Unexpected Stretching of Entangled Ring Macromolecules

In the melt state at equilibrium, entangled nonconcatenated ring macromolecules adapt more compact conformations compared to their linear analogs and do not form an entanglement network. We show here that, when subjected to uniaxial stretching, they exhibit a unique response, which sets them apart from any other polymer. Remarkably, whereas both linear and ring polymers strain-harden, the viscosity of the rings increases dramatically (the melt thickens) at very low stretch rates due to the unraveling of their conformations along the stretching direction. At high rates, stretching leads to viscosity thinning similar to that of entangled linear polymers, albeit with subtle differences.

Figure 1

(a) Photo of stretched polystyrene in the perpendicular direction. (b) Illustration of equilibrated specimens before stretching with different conformations of entangled linear (top) and ring (bottom) polymers. (c) Illustration of stretched specimens with different conformations of the same [as in (b)] linear (top) and ring (bottom) polymers, showing the dramatic change in conformation due to stretching [18]. For clarity, we color one macromolecule with blue in each case, to emphasize its conformation in the melt.

Figure 2

(a) Stress growth coefficient of linear ($185000\mathrm{g}/\mathrm{mol}$) and ring ($185000\mathrm{g}/\mathrm{mol}$) polymers at $130°\mathrm{C}$ and different extensional rates in the range $3\times {10}^{-3}-1{\mathrm{s}}^{-1}$. The linear viscoelastic envelopes (from Fig. S1) are depicted by solid lines. (b) The same data plotted as stress against Hencky strain in linear scale, showing that a steady state has been reached. The arrows indicate the start of steady state for the highest extensional rate.

Figure 3

Steady-state uniaxial extensional viscosity extracted from Fig. 2 at $130°\mathrm{C}$, as a function of the imposed extensional rate for the linear precursor (filled black squares), ring (open blue circles), and a linear polymer with molar mass $100000\mathrm{g}/\mathrm{mol}$ (gray stars) with about half molar mass (actually 54%). The respective zero-rate limiting viscosities extracted from the dynamic shear data (accounting for the Trouton ratio of 3 [14]) are indicated by the horizontal lines. The inverse relaxation times are shown for molar mass of $185000\mathrm{g}/\mathrm{mol}$ linear at the top (black) and for the respective ring polymers at the bottom (blue). The high-rate data of molar mass of $185000\mathrm{g}/\mathrm{mol}$ (linear and ring) polymers collapse within experimental uncertainty. The dashed line through the linear polymer data has a slope of $-0.5$ (see text). The dashed line through the ring data represents predictions of the phenomenological model (see text and the Supplemental Material). (Inset) Illustration of the stretched ring comprising a globular head with $N-n$ monomers and two double-folded tails with $n$ monomers (see also Supplemental Material [24]). The vertical arrows represent different characteristic times [24].