arXiv subjects

Sharon C. Glotzer

Publications and source records attributed to Sharon C. Glotzer.

At least 19 recordsLinked to original sources

arXiv2026

Dense Packing of Tetrahedra in Cylinders

We present the first systematic investigation of regular tetrahedra densely packed within a circular cylinder. Combining numerical simulations with exact analytical theory, we classify the densest configurations into two continuous, mathematically tractable families: chiral Tetra Helices and achiral Dimer Chains. Crucially, we reveal that the celebrated Boerdijk-Coxeter Helix is not an isolated anomaly, but a natural consequence of this cylindrical confinement. We further identify a striking symmetry-breaking bifurcation at a critical diameter, where the chiral helix coexists with an achiral dimer chain at a strictly identical packing fraction.

cond-mat.soft↗

arXiv2026

Anatomy of a Complex Crystallization Pathway

Using molecular dynamics simulations, we investigate the crystallization pathways of two exemplary systems that form the same complex crystal structure but differ fundamentally in the nature of their particle interactions. One system is composed of point particles interacting via an isotropic pair potential characteristic of metallic compounds, while the other system contains hard polyhedra whose interactions arise from emergent entropic forces. Despite the stark difference in the origins of the particle interactions, we find that both systems are polymorphic and share the same crystal polymorphs. Moreover, the two systems follow the same multistep crystallization pathways, and by examining the complex crystallization pathways on the single particle level, we find that the local structure evolution of the two systems is also similar. By mapping the hard particle system's interaction to an effective pairwise potential, we find that such resemblance arises from the particle interactions being effectively similar.

cond-mat.soft↗

arXiv2026

Exploratory digital alchemy for colloidal crystal discovery

Digital Alchemy (DA), introduced by Van Anders et al., is a statistical mechanics-based generalized thermodynamic ensemble method that employs computer simulations to optimize colloidal particle design. This approach applies the principles of statistical mechanics to predict and tailor particle attributes that lead to desired self-assembled structures or material properties. However, as an inverse design method, its main limitation is that the target structure must be known \textit{a priori}. Therefore, the optimal design from DA does not guarantee the targeted structure is the most or the only stable one. This highlights the importance of forward design with an exploratory scheme for optimizing novel colloid designs, which becomes more suitable in such cases. In this paper, we introduce Exploratory Digital Alchemy (EDA), an enhanced forward design scheme that begins by releasing the constraint of the target crystal from DA, followed by an exploration-oriented bias that has been extensively used in enhanced sampling methods such as metadynamics (MetaD). We demonstrate the utility of EDA through examples involving particles interacting via a two-dimensional Lennard-Jones Gauss potential (LJGP) and a three-dimensional oscillating pair potential (OPP). We applied EDA to study the free energy landscapes given different potential parameters of LJGP at different temperatures. With the exploratory scheme, we've also successfully identified a wide range of OPP potential parameters that stabilize metastable Frank-Kasper phases. Our approach fuses the standard DA framework with metadynamics, which could potentially be useful for studying alchemical reactions in a generalized ensemble.

cond-mat.soft↗

arXiv2026

Quantifying Local Point-Group-Symmetry Order in Complex Particle Systems

Crystals and other condensed phases are defined primarily by their inherent symmetries, which play a crucial role in dictating their structural properties. In crystallization studies, local order parameters (OPs) that describe bond orientational order are widely employed to investigate crystal formation. Despite their utility, these traditional metrics do not directly quantify symmetry, an important aspect for understanding the development of order during crystallization. To address this gap, we introduce a new set of OPs, called Point Group Order Parameters (PGOPs), designed to continuously quantify point group symmetry order. We demonstrate the strength and utility of PGOP in detecting order across different crystalline systems and compare its performance to commonly used bond-orientational order metrics. PGOP calculations for all non-infinite point groups are implemented in the open-source package SPATULA (Symmetry Pattern Analysis Toolkit for Understanding Local Arrangements), written in parallelized C++ with a Python interface. The code is publicly available on GitHub at https://github.com/glotzerlab/spatula.

