Reconfigurable assemblies of shape-changing nanorods

Shape control of deformable charge-patterned nanoparticles

Deformable nanoparticles (NPs) offer unprecedented opportunities as dynamic building blocks that can spontaneously reconfigure during assembly in response to environmental cues. Designing reconfigurable materials based on deformable NPs hinges on an understanding of the shapes that can be engineered in these NPs. We solve for the low-energy shapes of charge-patterned deformable NPs by using molecular dynamics-based simulated annealing to minimize a coarse-grained model Hamiltonian characterized with NP elastic and electrostatic energies subject to a volume constraint. We show that deformable spherical NPs of radius 50 nm whose surface is tailored with octahedrally distributed charged patches and double-cap charged patches adapt their shape differently in response to changes in surface charge coverage and ionic strength. We find shape transitions to rounded octahedra, faceted octahedra, faceted bowls, oblate spheroids, spherocylinders, dented beans, and dimpled rounded bowls. We demonstrate that similar shape transitions can be achieved in deformable NPs of different sizes. The effects of counterion condensation on the free-energetic drive associated with the observed deformations are examined via Manning model calculations that utilize simulation-derived estimates for the NP Coulomb energy under salt-free conditions. The charge-pattern-based shape control of deformable NPs has implications for the design of responsive nanocontainers and for assembling reconfigurable materials whose functionality hinges on the shape-shifting properties of their nanoscale building blocks.

Optimization of non-equilibrium self-assembly protocols using Markov state models

The promise of self-assembly to enable the bottom-up formation of materials with prescribed architectures and functions has driven intensive efforts to uncover rational design principles for maximizing the yield of a target structure. Yet, despite many successful examples of self-assembly, ensuring kinetic accessibility of the target structure remains an unsolved problem in many systems. In particular, long-lived kinetic traps can result in assembly times that vastly exceed experimentally accessible timescales. One proposed solution is to design non-equilibrium assembly protocols in which system parameters change over time to avoid such kinetic traps. Here, we develop a framework to combine Markov state model (MSM) analysis with optimal control theory to compute a time-dependent protocol that maximizes the yield of the target structure at a finite time. We present an adjoint-based gradient descent method that, in conjunction with MSMs for a system as a function of its control parameters, enables efficiently optimizing the assembly protocol. We also describe an interpolation approach to significantly reduce the number of simulations required to construct the MSMs. We demonstrate our approach with two examples; a simple semi-analytic model for the folding of a polymer of colloidal particles, and a more complex model for capsid assembly. Our results show that optimizing time-dependent protocols can achieve significant improvements in the yields of selected structures, including equilibrium free energy minima, long-lived metastable structures, and transient states.

Shape-Changing Particles: From Materials Design and Mechanisms to Implementation

Demands for next-generation soft and responsive materials have sparked recent interest in the development of shape-changing particles and particle assemblies. Over the last two decades, a variety of mechanisms that drive shape change have been explored and integrated into particulate systems. Through a combination of top-down fabrication and bottom-up synthesis techniques, shape-morphing capabilities extend from the microscale to the nanoscale. Consequently, shape-morphing particles are rapidly emerging in a variety of contexts, including photonics, microfluidics, microrobotics, and biomedicine. Herein, the key mechanisms and materials that facilitate shape changes of microscale and nanoscale particles are discussed. Recent progress in the applications made possible by these particles is summarized, and perspectives on their promise and key open challenges in the field are discussed.

Designing Surface Charge Patterns for Shape Control of Deformable Nanoparticles

Designing reconfigurable materials based on deformable nanoparticles (NPs) hinges on an understanding of the energetically favored shapes these NPs can adopt. Using simulations, we show that hollow, deformable, patchy NPs tailored with surface charge patterns such as Janus patches, stripes, and polyhedrally distributed patches differently adapt their shape in response to changes in patterns and ionic strength, transforming into capsules, hemispheres, variably dimpled bowls, and polyhedra. The links between anisotropy in NP surface charge, shape, and the elastic energy density are discussed.

