We report a transition from the ferroelectric nematic liquid crystal (NF) phase to a lower-temperature, apolar fluid phase having reentrant isotropic symmetry (IR), in the liquid crystal compound RM734 doped with small concentrations of the ionic liquids 1-Butyl-3-methylimidazolium hexafluorophosphate (BMIM-PF6) or 1-Ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMIM-TFSI). Even a trace amount of ionic liquid dopant facilitates the kinetic pathway for the transition from the NF to the IR, enabling simple cooling to produce this isotropic fluid phase rather than resulting in immediate crystallization. The IR was also obtained in the absence of specific ionic liquid doping by appropriate temperature cycling in three distinct, as-synthesized-and-purified batches of RM734, two commercial and one from our laboratory. Ionic liquid doping also stabilizes the smectic ZA, an additional birefringent antiferroelectric phase having the director parallel to fluid smectic layers, significantly increasing its temperature range between the paraelectric and ferroelectric nematic phases with increasing BMIM concentration.

We report a transition from the ferroelectric nematic liquid crystal (N_F) phase to a lower-temperature, antiferroelectric fluid phase having reentrant isotropic symmetry (I_A), in the liquid crystal compound RM734 doped with small concentrations of the ionic liquids BMIM or EMIM. Even a trace amount of ionic liquid dopant facilitates the kinetic pathway for the transition from the N_F to the I_A, enabling simple cooling to produce this isotropic fluid phase rather than resulting in crystallization. The I_A was also obtained in the absence of specific ionic liquid doping by appropriate temperature cycling in three distinct, as-synthesized-and-purified batches of RM734, two commercial and one from our laboratory. An additional birefringent, lamellar-modulated, antiferroelectric phase with the director parallel to the layers, resembling the smectic Z_A, is found between the paraelectric and ferroelectric nematic phases in RM734/BMIM mixtures.

Electronic electro-optic (EEO) phase modulation is a key emerging technology for the chip-scale inter-conversion of signals between the electronic and photonic domains. The recent discovery of the ferroelectric nematic (N_F) liquid crystal phase, a three dimensional fluid of rod-shaped organic molecules having near-perfect equilibrium polar molecular orientational order, offers attractive opportunities for the creation of second-order nonlinear optical materials for EEO. Here we propose and realize a design motif for NF EEO molecules in which few-nanometer-long molecular rods are functionalized both for electro-static end-to-end association, facilitating NF phase formation, and for chromophoric optical nonlinearity, enabling high EEO efficiency, a combination enabling an active second-order nonlinear EEO medium that is 100

Polarization flutter, produced by an applied AC electric field drives an equilibrium ferroelectric nematic (N_F) liquid crystal (LC) through a transition into a dissipative active ferroelectric nematic state exhibiting strong elasto-hydrodynamic intermolecular interaction. In such a fluttering ferroelectric, the typical equilibrium N_F textural features adopted to reduce electrostatic energy, such as preferences for director bend, and alignment of polarization parallel to LC/air interfaces, are overcome, giving way to nonequilibrium conjugate structures in which director splay, and alignment of polarization normal to N_F/air interfaces are preferred. Viewing the latter textures as those of an active nematic phase reveals that self-organization to reduce effective viscosity and resulting dissipation generates a flow-driven apparent nematic elasticity and interface structuring that dominates equilibrium LC elastic and surface forces.

We show that stable, freely suspended liquid crystal films can be made from the ferroelectric nematic (NF) phase and from the recently discovered polar, lamellar SmZA and SmAF phases. The NF films display two-dimensional, smectic-like parabolic focal conic textures comprising director/polarization bend that are a manifestation of the electrostatic suppression of director splay in the film plane. In the SmZA and SmAF phases, the smectic layers orient preferentially normal to the film surfaces, a condition never found in typical thermotropic or lyotropic lamellar LC phases, with the SmZA films exhibiting focal-conic fan textures mimicking the appearance of typical smectics in glass cells when the layers are oriented normal to the plates, and the SmAF films showing a texture of plaquettes of uniform in-plane orientation where both bend and splay are suppressed, separated by grain boundaries. The SmAF phase can also be drawn into thin filaments, in which X-ray scattering reveals that the smectic layer planes are normal to the filament axis. Remarkably, the filaments are mechanically stable even if they break, forming free-standing, fluid filaments supported only at one end. The unique architectures of these films and filaments are stabilized by the electrostatic self-interaction of the liquid crystal polarization field, which enables the formation of confined, fluid structures that are fundamentally different from those of their counterparts made using previously known liquid crystal phases.

