arXiv subjects

Gregory M. Grason

Publications and source records attributed to Gregory M. Grason.

At least 19 recordsLinked to original sources

arXiv2026

Frustrated shapes of solid domains in fluid membrane vesicles: From rolls and folds to crumples and wrinkles

Fluid-solid composite vesicles, comprising 2D solid domains integrated into a topologically-closed fluid bilayer membrane, exhibit complex morphologies arising from the geometric frustration between spherical closure of the membrane and 2D solid elasticity. This scenario is distinct from the better studied case of multi-fluid domain vesicles. Here, we study the elastic energies and shape equilibria of a closed vesicle membrane containing a single, flexible circular solid domain using discrete finite-element (Surface Evolver) simulations, determining the key physical and mechanical parameters to govern shape selection. While we find that the 2D solid (shear) elasticity has minimal impact on the highly-under inflated morphologies, the geometrically non-linear resistance of the solid to Gaussian curvature substantially impacts the shape and elastic patterns form for inflated vesicles, by an amount that it grows with ratio of vesicle size to the elastic thickness of solid. For sufficiently large (thin) vesicles we characterize a generic sequence of ground state patterns of solid shape with increasing inflation: from cylindrical rolls and isometric folds to spatially complex patterns of crumples and wrinkles and ultimately to smooth caps. This sequence of non-isometric patterns at high-inflation is shown to be governed by the same far-from-threshold mechanics used to describe similar shape transitions in microscopic sheets on curved liquid interfaces, establishing that inflated shapes are governed by two basic mechanical scales of membrane tension. We find our predictions for highly-anisotropic shape equilibria of fluid-solid composite vesicles closely match experimentally observed shapes of giant unilamellar vesicles of phase-separated DPPC and DOPC.

cond-mat.soft↗

arXiv2026

Topological and morphological signatures of disorder in a self-assembled, soft matter sponge network

Many soft matter systems exhibit ordered, polycontinuous network morphologies, such as the cubic (double) gyroid or diamond, as well as disordered network morphologies known generically as ``random sponges". While presumed to share similar local packing geometry, the structural relationship between these ordered and disordered network morphologies has remained obscure. We use slice and view scanning electron microscopy to analyze and compare multi-scale morphological features of an ordered double-gyroid morphology to the amorphous sponge morphology formed in the same block copolymer sample. We find that node valence of the minority component network of the sponge is mostly gyroidal (trivalent), with a small fraction of diamond-like (tetravalent) connections. We analyze mesoatoms -- space-filling volumes occupied by chains around each network node -- finding significant differences in shape and size between ordered and amorphous regions. Local block thickness and inter-domain curvature within mesoatomic units of the disordered sponge exhibits a surprisingly similar degree of dispersity to the ordered double-gyroid. The mean differences in local packing geometry derive from topological distinction: loops of the minority networks of the ordered double-gyroid are intercatenated, while loops of the disordered sponge are not. In this way, the sponge may be viewed as disordered variant of a single-gyroidal morphology. We exploit these topological differences to demarcate the boundary region between ordered and disordered networks and highlight modulations of the mesoatom motifs at the boundary. These observations point to new questions about potential metastability of disordered networks and their possible role as kinetic precursors to long-range ordered network morphologies.

cond-mat.soft↗

arXiv2026

Sculpting 2D Crystals via Membrane Contractions before and during Solidification

When phospholipids crystallize within the otherwise fluid membranes of giant unilamellar vesicles, the resulting molecularly-thin "2D" solids exhibit great variety in their morphology evolution. For instance within membranes containing moderate amounts of the crystallizing component, crystals grow with a fixed morphology depending on vesicle size. Conversely for membranes containing large amounts of the crystallizing species, we find small compact crystals on vesicles of all sizes. However on large vesicles, growing crystals sprout flower petals that lengthen progressively. These behaviors result from two combined mechanisms: First, like other 2D solids, the shear rigidity of phospholipid crystals renders them intolerant to morphologies with non-zero Gaussian curvature. As a result and especially at elevated membrane tension, the cost of bending elasticity is reduced, at the expense of line energy, by the formation of flowers as opposed to compact crystals. Second, the composition-dependent tension rise during cooling relaxes via water permeation of the membrane with a time constant scaling as $R^2$. The amount of crystal formed for a small decrease in temperature determines this composition-dependent increase in stress from thermal contractions versus solidification. Surface Evolver computations motivated using the predicted tension evolution to develop a processing space that maps to experimental observations for initial and growing crystal morphology. Important variable groups are identified, including a scaled ratio of bending to line energy, a vesicle size-independent group for membrane contractions, and a time constant for stress relaxation. Though processing stresses ultimately relax, the crystal morphology persists well beyond the processing window.

