Structure and thermodynamics of platelet dispersions

Fine tuning the structural colours of photonic nanosheet suspensions by polymer doping

Aqueous suspensions of nanosheets are readily obtained by exfoliating low-dimensional mineral compounds like H₃Sb₃P₂O₁₄. The nanosheets self-organize, at low concentration, into a periodic stack of membranes, i.e. a lamellar liquid-crystalline phase. Due to the dilution, this stack has a large period of a few hundred nanometres, it behaves as a 1-dimensional photonic material and displays structural colours. We experimentally investigated the dependence of the period on the nanosheet concentration. We theoretically showed that it cannot be explained by the usual DLVO interaction between uniform lamellae but that the particulate nature of nanosheet-laden membranes must be considered. Moreover, we observed that adding small amounts of 100 kDa poly(ethylene oxide) (PEO) decreases the period and allows tuning the colour throughout the visible range. PEO adsorbs on the nanosheets, inducing a strong reduction of the nanosheet charge. This is probably due to the Lewis-base character of the EO units of PEO that become protonated at the low pH of the system, an interpretation supported by theoretical modeling. Oddly enough, adding small amounts of 1 MDa PEO has the opposite effect of increasing the period, suggesting the presence of an additional intermembrane repulsion not yet identified. From an applied perspective, our work shows how the colours of these 1-dimensional photonic materials can easily be tuned not only by varying the nanosheet concentration (which might entail a phase transition) but also by adding PEO. From a theoretical perspective, our approach represents a necessary step towards establishing the phase diagram of aqueous suspensions of charged nanosheets.

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.

Shape-induced separation of nanospheres and aligned nanorods

We studied the phase separation and spatial arrangement of gold nanorods and nanospheres after evaporative self-assembly from aqueous suspension. Depending on the position relative to the contact line of the drying droplet, spheres and rods separate into various liquid-crystalline phases. Nanorods exhibit a strong preference for side-by-side alignment, giving rise to smectic phases; spheres in solution are forced out of these regions and form close-packed arrays. We discuss this self-separation into nanorod- and sphere-rich phases in terms of various interactions, including electrostatic, van der Waals, and deplection interactions forces. The experimental results are compared to quantitative calculations of the colloidal interaction energies. We also describe and discuss the role of the surfactant on the different crystal facets of the nanorods on the assembly process.

Multiphase coexistence and destabilization of liquid crystalline binary nanosheet colloids of titanate and clay

A plate-plate binary colloid system of photocatalytically active titanate and inert clay nanosheets shows macroscopically separated multiphase coexistence. Two liquid crystalline phases and one isotropic phase coexist at high titanate and low clay concentrations whereas the colloids are destabilized at high clay concentrations.

Bulk fluid phase behaviour of colloidal platelet-sphere and platelet-polymer mixtures

Using a geometry-based fundamental measure density functional theory, we calculate bulk fluid phase diagrams of colloidal mixtures of vanishingly thin hard circular platelets and hard spheres. We find isotropic-nematic phase separation, with strong broadening of the biphasic region, upon increasing the pressure. In mixtures with large size ratio of platelet and sphere diameters, there is also demixing between two nematic phases with differing platelet concentrations. We formulate a fundamental measure density functional for mixtures of colloidal platelets and freely overlapping spheres, which represent ideal polymers, and use it to obtain phase diagrams. We find that, for low platelet-polymer size ratio, in addition to isotropic-nematic and nematic-nematic phase coexistence, platelet-polymer mixtures also display isotropic-isotropic demixing. By contrast, we do not find isotropic-isotropic demixing in hard-core platelet-sphere mixtures for the size ratios considered.

Patchy worm-like micelles: solution structure studied by small-angle neutron scattering

Triblock terpolymers exhibit a rich self-organization behavior including the formation of fascinating cylindrical core-shell structures with a phase separated corona. After crystallization-induced self-assembly of polystyrene-block-polyethylene-block-poly(methyl methacrylate) triblock terpolymers (abbreviated as SEMs = Styrene-Ethylene-Methacrylates) from solution, worm-like core-shell micelles with a patchy corona of polystyrene and poly(methyl methacrylate) were observed by transmission electron microscopy. However, the solution structure is still a matter of debate. Here, we present a method to distinguish in situ between a Janus-type (two faced) and a patchy (multiple compartments) configuration of the corona. To discriminate between both models the scattering intensity must be determined mainly by one corona compartment. Contrast variation in small-angle neutron scattering enables us to focus on one compartment of the worm-like micelles. The results validate the existence of the patchy structure also in solution.