Computational studies of shape control of charged deformable nanocontainers

Biological matter is often compartmentalized by soft membranes that dynamically change their shape in response to chemical and mechanical cues. Deformable soft-matter-based nanoscale membranes or nanocontainers that mimic this behavior can be used as drug-delivery carriers that can adapt to evolving physiological conditions, or as dynamic building blocks for the design of novel hierarchical materials via assembly engineering. Here, we connect the intrinsic features of charged deformable nanocontainers such as their size, charge, surface tension, and elasticity with their equilibrium shapes for a wide range of solution conditions using molecular dynamics simulations. These links identify the fundamental mechanisms that establish the chemical and materials design control strategies for modulating the equilibrium shape of these nanocontainers. We show that flexible nanocontainers of radii ranging from 10-20 nm exhibit sphere-to-rod-to-disc shape transitions yielding rods and discs over a wide range of aspect ratio λ (0.3 < λ < 5). The shape transitions can be controlled by tuning salt and/or surfactant concentration as well as material elastic parameters. The shape changes are driven by reduction in the global electrostatic energy and are associated with dramatic changes in local surface elastic energy distributions. To illustrate the shape transition mechanisms, exact analytical calculations for idealized spheroidal nanocontainers in salt-free conditions are performed. Explicit counterion simulations near nanocontainers and associated Manning model calculations provide an assessment of the stability of observed shape deformations in the event of ion condensation.

Conformation Dependence of Diphenylalanine Self-Assembly Structures and Dynamics: Insights from Hybrid-Resolution Simulations

The molecular design of peptide-assembled nanostructures relies on extensive knowledge pertaining to the relationship between conformational features of peptide constituents and their behavior regarding self-assembly, and characterizing the conformational details of peptides during their self-assembly is experimentally challenging. Here, we demonstrate that a hybrid-resolution modeling method can be employed to investigate the role that conformation plays during the assembly of terminally capped diphenylalanines (FF) through microsecond simulations of hundreds or thousands of peptides. Our simulations discovered tubular or vesicular nanostructures that were consistent with experimental observation while reproducing critical self-assembly concentration and secondary structure contents in the assemblies that were measured in our experiments. The atomic details provided by our method allowed us to uncover diverse FF conformations and conformation dependence of assembled nanostructures. We found that the assembled morphologies and the molecular packing of FFs in the observed assemblies are linked closely with side-chain angle and peptide bond orientation, respectively. Of various conformations accessible to soluble FFs, only a select few are compatible with the assembled morphologies in water. A conformation resembling a FF crystal, in particular, became predominant due to its ability to permit highly ordered and energetically favorable FF packing in aqueous assemblies. Strikingly, several conformations incompatible with the assemblies arose transiently as intermediates, facilitating key steps of the assembly process. The molecular rationale behind the role of these intermediate conformations were further explained. Collectively, the structural details reported here advance the understanding of the FF self-assembly mechanism, and our method shows promise for studying peptide-assembled nanostructures and their rational design.

Molecular dynamics simulation of thermotropic bolaamphiphiles with a swallow-tail lateral chain: formation of cubic network phases

T-shaped bolaamphiphiles (TBA) with a swallow-tail lateral chain have been found to provide a fertile platform to produce complex liquid crystalline phases that are accessible through changes of temperature and lateral chain length and design. In this work, we use molecular simulations of a simple coarse-grained model to map out the phase behavior of this type of molecules. This model is based on the premise that the crucial details of the fluid structure stem from close range repulsions and the strong directional forces typical of hydrogen bonds. Our simulations confirm that TBAs exhibit a rich phase behavior upon increasing the length of their lateral chain. The simulations detect a double gyroid phase and an axial-bundle columnar phase which bear some structural resemblance to those found in the experiment. In addition, simulations predict two cocontinuous phases with 3D-periodicity: the "single" diamond and the "single" plumber's nightmare phase. Our analysis of energetic and entropic contributions to the free energy of phases formed by TBA with either swallow-tail or linear side-chains suggest that the 3D-periodic network phases formed by the former are stabilized by the large conformation entropy of the side-chains.

