Elucidating chirality transfer in liquid crystals of viruses.

Chirality is ubiquitous in nature across all length scales, with major implications spanning fields from biology, chemistry and physics to materials science. How chirality propagates from nanoscale building blocks to meso- and macroscopic helical structures remains an open issue. Here, working with a canonical system of filamentous viruses, we demonstrate that their self-assembly into chiral liquid crystal phases quantitatively results from the interplay between two main mechanisms of chirality transfer: electrostatic interactions from the helical charge patterns on the virus surface, and fluctuation-based helical deformations leading to viral backbone helicity. Our experimental and theoretical approach provides a comprehensive framework for deciphering how chirality is hierarchically and quantitatively propagated across spatial scales. Our work highlights the ways in which supramolecular helicity may arise from subtle chiral contributions of opposite handedness that act either cooperatively or competitively, thus accounting for the multiplicity of chiral behaviours observed for nearly identical molecular systems.

M13-Phage-Based Star-Shaped Particles with Internal Flexibility.

We report on the construction and the dynamics of monodisperse star-shaped particles, mimicking, at the mesoscale, star polymers. Such multiarm star-like particles result from the self-assembly of gold nanoparticles, forming the core, with tip-linked filamentous viruses (M13 bacteriophages) acting as spines in a sea urchin-like structure. By combining fluorescence and dark-field microscopy with dynamic light scattering, we investigate the diffusion of these hybrid spiny particles. We reveal the internal dynamics of the star particles by probing their central metallic core, which exhibits a hindered motion that can be described as a Brownian particle trapped in a harmonic potential. We therefore show that the filamentous viruses and specifically their tip proteins behave as entropic springs, extending the relevance of the study of such hybrid mesoscopic analogues of star polymers to phage biotechnology.

When bigger is faster: A self-Van Hove analysis of the enhanced self-diffusion of non-commensurate guest particles in smectics.

We investigate the anomalous dynamics in smectic phases of short host rods where, counter-intuitively, long guest rod-shaped particles diffuse faster than the short host ones due to their precise size mismatch. In addition to the previously reported mean-square displacement, we analyze the time evolution of the self-Van Hove functions G(r, t), as this probability density function uncovers intrinsic heterogeneous dynamics. Through this analysis, we show that the dynamics of the host particles parallel to the director becomes non-Gaussian and therefore heterogeneous after the nematic-to-smectic-A phase transition, even though it exhibits a nearly diffusive behavior according to its mean-squared displacement. In contrast, the non-commensurate guest particles display Gaussian dynamics of the parallel motion, up to the transition to the smectic-B phase. Thus, we show that the self-Van Hove function is a very sensitive probe to account for the instantaneous and heterogeneous dynamics of our system and should be more widely considered as a quantitative and complementary approach of the classical mean-squared displacement characterization in diffusion processes.

Phase behavior of hard cylinders.

Using isobaric Monte Carlo simulations, we map out the entire phase diagram of a system of hard cylindrical particles of length (L) and diameter (D) using an improved algorithm to identify the overlap condition between two cylinders. Both the prolate L/D > 1 and the oblate L/D < 1 phase diagrams are reported with no solution of continuity. In the prolate L/D > 1 case, we find intermediate nematic N and smectic SmA phases in addition to a low density isotropic I and a high density crystal X phase with I-N-SmA and I-SmA-X triple points. An apparent columnar phase C is shown to be metastable, as in the case of spherocylinders. In the oblate L/D < 1 case, we find stable intermediate cubatic (Cub), nematic (N), and columnar (C) phases with I-N-Cub, N-Cub-C, and I-Cub-C triple points. Comparison with previous numerical and analytical studies is discussed. The present study, accounting for the explicit cylindrical shape, paves the way to more sophisticated models with important biological applications, such as viruses and nucleosomes.

Speeding up Dynamics by Tuning the Noncommensurate Size of Rodlike Particles in a Smectic Phase.

Using simulations, we study the diffusion of rodlike guest particles in a smectic environment of rodlike host particles. We find that the dynamics of guest rods across smectic layers changes from a fast nematiclike diffusion to a slow hopping-type dynamics via an intermediate switching regime by varying the length of the guest rods with respect to the smectic layer spacing. We determine the optimal rod length that yields the fastest and the slowest diffusion in a lamellar environment. We show that this behavior can be rationalized by a complex 1D effective periodic potential exhibiting two energy barriers, resulting in a varying preferred mean position of the guest particle in the smectic layer. The interplay of these two barriers controls the dynamics of the guest particles yielding a slow, an intermediate, and a fast diffusion regime depending on the particle length.

