Ordering of Oblate Hard Particles between Hybrid Penetrable Walls.

We report a Monte Carlo (MC) simulation study of a model discotic liquid crystal (DLC) confined between hybrid walls with controllable penetrability. The model consists of oblate hard Gaussian overlap (HGO) particles. Particle-substrate interactions are modeled as follows: each substrate sees a particle as a disc of zero thickness and diameter D less than or equal to that of the actual particle, σ0, embedded inside the particle and located halfway along, and perpendicular to, its minor axis. This allows us to control the anchoring properties of the substrates, from planar (edge-on) for D ≈ 0 to homeotropic (face-on) for D ≈ σ0, which can be done independently at either substrate. Depending on the values of Ds ≡ D/σ0 at the top (Dst) and bottom (Dsb) substrates, we find domains in (Dsb, Dst) space in which particle alignment is uniform planar (UP), is uniform homeotropic (UH), or varies linearly from planar at one substrate to homeotropic at the other (Lin). These domains are separated by regions of bistability (P-Lin and H-Lin), which appear to be wider than for prolate HGOs, and there may be also a small tristable (P-H-Lin) region. Results are compared with the predictions of density functional theory, implemented at the level of Onsager's second-virial approximation with Parsons-Lee rescaling. As in the case of symmetric confinement studied previously, the agreement between theory and simulation is substantially less good than for prolate HGOs: in particular, for the investigated substrate separation L = 6σ0, the Lin configuration is never predicted. These discrepancies are likely a consequence of the fact that Onsager's theory is less accurate for discs than for rods.

Self-assembly and entropic effects in pear-shaped colloid systems. I. Shape sensitivity of bilayer phases in colloidal pear-shaped particle systems.

The role of particle shape in self-assembly processes is a double-edged sword. On the one hand, particle shape and particle elongation are often considered the most fundamental determinants of soft matter structure formation. On the other hand, structure formation is often highly sensitive to details of shape. Here, we address the question of particle shape sensitivity for the self-assembly of hard pear-shaped particles by studying two models for this system: (a) the pear hard Gaussian overlap (PHGO) and (b) the hard pears of revolution (HPR) model. Hard pear-shaped particles, given by the PHGO model, are known to form a bicontinuous gyroid phase spontaneously. However, this model does not replicate an additive object perfectly and, hence, varies slightly in shape from a "true" pear-shape. Therefore, we investigate in the first part of this series the stability of the gyroid phase in pear-shaped particle systems. We show, based on the HPR phase diagram, that the gyroid phase does not form in pears with such a "true" hard pear-shaped potential. Moreover, we acquire first indications from the HPR and PHGO pair-correlation functions that the formation of the gyroid is probably attributed to the small non-additive properties of the PHGO potential.

Self-assembly and entropic effects in pear-shaped colloid systems. II. Depletion attraction of pear-shaped particles in a hard-sphere solvent.

We consider depletion effects of a pear-shaped colloidal particle in a hard-sphere solvent for two different model realizations of the pear-shaped colloidal particle. The two models are the pear hard Gaussian overlap (PHGO) particles and the hard pears of revolution (HPR). The motivation for this study is to provide a microscopic understanding for the substantially different mesoscopic self-assembly properties of these pear-shaped colloids, in dense suspensions, that have been reported in the previous studies. This is done by determining their differing depletion attractions via Monte Carlo simulations of PHGO and HPR particles in a pool of hard spheres and comparing them with excluded volume calculations of numerically obtained ideal configurations on the microscopic level. While the HPR model behaves as predicted by the analysis of excluded volumes, the PHGO model showcases a preference for splay between neighboring particles, which can be attributed to the special non-additive characteristics of the PHGO contact function. Lastly, we propose a potentially experimentally realizable pear-shaped particle model, the non-additive hard pear of revolution model, which is based on the HPR model but also features non-additive traits similar to those of PHGO particles to mimic their depletion behavior.

