Chiral self-assembly of helical particles

Janus helices: From fully attractive to hard helices

The phase diagram of hard helices differs from its hard rods counterpart by the presence of chiral "screw" phases stemming from the characteristic helical shape, in addition to the conventional liquid crystal phases also found for rod-like particles. Using extensive Monte Carlo and Molecular Dynamics simulations, we study the effect of the addition of a short-range attractive tail representing solvent-induced interactions to a fraction of the sites forming the hard helices, ranging from a single-site attraction to fully attractive helices for a specific helical shape. Different temperature regimes exist for different fractions of the attractive sites, as assessed in terms of the relative Boyle temperatures, that are found to be rather insensitive to the specific shape of the helical particle. The temperature range probed by the present study is well above the corresponding Boyle temperatures, with the phase behaviour still mainly entropically dominated and with the existence and location of the various liquid crystal phases only marginally affected. The pressure in the equation of state is found to decrease upon increasing the fraction of attractive beads and/or on lowering the temperature at fixed volume fraction, as expected on physical grounds. All screw phases are found to be stable within the considered range of temperatures with the smectic phase becoming more stable on lowering the temperature. By contrast, the location of the transition lines do not display a simple dependence on the fraction of attractive beads in the considered range of temperatures.

Chiral copper-hydride nanoclusters: synthesis, structure, and assembly

An effective strategy is developed to synthesize a novel and stable layered Cu nanocluster using a one-pot reduction method. The cluster, with a molecular formula of [Cu₁₄(^tBuS)₃(PPh₃)₇H₁₀]BF₄ which has been unambiguously characterized by single crystal X-ray diffraction analysis, exhibits different structures from previously reported analogues with core-shell geometries. In the absence of chiral ligands, the cluster displays intrinsic chirality owing to the non-covalent ligand-ligand interactions (e.g., C-H⋯Cu interactions and C-H⋯π interactions) to lock the central copper core. The interlacing of chiral-cluster enantiomers forms a large cavity, which lays the foundation for a series of potential applications such as drug filling and gas adsorption. Moreover, the C-H⋯H-C interactions of phenyl groups between different cluster moieties promote the formation of a dextral helix and realization of the self-assembly of nanostructures.

Computer simulations of self-assembly of anisotropic colloids

Computer simulations have played a significant role in understanding the physics of colloidal self-assembly, interpreting experimental observations, and predicting novel mesoscopic and crystalline structures. Recent advances in computer simulations of colloidal self-assembly driven by anisotropic or orientation-dependent inter-particle interactions are highlighted in this review. These interactions are broadly classified into two classes: entropic and enthalpic interactions. They mainly arise due to shape anisotropy, surface heterogeneity, compositional heterogeneity, external field, interfaces, and confinements. Key challenges and opportunities in the field are discussed.

Effects of shape and solute-solvent compatibility on the efficacy of chirality transfer: Nanoshapes in nematics

Chirality, as a concept, is well understood at most length scales. However, quantitative models predicting the efficacy of the transmission of chirality across length scales are lacking. We propose here a modus operandi for a chiral nanoshape solute in an achiral nematic liquid crystal host showing that that chirality transfer may be understood by unusually simple geometric considerations. This mechanism is based on the product of a pseudoscalar chirality indicator and of a geometric shape compatibility factor based on the two-dimensional isoperimetric quotients for each nanoshape solute. The model is tested on an experimental set of precisely engineered gold nanoshapes. These libraries of calculated and in-parallel acquired experimental data among related nanoshapes pave the way for predictive calculations of chirality transfer in nanoscale, macromolecular, and biological systems, from designing chiral discriminators and enantioselective catalysts to developing chiral metamaterials and understanding nature's innate ability to transfer homochirality across length scales.

Amplifying inorganic chirality using liquid crystals

Chiral inorganic nanostructures have drawn extensive attention thanks to their unique physical properties as well as multidisciplinary applications. Amplifying inorganic chirality using liquid crystals (LCs) is an efficient way to enhance the parented inorganic asymmetry owing to chirality transfer. Herein, the universal synthetic methods and structural characterizations of chiral inorganic-doped LC hybrids are introduced. Additionally, the current progress and status of recent experiment and theory research about chiral interactions between inorganic nanomaterials (e.g. metal, semiconductor, perovskite, and magnetic oxide) and LCs are summarized in this review. We further present representative applications of these new hybrids in the area of encryption, sensing, optics, etc. Finally, we provide perspectives on this field in terms of material variety, new synthesis, and future practice. It is envisaged that LCs will act as a pivotal part in the amplification of inorganic chirality with versatile applications.