Depletion-driven morphological transitions in hexagonal crystallites of virus rods.

The assembly of nanometer-sized building blocks into complex morphologies is not only of fundamental interest but also plays a key role in material science and nanotechnology. We show that the shape of self-assembled superstructures formed by rod-like viruses can be controlled by tuning the attraction via the depletion interaction between the rods. Using non-adsorbing polymers as a depleting agent, we demonstrate that a hierarchical unidimensional self-organization into crystalline clusters emerges progressively upon increasing depletion attraction and enhanced growth kinetics. We observe a polymorphic change proceeding from two-dimensional (2D) crystalline monolayers at weak depletion to one-dimensional (1D) columnar fibers at strong depletion, via the formation of smectic fibrils at intermediate depletion strength. A simple theory for reversible polymerization enables us to determine the typical bond energy between monomeric units making up the smectic fibrils. We also demonstrate that gentle flow-assistance can be used to template filament-like structures into highly aligned supported films. Our results showcase a generic bottom-up approach for tuning the morphology of crystalline superstructures through modification of the interaction between non-spherical building blocks. This provides a convenient pathway for controlling self-organization, dimensionality and structure-formation of anisotropic nanoparticles for use in nanotechnology and functional materials.

Directing Liquid Crystalline Self-Organization of Rodlike Particles through Tunable Attractive Single Tips.

Dispersions of rodlike colloidal particles exhibit a plethora of liquid crystalline states, including nematic, smectic A, smectic B, and columnar phases. This phase behavior can be explained by presuming the predominance of hard-core volume exclusion between the particles. We show here how the self-organization of rodlike colloids can be controlled by introducing a weak and highly localized directional attractive interaction between one of the ends of the particles. This has been performed by functionalizing the tips of filamentous viruses by means of regioselectively grafting fluorescent dyes onto them, resulting in a hydrophobic patch whose attraction can be tuned by varying the number of bound dye molecules. We show, in agreement with our computer simulations, that increasing the single tip attraction stabilizes the smectic phase at the expense of the nematic phase, leaving all other liquid crystalline phases invariant. For a sufficiently strong tip attraction, the nematic state may be suppressed completely to get a direct isotropic liquid-to-smectic phase transition. Our findings provide insights into the rational design of building blocks for functional structures formed at low densities.

Elementary Edge and Screw Dislocations Visualized at the Lattice Periodicity Level in the Smectic Phase of Colloidal Rods.

Topological defects such as dislocations play a major role in science, from condensed matter and geophysics to cosmology. These line defects present in periodically ordered structures mediate phase transitions and determine many distinctive features of materials, from crystal growth to mechanical properties. However, despite theoretical predictions, the detailed structure of dislocations remains largely elusive. By using a model system of tip-labeled rod-shaped particles enabling improved resolution and contrast by optical microscopy, in situ visualization and quantitative characterization of elementary dislocations has been performed at the lattice periodicity level in a colloidal smectic phase. Thanks to the micrometer layer spacing, the displacement field around an edge dislocation has been experimentally established and compared with the profile predicted by elastic theory. The local morphology of screw dislocations has also been evidenced, with the determination of the core size as well as the chiral handedness of the defect. Self-diffusion experiments performed at the individual particle level reveal for the first time nematiclike or "melted" ordering of the defect core.

Chirality-controlled crystallization via screw dislocations.

Chirality plays an important role in science from enantiomeric separation in chemistry to chiral plasmonics in nanotechnology. However, the understanding of chirality amplification from chiral building blocks to ordered helical superstructures remains a challenge. Here, we demonstrate that topological defects, such as screw dislocations, can drive the chirality transfer from particle to supramolecular structure level during the crystallization process. By using a model system of chiral particles, which enables direct imaging of single particle incorporation into growing crystals, we show that the crystallization kinetic pathway is the key parameter for monitoring, via the defects, the chirality amplification of the crystalline structures from racemic to predominantly homohelical. We provide an explanation based on the interplay between geometrical frustration, racemization induced by thermal fluctuations, and particle chirality. Our results demonstrate that screw dislocations not only promote the growth, but also control the chiral morphology and therefore the functionality of crystalline states.

Rod-Like Virus-Based Multiarm Colloidal Molecules.

