Mechanically reconfigurable polyrotaxane networks

Abstract

Mechanically reconfigurable polyrotaxane (PT) hydrogel compositions are disclosed herein that include a plurality of cross-linked diamino-polyethylene glycol (ax-PEG) chains threaded with a plurality of α-cyclodextrin (α-CD) moieties, in which the ax-PEG chains are cross-linked using 1,3,5-triformylphloroglucinol (Tp) crosslinkers. In some aspects, the PT hydrogel compositions further include dangling polyethylene glycol (d-PEG) chains optionally threaded with additional α-CD moieties.

Description

Docket No.: 021343 / WOMECHANICALLY RECONFIGURABLE POLYROTAXANE NETWORKS CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of priority to U.S. Provisional Application No. 63 / 778,668 filed on 27 March 2025, the content of which is incorporated herein by reference in its entirety.STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with government support under DE-SC0022267 awarded by the Department of Energy (DOE) and DMR2413579 awarded by the National Science Foundation (NSF). The government has certain rights in the invention.MATERIAL INCORPORATED-BY-REFERENCE

[0003] Not applicable.FIELD OF THE DISCLOSURE

[0004] The present disclosure generally relates to mechanically reconfigurable hydrogel compositions and methods of fabrication thereof.BACKGROUND OF THE DISCLOSURE

[0005] Synthetic hydrogels mimic many characteristics of biological tissues, but they lack self-strengthening and adaptive growth capabilities. Synthetic polymer networks typically lack the ability to autonomously remodel and strengthen in response to mechanical stress, a capability commonly observed in natural materials.

[0006] Hydrogels are water-containing crosslinked polymer networks. Their mechanical properties are largely determined by the topology of polymer networks, the nature of crosslinkers (whether covalent, noncovalent, or mobile, Fig 1 A), and crosslinking density. For example, the toughness of the hydrogels is greatly enhanced by introducing double networks, while the strength of hydrogels can be significantly enlarged by constructing ideal network structures. Slide-ring mobile crosslinkers and noncovalent crosslinking motifs, including coordination bonds, ionic pairs, and highly entangled polymers, are also demonstrated to be powerful in improving the toughness of hydrogels due to their energy dissipation mechanisms. These hydrogels are similar to biological tissues, which enabled their applications as wearable sensors, tissueDocket No.: 021343 / WOadhesives, and soft robotics.

[0007] One of the biggest differences between current synthetic hydrogels and biological tissues is that synthetic hydrogels lack the ability to self-repair or strengthen under stress, unlike biological tissues that can regenerate through processes like scar formation or muscle strengthening. The existing designs are effective at minimizing mechanical degradation under repeated loading, but they fall short of enabling network growth. A few notable exceptions include mechanophore-enabled crosslinking and mechano-triggered secondary polymerization in hydrogels. These networks actively create growth sites for crosslinking but only for limited load cycles, as these reactive sites are gradually depleted under repeated stress. Addressing this problem requires enabling hydrogels to reinforce and regrow in response to applied forces adaptively, creating decay -resistant, self-reinforcing smart materials with sustained mechanical strength and resilience.

[0008] Biological materials, such as skin tissues (callus) and bone, possess the remarkable ability to sense, remember, and adapt to mechanical demand1'3. Through continuous remodeling and growth, they reorganize their molecular and structural building blocks to reinforce precisely in regions that experience repeated stress or strain, thereby enhancing durability and maintaining function over extended periods (Fig. la). This combination of mechanical learning, strain / stress memory, and localized reinforcement is central to biological longevity, yet it is almost entirely absent in synthetic polymer materials.

[0009] Synthetic polymer materials4'8, such as physically9,10or covalently11,12crosslinked polymers, tend to degrade mechanically over repeated use. Even in their advanced forms, such as self-healing polymers13,14, shape-memory polymers15,16, double networks17,18, and slide-ring systems19'21, these polymers lack the ability to reversibly reconfigure and sustain a strain-prescribed, spatially resolved network architecture. Mechanophore-based polymers offer mechanically triggered covalent transformations22'25, but such changes are generally irreversible and encode only single-use memory. To date, no synthetic polymer network has demonstrated an integrated set of capabilities that parallels those observed in biological systems, including continuous mechanical learning, adaptive reinforcement, environment-fed growth, and nonlocal remodeling.

[0010] The incorporation of reconfigurable, noncovalent active growth sitesDocket No.: 021343 / WOwithin hydrogels could address the challenge of reactive site depletion, enabling adaptive reinforcement and network growth in response to mechanical forces.

[0011] Other objects and features will be in part apparent and in part pointed out hereinafter.SUMMARY OF THE DISCLOSURE

[0012] In one aspect, an adapt-ring network hydrogel composition is disclosed that includes a first amount of diamino-polyethylene glycol (ax-PEG); a second amount of 1,3,5-triformylphloroglucinol (Tp) comprising three carbaldehyde moieties; a third amount of a-cyclodextrin (a-CD), each a-CD defining a central lumen passing therethrough; and a fourth amount of a 1M Na2SO4solution. At least a portion of the first and second amino moieties of the ax-PEGs are each covalently bound to one of the three carbaldehyde moieties of the Tp’s, and the central lumens of the third amount of a-CDs are threaded over the PEG chains of the first amount of ax-PEG. Each ax-PEG includes a first and a second amino moiety covalently bonded at opposite ends of a PEG chain.2. In some aspects, the ax-PEG further comprises a molecular mass ranging from about 4 kg / mol to about 20 kg / mol. In some aspects, the first amount ax-PEG comprises about 4 wt% of the composition. In some aspects, the third amount of a-CD comprises about 8 wt% of the composition. In some aspects, the composition further comprises a unit ethylene glycol (EG) to a-CD ratio of about 4.4:1. In some aspects, the composition further comprises ax-PEGS with a molecular mass of about 4 kg / mol and an average of about 10 a-CDs threaded on each ax-PEG. In some aspects, the composition further comprises ax-PEGS with a molecular mass of about 20 kg / mol and of an average of about 33 a-CDs threaded on each ax-PEG. In some aspects, the third amount of a-CDs are configured to freely slide over the PEG chains of the first amount ax-PEG threaded through the central lumens. In some aspects, the third amount of a-CDs are configured to spontaneously form a plurality of dense crystalline domains, each dense crystalline domain comprising a dense array of a-CDs from a portion of the third amount of a-CDs. In some aspects, the plurality of dense crystalline domains are configured to spontaneously reform into a plurality of stress-directed crystalline domains in response to a mechanical loading, wherein the plurality of stress-directed crystalline domains are at least one of fragmented, translocated, and aligned relative to the plurality of dense crystalline domains. In some aspects, the mechanical loading comprises at least one ofDocket No.: 021343 / WOcyclic loading and unloading, and stretch-and-sonication. In some aspects, the plurality of stress-directed crystalline domains are configured to spontaneously reform into a plurality of dense crystalline domains in response to a solvent annealing. In some aspects, the solvent annealing comprises a DMSO / H2O exchange. In some aspects, the composition further includes a fifth amount of dangling PEG (d-PEG) comprising a third amino moiety covalently bonded at one end of a dangling PEG chain, wherein the third amino moieties of the d-PEG are covalently bonded to free carbaldehyde moieties of the second amount of Tp; and a sixth amount of free a-CDs. In some aspects, the fifth amount of dangling PEG (d-PEG) further comprises a molecular mass ranging from about 1 kg / mol to about 10 kg / mol. In some aspects, the fifth amount of dangling PEG (d-PEG) is configured to thread through the free central lumens of the free a-CDs. In some aspects, the threaded free a-CDs are configured to spontaneously form a plurality of enlarged dense crystalline domains comprising an enlarged array of a-CDs from a portion of the third amount of a-CDs and a portion of the free a-CDs. In some aspects, the plurality of enlarged dense crystalline domains are configured to spontaneously reform into a plurality of stress-directed integrated crystalline domains in response to a mechanical loading, wherein the plurality of stress-directed integrated crystalline domains are at least one of fragmented, translocated, and aligned relative to the plurality of dense crystalline domains. In some aspects, the composition is configured to autonomously generate spatially self-organized, strain-dependent reinforcement. In some aspects, the spatially self-organized, strain-dependent reinforcement comprises strain-dependent reinforcement.DESCRIPTION OF THE DRAWINGS

[0013] There are shown in the drawings arrangements that are presently discussed, it being understood, however, that the present embodiments are not limited to the precise arrangements and instrumentalities shown. While multiple embodiments are disclosed, still other embodiments of the present disclosure will become apparent to those skilled in the art from the following detailed description, which shows and describes illustrative aspects of the disclosure. As will be realized, the disclosure is capable of modifications in various aspects, all without departing from the spirit and scope of the present disclosure. Accordingly, the drawings and detailed description are to be regarded as illustrative in nature and not restrictive.Docket No.: 021343 / WO

[0014] FIG. 1 A is a schematic diagram showing biological tissues, such as skin, that remodel and strengthen in response to repeated mechanical loading, leading to localized reinforcement (callus formation).

