Cooperative Chain Dynamics of Tracer Chains in Highly Entangled Polyethylene Melts

By neutron spin echo spectroscopy, we have studied the center of mass motion of short tracer chains on the molecular length scale within a highly entangled polymer matrix. The center of mass mean square displacements of the tracers independent of their molecular weight is subdiffusive at short times until it has reached the size of the tube $d$; then, a crossover to Fickian diffusion takes place. This observation cannot be understood within the tube model of reptation, but is rationalized as a result of important interchain couplings that lead to cooperative chain motion within the entanglement volume $\sim d^3$. Thus, the cooperative tracer chain motions are limited by the tube size $d$. If the center of mass displacement exceeds this size, uncorrelated Fickian diffusion takes over. Compared to the prediction of the Rouse model we observe a significantly reduced contribution of the tracer’s internal modes to the spectra corroborating the finding of cooperative rather than Rouse dynamics within $d^3$.

Figure 1

Illustration of the dynamic RPA effect on the scattering function from the PE1 tracer chain at $q$ values from above: 0.03, 0.05, $0.08{\AA }^{-1}$. The open symbols show the experimental NSE spectra, the solid colored lines the result of fitting with the dynamic RPA model, and dashed colored lines the RPA corrected scattering function. The results for $0.03{\AA }^{-1}$ and for longer tracers turned out to be affected by too high instrument background and were omitted.

Figure 2

(a) Center of mass mean square displacements MSD obtained from the RPA corrected NSE spectra. From above: PE1 (dots), PE2 (triangles), PE3 (squares), PE4 (stars); for better visibility the PE3 and PE4 MSD are shifted downwards by factors of 5 and 10, respectively. The dashed lines display the MSD due to Fickian diffusion, while the solid lines are fits to the subdiffusive regimes. (b) Master plot obtained by scaling the time axis by factors: PE1: 1.0; PE2: 0.26; PE3: 0.15; PE4: 0.075, symbols are the same as in part (a). The line indicates the Fickian diffusion law $⟨r_{\mathrm{com}}^2(t)⟩\sim t$. The arrow marks the crossover MSD. The inset displays the MSDs obtained for PE3 from $q=0.05{\AA }^{-1}$ (triangle) and from $q=0.078{\AA }^{-1}$ with (dots) and without (reversed triangle) correction for the internal Rouse modes.

Figure 3

Fickian diffusion coefficients at 490 K for different tracer chains as a function of number of monomers $N$: red dots: NSE; blue squares: scanning infrared microscopy [10]; pink triangles: PFG-NMR [19]. The interpolating black line marks a power law relationship: $D_{\mathrm{tr}}\sim N^{-1.85}$, the blue line shows the power law $D_{\text{Rouse}}\sim N^{-1}$.