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Turbulence is ubiquitous, from oceanic currents to small-scale biological and quantum systems. Self-sustained turbulent motion in microbial suspensions presents an intriguing example of collective dynamical behavior among the simplest forms of life and is important for fluid mixing and molecular transport on the microscale. The mathematical characterization of turbulence phenomena in active nonequilibrium fluids proves even more difficult than for conventional liquids or gases. It is not known which features of turbulent phases in living matter are universal or system-specific or which generalizations of the Navier–Stokes equations are able to describe them adequately. Here, we combine experiments, particle simulations, and continuum theory to identify the statistical properties of self-sustained meso-scale turbulence in active systems. To study how dimensionality and boundary conditions affect collective bacterial dynamics, we measured energy spectra and structure functions in dense Bacillus subtilis suspensions in quasi-2D and 3D geometries. Our experimental results for the bacterial flow statistics agree well with predictions from a minimal model for self-propelled rods, suggesting that at high concentrations the collective motion of the bacteria is dominated by short-range interactions. To provide a basis for future theoretical studies, we propose a minimal continuum model for incompressible bacterial flow. A detailed numerical analysis of the 2D case shows that this theory can reproduce many of the experimentally observed features of self-sustained active turbulence.

In nematic liquid crystals, the local orientation of the molecules hovers around an average direction. The orientational control bestows unusual optical properties. In theory, with the right sort of two-dimensional shape, it should be possible to create nematics with biaxial ordering, but this has proven elusive. Mundoor et al. dispersed colloidal rods into a nematic solvent (see the Perspective by Poulin). Within a range of temperature and concentration, the rods ordered orthogonally to the solvent molecules, thus giving the mixture the type of properties that one would expect from a biaxial liquid crystal. Science , this issue p. 768 ; see also p. 712 Self-assembly of colloidal and molecular rods yields orthorhombic nematics with switchable biaxial optical properties. Order and fluidity often coexist, with examples ranging from biological membranes to liquid crystals, but the symmetry of these soft-matter systems is typically higher than that of the constituent building blocks. We dispersed micrometer-long inorganic colloidal rods in a nematic liquid crystalline fluid of molecular rods. Both types of uniaxial building blocks, while freely diffusing, interact to form an orthorhombic nematic fluid, in which like-sized rods are roughly parallel to each other and the molecular ordering direction is orthogonal to that of colloidal rods. A coarse-grained model explains the experimental temperature-concentration phase diagram with one biaxial and two uniaxial nematic phases, as well as the orientational distributions of rods. Displaying properties of biaxial optical crystals, these hybrid molecular-colloidal fluids can be switched by electric and magnetic fields.

Biaxial nematic liquid crystals are fascinating systems sometimes referred to as the Higgs boson of soft matter because of experimental observation challenges. Here we describe unexpected states of matter that feature biaxial orientational order of colloidal supercritical fluids and gases formed by sparse rodlike particles. Colloidal rods with perpendicular surface boundary conditions exhibit a strong biaxial symmetry breaking when doped into conventional chiral nematic fluids. Minimization of free energy prompts these particles to orient perpendicular to the local molecular director and the helical axis, thereby imparting biaxiality on the hybrid molecular-colloidal system. The ensuing phase diagram features colloidal gas and liquid and supercritical colloidal fluid states with long-range biaxial orientational symmetry, as supported by analytical and numerical modeling at all hierarchical levels of ordering. Unlike for nonchiral hybrid systems, dispersions in chiral nematic hosts display biaxial orientational order at vanishing colloid volume fractions, promising both technological and fundamental research utility. The study of nematic hosts with anisotropic colloidal particles is reported, but not on the chiral counterparts. Here, the authors report on biaxial properties in a system of colloidal rods with designed surface anchoring doped into a chiral nematic host.

