Nematic nanotube gels

Preparing high-concentration individualized carbon nanotubes for industrial separation of multiple single-chirality species

Industrial production of single-chirality carbon nanotubes is critical for their applications in high-speed and low-power nanoelectronic devices, but both their growth and separation have been major challenges. Here, we report a method for industrial separation of single-chirality carbon nanotubes from a variety of raw materials with gel chromatography by increasing the concentration of carbon nanotube solution. The high-concentration individualized carbon nanotube solution is prepared by ultrasonic dispersion followed by centrifugation and ultrasonic redispersion. With this technique, the concentration of the as-prepared individualized carbon nanotubes is increased from about 0.19 mg/mL to approximately 1 mg/mL, and the separation yield of multiple single-chirality species is increased by approximately six times to the milligram scale in one separation run with gel chromatography. When the dispersion technique is applied to an inexpensive hybrid of graphene and carbon nanotubes with a wide diameter range of 0.8-2.0 nm, and the separation yield of single-chirality species is increased by more than an order of magnitude to the sub-milligram scale. Moreover, with present separation technique, the environmental impact and cost of producing single-chirality species are greatly reduced. We anticipate that this method promotes industrial production and practical applications of single-chirality carbon nanotubes in carbon-based integration circuits.

Phase transition from nematic to high-density disordered phase in a system of hard rods on a lattice

A system of hard rigid rods of length k on hypercubic lattices is known to undergo two phase transitions when chemical potential is increased: from a low density isotropic phase to an intermediate density nematic phase, and on further increase to a high-density phase with no orientational order. In this paper, we argue that, for large k, the second phase transition is a first-order transition with a discontinuity in density in all dimensions greater than 1. We show that the chemical potential at the transition is ≈kln[k/lnk] for large k, and that the density of uncovered sites drops from a value ≈(lnk)/k^{2} to a value of order exp(-ak), where a is some constant, across the transition. We conjecture that these results are asymptotically exact, in all dimensions d≥2. We also present evidence of coexistence of nematic and disordered phases from Monte Carlo simulations for rods of length 9 on the square lattice.

Micellar Lyotropic Nematic Gels

Lyotropic liquid crystal (LLC) gels are a new class of liquid crystal (LC) networks that combine the anisotropy of micellar LLCs with the mechanical stability of a gel. However, so far, only micellar LLC gels with lamellar and hexagonal structures have been obtained by the addition of gelators to LLCs. Here, the first examples of lyotropic nematic gels are presented. The key to obtain these nematic gels is the use of gelators that have a non-amphiphilic molecular structure and thus leave the size and shape of the micellar aggregates essentially unchanged. By adding these gelators to lyotropic nematic phases, an easy and reproducible way to obtain large amounts of lyotropic nematic gels is established. These nematic gels preserve the long-range orientational order and optical birefringence of a lyotropic nematic phase but have the mechanical stability of a gel. LLC nematic gels are promising new materials for elastic and anisotropic hydrogels to be applied as water-based stimuli-responsive actuators and sensors.

Tunable corrugated patterns in an active nematic sheet

Active matter locally converts chemical energy into mechanical work and, for this reason, it provides new mechanisms of pattern formation. In particular, active nematic fluids made of protein motors and filaments are far-from-equilibrium systems that may exhibit spontaneous motion, leading to actively driven spatiotemporally chaotic states in 2 and 3 dimensions and coherent flows in 3 dimensions (3D). Although these dynamic flows reveal a characteristic length scale resulting from the interplay between active forcing and passive restoring forces, the observation of static and large-scale spatial patterns in active nematic fluids has remained elusive. In this work, we demonstrate that a 3D solution of kinesin motors and microtubule filaments spontaneously forms a 2D free-standing nematic active sheet that actively buckles out of plane into a centimeter-sized periodic corrugated sheet that is stable for several days at low activity. Importantly, the nematic orientational field does not display topological defects in the corrugated state and the wavelength and stability of the corrugations are controlled by the motor concentration, in agreement with a hydrodynamic theory. At higher activities these patterns are transient and chaotic flows are observed at longer times. Our results underline the importance of both passive and active forces in shaping active matter and demonstrate that a spontaneously flowing active fluid can be sculpted into a static material through an active mechanism.

