Movable Cross-links Research Articles

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.

Dynamics of the Topological Network Formed by Movable Crosslinks: Effect of Sliding Motion on Dielectric and Viscoelastic Relaxation Behavior

We investigated the dynamics of the topological network formed by rotaxane-type movable crosslinks consisting of a poly(ethyl acrylate) backbone threaded through peracetylated cyclodextrins, which ...

Preparation of hydrophilic polymeric materials with movable cross-linkers and their mechanical property

Hydrophilic polymeric materials with movable cross-linkers were obtained by the bulk copolymerization of a hydrophilic cyclodextrin monomer (γCDAAmMe) and liquid acrylamide monomers. A 2D 1H-NOESY NMR study revealed that the main chains penetrated the CD ring units, which acted as movable cross-linking points. Copolymerization of γCDAAmMe with N,N-dimethyl acrylamide (DMAA) as a small main chain monomer results in hydrophilic movable cross-linked materials (pDMAA-γCDAAmMe (x)). On the other hand, using 4-acryloylmorpholine (ACMO) or N,N-dimethylaminopropyl acrylamide (DMAPAA) as a bulky main chain monomer disfavours the formation of movable cross-links due to steric hindrance between γCDAAmMe and the side chains. In the water content range of approximately 40–80 wt%, the Young's moduli of pDMAA-γCDAAmMe (1)s are similar to those of pDMAA-MBAAm (1). However, the fracture energy of movable cross-linked materials is higher than that of than materials covalently cross-linked with N,N′–methylenebis(acrylamide) (MBAAm). An addition of water enhanced the mobility of the main chain polymers, allowing the movable cross-linking points.

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.

(Invited) Sliding Dynamics and Mechanical Properties of Slide-Ring Gels

To overcome the trade-off relationship between stiffness and toughness of conventional polymer gels with covalent cross-links, introducing dynamical cross-links into polymer network is a promising strategy. A typical example of dynamically cross-linked gels is slide-ring gel, in which polymer chains are cross-linked by rings and the cross-linking points can slide along polymer chains. When slide-ring gels are deformed, the network structure of slide-ring gels is homogenized due to the sliding of the ring molecules, which causes their high deformability [1]. We have recently performed crack propagation tests on slide-ring gels and found that their fracture energy is dominated by the sliding distance of the movable cross-links [2]. In this work, we investigate the relationship between the macroscopic fracture toughness of slide-ring gels and nano-scale sliding dynamics of rings on polymer chains. Slide-ring gels are prepared by cross-linking ring molecules of polyrotaxanes, necklace-like supramolecules consisting of cyclodextrins and polyethylene glycol. The fracture energy of slide-ring gels keeps constant at strain rates below a certain value, and decreases at a high strain rate, where the movable cross-linking points cannot slide and behave like covalent cross-links. From the strain rate dependence of the fracture energy, we have estimated the time scale for the sliding dynamics of cross-links in slide-ring gels.

Pronounced effects of the densities of threaded rings on the strain-dependent Poisson's ratio of polyrotaxane gels with movable cross-links.

The density of threaded ring molecules (fCD) in polyrotaxane (PR) chains has pronounced effects on the strain-induced swelling of PR gels where the cross-linked ring molecules are slidable along the network strands. The equilibrium Poisson's ratio (μ∞), which is a measure of the strain-induced volume change, for the PR gel increases with an increase in elongation (λ) at moderate λ but becomes a constant value () at sufficiently large λ. When the modulus exceeds a threshold value (Ec), the λ dependence of μ∞ disappears due to the loss of the slidability of the cross-links. The fraction fCD significantly influences the values of and Ec. When fCD is sufficiently small (<14%), (≈0.25) agrees with the values of μ∞ for the classical gels in good solvents. When fCD is high (>25%), varies over a wide range (0.22 < < 0.33) depending on fCD and the cross-link concentration in a complicated way. The modulus Ec at fCD = 25% is more than twice as high as that at fCD = 5% due to the finite contribution of the larger amount of uncross-linked ring molecules via combinatorial entropy in the axial polymers. The origin of the markedly small values of μ∞ (less than 0.1) at small λ is also considered on the basis of the magnitude of the accompanying force reduction caused by the slidable function of the cross-links.

