Geometry of focal conics in sessile cholesteric droplets

Focal conic domains are defects characteristic of layered liquid crystal phases. Their association can build flowers where petals are the ellipses of the Dupin cyclides involved in these defects. We report here the observation of focal conic flowers in cholesteric droplets sessile on a glass surface and surrounded by glycerol. The observation of the droplets in different directions helps to solve the three dimensional architecture of the flower. The effects of the droplet size and of the pitch value are also reported.

High-pressure behavior of hydrophobically coated gold nanoparticle supercrystals: role of the structure

We report here an extensive high pressure small-angle X-ray scattering study on 3D supercrystals self-assembled from colloidal spherical gold crystalline nanoparticule (NPs). We used a large variety of NPs with different gold core diameter, from 2 to 10 nm, grafted with different ligands: alkane-thiols or oleylamine. The self assembly of these various NPs leads to supercrystals of different structures: face centered cubic (FCC), body centered cubic (BCC), as well as the C14 Frank and Kasper phase. Using a Diamond Anvil Cell to apply pressure on these wide range of samples, we provide a unique overview on the mechanical properties of gold NPs supercrystals. In particular, bulk modulii have been determined from low pressure regime and the different behavior between FCC and BCC structures has been interpreted as due to an easier restructuring of the ligand conformation in the FCC structure compared to the BCC structure. At higher pressure, a fingerprint of irreversible structural transition has been observed. We have ascribed this irreversibility to the sintering of nanoparticles and confirmed this interpretation by transmission electron microscopy.

Mechanics under pressure of gold nanoparticle supracrystals: the role of the soft matrix

We report on High Pressure Small Angle X-ray Scattering (HP-SAXS) measurements on 3D face-centered cubic (FCC) supracrystals (SCs) built from spherical gold nanoparticles (NPs). Dodecane-thiol ligands are grafted on the surface and ensure the stability of the gold NPs by forming a protective soft layer. Under a hydrostatic pressure of up to 12 GPa, the SC showed a high structural stability. The bulk elastic modulus of the SC was derived from the HP-SAXS measurements. The compression of the SC undergoes two stages: the first one related to the collapse of the voids between the NPs followed by the second one related to the compression of the soft matrix which gives a major contribution to the mechanical behavior. By comparing the bulk modulus of the SC to that of dodecane, the soft matrix appears to be less compressible than the crystalline dodecane. This effect is attributed to a less optimized chain packing under pressure compared to the free chains, as the chains are constrained by both grafting and confinement within the soft matrix. We conclude that these constraints on chain packing within the soft matrix enhance the stability of SCs under pressure.

The bulk modulus of 3D FCC supracrystals of spherical gold nanoparticles is determined using high pressure-SAXS measurements. The organic ligand shell is found to be less compressible than pure dodecane with the same chain length.

Precise size control of hydrophobic gold nanoparticles in the 2-5 nm range

We report a seed-mediated synthesis strategy to control the size of gold nanoparticles at the atomic scale in the 2-5 nm size range. Starting from 2 nm seeds, a regrowth in organic solvent with a designed amount of precursor can achieve in a predictive fashion a precise mean size with a 0.3 nm resolution. We show that these monodisperse nanoparticles assemble into a 2D hexagonal lattice over a distance that can span tens of micrometers.

Softness-driven complexity in supercrystals of gold nanoparticles

Many soft matter systems are composed of roughly spherical objects that can self-assemble in ordered structures. Unlike hard spheres, at high volume fraction these soft spheres adapt their shape to the local geometrical constraints and the question of space filling needs to be entirely revisited. Hydrophobically coated gold nanocrystals self-assemble in supercrystals and are good candidates to explore this question. When the soft coating is thin compared to the rigid core, a FCC structure is obtained, with a behaviour similar to that of hard spheres. In the opposite case, for a thick soft coating, a BCC structure is found instead. This paper focus on the intermediate region between these two classical structures. By varying the gold core radius R and the ligand fully extended length L, we establish a structure diagram based on a large experimental data set. The hexagonal Frank-Kasper C14 structure is observed for various values of R and L and can coexist with a FCC phase. Depending on the structure, values of the minimum thickness e of the ligand shell compared to L are different. These experimental results confirm that the C14 Frank-Kasper phase is a solution to the problem of filling the space with soft particles even with a rigid core and should help to establish pertinent models in order to predict the structures of the superlattices built by gold nanoparticles.

