arXiv subjects

Greg van Anders

Publications and source records attributed to Greg van Anders.

34 records · Page 2Linked to original sources

arXiv2017

Relevance of Packing to Colloidal Self-Assembly

Since the 1920s, packing arguments have been used to rationalize crystal structures in systems ranging from atomic mixtures to colloidal crystals. Packing arguments have recently been applied to complex nanoparticle structures, where they often, but not always, work. We examine when, if ever, packing is a causal mechanism in hard particle approximations of colloidal crystals. We investigate three crystal structures comprised of their ideal packing shapes. We show that, contrary to expectations, the ordering mechanism cannot be packing, even when the thermodynamically self-assembled structure is the same as that of the densest packing. We also show that the best particle shapes for hard particle colloidal crystals in the infinite pressure limit are imperfect versions of the ideal packing shape.

cond-mat.soft↗

arXiv2017

Engineering Entropy for the Inverse Design of Colloidal Crystals from Hard Shapes

Throughout the physical sciences, entropy stands out as a pivotal but enigmatic concept that, in materials design, often takes a backseat to energy. Here, we demonstrate how to precisely engineer entropy to achieve desired colloidal crystals. We demonstrate the inverse design of hard particles that assemble six different target colloidal crystals due solely to entropy maximization. Our approach efficiently samples $10^8$ particle shapes from 88- and 192-dimensional design spaces to discover thermodynamically optimal shapes. We design particle shapes that self assemble known crystals with optimized thermodynamic stability, as well as new crystal structures with no known atomic or other equivalent.

cond-mat.soft↗

arXiv2017

Shape Driven Solid--Solid Transitions in Colloids

Despite the fundamental importance of solid--solid transitions for metallurgy, ceramics, earth science, reconfigurable materials, and colloidal matter, the details of how materials transform between two solid structures are poorly understood. We introduce a class of {simple} model systems in which the direct control of local order, via colloid shape change, induces solid--solid phase transitions, and characterize how the transitions happen thermodynamically. We find that within a single shape family there are solid--solid transitions that can occur with or without a thermal activation barrier. Our results provide new means for the study of solid--solid phase transitions, and have implications for designing reconfigurable materials.

cond-mat.soft↗

arXiv2016

Crossover Behavior in the Packing and Assembly of Multivalent Lock-and-Key Colloids

Emergent behaviors occur in a vast array of systems across many scales, and are of fundamental physical importance because of the intrinsic difficulty in linking microscopic system properties to macroscopic behaviors. Here we study the emergent self-assembly behavior of model systems of recently synthesized families of concave dimpled hard spheres, or lock-and-key colloids. We find that as dimple size increases each family exhibits a crossover from a structure that does not reflect the particle symmetry to one that does and, surprisingly, the point at which this crossover occurs is approximately independent of the particle symmetry. Using a combination of numerical and analytic techniques we study systems at infinite and finite pressure, and find different common control parameters in each limit. Our results suggest there exists a set of experimentally realizable colloidal systems that exhibit complex emergent behaviors that can be traced to a common underlying microscopic control parameter.

cond-mat.mtrl-sci↗

arXiv2016

Digital Alchemy for Materials Design: Colloids and Beyond

Starting with the early alchemists, a holy grail of science has been to make desired materials by modifying the attributes of basic building blocks. Building blocks that show promise for assembling new complex materials can be synthesized at the nanoscale with attributes that would astonish the ancient alchemists in their versatility. However, this versatility means that making direct connection between building block attributes and bulk behavior is both necessary for rationally engineering materials, and difficult because building block attributes can be altered in many ways. Here we show how to exploit the malleability of the valence of colloidal nanoparticle "elements" to directly and quantitatively link building block attributes to bulk behavior through a statistical thermodynamic framework we term "digital alchemy". We use this framework to optimize building blocks for a given target structure, and to determine which building block attributes are most important to control for self assembly, through a set of novel thermodynamic response functions, moduli and susceptibilities. We thereby establish direct links between the attributes of colloidal building blocks and the bulk structures they form. Moreover, our results give concrete solutions to the more general conceptual challenge of optimizing emergent behaviors in nature, and can be applied to other types of matter. As examples, we apply digital alchemy to systems of truncated tetrahedra, rhombic dodecahedra, and isotropically interacting spheres that self assemble diamond, FCC, and icosahedral quasicrystal structures, respectively.

