Large-area, self-healing block copolymer membranes for energy conversion.

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 society1. 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 characteristics2. Self-assembled biological membranes, in which barrier and transport functions are decoupled3,4, provide the inspiration to address this problem5,6. 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 cm2 without defects. These membranes are self-healing, and their barrier function against the passage of ions (specific resistance of approximately 1 MΩ cm2) 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.

Crystalline restacking of 2D-materials from their nanosheets suspensions.

We report here the highly ordered restacking of the layered phosphatoantimonic dielectric materials H3(1-x)M3xSb3P2O14, (where M = Li, Na, K, Rb, Cs and 0 ≤ x ≤ 1), from their nanosheets dispersed in colloidal suspension, induced by a simple pH change using alkaline bases. H3Sb3P2O14 aqueous suspensions are some of the rare examples of colloidal suspensions based on 2D materials exhibiting a lamellar liquid crystalline phase. Because the lamellar period can reach several hundred nanometers, the suspensions show vivid structural colors and because these colors are sensitive to various chemicals, the suspensions can be used as sensors. The structures of the lamellar liquid crystalline phase and the restacked phase have been studied by X-ray scattering (small and wide angle), which has followed the dependence of the lamellar/restacked phase equilibrium on the cation exchange rate, x. The X-ray diffraction pattern of the restacked phase is almost identical to that of the M3Sb3P2O14 crystalline phase, showing that the restacking is highly accurate and avoids the turbostratic disorder of the nanosheets classically observed in nanosheet stacking of other 2D materials. Strikingly, the restacking process exhibits features highly reminiscent of a first-order phase transition, with the existence of a phase coexistence region where both ∼1 nm (interlayer spacing of the restacked phase) and ∼120 nm lamellar periods can be observed simultaneously. Furthermore, this first-order phase transition is well described theoretically by incorporating a Lennard-Jones-type lamellar interaction potential into an entropy-based statistical physics model of the lamellar phase of nanosheets. Our work shows that the precise cation exchange produced at room temperature by a classical neutralization reaction using alkaline bases leads to a crystal-like restacking of the exfoliated free Sb3P2O143- nanosheets from suspension, avoiding the turbostratic disorder typical of van der Waals 2D materials, which is detrimental to the controlled deposition of nanosheets into complex integrated electronic, spintronic, photonic or quantum structures.

Pre-Smectic Ordering and the Unwinding Helix in Monte Carlo Simulations of Cholesteric Liquid-Crystals.

In this paper, molecular chirality is studied for liquid-crystal fluids represented by hard rods with the addition of an attractive chiral dispersion term. Chiral forces between molecular pairs are assumed to be long-ranged and are described in terms of the pseudotensor of Goossens [W. J. A. Goossens, Mol. Cryst. Liq. Cryst. 1971, 12, 237-244]. Following Varga and Jackson [S. Varga and G. Jackson, Chem. Phys. Lett. 2003, 377, 6-12], this is combined with a hard-spherocylinder core. We investigate the relationship between molecular chirality and the helical pitch of the system, which occurs in the absence of full three-dimensional periodic boundary conditions. The dependence of the wavenumber of this pitch on the thermodynamic variables, temperature, and density is measured. We also explore the use of a novel surface boundary interaction model. As a result of this approach, we are able to lower the temperature of the system without the occurrence of nematic droplets, which would interfere with the formation of a uniaxial pitch. Regarding the theoretical predictions of Wensink and Jackson [H. H. Wensink and G. Jackson, J. Chem. Phys. 2009, 130, 234911], on the one hand, we have qualitative agreement with the observed non-monotonic density dependence of the wavenumber. Initially increasing with density, the wavenumber reaches a maximum, before falling as the density moves toward the point of phase transition from cholesteric to smectic. However, further analysis for shorter rods, in the presence of novel boundary conditions, reveals some disagreement with the theory, at least in this case; the unwinding of the cholesteric helix in the cholesteric phase occurs simultaneously with subtle increases in smectic ordering. These pre-smectic fluctuations have not been accounted for so far in theories on cholesterics but turn out to play a key role in controlling the pitch of cholesteric phases of rod-shaped mesogens with a small to moderate aspect ratio.