We report on the construction of multiarm colloidal molecules by tip-linking filamentous bacteriophages, functionalized either by biological engineering or chemical conjugation. The affinity for streptavidin of a genetically modified vector phage displaying Strep-tags fused to one end of the viral particle is measured by determining the dissociation constant, Kd. In order to improve both the colloidal stability and the efficiency of the self-assembly process, a biotinylation protocol having a chemical yield higher than 90% is presented to regioselectively functionalize the cystein residues located at one end of the bacteriophages. For both viral systems, a theoretical comparison is performed by developing a quantitative model of the self-assembly and interaction of the modified viruses with streptavidin compounds, which accurately accounts for our experimental results. Multiarm colloidal structures of different valencies are then produced by conjugation of these tip-functionalized viruses with streptavidin activated nanoparticles. We succeed to form stable virus-based colloidal molecules, whose number of arms, called valency, is solely controlled by tuning the molar excess. Thanks to a fluorescent labeling of the viral arms, the dynamics of such systems is also presented in real time by fluorescence microscopy.

Fast Diffusion of Long Guest Rods in a Lamellar Phase of Short Host Particles.

We investigate the dynamic behavior of long guest rodlike particles immersed in liquid crystalline phases formed by shorter host rods, tracking both guest and host particles by fluorescence microscopy. Counterintuitively, we evidence that long rods diffuse faster than short rods forming the one-dimensional ordered smectic-A phase. This results from the larger and noncommensurate size of the guest particles as compared to the wavelength of the energy landscape set by the lamellar stack of liquid slabs. The long guest particles are also shown to be still mobile in the crystalline smectic-B phase, as they generate their own voids in the adjacent layers.

Scaffolding of Enzymes on Virus Nanoarrays: Effects of Confinement and Virus Organization on Biocatalysis.

Organizing active enzyme molecules on nanometer-sized scaffolds is a promising strategy for designing highly efficient supported catalytic systems for biosynthetic and sensing applications. This is achieved by designing model nanoscale enzymatic platforms followed by thorough analysis of the catalytic activity. Herein, the virus fd bacteriophage is considered as an enzyme nanocarrier to study the scaffolding effects on enzymatic activity. Nanoarrays of randomly oriented, or directionally patterned, fd bacteriophage virus are functionalized with the enzyme glucose oxidase (GOx), using an immunological assembly strategy, directly on a gold electrode support. The scaffolding process on the virus capsid is monitored in situ by AFM (atomic force microscopy) imaging, while cyclic voltammetry is used to interrogate the catalytic activity of the resulting functional GOx-fd nanoarrays. Kinetic analysis reveals the ability to modulate the activity of GOx via nanocarrier patterning. The results evidence, for the first time, enhancement of the enzymatic activity due to scaffolding on a filamentous viral particle.

From soft to hard rod behavior in liquid crystalline suspensions of sterically stabilized colloidal filamentous particles.

The liquid crystalline phase behavior of a colloidal system of sterically stabilized rods is reported. Our colloidal suspensions consist of highly monodisperse, semi-flexible filamentous viruses which have been coated with neutral hydrophilic polymers by irreversibly binding poly(ethylene glycol) (PEG) to the surface of the virus particles. Depending on the size of the grafted polymer, up to three different phase transitions are observed (isotropic-to-chiral nematic, chiral nematic-to-smectic, and smectic-to-columnar). Each phase transition is shown to be independent of ionic strength, confirming the steric stabilization of the viral colloids. A direct, i.e. without any free parameters, comparison with theory and computer simulations of the volume fraction associated with the phase transition can be performed, showing a quantitative agreement with hard rod behavior at a low polymer chain size, and some deviation stemming from soft repulsion by increasing the polymer thickness coating of the rod. Specifically, we demonstrate that the columnar mesophase is not stabilized by electrostatic repulsion, and we discuss the conditions of its existence.

Electric field induced birefringence in non-aqueous dispersions of mineral nanorods.

Lanthanum phosphate (LaPO4) nanorods dispersed in the non-aqueous solvent of ethylene glycol form a system exhibiting large intrinsic birefringence, high colloidal stability and the ability to self-organize into liquid crystalline phases. In order to probe the electro-optical response of these rod dispersions we study here the electric-field-induced birefringence, also called Kerr effect, for a concentrated isotropic liquid state with an in-plane a.c. sinusoidal electric field, in conditions of directly applied (electrodes in contact with the sample) or externally applied (electrodes outside the sample cell) fields. Performing an analysis of the electric polarizability of our rod-like particles in the framework of Maxwell-Wagner-O'Konski theory, we account quantitatively for the coupling between the induced steady-state birefringence and the electric field as a function of the voltage frequency for both sample geometries. The switching time of this non-aqueous transparent system has been measured, and combined with its high Kerr coefficients and its features of optically isotropic "off-state" and athermal phase behavior, this represents a promising proof-of-concept for the integration of anisotropic nanoparticle suspensions into a new generation of electro-optical devices.

