Slide-ring Gels Research Articles

Sliding on Slide-Ring Gels

Recent investigations have pointed to physical entanglements that greatly outnumber chemical crosslinks as key sources of energy dissipation and low friction in hydrogel networks. Slide-ring gels are an emerging class of hydrogels described by their mobile crosslinks, which are formed by rings topologically constrained to slide along linear polymer chains within the network. These materials have enjoyed decades of study by polymer chemists but have been underexplored by the tribology community. In this work, we synthesized a pseudo-rotaxane crosslinker from poly(ethylene glycol) diacrylate (PEG-diacrylate) and α-cyclodextrin-acrylate followed by hydrogel networks by connecting the sliding crosslinks with polyacrylamide chains. The mechanical and tribological properties of slide-ring hydrogels were investigated using a custom-built microtribometer. Slide-ring hydrogels exhibit unique behavior compared to conventional covalently crosslinked polyacrylamide hydrogels and offer a vast design space for future investigations.Graphical

Exploring the Impact of Ring Mobility on the Macroscopic Properties of Doubly Threaded Slide‐Ring Gel Networks

AbstractThe integration of mechanically interlocked molecules (MIMs) into polymeric materials has led to the development of mechanically interlocked polymers (MIPs). One class of MIPs that have gained attention in recent years are slide‐ring gels (SRGs), which are generally accessed by crosslinking rings on a main‐chain polyrotaxane. The mobility of the interlocked crosslinking moieties along the polymer backbone imparts enhanced properties onto these networks. An alternative synthetic approach to SRGs is to use a doubly threaded ring as the crosslinking moiety, yielding doubly threaded slide‐ring gel networks (dt‐SRGs). In this study, a photo‐curable ligand‐containing thread was used to assemble a series of metal‐templated pseudo[3]rotaxane crosslinkers that allow access to polymer networks that contain doubly threaded interlocked rings. The physicochemical and mechanical properties of these dt‐SRGs with varying size of the ring crosslinking moieties were investigated and compared to an entangled gel (EG) prepared by polymerizing the metal complex of the photo‐curable ligand‐containing thread, and a corresponding covalent gel (CG). Relative to the EG and CG, the dt‐SRGs exhibit enhanced swelling behavior, viscoelastic properties, and stress relaxation characteristics. In addition, the macroscopic properties of dt‐SRGs could be altered by “locking” ring mobility in the structure through remetalation, highlighting the impact of the mobility of the crosslinks.

Exploring the Impact of Ring Mobility on the Macroscopic Properties of Doubly Threaded Slide-Ring Gel Networks.

The integration of mechanically interlocked molecules (MIMs) into polymeric materials has led to the development of mechanically interlocked polymers (MIPs). One class of MIPs that have gained attention in recent years are slide-ring gels (SRGs), which are generally accessed by crosslinking rings on a main-chain polyrotaxane. The mobility of the interlocked crosslinking moieties along the polymer backbone imparts enhanced properties onto these networks. An alternative synthetic approach to SRGs is to use a doubly threaded ring as the crosslinking moiety, yielding doubly threaded slide-ring gel networks (dt-SRGs). In this study, a photo-curable ligand-containing thread was used to assemble a series of metal-templated pseudo[3]rotaxane crosslinkers that allow access to polymer networks that contain doubly threaded interlocked rings. The physicochemical and mechanical properties of these dt-SRGs with varying size of the ring crosslinking moieties were investigated and compared to an entangled gel (EG) prepared by polymerizing the metal complex of the photo-curable ligand-containing thread, and a corresponding covalent gel (CG). Relative to the EG and CG, the dt-SRGs exhibit enhanced swelling behavior, viscoelastic properties, and stress relaxation characteristics. In addition, the macroscopic properties of dt-SRGs could be altered by "locking" ring mobility in the structure through remetalation, highlighting the impact of the mobility of the crosslinks.

Effect of Ring Mobility on the Dynamics of the Slide-Ring Gels

Effect of Ring Mobility on the Dynamics of the Slide-Ring Gels

Micromechanics and damage in slide-ring networks.

