Nematic order macroscopic

In the framework of irreversible thermodynamics (compare, for example, [31, 32]) the macroscopic variables of a system can be divided into those due to conservation laws (here mass density p, momentum density g = pv with the velocity field v and energy density e) and those reflecting a spontaneously broken continuous symmetry (here the layer displacement u characterizes the broken translational symmetry parallel to the layer normal). For a smectic A liquid crystal the director h of the underlying nematic order is assumed to be parallel to the layer normal p. So far, only in the vicinity of a nematic-smectic A phase transition has a finite angle between h and p been shown to be of physical interest [33],... 

Following the lines proposed above will give a prediction of the pattern formed above onset. For a transition from undulating lamellae to reorientated lamellae or to multilamellar vesicles, defects have to be created for topological reasons. Since the order parameter varies spatially in the vicinity of the defect core, a description of such a process must include the full (tensorial) nematic order parameter as macroscopic dynamic variables. 

Typical 23 Na NMR spectra recorded within dense Laponite dispersion are shown in Figure 2, clearly exhibiting a large residual quadrupolar splitting [9] fingerprint of the macroscopic nematic ordering of these dense Laponite dispersions (more than 23% w/w). The cancellation of this residual quadrupolar... 

As early as 1938, Langmuir observed the phase separation of clay suspensions into an isotropic phase and a birefringent gel at the macroscopic level in test-tubes [9]. However, in the same report, he noted that this property of phase separation was gradually lost with time, which he tentatively explained by the incorporation of impurities diffusing from the glass tubes. He also compared this system to normal liquid crystals. Later, in 1956, Emerson observed a banded texture similar to that displayed by the Tobacco Mosaic Virus [48]. The investigation of clay suspensions from the structural point of view has been recently resumed. However, the study of the nematic order of suspensions of montmorillonite clays is in fact complicated by their gel properties. In spite of sustained efforts to understand its nature, the gelation mechanism has not yet been fully elucidated [49]. 

The most important coupling to deformations of the network is the one that is linear in both the strain of the network and the nematic order parameter. As has been discussed earlier in this section this leads to the consequence that the strain tensor can be used as an order parameter for the nematic-isotropic transition in nematic sidechain elastomers, just as the dielectric or the diamagnetic tensor are used as macroscopic order parameters to characterize this phase transition in low molecular weight materials. But it has also been stressed that nonlinear elastic effects as well as nonlinear coupling terms between the nematic order parameter and the strain tensor must be taken into account as soon as effects that are nonlinear in the nematic order parameter are studied [4, 25]. So far, no deviation from classical mean field behavior concerning the critical exponents has been detected in the static properties of this transition and correspondingly there are no reports as yet discussing static critical fluctuations. 

Since there are very few dynamic experimental investigations of pretransitional effects [8], not much modeling has been reported to date either. Based on work for the macroscopic dynamics of the nematic-isotropic transition in sidechain polymers [27 -29], it has been suggested [28] that the non-meanfield exponent observed in dynamic stress-optical experiments [8] can be accounted for at least qualitatively by the mode-coupling model [28, 29]. Intuitively this qualitatively new dynamic behavior can be traced back to static nonlinear coupling terms between the nematic order parameter and the strain tensor. 

Ultrasonic experiments using laser induced phonon spectroscopy have been performed in a nematic liquid single crystal elastomer [48]. The experiments reveal a dispersion step for the speed of sound and a strong anisotropy for the acoustic attenuation constant in the investigated frequency range (100 MHz -1 GHz). These results are consistent with a description of LCEs using macroscopic dynamics [54-56] and reflect a coupling between elastic effects and the nematic order parameter as analyzed in detail previously [48]. 

The elastic theory has been derived for a macroscopic scale, larger than the coherence length of the nematic order (typically 5 nm, several times larger than the molecule length). One may ask whether this theory is suited to explain SFA experiments, typically dealing with a 10 nm thickness. 

Phases in thermodynamic systems are then macroscopic homogeneous parts with distinct physical properties. For example, densities of extensive thermodynamical variables, such as particle number N of the fth species, enthalpy U, volume V, entropy S, and possible order parameters, such as the nematic order parameter for a liquid crystalline polymer etc, differ in such coexisting phases. In equilibrium, intensive thermodynamic variables, namely T,p, and the chemical potentials pi have to be the same in all phases. Coexisting phases are separated by well-defined interfaces (the width and internal structure of such interfaces play an important role in the kinetics of the phase transformation (1) and in other... 

In the nematic phase, one can induce macroscopic orientation by controlling the surface boundary conditions. However, because nematic ordering is the result of a spontaneously broken symmetry, fluctuations of the director n are a soft mode. Indeed a macroscopically oriented nematic phase is much more turbid than a macro-scopically oriented smectic-A phase because of light scattering from orientational fluctuation domains. The layered structure of the smectic-A phase suppresses these orientational fluctuations, and it is this coupling that affects the character of the transition (see [5] for a broad survey of such phase transitions). However, smectic phases exhibit one-dimensional orientational order, characterized by the Landau-Peierls fluctuation of the layer spacing [6, 7]. As a result, the essential features needed to capture the NA transition are ... 

Other more exotic types of calamitic liquid crystal molecules include those having chiral components. This molecular modification leads to the formation of chiral nematic phases in which the director adopts a natural helical twist which may range from sub-micron to macroscopic length scales. Chirality coupled with smectic ordering may also lead to the formation of ferroelectric phases [20]. 

Figure 7.1 Illustration of different aggregation states obtained (from left to right) by increasing temperature crystal (K), smectic C (SmC), nematic (N) and isotropic (I). Row a shows macroscopic appearance of samples in row b, short-range microscopic ordering is represented (each bar represents a molecule) thermotropic phase diagram of row c illustrates relevant transition temperatures (Tm melting temperature Tsmc-N transition temperature between SmC and N Tc clearing temperature) row d shows different texture of different states as seen through polarizing microscope (with crossed polars, isotropic phase appears black).

---