Theories of Birefringence Induced in Liquids by Ultrasonic Waves

Abstract

Some liquids and solutions become doubly refracting and behave as uniaxial crystals when traversed by acoustic waves of high frequency. In many aspects the induced birefringence is analogous to birefringence due to flow. Theories for this behavior are presented and discussed in detail. For liquids and solutions of flexible macromolecules the birefringence is proportional to the square root of the acoustic intensity and to the frequency of the wave, but for colloidal solutions it varies directly as the intensity and is independent of frequency. It is shown that from measurements of the birefringence, values of relaxation times and diffusion constants can be obtained. The method has a number of advantages over flow birefringence studies and in common with the latter does not depend on the possession of a permanent dipole moment by the molecules.

On the frequency dependence of ultrasonically induced birefringence in isotropic phase of liquid crystal: 5CB (p-n-pentyl p′-cyanobiphenyl)

“…͑28͒. 23,24 His treatment is very akin to ours in coupling the anisotropy tensor of the molecular orientation to the traceless part of the strain rate tensor. Our treatment, however, is based on a standard theory of irreversible thermodynamics and gives a concrete expression for the proportionality constant that appeared in his theory.…”

“…͑28͒, if the term 6D is replaced by ⌫. The formula for flow birefringence is also obtained in the same framework as 24,25 ͯ ⌬n f G ͯ Peterlin ϭn ͩ n 2 ϩ2 3n ͪ 2 4…”

“…Peterlin derived the following expression for ultrasonically induced birefringence using the rotational diffusion equation for an ellipsoid under a longitudinal ultrasound: 24,25 ⌬n rms Peterlin ϭn ͩ n 2 ϩ2 3n ͪ 2 4…”

“…We also compare our results with the earlier theories. 1,[23][24][25] The isotropic phase of liquid crystals is most appropriate to examine the expression obtained here, because the relaxation frequencies of the orientational motions are the same order of magnitude as the ultrasonic frequencies usually used for ultrasonic relaxation studies. 26 Besides, the flow birefringence for isotropic phase of liquid crystal, 5CB, has been already reported by Martinoty et al 7 The values of the flow birefringence and the relaxation frequencies are required to reproduce the frequency dependence of the ultrasonically induced birefringence.…”

Translational–rotational coupling in supercooled liquids: Heterodyne detected density induced molecular alignment

“…Molecular alignment caused by flow, stress, or strain is well known in the context of polymer processing, 7,30 where it can lead to unwanted optical properties of the materials. Flow birefringence, in which viscous liquids, 31 particles in a liquid, 32,33 or liquid crystals 34 are subjected to a shearing force causing birefringence has received a great deal of study. Depolarized light scattering experiments of anisotropic fluids have been interpreted in a similar manner using flow-rotational coupling.…”