THE ORIGINS OF AVOIDED CROSSINGS IN POLYMER DISPERSION-CURVES

A purely mathematical heuristic model is examined in order to explain the existence of an avoided crossing between two dispersion curves cal culated for a certain potential energy surface designed to simulate th e dynamics of a linear polyethylene chain. The model shows that a thir d mode coupled to a two-mode Fermi-resonant system is able to create a marked instability in a vibrational spectrum. It is noted that such a n explanation would require a fourth-order coupling term, which is the reason given for the failure of normal mode analysis to properly iden tify this dynamical effect.