Self-Assembly of Mesophases from Nanoparticles

Chiroptical Strain Sensors from Electrospun Cadmium Sulfide Quantum-Dot Fibers

Controllable synthesis of homochiral nano/micromaterials has been a constant challenge for fabricating various stimuli-responsive chiral sensors. To provide an avenue to this goal, we report electrospinning as a simple and economical strategy to form continuous homochiral microfibers with strain-sensitive chiroptical properties. First, electrospun homochiral microfibers from self-assembled cadmium sulfide (CdS) quantum dot magic-sized clusters (MSCs) are produced. Highly sensitive and reversible strain sensors are then fabricated by embedding these chiroptically active fibers into elastomeric films. The chiroptical response on stretching is indicated quantitatively as reversible changes in magnitude, spectral position (wavelength), and sign in circular dichroism (CD) and linear dichroism (LD) signals and qualitatively as a prominent change in the birefringence features under cross-polarizers. The observed periodic twisted helical fibrils at the surface of fibers provide insights into the origin of the fibers' chirality. The measurable shifts in CD and LD are caused by elastic deformations of these helical fibrillar structures of the fiber. To elucidate the origin of these chiroptical properties, we used field emission-electron microscopy (FE-SEM), atomic force microscopy (AFM), synchrotron X-ray analysis, polarized optical microscopy, as well as measurements to isolate the true CD, and contributions from photoelastic modulators (PEM) and LD. Our findings thus offer a promising strategy to fabricate chiroptical strain-sensing devices with multiple measurables/observables using electric-field-assisted spinning of homochiral nano/microfibers.

Lattice Model Results for Pattern Formation in a Mixture with Competing Interactions

A monolayer consisting of two types of particles, with energetically favored alternating stripes of the two components, is studied by Monte Carlo simulations and within a mesoscopic theory. We consider a triangular lattice model and assume short-range attraction and long-range repulsion between particles of the same kind, as well as short-range repulsion and long-range attraction for the cross-interaction. The structural evolution of the model upon increasing temperature is studied for equal chemical potentials of the two species. We determine the structure factor, the chemical potential-density isotherms, the specific heat, and the compressibility, and show how these thermodynamic functions are associated with the spontaneous formation of stripes with varying degrees of order.

Designer pair statistics of disordered many-particle systems with novel properties

The knowledge of exact analytical functional forms for the pair correlation function g2(r) and its corresponding structure factor S(k) of disordered many-particle systems is limited. For fundamental and practical reasons, it is highly desirable to add to the existing database of analytical functional forms for such pair statistics. Here, we design a plethora of such pair functions in direct and Fourier spaces across the first three Euclidean space dimensions that are realizable by diverse many-particle systems with varying degrees of correlated disorder across length scales, spanning a wide spectrum of hyperuniform, typical nonhyperuniform, and antihyperuniform ones. This is accomplished by utilizing an efficient inverse algorithm that determines equilibrium states with up to pair interactions at positive temperatures that precisely match targeted forms for both g2(r) and S(k). Among other results, we realize an example with the strongest hyperuniform property among known positive-temperature equilibrium states, critical-point systems (implying unusual 1D systems with phase transitions) that are not in the Ising universality class, systems that attain self-similar pair statistics under Fourier transformation, and an experimentally feasible polymer model. We show that our pair functions enable one to achieve many-particle systems with a wide range of translational order and self-diffusion coefficients D, which are inversely related to one another. One can design other realizable pair statistics via linear combinations of our functions or by applying our inverse procedure to other desirable functional forms. Our approach facilitates the inverse design of materials with desirable physical and chemical properties by tuning their pair statistics.

Self-Assembling of Nonadditive Mixtures Containing Patchy Particles with Tunable Interactions

Mixtures of nanoparticles (NPs) with hybridizing grafted DNA or DNA-like strands have been of particular interest because of the tunable selectivity provided for the interactions between the NP components. A richer self-assembly behavior would be accessible if these NP-NP interactions could be designed to give nonadditive mixing (in analogy to the case of molecular components). Nonadditive mixing occurs when the mixed-state volume is smaller (negative) or larger (positive) than the sum of the individual components' volumes. However, instances of nonadditivity in colloidal/NP mixtures are rare, and systematic studies of such mixtures are nonexistent. This work focuses on patchy NPs whose patches (coarsely representing grafted hybridizing DNA strands) not only encode selectivity across components but also impart a tunable nonadditivity by varying their extent of protrusion. To guide the exploration of the relationship between phase behavior and nonadditivity for different patches' designs, the NP-NP potential of mean force (PMF) and a nonadditive parameter were first calculated. For one-patch NPs, different lamellar morphologies were predominantly observed. In contrast, for mixtures of two-patch NPs and (fully grafted) spherical particles, a rich phase behavior was found depending on patch-patch angle and degree of nonadditivity, resulting in phases such as the gyroid, cylinder, honeycomb, and two-layered crystal. Our results also show that both minimum positive nonadditivity and multivalent interactions are necessary for the formation of ordered network mesophases in the class of models studied.