Grazing Incidence X-ray Diffraction Studies of Lipid-Peptide Mixed Monolayers during Shear Flow

Grazing incidence X-ray diffraction (GIXD) studies of monolayers of biomolecules at an air-water interface give quantitative information of in-plane packing, coherence length of crystalline domains, etc. Rheo-GIXD measurements can reveal quantitative changes in the nanocrystalline domains of a monolayer under shear. Here, we report GIXD studies of monolayers of alamethicin peptide, DPPC lipid, and their mixtures at an air-water interface under steady shear stress. The alamethicin monolayer and the mixed monolayer show a flow jamming transition. On the other hand, the pure 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) monolayer under constant stress flows steadily with a notable enhancement of the area/molecule and coherence lengths, suggesting the fusion of nanocrystallites during flow. The DPPC-alamethicin mixed monolayer shows no significant change in the area/DPPC molecule, but the coherence lengths of the individual phases (DPPC and alamethicin) increase, suggesting that the crystallites of individual phases grow bigger by merging of domains. More phase separation occurs in the system during flow. Our results show that rheo-GIXD has the potential to explore in situ molecular structural changes under rheological conditions for a diverse range of confined biomolecules at interfaces.

From Chains to Monolayers: Nanoparticle Assembly Driven by Smectic Topological Defects

In this Letter, we show how advanced hierarchical structures of topological defects in the so-called smectic oily streaks can be used to sequentially transfer their geometrical features to gold nanospheres. We use two kinds of topological defects, 1D dislocations and 2D ribbon-like topological defects. The large trapping efficiency of the smectic dislocation cores not only surpasses that of the elastically distorted zones around the cores but also surpasses the one of the 2D ribbon-like topological defect. This enables the formation of a large number of aligned NP chains within the dislocation cores that can be quasi-fully filled without any significant aggregation outside of the cores. When the NP concentration is large enough to entirely fill the dislocation cores, the LC confinement varies from 1D to 2D. We demonstrate that the 2D topological defect cores induce a confinement that leads to planar hexagonal networks of NPs. We then draw the phase diagram driven by NP concentration, associated with the sequential confinements induced by these two kinds of topological defects. Owing to the excellent large-scale order of these defect cores, not only the NP chains but also the NP hexagonal networks can be oriented along the desired direction, suggesting a possible new route for the creation of either 1D or 2D highly anisotropic NP networks. In addition, these results open rich perspectives based on the possible creation of coexisting NP assemblies of different kinds, localized in different confining areas of a same smectic film that would thus interact thanks to their proximity but also would interact via the surrounding soft matter matrix.

Metallurgy of soft spheres with hard core: From BCC to Frank-Kasper phases

Understanding how soft particles can fill the space is still an open question. Structures far from classical FCC or BCC phases are now commonly experimentally observed in many different systems. Models based on pair interaction between soft particles are at present much studied in 2D. Pair interactions with two different lengths have been shown to lead to quasicrystalline architectures. It is also the case for a hard core with a square repulsive shoulder potential. In 3D, global approaches have been proposed for instance by minimizing the interface area between the deformed objects in the case of foams or micellar systems or using a self-consistent mean-field theory in copolymer melts. In this paper we propose to compare a strong van der Waals attraction between spherical hard cores and an elastic energy associated to the deformation of the soft corona. This deformation is measured as the shift between the deformed shell compared to a corona with a perfect spherical symmetry. The two main parameters in this model are: the hard-core volume fraction and the weight of the elastic energy compared to the van der Waals one. The elastic energy clearly favours the BCC structure but large van der Waals forces favor Frank and Kasper phases. This result opens a route towards controlling the building of nanoparticle superlattices with complex structures and thus original physical properties.

