Modeling Dielectric Relaxation in Polymer Glass Simulations: Dynamics in the Bulk and in Supported Polymer Films

Abstract

We perform molecular dynamics simulations to study the dielectric relaxation of a bead-spring model for a polymer melt in the bulk and in supported films. By assigning dipole moments parallel and perpendicular to the backbone of all chains in the completed simulation trajectories, we calculate the dielectric spectra of so-called type-A polymers which exhibit relaxation processes due to the local motion of chain segments ("segmental mode") and due to fluctuations of the end-to-end vector ("normal mode"). We investigate the dependence of both processes on film thickness and chain length and for the segmental mode also on temperature T. We find that the relaxation of both modes is enhanced in the films relative to the bulk. For the segmental mode this difference between film and bulk dynamics increases on cooling toward the glass transition. By a layerresolved analysis of the segmental relaxation, we show that the acceleration of the average film dynamics is a consequence of a smooth gradient in relaxation, originating from both interfaces where the segmental dipoles relax much faster than in the bulk. Additionally, near the interfaces the segmental relaxation is more strongly stretched than in the center of the film where bulk behavior prevails. As the average film dynamics comprises contributions from all layers, the dielectric spectra of the films are broader than in the bulk at the same T. Finally, starting from the layer-resolved analysis which associates a dielectric function and so a capacitance with each layer, we suggest to think of a film as being a system of capacitors. The capacitors are arranged in series, if the electric (E) field is perpendicular to the plane of the film (the usual experimental situation), and in parallel, if the field is parallel to the plane. Because of these different arrangements of the capacitors, the resulting dielectric spectra depend on the direction of the E-field. For instance, we find that, although the segmental relaxation in each layer is taken to be the same for both field directions, the average dielectric spectra differ because the layer-dependent dielectric strength and the limiting high-frequency permittivity (ε ∞ ) enter into the average dielectric response in different ways for the E-field being perpendicular or parallel to the film plane.

Supercooled liquids with enhanced orientational order

“…The increase in De N exceeds 5.0 at 9 nm, and De N max decays progressively before settling to a constant value of 3.7, in films thicker than 15-20 nm. Given the purely additive contribution of each layer to the dielectric strength in our experimental configuration 33 , we might imagine a higher BOO in proximity to the interfaces, penetrating for a few nanometres. Such a length scale is larger than has been observed in metallic liquids in proximity to the crystal growth front 34 , where only a few atomic layers are affected.…”

The lifetime of the deviations from bulk behaviour in polymers confined at the nanoscale

“…Under these conditions, for non-polar systems (ζ = ∆ε/ε  1, where ε  is the value of the dielectric constant in the absence of molecular polarization), the electrical impedance of the whole film can be linearly expressed as the sum of the capacitance of the sublayers contributing to the dielectric signal. This procedure is justified by the observation that the molecular dynamics of the whole film corresponds to the dynamics averaged over the different sublayers 27 . With the goal of direct analysis of our data, we have chosen PS (ζ≈0.016), a polymer with a dielectric strength large enough to be determined precisely by an impedance analyser, but much smaller than its dielectric constant, which allowed us to avoid nonlinear convolutions.…”

Challenges in Multiscale Modeling of Polymer Dynamics

“…Aside from including a bending potential, there have now been a number of studies of the FENE model where the cutoff has been increased to include the attractive well, i.e., r cutoff =1.5∼2.5 σ. With the attractive well, the FENE model has been applied to study the glass transition temperature [127][128][129][130], scission and recombination in worm-like micelles and equilibrium polymers [131][132][133][134], surface tension [135], dielectric relaxation [136], polymer welding [137,138], strain hardening [121,122] and other properties.…”