Temperature effect in quasiharmonic infrared bands of stressed polymers

Abstract

The effect of temperature on vibrational frequency shifts in mechanically stressed polymer chains is analyzed. A single chain is modeled as a weakly coupled, one-dimensional series of anharmonic diatomic oscillators. The anharmonic potential is described as a perturbation of the harmonic potential with cubic and quartic terms. Expressions are derived for the dominant, quasiharmonic contribution to the temperature-dependent frequency shifting coefficient αc, and distinctions are drawn between the vibrational mode ’’mixing contribution’’ and the ’’anharmonic contribution.’’ αc is derived in terms of the Grüneisen parameter; and the resulting expression is −αc = α0+β0T, where α0 is the extrapolated T = 0 °K value of the frequency shifting coefficient, and β0 is constant. The predicted linear dependence of αc on temperature was found to be in excellent qualitative agreement with experimental studies on stress-induced infrared frequency shifts versus T in polypropylene.