[0015] FIG. IB is a schematic diagram illustrating an exemplary ARN hydrogel composed of a sparse PEG-based covalent network threaded with dense a-CD-based crystalline domains. Under mechanical loading, ARNs undergo strain-guided mechanical learning, in which large, randomly oriented crystalline domains transform into smaller, aligned, and slidable crystalline domains that encode the applied mechanical history. The energy landscape illustrates multiple out-of-equilibrium learned states defined by stimulus. Solvent annealing erases the learned network architecture, fully restoring the pristine state and enabling repeated cycles of learning and erasure.

[0016] FIG. 1C is a schematic diagram illustrating d-ARNs with dangling PEG chains for environment-fed growth. When supplied with external a-CD patches and subjected to repeated deformation, these networks exhibit nonlocal, mechanically guided, out-of-equilibrium growth, autonomously reinforcing regions of different strains.

[0017] FIG. ID is a graph summarizing spatial mapping of the modulus within d-ARN hydrogels for pristine, patched, and patched-with-motion conditions.

[0018] FIG. 2A is a schematic illustration of ARNs formed with different numbers of threaded a-CDs and ax-PEG lengths.

[0019] FIG. 2B is a graph summarizing nominal stress-strain curves of ARN hydrogels synthesized using different ax-PEGs.

[0020] FIG. 2C is a graph summarizing fracture energies of ARN(20k) hydrogels prepared with different fed a-CD concentrations.

[0021] FIG. 2D is a schematic diagram showing mechanical reconfiguration of ARN hydrogels under cyclic (un)loading or stretch-and-sonication, and their restoration via DMSO / H2O exchange.

[0022] FIG. 2E is a graph summarizing tensile curves of pristine ARN(20k) and ARN(20k)MT hydrogels trained by cyclic (un)loading at 100-600% strains at a tensile / recovery speed of 100 mm / min for 1,000 cycles.

[0023] FIG. 2F is a graph summarizing tensile curves of pristine ARN(20k),Docket No.: 021343 / WOARN(20k)MT, and ARN(20k)MT-restored hydrogels after DMSO / H2O exchange, along with samples partially restored by incubation in an oil bath at 70 °C for 1 or 3 days.

[0024] FIG. 2G is a graph summarizing tensile curves of ARN(20k) hydrogels after multiple cycles of mechanical training and restoration, demonstrating reversible switching between ARN(20k) and ARN(20k)MT states.

[0025] FIG. 2H is a graph summarizing tensile curves of ARN(20k), stretch-and-sonication-trained ARN(20k)ST, and ARN(20k)ST-restoredhydrogels following DMSO / H2O exchange.

[0026] FIG. 3 A contains graphs of WAXS (a) patterns of ARN(20k), ARN(20k)MT, and ARN(20k)sT hydrogels at parallel (II) and orthogonal (□) to the tensile direction. A simulated diffraction profile of a PEG600 / 6(a-CD) single crystal was included as a reference.

[0027] FIG. 3B contains graphs of SAXS patterns of ARN(20k), ARN(20k)MT, and ARN(20k)sr hydrogels at parallel (II) and orthogonal (□) to the tensile direction. A simulated diffraction profile of a PEG600 / 6(a-CD) single crystal was included as a reference.

[0028] FIG. 3C contains a coarse-grained molecular dynamics (MD) simulation snapshot obtained using the OVITO Open Visualization Tool of the pristine network with large, isotropic crystalline domains.

[0029] FIG. 3D contains a coarse-grained molecular dynamics (MD) simulation snapshot obtained using OVITO of ARN(20k)MT with smaller, aligned crystalline domains under 150% strain.

[0030] FIG. 3E contains a coarse-grained molecular dynamics (MD) simulation snapshot obtained using OVITO of ARN(20k)sT with further fragmented, highly oriented crystalline domains under 400% strain.

[0031] FIG. 3F is a graph summarizing the evolution of crystalline-domain size and number during simulated mechanical and sonication training, capturing force-driven fragmentation and alignment.

[0032] FIG. 3G is a graph summarizing the evolution of crystalline-domain stem content during simulated mechanical and sonication training, capturing force-driven fragmentation and alignment.Docket No.: 021343 / WO

[0033] FIG. 3H is a graph summarizing sliding displacements of average-sized crystalline domains during simulated tensile deformation. ARN(20k)MT and ARN(20k)sr sustain substantially greater axial sliding before rupture (x) than pristine ARN(20k). The rupture of the crystalline domain is marked by “x”.

[0034] FIG. 4A is a schematic diagram illustrating single-notched tensile tests for measuring fracture energy (single loading) and fatigue threshold (cyclic loading).

[0035] FIG. 4B is a graph summarizing tensile curves of ARN(20k), ARN(20k)MT, and ARN(20k)sT, and fracture strains (shaded regions) of their notched samples.

[0036] FIG. 4C is a graph summarizing crack extension per cycle dc / dN versus applied energy release rate G (J / m2) of ARN(20k), ARN(20k)MT, and ARN(20k)sT. The abscissa intercept defines the fatigue threshold.

[0037] FIG. 4D contains a series of photoelastic images of notched ARN(20k) under increasing strain, along with the proposed molecular pictures under mechanical loading.

[0038] FIG. 4E contains a series of photoelastic images of notched ARN(20k)MT under increasing strain, along with the proposed molecular pictures under mechanical loading.

[0039] FIG. 4F is a graph summarizing Young’s modulus versus fatigue threshold for ARN hydrogels compared with representative literature hydrogels, including single-network, entangled, double-network, and prestretched or thermally processed systems.

[0040] FIG. 4G is a graph comparing tensile strength and fatigue threshold enhancement ratios achieved through stimulus-facilitated training across ARN(20k) hydrogels and reported systems.

[0041] FIG. 5A is a schematic diagram illustrating an ARN(20k) hydrogel (120 x 11 x 1.5mm) mounted on a model knee joint and subjected to 12,000 bending cycles in an oil bath, where spatially varying strain converts an initially homogeneous network into a strain-adapted gradient architecture.

[0042] FIG. 5B contains DIC strain maps before and after adaptive learning.Docket No.: 021343 / WO

[0043] FIG. 5C contains DIC strain maps after adaptive learning.

[0044] FIG. 5D contains graphs summarizing normalized strain distribution from simulated bending of pristine ARN (upper, inset: a snapshot of the model joint simulation) and normalized strain profiles (lower) from DIC for pristine ARN and strain-adapted ARNAL. The sample center is defined as x = 0. The spatially encoded strain of ARNAL closely matched the bending strain distributions.

[0045] FIG. 6A is a schematic diagram illustrating environment-fed, mechanically guided growth in d-ARN(xk, yk) with dangling PEG chains enabling external a-CD uptake and crystalline domain growth.

[0046] FIG. 6B is a graph summarizing nominal stress-strain curves of d-ARN(20k, 4k) after immersion in a-CD bath containing a-CD concentrations of 0-100 mM after 1,200 cyclic (un)loading cycles.

[0047] FIG. 6C is a graph summarizing nominal stress-strain curves of d-ARN(20k, 4k)MT after immersion in a-CD bath containing a-CD concentrations of 0-100 mM after 1,200 cyclic (un)loading cycles.