Ray tracing matrix approach for refractive index mismatch aberrations in confocal microscopy

The 2×2 ray tracing matrix (RTM) method is employed for the description of optical aberrations caused by the refractive index mismatch (RIM) in fluorescent confocal polarization microscopy. We predict and experimentally confirm that due to the RIM a liquid crystal layer with highly non-uniform director distribution appears to be imaged as a layer with non-uniform thickness, which shows up in the roughness of the rear surface. For the off-axial focusing of the probing beam in a droplet dispersed in an immiscible liquid, we have developed an extended method still keeping the 2×2 dimensionality of the RTM.

Lasing in imperfectly aligned cholesterics

Optically pumped light emissions in imperfectly aligned dye-doped cholesteric cells with glance and frosted glass substrates of three different cell gap thicknesses are experimentally studied. Alignment imperfections show up in emission spectra by a broadening of the photonic bandgap (PhBG) lasing (allowed) lines at short- and long-wavelength PhBG edges and by an additional (forbidden) emission line inside the PhBG. Forbidden and allowed lines differ distinctively by their stability in the course of pumping. The origin of the forbidden line is discussed.

Evidence for a C14 Frank-Kasper Phase in One-Size Gold Nanoparticle Superlattices

The Frank-Kasper phases were already known in 1982 when quasi-crystals were discovered, but their complex architectures are now considered as making a link between simple close-packed periodic structures and some quasi-periodic ones. These tetrahedrally close packed structures are observed in many materials from elements to intermetallics as well as self-assembled soft materials like micellar systems, dendritric liquid crystals, star polymers, and more recently block copolymers or heated gold nanocrystal superlattices. We report here the existence of a Frank-Kasper phase with hexagonal symmetry (MgZn2 type, also labeled C14) in superlattices of monodisperse hydrophobically coated gold particles at room temperature obtained from suspensions in various solvents. The existence of such a structure in this system is analyzed in terms of geometrical parameters including gold core diameter, ligand length, and grafting density and an energetic approach based on van der Waals attraction. Hydrophobically coated gold nanoparticles is a new system that exhibits a Frank and Kasper phase built by one-size objects. This result opens a route toward a nanoparticle superlattice with complex structures and thus original physical properties.

Solvent-driven interactions between hydrophobically-coated nanoparticles

Interaction between hydrophobically-coated gold nanoparticles suspended in oil is usually described as the combination of strong attractive van der Waals attraction between the gold cores and interaction between the ligands. The latter interaction is expected to be purely repulsive if the suspending medium is a good solvent for the ligands or partially attractive for a bad solvent. By measuring the structure factor of interacting gold nanoparticles in various solvents, we show that the chemical affinity of the ligand with the solvent is not the only parameter that controls the interaction between the ligands and that the solvent conformation (small rigid or long flexible molecules) also plays a crucial role. Gold nanoparticles covered with hexanethiol or dodecanethiol thus undergo a larger attraction in n-dodecane or n-hexadecane compared to toluene or cyclohexane. As a consequence, self-assembly of these nanoparticles into superlattices appears at a much lower volume fraction than predicted in n-hexadecane or n-dodecane. Analogy with the behavior of polymer grafted colloids in a polymer melt is proposed to explain these unexpected results.

Growth and self-assembly of ultrathin Au nanowires into expanded hexagonal superlattice studied by in situ SAXS

We report the self-assembly of gold nanowires into hexagonal superlattices in liquid phase followed by in situ small-angle X-ray scattering and give new insights into their growth mechanism. The unprecedented large interwire distance of 8 nm strongly suggests the stabilization of the ultrathin gold nanowires by a ligand's double layer composed of oleylamine and oleylammonium chloride. The one-dimensional growth is discussed, opening perspectives toward the control growth and self-assemblies of metallic nanowires.