Programming emergent symmetries with saddle-splay elasticity.

The director field adopted by a confined liquid crystal is controlled by a balance between the externally imposed interactions and the liquid's internal orientational elasticity. While the latter is usually considered to resist all deformations, liquid crystals actually have an intrinsic propensity to adopt saddle-splay arrangements, characterised by the elastic constant [Formula: see text]. In most realisations, dominant surface anchoring treatments suppress such deformations, rendering [Formula: see text] immeasurable. Here we identify regimes where more subtle, patterned surfaces enable saddle-splay effects to be both observed and exploited. Utilising theory and continuum calculations, we determine experimental regimes where generic, achiral liquid crystals exhibit spontaneously broken surface symmetries. These provide a new route to measuring [Formula: see text]. We further demonstrate a multistable device in which weak, but directional, fields switch between saddle-splay-motivated, spontaneously-polar surface states. Generalising beyond simple confinement, our highly scalable approach offers exciting opportunities for low-field, fast-switching optoelectronic devices which go beyond current technologies.

Thermal Hysteresis and Seeding of Twisted Fibers Formed by Achiral Discotic Particles.

In this paper, molecular dynamics simulations of simple disc-shaped particles are used to investigate the free self-assembly of defect-free fibers. Depending on the choice of particle shape and interaction strength, the formed fibers are reproducibly either straight or, for reasons of packing efficiency, spontaneously chiral. As they grow radially, increasing stresses cause chiral fibers to untwist either continuously or via morphological rearrangement. It is also found that, due to the kinetics of fiber initiation, the isotropic solution has to be significantly supercooled before aggregation takes place. As a result, the thermal hysteresis of one formed fiber extends to 13.9% of the formation temperature. In the presence of a three-thread seed cluster of 15 particles, however, monotonic fiber growth is observed 9.3% above the normal formation temperature. Thus, as in many experimental systems, it is the kinetic pathway, rather than the thermodynamic stability of the final assembly, that dominates the observed behavior.

Purely entropic self-assembly of the bicontinuous Ia3d gyroid phase in equilibrium hard-pear systems.

We investigate a model of hard pear-shaped particles which forms the bicontinuous Ia[Formula: see text]d structure by entropic self-assembly, extending the previous observations of Barmes et al. (2003 Phys. Rev. E68, 021708. (doi:10.1103/PhysRevE.68.021708)) and Ellison et al. (2006 Phys. Rev. Lett.97, 237801. (doi:10.1103/PhysRevLett.97.237801)). We specifically provide the complete phase diagram of this system, with global density and particle shape as the two variable parameters, incorporating the gyroid phase as well as disordered isotropic, smectic and nematic phases. The phase diagram is obtained by two methods, one being a compression-decompression study and the other being a continuous change of the particle shape parameter at constant density. Additionally, we probe the mechanism by which interdigitating sheets of pears in these systems create surfaces with negative Gauss curvature, which is needed to form the gyroid minimal surface. This is achieved by the use of Voronoi tessellation, whereby both the shape and volume of Voronoi cells can be assessed in regard to the local Gauss curvature of the gyroid minimal surface. Through this, we show that the mechanisms prevalent in this entropy-driven system differ from those found in systems which form gyroid structures in nature (lipid bilayers) and from synthesized materials (di-block copolymers) and where the formation of the gyroid is enthalpically driven. We further argue that the gyroid phase formed in these systems is a realization of a modulated splay-bend phase in which the conventional nematic has been predicted to be destabilized at the mesoscale due to molecular-scale coupling of polar and orientational degrees of freedom.

Competition of lattice and basis for alignment of nematic liquid crystals.

