On the Effects of Different trans and cis Populations in Azobenzene Liquid Crystal Elastomers: A Monte Carlo Investigation.

We investigate main-chain liquid crystal elastomers (LCEs) formed by photoresponsive azobenzene units with different populations of trans and cis conformers (from fully trans to fully cis). We study their macroscopic properties as well as their molecular organization using extensive Monte Carlo simulations of a simple coarse-grained model where the trans and cis conformers are represented by soft-core biaxial Gay-Berne particles with size and interaction energy parameters obtained by fitting a bare bone azobenzene moiety represented at atomistic level. We find that increasing the fraction of cis conformers, as could be obtained by near-UV irradiation, shifts the nematic-isotropic transition to a lower temperature, consistently with experiment, while generating internal stress in a clamped sample. An analysis of pair distributions shows that the immediate surroundings of a bent cis molecule are slightly less dense and more orientationally disordered in comparison with that of a trans conformer. Comparing nematic and smectic LCEs, actuation in the smectic phase proved less effective, disrupting the smectic layers to some extent but preserving orientational order of the azobenzene moieties.

Effects of shape and solute-solvent compatibility on the efficacy of chirality transfer: Nanoshapes in nematics.

Chirality, as a concept, is well understood at most length scales. However, quantitative models predicting the efficacy of the transmission of chirality across length scales are lacking. We propose here a modus operandi for a chiral nanoshape solute in an achiral nematic liquid crystal host showing that that chirality transfer may be understood by unusually simple geometric considerations. This mechanism is based on the product of a pseudoscalar chirality indicator and of a geometric shape compatibility factor based on the two-dimensional isoperimetric quotients for each nanoshape solute. The model is tested on an experimental set of precisely engineered gold nanoshapes. These libraries of calculated and in-parallel acquired experimental data among related nanoshapes pave the way for predictive calculations of chirality transfer in nanoscale, macromolecular, and biological systems, from designing chiral discriminators and enantioselective catalysts to developing chiral metamaterials and understanding nature's innate ability to transfer homochirality across length scales.

The nematic-isotropic transition of the Lebwohl-Lasher model revisited.

We revisited the nematic-isotropic (NI) transition of the Lebwohl-Lasher lattice model with a detailed investigation of samples containing 200 × 200 × 200 particles. The large-scale Monte Carlo (MC) simulations involved were carried out following the standard Metropolis, as well as the cluster MC Wolff algorithms. A notable free-energy barrier was observed between the isotropic and nematic phase, leading to long-lived metastable states and hysteresis. We provide an improved estimate of the nematic-isotropic transition temperature TNI, of the supercooling and superheating temperatures, of the temperature of divergence of pretransitional effects [Formula: see text] as well as an analysis of the size distribution of the ordered domains above TNI, contributing to a better understanding of this transition of key importance for liquid crystals. This article is part of the theme issue 'Topics in mathematical design of complex materials'.

Topics in the mathematical design of materials.

We present a perspective on several current research directions relevant to the mathematical design of new materials. We discuss: (i) design problems for phase-transforming and shape-morphing materials, (ii) epitaxy as an approach of central importance in the design of advanced semiconductor materials, (iii) selected design problems in soft matter, (iv) mathematical problems in magnetic materials, (v) some open problems in liquid crystals and soft materials and (vi) mathematical problems on liquid crystal colloids. The presentation combines topics from soft and hard condensed matter, with specific focus on those design themes where mathematical approaches could possibly lead to exciting progress. This article is part of the theme issue 'Topics in mathematical design of complex materials'.

Elastic constants and the formation of topological defects in hybrid nematic cells: A Monte Carlo study.

We present a Monte Carlo study of the effects of elastic anisotropy on the topological defects which can be formed in nematic films with hybrid boundary conditions. We simulate the polarized microscopy images and analyze their evolution in uniaxial systems for different values of the Frank elastic constants.

From Point to Filament Defects in Hybrid Nematic Films.

We have studied nematic hybrid films with homeotropic alignment at the top surface and various controlled degrees of in plane ordering, going from a random degenerate organization to a completely uniform alignment along one direction, at the bottom one. We show, by Monte Carlo (MC) computer simulations and experiments on photopatterned films with the bottom support surface fabricated with in-plane order similar to the simulated ones, that the point defects observed in the case of random planar orientations at the bottom tend to arrange along a filament as the surface ordering is sufficiently increased. MC simulations complement the polarized microscopy texture observations allowing to inspect the 3D structure of the defects and examine the role of elastic constants.

