Optical order parameter

This model alleviates the concept of the somewhat ambiguous molecular anisometry that is based on an arbitrary choice of fixed molecular axes. So, for each of the A and B isomers, the isotropic absorbance Aa,b = Abs// + lAhsf yS, the anisotropy AA g = Absj - Absf and the optical order parameter g = AA ySA gare given by ... 

Figure 19 shows the subsequent photoinduced change of the three-dimensional optical order parameter of the sample. This is given by... 

Figure 19. Change of the normalized three-dimensional optical-order parameter of the LBK ( 2 10 156 monolayers) structure under successive UV (360nm) and blue-light (450mn) irradiations, which are respectively indicated by UV and B on the columns. One can see the large change (approximately one order of magnitude) in this order parameter when the film is exposed to the photoactive light. This confirms that the LBK structure is much more optically anisotropic vvhen the azo-molecules are in the irans form (columns New or B) than when they are in the cis form (UV).

To understand the transition to supersonic velocities we also make use of a description of the lattice in terms of both optical and acoustic order parameters. Here, we study a strictly ID model that is a direct map of the fPA structure. However, as far as the properties of the drifting polaron are concerned, the model is more general and quantitatively describes these properties in other polymeric systems, e.g., poly(paraphenylene vinylene) or polythiophene. In the ID model, the displacement of the lattice sites entering Equation 2.14 and Equation 2.16 is described by a single variable u . In the description of the geometry of conjugated polymers, fPA in particular, it is common to study a smoothed atomic displacement order parameter. This optical order parameter is given by... 

The polaron moving at supersonic velocities has a distinct difference compared to the static polaron, i.e., the absence of an acoustic compression of the lattice around the localized charge. However, the deformation described by the optical order parameter is more or less the same for the two types of defects. Our simulations show clearly that these optical deformations can move along the polymer chain at supersonic velocities. 

FIGURE 2.8 Time dependence of y (the optical order parameter defined in Equation 2.21 of a polaron moving in a two-chain system with different electric field strengths Eo). 

A particularly useful aspect of dichroic measurements is the chance to probe orientational order using more than one electronic transition in a molecule. Thus optical order parameters can be determined for different absorption bands, and if the transition moment directions are known, it is possible to determine both order parameters 5 and D. If it is assumed that there is a relationship between the uniaxial and biaxial order parameters, as given in Fig. 5 of Sec. 1 in this chapter, then it is possible to obtain both order parameters from the polarized spectra from a single absorption band [25]. This method has been applied [26] to the determination of order parameters of rigid aromatic probes, such as azulene, phenan-threne, and anthracene and related compounds. Dichroism measurements on impurity molecules in liquid crystal solvents have also been used [27, 28] to study inter-molecular interactions, and their influence on electronic absorption bands. Polarization effects of the type described above for sim-... 

X-ray, uv, optical, in, and magnetic resonance techniques are used to measure the order parameter in Hquid crystals. Values of S for a typical Hquid crystal are shown in Figure 3. The compound, -methoxyben2yHdene-/) - -butylaniHne (MBBA) is mesomorphic around room temperature. The order parameter ranges from 0.7 to 0.3 and discontinuously falls to 2ero at T, which is sometimes called the clearing temperature (1). 

M. Allain, P. Oswald, J. M. di Meglio. Structural defects and phase transition in a lyotropic system optical birefringence and order parameter measurements. Mol Cry St Liq Cryst 7625 161-169, 1988. 

The classical scheme for dichroism measurements implies measuring absorbances (optical densities) for light electric vector parallel and perpendicular to the orientation of director of a planarly oriented nematic or smectic sample. This approach requires high quality polarizers and planarly oriented samples. The alternative technique [50, 53] utilizes a comparison of the absorbance in the isotropic phase (Dj) with that of a homeotropically oriented smectic phase (Dh). In this case, the apparent order parameter for each vibrational oscillator of interest S (related to a certain molecular fragment) may be calculated as S = l-(Dh/Di) (l/f), where / is the thermal correction factor. The angles of orientation of vibrational oscillators (0) with respect to the normal to the smectic layers may be determined according to the equation... 

It is considered that, if ideal, optically active poly(alkyl(aryl)silane) homopolymer and copolymer systems could be obtained which had stiffer main-chain structures with longer persistence lengths, it should be possible to clarify the relationship between the gabs value and the chiral molar composition. The magnitude of the chirality of the polyisocyanates allowed precise correlations with the cooperativity models.18q In the theory of the cooperative helical order in polyisocyanates, the polymers are characterized by the chiral order parameter M, which is the fraction of the main chain twisting in one helical sense minus the fraction of the main chain twisting in the opposing sense. This order parameter is equal to the optical activity normalized by the value for an entirely one-handed helical polymer. The theory predicts... 

On a molecular level the director is not rigorously defined, but the molecular director is typically considered to be the average long axis of the molecules, oriented along the macroscopic director with some order parameter less than one. This type of anisotropic order is often called long-range orientational order and, combined with the nonresonant optical properties of the molecules, provides the combination of crystal-like optical properties with liquidlike flow behavior characteristic of liquid crystals. 

The fact that the order parameter vanishes above does not mean that Nature does not have an inkling of things to come well below (or above) T. Such indicators are indeed found in many instances in terms of the behaviour of certain vibrational modes. As early as 1940, Raman and Nedungadi discovered that the a-) transition of quartz was accompanied by a decrease in the frequency of a totally symmetric optic mode as the temperature approached the phase transition temperature from below. Historically, this is the first observation of a soft mode. Operationally, a soft mode is a collective excitation whose frequency decreases anomalously as the transition point is reached. In Fig. 4.4, we show the temperature dependence of the soft-mode frequency. While in a second-order transition the soft-mode frequency goes to zero at T, in a first-order transition the change of phase occurs before the mode frequency is able to go to zero. 

An interesting aspect of many structural phase transitions is the coupling of the primary order parameter to a secondary order parameter. In transitions of molecular crystals, the order parameter is coupled with reorientational or libration modes. In Jahn-Teller as well as ferroelastic transitions, an optical phonon or an electronic excitation is coupled with strain (acoustic phonon). In antiferrodistortive transitions, a zone-boundary phonon (primary order parameter) can induce spontaneous polarization (secondary order parameter). Magnetic resonance and vibrational spectroscopic methods provide valuable information on static as well as dynamic processes occurring during a transition (Owens et ai, 1979 Iqbal Owens, 1984 Rao, 1993). Complementary information is provided by diffraction methods. 

Figure 4.25 Comparison of the different order parameters for the 151 K second-order transition of PrAlOj. (After Sturge et al., 1975.) Unbroken line is the smooth curve through the internal displacement order parameter, cos 2(, from ESR measurements. Black circles represent the electronic order parameter from optical absorption studies. Squares represent the reduced macroscopic strain from elastic neutron scattering.

Norden et al. have examined the CD spectral changes of dyes oriented in a liquid crystal matrix, on variing the order parameter q, which is estimated by NMR observation 262). Kuball et al. presented a theoretical description of the optical activity of oriented molecules, and they found that the C D of the transition A of a given oriented molecule Ae (v) is described by ... 

It is useful to describe the amount of orienlalional order wilh a single quantity. X-ray. uv. optical, ir, and magnetic resonance techniques are used to measure ihe order parameter in liquid crystals. 

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