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 T_NI, 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 T_NI, 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.

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.

Influence of boundary conditions on the order and defects of biaxial nematic droplets

We employ Monte Carlo simulations to study the defects occurring in a nematic droplet formed by biaxial molecules. The simulations are carried out using a lattice model based on a dispersive orientational biaxial potential previously employed to establish the rich phase diagram of the system. The focus of the present investigation is on the molecular organization inside the droplet when bipolar and toroidal anchoring conditions at the surface are considered. In both cases, we describe how the defect structure arises in the system, and we analyze the behavior of the defect core region in connection with the elastic properties of the phase in a continuum theory perspective.

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 (N_bx) phase, and a smectic (S_bx) 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.

On the Defect Structure of Biaxial Nematic Droplets

We present a detailed Monte Carlo study of the effects of molecular biaxiality on the defect created at the centre of a nematic droplet with radial anchoring at the surface. We have studied a lattice model based on a dispersive potential for biaxial mesogens [Luckhurst et al., Mol. Phys. 30, 1345 (1975)] to investigate how increasing the biaxiality influences the molecular organisation inside the confined system. The results are compared with those obtained from a continuum theory approach. We find from both approaches that the defect core size increases by increasing the molecular biaxiality, hinting at a non universal behaviour previously not reported.

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.

Rotational diffusion of shape switching particles in nematic liquid crystals

The theory of rotational diffusion of particles of various symmetry embedded in a liquid crystal host, essential to interpret a variety of spectroscopic observables, has been available for some time, but only for the case of rigid molecules. Here we generalize the treatment and present a theory to describe the rotational diffusion of shape-changing particles dispersed in nematic liquid crystals. The interaction of the particles with the environment is modeled by an effective field potential, while the particles are allowed to assume an arbitrary discrete number of shapes. The transition between shapes is modeled by a Markovian process which is combined with rotational diffusion. Our model is applied to the simple case of a particle that can exchange between three shapes: a rod, a disk, and a sphere. We consider in detail the effect of shape transitions in some selected correlation functions which are relevant for experiments.

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

A mixture of mesogens with different anisotropies favours the biaxial nematic phase.

Molecular Dynamics Simulations and their Application to Thin-film Devices

The performance of devices based on organic semiconductors strongly depends on the molecular organisation in thin films. Due to the intrinsic complexity of these systems, a combination of theoretical modelling and experimental techniques is often the key to achieve a full understanding of their inner working. Here, we introduce the modelling of organic semiconductors by means of molecular dynamics simulations. We describe the basic theoretical framework of the technique and review the most popular class of force fields used to model organic materials, paying particular attention to the peculiarities of confined systems like nano-thick films. Representative studies of the organisation of organic functional materials in thin film phases are also reviewed.

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

Molecular-scale Monte Carlo simulations of liquid crystal-nanoparticle dispersions show the effect on the orientational order and on the clearing temperature of shape and concentration of the dopant nanoparticles.

Molecular dynamics of anhydrous glycolipid self-assembly in lamellar and hexagonal phases

The molecular dynamics of a synthetic branched chain glycolipid, 2-decyl-tetradecyl-β-d-maltoside (C_14-10G₂), in smectic and columnar liquid crystal phases.

Nematic liquid crystals in planar and cylindrical hybrid cells: Role of elastic anisotropy on the director deformations

Nematic samples filling a flat cell or the annular region between two concentric cylinders with hybrid anchoring conditions at the boundaries are investigated by setting up and minimizing their Frank elastic free energy. The coupling with the surfaces is taken to be strong on one side and weak on the other. The equations are numerically solved and the conditions for which the molecular organization inside the cell becomes uniform are analyzed. The classical calculation performed by G. Barbero and R. Barberi [J. Phys. 44, 609 (1983)] is reproduced and investigated from a different point of view, in order to compare the results of planar and cylindrical geometries. The results suggest that the cylindrical cell presents some unusual features deserving a more complete investigation. Although most part of the transitional phenomena are found for K(11)>K(33), a case not common for ordinary (lyotropic and thermotropic) liquid crystals, it is possible to find a completely uniform cell even for K(11)<K(33) in both the geometries considered here.

Molecular organization of nematic liquid crystals between concentric cylinders: role of the elastic anisotropy

The orientational order in a nematic liquid crystal sample confined to an annular region between two concentric cylinders is investigated by means of lattice Monte Carlo simulations. Strong anchoring and homeotropic orientations, parallel to the radial direction, are implemented at the confining surfaces. The elastic anisotropy is taken into account in the bulk interactions by using the pair potential introduced by Gruhn and Hess [T. Gruhn and S. Hess, Z. Naturforsch. A 51, 1 (1996)] and parametrized by Romano and Luckhurst [S. Romano, Int. J. Mod. Phys. B 12, 2305 (1998); Phys. Lett. A 302, 203 (2002); G. R. Luckhurst and S. Romano, Liq. Cryst. 26, 871 (1999)], i.e., the so-called GHRL potential. In the case of equal elastic constants, a small but appreciable deformation along the cylinder axis direction is observed, whereas when the values of K(11)/K(33) if K(22)=K(33) are low enough, all the spins in the bulk follow the orientation imposed by the surfaces. For larger values of K(11)/K(33), spontaneous deformations, perpendicular to the polar plane, increase significantly. Our findings indicate that the onset of these deformations also depends on the ratio K(22)/K(33) and on the radius of the cylindrical surfaces. Although expected from the elastic theory, no tangential component of the deformations was observed in the simulations for the set of parameters analyzed.