physics.comp-ph↗

arXiv2026

Entropic Colloidal Crystal Prediction: A Quantum Density Functional Theory Inspired Approach

In pursuit of a colloidal analogue to quantum density functional theory (DFT) predictions of atomic crystal structures, we report a new, classical DFT that predicts the relative thermodynamic stability of colloidal crystals of hard, convex particle shapes. In contrast to standard classical DFT approaches, our theory maps the hard particle system to an auxiliary system in which we treat the particles as fixed "nuclei" embedded in a fictitious, spatially varying density field that distributes throughout the auxiliary system. By minimizing the free energy of the auxiliary system, and through comparison with known equations of state and free energy calculations using thermodynamic integration, we show that the auxiliary system with the lowest free energy corresponds to the most probable crystal of hard shapes in the original system.

cond-mat.soft↗

arXiv2025

Using Particle Shape to Control Defects in Colloidal Crystals on Spherical Interfaces

Spherical particles confined to a sphere surface cannot pack densely into a hexagonal lattice without defects. In this study, we use hard particle Monte Carlo simulations to determine the effects of continuously deformable shape anisotropy and underlying crystal lattice preference on inevitable defect structures and their distribution within colloidal assemblies of hard rounded polyhedra confined to a closed sphere surface. We demonstrate that cube particles form a simple square assembly, overcoming lattice/topology incompatibility, and maximize entropy by distributing eight three-fold defects evenly on the sphere. By varying particle shape smoothly from cubes to spheres we reveal how the distribution of defects changes from square antiprismatic to icosahedral symmetry. Congruent studies of rounded tetrahedra reveal additional varieties of characteristic defect patterns within three, four, and six-fold symmetric lattices. This work has promising implications for programmable defect generation to facilitate different vesicle buckling modes using colloidal particle emulsions.

cond-mat.soft↗

arXiv2025

Emergent Microrobotic Behavior of Active Flexicles in Complex Environments

Collections of simple, self-propelled colloidal particles exhibit complex, emergent dynamical behavior, with promising applications in microrobotics. When confined within a deformable vesicle, self-propelled rods cluster and align, propelling the vesicle and inducing changes in the vesicle shape. We explore potential microrobotic capabilities of such vesicle-encapsulated particles, which form a composite particle system termed a `flexicle'. Using molecular dynamics simulations, we demonstrate that the alignment of rods enables flexicles to locomote and respond adaptively to their physical environment. When encountering solid boundaries or obstacles, the rods reorient at the interface, triggering novel emergent behaviors such as crawling, corner-preferencing, wall climbing, and object-latching. These interactions and accompanying internal rod re-arrangement lead to spontaneous, temporary differentiation of the rods into `latchers' and `navigators'. This division of labor among the rods enables coordinated locomotion and environmental response. Our findings establish flexicles as a versatile platform for programmable, geometry-sensitive microrobotic behavior, offering a step toward autonomous colloidal robotics.

cond-mat.soft↗

arXiv2025

Hybrid Monte Carlo Metadynamics (hybridMC-MetaD)

We propose the powerful integration of the Hybrid Monte Carlo (hybridMC) algorithm and Well-Tempered Metadynamics. This new algorithm, hybridMC-MetaD, enhances the flexibility and applicability of metadynamics by allowing for the utilization of a wider range of collective variables (CVs), namely non-differentiable CVs. We demonstrate the usage of hybridMC-MetaD through five examples of rare events in molecular dynamics (MD) simulations, including a rare transition in a model potential system, condensation of the argon system, crystallization in a nearly-hard sphere system, a nearly-hard bipyramid system and a colloidal suspension. By taking advantage of hybridMC, which combines molecular dynamics (MD) and MC, we are able to bias the transitions along non-differentiable CVs for all five cases, which would be unfeasible with conventional MD simulations. Enabled by metadynamics, we observed significant acceleration of the phase transitions and calculated free energy barriers using the hybridMC-MetaD simulation data. For the nearly-hard bipyramid system whose crystallization is primarily driven by entropy, we report the free energy surface for the first time. Through our case studies, we show that our hybridMC-MetaD scheme reduces the complexity of using metadynamics and increases its accessibility. We believe the hybridMC-MetaD algorithm will stimulate greater interest in, and foster broader applications of metadynamics.

