Relaxation spectra - multiple modes and mode decompositions

5 Relaxation spectra - multiple modes and mode decompositions 

Adachi, Watanabe, and their collaborators have ingeniously used type-A block copolymers to study aspects of subchain motion. The experimental approach is of enormous potential significance, because it offers one of the few possibilities as of this writing for measuring motional correlations between two identifiable, large parts of a polymer coil. The general approach is to examine dielectric relaxation of 

These studies are based on the connection between the dielectric loss function and the dipole-dipole correlation function, Eq. 7.7, which on integration by parts shows 

For a linear polymer containing type-A dipoles in which dipoles may be inserted in either direction, the total on-axis dipole moment of a single molecule may be written 

Here p, (r) is the dipole moment of an individual monomer unit, time-dependent because its direction in space may change, the sum proceeds over all N dipoles (whose junction atoms are therefore rationally labeled (0,1, and 0j = 

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