The smectic ZA phase: Antiferroelectric smectic order as a prelude to the ferroelectric nematic.

We have structurally characterized the liquid crystal (LC) phase that can appear as an intermediate state when a dielectric nematic, having polar disorder of its molecular dipoles, transitions to the almost perfectly polar-ordered ferroelectric nematic. This intermediate phase, which fills a 100-y-old void in the taxonomy of smectic LCs and which we term the "smectic ZA," is antiferroelectric, with the nematic director and polarization oriented parallel to smectic layer planes, and the polarization alternating in sign from layer to layer with a 180 Å period. A Landau free energy, originally derived from the Ising model of ferromagnetic ordering of spins in the presence of dipole-dipole interactions, and applied to model incommensurate antiferroelectricity in crystals, describes the key features of the nematic-SmZA-ferroelectric nematic phase sequence.

Observation of a uniaxial ferroelectric smectic A phase.

We report the observation of the smectic AF, a liquid crystal phase of the ferroelectric nematic realm. The smectic AF is a phase of small polar, rod-shaped molecules that form two-dimensional fluid layers spaced by approximately the mean molecular length. The phase is uniaxial, with the molecular director, the local average long-axis orientation, normal to the layer planes, and ferroelectric, with a spontaneous electric polarization parallel to the director. Polarization measurements indicate almost complete polar ordering of the ∼10 Debye longitudinal molecular dipoles, and hysteretic polarization reversal with a coercive field ∼2 × 105 V/m is observed. The SmAF phase appears upon cooling in two binary mixtures of partially fluorinated mesogens: 2N/DIO, exhibiting a nematic (N)-smectic ZA (SmZA)-ferroelectric nematic (NF)-SmAF phase sequence, and 7N/DIO, exhibiting an N-SmZA-SmAF phase sequence. The latter presents an opportunity to study a transition between two smectic phases having orthogonal systems of layers.

Polar in-plane surface orientation of a ferroelectric nematic liquid crystal: Polar monodomains and twisted state electro-optics.

We show that surface interactions can vectorially structure the three-dimensional polarization field of a ferroelectric fluid. The contact between a ferroelectric nematic liquid crystal and a surface with in-plane polarity generates a preferred in-plane orientation of the polarization field at that interface. This is a route to the formation of fluid or glassy monodomains of high polarization without the need for electric field poling. For example, unidirectional buffing of polyimide films on planar surfaces to give quadrupolar in-plane anisotropy also induces macroscopic in-plane polar order at the surfaces, enabling the formation of a variety of azimuthal polar director structures in the cell interior, including uniform and twisted states. In a π-twist cell, obtained with antiparallel, unidirectional buffing on opposing surfaces, we demonstrate three distinct modes of ferroelectric nematic electro-optic response: intrinsic, viscosity-limited, field-induced molecular reorientation; field-induced motion of domain walls separating twisted states of opposite chirality; and propagation of polarization reorientation solitons from the cell plates to the cell center upon field reversal. Chirally doped ferroelectric nematics in antiparallel-rubbed cells produce Grandjean textures of helical twist that can be unwound via field-induced polar surface reorientation transitions. Fields required are in the 3-V/mm range, indicating an in-plane polar anchoring energy of w P ∼3 × 10-3 J/m2.

First-principles experimental demonstration of ferroelectricity in a thermotropic nematic liquid crystal: Polar domains and striking electro-optics.

We report the experimental determination of the structure and response to applied electric field of the lower-temperature nematic phase of the previously reported calamitic compound 4-[(4-nitrophenoxy)carbonyl]phenyl2,4-dimethoxybenzoate (RM734). We exploit its electro-optics to visualize the appearance, in the absence of applied field, of a permanent electric polarization density, manifested as a spontaneously broken symmetry in distinct domains of opposite polar orientation. Polarization reversal is mediated by field-induced domain wall movement, making this phase ferroelectric, a 3D uniaxial nematic having a spontaneous, reorientable polarization locally parallel to the director. This polarization density saturates at a low temperature value of ∼6 µC/cm2, the largest ever measured for a fluid or glassy material. This polarization is comparable to that of solid state ferroelectrics and is close to the average value obtained by assuming perfect, polar alignment of molecular dipoles in the nematic. We find a host of spectacular optical and hydrodynamic effects driven by ultralow applied field (E ∼ 1 V/cm), produced by the coupling of the large polarization to nematic birefringence and flow. Electrostatic self-interaction of the polarization charge renders the transition from the nematic phase mean field-like and weakly first order and controls the director field structure of the ferroelectric phase. Atomistic molecular dynamics simulation reveals short-range polar molecular interactions that favor ferroelectric ordering, including a tendency for head-to-tail association into polar, chain-like assemblies having polar lateral correlations. These results indicate a significant potential for transformative, new nematic physics, chemistry, and applications based on the enhanced understanding, development, and exploitation of molecular electrostatic interaction.

