Vibrational Frequency Spectrum for Polymers

摘要

A method is given for calculating the vibrational frequency spectrum of a model linear polymer. The model is a chain ofNmasses having bending and stretching force constants. Each mass is quasiharmonically coupled to a Debye lattice which has a cutoff frequency ohgr;L. Each of the 3Nfree chain eigenfrequencies ohgr;jbecomes a band with a low frequency cutoffohgr;jmin2equals; ohgr;j2, a high frequency cutoffohgr;jmax2equals; ohgr;j2plus;ohgr;L2, and a pseudohyphen;nhyphen;dimensional Debye distributiongjlpar;ohgr;rpar;equals;nohgr;nminus;1sol;lpar;ohgr;jmaxnminus;ohgr;jminnrpar;forohgr;jminlang;ohgr;lang;ohgr;jmax. The total frequency distribution agrees closely with the results by Genensky and Newell for the Stockmayer and Hecht lattice using their force constants and compares reasonably well with results of GF matrix calculations for polyethylene.