MOLC. A reversible coarse grained approach using anisotropic beads for the modelling of organic functional materials.

We describe the development and implementation of a coarse grained (CG) modelling approach where complex organic molecules, and particularly the π-conjugated ones often employed in organic electronics, are modelled in terms of connected sets of attractive-repulsive biaxial Gay-Berne ellipsoidal beads. The CG model is aimed at reproducing realistically large scale morphologies (e.g. up to 100 nm thick films) for the materials involved, while being able to generate, with a back-mapping procedure, atomistic coordinates suitable, with limited effort, to be applied for charge transport calculations. Detailed methodology and an application to the common hole transporter material α-NPD are provided.

Multidimensional Potential Energy Surfaces Resolved at the RASPT2 Level for Accurate Photoinduced Isomerization Dynamics of Azobenzene.

We have used state-of-the-art ab initio restricted active RASPT2 computations using a 16 orbitals, 18 electrons active space to produce an extended three-dimensional map of the potential energy surfaces (PESs) of the ground and first nπ* excited states of azobenzene along CNNC torsion and the two CNN bending angles, which are the most relevant coordinates for the trans-cis photoisomerization process. Through comparison with fully unconstrained optimizations performed at the same level of theory, we show that the three selected coordinates suffice to correctly describe the photoisomerization mechanism and the S1-S0 crossing seam. We also provide a map of the nonadiabatic coupling between the two states in the region where they get closer in energy. Eventually, we show that treating the two CNN bending angles as independent coordinates is fundamental to break the symmetry and couple the two electronic states. The accuracy of the S0 and S1 PESs and couplings was validated with semiclassical dynamics simulations in the reduced space of the scanned coordinates, showing results in good agreement with published full-coordinate dynamics.

Highly Sensitive, Tunable Chirality Amplification through Space Visualized for Gold Nanorods Capped with Axially Chiral Binaphthyl Derivatives.

The creation and transmission of chirality in molecular systems is a well-known, widely applied notion. Our understanding of how the chirality of nanomaterials can be controlled, measured, transmitted through space, and applied is less well understood. Dynamic assemblies for chiral sensing or metamaterials engineered from chiral nanomaterials require exact methods to determine transmission and amplification of nanomaterial chirality through space. We report the synthesis of a series of gold nanorods (GNRs) with a constant aspect ratio of ∼4.3 capped with C2-symmetric, axially chiral binaphthyl thiols, preparation of dispersions in the nematic liquid crystal 5CB, measurements of the helical pitch, and the determination of the helical twisting power as well as the average distance between the chiral nanomaterial additives. By comparison to the neat organic chiral derivatives, we demonstrate how the amplification of chirality facilitated by GNRs decorated with chiral molecules can be used to clearly distinguish the chiral induction strength of a homologous series of binaphthyl derivatives, differing only in the length of the nontethered aliphatic chain, in the induced chiral nematic liquid crystal phase. Considering systematic errors in sample preparation and optical measurements, these chiral molecules would otherwise be deemed identical with respect to chiral induction. Notably, we find some of the highest ever-reported values of the helical twisting power. We further support our experimentally derived arguments of a more comprehensive understanding of chirality transfer by calculations of a suitable pseudoscalar chirality indicator.

Reversible water driven chirality inversion in cellulose-based helices isolated from Erodium awns.

Among the movements observed in some cellulosic structures produced by plants are those that involve the dispersion and burial of seeds, as for example in Erodium from the Geraniaceae plant family. Here we report on a simple and efficient strategy to isolate and tune cellulose-based hygroscopic responsive materials from Erodium awns' dead tissues. The stimuli-responsive material isolated forms left-handed (L) or right-handed (R) helical birefringent transparent ribbons in the wet state that reversibly change to R helices when the material dries. The humidity-driven motion of dead tissues is most likely due to a composite material made of cellulose networks of fibrils imprinted by the plant at the nanoscale, which reinforces a soft wall polysaccharide matrix. The inversion of the handedness is explained using computational simulations considering filaments that contract and expand asymmetrically. The awns of Erodium are known to present hygroscopic movements, forming R helices in the dry state, but the possibility of actuating chirality via humidity suggests that these cellulose-based skeletons, which do not require complicated lithography and intricate deposition techniques, provide a diverse range of applications from intelligent textiles to micro-machines.

