String-like Collective Motion in the $\alpha $- and $\beta $- Relaxation of a Coarse-Grained Polymer Melt.

The relaxation of glass-forming liquids occurs as a two-stage process- a $\beta $-relaxation process having a relaxation time $\tau_{\beta \thinspace \thinspace }$on the order of \textit{ps,} followed by an $\alpha $-relaxation process having a relaxation time $\tau_{\alpha \thinspace \thinspace }$that ranges from \textit{ps} to \textit{min} as the fluid is cooled towards its glass transition temperature. Of course, the dramatic change of $\tau_{\alpha \thinspace }$with temperature garners the most attention because the impressive changes in $\tau_{\alpha \thinspace }$ and direct relevance of these changes to applications of glassy materials, but there has also been much interest in $\beta $-relaxation observed in neutron and other high frequency measurement methods. We investigate a model glass-forming polymer melt and establish that collective motion has a large influence on relaxation in both the $\beta $- and $\alpha $-relaxation regimes where in both regimes the collective motion takes the form string-like exchange motion of the polymer segments. The temperature dependence of the average string length is \textit{inverted} in the $\beta $- and $\alpha $-relaxation regimes where we see a progressive suppression of collective motion upon cooling in the $\beta $-relaxation regime leads to a corresponding increase in the scale of collective motion in the $\alpha $ relaxation regime. We are able to model the string formation in both regimes in terms of equilibrium polymerization models.