Demixed and ordered phases in hard-rod mixtures

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.

Hard-body models of bulk liquid crystals

Hard models for particle interactions have played a crucial role in the understanding of the structure of condensed matter. In particular, they help to explain the formation of oriented phases in liquids made of anisotropic molecules or colloidal particles and continue to be of great interest in the formulation of theories for liquids in bulk, near interfaces and in biophysical environments. Hard models of anisotropic particles give rise to complex phase diagrams, including uniaxial and biaxial nematic phases, discotic phases and spatially ordered phases such as smectic, columnar or crystal. Also, their mixtures exhibit additional interesting behaviours where demixing competes with orientational order. Here we review the different models of hard particles used in the theory of bulk anisotropic liquids, leaving aside interfacial properties and discuss the associated theoretical approaches and computer simulations, focusing on applications in equilibrium situations. The latter include one-component bulk fluids, mixtures and polydisperse fluids, both in two and three dimensions, and emphasis is put on liquid-crystal phase transitions and complex phase behaviour in general.

Nematic-smectic transition of parallel hard spheroellipsoids

Spheroellipsoids are truncated ellipsoids with spherical end caps. If gradients are assumed to change smoothly at the junction of body and cap, the truncation height z0 determines the geometry uniquely. The resulting model particle has only two shape parameters, namely, the aspect ratio c/a of the basic ellipsoid and the cutoff z0/a. These two parameters can be tuned to yield a continuous transformation between a pure ellipsoid and a spherocylinder. Since parallel hard spherocylinders display a nematic-smectic A phase transition, while ellipsoids do not, the influence of the particle shape on the possibility of a smectic phase may be investigated. A density functional analysis is used to detect the dividing line, in the (c/a, z0/a) plane, between the presence and absence of the N-S transition. Since spheroellipsoids may be useful as generic model particles for anisotropic molecules, we provide a computationally efficient overlap criterion for a pair in a general, non-parallel configuration.

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.

Phase behaviour of parallel hard rods in confinement: an Onsager theory study

The effect of confinement on the positional ordering is examined in a system of parallel hard cylinders using the second virial theory of Onsager. Hard cylinders are arranged in a slit-like pore (two parallel planar hard walls) in such a way that the long axes of the particles are perpendicular to the surface of confining hard walls. We have incorporated the theories of the bulk and the confined systems into a single formalism, where a w(ij) kernel function provides the link between the bulk and confined systems. It is shown that the presence of hard walls inhibits the second order nematic-smectic A phase transition irrespective of the value of the wall-to-wall separation. Instead, due to accommodation problems of the cylinders into the pore, an infinite number of first order layering phase transitions appears. Coexisting curves, corresponding to the equilibrium between two phases having n and n + 1 smectic-like periods, are bounded with lower critical points. The gap between the average densities of the coexisting phases shrinks with increasing pore width, while the properties of the critical points monotonically move towards those of the nematic-smectic A phase transition of the bulk system (d --> ∞). The effect of only one hard wall is related to the bulk nematic-smectic A phase transition since a critical wetting transition of the wall induced layering takes place.