Large-Scale Normal Coordinate Analysis of Macromolecular Systems:  Thermal Properties of Polymer Particles and Crystals

Using novel modifications to a sparse matrix solver (ARPACK), a complete spectral analysis has been achieved for a 6000 atom polymer system involving all 18 000 degrees of freedom. A comparison of the thermal properties and spectra of an annealed polymer particle and crystal is presented. The density of states spectrum g(ω) shows a higher number of low-frequency modes for the polymer particle, which results in a higher heat capacity at low temperature. The distribution of energy level spacing shows some resemblance to that exhibited by random matrices. Finally, the displacement of low-frequency eigenvectors is shown to have a larger amplitude on the surface than in the interior of either the particle or crystal.