Bicarbonate insertion triggered self-assembly of chiral octa-gold nanoclusters into helical superstructures in the crystalline state

Constructing atomically precise helical superstructures of high order is an extensively pursued subject for unique aesthetic features and underlying applications. However, the construction of cluster-based helixes of well-defined architectures comes with a huge challenge owing to their intrinsic complexity in geometric structures and synthetic processes. Herein, we report a pair of unique P- and M-single stranded helical superstructures spontaneously assembled from R- and S-Au8c individual nanoclusters, respectively, upon selecting chiral BINAP (2,2′-bis(diphenylphosphino)-1,1′-binaphthalene) and hydrophilic o-H₂MBA (o-mercaptobenzoic acid) as protective ligands to induce chirality and facilitate the formation of helixes. Structural analysis reveals that the chirality of the Au8c individual nanoclusters is derived from the homochiral ligands and the inherently chiral Au₈ metallic kernel, which was further corroborated by experimental and computational investigations. More importantly, driven by the O–H⋯O interactions between (HCO₃⁻)₂ dimers and achiral o-HMBA⁻ ligands, R/S-Au8c individual nanoclusters can assemble into helical superstructures in a highly ordered crystal packing. Electrospray ionization (ESI) and collision-induced dissociation (CID) mass spectrometry of Au8c confirm the hydrogen-bonded dimer of Au8c individual nanoclusters in solution, illustrating that the insertion of (HCO₃⁻)₂ dimers plays a crucial role in the assembly of helical superstructures in the crystalline state. This work not only demonstrates an effective strategy to construct cluster-based helical superstructures at the atomic level, but also provides visual and reliable experimental evidence for understanding the formation mechanism of helical superstructures.

A pair of unprecedented helical superstructures via self-assembly of inherently homochiral Au₈ nanoclusters, [Au₈(R/S-BINAP)₃(o-HMBA)₂]·2(HCO₃), is obtained in the crystalline state, in which the HCO₃⁻ ions act as the bridge.

Tertiary Chiral Nanostructures from C-H⋅⋅⋅F Directed Assembly of Chiroptical Superatoms

We report the synthesis and structure of tertiary chiral nanostructures with 100 % optical purity. A novel synthetic strategy, using chiral reducing agent, R and S-BINAPCuBH₄ (BINAP is 2,2'-Bis(diphenylphosphino)-1,1'-binaphthyl), is developed to access to atomically precise, intrinsically chiral [Au₇ Ag₆ Cu₂ (R- or S-BINAP)₃ (SCH₂ Ph)₆ ]SbF₆ nanoclusters in one-pot synthesis. The clusters represent the first tri-metallic superatoms with inherent chirality and fair stability. Both metal distribution (primary) and ligand arrangement (secondary) of the enantiomers exhibited perfect mirror images, and unprecedentedly, the self-assembly driven by the C-H⋅⋅⋅F interaction between the phenyl groups of the superatom moieties and SbF₆ ^- anions induced the formation of bio-mimic left- and right-handed helices, achieving the tertiary chiral nanostructures. DFT calculations revealed the connections between the molecular details and chiral optical activity.

Shape-driven entropic self-assembly of an open, reconfigurable, binary host-guest colloidal crystal

Entropically driven self-assembly of hard anisotropic particles, where particle shape gives rise to emergent valencies, provides a useful perspective for the design of nanoparticle and colloidal systems. Hard particles self-assemble into a rich variety of crystal structures, ranging in complexity from simple close-packed structures to structures with 432 particles in the unit cell. Entropic crystallization of open structures, however, is missing from this landscape. Here, we report the self-assembly of a two-dimensional binary mixture of hard particles into an open host-guest structure, where nonconvex, triangular host particles form a honeycomb lattice that encapsulates smaller guest particles. Notably, this open structure forms in the absence of enthalpic interactions by effectively splitting the structure into low- and high-entropy sublattices. This is the first such structure to be reported in a two-dimensional athermal system. We discuss the observed compartmentalization of entropy in this system, and show that the effect of the size of the guest particle on the stability of the structure gives rise to a reentrant phase behavior. This reentrance suggests the possibility for a reconfigurable colloidal material, and we provide a proof-of-concept by showing the assembly behavior while changing the size of the guest particles in situ. Our findings provide a strategy for designing open colloidal crystals, as well as binary systems that exhibit co-crystallization, which have been elusive thus far.

Phase behavior of hard cylinders

Using isobaric Monte Carlo simulations, we map out the entire phase diagram of a system of hard cylindrical particles of length (L) and diameter (D) using an improved algorithm to identify the overlap condition between two cylinders. Both the prolate L/D > 1 and the oblate L/D < 1 phase diagrams are reported with no solution of continuity. In the prolate L/D > 1 case, we find intermediate nematic N and smectic SmA phases in addition to a low density isotropic I and a high density crystal X phase with I-N-SmA and I-SmA-X triple points. An apparent columnar phase C is shown to be metastable, as in the case of spherocylinders. In the oblate L/D < 1 case, we find stable intermediate cubatic (Cub), nematic (N), and columnar (C) phases with I-N-Cub, N-Cub-C, and I-Cub-C triple points. Comparison with previous numerical and analytical studies is discussed. The present study, accounting for the explicit cylindrical shape, paves the way to more sophisticated models with important biological applications, such as viruses and nucleosomes.