cond-mat.soft↗

arXiv2026

Supercritical Snapping and Controlled Launching via Dual Latch Gels

Natural organisms have evolved integrated Latch-Mediated Spring Actuation systems (LaMSA) that consist of multiple latches and springs to enhance power output and adapt to diverse environmental conditions. Similar designs are appealing yet largely unexplored in engineered materials due to the complexity of integrating multiple components into a single material platform. Here, we report a dual-latched magneto-elastic shell device capable of selectively activating the latches to regulate snapping pathways and energy output based on specific actuation requirements. Differential deswelling across the thickness acts as the motor to load the elastic energy into the shell, which is then released via the snap-through instability once the loading reaches the critical threshold, constituting an intrinsic mechanical latch. Activation of the external magnetic latch delays snapping onset beyond the threshold of the intrinsic latch, leading to a power-amplified supercritical snap-through instability as well as a bifurcation instability. The combined function of both latches allows for flexible control over energy storage and release. Additionally, this integrated LaMSA system possesses an untethered anchoring mechanism, enabling the device to launch in arbitrary directions from the substrate, driven by the energy released during snapping. We envision that the design principles of dual-latched LaMSA systems will create opportunities for power-dense actuation in engineered materials and robotic devices.

physics.app-ph↗

arXiv2025

Not even metastable: Cubic double-diamond in diblock copolymer melts

We study the thermodynamics of continuous transformations between two canonical, cubic network phases of block copolymer melts: double-gyroid, an equilibrium morphology for many systems; and double-diamond, often thought to be a close competitor. We use a strong-segregation approach to compute the free energy of double network morphologies as a function of two structural parameters that convert between two limiting cubic cases; a tetragonal stretch of the unit cell in combination with fusion of pairs of trihedal gyroid nodes into tetrahedral diamond nodes. For the simplest case of conformationally symmetric diblock melts, we find that cubic double-diamond sits at an unstable saddle point that is continuously deformable into the lower free energy gyroid, as well as a second metastable, tetragonal network composed by trihedral nodes. We confirm the broad instability of double-diamond at finite segregation using self-consistent field studies and further show that it derives directly from the entropic free energy cost of chain packing in the tubular domains of tetrahedral nodes. Correspondingly, we demonstrate two factors that quench the entropic cost of packing in the tubular domain -- homopolymer blending and elastic asymmetry between the blocks -- promoting double-diamond to a metastable state by way of free energy barrier that separates it from double-gyroid.

cond-mat.soft↗

arXiv2025

Magic sizes enable minimal-complexity, high-fidelity assembly of programmable shells

Recent advances in synthetic methods enable designing subunits that self-assemble into structures with precise, finite sizes and well-defined architectures, but yields are frequently suppressed by the formation of off-target metastable structures. Increasing the complexity (the number of distinct subunit types) can inhibit off-target structures, but leads to slower kinetics and higher synthesis costs. Here, we study icosahedral shells formed of programmable triangular subunits as a model system, and identify design principles that produce the highest target yield at the lowest complexity. We use a symmetry-based construction to create a range of design complexities, starting from the maximal symmetry Caspar-Klug assembly up to the fully addressable, zero-symmetry assembly. Kinetic Monte Carlo simulations reveal that the most prominent defects leading to off-target assemblies are disclinations at sites of rotational symmetry. We derive symmetry-based rules for identifying the optimal (lowest-complexity, highest-symmetry) design that inhibits these disclinations, leading to robust, high-fidelity assembly of targets with arbitrarily large, yet precise, finite sizes. The optimal complexity varies non-monotonically with target size, with `magic' sizes appearing for high-symmetry designs in which symmetry axes do not intersect vertices of the triangular net. The optimal designs at magic sizes require 12 times fewer inequivalent interaction-types than the (minimal symmetry) fully addressable construction, which greatly reduces the timescale and experimental cost required to achieve high fidelity assembly of large targets. This symmetry-based principle for pruning off-target assembly generalizes to diverse architectures with different topologies.

