Magnetic field effects on tactoids of plate-like colloids

Effect of electric fields on the director field and shape of nematic tactoids

Tactoids are spindle-shaped droplets of a uniaxial nematic phase suspended in the coexisting isotropic phase. They are found in dispersions of a wide variety of elongated colloidal particles, including actin, fd virus, carbon nanotubes, vanadium peroxide, and chitin nanocrystals. Recent experiments on tactoids of chitin nanocrystals in water show that electric fields can very strongly elongate tactoids even though the dielectric properties of the coexisting isotropic and nematic phases differ only subtly. We develop a model for partially bipolar tactoids, where the degree of bipolarness of the director field is free to adjust to optimize the sum of the elastic, surface, and Coulomb energies of the system. By means of a combination of a scaling analysis and a numerical study, we investigate the elongation and director field's behavior of the tactoids as a function of their size, the strength of the electric field, the surface tension, anchoring strength, the elastic constants, and the electric susceptibility anisotropy. We find that tactoids cannot elongate significantly due to an external electric field, unless the director field is bipolar or quasibipolar and somehow frozen in the field-free configuration. Presuming that this is the case, we find reasonable agreement with experimental data.

Electric-field-induced shape transition of nematic tactoids

The occurrence of new textures of liquid crystals is an important factor in tuning their optical and photonics properties. Here, we show, both experimentally and by numerical computation, that under an electric field chitin tactoids (i.e., nematic droplets) can stretch to aspect ratios of more than 15, leading to a transition from a spindlelike to a cigarlike shape. We argue that the large extensions occur because the elastic contribution to the free energy is dominated by the anchoring. We demonstrate that the elongation involves hydrodynamic flow and is reversible: the tactoids return to their original shapes upon removing the field.

Probing a self-assembled fd virus membrane with a microtubule

The self-assembly of highly anisotropic colloidal particles leads to a rich variety of morphologies whose properties are just beginning to be understood. This article uses computer simulations to probe a particle-scale perturbation of a commonly studied colloidal assembly, a monolayer membrane composed of rodlike fd viruses in the presence of a polymer depletant. Motivated by experiments currently in progress, we simulate the interaction between a microtubule and a monolayer membrane as the microtubule "pokes" and penetrates the membrane face-on. Both the viruses and the microtubule are modeled as hard spherocylinders of the same diameter, while the depletant is modeled using ghost spheres. We find that the force exerted on the microtubule by the membrane is zero either when the microtubule is completely outside the membrane or when it has fully penetrated the membrane. The microtubule is initially repelled by the membrane as it begins to penetrate but experiences an attractive force as it penetrates further. We assess the roles played by translational and rotational fluctuations of the viruses and the osmotic pressure of the polymer depletant. We find that rotational fluctuations play a more important role than the translational ones. The dependence on the osmotic pressure of the depletant of the width and height of the repulsive barrier and the depth of the attractive potential well is consistent with the assumed depletion-induced attractive interaction between the microtubule and viruses. We discuss the relevance of these studies to the experimental investigations.

Colloidal liquid crystals in rectangular confinement: theory and experiment

We theoretically and experimentally study nematic liquid crystal equilibria within shallow rectangular wells. We model the wells within a two-dimensional Oseen-Frank framework, with strong tangent anchoring, and obtain explicit analytical expressions for the director fields and energies of the 'diagonal' and 'rotated' solutions reported in the literature. These expressions separate the leading-order defect energies from the bulk distortion energy for both families of solutions. The continuum Oseen-Frank study is complemented by a microscopic mean-field approach. We numerically minimize the mean-field functional, including the effects of weak anchoring, variable order and random initial conditions. In particular, these simulations suggest the existence of higher-energy metastable states with internal defects. We compare our theoretical results to experimental director profiles, obtained using two types of filamentous virus particles, wild-type fd-virus and a modified stiffer variant (Y21M), which display nematic ordering in rectangular chambers, as found by confocal scanning laser microscopy. We combine our analytical energy expressions with experimentally recorded frequencies of the different equilibrium states to obtain explicit estimates for the extrapolation length, defined to be the ratio of the nematic elastic constant to the anchoring coefficient, of the fd-virus.