[0048] FIG. 6D is a graph summarizing relative a-CD uptake in d-ARN(20k, 4k, CD)MT versus d-ARN(20k, 4k, CD) across a-CD bath concentrations of 0 - 50 mM..

[0049] FIG. 6E is a graph summarizing fatigue threshold of d-ARN(20k, 4k) and d-ARN(20k, 4k)MT across a-CD bath concentrations of 0 - 100 mM.

[0050] FIG. 6F contains schematic diagrams and images illustrating an experimental setup for evaluating mechanically driven radial growth. d-ARN disks (D x h = 40 x 1.2 mm) were immersed in a-CD solutions (10-100 mM) and repeatedly punched (600 mm / min, 12 mm depth, 30,000 cycles). Representative images after punching are shown.

[0051] FIG. 6G is a graph summarizing a spatial distribution of a-CD uptake across dissected regions (D = 5 mm) of punched hydrogels.

[0052] FIG. 6H contains images of d-ARN(20k, 4k) hydrogel with a 35 mM a-CD patch when subjected to cyclic bending.

[0053] FIG. 61 contains images of d-ARN(20k, 4k) hydrogel with a 35 mM a-CD patch when subjected to cyclic bending overlaid with corresponding DIC strain mapsDocket No.: 021343 / WObefore and after 12,000 cycles of bending.

[0054] FIG. 6J is a graph summarizing corresponding normalized strain profiles (ex / emax) comparing patch-only and patch+bending conditions. The sample center is defined as x = 0.

[0055] FIG. 7 (aka SFIG. 1) contains a 1HNMR spectrum of PEG4k-(OTs)2(298 K, CDC13, 400 MHz).

[0056] FIG. 8 (aka SFIG. 2) contains a 1HNMR spectrum of PEG6k-(OTs)2(298 K, CDCl3, 400 MHz).

[0057] FIG. 9 (aka SFIG. 3) contains a 1HNMR spectrum of PEGiok-(OTs)2(298 K, CDCI3, 400 MHz).

[0058] FIG. 10 (aka SFIG. 4) contains a 1HNMR spectrum of PEG20k-(OTs)2 (298 K, CDCI3, 400 MHz).

[0059] FIG. 11 (aka SFIG. 5) contains a 1HNMR spectrum of MeO-PEG4k-OTs (298 K, CDCI3, 400 MHz).

[0060] FIG. 12 (aka SFIG. 6) contains a 1HNMR spectrum of ax-PEG4k(298 K, CDCI3, 400 MHz).

[0061] FIG. 13 (aka SFIG. 7) contains a 1HNMR spectrum of ax-PEG6k(298 K, CDCl3, 400 MHz).

[0062] FIG. 14 (aka SFIG. 8) contains a 1HNMR spectrum of ax-PEGiok (298 K, CDCI3, 400 MHz).

[0063] FIG. 15 (aka SFIG. 9) contains a 1HNMR spectrum of ax-PEG20k (298 K, CDCI3, 400 MHz).

[0064] FIG. 16 (aka SFIG. 10) contains a 1HNMR spectrum of d-PEG4k(298 K, CDCI3, 400 MHz).

[0065] FIG. 17A (aka Supplementary Fig. 1 la) is a graph summarizing nominal stress-strain curves of pristine ARN hydrogels with different ax-PEG lengths.

[0066] FIG. 17B (aka Supplementary Fig. 1 lb) is a graph summarizing fracture energy of pristine ARN hydrogels with different ax-PEG lengths.

[0067] FIG. 18A (aka Supplementary Fig. 12a) is a graph comparing nominalDocket No.: 021343 / WOstress-strain curves of ARN(20k) and CN(20k).

[0068] FIG. 18B (aka Supplementary Fig. 12b) is a graph comparing cyclic (un)loading curves of ARN(20k) and CN(20k).

[0069] FIG. 18C (aka Supplementary Fig. 12c) is a graph comparing hysteresis of ARN(20k) and CN(20k).

[0070] FIG. 19A (Supplementary Fig. 13a) is a graph summarizing ratedependence analysis of nominal stress-strain curves of ARN(20k) hydrogels at tensile (and recovery) speeds of 60 mm / min, 100 mm / min, 150 mm / min, and 200 mm / min, respectively.

[0071] FIG. 19B (Supplementary Fig. 13b) is a graph summarizing ratedependence analysis of cyclic (un)loading curves of ARN(20k) hydrogels at tensile (and recovery) speeds of 60 mm / min, 100 mm / min, 150 mm / min, and 200 mm / min, respectively.

[0072] FIG. 19C (Supplementary Fig. 13c) is a graph summarizing ratedependence analysis of hysteresis of ARN(20k) hydrogels at tensile (and recovery) speeds of 60 mm / min, 100 mm / min, 150 mm / min, and 200 mm / min, respectively.

[0073] FIG. 20A (aka Supplementary Fig. 14a) is a graph summarizing nominal stress-strain curves of ARN(20k) hydrogels synthesized at different a-CD feeding ratios.

[0074] FIG. 20B (aka Supplementary Fig. 14b) is a graph summarizing fracture energy of ARN(20k) hydrogels synthesized at different a-CD feeding ratios.

[0075] FIG. 21A (aka Supplementary Fig. 15a) is a schematic diagram illustrating an experimental setup of multi-cyclic (un)loading training of hydrogels.

[0076] FIG. 2 IB (aka Supplementary Fig. 15b) is a graph illustrating cyclic (un)loading training.

[0077] FIG. 21C (aka Supplementary Fig. 15c) is a graph summarizing shakedown behavior of samples.

[0078] FIG. 22A (aka Supplementary Fig. 16a) is a graph summarizing stresscycle curves of ARN(20k) during cyclic (un)loading training at a strain of 8 = 100%.

[0079] FIG. 22B (aka Supplementary Fig. 16b) is a graph summarizing stress-Docket No.: 021343 / WOstrain curves of ARN(20k) at N=1, 5, 25, 1000 at a strain of ε = 100%.

[0080] FIG. 22C (aka Supplementary Fig. 16c) is a graph summarizing stress-cycle curves of ARN(20k) during cyclic (un)loading training at a strain of ε = 300%.

[0081] FIG. 22D (aka Supplementary Fig. 16d) is a graph summarizing stress-strain curves of ARN(20k) at N=1, 5, 25, 1000 at a strain of ε = 300%.

[0082] FIG. 22E (aka Supplementary Fig. 16e) is a graph summarizing stress-cycle curves of ARN(20k) during cyclic (un)loading training at a strain of ε = 500%.

[0083] FIG. 22F (aka Supplementary Fig. 16f) is a graph summarizing stress-strain curves of ARN(20k) at N=1, 5, 25, 1000 at a strain of ε = 500%.

[0084] FIG. 23 (aka Figure SI 7) is a graph comparing tensile curves of pristine PN(20k), and cyclic (un)loading trained PN(20k)MT by stretching to 100% strain, 300% strain, and 500% strain at tensile / recovery speeds of 100 mm / min. Each specimen was trained for 1000 cycles.

[0085] FIG. 24A (aka Supplementary Fig. 18a) is a graph summarizing stress-cycle curves of ARN(20k) during cyclic (un)loading training at a tensile / recovery speed of 60 mm / min.

[0086] FIG. 24B (aka Supplementary Fig. 18b) is a graph summarizing stress-strain curves of ARN(20k) at N=1, 5, 25, 1000 at a tensile / recovery speed of 60 mm / min.

[0087] FIG. 24C (aka Supplementary Fig. 18c) is a graph summarizing stress-cycle curves of ARN(20k) during cyclic (un)loading training at a tensile / recovery speed of 150 mm / min.

[0088] FIG. 24D (aka Supplementary Fig. 18d) is a graph summarizing stress-strain curves of ARN(20k) at N=1, 5, 25, 1000 at a tensile / recovery speed of 150 mm / min.

[0089] FIG. 24E (aka Supplementary Fig. 18e) is a graph summarizing stress-cycle curves of ARN(20k) during cyclic (un)loading training at a tensile / recovery speed of 200 mm / min.

[0090] FIG. 24F (aka Supplementary Fig. 18f) is a graph summarizing stress-strain curves of ARN(20k) at N=1, 5, 25, 1000 at a tensile / recovery speed of 200Docket No.: 021343 / WOmm / min.

