Simulating the Lyotropic Phase Behavior of a Partially Self-Complementary DNA Tetramer.

DNA oligomers in solution have been found to develop liquid crystal phases via a hierarchical process that involves Watson-Crick base pairing, supramolecular assembly into columns of duplexes, and long-range ordering. The multiscale nature of this phenomenon makes it difficult to quantitatively describe and assess the importance of the various contributions, particularly for very short strands. We performed molecular dynamics simulations based on the coarse-grained oxDNA model, aiming to depict all of the assembly processes involved and the phase behavior of solutions of the DNA GCCG tetramers. We find good quantitative matching to experimental data at both levels of molecular association (thermal melting) and collective ordering (phase diagram). We characterize the isotropic state and the low-density nematic and high-density columnar liquid crystal phases in terms of molecular order, size of aggregates, and structure, together with their effects on diffusivity processes. We observe a cooperative aggregation mechanism in which the formation of dimers is less thermodynamically favored than the formation of longer aggregates.

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'.

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.

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.

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.

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.

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.

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.

On the field-induced switching of molecular organization in a biaxial nematic cell and its relaxation.

We investigate the switching of a biaxial nematic filling a flat cell with planar homogeneous anchoring using a coarse-grained molecular dynamics simulation. We have found that an aligning field applied across the film, and acting on specific molecular axes, can drive the reorientation of the secondary biaxial director up to one order of magnitude faster than that for the principal director. While the π/2 switching of the secondary director does not affect the alignment of the long molecular axes, the field-driven reorientation of the principal director proceeds via a concerted rotation of the long and transversal molecular axes. More importantly, while upon switching off a (relatively) weak or intermediate field, the biaxial nematic liquid crystal is always able to relax to the initial surface aligned director state; this is not the case when using fields above a certain threshold. In that case, while the secondary director always recovers the initial state, the principal one remains, occasionally, trapped in a nonuniform director state due to the formation of domain walls.

Communication: molecular dynamics and (1)H NMR of n-hexane in liquid crystals.

The NMR spectrum of n-hexane orientationally ordered in the nematic liquid crystal ZLI-1132 is analysed using covariance matrix adaptation evolution strategy (CMA-ES). The spectrum contains over 150 000 transitions, with many sharp features appearing above a broad, underlying background signal that results from the plethora of overlapping transitions from the n-hexane as well as from the liquid crystal. The CMA-ES requires initial search ranges for NMR spectral parameters, notably the direct dipolar couplings. Several sets of such ranges were utilized, including three from MD simulations and others from the modified chord model that is specifically designed to predict hydrocarbon-chain dipolar couplings. In the end, only inaccurate dipolar couplings from an earlier study utilizing proton-proton double quantum 2D-NMR techniques on partially deuterated n-hexane provided the necessary estimates. The precise set of dipolar couplings obtained can now be used to investigate conformational averaging of n-hexane in a nematic environment.

Molecular simulations elucidate electric field actuation in swollen liquid crystal elastomers.

Swollen elastomer liquid crystals undergo significant deformations by application of an electric field perpendicular to their alignment axis, as shown in experiments by Urayama et al. [Urayama K, Honda S, Takigawa T (2006) Macromolecules 39:1943-1949]. Here we clarify this surprising effect at the molecular level using large-scale Monte Carlo simulations of an off-lattice model based on a soft Gay-Berne potential. We provide the internal change of molecular organization, as well as the key observables during the actuation cycle.

Charge dissociation at interfaces between discotic liquid crystals: the surprising role of column mismatch.

