the rotational DOF, and φ(0) for the rotational degrees of freedom increases above φ(J). Moreover, the results for the slow dynamics of dense liquids composed of dimer- and ellipse-shaped particles are qualitatively the same, despite the fact that zero-temperature static packings of dimers are isostatic, while static packings of ellipses are hypostatic. Thus, zero-temperature contact counting arguments do not apply to structural relaxation of dense liquids of anisotropic particles near the glass transition.

Using DNA-driven assembled phospholipid nanodiscs as a scaffold for gold nanoparticle patterning.

Recently, a new class of materials emerged with the assembly of DNA-coated phospholipid nanodiscs into columnar BioNanoStacks. Within these stacks, lipid discs are periodically incorporated, resulting into quasi-one-dimensional superstructures. With each disc surrounded by two recombinant scaffolding proteins, we decided to examine whether the polyhistidine tags of these proteins could be utilized to bind additional molecules or particles to these BioNanoStacks. Here we demonstrate that patterning of gold nanoparticles onto these BioNanoStacks is indeed possible. Binding occurs via a nickel-mediated interaction between the nanogolds nitrilotriacetic acid and the histidine tags of the scaffold proteins surrounding the nanodiscs. Using Monte Carlo simulations, we determine that the binding of the nanogold particles to the stacks is not a random event. By comparing the simulation and experimental results, we find that there are preferred binding sites, which affects the binding statistics.