Phase diagram of a system of hard cubes on the cubic lattice

We study the phase diagram of a system of 2×2×2 hard cubes on a three-dimensional cubic lattice. Using Monte Carlo simulations, we show that the system exhibits four different phases as the density of cubes is increased: disordered, layered, sublattice ordered, and columnar ordered. In the layered phase, the system spontaneously breaks up into parallel slabs of size 2×L×L where only a very small fraction cubes do not lie wholly within a slab. Within each slab, the cubes are disordered; translation symmetry is thus broken along exactly one principal axis. In the solidlike sublattice-ordered phase, the hard cubes preferentially occupy one of eight sublattices of the cubic lattice, breaking translational symmetry along all three principal directions. In the columnar phase, the system spontaneously breaks up into weakly interacting parallel columns of size 2×2×L, where only a very small fraction cubes do not lie wholly within a column. Within each column, the system is disordered, and thus translational symmetry is broken only along two principal directions. Using finite-size scaling, we show that the disordered-layered phase transition is continuous, while the layered-sublattice and sublattice-columnar transitions are discontinuous. We construct a Landau theory written in terms of the layering and columnar order parameters which is able to describe the different phases that are observed in the simulations and the order of the transitions. Additionally, our results near the disordered-layered transition are consistent with the O(3) universality class perturbed by cubic anisotropy as predicted by the Landau theory.

Condensation and dissolution of nematic droplets in dispersions of colloidal rods with thermo-sensitive depletants

Nematic droplets are droplets composed of elongated molecules that tend to point in the same direction but do not have any positional order. Such droplets are well known to adopt a spindle shape called tactoid. How such droplets condensate or melt and how the orientational symmetry is broken remains however unclear. Here we use a colloidal system composed of filamentous viruses as model rod-like colloids and pnipam microgel particles to induce thermo-sensitive depletion attraction between the rods. Microscopy experiments coupled to particle tracking reveal that the condensation of a nematic droplet is preceded by the formation of a new phase, an isotropic droplet. As the viruses constitute an excellent experimental realization of hard rods, it follows that the phenomenology we describe should be relevant to diverse micro- and nano-sized rods that interact through excluded volume interactions. This transition between isotropic and nematic droplets provides a new and reversible pathway to break the symmetry and order colloidal rods within a droplet with an external stimulus, and could constitute a benchmark experiment for a variety of technologies relying on reconfigurable control of rods.

Aligned Carbon Nanotube Thin Films from Liquid Crystal Polyelectrolyte Inks

Single walled carbon nanotube thin films are fabricated by solution shearing from high concentration sodium nanotubide polyelectrolyte inks. The solutions are produced by simple stirring of the nanotubes with elemental sodium in dimethylacetamide, and the nanotubes are thus not subject to any sonication-induced damage. At such elevated concentrations (∼4 mg mL(-1)), the solutions exist in the liquid crystal phase and during deposition this order is transferred to the films, which are well aligned in the direction of shear with a 2D nematic order parameter of ∼0.7 determined by polarized absorption measurements. Compared to similarly formed films made from superacids, the polyelectrolyte films contain smaller bundles and a much narrower distribution of bundle diameters. After p-doping with an organic oxidizer, the films exhibit a very high DC electrical to optical conductivity ratio of σ(DC)/σ(OP) ∼ 35, corresponding to a calculated DC conductivity of over 7000 S cm(-1). When very thin (T550 ∼ 96%), smooth (RMS roughness, R(q) ∼ 2.2 nm), and highly aligned films made via this new route are used as the front electrodes of carbon nanotube-silicon solar cells, the power conversion efficiency is almost an order of magnitude greater than that obtained when using the much rougher (R(q) ∼ 20-30 nm) and less conductive (peak σ(DC)/σ(OP) ∼ 2.5) films formed by common vacuum filtration of the same starting material, and having the same transmittance.