We explore the mechanics and damage of slide-ring gels by developing a discrete model for the mechanics of chain-ring polymer systems that accounts for both crosslink motion and internal chain sliding. The proposed framework utilizes an extendable Langevin chain model to describe the constitutive behavior of polymer chains undergoing large deformation and includes a rupture criterion to innately capture damage. Similarly, crosslinked rings are described as large molecules that also store enthalpic energy during deformation and thus have their own rupture criterion. Using this formalism, we show that the realized mode of damage in a slide-ring unit is a function of the loading rate, distribution of segments, and inclusion ratio (number of rings per chain). After analyzing an ensemble of representative units under different loading conditions, we find that failure is driven by damage to crosslinked rings at slow loading rates, but polymer chain scission at fast loading rates. Our results indicate that increasing the strength of the crosslinked rings may improve the toughness of the material.

Elasticity of Slide-Ring Gels.

Slide-ring gels are polymer networks with cross-links that can slide along the chains. In contrast to conventional unentangled networks with cross-links fixed along the chains, the slide-ring networks are strain-softening and distribute tension much more uniformly between their strands due to the so-called "pulley effect". The sliding of cross-links also reduces the elastic modulus in comparison with the modulus of conventional networks with the same number density of cross-links and elastic strands. We develop a single-chain model to account for the redistribution of monomers between network strands of a primary chain. This model takes into account both the pulley effect and fluctuations in the number of monomers per network strand. The pulley effect leads to modulus reduction and uniform tension redistribution between network strands, while fluctuations in the number of strand monomers dominate the strain-softening, the magnitude of which decreases upon network swelling and increases upon deswelling.

A constitutive theory for large stretch behaviors of slide-ring gels by considering molecular frictions.

Synthetic slide-ring hydrogels display excellent mechanical properties, including high extensibility, low viscosity, high toughness, etc. Here, by considering molecular frictions induced by sliding of rings on polymer chains, we have developed a nonaffine constitutive theory for large stretch behaviors of these hydrogels. In the theory, a represented volume element of a cube is employed with one chain aligning along each cubic edge, similar to the classical 3-chain model. Different from the classical 3-chain model, crosslinks at each corner of the cube are now mobile due to ring sliding so that contour lengths of chains within the cube would adapt upon loading. Based on the virtual work principle at each time step, the stress-stretch relationship is then obtained using an explicit method. With the theory, we predict viscoelastic behaviors of several slide-ring hydrogels, which are in agreement with experiments. Our analysis clearly indicates that sliding of rings is critical for their high fracture energy. Our analysis also suggests that the molecular friction coefficient for ring sliding on chains can be very small at small stretching but large at large stretch, which might strongly depend on the normal force occurring at the interface between rings and polymer chains. This work provides insights into the understanding of the high mechanical performance of slide-ring hydrogels.

Chemorheological Monitoring of Cross-Linking in Slide-ring Gels Derived From α-cyclodextrin Polyrotaxanes.

Despite hundreds of studies involving slide-ring gels derived from cyclodextrin (CD)-based polyrotaxanes (PRs), their covalent cross-linking kinetics are not well characterized. We employ chemorheology as a tool to measure the gelation kinetics of a model slide-ring organogel derived from α-cyclodextrin/poly (ethylene glycol) PRs cross-linked with hexamethylenediisocyanate (HMDI) in DMSO. The viscoelastic properties of the gels were monitored in situ by small-amplitude oscillatory shear (SAOS) rheology, enabling us to estimate the activation barrier and rate law for cross-linking while mapping experimental parameters to kinetics and mechanical properties. Gelation time, gel point, and final gel elasticity depend on cross-linker concentration, but polyrotaxane concentration only affects gelation time and elasticity (not gel point), while temperature only affects gelation time and gel point (not final elasticity). These measurements facilitate the rational design of slide-ring networks by simple parameter selection (temperature, cross-linker concentration, PR concentration, reaction time).