cond-mat.soft↗

arXiv2025

From toroids to helical tubules: Kirigami-inspired programmable assembly of two-periodic curved crystals

Biology is full of intricate molecular structures whose geometries are inextricably linked to their function. Many of these structures exhibit varying curvature, such as the helical structure of the bacterial flagellum, which is critical for their motility. Because synthetic analogues of these shapes could be valuable platforms for nanotechnologies, including drug delivery and plasmonics, controllable synthesis of variable-curvature structures of various material systems, from fullerenes to supramolecular assemblies, has been a long-standing goal. Like two-dimensional crystals, these structures have a two-periodic symmetry, but unlike standard two-dimensional crystals, they are embedded in three dimensions with complex, spatially-varying curvatures that cause the structures to close upon themselves in one or more dimensions. Here, we develop and implement a design strategy to program the self-assembly of a complex spectrum of two-periodic curved crystals with variable periodicity, spatial dimension, and topology, spanning from toroids to achiral serpentine tubules to both left- and right-handed helical tubules. Our design strategy uses a kirigami-based mapping of 2D planar tilings to 3D curved crystals that preserves the periodicity, two-fold rotational symmetries, and subunit dimensions via the arrangement of disclination defects. We survey the modular geometry of these curved crystals and infer the addressable subunit interactions required to assemble them from triangular subunits. To demonstrate this design strategy, we program the self-assembly of toroids, helical- and serpentine-tubules from DNA origami subunits. A simulation model of the assembly pathways reveals physical considerations for programming the geometric specificity of angular folds in the curved crystal required to avoid defect-mediated misassembly.

cond-mat.soft↗

arXiv2025

Modular programming of interaction and geometric specificity enables assembly of complex DNA origami nanostructures

We present a modular DNA origami design approach to address the challenges of assembling geometrically complex nanoscale structures, including those with nonuniform Gaussian curvature. This approach features a core structure that completely conserves the scaffold routing across different designs and preserves more than 70% of the DNA staples between designs, dramatically reducing both cost and effort, while enabling precise and independent programming of subunit interactions and binding angles through adjustable overhang lengths and sequences. Using cryogenic electron microscopy, gel electrophoresis, and coarse-grained molecular dynamics simulations, we validate a set of robust design rules. We demonstrate the method's utility by assembling a variety of self-limiting structures, including anisotropic shells with controlled inter-subunit interactions and curvature, and a toroid with globally varying curvature. Our strategy is both cost-effective and versatile, providing a promising and efficient solution for the synthetic fabrication of complex nanostructures.

cond-mat.soft↗

arXiv2025

Self-limiting states of polar misfits: Frustrated assembly of warped-jigsaw particles

We study the ground state thermodynamics of a model class of geometrically frustrated assemblies, known as {\it warped-jigsaw} particles. While it is known that frustration in soft matter assemblies has the ability to propagate up to mesoscopic, multi-particle size scales, notably through the selection of self-limiting domain, little is understood about how the symmetry of shape-misfit at the particle scale influences emergent morphologies at the mesoscale. Here we show that polarity in the shape-misfit of warped-jigsaw puzzles manifests at a larger scale in the morphology and thermodynamics of the ground-state assembly of self-limiting domains. We use a combination of continuum theory and discrete particle simulations to show that the polar misfit gives rise to two mesoscopically distinct polar, self-limiting ribbon domains. Thermodynamic selection between the two ribbon morphologies is controlled by a combination of the binding anisotropy along distinct neighbor directions and the orientation of polar shape-misfit. These predictions are valuable as design features for ongoing efforts to program self-limiting assemblies through the synthesis of intentionally frustrated particles, and further suggests a generic classification of frustrated assembly behavior in terms of the relative symmetries of shape-misfit and the underlying long-range inter-particle order it frustrates.

