Anomalous columnar order of charged colloidal platelets

Phase behaviour of mixtures of charged soft disks and spheres

We have investigated the phase behaviour of mixtures of soft disks (Gay-Berne oblate ellipsoids, GB) and soft spheres (Lennard-Jones, LJ) with opposite charge as a model of ionic liquid crystals and colloidal suspensions. We have used constant volume Molecular Dynamics simulations and fixed the stoichiometry of the mixture in order to have electroneutrality; three systems have been selected GB : LJ = 1 : 2, GB : LJ = 1 : 1 and GB : LJ = 2 : 1. For each system we have selected three values of the scaled point charge q* of the GB particles, namely 0.5, 1.0 and 2.0 (and a corresponding negative scaled charge of the LJ particles that depends on the stoichiometric ratio). We have found a very rich mesomorphism with the formation, as a function of the scaled temperature, of the isotropic phase, the discotic nematic phase, the hexagonal columnar phase and crystal phases. While the structure of the high temperature phases was similar in all systems, the hexagonal columnar phases exhibited a highly variable morphology depending on the scaled charge and stoichiometry. On the one hand, GB : LJ = 1 : 2 systems form lamellar structures, akin to smectic phases, with an alternation of layers of disks (exhibiting an hexagonal columnar phase) and layers of LJ particles (in the isotropic phase). On the other hand, for the 2 : 1 stoichiometry we observe the formation of a frustrated hexagonal columnar phase with an alternating tilt direction of the molecular axis. We rationalize these findings based on the structure of the neutral ion pair dominating the behaviour at low temperature and high charge.

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.

Electrostatic potential of mean force between two curved surfaces in the presence of counterion connectivity

In this paper, we investigate effects of counterion connectivity (i.e., association of the counterions into a chain molecule) on the electrostatic potential of mean force (EPMF) between two similarly charged cylinder rods in a primitive model electrolyte solution by solving a classical density functional theory. The main findings include the following: (i) The counterion connectivity helps in inducing a like-charge-attractionlike (LCA-like) phenomenology even in a monovalent counterion solution wherein the LCA-like observation generally does not occur without the counterion connectivity. (ii) For divalent counterion solutions, the counterion connectivity can reinforce or weaken the LCA-like observation depending on the chain length N, and simply increases the equilibrium nearest surface separation of the rods corresponding to the minimum EPMF to nearly three times the counterion site diameter, whether N is large or small. (iii) If N is large enough, the LCA-like strength tends to be negatively correlated with the electrolyte concentration c over the entire range of the rod surface charge magnitude |σ*| considered; whereas if N drops, the correlation tends to become positive with decrease of the |σ*| value, and particularly for modest |σ*| values, the correlation relationship exhibits an extreme value phenomenon. (iv) In the case of a 1:1 electrolyte, the EPMF effects of the diameters of counterion and coion sites are similar in both situations with and without the counterion connectivity. All of these findings can be explained self-consistently by a recently proposed hydrogen-bonding style mechanism reinforced by one additional concept: flexibility of the counterion chain and the factors affecting it, like N and counterion site valence.

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.

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.

Monte Carlo computer simulation of sedimentation of charged hard spherocylinders

In this article we present a NVT Monte Carlo computer simulation study of sedimentation of an electroneutral mixture of oppositely charged hard spherocylinders (CHSC) with aspect ratio L/σ = 5, where L and σ are the length and diameter of the cylinder and hemispherical caps, respectively, for each particle. This system is an extension of the restricted primitive model for spherical particles, where L/σ = 0, and it is assumed that the ions are immersed in an structureless solvent, i.e., a continuum with dielectric constant D. The system consisted of N = 2000 particles and the Wolf method was implemented to handle the coulombic interactions of the inhomogeneous system. Results are presented for different values of the strength ratio between the gravitational and electrostatic interactions, Γ = (mgσ)/(e(2)/Dσ), where m is the mass per particle, e is the electron's charge and g is the gravitational acceleration value. A semi-infinite simulation cell was used with dimensions Lx ≈ Ly and Lz = 5Lx, where Lx, Ly, and Lz are the box dimensions in Cartesian coordinates, and the gravitational force acts along the z-direction. Sedimentation effects were studied by looking at every layer formed by the CHSC along the gravitational field. By increasing Γ, particles tend to get more packed at each layer and to arrange in local domains with an orientational ordering along two perpendicular axis, a feature not observed in the uncharged system with the same hard-body geometry. This type of arrangement, known as tetratic phase, has been observed in two-dimensional systems of hard-rectangles and rounded hard-squares. In this way, the coupling of gravitational and electric interactions in the CHSC system induces the arrangement of particles in layers, with the formation of quasi-two dimensional tetratic phases near the surface.