Chiral self-sorting of active semiflexible filaments with intrinsic curvature.

Many-body interactions in systems of active matter can cause particles to move collectively and self-organize into dynamic structures with long-range order. In cells, the self-assembly of cytoskeletal filaments is critical for cellular motility, structure, intracellular transport, and division. Semiflexible cytoskeletal filaments driven by polymerization or motor-protein interactions on a two-dimensional substrate, such as the cell cortex, can induce filament bending and curvature leading to interesting collective behavior. For example, the bacterial cell-division filament FtsZ is known to have intrinsic curvature that causes it to self-organize into rings and vortices, and recent experiments reconstituting the collective motion of microtubules driven by motor proteins on a surface have observed chiral symmetry breaking of the collective behavior due to motor-induced curvature of the filaments. Previous work on the self-organization of driven filament systems have not studied the effects of curvature and filament structure on collective behavior. In this work, we present Brownian dynamics simulation results of driven semiflexible filaments with intrinsic curvature and investigate how the interplay between filament rigidity and radius of curvature can tune the self-organization behavior in homochiral systems and heterochiral mixtures. We find a curvature-induced reorganization from polar flocks to self-sorted chiral clusters, which is modified by filament flexibility. This transition changes filament transport from ballistic to diffusive at long timescales.

Comparison of explicit and mean-field models of cytoskeletal filaments with crosslinking motors.

In cells, cytoskeletal filament networks are responsible for cell movement, growth, and division. Filaments in the cytoskeleton are driven and organized by crosslinking molecular motors. In reconstituted cytoskeletal systems, motor activity is responsible for far-from-equilibrium phenomena such as active stress, self-organized flow, and spontaneous nematic defect generation. How microscopic interactions between motors and filaments lead to larger-scale dynamics remains incompletely understood. To build from motor-filament interactions to predict bulk behavior of cytoskeletal systems, more computationally efficient techniques for modeling motor-filament interactions are needed. Here, we derive a coarse-graining hierarchy of explicit and continuum models for crosslinking motors that bind to and walk on filament pairs. We compare the steady-state motor distribution and motor-induced filament motion for the different models and analyze their computational cost. All three models agree well in the limit of fast motor binding kinetics. Evolving a truncated moment expansion of motor density speeds the computation by [Formula: see text]-[Formula: see text] compared to the explicit or continuous-density simulations, suggesting an approach for more efficient simulation of large networks. These tools facilitate further study of motor-filament networks on micrometer to millimeter length scales.

Collective motion of driven semiflexible filaments tuned by soft repulsion and stiffness.

In active matter systems, self-propelled particles can self-organize to undergo collective motion, leading to persistent dynamical behavior out of equilibrium. In cells, cytoskeletal filaments and motor proteins form complex structures important for cell mechanics, motility, and division. Collective dynamics of cytoskeletal systems can be reconstituted using filament gliding experiments, in which cytoskeletal filaments are propelled by surface-bound motor proteins. These experiments have observed diverse dynamical states, including flocks, polar streams, swirling vortices, and single-filament spirals. Recent experiments with microtubules and kinesin motor proteins found that the collective behavior of gliding filaments can be tuned by altering the concentration of the crowding macromolecule methylcellulose in solution. Increasing the methylcellulose concentration reduced filament crossing, promoted alignment, and led to a transition from active, isotropically oriented filaments to locally aligned polar streams. This emergence of collective motion is typically explained as an increase in alignment interactions by Vicsek-type models of active polar particles. However, it is not yet understood how steric interactions and bending stiffness modify the collective behavior of active semiflexible filaments. Here we use simulations of driven filaments with tunable soft repulsion and rigidity in order to better understand how the interplay between filament flexibility and steric effects can lead to different active dynamic states. We find that increasing filament stiffness decreases the probability of filament alignment, yet increases collective motion and long-range order, in contrast to the assumptions of a Vicsek-type model. We identify swirling flocks, polar streams, buckling bands, and spirals, and describe the physics that govern transitions between these states. In addition to repulsion and driving, tuning filament stiffness can promote collective behavior, and controls the transition between active isotropic filaments, locally aligned flocks, and polar streams.

