Anisotropic sample

In anisotropic samples, it is convenient to concentrate on the principal directions of deformation. In uniaxial stretch, the parallel and perpendicular radii are given by... 

A measurement of S(x) requires that the SANS spectrometer be calibrated by some absolute standard, a process which is often difficult to achieve with precision. An easier measurement in the ratio of scattering intensities of an anisotropic sample in two different directions. Figure 5 shows a graph of Sj (x)/S (x) versus x for the phantom model and the fixed junction case. 

An alternate method for obtaining angular information is to make use of the plane polarized nature of synchrotron radiation. It has long been known that XAS should exhibit a polarization dependence for anisotropic samples (18) however it is only recently that attempts have been made to exploit this effect. Early attempts to observe anisotropic XAS suffered from the low intensity and incomplete polarization of conventional x-ray sources. This work has been reviewed by Azaroff (19). 

Finally, n was determined by spectroscopic ellipsometry. The main drawback with this technique when applied to anisotropic samples is that the measured ellipsometric functions tanlF and cos A are related both to the incidence angle and the anisotropic reflectance coefficient for polarizations parallel and perpendicular to the incidence plane. The parameters thus have to be deconvolved from a set of measurements performed with different orientations of the sample [see (2.15) and (2.16)]. The complex refractive index determined by ellipsometry is reliable only in the spectral region where the sample can be considered as a bulk material. In fact, below the absorption... 

We next calculate the null setting of an ellipsometer from the reflection matrix in an anisotropic sample. The Jones vector for the reflected light is given by Eq. (2.15.44) for an anisotropic sample the off-diagonal elements of reflection matrix R are nonzero. 

When measuring absorption spectra, one records a signal that is related to the wavelength-dependent probability of making a spectroscopic transition. From the molecular point of view, this probability is proportional to the dot product jl p where (L is the molecular transition moment and p is the photon polarization direction. When the orientational distribution of the molecules is isotropic (not crystalline, liquid crystalline, or bound to a surface), its absorption spectrum represents the orientationally averaged probability of making a spectroscopic transition and the measured spectrum is independent of polarization direction. When the orientational distribution of the molecules is anisotropic, the probability of making a spectroscopic transition depends on the polarization direction, and that dependence can be exploited to deduce the direction of the transition moment relative to the laboratory frame. Because transition moments are often trivially related to the orientation of the molecule, structural information can be deduced from polarized absorption measurements on anisotropic samples. 

Ellipsometry can also be applied to transmission measurements linear birefringence and dichroism of an anisotropic sample cause differences in amplitudes and phase shifts for waves of different polarization azimuths. Such experiments seem to be of considerable interest for partially ordered systems such as liquid crystals (cf. Sec. 4.6), here the degrees of polarization P and Ppf, reveal information related to order and reorientation processes (Korte et al., 1993 Reins et al., 1993). 

Polarized incident radiation is necessary also when anisotropic samples such as stretched polymers (Flournoy and Schaffers, 1966) are studied. Crystals may require immersion in order to assure the necessary optical contact. Plastic selenium has proved to be useful (Gottlieb, 1968). In this way the three different infrared spectra of an orthorhombic single crystal were obtained which are shown in Fig. 2.7-10 (cf. Sec. 2.7.6.4 Schrader et al., 1971). The orientation of the optical axis or axes with respect to the experimental frame is crucial. For the evaluation the field components have to be considered separately in order to interprete the response of the oriented transitions correctly. Addressing different components equivalently is achieved by rotating the sample together with the internal reflexion element with respect to the beam (Hobbs et al., 1983 Palm, 1994). 

For anisotropic samples, the space correlation function will depend on the orientation imposed to the vector and P(q) will vary both with the scattering angle 6 and azimuthal angle define scattering form factors along the reference axes as ... 

To evaluate photoisomerization and photo-orientation parameters, and should be known, was calculated from the absorption spectrum of the polymer solution before irradiation, assuming the same extinction coefficient in the film and in solution bq was determined by the Fisher s method, modified by Rau, which holds not only for isotropic but also for anisotropic samples when the isotropic absorbance is considered (vide infra). For this determination, the isotropic absorbance change was recorded versus the irradiating light intensity, and the sample absorbance change was extracted for an irradiation flux extrapolated to infinity for three drbierent combinations of irradiation and analysis wavelengths 488-488, 532-488, and 532-532 nm, irradiation and analysis, respectively. These experiments... 

In the following it will be assumed that the sample has the same properties in all directions, that is, that it is isotropic. For anisotropic samples the description of optical activity is much more complicated. ... 

However, measurement of the first derivative spectrum means that, in the high field limit, only features corresponding to x, y and z orientations will be observed, thus greatly simplifying matters. Unfortunately, measuring in the high field limit is not always possible. For very anisotropic samples it may be necessary to immobilise polycrystalhne samples [e.g. in wax or as a pellet) in order to prevent torquing of the crystallites (see above). 

Synthesis of elastomers under uniform magnetic field can be used to prepare anisotropic samples. 

Figure 19 shows the dependence of the apparent elastic modulus on the quantity D. For the sake of comparison, results of compression measurements performed on both isotropic and anisotropic samples are shown. The composites contain Fe304 filler particles with concentration of 30wt%. In the case of isotropic samples, the apparent elastic modulus increases slightly within the experimental error of 5%. For anisotropic samples, the apparent modulus increases significantly under deformation up to the value D = 0.85. Above this value, the modulus does not change notably. 

We have also measured the swelling kinetics of anisotropic samples, loaded with either magnetite or iron particles. Figure 46 shows the swelling kinetics of magnetite-loaded mPDMS beads. The swelling kinetics of iron-loaded samples is also presented. 

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