Curvature instability of chiral colloidal membranes on crystallization (original) (raw)
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Geometric frustration in buckled colloidal monolayers
Nature, 2008
Geometric frustration arises when lattice structure prevents simultaneous minimization of local interactions. It leads to highly degenerate ground states and, subsequently, complex phases of matter such as water ice, spin ice and frustrated magnetic materials. Here we report a simple geometrically frustrated system composed of closely packed colloidal spheres confined between parallel walls. Diameter-tunable microgel spheres are self-assembled into a buckled triangular lattice with either up or down displacements analogous to an antiferromagnetic Ising model on a triangular lattice. Experiment and theory reveal single-particle dynamics governed by in-plane lattice distortions that partially relieve frustration and produce ground-states with zigzagging stripes and subextensive entropy, rather than the more random configurations and extensive entropy of the antiferromagnetic Ising model. This tunable soft matter system provides an uncharted arena in which the dynamics of frustration, thermal excitations and defects can be directly visualized.
Geometric frustration in buckled colloidal
Geometric frustration arises when lattice structure prevents simultaneous minimization of local interaction energies. It leads to highly degenerate ground states and, subsequently, to complex phases of matter, such as water ice, spin ice, and frustrated magnetic materials. Here we report a simple geometrically frustrated system composed of closely packed colloidal spheres confined between parallel walls. Diameter-tunable microgel spheres are self-assembled into a buckled triangular lattice with either up or down displacements, analogous to an antiferromagnetic Ising model on a triangular lattice. Experiment and theory reveal single-particle dynamics governed by in-plane lattice distortions that partially relieve frustration and produce ground states with zigzagging stripes and subextensive entropy, rather than the more random configurations and extensive entropy of the antiferromagnetic Ising model. This tunable soft-matter system provides a means to directly visualize the dynamics of frustration, thermal excitations and defects.
Correlation between crystalline order and vitrification in colloidal monolayers
Journal of Physics: Condensed Matter, 2015
We investigate experimentally the relationship between local structure and dynamical arrest in a quasi-2d colloidal model system which approximates hard discs. We introduce polydispersity to the system to suppress crystallisation. Upon compression, the increase in structural relaxation time is accompanied by the emergence of local hexagonal symmetry. Examining the dynamical heterogeneity of the system, we identify three types of motion : "zero-dimensional" corresponding to β-relaxation, "one-dimensional" or stringlike motion and "two-dimensional" motion. The dynamic heterogeneity is correlated with the local order, that is to say locally hexagonal regions are more likely to be dynamically slow. However we find that lengthscales corresponding to dynamic heterogeneity and local structure do not appear to scale together approaching the glass transition.
Mechanical Self-Assembly of a Strain-Engineered Flexible Layer: Wrinkling, Rolling, and Twisting
Physical Review Applied, 2016
Self-shaping of curved structures, especially those involving flexible thin layers, has attracted increasing attention because of their broad potential applications in e.g. nanoelectromechanical/micro-electromechanical systems (NEMS/MEMS), sensors, artificial skins, stretchable electronics, robotics, and drug delivery. Here, we provide an overview of recent experimental, theoretical, and computational studies on the mechanical self-assembly of strain-engineered thin layers, with an emphasis on systems in which the competition between bending and stretching energy gives rise to a variety of deformations, such as wrinkling, rolling, and twisting. We address the principle of mechanical instabilities, which is often manifested in wrinkling or multistability of strain-engineered thin layers. The principles of shape selection and transition in helical ribbons are also systematically examined. We hope that a more comprehensive understanding of the mechanical principles underlying these rich phenomena can foster the development of new techniques for manufacturing functional threedimensional structures on demand for a broad spectrum of engineering applications. many applications like flexible electronics, stretchable electronics, nanophotonics, robotics, and microfluidics. Furthermore, helices can be considered as a special subclass of structures formed through rolling. They are chiral structures with broken left-right symmetry [19], which can be either left-handed or right-handed with a mirror image that has an opposite handedness or chirality. It is natural to think that such symmetry-breaking comes from the chirality of the microscopic building units, but this is not always the case [12]. Spontaneous helical