End-to-end machine learning for experimental physics: using simulated data to train a neural network for object detection in video microscopy.

We demonstrate a method for training a convolutional neural network with simulated images for usage on real-world experimental data. Modern machine learning methods require large, robust training data sets to generate accurate predictions. Generating these large training sets requires a significant up-front time investment that is often impractical for small-scale applications. Here we demonstrate a 'full-stack' computational solution, where the training data set is generated on-the-fly using a noise injection process to produce simulated data characteristic of the experimental system. We demonstrate the power of this full-stack approach by applying it to the study of topological defect annihilation in systems of liquid crystal freely-suspended films. This specific experimental system requires accurate observations of both the spatial distribution of the defects and the total number of defects, making it an ideal system for testing the robustness of the trained network. The fully trained network was found to be comparable in accuracy to human hand-annotation, with four-orders of magnitude improvement in time efficiency.

Frustration between two- and three-dimensional smectic ordering leads to a biaxial nematic phase.

The bola-amphiphilic, T-shaped mesogen CT2 has an aromatic, biphenyl core terminated on both ends by hydrophilic groups and a semi-perfluorinated, aliphatic side chain. Upon cooling from the isotropic phase, the fluorinated tails and the polar, rod-like cores nanophase-segregate to form a fluid lamellar phase. At high temperatures, the biphenyl cores are orientationally disordered in two dimensions (2D) in the lamellar planes but on further cooling the cores order orientationally, giving a biaxial lamellar phase with 2D nematic in-plane ordering. At lower temperature, the aromatic and hydrophilic parts of the cores nanosegregate within the lamellae and 2D smectic correlations of the head groups develop. X-ray diffraction shows that this 2D smectic ordering is incompatible with the initial lamellar structure, with both structures becoming short-ranged, resulting in a 3D biaxial nematic phase with macroscopic orthorhombic symmetry featuring strong smectic correlations in two orthogonal spatial dimensions. Freeze-fracture transmission electron microscopy enables direct visualization of the resulting short-ranged periodic structures.

Theory of Cytoskeletal Reorganization during Cross-Linker-Mediated Mitotic Spindle Assembly.

Cells grow, move, and respond to outside stimuli by large-scale cytoskeletal reorganization. A prototypical example of cytoskeletal remodeling is mitotic spindle assembly, during which microtubules nucleate, undergo dynamic instability, bundle, and organize into a bipolar spindle. Key mechanisms of this process include regulated filament polymerization, cross-linking, and motor-protein activity. Remarkably, using passive cross-linkers, fission yeast can assemble a bipolar spindle in the absence of motor proteins. We develop a torque-balance model that describes this reorganization because of dynamic microtubule bundles, spindle-pole bodies, the nuclear envelope, and passive cross-linkers to predict spindle-assembly dynamics. We compare these results to those obtained with kinetic Monte Carlo-Brownian dynamics simulations, which include cross-linker-binding kinetics and other stochastic effects. Our results show that rapid cross-linker reorganization to microtubule overlaps facilitates cross-linker-driven spindle assembly, a testable prediction for future experiments. Combining these two modeling techniques, we illustrate a general method for studying cytoskeletal network reorganization.

Chiral Incommensurate Helical Phase in a Smectic of Achiral Bent-Core Mesogens.

An achiral, bent-core mesogen forms several tilted smectic liquid crystal phases, including a nonpolar, achiral de Vries smectic A which transitions to a chiral, ferroelectric state in applied electric fields above a threshold. At lower temperature, a chiral, ferrielectric phase with a periodic, supermolecular modulation of the tilt azimuth, indicated by a Bragg peak in carbon-edge resonant soft x-ray scattering, is observed. The absence of a corresponding resonant umklapp peak identifies the superlayer structure as a twist-bend-like helix that is only weakly modulated by the smectic layering.

Contributions of Microtubule Dynamic Instability and Rotational Diffusion to Kinetochore Capture.