cond-mat.soft↗

arXiv2025

Measuring multisubunit mechanics of geometrically-programmed colloidal assemblies via cryo-EM multi-body refinement

Programmable self-assembly has recently enabled the creation of complex structures through precise control of the interparticle interactions and the particle geometries. Targeting ever more structurally complex, dynamic, and functional assemblies necessitates going beyond the design of the structure itself, to the measurement and control of the local flexibility of the inter-subunit connections and its impact on the collective mechanics of the entire assembly. In this study, we demonstrate a method to infer the mechanical properties of multisubunit assemblies using cryogenic electron microscopy (cryo-EM) and RELION's multi-body refinement. Specifically, we analyze the fluctuations of pairs of DNA-origami subunits that self-assemble into tubules. By measuring the fluctuations of dimers using cryo-EM, we extract mechanical properties such as the bending modulus and interparticle spring constant. These properties are then applied to elastic models to predict assembly outcomes, which align well with experimental observations. This approach not only provides a deeper understanding of nanoparticle mechanics, but also opens new pathways to refining subunit designs to achieve precise assembly behavior. This methodology could have broader applications in the study of nanomaterials, including protein assemblies, where understanding the interplay of mechanical properties and subunit geometry is essential for controlling complex self-assembled structures.

cond-mat.soft↗

arXiv2024

Thermal Preconditioning of Membrane Stress to Control the Shapes of Ultrathin Crystals

We employ the phospholipid bilayer membranes of giant unilamellar vesicles as a free-standing environment for the growth of membrane-integrated ultrathin phospholipid crystals possessing a variety of shapes with 6-fold symmetry. Crystal growth within vesicle membranes, where more elaborate shapes grow on larger vesicles is dominated by the bending energy of the membrane itself, creating a means to manipulate crystal morphology. Here we demonstrate how cooling rate preconditions the membrane tension before nucleation, in turn regulating nucleation and growth, and directing the morphology of crystals by the time they are large enough to be visualized. The crystals retain their shapes during further growth through the two phase region. Experiments demonstrate this behavior for single crystals growing within the membrane of each vesicle, ultimately comprising up to 13% of the vesicle area and length scales of up to 50 microns. A model for stress evolution, employing only physical property data, reveals how the competition between thermal membrane contraction and water diffusion from tensed vesicles produces a size- and time-dependence of the membrane tension as a result of cooling history. The tension, critical in the contribution of bending energy in the fluid membrane regions, in turn selects for crystal shape for vesicles of a given size. The model reveals unanticipated behaviors including a low steady state tension on small vesicles that allows compact domains to develop, rapid tension development on large vesicles producing flower-shaped domains, and a stress relaxation through water diffusion across the membrane with a time constant scaling as the square of the vesicle radius, consistent with measurable tensions only in the largest vesicles.

cond-mat.soft↗

arXiv2024

Geometrically frustrated, mechanical metamaterial membranes: Large-scale stress accumulation and size-selective assembly

We study the effect of geometric frustration on dilational mechanical metamaterial membranes. While shape frustrated elastic plates can only accommodate non-zero Gaussian curvature up to size scales that ultimately vanish with their elastic thickness, we show that frustrated {\it metamembranes} accumulate hyperbolic curvatures up to mesoscopic length scales that are ultimately independent of the size of their microscopic constituents. A continuum elastic theory and discrete numerical model describe the size-dependent shape and internal stresses of axisymmetric, trumpet-like frustrated metamembranes, revealing a non-trivial crossover to a much weaker power-law growth in elastic strain energy with size than in frustrated elastic membranes. We study a consequence of this for the self-limiting assembly thermodynamics of frustrated trumpets, showing a several-fold increase the size range of self-limitation of metamembranes relative to elastic membranes.