Reversible shear-induced crystallization above equilibrium freezing temperature in a lyotropic surfactant system

We demonstrate a unique shear-induced crystallization phenomenon above the equilibrium freezing temperature (T(K)°) in weakly swollen isotropic (Li) and lamellar (La) mesophases with bilayers formed in a cationic-anionic mixed surfactant system. Synchrotron rheological X-ray diffraction study reveals the crystallization transition to be reversible under shear (i.e., on stopping the shear, the nonequilibrium crystalline phase Lc melts back to the equilibrium mesophase). This is different from the shear-driven crystallization below T(K)°, which is irreversible. Rheological optical observations show that the growth of the crystalline phase occurs through a preordering of the Li phase to an La phase induced by shear flow, before the nucleation of the Lc phase. Shear diagram of the Li phase constructed in the parameter space of shear rate (γ) vs. temperature exhibits Li → Lc and Li → La transitions above the equilibrium crystallization temperature T(K)°, in addition to the irreversible shear-driven nucleation of Lc in the Li phase below T(K)°. In addition to revealing a unique class of nonequilibrium phase transition, the present study urges a unique approach toward understanding shear-induced phenomena in concentrated mesophases of mixed amphiphilic systems.

Rheological behaviour of polyoxometalate-doped lyotropic lamellar phases

We study the influence of nanoparticle doping on the lyotropic liquid crystalline phase of the industrial surfactant Brij®30 (C₁₂E₄) and water, doped with spherical polyoxometalate nanoparticles smaller than the characteristic dimensions of the host lamellar phase. We present viscometry and in situ rheology coupled with small-angle X-ray scattering data that show that, with increasing doping concentration, the nanoparticles act to decrease the shear viscosity of the lamellar phase, and that a shear-induced transition to a multilamellar vesicle "onion" phase is pushed to higher shear rates, and in some cases completely suppressed. X-ray data reveal that the nanoparticles remain encapsulated within the membranes of the vesicles, thus indicating a viable method for the fabrication of nanoparticle incorporating organic vesicles.

Repulsion between inorganic particles inserted within surfactant bilayers

We study by synchrotron small-angle x-ray scattering highly aligned lamellar phases of a zwitterionic surfactant, doped with monodisperse and spherical hydrophobic inorganic particles as a function of particle concentration. Analysis of the structure factor of the two-dimensional fluid formed by the particles in the plane of the bilayer gives access to their membrane-mediated interaction, which is repulsive, with a contact value of about 4kBT and a range of 14 angstroms. Systematic application of this technique should lead to a better understanding of the interaction between membrane inclusions.

Photochromic hybrid organic-inorganic liquid-crystalline materials built from nonionic surfactants and polyoxometalates: elaboration and structural study

This work reports the elaboration and structural study of new hybrid organic-inorganic materials constructed via the coupling of liquid-crystalline nonionic surfactants and polyoxometalates (POMs). X-ray scattering and polarized light microscopy demonstrate that these hybrid materials, highly loaded with POMs (up to 18 wt %), are nanocomposites of liquid-crystalline lamellar structure (Lalpha), with viscoelastic properties close to those of gels. The interpretation of X-ray scattering data strongly suggests that the POMs are located close to the terminal -OH groups of the nonionic surfactants, within the aqueous sublayers. Moreover, these materials exhibit a reversible photochromism associated to the photoreduction of the polyanion. The photoinduced mixed-valence behavior has been characterized through ESR and UV-visible-near-IR spectroscopies that demonstrate the presence of W(V) metal cations and of the characteristic intervalence charge transfer band in the near-IR region, respectively. These hybrid nanocomposites exhibit optical properties that may be useful for applications involving UV-light-sensitive coatings or liquid-crystal-based photochromic switches. From a more fundamental point of view, these hybrid materials should be very helpful models for the study of both the static and dynamic properties of nano-objects confined within soft lamellar structures.