Dispersing carbon nanotubes by chiral network surfactants

Chiral network surfactants (CNSs) possessing miscibility with carbon nanotubes (CNTs) and chiral materials are applied to disperse CNTs. Ultraviolet-visible absorption spectroscopy is used to quantitatively determine the CNT concentration in homogeneous CNT-CNS dispersions, results indicate that CNSs with more mole fraction of polycyclic conjugated structure have better ability to load and disperse CNTs and the maximal concentration reaches 0.79 mg mL(-1). Fourier transform infrared imaging system is utilized to analyze the dispersibility of CNTs in CNT-CNS composites, and CNS with 6 mol % nonmesogens (S6) induces the best dispersibility. The CNT doped CNSs exhibit lower glass transition temperature, strengthened thermal stability, decreased the thermochromic temperature and enriched reflected colors of CNSs. Furthermore, S6 are used as a promoter to disperse CNTs in chiral host, here, a left-handed chiral liquid crystal (CLC) is selected, the miscibility between CNTs and CLCs is studied by polarized optical microscope, and CNTs can be effectively dispersed in CLCs by S6. The CNT dispersed CLCs can exhibit a faster electro-optical response process than neat CLCs.

Polydispersed rods on the square lattice

We study the grand-canonical solution of a system of hard polydispersed rods placed on the square lattice using transfer matrix and finite-size scaling calculations. We determine the critical line separating an isotropic from a nematic phase. No second transition to a disordered phase is found at high density, contrary to what is observed in the monodispersed case. The estimates of critical exponents and the central charge on the critical line are consistent with the Ising universality class.

Nematic ordering of SWNT in meso-structured thin liquid films of polystyrenesulfonate

The formation of nematic-like islands of single-walled carbon nanotubes (SWNT) in polystyrenesulfonate (PSS) dispersions confined into nanometrically thin films is reported. The SWNT are observed to assemble into orientationally ordered phases, where the intertube distance, as measured via transmission electron microscopy at cryogenic temperatures, matches the polyelectrolyte's bulk correlation length deduced from X-ray scattering. The micrometers-long islands of orientationally ordered carbon nanotubes are observed in both SWNT and double-walled carbon nanotubes (DWNT) but not in specimens prepared from similar dispersions of multiwalled carbon nanotubes (MWNT). These observations, together with relaxation and rheological experiments, suggest that the orientational ordering may result from coupling between confinement of the polymer-wrapped SWNT and DWNT and the microstructure of the solvated polyelectrolyte.

Phase transitions in a system of hard rectangles on the square lattice

The phase diagram of a system of monodispersed hard rectangles of size m × mk on a square lattice is numerically determined for m = 2,3 and aspect ratio k = 1,2,...,7. We show the existence of a disordered phase, a nematic phase with orientational order, a columnar phase with orientational and partial translational order, and a solidlike phase with sublattice order, but no orientational order. The asymptotic behavior of the phase boundaries for large k is determined using a combination of entropic arguments and a Bethe approximation. This allows us to generalize the phase diagram to larger m and k, showing that for k ≥ 7, the system undergoes three entropy-driven phase transitions with increasing density. The nature of the different phase transitions is established and the critical exponents for the continuous transitions are determined using finite size scaling.

Alignment of nematic and bundled semiflexible polymers in cell-sized confinement

The finite size of cells poses severe spatial constraints on the network of semiflexible filaments called the cytoskeleton, a main determinant of cell shape. At the same time, the high packing density of cytoskeletal filaments poses mutual packing constraints. Here we investigate the competition between excluded volume interactions in the bulk and surface packing constraints on the orientational ordering of confined actin filaments as a function of filament density and the presence of crosslinks. We grow fluorescently labeled actin filaments in shallow (thickness dz 3 μm), rectangular microchambers with a systematically varied length (dy between 5 and 100 μm) and in-plane aspect ratio (dx/dy between 1 and 10). We determine the nematic director field by image analysis of fluorescence confocal images. We find that high-density (nematic) solutions respond sensitively to changes in the size and aspect ratio of the chambers. In small chambers (dy ≤ 20 μm), filaments align parallel to the long walls as soon as the aspect ratio is ≥1.5, indicating that surface-induced ordering dominates. In larger chambers, the filaments instead align along the chamber diagonal, indicating that bulk packing constraints dominate. The nematic order parameter is maximal in small and highly anisometric chambers. In contrast to the nematic solutions, low-density (isotropic) solutions are rather insensitive to confinement. Bundled actin solutions behave similarly to nematic solutions, but are less well-ordered. Our observations imply that the orientational order of actin filaments in flat confining geometries is primarily determined by a balance between bulk and surface packing constraints with a minimal effect of the enthalpic cost of filament bending. Our assay provides an interesting platform for the future reconstitution of more complex, active cytoskeletal systems with actively treadmilling filaments or molecular motors.

