Vibrational spectral density in the long-wave range for a polymer chain with configurational disorder

Abstract

The calculation of the configurational averaged vibrational spectrum 〈 G( λ)〉 for a disordered polymer chain in the long-wavelength limit is presented. The possibility of constructing a simple continuous polymer chain model, which contains all necessary terms for the calculation of the potential energy, is considered. The configurational average of the spectral density is obtained by the replica method. To obtain analytical results, an expanded Hartree-Fock approximation is used; thereafter the configurational averaged spectral density is calculable by application of saddle-point integration. As a result of these calculations, a self-consistent equation is found, the solution of which gives 〈 G( λ)〉.