ribbons can form either under terminal loads (e.g., tensile forces or torques) [20] or in the absence of terminal loads [9,15,21-23]. Shape transitions between purely twisted ribbons (or helicoids), cylindrical helical ribbons, and tubules have been frequently observed in twist-nematic elastomers [1,24], peptides [22,25], strained multilayer composites [9,15,21-23], and nanoribbons [10,26]. These transitions are often driven by the complex interplay between molecular interactions, environmental stimuli, elastic properties, and nonlinear geometric effects. Twisting can exist in thin layers outside of the uniform helix shape subclass, and can occur even when the driving forces are not off-axis with respect to the geometric axes of the material [12]. Twists in thin layers have an associated handedness and can even switch handedness [17]. Off-axis competition between the internal chirality of the building units of the thin layer and macroscopic forces acting on the layer can also form twists. 4 The article covers analysis of these afore-mentioned deformation modes such as wrinkling, rolling and twisting, along with examples and applications of each. This is followed by a synthesis of current promising research directions and future applications. Readers interested in the mechanics of thin layer deformation are encouraged to refer to some excellent recent reviews for a more comprehensive understanding of recent developments [27-30]. Recently, wrinkling in nanoparticle films has received a great deal of attention. The most common films include graphene [31-33], nanocrystals [34-37], and nanotubes [38-40]. While the following discussion avoids focusing on nanoparticle films in depth, they are an important subset of wrinkling research and the reader is encouraged to refer to those articles. It should also be noted that while the discussion of wrinkling and rolling mechanics is primarily focused on inorganic materials, polymer sheets are becoming increasingly important in science and engineering. For a discussion of the specific mechanics of polymer surfaces, we point the reader to J. Rodriguez-Hernandez's excellent review [41]. II. Self-assembly and strain distribution in wrinkles A. Wrinkling vs. rolling in a strain-engineered flexible layer A flexible pre-strained layer attached to a fixed boundary, adopts a 3D structure in
Wrinkling crystallography on spherical surfaces
Proceedings of the National Academy of Sciences, 2014
We present the results of an experimental investigation on the crystallography of the dimpled patterns obtained through wrinkling of a curved elastic system. Our macroscopic samples comprise a thin hemispherical shell bound to an equally curved compliant substrate. Under compression, a crystalline pattern of dimples selforganizes on the surface of the shell. Stresses are relaxed by both out-of-surface buckling and the emergence of defects in the quasihexagonal pattern. Three-dimensional scanning is used to digitize the topography. Regarding the dimples as point-like packing units produces spherical Voronoi tessellations with cells that are polydisperse and distorted, away from their regular shapes. We analyze the structure of crystalline defects, as a function of system size. Disclinations are observed and, above a threshold value, dislocations proliferate rapidly with system size. Our samples exhibit striking similarities with other curved crystals of charged particles and colloids. Differences are also found and attributed to the far-fromequilibrium nature of our patterns due to the random and initially frozen material imperfections which act as nucleation points, the presence of a physical boundary which represents an additional source of stress, and the inability of dimples to rearrange during crystallization. Even if we do not have access to the exact form of the interdimple interaction, our experiments suggest a broader generality of previous results of curved crystallography and their robustness on the details of the interaction potential. Furthermore, our findings open the door to future studies on curved crystals far from equilibrium. mechanical instabilities | curved surfaces | pattern formation | packing | defects T he classic design of a soccer ball, with its 20 hexagonal (white) patches interspersed with 12 (black) pentagons, the buckminsterfullerene C 60 (1), virus capsules (2), colloidosomes (3), and geodesic architectural domes are all examples of crystalline packings on spherical surfaces. In contrast with crystals on flat surfaces, these structures cannot be constructed from a tiling of hexagons alone. Instead, disclinations--nonhexagonal elements such as the 12 pentagons on a soccer ball--are required by topology (5, 6), which constrains how the crystal order must comply with the geometry of the underlying surface. For example, seeding a hexagonal crystal with a pentagon (fivefold disclination) disrupts the perfect hexagonal symmetry and introduces a localized stress concentrator, which can be relaxed through out-ofplane deformation with positive Gaussian curvature (7, 8). Likewise, a heptagon (sevenfold disclination) induces a disturbance with negative Gaussian curvature.