X-ray scattering in the vorticity direction and rheometry from confined fluids.

An X-ray flexure-based microgap rheometer (X-FMR) has been designed for combining rheology and in situ small-angle X-ray scattering from the vorticity plane. The gap distance can be varied continuously from 500 µm down to several µm, which provides the unique possibility to generate a strong confinement for many complex fluids. A singular advantage of this setup is the possibility to directly probe the vorticity direction of the flow field with a microfocus X-ray beam and to probe the structural response of the fluid to combined shear and confinement in the vorticity plane. The sliding-plate setup operates over a wide range of shear rates of γ = 10(-3)-10(3) s(-1) and strains in the range of 10(-4)-10(2). The flexure-based bearing maintains the plate parallelism within 10(-5) rad. The X-FMR requires very small sample volumes on the order of 10 µl. The applicability of the device is demonstrated here with limited examples of a nematic suspension of fd virus (rods), and a crystalline suspension containing sterically stabilized polystyrene-butylacrylate latex particles.

Thermotropic orientational order of discotic liquid crystals in nanochannels: an optical polarimetry study and a Landau-de Gennes analysis.

Optical polarimetry measurements of the orientational order of a discotic liquid crystal based on a pyrene derivative confined in parallelly aligned nanochannels of monolithic, mesoporous alumina, silica, and silicon as a function of temperature, channel radius (3-22 nm) and surface chemistry reveal a competition of radial and axial columnar orders. The evolution of the orientational order parameter of the confined systems is continuous, in contrast to the discontinuous transition in the bulk. For channel radii larger than 10 nm we suggest several, alternative defect structures, which are compatible both with the optical experiments on the collective molecular orientation presented here and with a translational, radial columnar order reported in previous diffraction studies. For smaller channel radii our observations can semi-quantitatively be described by a Landau-de Gennes model with a nematic shell of radially ordered columns (affected by elastic splay deformations) that coexists with an orientationally disordered, isotropic core. For these structures, the cylindrical phase boundaries are predicted to move from the channel walls to the channel centres upon cooling, and vice-versa upon heating, in accord with the pronounced cooling/heating hystereses observed and the scaling behavior of the transition temperatures with the channel diameter. The absence of experimental hints of a paranematic state is consistent with a biquadratic coupling of the splay deformations to the order parameter.

Fractional hoppinglike motion in columnar mesophases of semiflexible rodlike particles.

We report on single-particle dynamics of strongly interacting filamentous fd virus particles in the liquid-crystalline columnar state in aqueous solution. From fluorescence microscopy, we find that rare, discrete events take place, in which individual particles engage in sudden, jumplike motion along the main rod axis. The jump length distribution is bimodal and centered at half- and full-particle lengths. Our Brownian dynamics simulations of hard semiflexible particles mimic our experiments and indicate that full-length jumps must be due to collective dynamics in which particles move in stringlike fashion in and between neighboring columns, while half jumps arise as a result of particles moving into defects. We find that the finite domain structure of the columnar phase strongly influences the observed dynamics.

Dispersions of monodisperse hybrid rod-like particles by mineralization of filamentous viruses.

In this work, we report on the synthesis through a direct chemical approach of hybrid organic/inorganic rod-like particles with a very high aspect ratio (length/diameter) by the use of a biotemplate, the fd virus. A synthetic route is proposed based on an initial step of steric stabilization of the colloidal template by hydrophilic polymer grafting. Thanks to this polymer functionalization, the filamentous viruses are well-dispersed in solution during their mineralization by different inorganic salts, leading to suspensions of individual hybrid rod-like particles such as virus/SiO2 and virus/TiO2. This aqueous solution based approach is shown to be highly reproducible, scalable for large production synthesis, and versatile to different inorganic materials.

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.

Orientational order of carbon nanotube guests in a nematic host suspension of colloidal viral rods.

In order to investigate the coupling between the degrees of alignment of elongated particles in binary nematic dispersions, surfactant stabilized single-wall carbon nanotubes (CNTs) have been added to nematic suspensions of colloidal rodlike viruses in aqueous solution. We have independently measured the orientational order parameter of both components of the guest-host system by means of polarized Raman spectroscopy and by optical birefringence, respectively. Our system allows us therefore to probe the regime where the guest particles (CNTs) are shorter and thinner than the fd virus host particles. We show that the degree of order of the CNTs is systematically smaller than that of the fd virus particles for the whole nematic range. These measurements are in good agreement with predictions of an Onsager-type second-viral theory, which explicitly includes the flexibility of the virus particles, and the polydispersity of the CNTs.