Anisotropic excitable media

An applied electric field can be the electric held component of an electromagnetic wave, in which case electronic excitations or other optical responses may ensue. These are the topic of the next chapter. Here, the concern is with electrostatics, specihcally, the dielectric, or insulative, properties of materials. In an electrical conductor, an applied electric held, E, produces an electric current - ions, in the case of an ionic conductor, or electrons, in the case of an electronic conductor. Electrical conductivity has already been examined in earlier chapters. In insulating solids, the topic of the current discussion, the response to an applied electric held is a static spatial displacement of the bound ions or electrons, resulting in an electrical polarization, P, or net dipole moment (charge separahon) per unit volume, which is a vector quantity. In a homogeneous linear and isotropic medium, the polarization and electric held are aligned. In an anisotropic medium, this need not be so. The fth component of the polarization is related to the jth component of the electric held by ... 

Partial orientation is much easier to achieve and generally sufficient to determine the direction of the transition moments, particularly with respect to any axes of symmetry that the molecules may have. Partial orientation can be achieved by photoselection using a linearly polarized excitation source, by application of an electric field or by dissolving the solute in a transparent anisotropic medium (liquid crystals, stretched polymers).182 Photoselection is the basis of emission anisotropy measurements discussed below. It is also used for molecules that can be either generated or destroyed photochemically in a rigid medium such as poly(methyl methacrylate) or glassy solvents at low temperature. Preferential alignments of dipolar molecules that are achievable by electrostatic fields are unfortunately fairly small. 

The conductor can thus be represented as an anisotropic medium with interrelated nonlinear magnetic and electrical properties. The current pattern that results in the conductor from the application of time-dependent external magnetic fields and excitation (transport) currents can be determined in principle, from Maxwell s equations. An integration of pJ and the /-dependent magnetic hysteresis over the entire conductor cross section can then be used to calculate the loss. 

The movement of a fluorophore embedded in a bilayer (generally in an anisotropic medium) is controlled by the 3D potential preferring certain (nonequivalent) orientations of the fluorophore in all three dimensions. At long times upon excitation, the system does not relax completely in aU 3D and the residual anisotropy is not zero. To date no general theory has been formulated however, particular models for the most frequently studied systems have been published by a number... 

In all of the present theories about the excitation of nematic or cholesteric liquids by an electric field, the mesomorphic material is treated as a continuous elastic anisotropic medium. The Oseen -Frank elastic theory is used to describe the interaction between the applied field and the fluid. The application of an electric field causes the liquid crystal to deform. For a material with a positive dielectric anisotropy, Ae = > 0, the director aligns in the direction of... 

Photoselection and photoorientation This elegant method allows one to obtain a set of partially oriented molecules in a completely isotropic medium. It makes use of the fact that the photoexcited ensemble of molecules is always anisotropic, and thus exhibits LD (transient dichroism). Moreover, if the excitation is followed by chemical transformation, and the environment is rigid enough to prevent molecular rotation, a permanent alignment of both reactant and product is obtained. Such photooriented samples can be studied by conventional LD techniques. Particularly attractive media for use in photoorientation are low-temperature rare gas matrices, which are inert and transparent in both the UV-visible and IR regions. 

Figure 4 Exponential decay curves for the time-resolved anisotropy of a fluorophore excited with a picosecond pulse of monochromatic light. The molecule is rotating with a rotational correlation time of 1 ns. Curve a represents a typical decay curve in an anisotropic medium, and curve b represents a typical decay curve in an isotropic medium. The limiting anisotropy rg and infinite time anisotropy are shown in the figure. 

This ratio is an indication of the structural order of the fluid matrix, and for an isotropic fluid it should be close to unity [4]. In order to differentiate between anisotropy of the medium and that of the molecular rotations, one should compare the V vs. To plots (determined from the steady-state anisotropy measurements at low temperatures in high density fluids at different excitation wavelengths) for a particular fluorophore embedded in an isotropic medium to a similar plot for the probe embedded in the test fluid. If, for example, a strong dependence of v on the value of ro is evident for both media and the ratio of in-plane to out-of-plane rotational rates is very high (>10), one can conclude that the rotations are anisotropic but the medium is isotropic. The technique of differential polarized phase fluorometry [8,12], which is beyond the scope of this chapter, has been successfully applied to study the types of rotations displayed by fluorophores embedded in different media. 

---