[0091] FIG. 25 (aka Figure SI 9) is a graph comparing tensile curves of pristine PN(20k)), cyclic (un)loading trained PN(20k)MT at tensile / recovery speeds of 60 mm / min, 100 mm / min, 150 mm / min, and 200 mm / min. Each specimen was trained for 1000 cycles at 300% strain at each cycle.

[0092] FIG. 26 (aka Figure S20) is a graph comparing tensile curves of pristine PN(20k)), cyclic (un)loading trained PN(20k)MT at 300% strain and a tensile / recovery speed of 100 mm / min for 250, 500, and 1000 cycles.

[0093] FIG. 27A (aka Figure S21 A) is a graph comparing nominal stress-strain curves of PN and PNMT hydrogels with different ax-PEG lengths.

[0094] FIG. 27B (aka Figure S21b) is a graph comparing fracture energy of PN and PNMT hydrogels with different ax-PEG lengths.

[0095] FIG. 28 (aka Figure S22) is a schematic diagram illustrating the restoration of the mechanical features of PN(20k)MT through the DMSO-water solvent exchange process. Inserted images are PN(20k), PN(20k)MT, DMSO-swelled PN(20k)MT, and PN(20k)restoredsamples, respectively.

[0096] FIG. 29 (aka Figure S23) is a schematic diagram illustrating a stretch-and-sonication training experiment setup used to conduct experiments as described in the examples herein.

[0097] FIG. 30 (aka Figure S24) is a schematic diagram illustrating crystalline domain structures inside PN(20k) and PN(20k)sr.

[0098] FIG. 31 A (aka Figure S25a) is a graph comparing tensile curves of PN(20k) and PN(20k)sr in different pre-strains at the sonication pulse of (10 s ON, 30 s OFF, 3 h).

[0099] FIG. 31B (aka Figure S25b) is a graph comparing tensile curves of PN(20k) and PN(20k)ST at the pre-strain of 1000% at the sonication pulse of (10 s ON, 30 s OFF, 3 h) and (15 s ON, 15 s OFF, 1.5 h).

[0100] FIG. 32A (aka Figure S26a) is a series of pre-stretched PN(20k) hydrogel with a pre-notch at the applied energy release rate of 21.6 J m-2 at the cycle number of 1, 50, 200, 600, and 1000 from left to right.Docket No.: 021343 / WO

[0101] FIG. 32B (aka Figure S26b) is a series of images of another pre-stretched PN(20k) hydrogel with a pre-notch at the applied energy release rate of 263.8 J m-2 at the cycle number of 1, 50, 200, 600, and 1000 from left to right.

[0102] FIG. 32C (aka Figure S26c) is a graph comparing the 1000th cyclic loading-unloading curve of PN(20k) at cyclic strains ranging from 20% to 50%.

[0103] FIG. 32D (aka Figure S26d) is a graph comparing extension of crack (Ac) of PN(20k) as a function of the number (N) of cycles at cyclic strains ranging from 20% to 50%.

[0104] FIG. 32E (aka Figure S26e) is a graph summarizing the extension per cycle of crack (dc / dN) of PN(20k)as a function of energy release rate (G) ranging from 0 - 240 J.m-2.

[0105] FIG. 33A (aka Figure S27a) is a series of images of pre-stretched PN(20k)MT hydrogel with a pre-notch at the applied energy release rate of 21.6 J m-2 at the cycle number of 1, 50, 200, 600, and 1000 from left to right.

[0106] FIG. 33B (aka Figure S27b) is a series of images of another pre-stretched PN(20k)MT hydrogel with a pre-notch at the applied energy release rate of 263.8 J m-2 at the cycle number of 1, 50, 200, 600, and 1000 from left to right.

[0107] FIG. 33C (aka Figure S27c) is a graph comparing the 1000th cyclic loading-unloading curve of PN(20k)MT hydrogel at cyclic strains ranging from 20% to 50%.

[0108] FIG. 33D (aka Figure S27d) is a graph comparing extension of crack (Ac) as a function of the number (N) of cycles of PN(20k)MT hydrogel at cyclic strains ranging from 20% to 50%.

[0109] FIG. 33E (aka Figure S27e) is a graph summarizing the extension per cycle of crack (dc / dN) of pre-stretched PN(20k)MT hydrogel as a function of energy release rate (G) ranging from 0 - 240 J.m-2.

[0110] FIG. 34A (aka Figure S28a) is a series of images of pre-stretched PN(20k)MT hydrogel with a pre-notch at the applied energy release rate of 21.6 J m-2 at the cycle number of 1, 50, 200, 600, and 1000 from left to right.

[0111] FIG. 34B (aka Figure S28b) is a series of images of another pre-stretchedDocket No.: 021343 / WOPN(20k)MT hydrogel with a pre-notch at the applied energy release rate of 263.8 J m-2 at the cycle number of 1, 50, 200, 600, and 1000 from left to right.

[0112] FIG. 34C (aka Figure S28c) is a graph comparing the 1000th cyclic loading-unloading curve of PN(20k)MT hydrogel at cyclic strains ranging from 20% to 50%.

[0113] FIG. 34D (aka Figure S28d) is a graph comparing extension of crack (Ac) as a function of the number (N) of cycles of PN(20k)MT hydrogel at cyclic strains ranging from 20% to 50%.

[0114] FIG. 34E (aka Figure S28e) is a graph summarizing the extension per cycle of crack (dc / dN) of pre-stretched PN(20k)MT hydrogel as a function of energy release rate (G) ranging from 0 - 240 J.m-2

[0115] FIG. 35 (aka Figure S29.) is a schematic illustration of the SAXS or WAXS experiment setup. To avoid blockage of scattering signals at 0° and 90°, the tensile direction of the specimen was maintained at about 45° of angle relative to the vertical plane.

[0116] FIG. 36 (aka Figure S30.) is a graph summarizing WAXS patterns (inserted) and profiles the simulated PXRD profile of PEG600-(OH)2 / 6(a-CD) (37), PN(20k), PN(20k)MT, and PN(20k)sr from bottom to top.

[0117] FIG. 37A (aka Figure S3 la.) is a graph summarizing SAXS patterns (inserted) and the correlated scattering intensity I versus vector q parallel (i.e., 9 = 0°, 7 / ’) or perpendicular (i.e., 9 = 90°, ‘1’) to the pre-stretched directions of PN(20k) hydrogel.

[0118] FIG. 37B (aka Figure S3 lb.) is a graph summarizing the sector average scattering intensity I versus q of PN(20k), and the fitted curve by combined DAB and cylinder form factors.

[0119] FIG. 38A (aka Figure S32a.) is a graph summarizing SAXS patterns (inserted) and the correlated scattering intensity I versus vector q parallel (i.e., 9 = 0°, 7 / ’) or perpendicular (i.e., 9 = 90°, ‘1’) to the pre-stretched directions of PN(20k)MT hydrogel.

[0120] FIG. 38B (aka Figure S32b.) is a graph summarizing the sector average scattering intensity I versus q of PN(20k)MT, and the fitted curve by combined DAB andDocket No.: 021343 / WOcylinder form factors.

[0121] FIG. 39A (aka Figure S33a.) is a graph summarizing SAXS patterns (inserted) and the correlated scattering intensity I versus vector q parallel (i.e., 9 = 0°, 7 / ’) or perpendicular (i.e., 9 = 90°, ‘1’) to the pre-stretched directions of PN(20k)sr hydrogel.

[0122] FIG. 39B (aka Figure S33b.) is a graph summarizing the sector average scattering intensity I versus q of PN(20k)sr, and the fitted curve by combined DAB and cylinder form factors.

[0123] FIG. 40A (aka Figure S34a.) contains ESEM images of PN(20k) (left), PN(20k)MT (middle), and PN(20k)sr (right); scale bar = 30 pm and inserted arrows illustrate the tensile directions.

[0124] FIG. 40B (aka Figure S34b.) contains ESEM images of PN(20k) (left), PN(20k)MT (middle), and PN(20k)sr (right); scale bar = 10 pm and inserted arrows illustrate the tensile directions.