cond-mat.soft↗

arXiv2024

Helical close-packing of anisotropic tubes

Helically close-packed states of filaments are common in natural and engineered material systems, ranging from nanoscopic biomolecules to macroscopic structural components. While the simplest models of helical close-packing, described by the ideal rope model, neglect anisotropy perpendicular to the backbone, physical filaments are often quite far from circular in their cross-section. Here, we consider an anisotropic generalization of the ideal rope model and show that cross-section anisotropy has a strongly non-linear impact on the helical close-packing configurations of helical filaments. We show that the topology and composition of the close-packing landscape depends on the cross-sectional aspect ratio and is characterized by several distinct states of self-contact. We characterize the local density of these distinct states based on the notion of confinement within a 'virtual' cylindrical capillary, and show that states of optimal density vary strongly with the degree of anisotropy. While isotropic filaments are densest in a straight configuration, any measure of anisotropy leads to helicity of the maximal density state. We show the maximally dense states exhibit a sequence of transitions in helical geometry and cross-sectional tilt with increasing anisotropy, from spiral tape to spiral screw packings. Furthermore, we show that maximal capillary density saturates in a lower bound for volume fraction of $π/4$ in the large-anisotropy, spiral-screw limit. While cross-sectional anisotropy is well-known to impact the mechanical properties of filaments, our study shows its strong effects to shape the configuration space and packing efficiency of this elementary material motif.

cond-mat.soft↗

arXiv2024

Shape equilibria of vesicles with rigid planar inclusions

Motivated by recent studies of two-phase lipid vesicles possessing 2D solid domains integrated within a fluid bilayer phase, we study the shape equilibria of closed vesicles possessing a single planar, circular inclusion. While 2D solid elasticity tends to expel Gaussian curvature, topology requires closed vesicles to maintain an average, non-zero Gaussian curvature leading to an elementary mechanism of shape frustration that increases with inclusion size. We study elastic ground states of the Helfrich model of the planar-fluid composite vesicles, analytically and computationally, as a function of planar fraction and reduced volume. Notably, we show that incorporation of a planar inclusion of only a few percent dramatically shifts the ground state shapes of vesicles from predominantly {\it prolate} to {\it oblate}, and moreover, shifts the optimal surface to volume ratio far from spherical shapes. We show that for sufficiently small planar inclusions, the elastic ground states break symmetry via a complex variety of asymmetric oblate, prolate, and triaxial shapes, while inclusion sizes above about $8\%$ drive composite vesicles to adopt axisymmetric oblate shapes. These predictions cast useful light on the emergent shape and mechanical responses of fluid-solid composite vesicles.

cond-mat.soft↗

arXiv2024

Symmetry-guided inverse design of self-assembling multiscale DNA origami tilings

Recent advances enable the creation of nanoscale building blocks with complex geometries and interaction specificities for self-assembly. This nearly boundless design space necessitates design principles for defining the mutual interactions between multiple particle species to target a user-specified complex structure or pattern. In this article, we develop a symmetry-based method to generate the interaction matrices that specify the assembly of two-dimensional tilings which we illustrate using equilateral triangles. By exploiting the allowed 2D symmetries, we develop an algorithmic approach by which any periodic 2D tiling can be generated from an arbitrarily large number of subunit species, notably addressing an unmet challenge of engineering 2D crystals with periodicities that can be arbitrarily larger than subunit size. To demonstrate the utility of our design approach, we encode specific interactions between triangular subunits synthesized by DNA origami and show that we can guide their self-assembly into tilings with a wide variety of symmetries, using up to 12 unique species of triangles. By conjugating specific triangles with gold nanoparticles, we fabricate gold-nanoparticle supercrystals whose lattice parameter spans up to 300 nm. Finally, to generate economical design rules, we compare the design economy of various tilings. In particular, we show that (1) higher symmetries allow assembly of larger unit cells with fewer subunits and (2) linear supercrystals can be designed more economically using linear primitive unit cells. This work provides a simple algorithmic approach to designing periodic assemblies, which may open new doors to the multiscale assembly of superlattices of nanostructured "metatoms" with engineered plasmonic functions.