Microtubule dynamic instability allows search and capture of kinetochores during spindle formation, an important process for accurate chromosome segregation during cell division. Recent work has found that microtubule rotational diffusion about minus-end attachment points contributes to kinetochore capture in fission yeast, but the relative contributions of dynamic instability and rotational diffusion are not well understood. We have developed a biophysical model of kinetochore capture in small fission-yeast nuclei using hybrid Brownian dynamics/kinetic Monte Carlo simulation techniques. With this model, we have studied the importance of dynamic instability and microtubule rotational diffusion for kinetochore capture, both to the lateral surface of a microtubule and at or near its end. Over a range of biologically relevant parameters, microtubule rotational diffusion decreased capture time, but made a relatively small contribution compared to dynamic instability. At most, rotational diffusion reduced capture time by 25%. Our results suggest that while microtubule rotational diffusion can speed up kinetochore capture, it is unlikely to be the dominant physical mechanism for typical conditions in fission yeast. In addition, we found that when microtubules undergo dynamic instability, lateral captures predominate even in the absence of rotational diffusion. Counterintuitively, adding rotational diffusion to a dynamic microtubule increases the probability of end-on capture.

Two-dimensional island emulsions in ultrathin, freely-suspended smectic liquid crystal films.

We report a novel type of two-dimensional colloidal emulsion, in which arrays of disc-shaped liquid crystal domains are created in ultrathin, freely-suspended, fluid smectic C liquid crystal films. After a film has been drawn across an aperture, an island emulsion is produced by repeatedly compressing and expanding the film while maintaining vigorous shear and extensional air flow across its area. Once formed, these emulsions restructure over a period of a few minutes to a stable state that then changes only slowly, over the course of several days. This stability enables study of the sedimentation of the emulsion under in-plane gravitation produced by tilting the film, during which the original island emulsion segregates into regions with different kinds of emulsions distinguished by the size, density, and degree of order of the islands. We observe a rich array of phenomena that includes the formation of chains of islands organized into two-dimensional smectics in the dilute phase, and island deformation and coalescence in the condensed phase.

Reliability of Orientational Order Parameters Determined from Two-dimensional X-ray Diffraction Patterns: A Simulation Study.

The orientational order parameter S2 is one of the most important quantities to describe the degree of long-range orientational ordering of liquid crystals. There are several approaches to experimentally measure this order parameter of liquid crystalline phases but every method includes substantial simplifications and assumptions. We present a simulation-based approach to elucidate the reliability of the method of Davidson, Petermann and Levelut to measure S2 via 2D X-ray experiments. We have found that this method slightly underestimates S2 by an absolute value of only 0.05 and thus provides reliable measures of S2 by X-ray diffraction.

Photoinduced and Thermal Relaxation in Surface-Grafted Azobenzene-Based Monolayers: A Molecular Dynamics Simulation Study.

Extensive atomistic molecular dynamics simulations have been employed to study the structure and molecular orientational relaxation of azobenzene-based monolayers grafted to a solid substrate. Systems with surface coverage of 0.6 nm(2)/molecule were investigated over a wide temperature range ranging from 298 K, where the mesogens show local ordering and the monolayer dynamics was found to be glassy, up to 700 K, where the azobenzene groups have a nearly isotropic orientational distribution, with a subnanosecond characteristic orientational relaxation time scale. Biased simulations that model single-molecule thermal excitation and conformational isomerization have been conducted to obtain insight into the mechanisms for photoinduced athermal fluidization and monolayer reorganization observed experimentally in this system. Our simulations clearly indicate that trans-cis conformational isomerization transitions of azobenzene units can lead to reorientation of mesogens and to the formation of a monolayer with strong macroscopic in-plane nematic order. While local heating created by excitation process can facilitate this process, thermal excitation alone is not sufficient to induce ordering in the monolayer. Instead, the work done by a molecule undergoing cis-trans isomerization on the cage of neighboring molecules is the key mechanism for photofluidization and orientational ordering in dMR monolayers exposed to linearly polarized light leading to relaxation dynamics that can be described in terms of higher effective temperature. The obtained simulation results are discussed in light of recent experimental data reported for these systems.

Microscopic origins of anisotropic active stress in motor-driven nematic liquid crystals.