cond-mat.mtrl-sci↗

arXiv2024

Graph-Theoretical Description and Continuity Problems for Stress Propagation Through Complex Strut Lattices

Interconnected networks of rigid struts are critical for application in lightweight, load-bearing structures. However, accurately modeling stress distribution in these strut lattices poses significant computational challenges due to its strong dependence on organizational patterns, boundary conditions, and collective effects. Leveraging two-dimensional strut lattices that enable visualization of local elastic deformation, we investigate how graph theory (GT) provides a framework for stress prediction. We investigate how the geometric features often neglected by GT play a crucial role in the behavior of anisotropic networks. We also address the challenge of topological continuity that arises when applying discrete mathematics to physical structures. We show that modified centrality parameters combining lattice topology with geometry more accurately predict local stress, as validated through birefringence imaging and finite element modeling. Finally, we show how further improvements are made by incorporating strut lattice boundary conditions into the centrality definition, in a manner that simultaneously simplifies the computational cost.

cond-mat.mtrl-sci↗

arXiv2024

Collective behavior of "flexicles"

In recent years the functionality of synthetic active microparticles has edged even closer to that of their biological counterparts. However, we still lack the understanding needed to recreate at the microscale key features of autonomous behavior exhibited by microorganisms or swarms of macroscopic robots. In this study, we propose a model for a three-dimensional deformable cellular composite particle consisting of self-propelled rod-shaped colloids confined within a flexible vesicle - a superstructure we call a "flexicle". Using molecular dynamics simulations, we investigate the collective behavior of dense systems comprised of many flexicles. We show that individual flexicles exhibit shape changes upon collisions with other flexicles that lead to rearrangement of the internal active rods that slow the flexicle motion significantly. This shape deformability gives rise to a diverse set of motility-induced phase separation phenomena and the spontaneous flow of flexicles akin to the migration of cells in dense tissues. Our findings establish a foundation for designing responsive cell-like active particles and developing strategies for controlling swarm migration and other autonomous swarm behaviors at cellular and colloidal scales.

cond-mat.soft↗

arXiv2024

Crystallization of Binary Nanocrystal Superlattices and the Relevance of Short-Range Attraction

The synthesis of binary nanocrystal superlattices (BNSLs) enables the targeted integration of orthogonal physical properties, like photoluminescence and magnetism, into a single superstructure, unlocking a vast design space for multifunctional materials. Yet, the formation mechanism of BNSLs remains poorly understood, restricting the use of simulation to predict the structure and properties of the superlattices. Here, we use a combination of in situ scattering and molecular simulation to elucidate the self-assembly of two common BNSLs through emulsion templating. Our self-assembly experiments reveal that no intermediate structures precede the formation of the final binary phases, indicating that their formation proceeds through classical nucleation. Using simulations, we find that, despite the formation of AlB2 and NaZn13 typically being attributed to entropy, their self-assembly is most consistent with the nanocrystals possessing short-range interparticle attraction, which we find can dramatically accelerate nucleation kinetics in BNSLs. We also find homogenous, classical nucleation in simulation, corroborating our experiments. These results establish a robust correspondence between experiment and theory, paving the way towards a priori prediction of BNSLs.

