Dynamics nematics

The results and applications in Chapters 2 to 5 for nematic liquid crystals are given in fairly full mathematical detail. It has been my experience that the stumbling block for many people comes at the first attempts at the actual calculations here I will reveal many details and more explanation than is usually given in articles and common texts, in the hope that readers will gain confidence in how to apply the main results from continuum theory to practical problems. These Chapters contain extensive derivations of the static and dynamic nematic theory and applications. Chapter 6, on the other hand, does not give as many detailed computations as those presented in the earlier Chapters it is my intention that it introduces the reader to a continuum theory of smectic C liquid crystals and it is probably written more in the style of an introductory review. This is partly because some of the calculations are similar for both nematic and smectic C materials, but with different physical parameters and some different physical interpretations. However, despite some of these similarities, smectic liquid crystals have some uniquely different mathematical problems, and these can only be touched upon within the remit of a book such as this. 

Allen M P, Warren M A, Wilson M R, Sauron A and Wiliam S 1996 Molecular dynamics calculation of elastic constants in Gay-Berne nematic liquid crystals J. Chem. Phys. 105 2850-8... 

Continuum theory has also been applied to analyse tire dynamics of flow of nematics [77, 80, 81 and 82]. The equations provide tire time-dependent velocity, director and pressure fields. These can be detennined from equations for tire fluid acceleration (in tenns of tire total stress tensor split into reversible and viscous parts), tire rate of change of director in tenns of tire velocity gradients and tire molecular field and tire incompressibility condition [20]. 

Furtlier details can be found elsewhere [20, 78, 82 and 84]. An approach to tire dynamics of nematics based on analysis of microscopic correlation fimctions has also been presented [85]. Various combinations of elements of tire viscosity tensor of a nematic define tire so-called Leslie coefficients [20, 84]. 

Brochard F, Pieranski P and Guyon E 1972 Dynamics of the orientation of a nematic-liquid-crystal film in a variable magnetic field Phys.Rev.Lett 2S 1681-3... 

Pieranski P, Brochard F and Guyon E 1973 Static and dynamic behavior of a nematic liquid crystal in a magnetic field. Part II Dynamics J.Physique 34 35-48... 

Microfilaments and Microtubules. There are two important classes of fibers found in the cytoplasm of many plant and animal ceUs that are characterized by nematic-like organization. These are the microfilaments and microtubules which play a central role in the determination of ceU shape, either as the dynamic element in the contractile mechanism or as the basic cytoskeleton. Microfilaments are proteinaceous bundles having diameters of 6—10 nm that are chemically similar to actin and myosin muscle ceUs. Microtubules also are formed from globular elements, but consist of hoUow tubes that are about 30 nm in diameter, uniform, and highly rigid. Both of these assemblages are found beneath the ceU membrane in a linear organization that is similar to the nematic Hquid crystal stmcture. 

Bedford, A., Drumheller, D.S., and Sutherland, H.J., On Modeling the Dynamics of Composite Materials, in Mechanics Today, Vol. 3 (edited by Nemat-NAsser, S.), Pergamon Press, New York, 1976, pp. 1-54. 

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

New optical (static as well as dynamic) techiuques for the stndy of long-range order in stractured continna are begiiming to appear and can be used to understand the constitutive properties and relations in complex (polymeric, nematic, and other stmctured) fluids. 

This article reviews progress in the field of atomistic simulation of liquid crystal systems. The first part of the article provides an introduction to molecular force fields and the main simulation methods commonly used for liquid crystal systems molecular mechanics, Monte Carlo and molecular dynamics. The usefulness of these three techniques is highlighted and some of the problems associated with the use of these methods for modelling liquid crystals are discussed. The main section of the article reviews some of the recent science that has arisen out of the use of these modelling techniques. The importance of the nematic mean field and its influence on molecular structure is discussed. The preferred ordering of liquid crystal molecules at surfaces is examined, along with the results from simulation studies of bilayers and bulk liquid crystal phases. The article also discusses some of the limitations of current work and points to likely developments over the next few years. 