[0125] FIG. 41 (aka Figure S35.) is a schematic illustration of a photoelasticity experimental setup.

[0126] FIG. 42A (aka Figure S36a) contains a series of photoelastic fringe pattern images in pristine and mechanically trained PN hydrogels for an unnotched PN(20k) hydrogel.

[0127] FIG. 42B (aka Figure S36b) contains a series of photoelastic fringe pattern images in pristine and mechanically trained PN hydrogels for a notched PN(20k) hydrogel.

[0128] FIG. 42C (aka Figure S36c) contains a series of photoelastic fringe pattern images in pristine and mechanically trained PN hydrogels for an unnotched PN(20k)MT hydrogel.

[0129] FIG. 42D (aka Figure S36d) contains a series of photoelastic fringe pattern images in pristine and mechanically trained PN hydrogels for a notched PN(20k) MT hydrogel.

[0130] FIG. 43A (aka Figure S37a) is an image of a regular lattice network of fully flexible polymer backbones represented as linear tubes in a PN(20k) bead-springDocket No.: 021343 / WOmodel.

[0131] FIG. 43B (aka Figure S37b) contains an image of a regular lattice network of fully flexible polymer backbones in FIG. 43A represented as linear tubes and a-CDs along the polymer backbones represented as beads in a PN(20k) bead-spring model.

[0132] FIG. 43C (aka Figure S37c) contains the PN(20k) bead-spring model of FIG. 43B equilibrated with an a-CD-a-CD attraction of e = 0.6.

[0133] FIG. 44A (aka Figure S38a) is a graph summarizing mean-square-displacement (MSD) of a-CDs along the polymer backbone with decreasing macrocycle-backbone σLJ values.

[0134] FIG. 44B (aka Figure S38b) is a graph summarizing changes in crystal fraction of crystalline domains during equilibration of pristine gel samples.

[0135] FIG. 44C (aka Figure S38c) is a graph summarizing changes in the number of crystals of the crystal fraction of crystalline domains during equilibration of pristine gel samples.

[0136] FIG. 44D (aka Figure S38d) is a graph of a stress-strain curve from an MD simulation of PN(20k) cyclic loading treatment after the first cyclic loading with a complete recovery to the initial box dimensions.

[0137] FIG. 44E (aka Figure S38e) is a graph of a stress-strain curve from an MD simulation of PN(20k) cyclic loading treatment after the second cyclic loading with a complete recovery to the initial box dimensions.

[0138] FIG. 44F (aka Figure S38f) is a graph of a stress-strain curve from an MD simulation of PN(20k) cyclic loading treatment after the third cyclic loading with a complete recovery to the initial box dimensions.

[0139] FIG. 44G (aka Figure S38g) is a graph of a stress-strain curve from an MD simulation of PN(20k) cyclic loading treatment after the first cyclic loading with a recovery to a strain of 150%.

[0140] FIG. 44H (aka Figure S38h) is a graph of a stress-strain curve from an MD simulation of PN(20k) cyclic loading treatment after the second cyclic loading with a complete to a strain of 150%.

[0141] FIG. 44I (aka Figure S38i) is a graph of a stress-strain curve from an MDDocket No.: 021343 / WOsimulation of PN(20k) cyclic loading treatment after the third cyclic loading with a complete recovery to a strain of 150%.

[0142] FIG. 45 (aka Figure S39) contains snapshots of PN(20k)MT networks at 150% strain after three iterative uniaxial deformation / recovery cycles.

[0143] FIG. 46A (aka Figure S40a) is a graph comparing the number of crystals within the crystalline domains before and after sonication at 1000% strain.

[0144] FIG. 46B (aka Figure S40b) is a graph summarizing the crystal fraction within the crystalline domains after sonication at 1000% strain.

[0145] FIG. 46C (aka Figure S40c) is a graph showing the stress-strain curve of the recovery of extended gels after sonication and crystallization.

[0146] FIG. 47 (Figure S41) contain snapshots of PN(20k)sr networks at 400% strain after sonication and recovery.

[0147] FIG. 48 (Figure S42.) is a graph summarizing crystalline domain orientation with respect to the deformation direction of the system after iterative mechanical deformations and sonication treatment.

[0148] FIG. 49A (Figure S43a) is a graph comparing nominal stress-strain curves of PN(20k, Ik) in different a-CD (Na₂SO₄ 1.0 M) aqueous solutions.

[0149] FIG. 49B (Figure S43b) is a graph comparing fracture energy of PN(20k, Ik) in different a-CD (Na₂SO₄ 1.0 M) aqueous solutions.

[0150] FIG. 50A (Figure S44a) is a graph comparing nominal stress-strain curves of d-PN(20k, 2k) in different a-CD (Na2SO4 1.0 M) aqueous solutions.

[0151] FIG. 50B (Figure S44b) is a graph comparing fracture energy of d-PN(20k, 2k) in different a-CD (Na2SO4 1.0 M) aqueous solutions.

[0152] FIG. 51A (Figure S45a) is a graph comparing nominal stress-strain curves of d-PN(20k, 4k) in different a-CD (Na2SO4 1.0 M) aqueous solutions.

[0153] FIG. 51B (Figure S45b) is a graph comparing fracture energy of d-PN(20k, 4k) in different a-CD (Na2SO4 1.0 M) aqueous solutions.

[0154] FIG. 52A (Figure S46a) is a graph comparing nominal stress-strain curves of d-PN(20k, 5k) in different a-CD (Na2SO4 1.0 M) aqueous solutions.Docket No.: 021343 / WO

[0155] FIG. 52B (Figure S46b) is a graph comparing fracture energy of d-PN(20k, 5k) in different a-CD (Na₂SO₄ 1.0 M) aqueous solutions.

[0156] FIG. 53A (Figure S47a) is a graph comparing nominal stress-strain curves of d-PN(20k, 10k) in different a-CD (Na₂SO₄ 1.0 M) aqueous solutions.

[0157] FIG. 53B (Figure S47b) is a graph comparing fracture energy of d-PN(20k, 10k) in different a-CD (Na₂SO₄ 1.0 M) aqueous solutions.

[0158] FIG. 54A (Figure S48a) is a graph summarizing stress over 1200 cycles of a training process in 0 mM of nominal stress-strain curves of d-PN(20k, 4k) in 0 mM of a-CD aqueous solution; tensile and recovery rates are 100 mm / min.

[0159] FIG. 54B (Figure S48b) is a graph comparing stress-strain curves at different cycles of the training process of FIG. 54 A.

[0160] FIG. 54C (Figure S48c) is a graph summarizing stress over 1200 cycles of a training process of d-PN(20k, 4k) in 10 mM of a-CD aqueous solution; tensile and recovery rates are 100 mm / min.

[0161] FIG. 54D (Figure S48d) is a graph comparing stress-strain curves at different cycles of the training process of FIG. 54C.

[0162] FIG. 54E (Figure S48e) is a graph summarizing stress over 1200 cycles of a training process of d-PN(20k, 4k) in 50 mM of a-CD aqueous solution; tensile and recovery rates are 100 mm / min.

[0163] FIG. 54F (Figure S48f) is a graph comparing stress-strain curves at different cycles of the training process of FIG. 54E.

[0164] FIG. 54G (Figure S48g) is a graph summarizing stress over 1200 cycles of a training process of d-PN(20k, 4k) in 100 mM of a-CD aqueous solution; tensile and recovery rates are 100 mm / min.

[0165] FIG. 54H (Figure S48h) is a graph comparing stress-strain curves at different cycles of the training process of FIG. 54G.

[0166] FIG. 55A (aka Figure S49a) is a graph comparing nominal stress-strain curves of d-PN(20k, 4k, a IIM)MT trained in different concentrations of a-CD aqueous solutions.

[0167] FIG. 55B (aka Figure S49b) is a graph summarizing changes in fractureDocket No.: 021343 / WOenergy of d-PN(20k, 4k, a IIM)MT hydrogels trained in different concentrations of a-CD aqueous solutions.

[0168] FIG. 55C (aka Figure S49c) is a graph summarizing changes in fatigue threshold values of d-PN(20k,4k, a hydrogels trained in different concentrations of a-CD aqueous solutions.