Rheology of polymer carbon nanotubes composites

In this review paper the rheology of polymer nanocomposites with dispersed carbon nanotubes is presented. The major factors controlling the rheology of these nanocomposites are the overall concentration of the nanotubes and their state of dispersion. Percolation of anisotropic nanotubes and the transition from isotropic to nematic structures bound the range of concentrations over which the rheological properties of these nanocomposites is dominated by the meso-scale structure and dispersion and are of significance to the processing of nanotube based polymer nanocomposites. The percolation threshold and the concentration for the isotropic to nematic transition are strong functions of the inverse of the effective aspect ratio of the dispersed nanotubes and therefore restrict the range of concentrations over which such nanocomposites can be deployed. In this review we briefly describe the rheology in the dilute regime, where especially for the case of polymer nanocomposites the rheology is dominated by that of the polymer. Subsequently, the percolation phenomenon and rheological significances are presented. Finally, both linear and non-linear rheologies of semi-dilute dispersions with random orientation of nanotubes are discussed in detail. Where possible, the rheological responses are contextualized through the underlying structure of the nanocomposites and interplay of different forces.

Aligned SWNT films from low-yield stress gels and their transparent electrode performance

Carbon nanotube films are promising for transparent electrodes for solar cells and displays. Large-area alignment of the nanotubes in these films is needed to minimize the sheet resistance. We present a novel coating method to coat high-density, aligned nanotubes over large areas. Carbon nanotube gel dispersions used in this study have aligned domains and a low yield stress. A simple shearing force allows these domains to uniformly align. We use this to correlate the transparent electrode performance of single-walled carbon nanotube films with the level of partial alignment. We have found that the transparent electrode performance improves with increasing levels of alignment and in a manner slightly better than what has been previously predicted.

Liquid crystals of carbon nanotubes and graphene

Liquid crystal ordering is an opportunity to develop novel materials and applications with spontaneously aligned nanotubes or graphene particles. Nevertheless, achieving high orientational order parameter and large monodomains remains a challenge. In addition, our restricted knowledge of the structure of the currently available materials is a limitation for fundamental studies and future applications. This paper presents recent methodologies that have been developed to achieve large monodomains of nematic liquid crystals. These allow quantification and increase of their order parameters. Nematic ordering provides an efficient way to prepare conductive films that exhibit anisotropic properties. In particular, it is shown how the electrical conductivity anisotropy increases with the order parameter of the nematic liquid crystal. The order parameter can be tuned by controlling the length and entanglement of the nanotubes. In the second part of the paper, recent results on graphene liquid crystals are reported. The possibility to obtain water-based liquid crystals stabilized by surfactant molecules is demonstrated. Structural and thermodynamic characterizations provide indirect but statistical information on the dimensions of the graphene flakes. From a general point of view, this work presents experimental approaches to optimize the use of nanocarbons as liquid crystals and provides new methodologies for the still challenging characterization of such materials.

