On phase behavior and dynamical signatures of charged colloidal platelets

Ground State Configurations and Metastable Phases of Charged Linear Rods

This computational study investigates the energy minimum, that is, ground state, of suspensions of monodisperse (single-component) charged linear rods at various densities and screening lengths. We find that closed-packed unidirectional configurations have the lowest energies for all studied cases. We further specify the lattice parameters for these crystalline structures. In addition, we identify a few metastable phases, including heliconical structures. These metastable heliconical phases are composed of hexagonal smectic C layers with particle orientations forming a conical helicoid with a short pitch of three layers. We evidence this by zero-temperature Monte Carlo simulations starting from an energy-minimized hexagonal cholesteric configuration, which rapidly transforms to a heliconical phase. Furthermore, this heliconical phase is remarkably stable even at finite temperatures and melts to a disordered phase at high temperatures. Finally, we conduct simulations at room temperature and conditions typical for cellulose nanocrystal suspensions to study the onset of nematic order and compare our results to available experimental data. Our findings suggest that electrostatics play an important role in the isotropic/anisotropic transition for dense suspensions of charged rods.

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.

Shear-induced glass-to-crystal transition in anisotropic clay-like suspensions

A new numerical framework based on Stokesian dynamics is used to study a shear-induced glass-to-crystal transition in suspensions of clay-like anisotropically charged platelets. The structures obtained in quiescent conditions are in agreement with previous Monte Carlo results: a liquid phase at very short interaction range (high salt concentration), phase separation and a gel without large scale density fluctuations at intermediate interaction ranges, and glassy states at very large interaction ranges. When initially glassy suspensions are sheared, hydrodynamic torques first rotate platelets so they can reach a transient quasi-nematic disordered state. These orientational correlations permit to unlock translational degrees of freedom and the platelets then form strings aligned with the velocity direction and hexagonally packed in the gradient-vorticity plane. Under steady shear, platelet orientations are correlated but the system is not nematic. After flow cessation and relaxation in quiescent conditions, positional and orientational order are further improved as the platelet suspension experiences a transition to a nematic hexagonal crystal. Energy calculations and the existence of residual stress anisotropy after relaxation show that this final structure is not an equilibrium state but rather a new ordered, arrested state. The transient, nematic, disordered state induced by shear immediately after startup and unlocking translational degrees of freedom is thought to be an initial step that may be generic for other suspensions of strongly anisotropic colloids with important translation-orientation coupling induced by long-range interactions.

Nematic Phase of Plate-like Semicrystalline Block Copolymer Single Crystals in Solution Studied by Small-Angle X-Ray Scattering

Crystalline block copolymers have been used to prepare plate-like colloidal systems with well-controlled size, shape, and size distribution. The isotropic-to-nematic (I-N) phase transition of the novel plate-like colloidal particle suspensions has been reported previously. In this work, we focus on the characterization of the solution structure of the crystals and the N-phase using small- and ultrasmall-angle X-ray scattering techniques (SAXS/USAXS). The system has polystyrene-block-poly(l-lactide) (PS-b-PLLA) block copolymer single crystals (BCSCs) with different sizes dispersed in p-xylene. These crystals are truncated lozenge in shape and have effective diameters ranging from 550 to 4000 nm with a uniform dry thickness of 18.0 nm. Scattering of the individual crystal in solution can be simplified using a disc model with a core layer of 9-10 nm due to the lower contrast of the tethered PS layer. BCSC suspensions filled in thin quartz capillaries are prepared for monitoring the structural information. SAXS measurements of the isotropic phase show a strong face-to-face correlation, indicating that platelets form small stacked clusters in solutions. The isotropic phase is thus a coexistence of single crystals and the stacked multiple-layered clusters. The face-to-face spacing, d, in the N phases is around 75-90 nm, which increases slightly upon increasing the size of crystals. For a given system, the spacing does not change with increasing concentration under the current experimental conditions. Finally, the possible formation of lamellar domains within the N phase is also discussed due to the lateral attraction of this system. These results demonstrate the importance of the lateral attraction between the polar crystalline PLLA blocks on the formation of the N phase: the BCSCs self-assemble into larger sheets via the lateral attraction, which further enhances the I-N transition.

Isotropic, nematic, and lamellar phases in colloidal suspensions of nanosheets

The phase diagram of colloidal suspensions of electrically charged nanosheets, such as clays, despite their many industrial uses, is not yet understood either experimentally or theoretically. When the nanosheet diameter is very large (∼100 nm to 1 µm), it is quite challenging to distinguish the lamellar liquid-crystalline phase from a nematic phase with strong stacking local order, often called "columnar" nematic. We show here that newly upgraded small-angle X-ray scattering beamlines at synchrotron radiation facilities provide high-resolution measurements which allow us to identify both phases unambiguously, provided that single domains can be obtained. We investigated dilute aqueous suspensions of synthetic Sb₃P₂O₁₄^3- nanosheets that self-organize into two distinct liquid-crystalline phases, sometimes coexisting in the same sample. Close examination of their X-ray reflection profiles in the directions perpendicular to the director demonstrates that these two mesophases are a columnar nematic and a lamellar phase. In the latter, the domain size reaches up to ∼20 µm, which means that each layer is made of >600 nanosheets. Because the lamellar phase was only rarely predicted in suspensions of charged disks, our results show that these systems should be revisited by theory or simulations. The unexpected stability of the lamellar phase also suggests that the rims and faces of Sb₃P₂O₁₄^3- nanosheets may have different properties, giving them a patchy particle character.

