Rubber Birefringence and Photoelasticity

Abstract

Abstract The phenomenon of birefringence, discovered in 1669 by Erasmus Bartholin and later studied by Christian Huygens, is well known for its appearance in transparent crystalline solids. It is to be traced essentially to internal anisotropy of crystals for light propagation, so that under certain conditions a single wave front may give rise to multiple coherent waves which can cause double refraction or other phenomena such as the appearance of fringes varying in brightness and color due to interference of emerging wave fronts. Birefringence may be expressed as the difference of the velocities of propagation in various directions in the birefringent medium and particularly as the difference between the maximum and the minimum velocity or, alternatively, between the maximum and the minimum refractive index or even as the phase difference between emerging waves, given frequently as a number of wavelengths. While true double refraction phenomena may be observed with ordinary light when the difference n1−n2 between the refractive indexes is very high, the interference phenomena may be obtained only with polarized light, but may be observed even with very small differences between indexes. This is not the place to treat extensively general concepts like polarizer, analyzer, ordinary wave, extraordinary wave, uniaxial crystal, biaxial crystal, etc. which can be found in any good optics treatise. Birefringence is not in any way limited to crystalline media, possessing inherent structural anisotropy. It may also appear in bodies which are normally isotropic, when structural anisotropy is caused by external forces. Then birefringence is quantitatively dependent on force intensities, even if not always in an easily detectable way. This is called “accidental birefringence” or “stress-birefringence”. It was observed by Seebeck in 1813, and later studied in 1816 by Brewster for glass. It is observable in many transparent materials. Stress-birefringence is particularly conspicuous in macromolecular substances, including elastomers, vulcanized or not, where it is determined by the orientation of molecular links. This, of course, may not be ascribed altogether to stress, but sometimes also to partial crystallinity. Other phenomena of accidental birefringence may be observed in liquids or in solutions, especially of elastomers, when they are subjected to a velocity gradient, as when flowing through a capillary tube or, more commonly, when sheared between two coaxial cylinders.