Formation of liquid crystalline phases in aqueous suspensions of platelet-like tripalmitin nanoparticles

Suspensions of platelet-like shaped tripalmitin nanocrystals stabilized by the pure lecithin DLPC and the lecithin blend S100, respectively, have been studied by small-angle x-ray scattering (SAXS) and optical observation of their birefringence at different tripalmitin (PPP) concentrations φ(PPP). It could be demonstrated that the platelets of these potential drug delivery systems start to form a liquid crystalline phase already at pharmaceutically relevant concentrations φ(PPP) of less than 10 wt. %. The details of this liquid crystalline phase are described here for the first time. As in a previous study [A. Illing et al., Pharm. Res. 21, 592 (2004)] some platelets are found to self-assemble into lamellar stacks above a critical tripalmitin concentration φ(PPP)(st) of 4 wt. %. In this study another critical concentration φ(PPP)(lc) ≈ 7 wt. % for DLPC and φ(PPP)(lc) ≈ 9 wt. % for S100 stabilized dispersions, respectively, has been observed. φ(PPP)(lc) describes the transition from a phase of randomly oriented stacked lamellae and remaining non-assembled individual platelets to a phase in which the stacks and non-assembled platelets exhibit an overall preferred orientation. A careful analysis of the experimental data indicates that for concentrations above φ(PPP)(lc) the stacked lamellae start to coalesce to rather small liquid crystalline domains of nematically ordered stacks. These liquid crystalline domains can be individually very differently oriented but possess an overall preferred orientation over macroscopic length scales which becomes successively more expressed when further increasing φ(PPP). The lower critical concentration for the formation of liquid crystalline domains of the DLPC-stabilized suspension compared to φ(PPP)(lc) of the S100-stabilized suspension can be explained by a larger aspect ratio of the corresponding tripalmitin platelets. A geometrical model based on the excluded volumes of individual platelets and stacked lamellae has been developed and successfully applied to reproduce the critical volume fractions for both, the onset of stack formation and the appearance of the liquid crystalline phase.

Structure and dynamics of interfaces between two coexisting liquid-crystalline phases

A phase-field-crystal model is used to access the structure and thermodynamics of interfaces between two coexisting liquid-crystalline phases in two spatial dimensions. Depending on the model parameters, there is a variety of possible coexistences between two liquid-crystalline phases, including a plastic triangular crystal (PTC). Here, we numerically calculate the profiles for the mean density and for the nematic order tensor across the interface for isotropic-PTC and columnar-PTC (or equivalently smectic-A-PTC) phase coexistence. As a general finding, the width of the interface with respect to the nematic order parameter characterizing the orientational order is larger than the width of the mean-density interface. In approaching the interface from the PTC side, at first, the mean density goes down, and then the nematic order parameter follows. The relative shift in the two profiles can be larger than a full lattice constant of the plastic crystal. Finally, we also present numerical results for the dynamic relaxation of an initial order-parameter profile towards its equilibrium interfacial profile. Our predictions for the interfacial profiles can, in principle, be verified in real-space experiments of colloidal dispersions.

Texture and shape of two-dimensional domains of nematic liquid crystals

We present a generalized approach to compute the shape and internal structure of two-dimensional nematic domains. By using conformal mappings, we are able to compute the director field for a given domain shape that we choose from a rich class, which includes drops with large and small aspect ratios and sharp domain tips as well as smooth ones. Results are assembled in a phase diagram that for given domain size, surface tension, anchoring strength, and elastic constant shows the transitions from a homogeneous to a bipolar director field, from circular to elongated droplets, and from sharp to smooth domain tips. We find a previously unaccounted for regime, where the drop is nearly circular, the director field bipolar, and the tip rounded. We also find that bicircular director fields, with foci that lie outside the domain, provide a remarkably accurate description of the optimal director field for a large range of values of the various shape parameters.

Self-assembly of 2D membranes from mixtures of hard rods and depleting polymers()

We combine simulations and experiments to elucidate the molecular forces leading to the assembly of two dimensional membrane-like structures composed of a one rod-length thick monolayer of aligned rods from an immiscible suspension of hard rods and depleting polymers. Computer simulations predict that monolayer membranes are thermodynamically stable above a critical rod aspect ratio and below a critical depletion interaction length scale. Outside of these conditions alternative structures such as stacked smectic columns or nematic droplets are thermodynamically stable. These predictions are confirmed by subsequent experiments using a model system of virus rod-like molecules and non-adsorbing polymer. Our work demonstrates that collective molecular protrusion fluctuations alone are sufficient to stabilize membranes composed of homogenous rods with simple excluded volume interactions.

Theoretical calculation of the phase behavior of colloidal membranes

We formulate a density functional theory that describes the phase behavior of hard rods and depleting polymers, as realized in recent experiments on suspensions of fd virus and nonadsorbing polymer. The theory predicts the relative stability of nematic droplets, stacked smectic columns, and a recently discovered phase of isolated monolayers of rods, or colloidal membranes. We find that a minimum rod aspect ratio is required for stability of colloidal membranes and that collective protrusion undulations are the dominant effect that stabilizes this phase. The theoretical predictions are shown to be qualitatively consistent with experimental and computational results.