cond-mat.soft↗

arXiv2024

Mesoscale Polymer Arrays: High Aspect Ratio Surface Structures and Their Digital Reconstruction

Inspired by adhesive bio-filamentous structure, such as bacterial pili, this work details the methods used to fabricate and characterize a surface-anchored array of thin, flexible and shape-responsive mesoscale polymer ribbons with a length-to-thickness aspect ratio of up to 100,000. The resulting structures exhibit geometrically complex and dynamic morphologies consistent with elastocapillary bending that experience an increase in curvature over hours of aging due to creep. We develop a computational image analysis framework to generate 3D reconstructions of these densely crowded geometries and extract quantitative descriptors to demonstrate morphological changes due to aging. We demonstrate the robustness of this quantitative method by characterizing the creep-induced change in an aging ribbon array's shape and develop a scaling relationship to describe the importance of ribbon thickness for shape and dynamical observations. These methods demonstrate an essential baseline to probe morphology-property relationships of mesoscale polymer ribbon arrays fabricated from a variety of materials in numerous environments. Through the introduction of perfluorodecalin droplets, we illustrate the potential of these ribbon arrays towards applications in adhesive, microrobotic, and biomedical devices.

cond-mat.soft↗

arXiv2024

Self-limiting stacks of curvature-frustrated colloidal plates: Roles of intra-particle versus inter-particle deformations

In geometrically frustrated assemblies local inter-subunit misfits propagate to intra-assembly strain gradients, giving rise to anomalous self-limiting assembly thermodynamics. Here, we use theory and coarse-grained simulation to study a recently developed class of ``curvamer'' particles, flexible shell-like particles that exhibit self-limiting assembly due to the build up of curvature deformation in cohesive stacks. To address a generic, yet poorly understood aspect of frustrated assembly, we introduce a model of curvamer assembly that incorporates both {\it intra-particle} shape deformation as well as compliance of {\it inter-particle} cohesive gaps, an effect we can attribute to a {\it finite range of attraction} between particles. We show that the ratio of intra-particle (bending elasticity) to inter-particle stiffness not only controls the regimes of self-limitation but also the nature of frustration propagation through curvamer stacks. We find a transition from uniformly-bound, curvature-focusing stacks at small size to gap-opened, uniformly curved stacks at large size is controlled by a dimensionless measure of inter- versus intra-curvamer stiffness. The finite range of inter-particle attraction determines range of cohesion in stacks are self-limiting, a prediction which is in strong agreement with numerical studies of our coarse-grained colloidal model. These predictions provide critical guidance for experimental realizations of frustrated particle systems designed to exhibit self-limitation at especially large multi-particle scales.

cond-mat.soft↗

arXiv2024

Economical routes to size-specific assembly of self-closing structures

Self-assembly is one of the prevalent strategies used by living systems to fabricate ensembles of precision nanometer-scale structures and devices. The push for analogous approaches to create synthetic nanomaterials has led to the development of a large class of programmable crystalline structures. However, many applications require `self-limiting' assemblies, which autonomously terminate growth at a well-defined size and geometry. For example, curved architectures such as tubules, vesicles, or capsids can be designed to self-close at a particular size, symmetry, and topology. But developing synthetic strategies for self-closing assembly has been challenging, in part because such structures are prone to polymorphism that arises from thermal fluctuations of their local curvature, a problem that worsens with increased target size. Here we demonstrate a strategy to eliminate this source of polymorphism in self-closing assembly of tubules by increasing the assembly complexity. In the limit of single-component assembly, we find that thermal fluctuations allow the system to assemble nearby, off-target structures with varying widths, helicities, and chirality. By increasing the number of distinct components, we reduce the density of off-target states, thereby increasing the selectivity of a user-specified target structure to nearly 100%. We further show that by reducing the design constraints by targeting either the pitch or the width of tubules, fewer components are needed to reach complete selectivity. Combining experiments with theory, our results reveal an economical limit, which determines the minimum number of components that are required to create arbitrary assembly sizes with full selectivity. In the future, this approach could be extended to more complex self-limited structures, such as shells or triply periodic surfaces.

cond-mat.soft↗