Cylindrical defect structures formed by chiral nematic liquid crystals in quasi-one-dimensional systems

Blue phases are three-dimensional self-assembly structures of liquid crystals with a lattice of line defects. They have attracted considerable interest as photonic materials. It is well known that blue phases occur in cholesteric liquid crystals (CLCs) under certain thermodynamic conditions; however, recent studies have indicated that confining surfaces may induce distinctive structural changes. For example, in a previous study, a quasi-two-dimensional (Q2D) confinement system was investigated with the aid of numerical calculations, and a stable Q2D Skyrmion structure was attained. Here, we performed molecular simulations to investigate the CLC phase behavior at the molecular scale for a quasi-one-dimensional (Q1D) nanotube system. Various morphological behaviors of CLCs were observed by changing the temperature and the radius of the nanotubes. In particular, we discovered a self-assembled structure with cylindrical (or ring-like) defects rather than lines by introducing a novel local orientation analysis. Our simulation results show that the self-assembly of CLCs offers a guide to control the intensity in Q1D systems and fundamental knowledge for their application to optical devices.

Morphological analysis of chiral rod clusters from a coarse-grained single-site chiral potential

We present a coarse-grained single-site potential for simulating chiral interactions, with adjustable strength, handedness, and preferred twist angle. As an application, we perform basin-hopping global optimisation to predict the favoured geometries for clusters of chiral rods. The morphology phase diagram based upon these predictions has four distinct families, including previously reported structures for potentials that introduce chirality based on shape, such as membranes and helices. The transition between these two configurations reproduces some key features of experimental results for fd bacteriophage. The potential is computationally inexpensive, intuitive, and versatile; we expect it will be useful for large scale simulations of chiral molecules. For chiral particles confined in a cylindrical container we reproduce the behaviour observed for fusilli pasta in a jar. Hence this chiropole potential has the capability to provide insight into structures on both macroscopic and molecular length scales.

Highly Sensitive, Tunable Chirality Amplification through Space Visualized for Gold Nanorods Capped with Axially Chiral Binaphthyl Derivatives

The creation and transmission of chirality in molecular systems is a well-known, widely applied notion. Our understanding of how the chirality of nanomaterials can be controlled, measured, transmitted through space, and applied is less well understood. Dynamic assemblies for chiral sensing or metamaterials engineered from chiral nanomaterials require exact methods to determine transmission and amplification of nanomaterial chirality through space. We report the synthesis of a series of gold nanorods (GNRs) with a constant aspect ratio of ∼4.3 capped with C₂-symmetric, axially chiral binaphthyl thiols, preparation of dispersions in the nematic liquid crystal 5CB, measurements of the helical pitch, and the determination of the helical twisting power as well as the average distance between the chiral nanomaterial additives. By comparison to the neat organic chiral derivatives, we demonstrate how the amplification of chirality facilitated by GNRs decorated with chiral molecules can be used to clearly distinguish the chiral induction strength of a homologous series of binaphthyl derivatives, differing only in the length of the nontethered aliphatic chain, in the induced chiral nematic liquid crystal phase. Considering systematic errors in sample preparation and optical measurements, these chiral molecules would otherwise be deemed identical with respect to chiral induction. Notably, we find some of the highest ever-reported values of the helical twisting power. We further support our experimentally derived arguments of a more comprehensive understanding of chirality transfer by calculations of a suitable pseudoscalar chirality indicator.

Manipulation of cholesteric liquid crystal phase behavior and molecular assembly by molecular chirality

Molecular simulation is used to study the effect of molecular chirality on liquid crystalline phase transition and molecular assembly behavior. Based on a flexible chain (FCh) model with helical arrangement of side beads, the phase behavior of FCh models with various molecular chiralities are studied as functions of pressure (or density). By modifying the molecular chirality of FCh, we can manipulate the relative stability of the nematic and cholesteric phases continuously; and we found that increasing molecular chirality may destabilize cholesteric order due to the effective reduction of chiral interactions. A semismectic phase is identified in the high-density region, in which the two-dimensional fluid layers overlap due to shift alignment formed by FCh particles. The global phase diagram of the FCh model is constructed and the potential energy surface is calculated to elucidate the formation of cholesteric phase in terms of two-body interactions.