Bundling dynamics regulates the active mechanics and transport in carbon nanotube networks and their nanocomposites

High-density carbon nanotube networks (CNNs) continue to attract interest as active elements in nanoelectronic devices, nanoelectromechanical systems (NEMS) and multifunctional nanocomposites. The interplay between the network nanostructure and its properties is crucial, yet current understanding remains limited to the passive response. Here, we employ a novel superstructure consisting of millimeter-long vertically aligned single walled carbon nanotubes (SWCNTs) sandwiched between polydimethylsiloxane (PDMS) layers to quantify the effect of two classes of mechanical stimuli, film densification and stretching, on the electronic and thermal transport across the network. The network deforms easily with an increase in the electrical and thermal conductivities, suggestive of a floppy yet highly reconfigurable network. Insight from atomistically informed coarse-grained simulations uncover an interplay between the extent of lateral assembly of the bundles, modulated by surface zipping/unzipping, and the elastic energy associated with the bent conformations of the nanotubes/bundles. During densification, the network becomes highly interconnected yet we observe a modest increase in bundling primarily due to the reduced spacing between the SWCNTs. The stretching, on the other hand, is characterized by an initial debundling regime as the strain accommodation occurs via unzipping of the branched interconnects, followed by rapid rebundling as the strain transfers to the increasingly aligned bundles. In both cases, the increase in the electrical and thermal conductivity is primarily due to the increase in bundle size; the changes in network connectivity have a minor effect on the transport. Our results have broad implications for filamentous networks of inorganic nanoassemblies composed of interacting tubes, wires and ribbons/belts.

Volume phase transitions of biaxial nematic elastomers

We present a mean-field theory to describe biaxial nematic phases of side-chain liquid crystalline elastomers. Novel biaxial nematic phases are theoretically predicted in a side-chain liquid crystalline polymer and gel, where side chains (mesogens) and rigid-backbone chains favor mutually perpendicular orientations. We calculate uniaxial and biaxial orientational order parameters and examine deformations of the gel and stable biaxial nematic phases of the liquid crystalline gel dissolved in isotropic solvents. We predict first-order uniaxial-biaxial nematic phase transitions of the gel and the volume of the gel is discontinuously changed at the phase transition temperature.

Conductivity anisotropy of assembled and oriented carbon nanotubes

An assembly of packed and oriented rodlike particles exhibit anisotropic physical properties. We investigate in the present work the anisotropic conductivity of films made of intrinsically conducting rods. These films are obtained from more or less ordered carbon nanotube liquid crystals. Their orientational order parameter is measured by polarized Raman spectroscopy. A relationship between the anisotropy of surface conductivity and orientational order parameter is determined. The experimental results are accounted for by a model that takes into account the number of intertube contacts and density of conductive pathways in different directions, as introduced by J. Fischer et al. for magnetically aligned nanotubes. We find that a good agreement, without any fitting parameter, of the proposed model and experiments is obtained when we consider a two-dimensional (2D) Gaussian distribution of the nanotube orientation. The conductivities parallel and perpendicular to the nematic director differ by almost an order of magnitude. This anisotropy is much greater than that of conventional dielectric liquid crystals, where the behavior is governed by the mobility anisotropy of ionic current carriers. The present results do not depend on the intrinsic properties of the nanotubes and are expected to be relevant for other assemblies of conducting rodlike particles, such as metallic or semi-conducting nanowires and ribbons.

Cholesteric and nematic liquid crystalline phase behavior of double-stranded DNA stabilized single-walled carbon nanotube dispersions

The first lyotropic cholesteric single-walled carbon nanotube (SWNT) liquid crystal phase was obtained by dispersing SWNTs in an aqueous solution of double-stranded DNA (dsDNA). Depending on the dispersion methodology, the polydomain nematic phase previously reported for other lyotropic carbon nanotube dispersions could also be obtained. The phase behavior and dispersion microstructure were affected by the relative concentrations of dsDNA and SWNT and whether small bundles were removed prior to concentrating the dispersions. This readily controlled phase behavior opens new routes for producing SWNT films with controlled morphology.

