Mechanically Interlocked Polymers in Dilute Solution under Shear and Extensional Flows: A Brownian Dynamics Study

Mechanically interlocked polymers (MIPs) are a novel class of polymer structures in which the components are connected by mechanical bonds instead of covalent bonds. We measure the single-molecule rheological properties of polyrotaxanes, daisy chains, and polycatenanes under steady shear and steady uniaxial extension using coarse-grained Brownian dynamics simulations with hydrodynamic interactions. We obtain key rheological features, including tumbling dynamics, molecular extension, stress, and viscosity. By systematically varying structural features, we demonstrate how MIP topology governs flow response. Compared to linear polymers, all three MIP architectures exhibit enhanced tumbling in shear flow and lower normal stress differences in extensional flow. While polyrotaxanes show higher shear and extensional viscosities, polycatenanes and daisy chains have lower viscosities. In extensional flow, polyrotaxanes and polycatenanes extend earlier than linear polymers. We find that mechanical bonds suppress shear thinning and alter the coil-stretch transition observed in linear polymers. These effects arise from the mechanically bonded rings in MIPs, which expand the polymer profile in gradient direction and increase backbone stiffness due to ring-backbone repulsions. This study provides key insights into MIP flow properties, providing the foundation for their systematic development in engineering applications.

💡 Research Summary

This paper presents a comprehensive Brownian dynamics (BD) investigation of mechanically interlocked polymers (MIPs)—specifically polyrotaxanes, daisy‑chain polymers, and polycatenanes—under steady shear and steady uniaxial extensional flows in dilute solution. Using a coarse‑grained bead‑spring model, the authors incorporate Weeks–Chandler–Andersen (WCA) non‑bonded interactions, finitely extensible nonlinear elastic (FENE) springs for bonded beads, and highly repulsive “cap” potentials to prevent dethreading of rings. Hydrodynamic interactions are accounted for through the Rotne–Prager–Yamakawa tensor, enabling realistic long‑range solvent‑mediated coupling. All quantities are nondimensionalized with the bead radius a, thermal energy kBT, and diffusion time τ = ζa²/kBT.

The simulations span a wide range of Weissenberg numbers (Wi = γ̇τR for shear, Wi = ε̇τR for extension) and cover polymers of varying backbone length, ring number, and ring density. For each flow condition the authors compute fractional extensions in flow (⟨X⟩/L), gradient (⟨Y⟩/L) and vorticity (⟨Z⟩/L) directions, tumbling frequency (ωτR), shear viscosity η, extensional viscosity ηE, first normal stress difference N1, and the first normal stress coefficient ψ1.

Key findings in shear flow: (i) All three MIP architectures exhibit markedly higher tumbling frequencies than comparable linear chains, indicating that the mechanically bonded rings promote faster stretch‑tumble cycles. (ii) Polyrotaxanes, which contain multiple rings threaded onto a linear backbone and capped at the ends, show the greatest flow‑direction extension and the strongest resistance to compression in the gradient direction. This leads to higher shear viscosities for polyrotaxanes, especially as ring number increases. (iii) By contrast, polycatenanes and daisy‑chains, whose rings are covalently linked to each other, display lower shear viscosities and reduced first normal stress differences, reflecting a more flexible overall architecture. (iv) Shear thinning is noticeably weaker for all MIPs, a consequence of the additional backbone stiffening induced by ring‑backbone steric repulsion.

Key findings in extensional flow: (i) At low Wi, MIPs extend earlier than linear polymers; the equilibrium shape of a ring‑decorated chain is already more elongated, so even weak extensional fields align the molecule more efficiently. (ii) Polyrotaxanes possess higher extensional viscosities at low to moderate Wi because the threaded rings increase the effective contour length and hinder further stretching. (iii) As Wi increases, all architectures approach a fully stretched state, and the differences in extension and viscosity diminish. (iv) A critical Wi (~100 for the studied polyrotaxanes) marks the onset of mechanical‑bond failure: hydrodynamic forces become sufficient to pull rings past the end caps, reproducing experimentally observed dethreading.

Across both flow types, the presence of mechanical bonds modifies the classic coil‑stretch transition observed in linear polymers. The rings act as “rigidifying” elements that raise the effective bending stiffness, thereby smoothing the transition and shifting the coil‑stretch threshold to lower Wi. The study also demonstrates that the density of mechanical bonds (number of rings per backbone length) provides a tunable lever for tailoring rheological response: higher ring density yields higher viscosities and stronger normal stresses in shear, but also more pronounced suppression of shear thinning.

The authors discuss the implications for material design. By selecting the type of MIP (polyrotaxane vs. polycatenane vs. daisy‑chain), the number and size of rings, and the strength of end caps, engineers can program specific flow‑dependent properties such as enhanced resistance to extensional deformation, reduced shear thinning, or targeted normal stress behavior. The identified failure Wi offers a design ceiling for applications requiring mechanical integrity under high‑rate processing (e.g., extrusion, fiber spinning).

In summary, this work provides the first systematic, quantitative mapping of how mechanical interlocking topology governs single‑molecule rheology in both shear and extensional flows. The findings bridge the gap between molecular architecture and macroscopic processing behavior, laying a solid foundation for the rational development of MIP‑based high‑performance polymeric materials.