[0169] FIG. 56A (aka Figure S50a) contains images of pre-stretched d-PN(20k, 4k, 0 mM) hydrogel with a pre-notch at the applied energy release rate of 11 J m-2 at the cycle number of 1, 250, 500, 750, and 1000 from left to right.

[0170] FIG. 56B (aka Figure S50b) contains images of another pre-stretched d-PN(20k, 4k, 0 mM) with a pre-notch at the applied energy release rate of 58 J m-2 at the cycle number of 1, 250, 500, 750 and 1000 from left to right.

[0171] FIG. 56C (aka Figure S50c) is a graph comparing the 1000th cyclic loading-unloading curves of unnotched d-PN(20k, 4k, 0 mM) hydrogels at different strains.

[0172] FIG. 56D (aka Figure S50d) is a graph comparing the extension of a crack (Ac) within unnotched d-PN(20k, 4k, 0 mM) hydrogels as a function of the number of load cycles (N).

[0173] FIG. 56E (aka Figure S50e) is a graph summarizing the extension per cycle (dc / dN) within unnotched d-PN(20k, 4k, 0 mM) hydrogels as a function of energy release rate G.

[0174] FIG. 57A (aka Figure S51a) contains images of pre-stretched d-PN(20k, 4k, 25 mM) hydrogel with a pre-notch at the applied energy release rate of 11 J m-2 at the cycle number of 1, 250, 500, 750, and 1000 from left to right.

[0175] FIG. 57B (aka Figure S5 lb) contains images of another pre-stretched d-PN(20k, 4k, 25 mM) with a pre-notch at the applied energy release rate of 58 J m-2 at the cycle number of 1, 250, 500, 750 and 1000 from left to right.

[0176] FIG. 57C (aka Figure S51c) is a graph comparing the 1000th cyclic loading-unloading curves of unnotched d-PN(20k, 4k, 25 mM) hydrogels at different strains.

[0177] FIG. 57D (aka Figure S5 Id) is a graph comparing the extension of a crackDocket No.: 021343 / WO(Ac) within unnotched d-PN(20k, 4k, 25 mM) hydrogels as a function of the number of load cycles (N).

[0178] FIG. 57E (aka Figure S5 le) is a graph summarizing the extension per cycle (dc / dN) within unnotched d-PN(20k, 4k, 25 mM) hydrogels as a function of energy release rate G.

[0179] FIG. 58A (aka Figure S52a) contains images of pre-stretched d-PN(20k, 4k, 35 mM) hydrogel with a pre-notch at the applied energy release rate of 11 J m-2 at the cycle number of 1, 250, 500, 750, and 1000 from left to right.

[0180] FIG. 58B (aka Figure S52b) contains images of another pre-stretched d-PN(20k, 4k, 35 mM) with a pre-notch at the applied energy release rate of 58 J m-2 at the cycle number of 1, 250, 500, 750 and 1000 from left to right.

[0181] FIG. 58C (aka Figure S52c) is a graph comparing the 1000th cyclic loading-unloading curves of unnotched d-PN(20k, 4k, 35 mM) hydrogels at different strains.

[0182] FIG. 58D (aka Figure S52d) is a graph comparing the extension of a crack (Ac) within unnotched d-PN(20k, 4k, 35 mM) hydrogels as a function of the number of load cycles (N).

[0183] FIG. 58E (aka Figure S52e) is a graph summarizing the extension per cycle (dc / dN) within unnotched d-PN(20k, 4k, 35 mM) hydrogels as a function of energy release rate G.

[0184] FIG. 59A (aka Figure S53a) contains images of pre-stretched d-PN(20k, 4k, 50 mM) hydrogel with a pre-notch at the applied energy release rate of 11 J m-2 at the cycle number of 1, 250, 500, 750, and 1000 from left to right.

[0185] FIG. 59B (aka Figure S53b) contains images of another pre-stretched d-PN(20k, 4k, 50 mM) with a pre-notch at the applied energy release rate of 58 J m-2 at the cycle number of 1, 250, 500, 750 and 1000 from left to right.

[0186] FIG. 59C (aka Figure S53c) is a graph comparing the 1000th cyclic loading-unloading curves of unnotched d-PN(20k, 4k, 50 mM) hydrogels at different strains.

[0187] FIG. 59D (aka Figure S53d) is a graph comparing the extension of a crackDocket No.: 021343 / WO(Ac) within unnotched d-PN(20k, 4k, 50 mM) hydrogels as a function of the number of load cycles (N).

[0188] FIG. 59E (aka Figure S53e) is a graph summarizing the extension per cycle (dc / dN) within unnotched d-PN(20k, 4k, 50 mM) hydrogels as a function of energy release rate G.

[0189] FIG. 60A (aka Figure S54a) contains images of pre-stretched d-PN(20k, 4k, 100 mM) hydrogel with a pre-notch at the applied energy release rate of 11 J m-2 at the cycle number of 1, 250, 500, 750, and 1000 from left to right.

[0190] FIG. 60B (aka Figure S54b) contains images of another pre-stretched d-PN(20k, 4k, 100 mM) with a pre-notch at the applied energy release rate of 58 J m-2 at the cycle number of 1, 250, 500, 750 and 1000 from left to right.

[0191] FIG. 60C (aka Figure S54c) is a graph comparing the 1000th cyclic loading-unloading curves of unnotched d-PN(20k, 4k, 100 mM) hydrogels at different strains.

[0192] FIG. 60D (aka Figure S54d) is a graph comparing the extension of a crack (Ac) within unnotched d-PN(20k, 4k, 100 mM) hydrogels as a function of the number of load cycles (N).

[0193] FIG. 60E (aka Figure S54e) is a graph summarizing the extension per cycle (dc / dN) within unnotched d-PN(20k, 4k, 100 mM) hydrogels as a function of energy release rate G.

[0194] FIG. 61 A (aka Figure S55a) contains images of pre-stretched d-PN(20k, 4k, 0 mM)MT hydrogel with a pre-notch at the applied energy release rate of 11 J m-2 at the cycle number of 1, 250, 500, 750, and 1000 from left to right.

[0195] FIG. 61B (aka Figure S55b) contains images of another pre-stretched d-PN(20k, 4k, 0 mM)MT with a pre-notch at the applied energy release rate of 58 J m-2 at the cycle number of 1, 250, 500, 750 and 1000 from left to right.

[0196] FIG. 61C (aka Figure S55c) is a graph comparing the 1000th cyclic loading-unloading curves of unnotched d- PN(20k, 4k, 0 mM)MT hydrogels at different strains.

[0197] FIG. 61D (aka Figure S55d) is a graph comparing the extension of a crackDocket No.: 021343 / WO(Ac) within unnotched d- PN(20k, 4k, 0 hydrogels as a function of the number of load cycles (N).

[0198] FIG. 61E (aka Figure S55e) is a graph summarizing the extension per cycle (dc / dN) within unnotched d- PN(20k, 4k, 0 mM)MT hydrogels as a function of energy release rate G.

[0199] FIG. 62A (aka Figure S56a) contains images of pre-stretched d-PN(20k, 4k, 15 mM)MT hydrogel with a pre-notch at the applied energy release rate of 11 J m-2 at the cycle number of 1, 250, 500, 750, and 1000 from left to right.

[0200] FIG. 62B (aka Figure S56b) contains images of another pre-stretched d-PN(20k, 4k,15 with a pre-notch at the applied energy release rate of 58 J m-2 at the cycle number of 1, 250, 500, 750 and 1000 from left to right.

[0201] FIG. 62C (aka Figure S56c) is a graph comparing the 1000th cyclic loading-unloading curves of unnotched d- PN(20k, 4k, 15hydrogels at different strains.

[0202] FIG. 62D (aka Figure S56d) is a graph comparing the extension of a crack (Ac) within unnotched d- PN(20k, 4k, 15 mM)MT hydrogels as a function of the number of load cycles (N).

[0203] FIG. 62E (aka Figure S56e) is a graph summarizing the extension per cycle (dc / dN) within unnotched d- PN(20k, 4k, 15 mM)MT hydrogels as a function of energy release rate G.