We investigate experimentally the relationship between local structure and dynamical arrest in a quasi-2d colloidal model system which approximates hard discs. We introduce polydispersity to the system to suppress crystallisation. Upon compression, the increase in structural relaxation time is accompanied by the emergence of local hexagonal symmetry. Examining the dynamical heterogeneity of the system, we identify three types of motion: 'zero-dimensional' corresponding to β-relaxation, 'one-dimensional' or stringlike motion and '2D' motion. The dynamic heterogeneity is correlated with the local order, that is to say locally hexagonal regions are more likely to be dynamically slow. However, we find that lengthscales corresponding to dynamic heterogeneity and local structure do not appear to scale together approaching the glass transition.
Elastic properties and line tension of self-assembled bilayer membranes
Physical Review E, 2013
The elastic properties of a self-assembled bilayer membrane are studied using the self-consistent field theory, applied to a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents. Examining the free energy of bilayer membranes with different geometries allows us to calculate their bending modulus, Gaussian modulus, two fourth-order membrane moduli, and the line tension. The dependence of these parameters on the microscopic characteristics of the amphiphilic chain, characterized by the volume fraction of the hydrophilic component, is systematically studied. The theoretical predictions are compared with the results from a simple monolayer model, which approximates a bilayer membrane by two monolayers. Finally the region of validity of the linear elasticity theory is analyzed by examining the higher-order contributions.
The role of molecular shape in bilayer elasticity and phase behavior
The Journal of Chemical Physics, 2004
A previously developed molecular level model for lipid bilayers Brown, JCP, 120, 1059 (2004)] is extended to allow for variations in lipid length and simulations under constant surface tension conditions. The dependence of membrane elasticity on bilayer thickness is obtained by adjusting lipid length at constant temperature and surface tension. Additionally, bilayer fluidity at various lipid lengths is quantified by analysis of a length versus temperature phase diagram at vanishing tension. Regions of solid, gel-like (hexatic) and fluid bilayer behavior are established by identification of phase boundaries. The main melting transition is found to be density driven; the melting temperature scales inversely with lipid length since thermal expansion increases with lipid aspect ratio.
Inward growth by nucleation: Multiscale self-assembly of ordered membranes
Science advances, 2018
Striking morphological similarities found between superstructures of a wide variety of seemingly unrelated crystalline membrane systems hint at the existence of a common formation mechanism. Resembling systems such as multiwalled carbon nanotubes, bacterial protein shells, or peptide nanotubes, the self-assembly of SDS/β-cyclodextrin complexes leads to monodisperse multilamellar microtubes. We uncover the mechanism of this hierarchical self-assembly process by time-resolved small- and ultrasmall-angle x-ray scattering. In particular, we show that symmetric crystalline bilayers bend into hollow cylinders as a consequence of membrane line tension and an anisotropic elastic modulus. Starting from single-walled microtubes, successive nucleation of new cylinders inside preexisting ones drives an inward growth. As both the driving forces that underlie the self-assembly behavior and the resulting morphologies are common to systems of ordered membranes, we believe that this formation mechan...
Intrinsic bending force in anisotropic membranes made of chiral molecules
Physical Review A, 1988
A linear term linked to molecular chirality occurs in the bending energy of membranes with C& or D2 symmetry. We find it to alternate in sign, depending on the direction of a cylindrical curvature, and discuss consequences for anisotropic solid membranes, tilted fluid bilayers, and ferroelectric smectic liquid crystals.