Unusual Fracture Behavior of Slide-Ring Gels with Movable Cross-Links.

In this study, the quasi-static fracture behavior of slide-ring gels (SR gels), in which movable cross-links can slide on polymer chains, is for the first time investigated and compared to that of conventional polymer gels with fixed cross-links (FC gels). For the usual FC gels, there is a trade-off relation between toughness (fracture energy [Formula: see text]) and stiffness (Young's modulus E): with increasing cross-linking density, the Young's modulus E increases, while fracture energy [Formula: see text] decreases. However, SR gels show an unusual fracture behavior that contradicts this trade-off relation. The fracture energy of SR gels is independent of the Young's modulus, in other words, the cross-linking density; moreover, it rises with increasing slidable range of movable cross-links on polymer chains. A new molecular model is proposed by attributing the unusual fracture properties of SR gels to the relative sliding movement between polymer chains and cross-links. Utilizing this concept, simultaneous fulfillment of high stiffness and high toughness in polymer gels can be realized.

Slide-ring shape memory polymers with movable cross-links

The development of shape memory materials to achieve recoverable high-strain capacities at high concentration of the crosslinker is still a great challenge due to their mutual exclusiveness. Here, slide-ring shape memory polymers (SMPs) with movable cross-links were prepared by varying the amount of the polyrotaxane cross-linkers. The slide-ring SMPs not only exhibit a combination of high strength and toughness, but also outstanding recoverable high-strain capacities and fast shape recovery. The elongation of the slide-ring SMPs at 1mol% crosslinker was as high as 881%, closer to physically cross-linked SMPs. As the growing deformation strain from 100% to 800%, the slide-ring SMPs still showed excellent shape memory performance with >90% shape fixity and shape recovery. The comparative analysis among movable cross-linking, chemical cross-linking and physical cross-linking SMPs in a different way revealed that the sliding effect of the polyrotaxane cross-linking is responsible for outstanding recoverable high-strain capacities of slide-ring SMPs. This design may provide a promising strategy for brittle shape memory materials to obtain high-strain capacities, such as epoxy resin and polylactic acid.

New aspects of nonlinear elasticity of polymer gels and elastomers revealed by stretching experiments in various geometries

AbstractThis review focuses on the novel features of nonlinear elasticity for a range of gels and elastomers that were recently revealed through experiments using various types of strain such as uniaxial and biaxial stretching. Particular emphasis is placed on the magnitude of the cross‐effect of strains in different directions which can be characterized by unequal biaxial stretching. The studied materials include (1) markedly swollen hydrogels with a water content of 98%, (2) tetra‐arm poly(ethylene glycol) (Tetra‐PEG) gels with nearly uniform network structures without entanglement couplings of network strands, (3) slide‐ring gels with movable crosslinks along network strands and (4) elastomer foams with low densities of polymer solids. The magnitude of the cross‐effect of strains reflects the structural features of networks and crosslinks as well as bulk compressibility for each material. We also summarize recent results on strain‐driven swelling and the accompanying force reduction phenomena under various types of stretching. Remaining issues to be investigated are presented on the basis of existing results. © 2016 Society of Chemical Industry

Applicability of a particularly simple model to nonlinear elasticity of slide-ring gels with movable cross-links as revealed by unequal biaxial deformation.

