RELATIONSHIPS AMONG STRESS-INDUCED RAMAN SHIFTS FOR ISOTROPIC AND UNIAXIALLY ORIENTED POLYMERS

It is shown that, although the shifts of Raman lines observed when ran dom or uniaxially oriented polymers are uniaxially stressed depend on the polarization directions of the incident and scattered radiation, t he shifts are not all independent. For a random sample, there is a ver y simple relationship between the four measurable shifts for small str esses, which is independent of the nature of the polymer or of the vib rational mode involved, so that only three of the shifts are independe nt. If the form of the Raman tenser is known, a further relationship e xists between the shifts, so that only two of them are independent. Fo r a uniaxially oriented polymer, the products of the shifts and corres ponding intensities are related in such a way that, if the form of the Raman tenser is known, only three of the four measurable values are i ndependent. The predictions are compared with experimental results on poly(ethylene terephthalate) and are confirmed within experimental unc ertainty. For a random sample, it is possible to deduce the form of th e function f(theta) that describes the average contribution to the shi ft produced by a chain making angle theta to the axis of stress. This function is found to have a form somewhere between that expected if th e shift were proportional to the resolved stress parallel to the chain and that expected if the shift were proportional to the resolved stra in.