The twist-bend nematic liquid crystal phase is a three-dimensional fluid in which achiral bent molecules spontaneously form an orientationally ordered, macroscopically chiral, heliconical winding of a ten nanometer-scale pitch in the absence of positional ordering. Here, the structure of the twist-bend phase of the bent dimer CB7CB and its mixtures with 5CB is characterized, revealing a hidden invariance of the self-assembly of the twist-bend structure of CB7CB, such that over a wide range of concentrations and temperatures, the helix pitch and cone angle change as if the ground state for a pitch of the TB helix is an inextensible heliconical ribbon along the contour formed by following the local molecular long axis (the director). Remarkably, the distance along the length for a single turn of this helix is given by 2πRmol, where Rmol is the radius of bend curvature of a single all-trans CB7CB molecule. This relationship emerges from frustrated steric packing due to the bent molecular shape: space in the fluid that is hard to fill attracts the most flexible molecular subcomponents, a theme of nanosegregation that generates self-assembled, oligomer-like correlations of interlocking bent molecules in the form of a brickwork-like tiling of pairs of molecular strands into duplex double-helical chains. At higher temperatures in the twist-bend phase, the cone angle is small, the director contour is nearly along the helix axis z, and the duplex chains are sequences of biaxial elements formed by overlapping half-molecule pairs, with an approximately 45° rotation of the biaxis between each such element along the chain.

Numerous measurements of the dielectric constant $\epsilon$ of the recently discovered ferroelectric nematic ($N_F$) liquid crystal (LC) phase report extraordinarily large values of $\epsilon^\prime$ (up to ~30,000). We show that what is in fact being measured in such experiments is the high capacitance of the non-ferroelectric, interfacial, insulating layers of nanoscale thickness that bound the $N_F$ material in typical cells. We analyze a parallel-plate cell filled with $N_F$ material of high-polarization $\mathbf{P}$, oriented parallel to the plates at zero applied voltage. Minimization of the dominant electrostatic energy renders $\mathbf{P}$ spatially uniform and orients it to make the electric field in the $N_F$ as small as possible, a condition under which the voltage applied to the cell appears almost entirely across the high-capacity interfacial layers. This coupling of orientation and charge creates a combined polarization-external capacitance (PCG) Goldstone reorientation mode requiring applied voltages orders of magnitude smaller than that of the $N_F$ layer alone to effectively transport charge across the $N_F$ layer. The $N_F$ layer acts as a low-value resistor and the interfacial capacitors as reversible energy storage reservoirs, lowering the restoring force (mass) of the PCG mode and producing strong reactive dielectric behavior. Analysis of data from several experiments on ferroelectric liquid crystals (chiral smectics C, bent-core smectics, and the $N_F$ phase supports the PCG model, showing that deriving dielectric constants from electrical impedance measurements of high-polarization ferroelectric LCs, without properly accounting for the self-screening effects of polarization charge and the capacitive contributions of interfacial layers, can result in overestimation of the $\epsilon^\prime$ values of the LC by many orders of magnitude.

Recently discovered ferroelectric nematic liquid crystals (FNLCs) offer the opportunity to make liquid crystalbased, high-speed electro-optic devices. The lack of a center of symmetry combined with having the polar axis oriented parallel to the long, polarizable molecular axis allows for large second-order nonlinear optical susceptibility and therefore a large Pockels effect. The electro-optic response at high frequencies is purely electronic, making possible high-speed modulators with bandwidths limited only by device architecture. Facile and thermodynamically stable alignment of the polar axis over large areas makes FNLCs an attractive alternative to organic crystals and poled polymers, which have been pursued for decades as Pockels materials. A novel methodology for characterizing the electro-optic coefficient (r33) of this new class of Pockels material was developed. Using this methodology, FNLCs engineered to have large nonlinearities were demonstrated to have r33 values approaching that of lithium niobate.