[0204] FIG. 63 A (aka Figure S57a) contains images of pre-stretched d-PN(20k, 4k, 25 mM)MT hydrogel with a pre-notch at the applied energy release rate of 11 J m-2 at the cycle number of 1, 250, 500, 750, and 1000 from left to right.

[0205] FIG. 63B (aka Figure S57b) contains images of another pre-stretched d-PN(20k, 4k, 25 mM)MT with a pre-notch at the applied energy release rate of 58 J m-2 at the cycle number of 1, 250, 500, 750 and 1000 from left to right.

[0206] FIG. 63C (aka Figure S57c) is a graph comparing the 1000th cyclic loading-unloading curves of unnotched d- PN(20k, 4k, 25 mM)MT hydrogels at different strains.

[0207] FIG. 63D (aka Figure S57d) is a graph comparing the extension of a crackDocket No.: 021343 / WO(Ac) within unnotched d- PN(20k, 4k, 25 mM)MT hydrogels as a function of the number of load cycles (N).

[0208] FIG. 63E (aka Figure S57e) is a graph summarizing the extension per cycle (dc / dN) within unnotched d- PN(20k, 4k, 25 mM)MT hydrogels as a function of energy release rate G.

[0209] FIG. 64A (aka Figure S58a) contains images of pre-stretched d-PN(20k, 4k, 35 mM)MT hydrogel with a pre-notch at the applied energy release rate of 11 J m-2 at the cycle number of 1, 250, 500, 750, and 1000 from left to right.

[0210] FIG. 64B (aka Figure S58b) contains images of another pre-stretched d-PN(20k, 4k,35 with a pre-notch at the applied energy release rate of 58 J m-2 at the cycle number of 1, 250, 500, 750 and 1000 from left to right.

[0211] FIG. 64C (aka Figure S58c) is a graph comparing the 1000th cyclic loading-unloading curves of unnotched d- PN(20k, 4k, 35hydrogels at different strains.

[0212] FIG. 64D (aka Figure S58d) is a graph comparing the extension of a crack (Ac) within unnotched d- PN(20k, 4k, 35 mM)MT hydrogels as a function of the number of load cycles (N).

[0213] FIG. 64E (aka Figure S58e) is a graph summarizing the extension per cycle (dc / dN) within unnotched d- PN(20k, 4k, 35 mM)MT hydrogels as a function of energy release rate G.

[0214] FIG. 65A (aka Figure S59a) contains images of pre-stretched d-PN(20k, 4k, 50 mM)MT hydrogel with a pre-notch at the applied energy release rate of 11 J m-2 at the cycle number of 1, 250, 500, 750, and 1000 from left to right.

[0215] FIG. 65B (aka Figure S59b) contains images of another pre-stretched d-PN(20k, 4k, 50 mM)MT with a pre-notch at the applied energy release rate of 58 J m-2 at the cycle number of 1, 250, 500, 750 and 1000 from left to right.

[0216] FIG. 65C (aka Figure S59c) is a graph comparing the 1000th cyclic loading-unloading curves of unnotched d- PN(20k, 4k, 50 mM)MT hydrogels at different strains.

[0217] FIG. 65D (aka Figure S59d) is a graph comparing the extension of a crackDocket No.: 021343 / WO(Ac) within unnotched d- PN(20k, 4k, 50 mM)MT hydrogels as a function of the number of load cycles (N).

[0218] FIG. 65E (aka Figure S59e) is a graph summarizing the extension per cycle (dc / dN) within unnotched d- PN(20k, 4k, 50 mM)MT hydrogels as a function of energy release rate G.

[0219] FIG. 66A (aka Figure S60a) contains images of pre-stretched d-PN(20k, 4k, 100 mM)MT hydrogel with a pre-notch at the applied energy release rate of 11 J m-2 at the cycle number of 1, 250, 500, 750, and 1000 from left to right.

[0220] FIG. 66B (aka Figure S60b) contains images of another pre-stretched d-PN(20k, 4k, 100with a pre-notch at the applied energy release rate of 58 J m-2 at the cycle number of 1, 250, 500, 750 and 1000 from left to right.

[0221] FIG. 66C (aka Figure S60c) is a graph comparing the 1000th cyclic loading-unloading curves of unnotched d- PN(20k, 4k, 100hydrogels at different strains.

[0222] FIG. 66D (aka Figure S60d) is a graph comparing the extension of a crack (Ac) within unnotched d- PN(20k, 4k, 100 mM)MT hydrogels as a function of the number of load cycles (N).

[0223] FIG. 66E (aka Figure S60e) is a graph summarizing the extension per cycle (dc / dN) within unnotched d- PN(20k, 4k, 100 mM)MT hydrogels as a function of energy release rate G.

[0224] FIG. 67 (aka Figure S61) is a graph that includes WAXS patterns (inserted) and profiles of the simulated of PEG600-(OH)2 / 6(a-CD)(bottom), 0 mM a-CD immersed d-PN(20k, 4k, 0 mM) (middle) and 0 mM a-CD trained d-PN(20k, 4k, 0 mM)MT (top) hydrogels parallel (i.e., 9 = 0°, 7 / ’) and perpendicular (i.e., 9 = 90°, ‘1’) to the tensile direction.

[0225] FIG. 68 (aka Figure S62) is a graph that includes WAXS patterns (inserted) and profiles of the simulated of PEG600-(OH)2 / 6(a-CD)(bottom), 35 mM a-CD immersed d-PN(20k, 4k, 35 mM) (middle) and 35 mM a-CD trained d-PN(20k, 4k, 35 IIIM)MT (top) hydrogels parallel (i.e., 9 = 0°, 7 / ’) and perpendicular (i.e., 9 = 90°, ‘1’) to the tensile direction.

[0226] FIG. 69 (aka Figure S63) is a graph that includes WAXS patternsDocket No.: 021343 / WO(inserted) and profiles of the simulated of PEG600-(OH)2 / 6(a-CD)(bottom), 50 mM a-CD immersed d-PN(20k, 4k, 50 mM) (middle) and 50 mM a-CD trained d-PN(20k, 4k, 50 mM)MT (top) hydrogels parallel (i.e., 9 = 0°, 7 / ’) and perpendicular (i.e., 9 = 90°, ‘1’) to the tensile direction.

[0227] FIG. 70A (aka Figure S64) is a graph that includes a SAXS pattern (inserted) and the correlated scattering intensity I versus vector q parallel (i.e., 9 = 0°, 7 / ’) or perpendicular (i.e., 9 = 90°, ‘1’) to the pre-stretched directions of d-PN(20k, 4k, 0 mM) hydrogel.

[0228] FIG. 70B (aka Figure S64) is a graph that summarizes the sector average scattering intensity I versus q of d-PN(20k, 4k, 0 mM), and the fitted curve by combined DAB and cylinder form factors.

[0229] FIG. 70C (aka Figure S64) is a graph that includes a SAXS pattern (inserted) and the correlated scattering intensity I versus vector q parallel (i.e., 9 = 0°, 7 / ’) or perpendicular (i.e., 9 = 90°, ‘1’)MT to the pre-stretched directions of d-PN(20k, 4k, 0 mM) hydrogel.

[0230] FIG. 70D (aka Figure S64) is a graph that summarizes the sector average scattering intensity I versus q of d-PN(20k, 4k, 0 mM) MT, and the fitted curve by combined DAB and cylinder form factors.

[0231] FIG. 71 A (aka Figure S65) is a graph that includes a SAXS pattern (inserted) and the correlated scattering intensity I versus vector q parallel (i.e., 9 = 0°, 7 / ’) or perpendicular (i.e., 9 = 90°, ‘1’) to the pre-stretched directions of d-PN(20k, 4k, 35 mM) hydrogel.

[0232] FIG. 7 IB (aka Figure S65) is a graph that summarizes the sector average scattering intensity I versus q of d-PN(20k, 4k, 35 mM), and the fitted curve by combined DAB and cylinder form factors.

[0233] FIG. 71C (aka Figure S65) is a graph that includes a SAXS pattern (inserted) and the correlated scattering intensity I versus vector q parallel (i.e., 9 = 0°, 7 / ’) or perpendicular (i.e., 9 = 90°, ‘1’)MT to the pre-stretched directions of d-PN(20k, 4k, 35 mM) hydrogel.

