Dielectric relaxation of dipole-inverted polar polymers as studied by computer simulations

We use molecular dynamics simulations to examine the dielectric relaxation of polar macromolecules with dipoles parallel to the chain backbone. Analys is of the simulation trajectories closely follows the treatment of Watanabe and co-workers for experimental results of dipole-inverted cis-polyisopren e solutions (Macromolecules 1995, 28, 6443). The important observable quant ity in experiments and simulations is the dielectric loss spectrum epsilon "(omega), whose shape reflects the distribution of relaxation processes for the global chain motion. The observed broadening of the spectra with incre asing polymer concentration, classically attributed to overlapping of the c hains, is analyzed quantitatively using a local correlation function C(n,t; m) = 1/a(2) [u(n,t).u(m,0)], where u(n,t) is the bond vector of the nth seg ment of the chain at time t, and a(2) = [u(2)]. At long times, C(n,t;m) can be expanded as a sum of its eigenmodes: C(n,t;m) = 2/N(n)Sigma(p=1)f(p)(m) f(p)(m) exp(-t/tau(p)), where N is the size of the chain and tau(p) and f(p ) are the relaxation time and the eigenfunction of the pth mode. From simul ations we calculate the time correlation functions and dielectric loss spec tra of multi-inverted and asymmetrically inverted polar polymers. We comput e the relaxation times tau(p) and the eigenfunctions of C(t,n;m). The relax ation times follow a power-law dependence tau p proportional to p(-gamma), with gamma similar or equal to 2.08, and the ratios tau(p)/tau(1) remain in dependent of the concentration, a behavior predicted by the Rouse model. On the other hand, the dependence off, on n deviates progressively with incre asing density from the Rouse model sinusoidal prediction. The results revea l that the broadening of the spectra is a result of changes in the distribu tion of eigenmodes (f(p)), and not in the relaxation time span gamma. Our. findings are consistent with the experimental observations, clearly demonst rating the adequacy of simulations for investigating the dynamic behavior o f macromolecular systems.