Floating nematic phase in colloidal platelet-sphere mixtures

The phase behaviour of colloidal dispersions is interesting for fundamental reasons and for technological applications such as photonic crystals and electronic paper. Sedimentation, which in everyday life is relevant from blood analysis to the shelf life of paint, is a means to determine phase boundaries by observing distinct layers in samples that are in sedimentation-diffusion equilibrium. However, disentangling the effects due to interparticle interactions, which generate the bulk phase diagram, from those due to gravity is a complex task. Here we show that a line in the space of chemical potentials µ(i), where i labels the species, represents a sedimented sample and that each crossing of this sedimentation path with a binodal generates an interface under gravity. Complex phase stacks can result, such as the sandwich of a floating nematic layer between top and bottom isotropic phases that we observed in a mixture of silica spheres and gibbsite platelets.

Connectivity percolation in suspensions of hard platelets

We present a study on connectivity percolation in suspensions of hard platelets by means of Monte Carlo simulation. We interpret our results using a contact-volume argument based on an effective single-particle cell model. It is commonly assumed that the percolation threshold of anisotropic objects scales as their inverse aspect ratio. While this rule has been shown to hold for rodlike particles, we find that for hard platelike particles the percolation threshold is nonmonotonic in the aspect ratio. It exhibits a shallow minimum at intermediate aspect ratios and then saturates to a constant value. This effect is caused by the isotropic-nematic transition preempting the percolation transition. Hence the common strategy to use highly anisotropic, conductive particles as fillers in composite materials in order to produce conduction at low filler concentration is expected to fail for platelike fillers such as graphene and graphite nanoplatelets.

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.

Phase behaviour of binary mixtures of diamagnetic colloidal platelets in an external magnetic field

Using fundamental measure density functional theory we investigate paranematic-nematic and nematic-nematic phase coexistence in binary mixtures of circular platelets with vanishing thicknesses. An external magnetic field induces uniaxial alignment and acts on the platelets with a strength that is taken to scale with the platelet area. At particle diameter ratio λ = 1.5 the system displays paranematic-nematic coexistence. For λ = 2, demixing into two nematic states with different compositions also occurs, between an upper critical point and a paranematic-nematic-nematic triple point. Increasing the field strength leads to shrinking of the coexistence regions. At high enough field strength a closed loop of immiscibility is induced and phase coexistence vanishes at a double critical point above which the system is homogeneously nematic. For λ = 2.5, besides paranematic-nematic coexistence, there is nematic-nematic coexistence which persists and hence does not end in a critical point. The partial orientational order parameters along the binodals vary strongly with composition and connect smoothly for each species when closed loops of immiscibility are present in the corresponding phase diagram.

A fluorescence correlation spectroscopy study of macromolecular tracer diffusion in polymer solutions

We discuss the manner in which the dynamics of tracer polystyrene chains varies with the concentration of matrix polystyrene chains dissolved in toluene. Using fluorescence correlation spectroscopy and theory, it is shown that the cooperative diffusion coefficient of the matrix polystyrene chains can be measured by fluorescence correlation spectroscopy in the semidilute entangled concentration regime. In addition the self-diffusion coefficient of the tracer polystyrene chains can be detected for arbitrary concentrations. The measured cooperative diffusion coefficient is independent of the molecular weight of the tracer polystyrene chains because it is a characteristic feature of the transient entanglement network.

Experimental observation of fractionated crystallization in polydisperse platelike colloids

We have discovered that the long-term aging of the hexagonal columnar liquid-crystal phase of polydisperse gibbsite platelets leads to fractionated crystallization, that is, to the formation of coexisting columnar crystals with different periods. This process was revealed by microradian X-ray diffraction demonstrating the splitting of the Bragg intercolumnar reflections into sequences of sharper reflections. The fractionated crystallization was observed in a number of samples of sterically stabilized as well as charge-stabilized polydisperse gibbsite platelets.

Bulk phase behavior of binary hard platelet mixtures from density functional theory

We investigate isotropic-isotropic, isotropic-nematic, and nematic-nematic phase coexistence in binary mixtures of circular platelets with vanishing thickness, continuous rotational degrees of freedom, and radial size ratios lambda up to 5. A fundamental measure density functional theory, previously used for the one-component model, is presented and results are compared against those from Onsager theory as a benchmark. For lambda<or=1.7 the system displays isotropic-nematic phase coexistence with a widening of the biphasic region for increasing values of lambda . For size ratios lambda>or=2, we find that demixing into two nematic states becomes stable and an isotropic-nematic-nematic triple point can occur. Fundamental measure theory gives a smaller isotropic-nematic biphasic region than Onsager theory and locates the transition at lower densities. Furthermore, nematic-nematic demixing occurs over a larger range of compositions at a given value of lambda than found in Onsager theory. Both theories predict the same topologies of the phase diagrams. The partial nematic order parameters vary strongly with composition and indicate that the larger particles are more strongly ordered than the smaller particles.