Molecular Scale Dynamics of Large Ring Polymers

We present neutron scattering data on the structure and dynamics of melts from polyethylene oxide rings with molecular weights up to ten times the entanglement mass of the linear counterpart. The data reveal a very compact conformation displaying a structure approaching a mass fractal, as hypothesized by recent simulation work. The dynamics is characterized by a fast Rouse relaxation of subunits (loops) and a slower dynamics displaying a lattice animal-like loop displacement. The loop size is an intrinsic property of the ring architecture and is independent of molecular weight. This is the first experimental observation of the space-time evolution of segmental motion in ring polymers illustrating the dynamic consequences of their topology that is unique among all polymeric systems of any other known architecture.

Figure 1

SANS data for the 5 K (green symbols), 10 K (red symbols), and 20 K (blue symbols) rings plotted versus $Q{R}_g$. The data yield a perfect master curve in the low $Q{R}_g$ regime. The dashed black line up to $Q{R}_g=3.5$ represents a fit to the data, the colored lines in the high $Q{R}_g$ regime are guides for the eyes. The inset shows the $N$ dependence of $R_g^2$ (red line: Gaussian expectation [26], black line: experimental data including one additional small 2 K PEO ring [9]).

Figure 2

NSE spectra for the 10 K (left panel) and 20 K (right panel) ring for $Q$ values (from top to down) 0.03, 0.05, 0.08, 0.1, 0.13, and $0.2{\AA }^{-1}$ at $T=413\mathrm{K}$. Full and empty symbols (left panel) refer to two different wavelength setups. Lines and inset, see text.

Figure 3

Center of mass mean squared displacement. $N$ versus time for low $Q=0.05{\AA }^{-1}$ for the 5 K (green), 10 K (red) and 20 K (blue) rings. The inset shows the molecular weight dependence of the diffusion coefficient approaching $D\propto N^{-2}$ for high $N$.

Figure 4

Time dependent m.s.d. of the 20 K ring. Blue line: loop relaxation at short times. Red line: dynamics of the loops derived from the motions of the slowly decaying low $p$ modes. Purple line: sum of both with a slope of $t^{0.32}$ at intermediate times. This slope is indicated by the dashed black line.