Optimizing Chain Topology of Bottle Brush Copolymer for Promoting the Disorder-to-Order Transition

The order-disorder transitions (ODT) of core-shell bottle brush copolymer and its structural isomers were investigated by dissipative particle dynamics simulations and theoretically by random phase approximation. Introducing a chain topology parameter λ which parametrizes linking points between M diblock chains each with N monomers, the degree of incompatibility at ODT ((χN)ODT; χ being the Flory-Huggins interaction parameter between constituent monomers) was predicted as a function of chain topology parameter (λ) and the number of linked diblock chains per bottle brush copolymer (M). It was found that there exists an optimal chain topology about λ at which (χN)ODT gets a minimum while the domain spacing remains nearly unchanged. The prediction provides a theoretical guideline for designing an optimal copolymer architecture capable of forming sub-10 nm periodic structures even with non-high χ components.

Multiscale hierarchical structures from a nanocluster mesophase

Spontaneous hierarchical self-organization of nanometre-scale subunits into higher-level complex structures is ubiquitous in nature. The creation of synthetic nanomaterials that mimic the self-organization of complex superstructures commonly seen in biomolecules has proved challenging due to the lack of biomolecule-like building blocks that feature versatile, programmable interactions to render structural complexity. In this study, highly aligned structures are obtained from an organic-inorganic mesophase composed of monodisperse Cd₃₇S₁₈ magic-size cluster building blocks. Impressively, structural alignment spans over six orders of magnitude in length scale: nanoscale magic-size clusters arrange into a hexagonal geometry organized inside micrometre-sized filaments; self-assembly of these filaments leads to fibres that then organize into uniform arrays of centimetre-scale bands with well-defined surface periodicity. Enhanced patterning can be achieved by controlling processing conditions, resulting in bullseye and 'zigzag' stacking patterns with periodicity in two directions. Overall, we demonstrate that colloidal nanomaterials can exhibit a high level of self-organization behaviour at macroscopic-length scales.

Dynamics and phase behavior of two-dimensional size-asymmetric binary mixtures of core-softened colloids

The self-assembly of binary colloidal mixtures provides a bottom-up approach to create novel functional materials. To elucidate the effect of composition, temperature, and pressure on the self-assembly behavior of size-asymmetric mixtures, we performed extensive dynamics simulations of a simple model of polymer-grafted colloids. We have used a core-softened interaction potential and extended it to represent attractive interactions between unlike colloids and repulsions between like colloids. Our study focused on size-asymmetric mixtures where the ratio between the sizes of the colloidal cores was fixed at σ_Bσ_A=0.5. We have performed extensive simulations in the isothermal-isobaric and canonical (NVT) ensembles to elucidate the phase behavior and dynamics of mixtures with different stoichiometric ratios. Our simulation results uncovered a rich phase behavior, including the formation of hierarchical structures with many potential applications. For compositions where small colloids are the majority, sublattice melting occurs for a wide range of densities. Under these conditions, large colloids form a well-defined lattice, whereas small colloids can diffuse through the system. As the temperature is decreased, the small colloids localize, akin to a metal-insulator transition, with the small colloids playing a role similar to electrons. Our results are summarized in terms of phase diagrams.

Softness-Enhanced Self-Assembly of Pyrochlore- and Perovskite-like Colloidal Photonic Crystals from Triblock Janus Particles

It remains extremely challenging to build three-dimensional photonic crystals with complete photonic bandgaps by simple and experimentally realizable colloidal building blocks. Here, we demonstrate that particle softness can enhance both the self-assembly of pyrochlore- and perovskite-like lattice structures from simple deformable triblock Janus colloids and their photonic bandgap performances. Dynamics simulation results show that the region of stability of pyrochlore lattices can be greatly expanded by appropriately increasing softness, and the perovskite lattices are unexpectedly obtained at enough high softness. Photonic calculations show that the direct pyrochlore lattices formed from overlapping soft triblock Janus particles exhibit even larger photonic bandgaps than the ideal nonoverlapping pyrochlore lattice, and proper overlap arising from softness can also dramatically improve the photonic properties of the inverse pyrochlore and perovskite lattices. Our study offers a new and feasible self-assembly path toward three-dimensional photonic crystals with large and robust photonic bandgaps.

