Local optical anisotropy

The basis of the majority of specific liquid crystal electrooptical effects is found in the reorientation of the director (the axis of preferred orientation of the molecules) in the macroscopic volume of the material under the influence of an externally applied field or the fiow of the liquid. Anisotropy of the electrical properties of the medium (of the dielectric susceptibility and the electrical conductivity) is the origin for reorientation, whereas the dynamics of the process also depend on the viscoelastic properties and the initial orientation of the director of the mesophase relative to the field. The optical properties of the medium, its local optical anisotropy, are changed as a result of this reorientation of the director (either occurring locally or throughout the whole of the sample) and underlies all the known electrooptical effects. 

Pressure of the overburden does not cause chemical reactions which lead to a higher rank. Experiments have shown that static pressure even retards coalification processes. By contrast, pressure affects the physical properties, notably the porosity and moisture content in low rank coals. Further, the optical anisotropy of vitrinites (which is a tension anisotropy) is caused by pressure. Shearing movements have influenced the chemical coalification only occasionally and locally in the foredeeps that we have studied (for instance in the immediate vicinity of overthrusts). In such cases the tectonic movements probably were so quick that the friction heat and the shearing could operate. Shearing in no way can account for the gradual increase in coal rank with depth. 

Woemer et al. 373) produced polyacetylene with locally oriented regions and an optical anisotropy of 2 x by polymerization on crystals of biphenyl. Yamashita and co-workers 374,375) have recently reported epitaxial polymerization of acetylene on crystals of anthracene, naphthalene and biphenyl where fibrils of cis- or trans-polymer formed, crystallographically aligned with the substrate. Fincher et al. 376) produced a 3 x extension which gave a 4 x optical anisotropy. 

The optical measurements presented in the previous chapters can be used to either characterize local, microstractural properties or as probes of bulk responses to orientation processes. In either case, it is normally desirable to make the connection between experimental observables and their molecular or microstractural origins. The particular molecular properties that are probed will naturally depend on the physical interaction between the light and the material. This chapter explores molecular models and theories that describe these interactions and identifies the properties of complex materials that can be extracted from measurements of optical anisotropies. The presentation begins with a discussion of molecular models that are applied to polymeric materials. Using these models, optical phenomena such as birefringence, dichroism, and Rayleigh and Raman scattering are predicted. Models appropriate for particulate systems are also developed. 

Flow birefringence is due to the optical anisotropy created by the orientation of the macromolecules within the flow field. In a plane flow, if we denote by I and II the principal axes of the refractive index tensor (principal axes are those for which the tensor is diagonal they are defined by the eigenvectors of the tensor), the local birefringence A is defined as ... 

The director defines the local optical axis. The most obvious indication of the anisotropy of nematics is their birefringence. Since nematics are composed of elongated molecules their extraordinary refractive index ng is always larger than the ordinary one Ho, i.e. nematics have a positive optical anisotropy Ua = Ue — Ho- When light is passing through a nematic layer, an optical path difference... 

As a technique complementary to AFM, near-field scanning optical microscopy (NSOM) studies have reported the nanoscale topographic and fluorescence features of poly(fluorene)s [156-158]. From the NSOM experiments, it is possible to quantify the film optical anisotropy on the local scale by measuring the polarization of the emitted light. The intensity of fluorescence is found to be the most when collected perpendicular to the fibril axis. Since the fluorescence is polarized along the conjugated backbone, this indicates that the ribbons are indeed composed of poly(fluorene) chains stacked orthogonal to the ribbon axis. 

As a consequence, the refraction index component perpendicular to the director n is larger in case b than in case c, and the component n is smaller. Therefore, the optical anisotropy An = n — n i in case b is smaller. To take the new situation into account, two local order parameters are introduced for the uniaxial nematic phase, one is the same as discussed above for the longitudinal molecular axes (5 = 5 ), and the other describes the local order of the shortest molecular axes that is local biaxiality (D) ... 

Where does such a strong scattering anisotropy originate from It is evident that the optical anisotropy of nematic hquid crystals plays the crucial role. In fact, the scattering is caused by fluctuations of the director n, i.e. the local orientation of the order parameter tensor. The local changes in orientation of n imply local changes in orientation of the optical indicatrix. 

The depolarized spectrum is dominated by local fluctuations of the optical anisotropy owing to an overall orientation of stiff molecules, local motions of optically anisotropic segments or internal Ronse-Zimm modes for flexible chain molecnles. The depolarized spectrum thus reflects dynamics of collective molec-nlar orientation when the interaction between translation and rotation can be neglected. 

Let us assume a planar texture (helical axis at right angles to the boundaries) and a positive dielectric anisotropy. When an electric field is applied parallel to the helical axis the local optical axis experiences a dielectric torque which tries to tip it out of the cholesteric plane. The boundary forces, on the other hand, act in a direction to sustain the planar texture. Assuming that the deformation is uniform in the plane of the sample, Leslie [70] was able to show that below a certain threshold voltage Ug no deformation occurs. Above Ug the local optic axis tips out of the cholesteric plane conical deformation . Ug is given by... 

As noted above, the in-phase and quadrature spectra represent components of dynamic optical anisotropy caused by the re-orientational behaviour characteristic of the type and local environment of each group. Reorientation processes tend to synchronize if there is a specific chemical interaction or connectivity between them, and herein lies the value of correlation analysis, in that it provides a valuable method for studying the time dependent variation of infrared dichro-ism signals. 

In semiconductor nanostructures, local field effects are mostly due to a surface charge polarization contribution, which is essentially a macroscopic classical term, that is very important in optical properties calculations. For instance, surface polarization is responsible for a strong optical anisotropy of elongated nanocrystals [36]. We can say that the one-particle contribution represents the optical properties of an isolated, stand-alone nanocrystal, the intrinsic properties due to the delocalized states and the quantum confinement effects. One-particle contributions do not take into account the influence of the external environment into the optical properties, such as the macroscopic polarization of the surface bonds. On the contrary, the methods beyond one-particle calculations, based on the inversion of the dielectric matrix or, as we will see below, a time-dependent tight-binding formulation, take into account more properly the influence of the external environment, in particular the charge transfer within the nanocrystals and at the surface. 

An external electric field interacts with the local dielectric anisotropy of a blue phase and contributes e E /An to the energy of the liquid crystal [45]. The field distorts the cubic lattice and results in a change in the angular (or spectral) positions of Bragg s reflections. Moreover, field-induced phase transitions to novel phases have been observed [42, 46, 47]. The field can also induce birefringence parallel to the field direction, due to the optical biaxiality of the distorted cubic lattice [48]. 

An increasingly important tool to determine the strain-induced anisotropy is MOKE (magneto-optical Kerr effect). In section 2 we mentioned already the calculations by Freeman et al. (1999). Experimentally, e.g. Ali and Watts (1999) (see also references therein) apply a bending device to induce strains in a controlled way, and determine the (local) curvature and the strains by optical interferometry or by direct measurement (stylus). The properties of the substrate are incorporated in a finite-element modelling calculation, thus allowing an absolute determination of the film properties. Compare also Stobiecki et al. (2000), who studied the strain induced anisotropy in FeB/Cu/FeB trilayers, using Kerr magnetometry (MOKE). 

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