Synthesis of Single-Crystalline Platinum Nanorods within a Soft Crystalline Surfactant-PtIIComplex

Single-crystalline platinum nanorods, monodisperse in diameter, are synthesized through a simple process at room temperature, in cetyltrimethyl ammonium bromide (CTAB) solution. The complexation of the CTA+ surfactant ion with tetrachloroplatinate in the presence of hexanol leads to the formation of a precipitate with a lamellar crystalline structure. The reduction of Pt(II) metal ions to Pt(0) is carried out using gamma radiolysis. Transmission electron microscopy (TEM) observations of the nanoparticles extracted from the solution, three weeks after radiolysis, revealed single-crystalline Pt nanorods, monodisperse in diameter (3-4 nm) and 20-60 nm long. By following the shape of the nanorods at various stages of the growth, it was found that the single-crystalline nanorods grow by coalescence of spherical seeds 3-4 nm in diameter. This suggests an aggregative mechanism similar to that recently observed for silver particles in solution.

New investigation on the tetragonal liquid-crystalline phase or SmQ

Chiral liquid crystals, for which twist and smectic order strongly compete, can exhibit complex architectures. This is the case of the SmQ phase which shows a high degree of 3D order (tetragonal or hexagonal) as well as a liquid signature. We have combined X-ray scattering and optical observations on a new compound exhibiting a SmQ phase to discriminate between the two models proposed by A.M. Levelut et al. (J. Phys. II 7, 981 (1997)) at the molecular level for the phase with the I4(1)22 space group.

Faceted monodomains of liquid crystal smectic blue phases

Smectic blue phases (BP(Sm)) are mesophases of thermotropic liquid crystals, which exhibit both three-dimensional orientational order, such as classical blue phases, and smectic positional order. The BP(Sm) phases appear as the three-dimensional counterpart of the twist grain boundary phases. By growing large faceted monocrystals of BP(Sm) phase, we provide, for the first time at the length scale of the lattice parameter, information on the symmetry of the orientational unit cell. This study leads us to suggest an orthorhombic structure, contrary to the previous results obtained by x-ray scattering at the length scale of the smectic order.

Influence of the molecular tilt on the structure of smectic blue phases

Smectic blue phases (BP(sm)) are original physical systems of thermotropic liquid crystals, displaying a double geometrical frustration: the extension of chirality in the three spatial dimensions, such as classical blue phases, and the competition between smectic order and helical twist, such as twist grain boundary (TGB) phases. We report experimental evidence of the influence of the underlying TGB((A) or (C)) phase on the BP(sm) structure.

Structural investigations on smectic blue phases

Smectic blue phases ( BP(Sm)) are thermotropic liquid crystalline phases which exhibit both three-dimensional orientational order, such as classical blue phases, and smectic positional order. BP(Sm) appear as the three-dimensional counterpart of twist grain boundary phases. X-ray scattering and optical polarizing microscopy provide information on the hexagonal and cubic symmetries of these new phases.

Hexagonal symmetry for smectic blue phases

Smectic blue phases are liquid crystalline phases which exhibit both three-dimensional-orientational order and smectic positional order. X-ray scattering experiments reveal that at least one of these phases is not cubic, as classical blue phases, but offers a hexagonal symmetry. A comparison of the experimental patterns with the scattering patterns given by smectic double twist tubes sketched by Kamien is proposed.

Tensorial x-ray structure factor in smectic liquid crystals

The amplitudes and the polarizations of the different resonant reflections characterizing the modulation of the orientational order in smectic liquid crystals are derived from the molecular tensorial structure factor. In the case of a commensurate helicoidal modulation, our conclusions are consistent with the previous predictions of Dimitrienko. We have extended Dimitrienko's prediction to incommensurate helicoidal structures and to commensurate but nonhelicoidal modulations. We have compared the estimated values for different models of modulations with the same period, with the experimental data obtained on different smectic-C variants. These comparisons enable us to discriminate between the different models.