Interactions Between Carbon Nanotubes and Liquid Crystals in Binary Nematic Electro-Optic Cells

We studied the effects of multiwalled carbon nanotubes (MWCNTs) on the Freedericksz transition of a liquid crystal (LC) and calibrated the altitudinal angle of CNTs as a function of the electric field. In addition, we directed the azimuthal angle which gave us complete control of the 3D orientation of the CNTs. We constructed anti-parallel electro-optic cells using a nanocomposite at a concentration of 0.01% CNTs with 4-Cyano-4'-pentylbiphenyl (5CB) liquid crystal. This low concentration was necessary to achieve maximum transmission of electromagnetic radiation through the cell and to minimize the Van der Waals attraction between the CNTs responsible for their aggregation. We chose two dimensional microscopic transmission ellipsometry (2D-MTE) to measure the phaseshift of the polarized electromagnetic radiation through the cell and to derive from it the altitudinal angle of the CNTs. Our results show that in the presence of CNTs the Freedericksz transition occurs at 55% of the transitional electric field as compared to the control electro-optic cell without CNTs. The width of the Freedericksz transition narrows by a similar factor. The switching time of the cell decreased in the presence CNTs by 18.5%.

Topological transitions in carbon nanotube networks via nanoscale confinement

Efforts aimed at large-scale integration of nanoelectronic devices that exploit the superior electronic and mechanical properties of single-walled carbon nanotubes (SWCNTs) remain limited by the difficulties associated with manipulation and packaging of individual SWNTs. Alternative approaches based on ultrathin carbon nanotube networks (CNNs) have enjoyed success of late with the realization of several scalable device applications. However, precise control over the network electronic transport is challenging due to (i) an often uncontrollable interplay between network coverage and its detailed topology and (ii) the inherent electrical heterogeneity of the constituent SWNTs. In this article, we use template-assisted fluidic assembly of SWCNT networks to explore the effect of geometric confinement on the network topology. Heterogeneous SWCNT networks dip-coated onto submicrometer wide ultrathin polymer channels become increasingly aligned with decreasing channel width and thickness. Experimental-scale coarse-grained computations of interacting SWCNTs show that the effect is a reflection of a topology that is no longer dependent on the network density, which in turn emerges as a robust knob that can induce semiconductor-to-metallic transitions in the network response. Our study demonstrates the effectiveness of directed assembly on channels with varying degrees of confinement as a simple tool to tailor the conductance of the otherwise heterogeneous network, opening up the possibility of robust large-scale CNN-based devices.

Thermally switchable one- and two-dimensional arrays of single-walled carbon nanotubes in a polymeric system

Fabrication of highly ordered arrays of single-walled carbon nanotubes (SWNTs) has been of great interest for a wide range of potential applications. Here, we report thermally switchable one- and two-dimensional arrays of individually isolated SWNTs formed by cooperative self-assembly of functionalized SWNTs and a block copolymer/water system. Small-angle X-ray scattering measurements reveal that when the block copolymer/water system is in an isotropic phase, two-dimensional hexagonal arrays of SWNTs are formed by depletion attraction, and when the block copolymer/water system is in a lamellar phase, one-dimensional lattices of SWNTs intercalated in the polar regions of the polymeric lamellar structure are formed by entropically driven segregation and two-dimensional depletion attraction. These two SWNT arrays are thermally interchangeable, following the temperature-dependent phase behavior of the block copolymer/water system.

True solutions of single-walled carbon nanotubes for assembly into macroscopic materials

Translating the unique characteristics of individual single-walled carbon nanotubes into macroscopic materials such as fibres and sheets has been hindered by ineffective assembly. Fluid-phase assembly is particularly attractive, but the ability to dissolve nanotubes in solvents has eluded researchers for over a decade. Here, we show that single-walled nanotubes form true thermodynamic solutions in superacids, and report the full phase diagram, allowing the rational design of fluid-phase assembly processes. Single-walled nanotubes dissolve spontaneously in chlorosulphonic acid at weight concentrations of up to 0.5 wt%, 1,000 times higher than previously reported in other acids. At higher concentrations, they form liquid-crystal phases that can be readily processed into fibres and sheets of controlled morphology. These results lay the foundation for bottom-up assembly of nanotubes and nanorods into functional materials.