Effects of Lateral and Terminal Chains of X-Shaped Bolapolyphiles with Oligo(phenylene ethynylene) Cores on Self-Assembly Behaviour. Part 1: Transition between Amphiphilic and Polyphilic Self-Assembly in the Bulk

Polyphilic self-assembly leads to compartmentalization of space and development of complex structures in soft matter on different length scales, reaching from the morphologies of block copolymers to the liquid crystalline (LC) phases of small molecules. Whereas block copolymers are known to form membranes and interact with phospholipid bilayers, liquid crystals have been less investigated in this respect. Here, series of bolapolyphilic X-shaped molecules were synthesized and investigated with respect to the effect of molecular structural parameters on the formation of LC phases (part 1), and on domain formation in phospholipid bilayer membranes (part 2). The investigated bolapolyphiles are based on a rod-like π-conjugated oligo(phenylene ethynylene) (OPE) core with two glycerol groups being either directly attached or separated by additional ethylene oxide (EO) units to both ends. The X-shape is provided by two lateral alkyl chains attached at opposite sides of the OPE core, being either linear, branched, or semiperfluorinated. In this report, the focus is on the transition from polyphilic (triphilic or tetraphilic) to binary amphiphilic self-assembly. Polyphilic self-assembly, i.e., segregation of all three or four incorporated units into separate nano-compartments, leads to the formation of hexagonal columnar LC phases, representing triangular honeycombs. A continuous transition from the well-defined triangular honeycomb structures to simple hexagonal columnar phases, dominated by the arrangement of polar columns on a hexagonal lattice in a mixed continuum formed by the lipophilic chains and the OPE rods, i.e., to amphiphilic self-assembly, was observed by reducing the length and volume of the lateral alkyl chains. A similar transition was found upon increasing the length of the EO units involved in the polar groups. If the lateral alkyl chains are enlarged or replaced by semiperfluorinated chains, then the segregation of lateral chains and rod-like cores is retained, even for enlarged polar groups, i.e., the transition from polyphilic to amphiphilic self-assembly is suppressed.

Emergence of tilt in square honeycomb liquid crystals

First liquid crystalline phases with tilted organization of rod-like aromatics in a square honeycomb structure were discovered. The developing tilt is temperature, chain length and chain volume dependent, and has a dramatic effect on the optical properties, occasionally leading to an inversion of birefringence. The observed effects of chain branching on tilt contributes to a general understanding of lateral chain engineering in tailoring the self-assembly of π-conjugated molecular rods.

Transformative Two-Dimensional Array Configurations by Geometrical Shape-Shifting Protein Microstructures

Two-dimensional (2D) geometrical shape-shifting is prevalent in nature, but remains challenging in man-made "smart" materials, which are typically limited to single-direction responses. Here, we fabricate geometrical shape-shifting bovine serum albumin (BSA) microstructures to achieve circle-to-polygon and polygon-to-circle geometrical transformations. In addition, transformative two-dimensional microstructure arrays are demonstrated by the ensemble of these responsive microstructures to confer structure-to-function properties. The design strategy of our geometrical shape-shifting microstructures focuses on embedding precisely positioned rigid skeletal frames within responsive BSA matrices to direct their anisotropic swelling under pH stimulus. This is achieved using layer-by-layer two photon lithography, which is a direct laser writing technique capable of rendering spatial resolution in the sub-micrometer length scale. By controlling the shape, orientation and number of the embedded skeletal frames, we have demonstrated well-defined arc-to-corner and corner-to-arc transformations, which are essential for dynamic circle-to-polygon and polygon-to-circle shape-shifting, respectively. We further fabricate our shape-shifting microstructures in periodic arrays to experimentally demonstrate the first transformative 2D patterned arrays. Such versatile array configuration transformations give rise to structure-to-physical properties, including array porosity and pore shape, which are crucial for the development of on-demand multifunctional "smart" materials, especially in the field of photonics and microfluidics.

Polymorphic Ring-Shaped Molecular Clusters Made of Shape-Variable Building Blocks

Self-assembling molecular building blocks able to dynamically change their shapes, is a concept that would offer a route to reconfigurable systems. Although simulation studies predict novel properties useful for applications in diverse fields, such kinds of building blocks, have not been implemented thus far with molecules. Here, we report shape-variable building blocks fabricated by DNA self-assembly. Blocks are movable enough to undergo shape transitions along geometrical ranges. Blocks connect to each other and assemble into polymorphic ring-shaped clusters via the stacking of DNA blunt-ends. Reconfiguration of the polymorphic clusters is achieved by the surface diffusion on mica substrate in response to a monovalent salt concentration. This work could inspire novel reconfigurable self-assembling systems for applications in molecular robotics.