The recently discovered ferroelectric nematic (N-F) liquid-crystal phase exhibits a spontaneous polarization field that is both orientationally fluid like a liquid crystal and large in magnitude like a solid ferroelectric. This combination imparts this phase with a unique electrostatic phenomenology and response to applied fields. Here we probe this phase by applying a small electric field to ferroelectric nematics confined in microchannels that connect electrodes through straight and curved paths and find that the N-F phase smoothly orders with its polarization following the channels despite their winding paths. This implies a corresponding behaviour of the electric field. On inversion of the electric field, the polar order undergoes a multistage switching process dominated by electrostatic interactions. We also find multistage polarization switching dynamics in the numerical simulations of a quasi-two-dimensional continuum model of channel-confined N-F liquid crystals, enabling the exploration of their internal structural and electrical self-organization. This indicates that polarization alignment and electric-field guiding are direct consequences of fluid superscreening-the prompt elimination of electric-field components normal to the channel walls by polarization reorientation. This response mimics the behaviour expected for ultrahigh-permittivity dielectrics, but with patterns of charge accumulation and local ordering unique to fluid ferroelectrics. The ferroelectric uniaxial nematic liquid-crystal phase features a freely reorientable polarization field. When confined in microchannels and subjected to electric fields, this polarization is now found to align with the channels due to a superscreening effect.

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.

The organic mesogens RM734 and DIO are members of separate molecular families featuring distinct molecular structures. These families, at the present time, are the only ones known to exhibit a ferroelectric nematic liquid crystal (LC) phase. Here we present an experimental investigation of the phase diagram and electro-optics of binary mixtures of RM734 and DIO. We observe paraelectric nematic (N) and ferroelectric nematic (NF) phases in both materials, each of which exhibits complete miscibility across the phase diagram, showing that the paraelectric and ferroelectric are the same phases in RM734 as in DIO. Remarkably, these molecules form ideal mixtures with respect to both the paraelectric-ferroelectric nematic phase behavior and the ferroelectric polarization density of the mixtures, the principal order parameter of the transition. Ideal mixing is also manifested in the orientational viscosity, and the onset of glassy dynamics at low temperature. This behavior is attributable in part to the similarity of their overall molecular shape and net longitudinal dipole moment (~ 11 Debye), and to a common tendency for head-to-tail molecular association. In contrast, the significant difference in molecular structures leads to poor solubility in the crystal phases, enhancing the stability of the ferroelectric nematic phase at low temperature in the mixtures and making possible room temperature electro-optic effects. In the mixtures with excess DIO, an intermediate phase appears via an ultraweak, first-order transition from the N phase, in a narrow temperature range between the paraelectric and ferroelectric nematics.

Living systems exhibit self-organization, a phenomenon that enables organisms to perform functions essential for life. The interior of living cells is a crowded environment in which the self-assembly of cytoskeletal networks is spatially constrained by membranes and organelles. Cytoskeletal filaments undergo active condensation in the presence of crosslinking motor proteins. In past studies, confinement has been shown to alter the morphology of active condensates. Here, we perform simulations to explore systems of filaments and crosslinking motors in a variety of confining geometries. We simulate spatial confinement imposed by hard spherical, cylindrical, and planar boundaries. These systems exhibit non-equilibrium condensation behavior where crosslinking motors condense a fraction of the overall filament population, leading to coexistence of vapor and condensed states. We find that the confinement lengthscale modifies the dynamics and condensate morphology. With end-pausing crosslinking motors, filaments self-organize into half asters and fully-symmetric asters under spherical confinement, polarity-sorted bilayers and bottle-brush-like states under cylindrical confinement, and flattened asters under planar confinement. The number of crosslinking motors controls the size and shape of condensates, with flattened asters becoming hollow and ring-like for larger motor number. End pausing plays a key role affecting condensate morphology: systems with end-pausing motors evolve into aster-like condensates while those with non-end-pausing crosslinking motor proteins evolve into disordered clusters and polarity-sorted bundles.

