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. Analysis of the simulation trajectories closely follows the treatment of Watanabe and co-workers for experimental results of dipole-inverted cis-polyisoprene solutions. The important observable quantity in experiments and simulations is the dielectric loss spectrum ε″(ω), whose shape reflects the distribution of relaxation processes for the global chain motion. The observed broadening of the spectra with increasing polymer concentration, classically attributed to overlapping of the chains, is analyzed quantitatively using a local correlation function C(n,t;m) = 1/a² 〈u(n,t)·u(m,O)〉, where u(n,t) is the bond vector of the nth segment of the chain at time t, and a² = 〈u²〉. At long times, C(n,t;m) can be expanded as a sum of its eigenmodes: C(n,t;m) = 2/NΣ_{p = 1}ⁿf_p(n)f_p(m)exp(-t/τ_p), where N is the size of the chain and τ_p and f_p are the relaxation time and the eigenfunction of the pth mode. From simulations we calculate the time correlation functions and dielectric loss spectra of multi-inverted and asymmetrically inverted polar polymers. We compute the relaxation times τ_p and the eigenfunctions of C(t,n;m). The relaxation times follow a power-law dependence τ_p∝p^-y, with γ≈2.08, and the ratios τ_p/τ₁ remain independent of the concentration, a behavior predicted by the Rouse model. On the other hand, the dependence of f_p on n deviates progressively with increasing density from the Rouse model sinusoidal prediction. The results reveal that the broadening of the spectra is a result of changes in the distribution of eigenmodes (f_p), and not in the relaxation time span γ. Our findings are consistent with the experimental observations, clearly demonstrating the adequacy of simulations for investigating the dynamic behavior of macromolecular systems.