Measurement of birefringence

In solids there are two general methods used for the determination of An. One is the transmission method while the other is a compensator technique. Each has advantages and disadvantages and thus the method chosen depends highly on the experimental circumstances as well as on the material itself. It is worth pointing out that the above discussion applies to both uniaxially and biaxially oriented systems. Two other methods not to be discussed here are interference microscopy and refractometry.  

Most of the methods depend upon the optical retardation, R, defined 

By monitoring T using a photomultiplier, R can be determined. Note that the sign of R is unknown since T varies with the sine squared of R hence, one must determine the sign by another method. Also T is a multivalued function of so that the order of the retardation must be established via another route. 

Although the transmission method suffers somewhat from its lack of sensitivity to very small changes in R, one great advantage of this technique is its application where high speed deformation is involved. If one can monitor the thickness change with extension ratio then An can be calcalated as a function of elongation. 

The number of compensator methods are numerous and will not be discussed in detail here. The interested reader is referred to Refs. 6-8. Basically what is involved is that a known retardation is used to nullify or compensate the retardation induced by the sample. This amounts to putting some birefringent (anisotropic) material into the light path, e.g. a wedge or plate of quartz or calcite. By changing the thickness of such a material the degree of optical retardation can be controlled— recall eqn. (3). 

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The uniaxial orientation parameter related to the orientation of polymer chains gains particular importance, because it can also be determined by measurement of birefringence [250,252],... 

For systems where the stress-optical rule applies, birefringence measurements offer several advantages compared with mechanical methods. For example, transient measurements of the first normal stress difference can be readily obtained optically, whereas this can be problematic using direct mechanical techniques. Osaki and coworkers [26], using a procedure described in section 8.2.1 performed transient measurements of birefringence and the extinction angle on concentrated polystyrene solutions, from which the shear stress and first normal stress difference were calculated. Interestingly, N j was observed to... 

The optical apparatus used in this study was designed according to the strategy described in section 8.4.3, which permits the simultaneous measurement of birefringence and dichroism. The source was a infrared diode laser that generates light at a wavelength in the... 

Dynamo-optical and strain-optical coefficients can be estimated from measurements of birefringence An under elongational flow or shear flow, correspondingly... 

Before proceeding with discussion of the measurement of birefringence of a fiber it should be pointed out that if biaxial orientation exists in a film all three birefringence values must be determined to characterize the optical anisotropy. 

Of course with most types of bicomponent fiber, the measurement of birefringence is not possible because of the interference of the different polymer groups along the fiber axis. Also, with deeply dyed fibers, the results if obtainable are unreliable because of the interference from the dye molecule. 

Kim, K.H., Cho, H.H., Ito, H., Kikutani, T., 2008. Fiber structure development in high-speed melt spinning of poly(trimethylene terephthalate) (PIT)—on-line measurement of birefringence. J. Polym. Sci. B Polym. Phys. 46, 847 56. 

Relaxation birefringence is meant to imply the measurement of birefringence during stress relaxation of a deformed material. The typical application has concerned rubbers and rubberlike materials where the objective is to test the degree of ideal Gaussian rubber elasticity by utilising the stress optical law given earlier in eqn. (10). 

Measurements of birefringence An, and the UV or visible dichroic ratio D were made on films cast from tetrahydrofuran solution as a function of extension (up to 200%) at 80"C. At this temperature the polymer behaves as a rubberlike material, effectively cross-linked by the... 

Various stress-strain-birefringence measurements have motivated the approach I shall follow later. The measurement of birefringence is done on strips pulled in tension the birefringence is the difference in the index of refraction for light polarized parallel and perpendicular to the direction of stretching. 

The simplicity of measurements of birefringence hide their physical complexity. It may be beneficial to obtain the intrinsic value (eqn (11)) using measurements coupled to an experimentally more complicated method of orientation measurement, and then to use birefringence as a secondary technique. As with absorption methods, refractive index measurements can only give (R2(cosa)) but not the higher-order components of the orientation distribution. 

McBride, D.J., Hahn, R.A. and Silver, F.H. (1985) Morphological characterization of tendon development during chick embrvogenesis Measurement of birefringence retardation. Int. J. Biol. MacromoL, 7, 71-76. 

Electrospinning of nanofibers, measurement of birefringence and fiber dimensions in the mat, discussed. 

Samuels [91] obtained justification for this argument by combining such sonic modulus and X-ray diffraction measurements with the measurement of birefringence. Now the birefringence of a polymer on the two-phase model (ignoring form birefringence) is given by... 

The parameters average values (amplitudes). Note that is the Hermans orientation function. The full description of uniaxial orientation /(0) cannot thus be attained by a single measurement of birefringence. The Hermans orientation function can be given a simple interpretation. A sample with orientation f may be considered to consist of perfectly aligned molecules of the mass fraction / and randomly oriented molecules of the mass fraction 1 — /. Liquid-crystalline polymers are often characterized by their order parameter, denoted S (Chapter 6). This quantity is equivalent to the Hermans orientation function. 

The parameters average values. Note that fj is the Hermans orientation function. The full description of uniaxial orientation /(0) can thus not be given by a single measurement of birefringence. 

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