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

Atomistic simulations of nano-thick free 8CB smectic films show the change of order across the film with temperature and thickness.

Multiscale modeling of the electrostatic impact of self-assembled monolayers used as gate dielectric treatment in organic thin-film transistors

This study sheds light on the microscopic mechanisms by which self-assembled monolayers (SAMs) determine the onset voltage in organic thin-film transistors (OTFTs). Experiments and modeling are combined to investigate the self-assembly and electrostatic interaction processes in prototypical OTFT structures (SiO2/SAM/pentacene), where alkylated and fluoroalkylated silane SAMs are compared. The results highlight the coverage-dependent impact of the SAM on the density of semiconductor states and enable the rationalization and the control of the OTFT characteristics.

Predicting the anchoring of liquid crystals at a solid surface: 5-cyanobiphenyl on cristobalite and glassy silica surfaces of increasing roughness

We employ atomistic molecular dynamics simulations to predict the alignment and anchoring strength of a typical nematic liquid crystal, 4-n-pentyl-4'-cyano biphenyl (5CB), on different forms of silica. In particular, we study a thin (~20 nm) film of 5CB supported on surfaces of crystalline (cristobalite) and amorphous silica of different roughness. We find that the orientational order at the surface and the anchoring strength depend on the morphology of the silica surface and its roughness. Cristobalite yields a uniform planar orientation and increases the order at the surface with respect to the bulk whereas amorphous glass has a disordering effect. Despite the low order at the amorphous surfaces, a planar orientation is established with a persistence length into the film higher than the one obtained for cristobalite.

Exploring the energy landscape of the charge transport levels in organic semiconductors at the molecular scale

The extraordinary semiconducting properties of conjugated organic materials continue to attract attention across disciplines including materials science, engineering, chemistry, and physics, particularly with application to organic electronics. Such materials are used as active components in light-emitting diodes, field-effect transistors, or photovoltaic cells, as a substitute for (mostly Si-based) inorganic semiconducting materials. Many strategies developed for inorganic semiconductor device building (doping, p-n junctions, etc.) have been attempted, often successfully, with organics, even though the key electronic and photophysical properties of organic thin films are fundamentally different from those of their bulk inorganic counterparts. In particular, organic materials consist of individual units (molecules or conjugated segments) that are coupled by weak intermolecular forces. The flexibility of organic synthesis has allowed the development of more efficient opto-electronic devices including impressive improvements in quantum yields for charge generation in organic solar cells and in light emission in electroluminescent displays. Nonetheless, a number of fundamental questions regarding the working principles of these devices remain that preclude their full optimization. For example, the role of intermolecular interactions in driving the geometric and electronic structures of solid-state conjugated materials, though ubiquitous in organic electronic devices, has long been overlooked, especially when it comes to these interfaces with other (in)organic materials or metals. Because they are soft and in most cases disordered, conjugated organic materials support localized electrons or holes associated with local geometric distortions, also known as polarons, as primary charge carriers. The spatial localization of excess charges in organics together with low dielectric constant (ε) entails very large electrostatic effects. It is therefore not obvious how these strongly interacting electron-hole pairs can potentially escape from their Coulomb well, a process that is at the heart of photoconversion or molecular doping. Yet they do, with near-quantitative yield in some cases. Limited screening by the low dielectric medium in organic materials leads to subtle static and dynamic electronic polarization effects that strongly impact the energy landscape for charges, which offers a rationale for this apparent inconsistency. In this Account, we use different theoretical approaches to predict the energy landscape of charge carriers at the molecular level and review a few case studies highlighting the role of electrostatic interactions in conjugated organic molecules. We describe the pros and cons of different theoretical approaches that provide access to the energy landscape defining the motion of charge carriers. We illustrate the applications of these approaches through selected examples involving OFETs, OLEDs, and solar cells. The three selected examples collectively show that energetic disorder governs device performances and highlights the relevance of theoretical tools to probe energy landscapes in molecular assemblies.

Computer simulations of the ordering in a hybrid cylindrical film of nematic liquid crystals

We present an investigation of the ordering in a nematic liquid-crystal film confined between two cylindrical surfaces with antagonistic (radial and planar) anchoring alignments. A Monte Carlo study of a Lebwohl-Lasher model with suitable boundary conditions has been performed to calculate the ordering and the molecular organization for different film thicknesses. The simulation results are compared with some theoretical predictions obtained with the elastic continuum approach. The agreement between theory and simulation is improved as the thickness decreases.