Calculation of flexoelectric coefficients for a nematic liquid crystal by atomistic simulation

Molecular Simulation Approaches to the Study of Thermotropic and Lyotropic Liquid Crystals

Over the last decade, the availability of computer time, together with new algorithms capable of exploiting parallel computer architectures, has opened up many possibilities in molecularly modelling liquid crystalline systems. This perspective article points to recent progress in modelling both thermotropic and lyotropic systems. For thermotropic nematics, the advent of improved molecular force fields can provide predictions for nematic clearing temperatures within a 10 K range. Such studies also provide valuable insights into the structure of more complex phases, where molecular organisation may be challenging to probe experimentally. Developments in coarse-grained models for thermotropics are discussed in the context of understanding the complex interplay of molecular packing, microphase separation and local interactions, and in developing methods for the calculation of material properties for thermotropics. We discuss progress towards the calculation of elastic constants, rotational viscosity coefficients, flexoelectric coefficients and helical twisting powers. The article also covers developments in modelling micelles, conventional lyotropic phases, lyotropic phase diagrams, and chromonic liquid crystals. For the latter, atomistic simulations have been particularly productive in clarifying the nature of the self-assembled aggregates in dilute solution. The development of effective coarse-grained models for chromonics is discussed in detail, including models that have demonstrated the formation of the chromonic N and M phases.

Single molecule translocation in smectics illustrates the challenge for time-mapping in simulations on multiple scales

Understanding the connections between the characteristic dynamical time scales associated with a coarse-grained (CG) and a detailed representation is central to the applicability of the coarse-graining methods to understand molecular processes. The process of coarse graining leads to an accelerated dynamics, owing to the smoothening of the underlying free-energy landscapes. Often a single time-mapping factor is used to relate the time scales associated with the two representations. We critically examine this idea using a model system ideally suited for this purpose. Single molecular transport properties are studied via molecular dynamics simulations of the CG and atomistic representations of a liquid crystalline, azobenzene containing mesogen, simulated in the smectic and the isotropic phases. The out-of-plane dynamics in the smectic phase occurs via molecular hops from one smectic layer to the next. Hopping can occur via two mechanisms, with and without significant reorientation. The out-of-plane transport can be understood as a superposition of two (one associated with each mode of transport) independent continuous time random walks for which a single time-mapping factor would be rather inadequate. A comparison of the free-energy surfaces, relevant to the out-of-plane transport, qualitatively supports the above observations. Thus, this work underlines the need for building CG models that exhibit both structural and dynamical consistency to the underlying atomistic model.

Optimization of the GAFF force field to describe liquid crystal molecules: the path to a dramatic improvement in transition temperature predictions

Systematic optimization of the General Amber Force Field (GAFF) for mesogenic fragments leads to a dramatic improvement in the modelling of liquid crystal clearing points.

Two-beam energy exchange in a hybrid photorefractive-flexoelectric liquid-crystal cell

We develop a semiquantitative theory to describe the experimentally observed energy gain when two light beams intersect in hybrid organic-inorganic photorefractives. These systems consist of a nematic liquid-crystal (LC) layer placed between two photorefractive windows. A periodic space-charge field is induced by the interfering light beams in the photorefractive windows. The field penetrates into the LC, interacting with the nematic director and giving rise to a diffraction grating. LC flexoelectricity is the principal physical mechanism driving the grating structure. Each light beam diffracts from the induced grating, leading to an apparent energy gain and loss within each beam. The LC optics is described in the Bragg regime. In the theory the exponential gain coefficient is a product of a beam interference term, a flexoelectricity term and a space-charge term. The theory has been compared with results of an experimental study on hybrid cells filled with the LC mixture TL 205. Experimentally the energy gain is maximal at much lower grating wave numbers than is predicted by naïve theory. However, if the director reorientation is cubic rather than linear in the space-charge field term, then good agreement between theory and experiment can be achieved using only a single fitting parameter. We provide a semiquantitative argument to justify this nonlinearity in terms of electric-field-induced local phase separation between different components of the liquid crystal.

Classical simulations from the atomistic to the mesoscale and back: coarse graining an liquid crystal

We describe the development of a coarse grained model for molecular dynamics (MD) simulations of a liquid-crystalline (LC) compound with an azobenzene mesogen. It is investigated how coarse graining methods originally developed to simulate amorphous polymeric systems can be extended to liquid crystals. The coarse grained (CG) model is constructed in a way that it allows carrying over of chemical details (i.e. the form of specific/attractive interactions) from the atomistic to the CG level, devising a new route to construct mesoscale models for liquid crystals with a close link to chemically more realistic atomistic ones. In addition it is possible to switch between the atomistic and the CG levels of resolution on demand through an inverse mapping procedure. By this we obtain representative large-scale atomistic coordinates based on CG structures and long-time atomistic trajectories generated from CG mesoscale simulations.