Do Aqueous Suspensions of Smectite Clays Form a Smectic Liquid-Crystalline Phase?

Bottom-up strategies for the production of well-defined nanostructures often rely on the self-assembly of anisotropic colloidal particles (nanowires and nanosheets). These building blocks can be obtained by delamination in a solvent of low-dimensionality crystallites. To optimize particle availability, determination of the delamination mechanism and the different organization stages of anisotropic particles in dispersion is essential. We address this fundamental issue by exploiting a recently developed system of fluorohectorite smectite clay mineral that delaminates in water, leading to colloidal dispersions of single-layer, very large (≈20 µm) clay sheets at high dilution. We show that when the clay crystallites are dispersed in water, they swell to form periodic one-dimensional stacks of fluorohectorite sheets with very low volume fraction (<1%) and therefore huge (≈100 nm) periods. Using optical microscopy and synchrotron X-ray scattering, we establish that these colloidal stacks bear strong similarities, yet subtle differences, with a smectic liquid-crystalline phase. Despite the high dilution, the colloidal stacks of sheets, called colloidal accordions, are extremely robust mechanically and can persist for years. Moreover, when subjected to AC electric fields, they rotate as solid bodies, which demonstrates their outstanding internal cohesion. Furthermore, our theoretical model captures the dependence of the stacking period on the dispersion concentration and ionic strength and explains, invoking the Donnan effect, why the colloidal accordions are kinetically stable over years and impervious to shear and Brownian motion. Because our model is not system specific, we expect that similar colloidal accordions frequently appear as an intermediate state during the delamination process of two-dimensional crystals in polar solvents.

Fine tuning the structural colours of photonic nanosheet suspensions by polymer doping.

Aqueous suspensions of nanosheets are readily obtained by exfoliating low-dimensional mineral compounds like H3Sb3P2O14. The nanosheets self-organize, at low concentration, into a periodic stack of membranes, i.e. a lamellar liquid-crystalline phase. Due to the dilution, this stack has a large period of a few hundred nanometres, it behaves as a 1-dimensional photonic material and displays structural colours. We experimentally investigated the dependence of the period on the nanosheet concentration. We theoretically showed that it cannot be explained by the usual DLVO interaction between uniform lamellae but that the particulate nature of nanosheet-laden membranes must be considered. Moreover, we observed that adding small amounts of 100 kDa poly(ethylene oxide) (PEO) decreases the period and allows tuning the colour throughout the visible range. PEO adsorbs on the nanosheets, inducing a strong reduction of the nanosheet charge. This is probably due to the Lewis-base character of the EO units of PEO that become protonated at the low pH of the system, an interpretation supported by theoretical modeling. Oddly enough, adding small amounts of 1 MDa PEO has the opposite effect of increasing the period, suggesting the presence of an additional intermembrane repulsion not yet identified. From an applied perspective, our work shows how the colours of these 1-dimensional photonic materials can easily be tuned not only by varying the nanosheet concentration (which might entail a phase transition) but also by adding PEO. From a theoretical perspective, our approach represents a necessary step towards establishing the phase diagram of aqueous suspensions of charged nanosheets.

Multiphase Coexistences in Rod-Polymer Mixtures.

Using recently derived analytical equations of state for hard rod dispersions, we predict the phase behavior of athermal rod-polymer mixtures with free volume theory. The rods are modeled as hard spherocylinders, while the nonadsorbing polymer chains are described as penetrable hard spheres. It is demonstrated that all of the different types of phase states that are stable for pure colloidal rod dispersions can coexist with any combination of these phases if polymers are added, depending on the concentrations, rod aspect ratio, and polymer-rod size ratio. This includes novel two-, three-, and four-phase coexistences and isostructural coexistences between dilute and concentrated phases of the same kind, even for the more ordered (liquid) crystal phases. This work provides insight into the conditions at which particular multiphase coexistences are expected for well-defined model colloidal rod-polymer mixtures. We provide a quantitative map detailing the various types of isostructural coexistences, which confirms an early qualitative hypothesis by Bolhuis et al. ( J. Chem. Phys. 107, 1997 1551).