cond-mat.soft↗

arXiv2015

Shape Allophiles Improve Entropic Assembly

We investigate a class of "shape allophiles" that fit together like puzzle pieces as a method to access and stabilize desired structures by controlling directional entropic forces. Squares are cut into rectangular halves, which are shaped in an allophilic manner with the goal of re-assembling the squares while self-assembling the square lattice. We examine the assembly characteristics of this system via the potential of mean force and torque, and the fraction of particles that entropically bind. We generalize our findings and apply them to self-assemble triangles into a square lattice via allophilic shaping. Through these studies we show how shape allophiles can be useful in assembling and stabilizing desired phases with appropriate allophilic design.

cond-mat.soft↗

arXiv2014

Understanding shape entropy through local dense packing

Entropy drives the phase behavior of colloids ranging from dense suspensions of hard spheres or rods to dilute suspensions of hard spheres and depletants. Entropic ordering of anisotropic shapes into complex crystals, liquid crystals, and even quasicrystals has been demonstrated recently in computer simulations and experiments. The ordering of shapes appears to arise from the emergence of directional entropic forces (DEFs) that align neighboring particles, but these forces have been neither rigorously defined nor quantified in generic systems. Here, we show quantitatively that shape drives the phase behavior of systems of anisotropic particles upon crowding through DEFs. We define DEFs in generic systems, and compute them for several hard particle systems. We show that they are on the order of a few kT at the onset of ordering, placing DEFs on par with traditional depletion, van der Waals, and other intrinsic interactions. In experimental systems with these other interactions, we provide direct quantitative evidence that entropic effects of shape also contribute to self-assembly. We use DEFs to draw a distinction between self-assembly and packing behavior. We show that the mechanism that generates directional entropic forces is the maximization of entropy by optimizing local particle packing. We show that this mechanism occurs in a wide class of systems, and we treat, in a unified way, the entropy-driven phase behavior of arbitrary shapes incorporating the well-known works of Kirkwood, Onsager, and Asakura and Oosawa.

cond-mat.soft↗

arXiv2014

Entropically Patchy Particles: Engineering Valence through Shape Entropy

Patchy particles are a popular paradigm for the design and synthesis of nanoparticles and colloids for self-assembly. In "traditional" patchy particles, anisotropic interactions arising from patterned coatings, functionalized molecules, DNA, and other enthalpic means create the possibility for directional binding of particles into higher-ordered structures. Although the anisotropic geometry of non-spherical particles contributes to the interaction patchiness through van der Waals, electrostatic, and other interactions, how particle shape contributes entropically to self-assembly is only now beginning to be understood. It has been recently demonstrated that, for hard shapes, entropic forces are directional. A newly proposed theoretical framework that defines and quantifies directional entropic forces demonstrates the anisotropic--that is, patchy--nature of these emergent, attractive forces. Here we introduce the notion of entropically patchy particles as the entropic counterpart to enthalpically patchy particles. Using three example "families" of shapes, we judiciously modify entropic patchiness by introducing geometric features to the particles so as to target specific crystal structures, which then assembled with Monte Carlo simulations. We quantify the emergent entropic valence via a potential of mean force and torque. We generalize these shape operations to shape anisotropy dimensions, in analogy with the anisotropy dimensions introduced for enthalpically patchy particles. Our findings demonstrate that entropic patchiness and emergent valence provide a way of engineering directional bonding into nanoparticle systems, whether in the presence or absence of additional, non-entropic forces.

cond-mat.soft↗

arXiv2011

Accelerating the solution of families of shifted linear systems with CUDA

We describe the GPU implementation of shifted or multimass iterative solvers for sparse linear systems of the sort encountered in lattice gauge theory. We provide a generic tool that can be used by those without GPU programming experience to accelerate the simulation of a wide array of theories. We stress genericity, which is important to allow the simulation of candidate theories for new physics at LHC, and for the study of various supersymmetric theories. We find significant speed ups, which we conservatively bound below at at least twelve times, that promise to put a variety of research questions within practical reach.