Inverse design of equilibrium cluster fluids applied to a physically informed model

Inverse design strategies have proven highly useful for the discovery of interaction potentials that prompt self-assembly of a variety of interesting structures. However, often the optimized particle interactions do not have a direct relationship to experimental systems. In this work, we show that Relative Entropy minimization is able to discover physically meaningful parameter sets for a model interaction built from depletion attraction and electrostatic repulsion that yield self-assembly of size-specific clusters. We then explore the sensitivity of the optimized interaction potentials with respect to deviations in the underlying physical quantities, showing that clustering behavior is largely preserved even as the optimized parameters are perturbed.

Phase behavior of a two-dimensional core-softened system: new physical insights

In this work, we report results of extensive computer simulations regarding the phase behavior of a core-softened system. By using structural and thermodynamic descriptors, as well as self-diffusion coefficients, we provide a comprehensive view of the rich phase behavior displayed by the particular instance of the model studied in here. Our calculations agree with previously published results focused on a smaller region in the temperature-density parameter space (Dudalov et al 2014 Soft Matter 10 4966). In this work, we explore a broader region in this parameter space, and uncover interesting fluid phases with low-symmetry local order, that were not reported by previous works. Solid phases were also found, and have been previously characterized in detail by (Kryuchkov et al 2018 Soft Matter 14 2152). Our results support previously reported findings, and provide new physical insights regarding the emergence of order as disordered phases transform into solids by providing radial distribution function maps and specific heat data. Our results are summarized in terms of a phase diagram.

Thermodynamics and ordering kinetics in asymmetric PS-b-PMMA block copolymer thin films

The ordering kinetics of standing cylinder-forming polystyrene-block-poly(methyl methacrylate) block copolymers (molecular weight: 39 kg mol^-1) close to the order-disorder transition is experimentally investigated following the temporal evolution of the correlation length at different annealing temperatures. The growth exponent of the grain-coarsening process is determined to be 1/2, signature of a curvature-driven ordering mechanism. The measured activation enthalpy and the resulting Meyer-Neldel temperature for this specific copolymer along with the data already known for PS-b-PMMA block copolymers in strong segregation limit allow investigation of the interplay between the ordering kinetics and the thermodynamic driving force during the grain coarsening. These findings unveil various phenomena concomitantly occurring during the thermally activated ordering kinetics at segmental, single chain, and collective levels.

Enhanced sampling of cylindrical microphase separation via a shell-averaged bond-orientational order parameter

The formation of a hexagonal phase from disordered phase is one of the typical order-disorder transitions (ODTs) observed in asymmetric diblock copolymer systems. In order to drive this transition in a particle-based simulation, we introduce a shell-based bond-orientational order parameter that selectively responds to the mesoscopic order of the hexagonal cylinder phase. From metadynamics simulations in a bond-free particle model system, the characteristic pathway involved with the underlying free energy surface is deduced for the disordered-to-hexagonal transition. It is shown consecutively that the transition pathway and the metastable state are reproduced in dissipative particle dynamics simulations for the corresponding transition in a bulk asymmetric block copolymer melt system. These agreements suggest that efficient strategies for enhanced sampling with particle-based simulations of block copolymer systems can be devised using coarse-grained pictures of the mesoscopic order.

Hierarchical complex self-assembly in binary nanoparticle mixtures

Hierarchical self-assembly of soft matter provides a powerful route to create complex materials with enhanced physical properties. The understanding of the fundamental processes leading to such organization can provide design rules to create new functional materials. In this work, we use a simple model of polymer-grafted nanoparticles to explore the self-assembly of binary mixtures. By using Monte Carlo simulations we study the interplay of composition, density and particle sizes on the self-organization of such nanoparticle systems. It is found that complex hierarchical organization can take place for conditions where one-component systems form simple lattices. In particular, a mixture where one component forms a structure with 18-fold symmetry in a sea of an apparent disordered phase of the second component is observed to emerge for certain parameter combinations.