Many nanoparticle-based chiral liquid crystals are composed of polydisperse rod-shaped particles with considerable spread in size or shape, affecting the mesoscale chiral properties in, as yet, unknown ways. Using an algebraic interpretation of Onsager-Straley theory for twisted nematics, we investigate the role of length polydispersity on the pitch of nanorod-based cholesterics with a continuous length polydispersity, and find that polydispersity enhances the twist elastic modulus, K 2 , of the cholesteric material without affecting the effective helical amplitude, K t . In addition, for the infinitely large average aspect ratios considered here, the dependence of the pitch on the overall rod concentration is completely unaffected by polydispersity. For a given concentration, the increase in twist elastic modulus (and reduction of the helical twist) may be up to 50% for strong size polydispersity, irrespective of the shape of the unimodal length distribution. We also demonstrate that the twist reduction is reinforced in bimodal distributions, obtained by doping a polydisperse cholesteric with very long rods. Finally, we identify a subtle, non-monotonic change of the pitch across the isotropic-cholesteric biphasic region.

Fundamental relationships are believed to exist between the symmetries of building blocks and the condensed matter phases that they form 1 . For example, constituent molecular and colloidal rods and disks impart their uniaxial symmetry onto nematic liquid crystals, such as those used in displays 1 , 2 . Low-symmetry organizations could form in mixtures of rods and disks 3 – 5 , but entropy tends to phase-separate them at the molecular and colloidal scales, whereas strong elasticity-mediated interactions drive the formation of chains and crystals in nematic colloids 6 – 11 . To have a structure with few or no symmetry operations apart from trivial ones has so far been demonstrated to be a property of solids alone 1 , but not of their fully fluid condensed matter counterparts, even though such symmetries have been considered theoretically 12 – 15 and observed in magnetic colloids 16 . Here we show that dispersing highly anisotropic charged colloidal disks in a nematic host composed of molecular rods provides a platform for observing many low-symmetry phases. Depending on the temperature, concentration and surface charge of the disks, we find nematic, smectic and columnar organizations with symmetries ranging from uniaxial 1 , 2 to orthorhombic 17 – 21 and monoclinic 12 – 15 . With increasing temperature, we observe unusual transitions from less- to more-ordered states and re-entrant 22 phases. Most importantly, we demonstrate the presence of reconfigurable monoclinic colloidal nematic order, as well as the possibility of thermal and magnetic control of low-symmetry self-assembly 2 , 23 , 24 . Our experimental findings are supported by theoretical modelling of the colloidal interactions between disks in the nematic host and may provide a route towards realizing many low-symmetry condensed matter phases in systems with building blocks of dissimilar shapes and sizes, as well as their technological applications. Dispersion of colloidal disks in a nematic liquid crystal reveals several low-symmetry phases, including monoclinic colloidal nematic order, with interchange between them achieved through variations in temperature, concentration and surface charge.

Membranes are widely used for separation processes in applications such as water desalination, batteries and dialysis, and are crucial in key sectors of our economy and society 1 . The majority of technologically exploited membranes are based on solid polymers and function as passive barriers, whose transport characteristics are governed by their chemical composition and nanostructure. Although such membranes are ubiquitous, it has proved challenging to maximize selectivity and permeability independently, leading to trade-offs between these pertinent characteristics 2 . Self-assembled biological membranes, in which barrier and transport functions are decoupled 3 , 4 , provide the inspiration to address this problem 5 , 6 . Here we introduce a self-assembly strategy that uses the interface of an aqueous two-phase system to template and stabilize molecularly thin (approximately 35 nm) biomimetic block copolymer bilayers of scalable area that can exceed 10 cm 2 without defects. These membranes are self-healing, and their barrier function against the passage of ions (specific resistance of approximately 1 MΩ cm 2 ) approaches that of phospholipid membranes. The fluidity of these membranes enables straightforward functionalization with molecular carriers that shuttle potassium ions down a concentration gradient with exquisite selectivity over sodium ions. This ion selectivity enables the generation of electric power from equimolar solutions of NaCl and KCl in devices that mimic the electric organ of electric rays. We introduce a self-assembly strategy that uses the interface of an aqueous two-phase system to template and stabilize molecularly thin biomimetic block copolymer bilayers of scalable area that can exceed 10 cm 2 without defects.