Significance Liquid crystal science grows in richness and applicability with each new phase that is found or created. The recent discovery of the ferroelectric nematic was both thrilling and unexpected, since it appeared in new molecules not much different in structure from many similar materials studied over the last 100 years. Clearly, significant secrets remain to be discovered in the complexities of organic molecular architecture and interaction. A fundamental question following the ferroelectric nematic discovery was whether there could also be a ferroelectric smectic A, the nematic-companion phase obtained when molecules spontaneously position to form planar, fluid layers normal to their molecular long axes. Here, we report such a phase, broadening the ferroelectric nematic realm.

The combination of large spontaneous polarization and fluidity makes the newly discovered ferroelectric nematic liquid crystalline phase (NF) responsive to electric fields in ways that have no counterpart in other materials. We probe this sensitive field response by confining a NF fluid in microchannels that connect electrodes through straight and curved paths. We find that by applying electric fields as low as E c.a. 0.5 V/mm, the NF phase orders with its polarization smoothly following the winding paths of the channels even when oriented antiparallel to the line connecting positive to negative electrodes, implying analogous behavior of the electric field. Upon inversion of E, the polar order undergoes a complex multistage switching process dominated by electrostatic interactions. Multistage polarization switching dynamics is also found in numerical simulations of a quasi-2D continuum model of NF liquid crystals in microchannels, which also clarify the conditions under which the electric field is guided by the microchannels. Experiments and theory indicate that all observations are direct consequences of the prompt effective screening of electric field components normal to the channel walls. This electric "superscreening" effect emerges as a distinctive property of the NF phase, capable of inducing conditions in which both the polarization and the electric field are guided by microchannels.

The cytoskeleton – a collection of polymeric filaments, molecular motors, and crosslinkers – is a foundational example of active matter, and in the cell assembles into organelles that guide basic biological functions. Simulation of cytoskeletal assemblies is an important tool for modeling cellular processes and understanding their surprising material properties. Here, we present aLENS (a Living Ensemble Simulator), a novel computational framework designed to surmount the limits of conventional simulation methods. We model molecular motors with crosslinking kinetics that adhere to a thermodynamic energy landscape, and integrate the system dynamics while efficiently and stably enforcing hard-body repulsion between filaments. Molecular potentials are entirely avoided in imposing steric constraints. Utilizing parallel computing, we simulate tens to hundreds of thousands of cytoskeletal filaments and crosslinking motors, recapitulating emergent phenomena such as bundle formation and buckling. This simulation framework can help elucidate how motor type, thermal fluctuations, internal stresses, and confinement determine the evolution of cytoskeletal active matter.

Significance The devices of the portable computing revolution are being made possible by nematic liquid crystal display (LCD) technology. The optical changes viewed in a dynamic LCD image are based on reorienting molecules by coupling electronically generated electric fields to molecular dielectric anisotropy. This takes place in appropriate fluid electro-optic structures stabilized by nonpolar orientational coupling of molecules to surfaces. The recent observation of ferroelectric nematics having spontaneous macroscopic electric polarization density has introduced a much stronger polar coupling of electric field to molecular reorientation in nematics. This development opens opportunities for advanced electro-optics, but these will require polar control of molecular orientation by surfaces. The generation of polar-structured surfaces and their coupling to nematic polarity is demonstrated in this paper. 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 wP ∼3 × 10−3 J/m2.

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 phase transition from polar flocks to self-sorted chiral clusters, which is modified by filament flexibility. This phase transition changes filament transport from ballistic to diffusive at long timescales.

Smectic liquid crystal films a few molecular layers thick that are freely suspended in air are used as a model system to study the coalescence of fluids in two dimensions. High-speed video microscopy is used to observe the coalescence of islands, which are thicker, disk-shaped regions of the film, in a process driven by the line tension associated with edge dislocations along the island boundaries and limited by viscous dissipation in the liquid crystal and in the surrounding air. The early time growth of the bridge connecting the merging islands reveals much slower dynamics than predicted by Hopper's classical hydrodynamic model of coalescence of two infinitely long, fluid cylinders in vacuum, a discrepancy proposed to be due to significant dissipation in the background film and in the air that is not included in Hopper's theory. At late times, the elliptical merged island relaxes exponentially to a circular shape, at rates that are described quantitatively by a model originally developed to describe the evolution of fluid domains in Langmuir films.

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 $10^3$--$10^6$ 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.