Dynamic Monte Carlo algorithm for out-of-equilibrium processes in colloidal dispersions

Field-induced isotropic-to-nematic phase transition of colloidal rods studied with Dynamic Monte Carlo simulations.

Smectic phases in ionic liquid crystals

Ionic liquid crystals (ILCs) are anisotropic mesogenic molecules which carry charges and therefore combine properties of liquid crystals, e.g. the formation of mesophases, and of ionic liquids, such as low melting temperatures and tiny triple-point pressures. Previous density functional calculations have revealed that the phase behavior of ILCs is strongly affected by their molecular properties, i.e. their aspect ratio, the loci of the charges, and their interaction strengths. Here, we report new findings concerning the phase behavior of ILCs as obtained by density functional theory and Monte Carlo simulations. The most important result is the occurrence of a novel, wide smectic-A phase [Formula: see text], at low temperature, the layer spacing of which is larger than that of the ordinary high-temperature smectic-A phase [Formula: see text]. Unlike the ordinary smectic S _A phase, the structure of the [Formula: see text] phase consists of alternating layers of particles oriented parallel to the layer normal and oriented perpendicular to it.

Isotopic Effect on the Gel and Glass Formation of a Charged Colloidal Clay: Laponite

The time evolution of both dynamic and static structure factors of a charged colloidal clay, Laponite, dispersed in both H₂O and D₂O solvents has been investigated through multiangle dynamic light scattering (DLS) and small-angle X-ray scattering (SAXS) as a function of weight concentration. The aging phenomenology and the formation of arrested states, both gel and glass, are preserved in D₂O, while the dynamics is slowed down with respect to water. These findings are important to understand the role played by the solvent in the interparticle interactions and for techniques such as neutron scattering and nuclear magnetic resonance that allow for the extension of the accessible scattering vectors and time scales.

A liquid-crystalline hexagonal columnar phase in highly-dilute suspensions of imogolite nanotubes

Liquid crystals have found wide applications in many fields ranging from detergents to information displays and they are also increasingly being used in the ‘bottom-up' self-assembly approach of material nano-structuration. Moreover, liquid-crystalline organizations are frequently observed by biologists. Here we show that one of the four major lyotropic liquid-crystal phases, the columnar one, is much more stable on dilution than reported so far in literature. Indeed, aqueous suspensions of imogolite nanotubes, at low ionic strength, display the columnar liquid-crystal phase at volume fractions as low as ∼0.2%. Consequently, due to its low visco-elasticity, this columnar phase is easily aligned in an alternating current electric field, in contrast with usual columnar liquid-crystal phases. These findings should have important implications for the statistical physics of the suspensions of charged rods and could also be exploited in materials science to prepare ordered nanocomposites and in biophysics to better understand solutions of rod-like biopolymers.

Liquid crystals are grouped into four main classes—nematic, lamellar, cubic and columnar—depending on their symmetries. Here, the authors show for the first time that a columnar phase can form in suspensions of imogolite nanotubes at very low concentrations.

Interplay of anisotropy in shape and interactions in charged platelet suspensions

Motivated by the intriguing phase behavior of charged colloidal platelets, we investigate the structure and dynamics of charged repulsive disks by means of Monte Carlo simulations. The electrostatic interactions are taken into account through an effective two-body potential, obtained within the nonlinear Poisson-Boltzmann formalism, which has the form of anisotropic screened Coulomb potential. Recently, we showed that the original intrinsic anisotropy of the electrostatic potential in competition with excluded volume effects leads to a rich phase behavior that not only includes various liquid-crystalline phases but also predicts the existence of novel structures composed of alternating nematic-antinematic sheets. Here, we examine the structural and dynamical signatures of each of the observed structures for both translational and rotational degrees of freedom. Finally, we discuss the influence of effective charge value and our results in relation to experimental findings on charged platelet suspensions.

Helical buckling in columnar assemblies of soft discotic mesogens

We investigate the emergence of chiral meso-structures in one-dimensional fluids consisting of stacked discotic particles and demonstrate that helical undulations are generated spontaneously from internal elastic stresses. The stability of these helical conformations arises from an interplay between long-ranged soft repulsions and nanopore confinement which is naturally present in columnar liquid crystals. Using a simple mean-field theory based on microscopic considerations we identify generic scaling expressions for the typical buckling radius and helical pitch as a function of the density and interaction potential of the constituent particles.

Generalized Onsager theory for strongly anisometric patchy colloids

The implications of soft "patchy" interactions on the orientational disorder-order transition of strongly elongated colloidal rods and flat disks is studied within a simple Onsager-van der Waals density functional theory. The theory provides a generic framework for studying the liquid crystal phase behaviour of highly anisometric cylindrical colloids which carry a distinct geometrical pattern of repulsive or attractive soft interactions localized on the particle surface. In this paper, we apply our theory to the case of charged rods and disks for which the local electrostatic interactions can be described by a screened-Coulomb potential. We consider infinitely thin rod like cylinders with a uniform line charge and infinitely thin discotic cylinders with several distinctly different surface charge patterns. Irrespective of the backbone shape the isotropic-nematic phase diagrams of charged colloids feature a generic destabilization of nematic order at low ionic strength, a dramatic narrowing of the biphasic density region, and a reentrant phenomenon upon reducing the electrostatic screening. The low screening regime is characterized by a complete suppression of nematic order in favor of positionally ordered liquid crystal phases.

Gel, glass and nematic states of plate-like particle suspensions: charge anisotropy and size effects

The influence of the charge anisotropy and platelet size on the formation of gel and glass states and nematic phases in suspensions of plate-like particles is investigated using Monte Carlo simulations in the canonical ensemble.