Thermally reconfigurable monoclinic nematic colloidal fluids.

Fundamental relationships are believed to exist between the symmetries of building blocks and the condensed matter phases that they form1. For example, constituent molecular and colloidal rods and disks impart their uniaxial symmetry onto nematic liquid crystals, such as those used in displays1,2. Low-symmetry organizations could form in mixtures of rods and disks3-5, 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 colloids6-11. 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 alone1, but not of their fully fluid condensed matter counterparts, even though such symmetries have been considered theoretically12-15 and observed in magnetic colloids16. 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 uniaxial1,2 to orthorhombic17-21 and monoclinic12-15. With increasing temperature, we observe unusual transitions from less- to more-ordered states and re-entrant22 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-assembly2,23,24. 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.

Destabilization of the Nematic Phase of Clay Nanosheet Suspensions by Polymer Adsorption.

Complex aqueous mixtures comprised of swelling clays and hydrosoluble polymers naturally occur in soils and play a major role in pedogenesis. They are also very often used for formulating oil-well drilling fluids, paints, and personal-care products. The suspensions of some natural clays, thanks to their large nanoparticle aspect ratio, spontaneously form nematic liquid-crystalline phases where the particles align parallel to each other, which affects their flow properties. We observed that adding small amounts of hydrosoluble polymers to these clay suspensions destabilizes the nematic phase with respect to the isotropic (disordered) phase. The polymers that we used (poly(ethylene oxide) and dextran) were too small to adopt particle-bridging conformations and small-angle X-ray scattering experiments showed that the structure of the nematic phase is not altered by polymer doping. However, the adsorption isotherm shows that the macromolecules adsorb onto the clay nanosheets, effectively coating them with a polymer layer. Our extension of Onsager's theory for polymer-coated platelets properly captures the experimental phase diagram and shows how the nematic phase destabilization can be due to the polymer adsorbing more on the platelet faces than at the rim. Because the flow properties of the nematic phase are very different from those of the isotropic phase, the presence or absence of the former phase is an important factor to be determined and considered to explain the rheological behavior of these complex systems.

Tetrahedrality Dictates Dynamics in Hard Sphere Mixtures.

The link between local structure and dynamical slowdown in glassy fluids has been the focus of intense debate for the better part of a century. Nonetheless, a simple method to predict the dynamical behavior of a fluid purely from its local structural features is still missing. Here, we demonstrate that the diffusivity of perhaps the most fundamental family of glass formers-hard sphere mixtures-can be accurately predicted based on just the packing fraction and a simple order parameter measuring the tetrahedrality of the local structure. Essentially, we show that the number of tetrahedral clusters in a hard sphere mixture is directly linked to its global diffusivity. Moreover, the same order parameter is capable of locally pinpointing particles in the system with high and low mobility. We attribute the power of the local tetrahedrality for predicting local and global dynamics to the high stability of tetrahedral clusters, the most fundamental building and densest-packing building blocks for a disordered fluid.

Rotational and translational dynamics in dense fluids of patchy particles.

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 enhances the local icosahedral structure and the other one that does not strongly affect the 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.

Slowing down supercooled liquids by manipulating their local structure.

Glasses remain an elusive and poorly understood state of matter. It is not clear how we can control the macroscopic dynamics of glassy systems by tuning the properties of their microscopic building blocks. In this paper, we propose a simple directional colloidal model that reinforces the optimal icosahedral local structure of binary hard-sphere glasses. We show that this specific symmetry results in a dramatic slowing down of the dynamics. Our results open the door to controlling the dynamics of dense glassy systems by selectively promoting specific local structural environments.

Long-time anomalous swimmer diffusion in smectic liquid crystals.

