Negative Eigenvalue Theorem Research Articles

Vibrational spectrum of chain molecules with conformational disorder: polyethylene

The problem of the lattice dynamics of crystalline polyethylene containing a random distribution of geometrical defects is considered with a view to understanding some features of its infra-red and Raman spectra which cannot be explained in terms of k=0 spectroscopically active modes. A general method is proposed for the construction of the dynamical matrix of such a conformationally random polymer chain. The negative eigenvalue theorem is used for the calculation of the density of the vibrational eigenstates from the resulting very large matrices. Calculations are performed for several models containing the energetically more favoured conformational defects. The problem of the vibrational perturbations introduced by the defects in the lattice dynamics of the perfect crystal is discussed for crystals containing chain molecules. In addition to the activation of all band modes, gap and in-band resonances due to localized vibrations of the defects are found. Evidence is derived from calculations, and verifie...

Vibrational Analysis of Random Polymers

The frequency distributions of some isotopically random polymers are calculated by applying Dean's negative eigenvalue theorem. It is shown that the results of calculation are in good agreement with the infrared spectra of polymers of cis-CHD = CHD and trans-CHD = CHD, giving strong confirmation to the previous view that the polymerization by a Ziegler-type catalyst occurs with the cis opening of the double bond. The spectra of copolymers of CH2 = CH2, CHD = CD2, and CD2 = CD2 are also discussed. The effects of randomness and deuterium content on the frequency distribution are studied.