cond-mat.mtrl-sci↗

arXiv2024

Change Point Detection of Events in Molecular Simulations using dupin

Particle tracking is commonly used to study time-dependent behavior in many different types of physical and chemical systems involving constituents that span many length scales, including atoms, molecules, nanoparticles, granular particles, etc. Behaviors of interest studied using particle tracking information include disorder-order transitions, thermodynamic phase transitions, structural transitions, protein folding, crystallization, gelation, swarming, avalanches and fracture. A common challenge in studies of these systems involves change detection. Change point detection discerns when a temporal signal undergoes a change in distribution. These changes can be local or global, instantaneous or prolonged, obvious or subtle. Moreover, system-wide changes marking an interesting physical or chemical phenomenon (e.g. crystallization) are often preceded by events (e.g. pre-nucleation clusters) that are localized and can occur anywhere at anytime in the system. For these reasons, detecting events in particle trajectories generated by molecular simulation is challenging and typically accomplished via ad hoc solutions unique to the behavior and system under study. Consequently, methods for event detection lack generality, and those used in one field are not easily used by scientists in other fields. Here we present a new Python-based tool, dupin, that allows for event detection from particle trajectory data irrespective of the system details. dupin works by creating a signal representing the simulation and partitioning the signal based on events (changes within the trajectory). This approach allows for studies where manual annotating of event boundaries would require a prohibitive amount of time. Furthermore, dupin can serve as a tool in automated and reproducible workflows. We demonstrate the application of dupin using two examples and discuss its applicability to a wider class of problems.

physics.comp-ph↗

arXiv2023

Layer-by-Layer Assembled Nanowire Networks Enable Graph Theoretical Design of Multifunctional Coatings

Multifunctional coatings are central for information, biomedical, transportation and energy technologies. These coatings must possess hard-to-attain properties and be scalable, adaptable, and sustainable, which makes layer-by-layer assembly (LBL) of nanomaterials uniquely suitable for these technologies. What remains largely unexplored is that LBL enables computational methodologies for structural design of these composites. Utilizing silver nanowires (NWs), we develop and validate a graph theoretical (GT) description of their LBL composites. GT successfully describes the multilayer structure with nonrandom disorder and enables simultaneous rapid assessment of several properties of electrical conductivity, electromagnetic transparency, and anisotropy. GT models for property assessment can be rapidly validated due to (1) quasi-2D confinement of NWs and (2) accurate microscopy data for stochastic organization of the NW networks. We finally show that spray-assisted LBL offers direct translation of the GT-based design of composite coatings to additive, scalable manufacturing of drone wings with straightforward extensions to other technologies.

physics.app-ph↗

arXiv2023

Complex motion of steerable vesicular robots filled with active colloidal rods

While the collective motion of active particles has been studied extensively, effective strategies to navigate particle swarms without external guidance remain elusive. We introduce a method to control the trajectories of two-dimensional swarms of active rod-like particles by confining the particles to rigid bounding membranes (vesicles) with non-uniform curvature. We show that the propelling agents spontaneously form clusters at the membrane wall and collectively propel the vesicle, turning it into an active superstructure. To further guide the motion of the superstructure, we add discontinuous features to the rigid membrane boundary in the form of a kinked tip, which acts as a steering component to direct the motion of the vesicle. We report that the system's geometrical and material properties, such as the aspect ratio and Peclet number of the active rods as well as the kink angle and flexibility of the membrane, determine the stacking of active particles close to the kinked confinement and induce a diverse set of dynamical behaviors of the superstructure, including linear and circular motion both in the direction of, and opposite to, the kink. From a systematic study of these various behaviors, we design vesicles with switchable and reversible locomotions by tuning the confinement parameters. The observed phenomena suggest a promising mechanism for particle transportation and could be used as a basic element to navigate active matter through complex and tortuous environments.

