Vibrational Relaxation in Atactic Polystyrene:  A Calculation of the Frequency Correlation Functions of Ring Stretching Modes and Their Variation with Temperature

Time correlation functions and their variation with temperature have been calculated for the modes observed near 1601 and 1583 cm-1 in the infrared spectra of atactic polystyrene. The correlation functions deviate from the Kubo−Rothschild model describing the fast modulation limit but can be modeled by simply assuming that there is a fast relaxation process characterized by a single relaxation time that is inhomogeneously broadened. It is noted that as long as the relaxations associated with inhomogeneous broadening are all relatively slow processes (in terms of vibrational relaxations), then their only contribution to the band profile would be through a Gaussian term that modifies the simple Kubo−Rothschild expression. The factors that contribute to this inhomogeneous broadening are discussed. Dynamic heterogeneity presumably plays a significant role, but in addition the 1583 cm-1 band appears to be influenced by an anharmonic coupling to lower frequency modes that provides an additional mechanism of relaxation. As a result, this mode is particularly sensitive to temperature, displaying changes in the relaxation time and second moments that show a transition near 80 °C, about 20 °C below the thermally observed Tg.