The strain energy density function (F) of the polyrotaxane-based slide-ring (SR) gels with movable cross-links along the network strands is characterized by unequal biaxial stretching which can achieve various types of deformation. The SR gels as prepared without any post-preparation complication exhibit considerably smaller values of the ratio of the stresses (σy/σx) in the stretched (x) and constrained (y) directions in planar extension than classical chemical gels with heterogeneous and nearly homogeneous network structures do. This feature of the SR gels leads to the peculiar characteristic that the strain energy density function (F) has no explicit cross term of strains in different directions, which is in contrast to F with explicit strain cross terms for most chemical gels and elastomers. The biaxial stress-strain data of the SR gels are successfully described by F of the Gent model with only two parameters (small-strain shear modulus and a parameter representing ultimate elongation), which introduces the finite extensibility effect into the neo-Hookean model with no explicit cross term of strain. The biaxial data of the deswollen SR gels examined in previous study, which underwent a considerable reduction in volume from the preparation state, are also well described by the Gent model, which is in contrast to the case of the classical chemical gels that the stress-strain relations before and after large deswelling are not described by a common type of F due to a significant degree of collapse of the network strands in the deswollen state. These intriguing features of nonlinear elasticity of the SR gels originate from a novel function of the slidable cross-links that can maximize the arrangement entropy of cross-linked and non-cross-linked cyclic molecules in the deformed networks.

From topological gels to slide‐ring materials

ABSTRACTA novel type of gel, called a topological gel, has been recently developed with a supramolecular architecture with topological characteristics. In the topological gel, polymer chains with bulky end groups are neither covalently crosslinked as in chemical gels nor attractively interacting as in physical gels but are topologically interlocked by figure‐eight shaped crosslinks. Hence, these crosslinks can pass along the polymer chains freely to equalize the tension of the threading polymer chains similarly to pulleys; this is called the pulley effect. This concept can be applied not only to gels but also to a wide variety of polymeric materials without solvents. Then, polymeric materials with movable crosslinks are referred to as slide‐ring materials (SRMs) in a wider sense. Here, we review the synthesis, structure, physical properties, and applications of topological gels and SRMs. In particular, slide‐ring elastomers show remarkable scratch‐proof properties for application to coating materials for automobiles, cell phones, mobile computers, golf clubs, and so on. © 2014 The Authors Journal of Applied Polymer Science Published by Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 40509.

High-strain shape memory polymers with movable cross-links constructed by interlocked slide-ring structure

A novel type of shape memory polymer network with movable cross-links is designed and fabricated, which is different from the conventional chemically cross-linked or physically cross-linked networks. The unique interlocked slide-ring structure endows the material with outstanding shape memory performance even at high strain.

Pressure‐Responsive Polymer Membranes of Slide‐Ring Gels with Movable Cross‐Links

Polymer membranes comprising slide-ring gels with movable cross-links exhibit a nonlinear pressure-dependence in the fluidic flow rate. The proportional constant between the flow rate and pressure significantly changes at a critical pressure. The slide-ring gels are promising polymer membrane materials, which would allow for the on-off control of fluid permeability using an imposed pressure.

Influence of Structural Characteristics on Stretching-Driven Swelling of Polyrotaxane Gels with Movable Cross Links

Stretching-driven swelling of polyrotaxane (PR) gels whose cross-linked cyclic molecules can slide along the network strands in response to imposed strain is investigated as functions of cross-link...

Mechanics of slide-ring gels: novel entropic elasticity of a topological network formed by ring and string

Slide-ring (SR) gels are polymer networks with movable cross-links that are prepared by cross-linking polyrotaxane (PR) in which many cyclic molecules are threaded into a linear polymer chain. The elastic modulus E of SR gels shows a unique dependence on cross-linking density: at a high cross-linking density, E decreases with increasing cross-linking density. This tendency is not in agreement with conventional rubber elasticity theory. In order to explain this abnormal dependence, we propose a novel molecular theory for SR gels, which considers the alignment entropy of cyclic molecules on polymer networks. The alignment yields new entropic elasticity of the slidable network in SR gels.