Molecular-Level Elucidation of a Fracture Process in Slide-Ring Gels via Coarse-Grained Molecular Dynamics Simulations

Slide-ring (SR) gels with slidable cross-linked cyclic molecules exhibit considerably higher fracture toughness than conventional fixed cross-link (FC) gels. However, the mechanical properties of SR gels are still unsatisfactory, and thus, these gels cannot be practically applied. Therefore, molecular scale insights into the fracture mechanism of SR gels are required to improve their mechanical properties. This study conducted tensile strain simulations of FC and SR gels using a coarse-grained molecular dynamics (CGMD) method to elucidate the fracture mechanism of SR gels. The CGMD simulations showed that the SR gels exhibited higher fracture toughness than the FC gels. In the FC gels, the axis chains easily broke under a low strain because fixed cross-links constrain the polymer chain, resulting in stress concentration on the axis chains. On the contrary, in the SR gels, the axis chains did not break until a high strain was applied because the cross-linked cyclic molecules slide not to accumulate stress concentration. The analysis of the fracture mechanism of the SR gels revealed that the chain-ends are the origin of the fracture in the SR gels. The cross-linked and un-cross-linked cyclic molecules slide on the axis chains and are stacked around the chain-ends. The stacked cross-linked cyclic molecules induced stress concentrations around the chain-ends. Next, we investigated the effect of coverage on the SR gels. We found that low-coverage SR gels exhibited higher fracture toughness and ultimate strength than high-coverage SR gels because the stacked un-cross-linked cyclic molecules prevent cross-linked cyclic molecules from sliding, leading to a low fracture toughness caused by the stress concentration at the chain-ends. The axis chains of the low-coverage SR gels with a high fracture toughness deformed to the strain direction until a high strain. Thus, the low-coverage SR gels showed a high orientation toward the strain direction. A high orientation contributes to the uniform distribution of mechanical stress on the chains, leading to a high ultimate strength. Although the SR gels generally exhibit a low ultimate strength, SR gels with a low coverage ratio of 5% showed a higher ultimate strength than FC gels. Finally, we propose that, compared with the high-coverage SR gels, the low-coverage SR gels exhibit both higher fracture toughness and ultimate strength, based on the atomistic insight pertaining to the mechanism by which the low-coverage SR gels possess free space for cross-linked cyclic molecules to move to the chain-ends until a high strain is applied.

Untangling the mechanics of entanglements in slide-ring gels towards both super-deformability and toughness.

Entanglement plays a critical role in determining the dynamic properties of polymer systems, e.g., resulting in slip links and pulley effects for achieving large deformation and high strength. Although it has been studied for decades, the mechanics of entanglements for stiffness-toughness conflict is not well understood. In this study, topological knot theory incorporating an extended tube model is proposed to understand the entanglements in a slide-ring (SR) gel, which slips over a long distance to achieve large deformation and high toughness via the pulley effect. Based on topological knot theory, the sliding behavior and pulley effect of entanglements among molecular chains and cross-linked rings are thoroughly investigated. Based on rubber elasticity theory, a free-energy function is formulated to describe mechanical toughening and slipping of topological knots, while the SR gel retains the same binding energy. Finally, the effectiveness of the proposed model is verified using both finite element analysis and experimental results reported in the literature.

Simplifying topological entanglements by entropic competition of slip-links

Topological entanglements are abundant, and often detrimental, in polymeric systems in biology and materials science. Here we theoretically investigate the topological simplification of knots by diffusing slip-links (SLs), which may represent biological or synthetic molecules, such as structural maintenance of chromosome proteins or cyclodextrins in slide-ring gels. We find that SLs entropically compete with knots and can localize them, greatly facilitating their downstream simplification by transient strand-crossing. We further show that the efficiency of knot localization depends strongly on the topology of the SL network, and, informed by our findings, we discuss potential strategies to control the topology of biological and synthetic materials.

Molecular Simulation and Theoretical Analysis of Slide-Ring Gels under Biaxial Deformation.

