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

TL;DR

This work addresses how mechanical bonds in mechanically interlocked polymers (MIPs) shape their flow behavior in dilute solutions under steady shear and uniaxial extension. Using coarse-grained Brownian dynamics with hydrodynamic interactions, the authors simulate polyrotaxanes, daisy chains, and polycatenanes across varying architectures and flow strengths, extracting tumbling dynamics, molecular extension, and viscoelastic stresses. The study reveals topology-specific rheology: all MIPs exhibit enhanced tumbling in shear, reduced normal-stress differences in extension, and weaker shear thinning, with extensional and shear viscosities showing distinct trends tied to ring density, ring size, and segment arrangements. These insights establish topology-driven design principles for MIPs in damping, drag-reduction, and smart-material applications, while highlighting degradation mechanisms at high flow where bonds can cross or dethread.

Abstract

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.

Figures (18)

• Figure 1: Schematic representation of polymers: (a) linear polymer, (b) polyrotaxane, (c) daisy chain, and (d) polycatenane. Yellow and blue beads are equivalent, the colors are chosen to highlight the interlocked architecture. Green beads are end caps to prevent dethreading in polyrotaxanes and daisy chains.
• Figure 2: Polyrotaxanes properties in extensional flow as a function of Weissenberg number (Wi): (a) fractional extension in flow direction $( \langle X \rangle / L)$, (b) first normal stress difference $(N_{1})$, (c) extensional viscosity $(\eta_{e})$. Linear polymers are shown in shades of gray with darker shades indicating more beads. Polyrotaxanes with 40, 80, and 120 backbone beads ($N_{bb}$) are shown in blue, green, and red, respectively; darker shades indicate higher ring density ($N_\mathrm{rings}/N_{bb}$). The rings in the polyrotaxanes are composed of 8 beads, regardless of backbone length.
• Figure 3: Polyrotaxane properties in shear flow as a function of Weissenberg number (Wi): (a) fractional extension in flow direction $( \langle X \rangle / L)$, (b) shear viscosity ($\eta$), (c) tumbling frequency ($\omega\tau_{R}$), and (d) first normal stress coefficient ($\psi_1$). Linear polymers are shown in shades of gray with darker shades indicating more beads. Polyrotaxanes with 40, 80, and 120 backbone beads ($N_{bb}$) are shown in blue, green, and red, respectively; darker shades indicate higher ring density ($N_\mathrm{rings}/N_{bb}$). The rings in the polyrotaxanes are composed of 8 beads, regardless of backbone length. Fitted power law exponents for $\mathrm{Wi}>10^{2}$ for $\eta$ and $\psi_1$ are reported in SI Tables E.1 and E.2, respectively.
• Figure 4: Daisy chain properties in extensional flow as a function of Weissenberg number (Wi): (a) fractional extension in flow direction $( \langle X \rangle / L)$, (b) first normal stress difference $(N_{1})$, (c) extensional viscosity $(\eta_{e})$. Linear polymers are shown in shades of gray with darker shades indicating more beads. Daisy chains with 8, 16, and 32 beads per segment (BPS) are shown in blue, green, and red, respectively; darker shades indicate more segments ($N_\mathrm{seg}$). The rings in all daisy chains are composed of 8 beads.
• Figure 5: Daisy chain properties in shear flow as a function of Weissenberg number (Wi): (a) fractional extension in flow direction $( \langle X \rangle / L)$, (b) shear viscosity ($\eta$), (c) tumbling frequency ($\omega\tau_{R}$), and (d) first normal stress coefficient ($\psi_1$). Linear polymers are shown in shades of gray with darker shades indicating more beads. Daisy chains with 8, 16, and 32 beads per segment (BPS) are shown in blue, green, and red, respectively; darker shades indicate higher number of segments ($N_\mathrm{seg}$). The rings in all daisy chains are composed of 8 beads. Fitted power law exponents for $\mathrm{Wi}>10^{2}$ for $\eta$ and $\psi_1$ are reported in SI Tables E.1 and E.2, respectively.