Mechanical scission of a knotted polymer

Abstract

Molecular knots and entanglements form randomly and spontaneously in both biological and synthetic polymer chains. It is known that macroscopic materials, such as ropes, are substantially weakened by the presence of knots, but until now it has been unclear whether similar behaviour occurs on a molecular level. Here we show that the presence of a well-defined overhand knot in a polymer chain substantially increases the rate of scission of the polymer under tension (≥2.6× faster) in solution, because deformation of the polymer backbone induced by the tightening knot activates otherwise unreactive covalent bonds. The fragments formed upon severing of the knotted chain differ from those that arise from cleavage of a similar, but unknotted, polymer. Our solution studies provide experimental evidence that knotting can contribute to higher mechanical scission rates of polymers. It also demonstrates that entanglement design can be used to generate mechanophores that are among the most reactive described to date, providing opportunities to increase the reactivity of otherwise inert functional groups.

Fig. 1. Mechanical scission of an overhand knot in a polymer by cavitation-induced elongational flow.

a, Cavitation-induced elongational flow is used to stretch a gated overhand knot (a trefoil knot) derivatized with actuating polymer chains. b, Scission of the Diels–Alder gate in trefoil knot 1 reveals a transient overhand knot that contracts and eventually breaks upon continuous elongation. Red arrows indicate the direction of the force. Plain and dashed reaction arrows indicate covalent and non-covalent processes, respectively. Potential scissile bonds of the knot are shown in red.

Fig. 2. Mechanical activation of chain-centred knot 1, gate 2 and linear ligand 3.

a, Mechanical activation of chain-centred knot 1 and isolation of the resulting fragments. Conditions: (i) ultrasound (20 kHz, 11.5 W cm⁻², 1 s on/2 s off), CH₃CN, 5–10 °C, 180 min; (ii) NaOH. b, The overlay of gel-permeation chromatography traces at various sonication times of chain-centred knot 1 (tetrahydrofuran, 1 ml min⁻¹) is consistent with a rupture in the central region of the polymer. c, Partial ¹H NMR (500 MHz, CDCl₃) spectra of knot 1 before (i) and after (ii) sonication, along with a reference compound (iii), indicate opening of the gate adduct through mechanical activation. d, Mass spectrometry (electrospray ionisation high-resolution mass spectrometry, negative ion mode) identification of fragments 4, 5 and 6 in the hydrolysed post-sonication mixture. e, Structure of chain-centred gate (2) and linear ligand (3). f, Dissociation kinetics of chain-centred knot (1), gate (2) and linear ligand (3). M_t = M_n at time t, M₀ = M_n at 0 min. Solid lines correspond to a linear fit; R² (goodness of fit) = 0.963, 0.976 and 0.988 for 1, 2 and 3, respectively. Each point corresponds to the average of three sonication experiments. Data are presented as means ± s.e.m. Coloured areas indicate 95% confidence levels. Source data

Fig. 3. Computational analysis of knot scission.

a, CoGEF simulation (UB3LYP/6-31G*, gas phase) on a model knot; anchor atoms are shown in red. b, Tensile deformation of scissile (labelled a) and non-scissile (labelled b and c) C–O_napht bonds. c, Angular deformation around the scissile bond (α) and a naphthyl group (β). d, CoGEF structures at onset (i), maximal deformation (ii) and after scission (iii) correspond to the states highlighted in a. Source data