Numerical studies of disordered-chain vibrations. I. Low-frequency modes of polymethylene-like skeletal chains

The vibrational density of states and isotropic Raman spectra of ensembles of conformationally disordered polymethylene-like skeletal chains have been computed numerically in the low-frequency CCC bending region below 600 cm−1. Chain lengths ranged from 8 to 25 atoms and the average trans-bond concentration varied from 0% to 100%. The calculated Raman spectra of the disordered chains are notable in that they display a progression of D-LAM-k bands. The existence of this progression indicates that the skeletal vibrations of the disordered-chain ensemble can, to some extent, be described in terms of a phase-angle model of the type normally associated with ordered chains. The applicability of a phase-angle model is also indicated by the frequency distribution of standing waves obtained from a harmonic analysis of the normal coordinates.