Slide-ring (SR) gels, a new type of gels that have cross-links moving along the chains, are known to have unique mechanical characteristics. In the case of biaxial deformations, it has been experimentally shown that the stress–strain (S–S) relationships of SR gels can be well described by the neo-Hookean (NH) model. This behavior is quite different from that of conventional chemical gels, where the S–S curves deviate from the NH model. To understand the molecular mechanism of such peculiar elastic properties of SR gels, we studied the effects of movable cross-links by using molecular simulations and theoretical analysis. We calculate the S–S relationships in biaxial deformation for two types of models: slip model, where the cross-links can slide along chains representing SR gels, and non-slip model, which corresponds to conventional chemical gels. In the theoretical analysis, we calculate the S–S relationships by using the models with the Gaussian and the Langevin chains to investigate the nonlinear stretching effect of the chain in the slip and non-slip models. As a result, we found that the peculiar elastic behaviors of SR gels in biaxial deformations are well explained by the effect of movable cross-links suppressing the nonlinear stretching of the chain.

Softness, Elasticity, and Toughness of Polymer Networks with Slide-Ring Cross-Links.

Slide-ring (SR) gels cross-linked by ring molecules are characterized by softness (low Young’s modulus), elasticity (low hysteresis loss), and toughness (large fracture energy). In this article, the mechanical and fracture properties of SR gels are reviewed to clarify the physical understanding of the relationship between the molecular-level sliding dynamics of the slide-ring cross-links and macroscopic properties of SR gels. The low Young’s modulus and large fracture energy of SR gels are expressed by simple equations as a function of the degree of sliding movement. The dynamic fracture behaviors of SR gels gives us the time scale of the sliding dynamics of the cross-links, which is at the micro-sec scale. The fast sliding motion of the cross-links leads to the elasticity of the SR gels. The SR concept can be applied to solvent-free elastomers and composite materials.

Material properties and applications of mechanically interlocked polymers

Mechanically interlocked polymers (MIPs), such as polyrotaxanes and polycatenanes, are polymer architectures that incorporate a mechanical bond. In a polyrotaxane, the mechanical bond is the result of a linear dumbbell component threaded through a ring, while in a polycatenane, it is the consequence of interlocked ring components. The interlocked nature of these architectures can result in high degrees of conformational freedom and mobility of their components, which can give rise to unique property profiles. In recent years, the synthesis and studies of a range of MIPs has allowed researchers to build an initial understanding of how incorporating mechanical bonds within a polymer structure impacts its material properties. This Review focuses on the understanding of these structure–property relationships with an outlook towards their applications, specifically focusing on four main classes of MIPs: polyrotaxanes, slide-ring gels, daisy-chain polymers and polycatenanes.

Crack velocity dependent toughness of polyrotaxane networks: The sliding dynamics of rings on polymer under stretching

We investigate the fracture toughness of slide-ring (SR) gels, in which polymer chains are cross-linked by ring molecules, at various strain rates to evaluate the sliding speed of the cross-linking points. SR gels show a drastic decrease of the fracture energy at crack velocities higher than a critical value, since the sliding motion of the rings cannot catch up with the high deformation rates. From the critical transition velocity, we estimated the characteristic time scale of the sliding dynamics to be micro-seconds under the single-layer fracture assumption.

Post-synthesis modification of slide-ring gels for thermal and mechanical reconfiguration.

Ring-sliding behavior in polyrotaxanes imbues gels, elastomers, and glasses with remarkable stress-dissipation and actuation properties. Since these properties can be modulated and tuned by structural parameters, many efforts have been devoted to developing synthetic protocols that define the structures and properties of slide-ring materials. We introduce post-synthetic modifications of slide-ring gels derived from unmodified α-cyclodextrin and poly(ethylene glycol) polyrotaxanes that enable (i) actuation and control of the thermo-responsive lower critical solution temperature (LCST) behavior of ring-modified slide-ring hydrogels, and (ii) chemically bonding separate gels into hybrid or shape-reconfigured macro-structures with a slide-ring adhesive solution. The mechanical properties of the post-modified gels have been characterized by shear rheology and uniaxial tensile tests, while the corresponding xerogels were characterized by wide-angle X-ray scattering. These demonstrations show that post-synthetic modification offers a practical solution for re-configuring the properties and shapes of slide-ring gels.