Due to elastic anisotropy, two-dimensional patterning of substrates can promote weak azimuthal alignment of adjacent nematic liquid crystals. Here we consider how such alignment can be achieved using a periodic square lattice of circular or elliptical motifs. In particular, we examine ways in which the lattice and motif can combine to favor differing orientations. Using Monte Carlo simulation and continuum elasticity we find, for circular motifs, that the coverage fraction controls both the polar anchoring angle and a transition in the azimuthal orientation. If the circles are generalized to ellipses, arbitrary control of the effective easy axis and effective anchoring potential becomes achievable by appropriate tuning of the ellipse motif relative to the periodic lattice patterning. This has possible applications in both monostable and bistable liquid crystal device contexts.

Bicontinuous minimal surface nanostructures for polymer blend solar cells.

This paper presents the first examination of the potential for bicontinuous structures such as the gyroid structure to produce high efficiency solar cells based on conjugated polymers. The solar cell characteristics are predicted by a simulation model that shows how the morphology influences device performance through integration of all the processes occurring in organic photocells in a specified morphology. In bicontinuous phases, the surface defining the interface between the electron and hole transporting phases divides the volume into two disjoint subvolumes. Exciton loss is reduced because the interface at which charge separation occurs permeates the device so excitons have only a short distance to reach the interface. As each of the component phases is connected, charges will be able to reach the electrodes more easily. In simulations of the current-voltage characteristics of organic cells with gyroid, disordered blend and vertical rod (rods normal to the electrodes) morphologies, we find that gyroids have a lower than anticipated performance advantage over disordered blends, and that vertical rods are superior. These results are explored thoroughly, with geminate recombination, i.e. recombination of charges originating from the same exciton, identified as the primary source of loss. Thus, if an appropriate materials choice could reduce geminate recombination, gyroids show great promise for future research and applications.

Coarse-grained simulation of amphiphilic self-assembly.

The authors present a computer simulation study of amphiphilic self-assembly performed using a computationally efficient single-site model based on Gay-Berne [J. Chem. Phys. 74, 3316 (1981)] and Lennard-Jones particles. Molecular dynamics simulations of these systems show that free self-assembly of micellar, bilayer, and inverse micelle arrangements can be readily achieved for a single model parametrization. This self-assembly is predominantly driven by the anisotropy of the amphiphile-solvent interaction, amphiphile-amphiphile dispersive interactions being found to be of secondary importance. While amphiphile concentration is the main determinant of phase stability, molecular parameters such as head group size and interaction strength also have measurable affects on system properties.

The role of attractive interactions in rod-sphere mixtures.

We present a computer simulation study of binary mixtures of prolate Gay-Berne particles and Lennard-Jones spheres. Results are presented for three such rod-sphere systems which differ from each other only in the interaction between unlike particles. Both the mixing-demixing behavior and the transitions between the isotropic and any liquid crystalline phases are studied for each system, as a function of temperature and concentration ratio. For systems which show macroscopic demixing, the rod-sphere interaction is shown to give direct control over interfacial anchoring properties, giving rise to the possibility of micellar phase formation in the case of homeotropic anchoring. Additionally, it is shown that on incorporating high concentrations of spheres into a system of rods with weak demixing properties, microphase-separated structures can be induced, including bicontinuous and lamellar arrangements.

Molecular simulation of chevrons in confined smectic liquid crystals.

Chevron structures adopted by confined smectic liquid crystals are investigated via molecular dynamics simulations of the Gay-Berne model. The chevrons are formed by quenching nematic films confined between aligning planar substrates whose easy axes have opposing azimuthal components. When the substrates are perfectly smooth, the chevron formed migrates rapidly towards one of the confining walls to yield a tilted layer structure. However, when substrate roughness is included, by introducing a small-amplitude modulation to the particle-substrate interaction well depth, a symmetric chevron is formed which remains stable over sufficiently long run times for detailed structural information, such as the relevant order parameters and director orientation, to be determined. For both smooth and rough boundaries, the smectic order parameter remains nonzero across the entire chevron, implying that layer identity is maintained across the chevron tip. Also, when the surface-stabilized chevron does eventually revert to a tilted layer structure, it does so via surface slippage, such that layer integrity is maintained throughout the chevron to tilted layer relaxation process.