A generalized deep learning approach for local structure identification in molecular simulations

Identifying local structure in molecular simulations is of utmost importance. The most common existing approach to identify local structure is to calculate some geometrical quantity referred to as an order parameter. In simple cases order parameters are physically intuitive and trivial to develop (e.g., ion-pair distance), however in most cases, order parameter development becomes a much more difficult endeavor (e.g., crystal structure identification). Using ideas from computer vision, we adapt a specific type of neural network called a PointNet to identify local structural environments in molecular simulations. A primary challenge in applying machine learning techniques to simulation is selecting the appropriate input features. This challenge is system-specific and requires significant human input and intuition. In contrast, our approach is a generic framework that requires no system-specific feature engineering and operates on the raw output of the simulations, i.e., atomic positions. We demonstrate the method on crystal structure identification in Lennard-Jones (four different phases), water (eight different phases), and mesophase (six different phases) systems. The method achieves as high as 99.5% accuracy in crystal structure identification. The method is applicable to heterogeneous nucleation and it can even predict the crystal phases of atoms near external interfaces. We demonstrate the versatility of our approach by using our method to identify surface hydrophobicity based solely upon positions and orientations of surrounding water molecules. Our results suggest the approach will be broadly applicable to many types of local structure in simulations.

Following the nucleation pathway from disordered liquid to gyroid mesophase

Mesophases have order intermediate between liquids and crystals and arise in systems with frustration, such as surfactants, block copolymers, and Janus nanoparticles. The gyroid mesophase contains two interpenetrated, nonintersecting chiral networks that give it properties useful for photonics. It is challenging to nucleate a gyroid from the liquid. Elucidating the reaction coordinate for gyroid nucleation could assist in designing additives that facilitate the formation of the mesophase. However, the complexity of the gyroid structure and the extreme weakness of the first-order liquid to gyroid transition make this a challenging quest. Here, we investigate the pathway and transition states for the nucleation of a gyroid from the liquid in molecular simulations with a mesogenic binary mixture. We find that the gyroid nuclei at the transition states have a large degree of positional disorder and are not compact, consistent with the low surface free energy of the liquid-gyroid interface. A combination of bond-order parameters for the minor component is best to describe the passage from liquid to gyroid, among those we consider. The committor analyses, however, show that this best coordinate is not perfect and suggests that accounting for the relative ordering of the two interpenetrated networks in infant nuclei, as well as for signatures of ordering in the major component of the mesophase, would improve the accuracy of the reaction coordinate for gyroid formation and its use to evaluate nucleation barriers. To our knowledge, this study is the first to investigate the reaction coordinate and critical nuclei for the formation of any mesophase from an amorphous phase.

Two-Step to One-Step Nucleation of a Zeolite through a Metastable Gyroid Mesophase

The importance of nonclassical nucleation pathways in the formation of complex crystals has become apparent in recent years. Nonclassical pathways were unraveled for, among others, the crystallization of proteins, colloids, and clathrates. In those cases, the formation of a metastable fluid with density close to the crystal decreases the crystallization barrier. Recent simulations indicate that mesophases can facilitate the nucleation of zeolites. Here, we use molecular simulations to investigate the role of a gyroid mesophase on the crystallization of a model zeolite from liquid. The nucleation pathway is always nonclassical. At warmer temperatures, the mechanism proceeds in two well-defined steps: nucleation of a metastable gyroid followed by its crystallization into a zeolite. At colder temperatures, the second barrier becomes negligible, and the crystallization occurs in one step. This second scenario is also nonclassical, as the critical nucleus for the crystallization has the structure of the gyroid and seamlessly transforms into a zeolite as it grows past its critical size. To our knowledge, this is the first report of a nonclassical mechanism of crystallization mediated by a mesophase.

Why Is Gyroid More Difficult to Nucleate from Disordered Liquids than Lamellar and Hexagonal Mesophases?

Block copolymers, surfactants, and biomolecules form lamellar, hexagonal, and gyroid mesophases. Across these systems, the nucleation of lamellar from the disordered liquid is the easiest and the nucleation of gyroid the most challenging. This poses the question of what are the factors that determine the rates of nucleation of the mesophases and whether they are controlled by the complexity of the structures or the thermodynamics of nucleation. Here, we use molecular simulations to investigate the nucleation and thermodynamics of lamellar, hexagonal, and gyroid in a binary mixture of particles that produces the same mesophases as those of surfactants and block copolymers. We demonstrate that a combination of averaged bond-order parameters q̅₂ and q̅₈ identifies and distinguishes the three mesophases. We use these parameters to track the microscopic process of nucleation of each mesophase and investigate the existence of heterogeneous nucleation (cross-nucleation) between mesophases. We estimate the surface tensions of the liquid/mesophase interfaces from nucleation rates using classical nucleation theory and find that they are comparable for the three mesophases with values that are about a third of those expected for liquid-crystal interfaces. The driving forces for nucleation, on the other hand, are quite different and increase in the order gyroid < hexagonal < lamellar at any temperature. We find that the nucleation rates of the mesophases follow the order of their driving forces. We conclude that the difficulty to nucleate the gyroid originates in its lower temperature of melting and extremely low entropy of melting compared to those of the hexagonal and lamellar mesophases.