Alignment of tellurium nanorods via a magnetization-alignment-demagnetization ("MAD") process assisted by an external magnetic field

Tellurium (Te) nanorods have been successfully aligned on a solid substrate via a magnetization-alignment-demagnetization ("MAD") process in the presence of an external magnetic field. Te nanorods carrying a poly(tert-butyl methacrylate) shell were first converted into magnetic nanocylinders by assembling magnetite nanoparticles on their surface via a hydrophobic interaction in THF. We demonstrate that, below a critical concentration of the nanoparticles, this assembly process is able to quantitatively tune the magnetite nanoparticles' density on the nanorods in terms of their stoichiometric ratio. Due to the polymer and surfactant on their surface, the formed magnetic nanocylinders are soluble in THF and aligned when dried on a solid substrate in the presence of an external magnetic field. The demagnetization of the prealigned nanocylinders was achieved via an acid-etching process, leaving Te nanorods in an aligned state. This MAD process can be extended as a general procedure for other nonmagnetic 1-D nanostructures. Additionally, the nonetched magnetic nanocylinders can be potentially applied in field of magnetorheology.

Anisotropic thin films of single-wall carbon nanotubes from aligned lyotropic nematic suspensions

Lyotropic nematic aqueous suspensions of single-wall carbon nanotubes can be uniformly aligned in thin cells by shearing. Homogeneous anisotropic thin films of nanotubes can be prepared by drying the nematic. Optical transmission between parallel or crossed polarizers is measured and described in order to estimate the dichroic ratio. The order parameter is measured using polarized Raman spectroscopy and found to be quite weak due to entanglement of the nanotubes and/or to an intrinsic viscoelastic behavior of the nanotube suspensions.

Carbon nanotubes as liquid crystals

Carbon nanotubes are the best of known materials with a combination of excellent mechanical, electronic, and thermal properties. To fully exploit individual nanotube properties for various applications, the grand challenge is to fabricate macroscopic ordered nanotube assemblies. Liquid-crystalline behavior of the nanotubes provides a unique opportunity toward reaching this challenge. In this Review, the recent developments in this area are critically reviewed by discussing the strategies for fabricating liquid-crystalline phases, addressing the solution properties of liquid-crystalline suspensions, and exploiting the practical techniques of liquid-crystal routes to prepare macroscopic nanotube fibers and films.

Defects in nematic membranes can buckle into pseudospheres

Many factors influence the shapes of living and manufactured membranes. In addition to boundary conditions, surface tension, and curvature, the ordering of particles embedded in or attached to a membrane can strongly influence its equilibrium shape. As a simple model of such ordering, we consider rodlike particles that align to form a so-called nematic phase in the plane of the membrane. We call any sheet with such embedded orientational order a nematic membrane. Nematic membranes can occur in biological cells, liquid crystal films, manufactured materials, and other soft matter systems. By formulating the free energy of nematic films using tensor contractions from differential geometry, we elucidate the elastic terms allowed by symmetry, and indicate differences from hexatic membranes. We find that topological defects in the orientation field can cause the membrane to buckle over a size set by the competition between surface tension and in-plane elasticity. In the absence of bending rigidity the resulting shape is universal, known as a parabolic pseudosphere or a revolved tractrix. This buckling is the two-dimensional analog of the bent cores of line defects that are frequently observed in bulk nematic liquid crystals. Bending costs oppose such buckling and modify the shape in a predictable manner. In particular, the anisotropic rigidities of nematic membranes lead to different shapes for aster and vortex defects, in principle enabling measurement of couplings specific to nematic membranes.

The influence of the carbon nanotube on the structural and dynamical properties of cholesterol cluster

We have performed the molecular dynamics simulations for the free cholesterol cluster and the same cluster located near the carbon nanotube. We have found that the cholesterol molecules quite evenly cover the surface of single walled armchair (10, 10) carbon nanotube, forming the molecular layer. Moreover, the characteristic alignment of cholesterol molecules within the layer (along the nanotube) is observed. The comparison of the structural and dynamical observable characterizing cholesterol molecule is presented and discussed, both for the cluster with and without the presence of the nanotube.