Pentacene Crystal Growth on Silica and Layer-Dependent Step-Edge Barrier from Atomistic Simulations.

Understanding and controlling the growth of organic crystals deposited from the vapor phase is important for fundamental materials science and necessary for applications in pharmaceutical and organic electronics industries. Here, this process is studied for the paradigmatic case of pentacene on silica by means of a specifically tailored computational approach inspired by the experimental vapor deposition process. This scheme is able to reproduce the early stages of the thin-film formation, characterized by a quasi layer-by-layer growth, thus showcasing its potential as a tool complementary to experimental techniques for investigating organic crystals. Crystalline islands of standing molecules are formed at a critical coverage, as a result of a collective reorientation of disordered aggregates of flat-lying molecules. The growth then proceeds by sequential attachment of molecules at the cluster and then terrace edges. Free-energy calculations allowed us to characterize the step-edge barrier for descending the terraces, a fundamental parameter for growth models for which only indirect experimental measurements are available. The barrier is found to be layer-dependent (approximately 1 kcal/mol for the first monolayer on silica, 2 kcal/mol for the second monolayer) and to extend over a distance comparable with the molecular length.

Chirality amplification by desymmetrization of chiral ligand-capped nanoparticles to nanorods quantified in soft condensed matter.

Induction, transmission, and manipulation of chirality in molecular systems are well known, widely applied concepts. However, our understanding of how chirality of nanoscale entities can be controlled, measured, and transmitted to the environment is considerably lacking behind. Future discoveries of dynamic assemblies engineered from chiral nanomaterials, with a specific focus on shape and size effects, require exact methods to assess transmission and amplification of nanoscale chirality through space. Here we present a remarkably powerful chirality amplification approach by desymmetrization of plasmonic nanoparticles to nanorods. When bound to gold nanorods, a one order of magnitude lower number of chiral molecules induces a tighter helical distortion in the surrounding liquid crystal-a remarkable amplification of chirality through space. The change in helical distortion is consistent with a quantification of the change in overall chirality of the chiral ligand decorated nanomaterials differing in shape and size as calculated from a suitable pseudoscalar chirality indicator.

Molecular organizations of conical mesogenic fullerenes.

We have studied liquid crystal phases formed by fullerenes functionalized with mesogenic groups yielding a cone-shaped molecular structure. We have modelled these shuttlecock-like molecules with a set of Gay-Berne particles grafted with flexible springs to a spherical core and we have studied, using Monte Carlo simulations, their phase organization, also with a view to examining their possible use as candidate organic photovoltaic materials. We have found that, upon cooling from the isotropic phase, the system forms a columnar phase, like in the experimental work of Kato and coworkers [T. Kato et al., Nature, 2002, 419, 702]. However the phase is made of polar stacks extending not more than about ten molecules, which could limit their usefulness in enhancing and directing charge transport for possible photovoltaic applications.

Can off-centre mesogen dipoles extend the biaxial nematic range?

We have investigated the possibility of extending the stability range of the biaxial nematic phase by adding an off-centre dipole of various strengths and orientations to elongated biaxial Gay-Berne (GB) mesogens yielding a relatively narrow biaxial nematic (Nbx) phase, and a smectic (Sbx) phase when dipole-less. The effect of dipoles is not easy to predict, and our previous investigations have shown the limited benefits of having a central dipole. Here we show, employing molecular dynamics (MD) simulations, that a not too strong off-centre dipole positioned along the longest axis of the nematogen can extend the temperature range of stability of the biaxial nematic phase, also shifting it towards lower temperatures.

Energetic fluctuations in amorphous semiconducting polymers: Impact on charge-carrier mobility.

We present a computational approach to model hole transport in an amorphous semiconducting fluorene-triphenylamine copolymer (TFB), which is based on the combination of molecular dynamics to predict the morphology of the oligomeric system and Kinetic Monte Carlo (KMC), parameterized with quantum chemistry calculations, to simulate hole transport. Carrying out a systematic comparison with available experimental results, we discuss the role that different transport parameters play in the KMC simulation and in particular the dynamic nature of positional and energetic disorder on the temperature and electric field dependence of charge mobility. It emerges that a semi-quantitative agreement with experiments is found only when the dynamic nature of the disorder is taken into account. This study establishes a clear link between microscopic quantities and macroscopic hole mobility for TFB and provides substantial evidence of the importance of incorporating fluctuations, at the molecular level, to obtain results that are in good agreement with temperature and electric field-dependent experimental mobilities. Our work makes a step forward towards the application of nanoscale theoretical schemes as a tool for predictive material screening.