Simulated anchoring of a nematic liquid crystal at a polymer surface

Liquid-crystal anchoring at a polymer surface arises from interactions at several different length scales. At the molecular level, a liquid-crystal molecule may tend to align with the substrate polymer chain, while at the nanometer length scale grooves can exist that arise from the periodic repeat structure of a polymer chain or from nanometer-scale undulations due to surface stresses. On a still longer scale there is the secondary effect of grooves or surface inhomogeneities. We have performed a total of more than 900 ns of atomistic molecular dynamics simulations in order to study the relative importance of the molecular-level interaction and the topography of the polymer surface in liquid-crystal anchoring. Substrates were constructed in which grooves were induced along a direction perpendicular to the constituent molecular chains. In the results presented for the case of 32 5CB molecules on a poly(vinyl alcohol) substrate, the liquid-crystal director orientation appeared to be determined principally by the substrate chain orientation. Only for the deepest grooves did the director align along the grooves and perpendicular to the substrate molecular chain direction.

Molecular orientational and dipolar correlation in the liquid crystal mixture E7: a molecular dynamics simulation study at a fully atomistic level

Molecular dynamics simulations are reported for the four component nematic liquid crystal mixture E7, which is used commercially. We are able to show the growth of a nematic phase directly from an isotropic liquid over a 100 ns period for an all-atom model, and study orientational and dipole order within the nematic phase. The simulations show that the cyanoterphenyl component of the mixture, 5CT, is more ordered than the three cyanobiphenyl components. The simulations show also that both parallel and anti-parallel dipole correlation take place in E7 but that the strong anti-parallel dipole correlation is localised to particular arrangements of molecules. It is possible to identify two key preferred configurations for molecular pairs in the fluid, which explain the form of the dipole correlation function, g(1)(r).

Atomistic simulations of a thermotropic biaxial liquid crystal

We have performed molecular dynamics simulations of a 2,5-bis-(p-hydroxyphenyl)-1,3,4-oxadiazole mesogen (ODBP-Ph-C(7)) at a fully atomistic level for a range of temperatures within the region that has experimentally been assigned to a biaxial nematic phase. Analysis of the data shows that the simulated nematic phase is biaxial but that the degree of biaxiality is small. The simulations show also the formation of ferroelectric domains in the nematic where the molecular short axis is aligned with the oxadiazole dipoles parallel to each other. Removal of electrostatic interactions leads to destabilization of ferroelectric domains and destabilization of the biaxiality. An additional simulation shows the slow growth of a mesophase directly from the isotropic fluid over a period of approximately 50 ns. This is the first time this has been achieved within the framework of an all-atom model.

Atomistic simulation of a model liquid crystal

We present atomistic molecular dynamics computer simulations of the bulk phases of a model liquid crystal system based on 8CB. The model differs from real 8CB because it employs a united-atom description to eliminate all hydrogen atoms, and neglects all long-range electrostatic interactions. Despite this simplification, the pressure-temperature phase diagram shows an order-disorder transition, in which isotropic, smectic, and nematiclike behaviors are observed. A detailed analysis of the inter- and intramolecular structures of the ordered phases is given, together with an examination of finite size effects and the equilibration times of the system. It is shown that, whereas a system may appear to be thermodynamically and mechanically equilibrated after a period of 10-15 ns, it is possible for an imprint of the starting configuration to persist for much longer time scales. In the present case, however, such an imprint does not appear to affect the observed phase behavior.

Dipolar interactions, molecular flexibility, and flexoelectricity in bent-core liquid crystals

The effects of dipolar interactions and molecular flexibility on the structure and phase behavior of bent-core molecular fluids are studied using Monte Carlo computer simulations. Some calculations of flexoelectric coefficients are also reported. The rigid cores of the model molecules consist of either five or seven soft spheres arranged in a "V" shape with external bend angle gamma. With purely repulsive sphere-sphere interactions and gamma = 0 degrees (linear molecules) the seven-sphere model exhibits isotropic, uniaxial nematic, and untilted and tilted smectic phases. With gamma > or = 20 degrees the untilted smectic phases disappear, while the system with gamma > or = 40 degrees shows a direct tilted smectic-isotropic fluid transition. The addition of electrostatic interactions between transverse dipole moments on the apical spheres is generally seen to reduce the degree of molecular inclination in tilted phases, and destabilizes the nematic and untilted smectic phases of linear molecules. The effects of adding three-segment flexible tails to the ends of five-sphere bent-core molecules are examined using configurational-bias Monte Carlo simulations. Only isotropic and smectic phases are observed. On the one hand, molecular flexibility gives rise to pronounced fluctuations in the smectic-layer structure, bringing the simulated system in better correspondence with real materials; on the other hand, the smectic phase shows almost no tilt. Lastly, the flexoelectric coefficients of various nematic phases--with and without attractive sphere-sphere interactions--are presented. The results are encouraging, but a large computational effort is required to evaluate the appropriate fluctuation relations reliably.