Orientational correlations and the effect of spatial gradients in the equilibrium steady state of hard rods in two dimensions: a study using deposition-evaporation kinetics

Deposition and evaporation of infinitely thin hard rods (needles) is studied in two dimensions using Monte Carlo simulations. The ratio of deposition to evaporation rates controls the equilibrium density of rods, and increasing it leads to an entropy-driven transition to a nematic phase in which both static and dynamical orientational correlation functions decay as power laws, with exponents varying continuously with deposition-evaporation rate ratio. Our results for the onset of the power-law phase agree with those for a conserved number of rods. At a coarse-grained level, the dynamics of the nonconserved angle field is described by the Edwards-Wilkinson equation. Predicted relations between the exponents of the quadrupolar and octupolar correlation functions are borne out by our numerical results. We explore the effects of spatial inhomogeneity in the deposition-evaporation ratio by simulations, entropy-based arguments, and a study of the additional terms introduced in the free energy. The primary effect is that needles tend to align along the local spatial gradient of the ratio. A uniform gradient thus induces a uniformly aligned state, as does a gradient which varies randomly in magnitude and sign, but acts only in one direction. Random variations of deposition-evaporation rates in both directions induce frustration, resulting in a state with glassy characteristics.

Cracks and topological defects in lyotropic nematic gels

We report on the effects of the coupling of nematic order and elasticity in anisotropic lyotropic gels consisting of large nematic domains of surfactant coated single wall carbon nanotubes embedded in a cross-linked N-isopropyl acrylamide polymer matrix. We observe the following striking features: (i) undulations and then cusping of the gel sidewalls, (ii) a nematic director field that evolves as the gel sidewalls deform, (iii) networks of surface cracks that are orthogonal to the nematic director field, and (iv) fissures at the sidewall cusps and associated topological defects that would not form in liquid nematics.

Anisotropy of sheared carbon-nanotube suspensions

We measure the anisotropy of sheared carbon-nanotube suspensions for a broad range of concentration, aspect ratio, and strain rate using a variety of methods. Our measurements highlight the importance of excluded-volume interactions in the semidilute regime, with scaling in terms of a dimensionless shear rate. Our results also suggest that such interactions might be exploited to fractionate carbon nanotubes by length in simple shear flow.

Photomechanical actuation in polymer-nanotube composites

For some systems, energy from an external source can trigger changes in the internal state of the structure, leading to a mechanical response much larger than the initial input. The ability to unlock this internal work in a solid-state structure is of key importance for many potential applications. We report a novel phenomenon of photo-induced mechanical actuation observed in a polymer-nanotube composite when exposed to infrared radiation. At small strains the sample tends to expand, when stimulated by photons, by an amount that is orders of magnitude greater than the pristine polymer. Conversely, at larger applied pre-strain, it will contract under identical infrared excitation. The behaviour is modelled as a function of orientational ordering of nanotubes induced by the uniaxial extension. It is thought that no other materials can display this continuously reversible response of so large a magnitude, making rubber nanocomposites important for actuator applications.

Viscoelasticity of single wall carbon nanotube suspensions

We investigate the viscoelastic properties of an associating rigid rod network: aqueous suspensions of surfactant stabilized single wall carbon nanotubes (SWNTs). The SWNT suspensions exhibit a rigidity percolation transition with an onset of solidlike elasticity at a volume fraction of 0.0026; the percolation exponent is 2.3+/-0.1. At large strain, the solidlike samples show volume fraction dependent yielding. We develop a simple model to understand these rheological responses and show that the shear dependent stresses can be scaled onto a single master curve to obtain an internanotube interaction energy per bond approximately 40k(B)T. Our experimental observations suggest SWNTs in suspension form interconnected networks with bonds that freely rotate and resist stretching. Suspension elasticity originates from bonds between SWNTs rather than from the stiffness or stretching of individual SWNTs.

Direct measurement of the polarized optical absorption cross section of single-wall carbon nanotubes

We determine optical absorption cross sections of single-wall carbon nanotubes for visible light copolarized and cross polarized with respect to the nanotube axis. The need for perfectly aligned ensembles in absorbance measurements is eliminated by using Raman scattering to measure the nematic order parameter in magnetically aligned nanotube suspensions. The absorbance data allow the first quantitative, spectral comparisons with theories of local field depolarization, and provide benchmark spectra for simple, rapid, and quantitative measurements of alignment within nanotube dispersions.