Predicting the Conditions for Homeotropic Anchoring of Liquid Crystals at a Soft Surface. 4-n-Pentyl-4'-cyanobiphenyl on Alkylsilane Self-Assembled Monolayers.

We have studied, using atomistic molecular dynamics simulations, the alignment of the nematic liquid-crystal 4-n-pentyl-4'-cyanobiphenyl (5CB) on self-assembled monolayers (SAMs) formed from octadecyl- and/or hexyltrichlorosilane (OTS and HTS) attached to glassy silica. We find a planar alignment on OTS at full coverage and an intermediate situation at partial OTS coverage because of the penetration of 5CB molecules into the monolayer, which also removes the tilt of the OTS SAM. Binary mixtures of HTS and OTS SAMs instead induce homeotropic (i.e., perpendicular) alignment. A comparison with the existing experimental literature is provided.

Can multi-biaxial mesogenic mixtures favour biaxial nematics? A computer simulation study.

Extending the range of existence of biaxial nematic phases is key to their use in applications. Here, we have investigated using extensive molecular dynamics (MD) simulations of a coarse-grained model the possible advantages of using mesogenic mixtures. We have studied the phase organisation of five thermotropic mixtures of biaxial Gay-Berne (GB) ellipsoidal particles having the same volume, but different shapes and interactions, with aspect ratios ranging from rod-like to disc-like and, choosing fractional compositions so as to model a Gaussian dispersity of shapes. The parameterisation is based on a previous GB model with biaxialities of opposite sign for steric and attractive interactions which was shown to exhibit a stable biaxial nematic phase. We found that mixing different biaxial GB particles has an overall stabilising effect on the biaxial nematic phase with respect to temperature, layering and, to some extent also demixing. The mixtures show a decrease of ordering transition temperatures, a widening of nematic temperature ranges, and the formation of smectic phases at lower temperatures.

Wetting behaviour and contact angles anisotropy of nematic nanodroplets on flat surfaces.

We have studied the wetting behaviour of liquid crystal nanodroplets deposited on a planar surface, modelling the mesogens with Gay-Berne ellipsoids and the support surface with a slab of Lennard-Jones (LJ) spherical particles whose mesogen-surface affinity can be tuned. A crystalline and an amorphous planar surface, both showing planar anchoring, have been investigated: the first is the (001) facet of a LJ fcc crystal, the second is obtained from a disordered LJ glass. In both cases we find that the deposited nanodroplet is, in general, elongated and that the contact angle changes around its contour. Simulations for the crystalline substrate show that the angle of contact turns reversibly from anisotropic to isotropic when crossing the clearing transition. As far as we know this is a novel, not yet explored effect for thermotropic liquid crystals, that we hope will stimulate experimental investigations.

Doping liquid crystals with nanoparticles. A computer simulation of the effects of nanoparticle shape.

We have studied, using Monte Carlo computer simulations, the effects that nanoparticles of similar size and three different shapes (spherical, elongated and discotic) dispersed at different concentrations in a liquid crystal (LC), have on the transition temperature, order parameter and mobility of the suspension. We have modelled the nanoparticles as berry-like clusters of spherical Lennard-Jones sites and the NP with a Gay-Berne model. We find that the overall phase behaviour is not affected by the addition of small amounts (xN = 0.1-0.5%) of nanoparticles, with the lowest perturbation obtained with disc-like nanoparticles at the lowest concentration. We observe a general decrease of the clearing temperature and a reduction in the orientational order with a change in its temperature variation, particularly in the case of the xN = 0.5% dispersions and with a more pronounced effect when the nanoparticles are spherical.

Molecular organization in freely suspended nano-thick 8CB smectic films. An atomistic simulation.

We present an atomistic molecular dynamics simulation of freely suspended films of the smectic liquid crystal 8CB formed by nl = 2, 3,…,10, 20 theoretical monolayers, determining their orientational and positional order as a function of the film thickness. We find that films are always composed by bilayers of antiparallel molecules, and that in the case of odd nl, the system prefers to self-assemble in (nl + 1)/2 bilayers, with an increase of surface tension with respect to even nl samples. We also show that external layers have higher positional and orientational order, and that upon heating the disordering of the system proceeds from the inside, with the central layers progressively losing their smectic character, while the external ones are more resistant to temperature changes and keep the film from breaking.