hep-lat↗

arXiv2010

First Results from Lattice Simulation of the PWMM

We present results of lattice simulations of the Plane Wave Matrix Model (PWMM). The PWMM is a theory of supersymmetric quantum mechanics that has a well-defined canonical ensemble. We simulate this theory by applying rational hybrid Monte Carlo techniques to a naive lattice action. We examine the strong coupling behaviour of the model focussing on the deconfinement transition.

hep-th↗

arXiv2010

Holographic Non-Fermi Liquids and the Luttinger Theorem

We show that the Luttinger theorem, a robust feature of Fermi liquids, can be violated in non-Fermi liquids. We compute non-Fermi liquid Green functions using duality to black holes and find that the volume of the Fermi surface depends exponentially on the scaling dimension, which is a measure of the coupling. This demonstrates that Luttinger's theorem does not extend to non-Fermi liquids. We comment on possible experimental signatures.

hep-th↗

arXiv2009

Comments on Holographic Fermi Surfaces

Recently, a mechanism for the development of a fermi surface in a holographic model of large N QCD with a baryon chemical potential was proposed. We examine similar constructions to determine when this mechanism persists. We find a class of models in which it does.

hep-th↗

arXiv2007

Coarse-Graining the Lin-Maldacena Geometries

The Lin-Maldacena geometries are nonsingular gravity duals to degenerate vacuum states of a family of field theories with SU(2|4) supersymmetry. In this note, we show that at large N, where the number of vacuum states is large, there is a natural `macroscopic' description of typical states, giving rise to a set of coarse-grained geometries. For a given coarse-grained state, we can associate an entropy related to the number of underlying microstates. We find a simple formula for this entropy in terms of the data that specify the geometry. We see that this entropy function is zero for the original microstate geometries and maximized for a certain ``typical state'' geometry, which we argue is the gravity dual to the zero-temperature limit of the thermal state of the corresponding field theory. Finally, we note that the coarse-grained geometries are singular if and only if the entropy function is non-zero.

hep-th↗

arXiv2007

General Lin-Maldacena solutions and PWMM Instantons from supergravity

We use the Lin-Maldacena prescription to demonstrate how to find the supergravity solutions dual to arbitrary vacua of the plane wave matrix model and maximally supersymmetric Yang-Mills theory on RxS^2, by solving the auxiliary electrostatics problem. We then apply the technique to study instantons at strong coupling in the matrix model.

hep-th↗

arXiv2006

Little String Theory from Double-Scaling Limits of Field Theories

We show that little string theory on S^5 can be obtained as double-scaling limits of the maximally supersymmetric Yang-Mills theories on RxS^2 and RxS^3/Z_k. By matching the gauge theory parameters with those in the gravity duals found by Lin and Maldacena, we determine the limits in the gauge theories that correspond to decoupling of NS5-brane degrees of freedom. We find that for the theory on RxS^2, the 't Hooft coupling must be scaled like ln^3(N), and on RxS^3/Z_k, like ln^2(N). Accordingly, taking these limits in these field theories gives Lagrangian definitions of little string theory on S^5.

hep-th↗

arXiv2006

Little String Theory from a Double-Scaled Matrix Model

Following Lin and Maldacena, we find exact supergravity solutions dual to a class of vacua of the plane wave matrix model by solving an electrostatics problem. These are asymptotically near-horizon D0-brane solutions with a throat associated with NS5-brane degrees of freedom. We determine the precise limit required to decouple the asymptotic geometry and leave an infinite throat solution found earlier by Lin and Maldacena, dual to Little String Theory on S^5. By matching parameters with the gauge theory, we find that this corresponds to a double scaling limit of the plane wave matrix model in which N \to \infty and the 't Hooft coupling λscales as \ln^4(N), which we speculate allows all terms in the genus expansion to contribute even at infinite N. Thus, the double-scaled matrix quantum mechanics gives a Lagrangian description of Little String Theory on S^5, or equivalently a ten-dimensional string theory with linear dilaton background.

hep-th↗