Highly Elastic Slide-Ring Hydrogel with Good Recovery as Stretchable Supercapacitor.

As a new material with excellent mechanical properties and good stability, slide-ring gels have attracted attention and research. However, they cannot be widely used due to their relatively complicated synthesis. Herein, we use 6-acrylamidomethylether-modified α-cyclodextrin (αCDAAmMe) and PEG20000 diacrylate (PEG20000 DA) to construct a polypseudorotaxane. Then, the polypseudorotaxane reacts with acrylamide via a photo-initiated polymerization in situ to conveniently obtain a slide-ring hydrogel with good elastic property and high recovery property. The hydrogel can be easily stretched to 22.5 times of its original length but recovered rapidly and almost reversibly. These results enable the application of hydrogel to make an intrinsically stretchable and compressible supercapacitor after doping ions and the adhesion of commercially available carbon nanotube (CNT) paper as electrodes, giving the ionic conductivity of 17.0 mS cm-1 (comparable to that of the commercial PVA/H3 PO4 electrolyte) and the capacitance of 0.87 μF cm-2 (at the scan speed of 100 mV s-1 ), and its capacitance can be further enhanced under stretching.

Molecular Dynamics Simulation and Theoretical Model of Elasticity in Slide-Ring Gels.

In this study, molecular dynamics (MD) simulations were carried out on the uniaxial deformation of slide-ring (SR) networks with slidable cross-links to understand the relationship between the sliding of the cross-linking points and the Young's moduli of SR gels, which are lower than those of covalently cross-linked gels with the same cross-linking densities. The slidability of the cross-links in SR gels was characterized by the rate of change of the segment number between the cross-links, Nslide, estimated by the MD simulation. We have successfully constructed a molecular model for the elasticity of SR gels and proposed a simple equation for the Young's moduli of SR gels as a function of Nslide. The theoretical model was compared with the MD simulation results and experimental data.

Dynamic Light Scattering Study on Particle Diffusion in Slide-Ring Gels: Enhanced Fluctuation of Sliding Networks

In slide-ring (SR) gels, polymer chains are cross-linked by rings and can slide through the cross-linking points. The high chain mobility in SR gels is responsible for their unique physical properties such as softness, high deformability, and crack resistance. In this study, the dynamics of the polymer network in SR gels was investigated by the microrheological technique. The diffusion coefficients of the silica nanoparticles in SR gels with different cross-linking densities were measured by dynamic light scattering (DLS). It was found that the diffusion coefficient of the probe particles in the SR gels does not decrease monotonically with increasing cross-linking density even though their mesh sizes are close to the particle size. This suggests that the slidability of the cross-linking points enhances fluctuation of the polymer networks in the SR gels.

Crack propagation resistance of slide-ring gels

The crack propagation behavior of pre-cut slide-ring (SR) gels with movable cross-links is investigated and compared to that of fixed cross-link (FC) gels under uniaxial stretching at a constant speed. Two fracture stages with 20-fold difference in crack velocity are observed for both SR and FC gels. At the beginning, the crack propagates slowly, and the crack propagation resistance is in good accordance with the evaluation based on tearing modulus Tr, the initial slope of J-integral – crack tip opening displacement (CTOD) curve. Higher Tr and slower crack velocity are observed in SR gels compared to FC gels with similar modulus. Moreover, Tr decreases and crack velocity increases with increasing modulus (cross-linking density) for FC gels, whilst both parameters are modulus-independent for SR gels. This means that the slow mode crack propagation resistance of SR gels is dominated by the sliding movement of cross-links instead of the cross-linking density. However, as the strain energy input exceeds a critical value, crack accelerates abruptly and overtakes the sliding dynamics of the cross-links, thus the fracture behavior of SR gels resembles that of FC gels. Our results have revealed the strong correlation between the cross-link mobility and crack propagation resistance of SR gels.