The rapid rise in computer speed over recent years has led to atom-based simulations of liquid crystals becoming an important new area of research. Molecular mechanics and Monte Carlo studies of isolated liquid crystal molecules are now routine. However, care must be taken to model properly the influence of a nematic mean field if information about molecular structure in a mesophase is required. The current state-of-the-art consists of studies of (in the order of) 100 molecules in the bulk, in contact with a surface, or in a bilayer in contact with a solvent. Current simulation times can extend to around 10 ns and are sufficient to observe the growth of mesophases from an isotropic liquid. The results from a number of studies look very promising, and a wealth of structural and dynamic data now exists for bulk phases, monolayers and bilayers. Continued development of force fields for liquid crystals will be particularly important in the next few years, and particular emphasis must be placed on the development of all-atom force fields that are able to reproduce liquid phase densities for small molecules. Without these it will be difficult to obtain accurate phase transition temperatures. It will also be necessary to extend atomistic models to several thousand molecules to remove major system size effects which are present in all current work. This will be greatly facilitated by modern parallel simulation methods that allow molecular dynamics simulations to be carried out in parallel on multi-processor systems [115]. 

Berry, G.C. Static and Dynamic Light Scattering on Moderately Concentraded Solutions Isotropic Solutions of Flexible and Rodlike Chains and Nematic Solutions of Rodlike Chains. VoL 114, pp, 233-290. 

The SD is a phase separation process usually occurring in systems consisting of more than two components such as in solutions or blends. However, in the present case the system employed is composed of one component of pure PET. In this case, what triggers such an SD type phase separation Doi et al. [24, 25] proposed a dynamic theory for the isotropic-nematic phase transition for liquid crystalline polymers in which they showed that the orientation process... 

Thermotropic cholesterics have several practical applications, some of which are very widespread. Most of the liquid crystal displays produced use either the twisted nematic (see Figure 7.3) or the supertwisted nematic electrooptical effects.6 The liquid crystal materials used in these cells contain a chiral component (effectively a cholesteric phase) which determines the twisting direction. Cholesteric LCs can also be used for storage displays utilizing the dynamic scattering mode.7 Short-pitch cholesterics with temperature-dependent selective reflection in the visible region show different colors at different temperatures and are used for popular digital thermometers.8... 

When r s, one has interconversion between operators Br and Bs, and Rrs is a cross-relaxation rate. Note that the cross-relaxation may or may not contain interference effects depending on the indices l and /, which keep track of interactions Cyj and C,. Cross-correlation rates and cross-relaxation rates have not been fully utilized in LC. However, there is a recent report41 on this subject using both the 13C chemical shielding anisotropy and C-H dipolar coupling relaxation mechanisms to study a nematic, and this may be a fruitful arena in gaining dynamic information for LC. We summarize below some well known (auto-)relaxation rates for various spin interactions commonly encountered in LC studies. 

NMR spectra and Tj measurements at different temperatures. The local polymer chain motion varies over a frequency range of 104-106 Hz in the nematic phase. The activation energy of this motion is found to increase with decreasing number ( ) of methylene units in the spacer, and exhibits odd-even fluctuations. In a study of a homologous series of main-chain LC polyesters, 13C CP/MAS and variable-temperature experiments reveal a conformation-ally more homogeneous and a less dynamic nature for the even-chained than for the odd-chained polymer structures.300... 

Lyotropic polymeric LC, formed by dissolving two aromatic polyamides in concentrated sulphuric acid, have been studied using variable-director 13C NMR experiments.324 The experimental line shapes at different angles w.r.t the external field were used to extract macromolecular order and dynamic in these ordered fluids. An interesting application of lyotropic LC is for the chiral discrimination of R- and S-enantiomers, and has recently been demonstrated by Courtieu and co-workers.325 The idea was to include a chiral compound 1-deutero-l-phenylethanol in a chiral cage (e.g., /1-cyclodextrin) which was dissolved and oriented by the nematic mean field in a cromolyn-water system. Proton-decoupled 2H NMR spectrum clearly showed the quad-rupolar splittings of the R- and S-enantiomers. The technique is applicable to water-soluble solutes. 

MSA. Static and dynamic scattering are reported on a nematic phase with a smooth texture, and the... 

Six viscosity coefficients required for a description of the dynamics of an incompressible, nematic liquid crystal. 

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