Peculiar Nonlinear Elasticity of Polyrotaxane Gels with Movable Cross-Links Revealed by Multiaxial Stretching

A peculiar rubber elasticity feature of polyrotaxane (PR) gels with cross-links capable of moving along network strands is revealed by general biaxial strain testing that varies the strains in the two orthogonal directions. The influence of the strain in one direction on the stress in the other direction in the PR gels with sufficiently low cross-link concentrations is much smaller than that in conventional elastomers and gels with fixed cross-links. The stress–strain behavior of the PR gels under various types of deformation is exceptionally close to the prediction of the neo-Hookean model with no explicit strain-coupling between the different principal directions other than that resulting from volume conservation. The minimal strain-coupling between different two directions is a pronounced feature for PR gels with movable cross-links to vary the network topology in response to imposed deformation.

Novel entropic elasticity of polymeric materials: why is slide-ring gel so soft?

We have recently developed a slide-ring gel that is different from physical and chemical gels by crosslinking polyrotaxane, a necklace-like supramolecule. Slide-ring gel, consisting of movable crosslinks and free uncrosslinked cyclic molecules, shows peculiar mechanical properties, different from conventional chemical gels. For instance, slide-ring gel shows quite a low Young's modulus, which is not proportional to crosslinking density and is much lower than that of chemical gels with the same density. This low modulus arises from differences in the molecular mechanism of entropic elasticity; whereas conformational entropy is mainly responsible for elasticity in typical chemical gels and rubbers, the mechanical properties of slide-ring gel are inherently governed by the arrangement entropy of free cyclic molecules in polyrotaxane, as well as the conformational entropy of the axis polymer. This means that the softness of slide-ring gel is due to novel entropic elasticity, which is also expected to provide a sliding state and a sliding transition.

Anomaly in Stretching-Induced Swelling of Slide-Ring Gels with Movable Cross-Links

Stretching-induced swelling is investigated for polyrotaxane (PR)-based slide-ring gels with movable cross-links. The osmotic Poisson’s ratio (μos), which is a measure of strain-induced swelling, is examined as a function of imposed stretching (αx) for three types of PR gels with various degrees of the mobility of slide-rings. Classical gels with topologically fixed cross-links and PR gels with constrained slide-rings exhibit αx-independent μos. In contrast, PR gels with highly mobile slide-rings exhibit αx-dependent μos. The μos increases with αx in the case of moderate stretching (αx < 1.5), whereas it levels off in the case of high stretching (αx > 1.5). An increase in μos with elongation results from the molecular pulley effect of slide-rings that homogenizes the structure of deformed networks. The pulley effect suppresses the stretching-induced swelling that originates from an entropic force to reduce the configurational anisotropy of the deformed networks.

Chromic Slide-Ring Gel Based on Reflection from Photonic Bandgap

Here we report on a chromic slide-ring gel consisting of polyrotaxane by using a close-packed colloidal crystal as a template. In the slide-ring gel, the polymer chains with bulky end groups are not covalently cross-linked like chemical gels nor do they interact attractively like physical gels, but are topologically interlocked by figure-of-eight cross-links. The slide-ring gel has freely movable cross-links, which have a pulley effect on tensile deformation. This effect improves the mechanical properties of polymer gels. In this work, this physically and mechanically optimized polymer gel was used to make stimuli-responsive photonic band gap materials. Our gel exhibits solvatochromic behavior based on the change in structural color.

Complementary use of small-angle neutron scattering and dynamic light scattering studies for structure analysis and dynamics of polymer gels

Small-angle neutron scattering (SANS) and dynamic light scattering (DLS) have been complementarily employed in order to investigate the structure and dynamics of slide-ring (SR) gels, a class of novel polymer gels having advanced mechanical properties. SR gels consist of long flexible polymer chains and movable cross-links along the polymer chain. It is demonstrated that complementary use is necessary to explore the dynamics of SR gels. The sliding capability was verified by DLS and a low level of frozen inhomogeneities, originating from the sliding motion, was observed by SANS. DLS was also used to determine the sol–gel transition threshold and to decompose the scattering intensity into the dynamic fluctuating component and the frozen inhomogeneities. Both techniques clearly indicate the presence of the sliding mode in SR gels, which plays significant roles in the advanced mechanical and swelling properties.