The dynamics of self-locomotion of active particles in aligned or liquid crystalline fluids strongly deviates from that in simple isotropic media. We explore the long-time dynamics of a swimmer moving in a three-dimensional smectic liquid crystal and find that the mean-square displacement transverse to the director exhibits a distinct logarithmic tail at long times. The scaling is distinctly different from that in an isotropic or nematic fluid and hints at the subtle but important role of the director fluctuation spectrum in governing the long-time motility of active particles. Our findings are based on a generic hydrodynamic theory and Brownian dynamics computer simulation of a three-dimensional soft mesogen model.

Hybrid molecular-colloidal liquid crystals.

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.

Structure and Interfacial Tension of a Hard-Rod Fluid in Planar Confinement.

The structural properties and interfacial tension of a fluid of rodlike hard-spherocylinder particles in contact with hard structureless flat walls are studied by means of Monte Carlo simulation. The calculated surface tension between the rod fluid and the substrate is characterized by a nonmonotonic trend as a function of the bulk concentration (density) over the range of isotropic bulk concentrations. As suggested by earlier theoretical studies, a surface-ordering scenario is confirmed by our simulations: the local orientational order close to the wall changes from uniaxial to biaxial nematic when the bulk concentration reaches about 85% of the value at the onset of the isotropic-nematic phase transition. The surface ordering coincides with a wetting transition whereby the hard wall is wetted by a nematic film. Accurate values of the fluid-solid surface tension, the adsorption, and the average particle-wall contact distance are reported (over a broad range of densities into the dense nematic region for the first time), which can serve as a useful benchmark for future theoretical and experimental studies on confined rod fluids. The simulation data are supplemented with predictions from second-virial density functional theory, which are in good qualitative agreement with the simulation results.

Following fluctuating signs: Anomalous active superdiffusion of swimmers in anisotropic media.

Active (i.e., self-propelled or swimming) particles moving through an isotropic fluid exhibit conventional diffusive behavior. We report anomalous diffusion of an active particle moving in an anisotropic nematic background. While the translational motion parallel to the nematic director shows ballistic behavior, the long-time transverse motion is superdiffusive, with an anomalous scaling proportional to tlnt of the mean-square displacement with time t. This behavior is predicted by an analytical theory that we present here and is corroborated by numerical simulation of active particle diffusion in a simple lattice model for a nematic liquid crystal. It is universal for any collection of self-propelled elements (e.g., bacteria or active rods) moving in a nematic background, provided only that the swimmers are sufficiently dilute that their interactions with each other can be neglected and that they do not perform hairpin turns.

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.

Fluid dynamics of bacterial turbulence.

Self-sustained turbulent structures have been observed in a wide range of living fluids, yet no quantitative theory exists to explain their properties. We report experiments on active turbulence in highly concentrated 3D suspensions of Bacillus subtilis and compare them with a minimal fourth-order vector-field theory for incompressible bacterial dynamics. Velocimetry of bacteria and surrounding fluid, determined by imaging cells and tracking colloidal tracers, yields consistent results for velocity statistics and correlations over 2 orders of magnitude in kinetic energy, revealing a decrease of fluid memory with increasing swimming activity and linear scaling between kinetic energy and enstrophy. The best-fit model allows for quantitative agreement with experimental data.

Meso-scale turbulence in living fluids.

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.

Size fractionation in a phase-separated colloidal fluid.

Phase separation of a polydisperse colloidal dispersion implies size fractionation. An application of this effect is given by size-selective purification procedures associated with the colloidal synthesis of so-called monodisperse nanoparticles. We used electron microscopy to determine detailed particle size distributions of coexisting colloidal fluid phases containing highly polydisperse iron oxide nanoparticles with a log-normal distribution (sigma = 0.54 for the total system). Analysis of N approximately 10000 particles per phase yields the first five statistical moments of the distributions. Within experimental error, the interdependence of the statistical moments is in quantitative agreement with the "universal law of fractionation" proposed by Evans, Fairhurst, and Poon [Phys. Rev. Lett. 1998, 81, 1326], even though the theory was derived in the limit of slight polydispersity.