On phase behavior and dynamical signatures of charged colloidal platelets

Charged platelet suspensions, such as swelling clays, disc-like mineral crystallites or exfoliated nanosheets are ubiquitous in nature. Their phase behaviours are nevertheless still poorly understood: while some clay suspensions form arrested states at low densities, others exhibit an equilibrium isotropic-nematic transition at moderate densities. These observations raise fundamental questions about the influence of electrostatic interactions on the isotropic-nematic transition and the organisation of charged platelets. We investigate the competition between anisotropic excluded-volume and repulsive electrostatic interactions in suspensions of charged colloidal discs, by means of Monte-Carlo simulations and characterization of the dynamics of the structures. We show that the original intrinsic anisotropy of the electrostatic potential between charged platelets not only rationalizes generic features of the complex phase diagram of charged colloidal platelets such as Gibbsite and Beidellite clays, but also predicts the existence of novel structures. Furthermore, we find evidences of a strong slowing down of the dynamics upon increasing density.

Size and boundary effects on the diffusive behavior of elongated colloidal particles in a strongly confined dense dispersion

In very recent experimental work, diffusive motion of individual particles in a dense columnar phase of colloidal suspension of filamentous virus particles probed by means of fluorescence video microscopy [S. Naderi, E. Pouget, P. Ballesta, P. van der Schoot, M. P. Lettinga, and E. Grelet, Phys. Rev. Lett. 111, 037801 (2013)]. Rare events were observed in which the minority fluorescently labeled particles engage in sudden, jump-like motion along the director. The jump length distribution turned out to be biased towards a half and a full particle length. We suggest these events may be indicative of two types of particle motion, one in which particles overtake other particles in the same column and the other where a column re-equilibrates after a particle leaves a column either to enter into another column or into a void defect on the lattice. Our Brownian dynamics simulations of a quasi one-dimensional system of semi-flexible particles, subject to a Gaussian confinement potentials mimicking the effects of the self-consistent molecular field in the columnar phase, support this idea. We find that the frequency of overtaking depends on the linear fraction of particles and the steepness of the confining potential. The re-equilibration time of a column after a particle is removed from it is much shorter than the self-diffusion timescale. For the case of large system sizes and periodic boundary conditions, overtaking events do not present themselves as full-length jumps. Only if the boundary conditions are reflecting and the system is sufficiently small, full length jumps are observed in particle trajectories. The reason is that only then the amplitude of the background fluctuations is smaller than a particle length. Increasing the bending flexibility of the particles on the one hand enhances the ability of particles to overtake each other but on the other it enhances fluctuations that wash out full jumps in particle trajectories.

Liquid crystal phase transitions in suspensions of mineral colloids: new life from old roots

A review is given of the field of mineral colloidal liquid crystals: liquid crystal phases formed by individual mineral particles within colloidal suspensions. Starting from their discovery in the 1920s, we discuss developments on the levels of both fundamentals and applications. We conclude by highlighting some promising results from recent years, which may point the way towards future developments.

Liquid Crystal Phases in Suspensions of Charged Plate-Like Particles

Anisotropic interactions in colloidal suspensions have recently emerged as a route for the design of new soft materials. Nonisotropic particles can form nematic, smectic, hexatic, and columnar liquid crystals. Although the formation of these phases is well rationalized when excluded volume is solely at play, the role of electrostatic interactions still remains unclear and even less so when particles present a charge heterogeneity, for example, clays. Here, we use Monte Carlo simulations of concentrated suspensions of charged disk-like particles to reveal the role of Coulomb interactions and charge anisotropy underlying liquid crystal formation and structures. We observe a vast zoo of exotic structures, going from hexatic to columnar phases, which are shown to be controlled by the charge anisotropy. The particle volume fraction at which these phases start to form is found to decrease with increasing Coulomb interactions and charge anisotropy, which suggests a route to tune the structure of aqueous liquid crystals.