Stress-optical rule

Scattering or form birefringence contributions will cause a deviation in the stress optical rule. As seen in equation (7.36), these effects do not depend on the second-moment tensor, but increase linearly with chain extension. 

The presence of the fourth-rank tensor in (7.127) and its absence in (7.11) suggests that the stress optical rule should not apply for dilute solutions of rigid rods. Unfortunately, because of the difficulty of acquiring truly rigid rods, and the problems of making measurements of stress in dilute systems, there are no data available on dilute rigid rod solutions where the stress optical rule can be investigated on this class of polymer liquids. 

Early work on the use of optical methods on the dynamics of polymeric liquids focused on establishing the validity of the stress-optical rule. A comprehensive account of this research can be found in the books by Janeschitz-Kriegl [29] and Wales [84], The majority of studies have considered simple shear flow, and the rule has been found to hold up to... 

Extensive work investigating the stress-optical rule has also been performed on polymer solutions [101]. Here the rule can be successfully applied if the solvent contributions to the birefringence are properly subtracted. Care must be taken, however, to avoid form birefringence effects if there is a large refractive index contrast between the polymer and the solvent. 

Investigations of the stress-optical rule in extensional flow are fewer in number due to the difficulty in establishing this flow. Using an extrusion device, van Aken and Jan-eschitz-Kriegl [102] produced extensional flows in melts by forcing the material through a... 

As discussed in section 7.1.6.4, semidilute solutions of rodlike polymers can be expected to follow the stress-optical rule as long as the concentration is sufficiently below the onset of the isotropic to nematic transition. Certainly, once such a system becomes nematic and anisotropic, the stress-optical rule cannot be expected to apply. This problem was studied in detail using an instrument capable of combined stress and birefringence measurements by Mead and Larson [109] on solutions of poly(y benzyl L-glutamate) in m-cresol. A pretransitional increase in the stress-optical coefficient was observed as the concentration approached the transition to a nematic state, in agreement of calculations based on the Doi model of polymer liquid crystals [63]. In addition to a dependence on concentration, the stress-optical coefficient was also seen to be dependent on shear rate, and on time for transient shear flows. 

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... 

Breakdown of the stress-optic rule can also occur in multiphase or multicomponent mixtures, as well as in melts with crystalline domains. However, as in glassy polymers, for miscible blends, a revised stress-optic law can sometimes be recovered by breaking the stress and birefringence tensors into two components, one for each component in the blend (Zawada et al. 1994 Kannan and Komfield 1994). 

Appendix 18.B — The Stress-Optical Rule in the Case of Simple Shear... 

As Txy is relatively easy to measure, Eq. (18.B.12) is often used to check the validity of the stress-optical rule and determine the value of C. 

---