Collective oscillation in dense suspension of self-propelled chiral rods

Active particles capable of self-propulsion commonly exhibit rich collective dynamics and have attracted increasing attention due to their applications in biology, robotics, social transport, and biomedicine. However, it remains unclear how the geometric features of active particles affect their collective behaviors. In this paper, we explore the collective dynamics of L-shaped active rods. We show that a dense suspension of self-propelled L-shaped rods exhibits fascinating non-equilibrium oscillatory dynamic clustering. A new oscillation phase can form due to distinct collisions and aggregation mechanisms arising from the L-shaped chirality of elements. A generic diagram of emerging states is provided over a wide range of geometric parameters. Our findings show that the comparative strength between the periodic separation and proximity effect from chirality and the alignment effect from elongated geometry drive the formation and transition of dynamic patterns. This chirality-triggered oscillation phase suggests a new route to understand active matter and paves a way for emerging applications.

Chirality amplification by desymmetrization of chiral ligand-capped nanoparticles to nanorods quantified in soft condensed matter

Induction, transmission, and manipulation of chirality in molecular systems are well known, widely applied concepts. However, our understanding of how chirality of nanoscale entities can be controlled, measured, and transmitted to the environment is considerably lacking behind. Future discoveries of dynamic assemblies engineered from chiral nanomaterials, with a specific focus on shape and size effects, require exact methods to assess transmission and amplification of nanoscale chirality through space. Here we present a remarkably powerful chirality amplification approach by desymmetrization of plasmonic nanoparticles to nanorods. When bound to gold nanorods, a one order of magnitude lower number of chiral molecules induces a tighter helical distortion in the surrounding liquid crystal-a remarkable amplification of chirality through space. The change in helical distortion is consistent with a quantification of the change in overall chirality of the chiral ligand decorated nanomaterials differing in shape and size as calculated from a suitable pseudoscalar chirality indicator.

Self-Assembled Chiral Photonic Crystals from a Colloidal Helix Racemate

Chiral crystals consisting of microhelices have many optical properties, while presently available fabrication processes limit their large-scale applications in photonic devices. Here, by using a simplified simulation method, we investigate a bottom-up self-assembly route to build up helical crystals from the smectic monolayer of a colloidal helix racemate. With increasing the density, the system undergoes an entropy-driven cocrystallization by forming crystals of various symmetries with different helical shapes. In particular, we identify two crystals of helices arranged in binary honeycomb and square lattices, which are essentially composed of two sets of opposite-handed chiral crystals. Photonic calculations show that these chiral structures can have large complete photonic band gaps. In addition, in the self-assembled chiral square crystal, we also find dual polarization band gaps that selectively forbid the propagation of circularly polarized light of a specific handedness along the helical axis direction. The self-assembly process in our proposed system is robust, suggesting possibilities of using chiral colloids to assemble photonic metamaterials.

Twisting with a twist: supramolecular helix fluctuations in chiral nematics

Most theoretical descriptions of lyotropic cholesteric liquid crystals to date focus on homogeneous systems in which the rod concentration, as opposed to the rod orientation, is uniform. In this work, we build upon the Onsager-Straley theory for twisted nematics and study the effect of weak concentration gradients, generated by some external potential, on the cholesteric twist. We apply our theory to chiral nematics of nanohelices in which the supramolecular helix sense is known to spontaneously change sign upon variation of particle concentration, passing through a so-called compensation point at which the mesoscopic twist vanishes. We show that the imposed field offers exquisite control of the handedness and magnitude of the helicoidal director field, even at weak field strengths. Within the same framework we also quantify the director fluctuation spectrum and find evidence for a correlation length diverging at the compensation point.

Simulating the pitch sensitivity of twisted nematics of patchy rods

Stiff, elongated biomolecules such as filamentous viruses, DNA or cellulose nanocrystals are known to form liquid crystals often exhibiting a helical supramolecular organization. Little is known about the microscopic origin, size and handedness of the helical pitch in these, so-called cholesteric phases. Experimental observations in chiral lyotropics suggest that long-ranged chiral forces of electrostatic origin acting between the mesogens are responsible for such organization. Using large-scale computer simulation we study the sensitivity of the pitch imparted by soft microscopic helices and confirm that the helical sense is sensitive to a change of packing fraction, magnitude of the molecular pitch and amplitude of the chiral interactions. In particular, we find evidence that the cholesteric helix sense may change spontaneously upon variation of particle density, at fixed molecular chirality. These pitch inversions have been reported in recent theoretical studies but simulation evidence remains elusive. We rationalize these sudden changes in the supramolecular helical symmetry on the basis of detailed measurements of the mean-torque generated by the twisting of the helices. The simulation methodology employed does not require confining the twisted nematic in a slab geometry and allows for a simultaneous measurement of the pitch and the twist elastic constant. We find that the twist elastic constant increases almost linearly with density suggesting that twisted nematic shows no signs of anomalous stiffening due to pre-smectic fluctuations at higher packing fraction.