The high purity and superior quality of the synthetic clay mineral fluorohectorite allows for studies of phenomena that are masked by imperfections and the inhomogeneous charge distribution in the case of natural clay minerals. We have exploited this opportunity offered by synthetic fluorohectorite and report here digital optical microscopy observations of salinity controlled macroscopic swelling and deswelling behavior of extra-large nanolamellar clay mineral particle accordions of various sizes. We find that clay particle accordions, immersed in a saline solution, at sufficiently high salinity, are in their crystalline swelling region, with only a few water layers hydrating the accordion interlayer nano-spaces, corresponding to an interlayer spacing of about 1.5 nm. Using a micropipette as a micro-tweezer and thereby transferring accordions carefully back and forth between high and low salinity solutions, we observe well defined macroscopic accordion transitions between the crystalline swelling regime and an osmotic swelling regime where the interlayer spacings reach tens of nanometers, calculated from accordion thicknesses measured by digital imaging. The transitions display a clear first order character as evidenced by threshold salinity levels for their abrupt onsets as well as clear hysteresis with retention of crystalline or osmotic state memory, as salinity is increased or lowered. The experimental observations are supported by a theoretical model of the accordion interlayer spacing based on a Donnan equilibrium originating from the salinity gradient between the embedding saline solution and the ionic strength in the clay interlayers in the osmotic swelling regime.

The effect of short chain grafting on the liquid crystalline (LC) ordering of nano-crystals is investigated using molecular dynamics simulations of a coarse-grained grafted nano-rod model. Monodisperse nano-rods, with aspect ratios typical of cellulose nano-crystals (CNCs) are grafted randomly with oligomers at different grafting densities. LC ordering depends non-trivially on grafting density as the effective nano-rod shape and softness is modified. Ungrafted rods exhibit Nematic and tilted Smectic-C phases. At 25\\% grafting, the addition of a few side chains entirely suppresses Smectic order and instead a persistent Nematic phase is favoured. Intermediary grafting, around 50\\%, results in a Nematic and the reappearance of tilted Smectic-F phases. Heavier grafting facilitates direct transitions to either Smectic-I with extreme tilt (75\\%) or an un-tilted Smectic-B (100\\%). Such behaviour falls outside of current hard or soft-rod descriptions of phase-transitions in rod-like LC systems and points to undiscovered LC behaviour in both shape-purified grafted/un-grafted CNCs.

Living polymers composed of non-covalently bonded building blocks with weak backbone flexibility may self-assemble into thermoresponsive lyotropic liquid crystals. We demonstrate that the reversible polymer assembly and phase behavior can be controlled by the addition of (non-adsorbing) rigid colloidal discs which act as an entropic reorienting ``template\" onto the supramolecular polymers. Using a particle-based second-virial theory that correlates the various entropies associated with the polymers and discs, we demonstrate that small fractions of discotic additives promote the formation of a polymer nematic phase. At larger disc concentrations, however, the phase is disrupted by collective disc alignment in favor of a discotic nematic fluid in which the polymers are dispersed anti-nematically. We show that the anti-nematic arrangement of the polymers generates a non-exponential molecular-weight distribution and stimulates the formation of oligomeric species. At sufficient concentrations the discs facilitate a liquid-liquid phase separation which can be brought into simultaneously coexistence with the two fractionated nematic phases, providing evidence for a four-fluid coexistence in reversible shape-dissimilar hard-core mixtures without cohesive interparticle forces. We stipulate the conditions under which such a phenomenon could be found in experiment.

We explore the effect of directionality on rotational and translational relaxation in glassy systems of patchy particles. Using molecular dynamics simulations we analyze the impact of two distinct patch geometries, one that enhance local icosahedral structure and one which does not strongly affect local order. We find that in nearly all investigated cases, rotational relaxation takes place on a much faster time scale than translational relaxation. By comparing to a simplified dynamical Monte Carlo model, we illustrate that rotational diffusion can be qualitatively explained as purely local motion within a fixed environment, which is not coupled strongly to the cage-breaking dynamics required for translational relaxation. Nonetheless, icosahedral patch placement has a profound effect on the local structure of the system, resulting in a dramatic slowdown at low temperatures which is strongest at an intermediate \"optimal\" patch size.