Effect of shape on the self-assembly of faceted patchy nanoplates with irregular shape into tiling patterns

Recent reports of the synthesis and assembly of faceted nanoplates with a wide range of shapes and composition motivates the possibility of a new class of two-dimensional materials with specific patterns targeted for a host of exciting properties. Yet, studies of how nanoplate shape controls their assembly - knowledge necessary for their inverse design from target structures - has been performed for only a handful of systems. By constructing a general framework in which many known faceted nanoplates may be described in terms of four anisotropy dimensions, we discover design rules to guide future synthesis and assembly. We study via Monte Carlo simulations attractive polygons whose shape is altered systematically under the following four transformations: faceting, pinching, elongation and truncation. We report that (i) faceting leads to regular porous structures (ii) pinching stabilizes complex structures such as dodecagonal quasicrystals (iii) elongation leads to asymmetric phase behavior, where low and high aspect ratio nanoplates self-assemble completely different structures and (iv) low and high degrees of truncation transform a complex self-assembler into a disk-like assembler, providing design ideas that could lead to switchable structures. We provide important insight into how the shape and attractive interactions of a nanoplate can be exploited or designed to target specific classes of structures, including space-filling, porous, and complex tilings.

Dynamic visualization of nanoscale vortex orbits

Due to the atomic-scale resolution, scanning tunneling microscopy is an ideal technique to observe the smallest objects. Nevertheless, it suffers from very long capturing times in order to investigate dynamic processes at the nanoscale. We address this issue, for vortex matter in NbSe2, by driving the vortices using an ac magnetic field and probing the induced periodic tunnel current modulations. Our results reveal different dynamical modes of the driven vortex lattices. In addition, by recording and synchronizing the time evolution of the tunneling current at each pixel, we visualize the overall dynamics of the vortex lattice with submillisecond time resolution and subnanometer spatial resolution.

Gold nanorod linking to control plasmonic properties in solution and polymer nanocomposites

A novel, solution-based method is presented to prepare bifunctional gold nanorods (B-NRs), assemble B-NRs end-to-end in various solvents, and disperse linked B-NRs in a polymer matrix. The B-NRs have poly(ethylene glycol) grafted along its long axis and cysteine adsorbed to its ends. By controlling cysteine coverage, bifunctional ligands or polymer can be end-grafted to the AuNRs. Here, two dithiol ligands (C6DT and C9DT) are used to link the B-NRs in organic solvents. With increasing incubation time, the nanorod chain length increases linearly as the longitudinal surface plasmon resonance shifts toward lower adsorption wavelengths (i.e., red shift). Analogous to step-growth polymerization, the polydispersity in chain length also increases. Upon adding poly(ethylene glycol) or poly(methyl methacrylate) to chloroform solution with linked B-NR, the nanorod chains are shown to retain end-to-end linking upon spin-casting into PEO or PMMA films. Using quartz crystal microbalance with dissipation (QCM-D), the mechanism of nanorod linking is investigated on planar gold surfaces. At submonolayer coverage of cysteine, C6DT molecules can insert between cysteines and reach an areal density of 3.4 molecules per nm(2). To mimic the linking of Au NRs, this planar surface is exposed to cysteine-coated Au nanoparticles, which graft at 7 NPs per μm(2). This solution-based method to prepare, assemble, and disperse Au nanorods is applicable to other nanorod systems (e.g., CdSe) and presents a new strategy to assemble anisotropic particles in organic solvents and polymer coatings.

Development of structural complexity by liquid-crystal self-assembly

Since the discovery of the liquid-crystalline state of matter 125 years ago, this field has developed into a scientific area with many facets. This Review presents recent developments in the molecular design and self-assembly of liquid crystals. The focus is on new exciting soft-matter structures distinct from the usually observed nematic, smectic, and columnar phases. These new structures have enhanced complexity, including multicompartment and cellular structures, periodic and quasiperiodic arrays of spheres, and new emergent properties, such as ferroelctricity and spontaneous achiral symmetry-breaking. Comparisons are made with developments in related fields, such as self-assembled monolayers, multiblock copolymers, and nanoparticle arrays. Measures of structural complexity used herein are the size of the lattice, the number of distinct compartments, the dimensionality, and the logic depth of the resulting supramolecular structures.

