Dynamics of Liquid Crystals

R. W. Pastor. Techniques and applications of Langevin dynamics simulations. In G. R. Luckhurst and C. A. Veracini, editors. The Molecular Dynamics of Liquid Crystals, pages 85-138. Kluwer Academic, Dordrecht, The Netherlands, 1994. 

Zannoni C (1994) In Luckhurst GR, Veracini CA (eds) Molecular dynamics of liquid crystals, chap 2. Kluwer, Dordrecht... 

The advent of the FFC instruments has opened a number of important application areas (molecular dynamics of liquid crystals, paramagnetic contrast MRI agents, proteins, polymers, etc.) and has thus provided a powerful impulse for further development of variable-field NMR relaxometry. Since 1996, Stelar entered the field and, building on the Noack-Schweikert technology (67), started producing the first commercial FFC NMR relaxometers. The availability of such instruments has further enhanced the drive towards new applications, apart from confirming the enormous potential of the technique as a primary tool for the study of molecular dynamics of even quite complex systems. 

The final chapter on applications of optical rheometric methods brings together examples of their use to solve a wide variety of physical problems. A partial list includes the use of birefringence to measure spatially resolved stress fields in non-Newtonian flows, the isolation of component dynamics in polymer/polymer blends using spectroscopic methods, the measurement of the structure factor in systems subject to field-induced phase separation, the measurement of structure in dense colloidal dispersions, and the dynamics of liquid crystals under flow. 

G. R. Luckhurst, C. A. Veracini, NATO, The molecular dynamics of liquid crystals (Kluwer Academic Publishers, Dordrecht Boston, 1994). 

S. Sarman, Nonequilibrium Molecular Dynamics of Liquid Crystal Shear Flow, J. Chem. Phys. 103 (1995) 10378. 

Kitzerow et al. in 1993 formed blue phases of polymeric liquid crystal monomers and polymerized these monomers while maintaining the blue-phase structure, leading to a solid resin of fixed blue-phase structure [22]. Such a substance, although maintaining the blue-phase structure, provided none of the dynamics of liquid crystal, since all the constituent molecules were polymerized. 

Yusuf Y, Ono Y, Sumisaki Y, Cladis PE, Brand HR, Finkelmann H, Kai S. 2004b. Swelling dynamics of liquid crystal elastomers swollen with low molecular weight liquid crystals. Phys Rev E 69 021710. 

The chapters of this book expand on the ideas mentioned here, as well as others that have arisen from the efforts of many talented scientists studying this rather unusual phenomenon over the past 40 years. To get the most out of this book, the reader should be familiar with the basics of liquid crystal phenomenology, including molecular structure, phases, textures, and typical sample geometries, as well as theoretical concepts, including curvature elasticity theory and some elements of the fluid dynamics of liquid crystals. 

Information about the dynamics of liquid crystals in a planar cell after applying an electric field can be obtained from the measured phase difference 5. These experiments were described elsewhere Using the relation ... 

Kats, E.I., Lebedev, V.V. Fluctuation effects in the Dynamics of Liquid Crystals. Springer-Verlag, New York (1993)... 

We shall discuss here the macroscopic dynamics of liquid crystals that is an area of hydrodynamics or macroscopic properties related to elasticity and viscosity. With respect to the molecular dynamics, which deals, for example, with NMR, molecular diffusion or dipolar relaxation of molecules, the area of hydrodynamics is a long scale, both in space and time. The molecular dynamics deals with distances of about molecular size, a 10 A, i.e., with wavevectors about 10 cm , however, in the vicinity of phase transitions, due to critical behaviour, characteristic lengths of short-range correlations can be one or two orders of magnitude larger. Therefore, as a limit of the hydrodynamic approach we may safely take the range of wavevectors q 10 cm and corresponding frequencies (O c q 10 - 10 = 10"s (c is sound velocity). 

This torque plays an important role in the dynamics of liquid crystals. A non-uniform translational motion will cause the liquid crystal to rotate. 

Figure 8.7 shows the electrode configuration of the IPS mode under study. The electrode gap is ( 10 pm) and width co ( 5 pm). When backflow and inertial effects are ignored, the dynamics of liquid crystal director rotation is described by the following Erickson-Leslie equation [4,9] ... 

Luckhurst, G.R. (ed) (1994) The Molecular Dynamics of Liquid Crystals (Dordrecht Kluwer Academic). 

Fluctuational Effects in the Dynamics of Liquid Crystals E.I. Kats and V.V. Lebedev... 

Another way to detect slow motions is by deuteron transverse spin relaxation experiments using a modified Carr-Purcell-Meiboom-Gill spin echo pulse sequence [42-44]. Information about the dynamics of liquid crystals can be retrieved from the frequency dispersion (see Fig. 2) and the anisotropy of relaxation rates. 

An example of typical ESR spectra, measured in the first derivative mode, is shown in Fig. 12. Just like NMR, ESR can be used to detect phase transitions and to study the orientation and dynamics of liquid crystals. The spectra shown in Fig. 12, for example, are from a study comparing the dynamics of the spin label at the end of the polymer chain and the freely dissolved spin probe in a liquid-crystalline polyether by continuous wave ESR (Fig. 12) and 2D Fourier transform ESR experiments [137]. The end label showed smaller ordering and larger reorientational rates than the dissolved spin probe. Furthermore, it was demonstrated that the advanced 2D FT ESR experiments (see below) on the end-labeled polymer chain could not be explained by the conventional Brownian model of reorientation, although this model could explain the ID spectra. This led to the development of a new motional model of a slowly relaxing local structure, which enabled differentiation between the local internal modes experienced by the end label and the collective reorganization of the polymer molecules around the label. The latter was shown to be slower by two orders of magnitude. 

The theory of neutron scattering has been explained in several good text books [1-3]. The aim of this introduction is to emphasize the features that distinguish neutron scattering from X-ray diffraction, and allow information on the structure and dynamics of liquid crystals to be determined. Generally, such information is not available from other scattering or spectroscopic techniques. 

The following points indicate why neutron scattering provides information on the structure and dynamics of liquid crystals that is not available by other methods ... 

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