The semiconducting and self-assembling properties of columnar discotic liquid crystals have stimulated intense research toward their application in organic solar cells, although with a rather disappointing outcome to date in terms of efficiencies. These failures call for a rational strategy to choose those molecular design features (e.g., lattice parameter, length and nature of peripheral chains) that could optimize solar cell performance. With this purpose, in this work we address for the first time the construction of a realistic planar heterojunction between a columnar donor and acceptor as well as a quantitative measurement of charge separation and recombination rates using state of the art computational techniques. In particular, choosing as a case study the interface between a perylene donor and a benzoperylene diimide acceptor, we attempt to answer the largely overlooked question of whether having well-matching donor and acceptor columns at the interface is really beneficial for optimal charge separation. Surprisingly, it turns out that achieving a system with contiguous columns is detrimental to the solar cell efficiency and that engineering the mismatch is the key to optimal performance.

Supramolecular organization of functional organic materials in the bulk and at organic/organic interfaces: a modeling and computer simulation approach.

The molecular organization of functional organic materials is one of the research areas where the combination of theoretical modeling and experimental determinations is most fruitful. Here we present a brief summary of the simulation approaches used to investigate the inner structure of organic materials with semiconducting behavior, paying special attention to applications in organic photovoltaics and clarifying the often obscure jargon hindering the access of newcomers to the literature of the field. Special attention is paid to the choice of the computational "engine" (Monte Carlo or Molecular Dynamics) used to generate equilibrium configurations of the molecular system under investigation and, more importantly, to the choice of the chemical details in describing the molecular interactions. Recent literature dealing with the simulation of organic semiconductors is critically reviewed in order of increasing complexity of the system studied, from low molecular weight molecules to semiflexible polymers, including the challenging problem of determining the morphology of heterojunctions between two different materials.

Quinquephenyl: the simplest rigid-rod-like nematic liquid crystal, or is it? An atomistic simulation.

We have performed an atomistic molecular-dynamics study on the molecular organization and liquid-crystalline properties of quinquephenyl (P5), a prototypical mesogen that is of interest for organic electronics. The thermotropic behavior reveals different mesophases. When cooling down from the isotropic phase, a transition to nematic (≈715 K) is found, then a smectic SA (≈657 K) and another smectic, SXA (≈642 K), before a crystalline phase is recovered (≈617 K). This phase sequence is compared with experimental findings. The different phases are described in terms of their molecular organization, orientational and positional order parameters, and pair distribution functions, as well as of their dynamics properties. In particular, the smectic phases that have not yet been characterized experimentally are discussed. By analyzing the effective shape of P5, it is concluded that its internal torsions and bending make it less rigid than could be expected.

Order and conformation of biphenyl in cyanobiphenyl liquid crystals: a combined atomistic molecular dynamics and 1H NMR study.

The alignment of biphenyl (2P) in the liquid-crystal phases of 4-n-pentyl-4'-cyanobiphenyl (5CB) and 4-n-octyl-4'-cyanobiphenyl (8CB) is investigated by using a combination of predictive atomistic molecular dynamics (MD) simulations and (1)H liquid-crystal nuclear magnetic resonance (LXNMR) residual dipolar coupling measurements. A detailed comparison and validation of the MD results with LXNMR is provided, showing a good agreement between the simulated and experimental dipolar couplings at the same reduced temperature. MD is then used to examine the location of 2P in the smectic phase, which is unavailable to LXNMR, and 2P is found to be rather uniformly distributed. The combination of MD and NMR spectroscopy provides detailed information about the order, interconnection between orientation and conformation, local positional order, and interactions with the liquid-crystalline solvent.

Point and line defects in checkerboard patterned hybrid nematic films: A computer simulation investigation.

We consider a nematic liquid crystal film confined to a flat cell with homeotropic and planar patterned hybrid anchoring and show, using Monte Carlo simulations, the possibility of the system to stabilize line and point defects. The planar anchoring surface is patterned with a chessboardlike grid of squares with alternating random or parallel homogeneous planar anchoring. The simulations show only line defects when the individual domains are small enough, but also point defects when the domain size is significantly larger than the sample thickness. In the latter case, defect lines are not observed in domains with random surface anchoring, although lines and points are connected by a thick line which separates two regions with different director tilts. Increasing the anchoring strength, the defect lines appear a few layers above the surface, with the two ends just above the randomly oriented domains.