The cytoskeleton, despite comprising relatively few building blocks, drives an impressive variety of cellular phenomena ranging from cell division to motility. These building blocks include filaments, motor proteins, and static crosslinkers. Outside of cells, these same components can form novel materials exhibiting active flows and nonequilibrium contraction or extension. While dipolar extensile or contractile active stresses are common in nematic motor-filament systems, their microscopic origin remains unclear. Here we study a minimal physical model of filaments, crosslinking motors, and static crosslinkers to dissect the microscopic mechanisms of stress generation in a two-dimensional system of orientationally aligned rods. We demonstrate the essential role of filament steric interactions which have not previously been considered to significantly contribute to active stresses. With this insight, we are able to tune contractile or extensile behavior through the control of motor-driven filament sliding and crosslinking. This work provides a roadmap for engineering stresses in active liquid crystals. The mechanisms we study may help explain why flowing nematic motor-filament mixtures are extensile while gelled systems are contractile.

Chiral heliconical ground state of nanoscale pitch in a nematic liquid crystal of achiral molecular dimers.

Freeze-fracture transmission electron microscopy study of the nanoscale structure of the so-called "twist-bend" nematic phase of the cyanobiphenyl (CB) dimer molecule CB(CH2)7CB reveals stripe-textured fracture planes that indicate fluid layers periodically arrayed in the bulk with a spacing of d ~ 8.3 nm. Fluidity and a rigorously maintained spacing result in long-range-ordered 3D focal conic domains. Absence of a lamellar X-ray reflection at wavevector q ~ 2π/d or its harmonics in synchrotron-based scattering experiments indicates that this periodic structure is achieved with no detectable associated modulation of the electron density, and thus has nematic rather than smectic molecular ordering. A search for periodic ordering with d ~ in CB(CH2)7CB using atomistic molecular dynamic computer simulation yields an equilibrium heliconical ground state, exhibiting nematic twist and bend, of the sort first proposed by Meyer, and envisioned in systems of bent molecules by Dozov and Memmer. We measure the director cone angle to be θ(TB) ~ 25° and the full pitch of the director helix to be p(TB) ~ 8.3 nm, a very small value indicating the strong coupling of molecular bend to director bend.

Multiscale polar theory of microtubule and motor-protein assemblies.

Microtubules and motor proteins are building blocks of self-organized subcellular biological structures such as the mitotic spindle and the centrosomal microtubule array. These same ingredients can form new "bioactive" liquid-crystalline fluids that are intrinsically out of equilibrium and which display complex flows and defect dynamics. It is not yet well understood how microscopic activity, which involves polarity-dependent interactions between motor proteins and microtubules, yields such larger-scale dynamical structures. In our multiscale theory, Brownian dynamics simulations of polar microtubule ensembles driven by cross-linking motors allow us to study microscopic organization and stresses. Polarity sorting and cross-link relaxation emerge as two polar-specific sources of active destabilizing stress. On larger length scales, our continuum Doi-Onsager theory captures the hydrodynamic flows generated by polarity-dependent active stresses. The results connect local polar structure to flow structures and defect dynamics.

Molecular structure of the discotic liquid crystalline phase of hexa-peri-hexabenzocoronene/oligothiophene hybrid and their charge transport properties.

Using atomistic molecular dynamics simulation, we study the discotic columnar liquid crystalline (LC) phases formed by a new organic compound having hexa-peri-Hexabenzocoronene (HBC) core with six pendant oligothiophene units recently synthesized by Nan Hu et al. [Adv. Mater. 26, 2066 (2014)]. This HBC core based LC phase was shown to have electric field responsive behavior and has important applications in organic electronics. Our simulation results confirm the hexagonal arrangement of columnar LC phase with a lattice spacing consistent with that obtained from small angle X-ray diffraction data. We have also calculated various positional and orientational correlation functions to characterize the ordering of the molecules in the columnar arrangement. The molecules in a column are arranged with an average twist of 25° having an average inter-molecular separation of ∼5 Å. Interestingly, we find an overall tilt angle of 43° between the columnar axis and HBC core. We also simulate the charge transport through this columnar phase and report the numerical value of charge carrier mobility for this liquid crystal phase. The charge carrier mobility is strongly influenced by the twist angle and average spacing of the molecules in the column.

Mutual diffusion of inclusions in freely suspended smectic liquid crystal films.

We study experimentally and theoretically the hydrodynamic interaction of pairs of circular inclusions in two-dimensional, fluid smectic membranes suspended in air. By analyzing their Brownian motion, we find that the radial mutual mobilities of identical inclusions are independent of their size but that the angular coupling becomes strongly size dependent when their radius exceeds a characteristic hydrodynamic length. These observations are described well for arbitrary inclusion separations by a model that generalizes the Levine-MacKintosh theory of point-force response functions and uses a boundary-element approach to calculate the mobility matrix for inclusions of finite extent.