Packing and self-assembly of truncated triangular bipyramids

Motivated by breakthroughs in the synthesis of faceted nano- and colloidal particles, as well as theoretical and computational studies of their packings, we investigate a family of truncated triangular bipyramids. We report dense periodic packings with small unit cells that were obtained via numerical and analytical optimization. The maximal packing fraction φ(max) changes continuously with the truncation parameter t. Eight distinct packings are identified based on discontinuities in the first and second derivatives of φ(max)(t). These packings differ in the number of particles in the fundamental domain (unit cell) and the type of contacts between the particles. In particular, we report two packings with four particles in the unit cell for which both φ(max)(t) and φ(max)'(t) are continuous and the discontinuity occurs in the second derivative only. In the self-assembly simulations that we perform for larger boxes with 2048 particles, only one out of eight packings is found to assemble. In addition, the degenerate quasicrystal reported previously for triangular bipyramids without truncation [Haji-Akbari et al., Phys. Rev. Lett. 107, 215702 (2011)] assembles for truncations as high as 0.45. The self-assembly propensities for the structures formed in the thermodynamic limit are explained using the isoperimetric quotient of the particles and the coordination number in the disordered fluid and in the assembled structure.

Harnessing Dynamic Covalent Bonds in Patchy Nanoparticles: Creating Shape-Shifting Building Blocks for Rational and Responsive Self-Assembly

Using computational modeling, we suggest and demonstrate a novel class of building blocks for nanoparticle self-assembly, that is, shape-shifting patchy nanoparticles. These nanoparticles are designed by harnessing dynamic covalent bonds between nanoparticles and patches decorated on them. The breaking and reforming of these bonds in response to their environment allow the patches to undergo a structural rearrangement that shifts the location or number of patches. Our simulations for the assembled superstructures and kinetic pathway of two types of these building blocks demonstrate that shape-shifting patchy nanoparticles delicately meet two emerging design concepts of next generation materials: rational self-assembly and responsive matter. In this context, these nanoparticles may enable new generations of materials with reconfigurable property as well as controllable topologies in a dynamical manner.

Shaping phases by phasing shapes

Incorporation of shape-shifting building blocks into self-assembled systems has emerged as a promising concept for dynamic structural control. The computational work by Nguyen et al. reported in this issue of ACS Nano examines the phase reconfigurations and kinetic pathways for systems built from shape-shifting building blocks. The studies illustrate several unique properties of such systems, including more efficient packings, novel structures that are distinctive from those obtained through conventional self-assembly, and reversible multistep shape-shifting pathways. The proposed assembly strategy is potentially applicable to a diverse range of systems because it relies on a change of geometrical constraints, which are common across all length scales. Recent developments in the areas of responsive materials and self-assembly methods provide feasible platforms for experimental realizations of shape-shifting reconfigurations; such systems might enable the next generation of dynamically switchable materials and reconfigurable devices.

Self-assembly and reconfigurability of shape-shifting particles

Reconfigurability of two-dimensional colloidal crystal structures assembled by anisometric particles capable of changing their shape were studied by molecular dynamics computer simulation. We show that when particles change shape on cue, the assembled structures reconfigure into different ordered structures, structures with improved order, or more densely packed disordered structures, on faster time scales than can be achieved via self-assembly from an initially disordered arrangement. These results suggest that reconfigurable building blocks can be used to assemble reconfigurable materials, as well as to assemble structures not possible otherwise, and that shape shifting could be a promising mechanism to engineer assembly pathways to ordered and disordered structures.

Continuous phase transformation in nanocube assemblies

The phase behavior of 3D assemblies of nanocubes in a ligand-rich solution upon solvent evaporation was experimentally investigated using small-angle x-ray scattering and electron microscopy. We observed a continuous transformation of assemblies between simple cubic and rhombohedral phases, where a variable angle of rhombohedral structure is determined by ligand thickness. We established a quantitative relationship between the particle shape evolution from cubes to quasispheres and the lattice distortion during the transformation, with a pathway exhibiting the highest known packing.