Physical Review B

Over the 100 years since its discovery, liquid crystals have been the intriguing subject for both academia and industries. The textbook of de Gennes The Physics of Liquid Crystals published in 1974 is still the bible for many LC researchers, but new subjects unmentioned in the book have also risen for these years. This chapter describes the story of the recent developments and the future perspectives in physics of liquid crystals, especially focusing on the contributions by Japanese research groups for the last decade.

Physics of Liquid Crystals

인공고관절의 세라믹 볼 헤드의 기계적 안정성 평가를 위한 3 차원 유한요소 해석

With its roots in kinetic theory and the cellular automaton concept, the lattice-Boltzmann (LB) equation can be used to obtain continuum flow quantities from simple and local update rules based on particle interactions. The simplicity of formulation and its versatility explain the rapid expansion of the LB method to applications in complex and multiscale flows. We review many significant developments over the past decade with specific examples. Some of the most active developments include the entropic LB method and the application of the LB method to turbulent flow, multiphase flow, and deformable particle and fiber suspensions. Hybrid methods based on the combination of the Eulerian lattice with a Lagrangian grid system for the simulation of moving deformable boundaries show promise for more efficient applications to a broader class of problems. We also discuss higherorder boundary conditions and the simulation of microchannel flow with finite Knudsen number. Additionally, the remarkable scalability of the LB method for parallel processing is shown with examples. Teraflop simulations with the LB method are routine, and there is no doubt that this method will be one of the first candidates for petaflop computational fluid dynamics in the near future.

Lattice-Boltzmann Method for Complex Flows

Recent developments in density functional theory (DFT) methods applicable to studies of large periodic systems are outlined. During the past three decades, DFT has become an essential part of computational materials science, addressing problems in materials design and processing. The theory allows us to interpret experimental data and to generate property data (such as binding energies of molecules on surfaces) for known materials, and also serves as an aid in the search for and design of novel materials and processes. A number of algorithmic implementations are currently being used, including ultrasoft pseudopotentials, efficient iterative schemes for solving the one-electron DFT equations, and computationally efficient codes for massively parallel computers. The first part of this article provides an overview of plane-wave pseudopotential DFT methods. Their capabilities are subsequently illustrated by examples including the prediction of crystal structures, the study of the compressibility of minerals, and applications to pressure-induced phase transitions. Future theoretical and computational developments are expected to lead to improved accuracy and to treatment of larger systems with a higher computational efficiency. c 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 895-910, 2000

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Electronic structure, properties, and phase stability of inorganic crystals: A pseudopotential plane-wave study

A review is presented of molecular and mesoscopic computer simulations of liquid crystalline systems. Molecular simulation approaches applied to such systems are described, and the key findings for bulk phase behaviour are reported. Following this, recently developed lattice Boltzmann approaches to the mesoscale modelling of nemato-dynamics are reviewed. This paper concludes with a discussion of possible areas for future development in this field.

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Computer simulation of liquid crystals

In this paper, we report a generalized form for the range parameter governing the pair interaction between soft ellipsoidal particles. For nonequivalent uniaxial particles, we extend the Berne-Pechukas Gaussian overlap formalism to obtain an explicit expression for this range parameter. We confirm that this result is identical to that given by an approach that is not widely recognized, based on an approximation to the Perram-Wertheim hard-ellipsoid contact function. We further illustrate the power of the latter route by using it to write down the range parameter for the interaction between two nonequivalent biaxial particles. An explicit interaction potential for nonequivalent uniaxial particles is obtained by importing the uniaxial range parameter result into the standard Gay-Berne form. A parametrization of this potential is investigated for a rod-disk interaction.

Extension and generalization of the Gay-Berne potential

A three-dimensional lattice spring model of a heterogeneous material is presented. For small deformations, the model is shown to recover the governing equations for an isotropic elastic medium. The model gives reasonable agreement with theoretical predictions for the elastic fields generated by a spherical inclusion, although for small particle sizes the discretization of the underlying lattice causes some departures from the predicted values. Plasticity is introduced by decreasing the elastic moduli locally whilst maintaining stress continuity. Results are presented for a spherical inclusion in a plastic matrix and are found to be in good agreement with the predictions of Wilner (1988 J. Mech. Phys. Solids 36 141-65).

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A lattice spring model of heterogeneous materials with plasticity

Liquid crystals in complex geometries formed by polymer and porous networks

In this paper we present results from molecular dynamics simulations performed using a system of Gay-Berne particles confined between two substrates in a slab geometry. We use a nonseparable anisotropic molecule-substrate interaction potential and investigate weak and moderate molecule-substrate coupling strengths. We find that for both coupling strengths a well-defined, tilted molecular layer forms at each wall and that the pretilt angle and layer density are only weakly dependent on temperature as the central region is cooled through isotropiclike and nematiclike regions. The orientationally ordered fluid formed at the center of the film is tilted in sympathy with the surface layers. At low temperatures, however, where the central region adopts a layered arrangement, a sharp change is observed in the pretilt angle. This transition is more marked in the weak-coupling system where the high-temperature tilted surface layers adopt an approximately planar arrangement at low temperatures and the system resembles a bookshelf-geometry smectic film. In the moderate-coupling system, the surface layers maintain some tilt in the presence of the layered central region, leading to a smectic-stripe phase arrangement.

Douglas J. Cleaver

Papers

Computer simulation of liquid crystals

Extension and generalization of the Gay-Berne potential

A lattice spring model of heterogeneous materials with plasticity

Liquid crystals in complex geometries formed by polymer and porous networks

Computer simulation studies of confined liquid-crystal films