cond-mat.soft↗

arXiv2023

Quasicrystalline Nanocrystal Superlattice with Partial Matching Rules

Expanding the library of self-assembled superstructures provides insight into the behavior of atomic crystals and supports the development of materials with mesoscale order. Here we build upon recent findings of soft matter quasicrystals and report a quasicrystalline binary nanocrystal superlattice that exhibits correlations in the form of partial matching rules reducing tiling disorder. We determine a three-dimensional structure model through electron tomography and direct imaging of surface topography. The 12-fold rotational symmetry of the quasicrystal is broken in sub-layers, forming a random tiling of rectangles, large triangles, and small triangles with 6-fold symmetry. We analyze the geometry of the experimental tiling and discuss factors relevant for the stabilization of the quasicrystal. Our joint experimental-computational study demonstrates the power of nanocrystal superlattice engineering and further narrows the gap between the richness of crystal structures found with atoms and in soft matter assemblies.

cond-mat.mtrl-sci↗

arXiv2023

Rationalizing Euclidean Assemblies of Hard Polyhedra from Tessellations in Curved Space

Entropic self-assembly is governed by the shape of the constituent particles, yet a priori prediction of crystal structures from particle shape alone is non-trivial for anything but the simplest of space-filling shapes. At the same time, most polyhedra are not space-filling due to geometric constraints, but these constraints can be relaxed or even eliminated by sufficiently curving space. We show using Monte Carlo simulations that the majority of hard Platonic shapes self-assemble entropically into space-filling crystals when constrained to the surface volume of a 3-sphere. As we gradually decrease curvature to "flatten" space and compare the local morphologies of crystals assembling in curved and flat space, we show that the Euclidean assemblies can be categorized either as remnants of tessellations in curved space (tetrahedra and dodecahedra) or non-tessellation-based assemblies caused by large-scale geometric frustration (octahedra and icosahedra).

cond-mat.soft↗

arXiv2022

Curvature-Controlled Geometrical Lensing Behavior in Self-Propelled Colloidal Particle Systems

In many biological systems, the curvature of the surfaces cells live on influence their collective properties. Curvature should likewise influence the behavior of active colloidal particles. We show using molecular simulation of self-propelled active particles on surfaces of Gaussian curvature (both positive and negative) that curvature sign and magnitude can alter the system's collective behavior. Curvature acts as a geometrical lens and shifts the critical density of motility-induced phase separation (MIPS) to lower values for positive curvature and higher values for negative curvature, which we explain theoretically by the nature of parallel lines in spherical and hyperbolic space. Curvature also fluidizes dense MIPS clusters due to the emergence of defect patterns disrupting the crystalline order inside the clusters. Using our findings, we engineer three confining surfaces that strategically combine regions of different curvature to produce a host of novel dynamic phases, including cyclic MIPS on sphercylinders, wave-like MIPS on spherocones, and cluster fluctuations on metaballs.

cond-mat.soft↗

arXiv2021

Tuning Stoichiometry to Promote Formation of Binary Colloidal Superlattices

The self-assembly of binary nanoparticle superlattices from colloidal mixtures is a promising method for the fabrication of complex colloidal co-crystal structures. However, binary mixtures often form amorphous or metastable phases instead of the thermodynamically stable phase. Here we show that in binary mixtures of differently sized spherical particles, an excess of the smaller component can promote -- and, in some cases, may be necessary for -- the self-assembly of a binary co-crystal. Using computer simulations, we identify two mechanisms responsible for this phenomenon. First, excess small particles act like plasticizers and enable systems to reach a greater supersaturation before kinetic arrest occurs. Second, they can disfavor competing structures that may interfere with the growth of the target structure. We find the phase behavior of simulated mixtures of hard spheres closely matches published experimental results. We demonstrate the generality of our findings for mixtures of particles of arbitrary shape by presenting a binary mixture of hard shapes that only self-assembles with an excess of the smaller component. mixtures of particles of arbitrary shape by presenting a binary mixture of hard shapes that only self-assembles with an excess of the smaller component.

cond-mat.soft↗