Birefringence definition

Many papers deal with the crystallization of polymer melts and solutions under the conditions of molecular orientation achieved by the methods described above. Various physical methods have been used in these investigations electron microscopy, X-ray diffraction, birefringence, differential scanning calorimetry, etc. As a result, the properties of these systems have been described in detail and definite conclusions concerning their structure have been drawn (e.g.4 13 19,39,52)). 

In the derivation of eqn. (7) it was assumed that n (number of equivalent random links) is the same for all chains. For our samples (B2 system, Mw/Mn=1.45), this assumption is definitely not correct. Therefore, it is desirable to obtain birefringence results on networks prepared from monodisperse polymer (in that n is constant), before the validity of n itself is questioned. 

Injection molding requires the barrel temperature to be about 350°C with a barrel pressure in excess of 138 MPa. The mold is maintained at 110°C to ensure uniform flow and high definition, and to discourage an uneven index of refraction, birefringence. The CD is about four one-hundredths of an inch (0.5 mm) thick. For prerecorded CDs, the PC is compression-molded on a stamper imprinted with the recorder information. This takes about 4 sec. Once the clear piece of polycarbonate is formed, a thin, reflective aluminum layer is sputtered onto the disc. Then, a thin acrylic layer is sprayed over the aluminum to protect it. The label is then printed onto the acrylic surface and the CD is complete. This process is described later in greater detail. 

In Fig. 5.4 results are plotted, as obtained by Tsvetkov, Garmonova and Stankevich (166) on solutions of linear oligomers of polyoxy-propylene glycol in cyclohexanol at 20° C (full circles). For comparison the ratio of birefringence and shear stress as obtained in the limit of zero shear stress on the bulk oligomers, are inserted (open squares). [Cf. the definition of [ ]/[ ] by eq. (2.33)]. As these bulk materials form viscous... 

Recently, a second-order nonlinear photonic crystal has been realized.38 In this nonlinear optical bandgap material, there is a periodicity in the nonlinear optical properties of the engineered material. With this definition, a periodically poled second-order nonlinear optical material could be called a nonlinear photonic crystal. However, its linear optical properties do not show a periodicity, except for the (small and useless for bireffingent phase-matching) poling-induced birefringence. Here, the material is the same in the complete structure. It is only periodically made into a non-centrosymmetric structure for second-order nonlinear and phase-matching... 

Analogous to the definitions of linear birefringence and linear dichroism following equations (2.15) and (2.21), the form of equation (2.30) suggests the following optical anisotropies for circularly polarized light ... 

We remark that since in any experiment the phase shift between the square of the field is proportional to cos2 tot and thus the second harmonic of birefringence is resolved with the accuracy of arbitrary addition or subtraction of 180°, the definition of v / is not unique. In principle, the curves in Figure 4.36 may be dissected at the points /(coxB) = 180° and replotted as if growing anew from zero at each cut. 

The purpose of such a device consists in changing the orientation of the polarization plane of a beam by 90°. That means the initial Stokes vector 1,1,0,0 of a horizontally polarized beam becomes 1,-1,0,0 after passing through the retarder. Retarders are most often birefringent crystals of definite thickness. If the fast and slow axes of such a crystal orthogonal to each other are crossed at 45° with respect to the polarization plane, the retarder rotates the latter by 90°. The Stokes-Mueller transformation corresponding to this experiment should be ... 

Birefringent retarders are made of anisotropic uniaxial crystals such as calcite, a-quartz, sapphire, zinc sulphide, cadmium selenide and others. As Eq. (3.2-14) shows, the produced retardation is exact for a definite wavenumber or for its multiples. Between them all remaining possible polarization states are passed through. 

It has been demonstrated that molecular orientation can be achieved starting with a low molecular weight species which is oriented in an elongational flow and subsequently cured under UV-irradiation. The orientation of the monomer is frozen-in by the ultra-fast process of polymerization and crosslinking. Both extrusion and stretching can be carried out at relatively low temperatures and pressures. Polymer filaments produced in this way are definitely anisotropic as is evidenced by their birefringence and by a strong increase of the tensile modulus and a decrease of the thermal expansion coefficient in the axial direction. 

The formation of crystalline precipitates from starch sols by treatment with alcohol has been repeatedly mentioned in the literature. Alsberg describes birefringent crystal clusters obtained in this manner from autoclaved starch sols. WiegeP has recently reported crystalline formations obtained by treating starch pastes with various aliphatic alcohols, dioxane or ethylene chloride. However, the significance of these crystalline formations as a definite starch component has not been generally recognized, and little attempt has been made to isolate and purify this material. 

Oil and amorphous or crystalline materials can be easily distinguished under the microscope. Oil is simply a secondary liquid phase. Amorphous material generally has no definitive shape with no birefringence under polarized light. Crystalline materials typically have a defined shape, showing birefringence under polarized light (Stoiber and Morse 1994). 

The study of fiber birefringence is not however a purely academic exercise but has definite practical applications, some of which are... 

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