[0234] FIG. 7 ID (aka Figure S65) is a graph that summarizes the sector average scattering intensity I versus q of d-PN(20k, 4k, 35 mM) MT, and the fitted curve byDocket No.: 021343 / WOcombined DAB and cylinder form factors.

[0235] FIG. 72A (aka Figure S66) is a graph that includes a SAXS pattern (inserted) and the correlated scattering intensity I versus vector q parallel (i.e., 9 = 0°, 7 / ’) or perpendicular (i.e., 9 = 90°, ‘1’) to the pre-stretched directions of d-PN(20k, 4k, 50 mM) hydrogel.

[0236] FIG. 72B (aka Figure S66) is a graph that summarizes the sector average scattering intensity I versus q of d-PN(20k, 4k, 50 mM), and the fitted curve by combined DAB and cylinder form factors.

[0237] FIG. 72C (aka Figure S66) is a graph that includes a SAXS pattern (inserted) and the correlated scattering intensity I versus vector q parallel (i.e., 9 = 0°, 7 / ’) or perpendicular (i.e., 9 = 90°, ‘1’)MT to the pre-stretched directions of d-PN(20k, 4k, 50 mM) hydrogel.

[0238] FIG. 72D (aka Figure S66) is a graph that summarizes the sector average scattering intensity I versus q of d-PN(20k, 4k, 50 mM) MT, and the fitted curve by combined DAB and cylinder form factors.

[0239] FIG. 73A (aka Figure S67) is an image of the setup of a punching experiment.

[0240] FIG. 73B (aka Figure S67) is an image of a puncher used in the experiments shown in FIG. 73 A.

[0241] FIG. 73C (aka Figure S67) is an image of a pristine d-PN(20k, 4k) disk obtained from a 100 mM a-CD bath and used in the experiment shown in FIG. 73 A.

[0242] FIG. 73D (aka Figure S67) is an image of a punched d-PN(20k, 4k) disk.

[0243] FIG. 74 (aka Figure S68) is a schematic diagram summarizing the workflow of a punching experiment.

[0244] FIG. 75A (aka Figure S69A) is a map summarizing a simulated stress distribution of the punching experiment.

[0245] FIG. 75B (aka Figure S69B) is a graph summarizing absorbed a-CD ratios (y-axis on the left) and simulated stress (y-axis on the right) in relation to the location of the dissected samples; the center of the disk is set as 0.

[0246] FIG. 76A (aka Figure S70A) is a graph summarizing the recorded forceDocket No.: 021343 / WOversus punched cycles in 10mM α-CD aqueous solutions (with 1.0 M Na2SO4).

[0247] FIG. 76B (aka Figure S70B) is an image of the sample after the punching experiment of FIG. 76 A.

[0248] FIG. 76C (aka Figure S70C) is a graph summarizing the recorded force versus punched cycles in lOmM a-CD aqueous solutions (with 1.0 M Na2SO4).

[0249] FIG. 76D (aka Figure S70D) is an image of the sample after the punching experiment of FIG. 76C.

[0250] FIG. 76E (aka Figure S70E) is a graph summarizing the recorded force versus punched cycles in lOmM a-CD aqueous solutions (with 1.0 M Na2SO4).

[0251] FIG. 76F (aka Figure S70F) is an image of the sample after the punching experiment of FIG. 76E.DETAILED DESCRIPTION

[0252] Disclosed herein are polyrotaxane hydrogel compositions featuring a- cyclodextrin (a-CD)-based crystalline domains that undergo mechanical reconfiguration and growth under stress. Upon mechanical training, the hydrogels, initially crosslinked by large, randomly oriented crystalline domains, are restructured into networks with smaller, directional, and slidable crystalline domains, resulting in significant enhancements in fracture energy (40 kilojoules per square meter) and fatigue threshold (1.3 kilojoules per square meter). Additionally, by introducing dangling polymer chains that allow for further a-CD threading, active growth of the crystalline domains was achieved, demonstrating actively enhanced fatigue resistance for synthetic hydrogels.

[0253] In various aspects, adapt-ring networks (ARNs), a class of polyrotaxane- based materials that enable mechanically guided, out-of-equilibrium network reconfiguration and growth are disclosed herein (Fig. 1). ARNs are composed of a sparse PEG-based covalent network, threaded with dense arrays of a-cyclodextrins (a- CDs), which crystallize into mechanically reconfigurable domains (Fig. lb). Under mechanical loading, either cyclic (un)loading or stretch-and-sonication, the crystalline domains undergo strain-directed fragmentation, translocation, and alignment, forming various kinetically trapped architectures that encode different local mechanical history (Fig. lb). This transformation produces up to an order-of-magnitude increases in Young’s modulus, tensile strength, fracture energy, and fatigue threshold, representingDocket No.: 021343 / WOsome of the most pronounced self-strengthening responses reported in synthetic hydrogels. Notably, this mechanically learned architecture is fully reversible. Solvent annealing erases the learned state and restores the pristine domain topology, enabling ARNs to repeatedly learn, erase, and relearn under different mechanical regimes.Beyond uniform training, ARNs also exhibit spatially resolved adaptive learning, converting homogeneous networks into strain-defined gradient architectures without any external patterning. Extending this adaptive learning behavior, we developed ARNs with dangling PEG chains (d-ARNs, Fig. 1c) that exchange molecular components with the environment, enabling out-of-equilibrium, environment-fed, mechanically guided crystalline-domain growth, heuristically analogous to biological reinforcement processes. These d-ARN hydrogels take up external a-CDs in a strain-dependent manner, producing spatially gradient reinforcement, including nonlocal strengthening that propagates far beyond the site of chemical stimulus (Fig. Id). Such remote mechanochemical remodeling has not been observed in synthetic hydrogels and represents a fundamental shift in how polymer networks can evolve under mechanical and chemical fields.

[0254] In various aspects, an ARN consists of a covalently crosslinked network and a crystalline domain-based physical network that is formed by the threaded a-CDs on the PEG axles (Fig. 2a). Unlike traditional semi-crystalline polymers, the crystalline domains of the ARN are not only size reconfigurable, but also location reconfigurable, when these threaded a-CDs translocate along the PEG axles. To reconfigure the a-CD-based crystalline domains in ARN, an external stimulus, such as force, is selectively transduced to the crystalline domains rather than to the covalent crosslinking points. A uniform covalently crosslinked network with a topology resembling an ideal network12and a low crosslinking density may fit the prerequisite. Therefore, a series of ARN hydrogels consisting of a 3-connected ketoenamine-crosslinked PEG network was constructed with various threaded a-CDs.

[0255] As presented in the examples herein, it was demonstrated that a-cyclodextrin (a-CD)-based polyrotaxane network (PN) hydrogels exhibited a unique mechanically reconfigurable self-strengthening and growth capability. These behaviors are triggered through straightforward cyclic (un)loading or stretch-and-soni cation processes (Fig. IB), in which these polyrotaxane hydrogels feature hydrogen-bonded a-CD-based crystalline domains acting as mechanically reconfigurable noncovalentDocket No.: 021343 / WOcrosslinkers. When these hydrogels are stretched, their crystalline domains are mechanically reorganized from large, randomly oriented, and highly connected crosslinkers into small, directional, and less connected ones (Fig. IB). The reconfigured small crystalline domains slide along the axles upon mechanical loading, similar to slide-ring crosslinkers. When free dangling polyethylene glycol (d-PEG) chains were introduced to the polyrotaxane networks (d-PN, Fig. 1C), a-CDs in the aqueous bath thread onto these chains, co-cry stall izi ng to reinforce the existing crystalline domains, mimicking a scar formation process. Interestingly, this hydrogel reinforcement process becomes significantly more effective when the hydrogels are simultaneously trained and strengthened, demonstrating an out-of-equilibrium adaptive growth behavior not previously observed in synthetic hydrogels.

[0256] As demonstrated in the examples herein, the disclosed a-cyclodextrin (a-CD)-based polyrotaxane network (PN) hydrogels exhibited mechanically reconfigurable self-strengthening and growth capabilities. These behaviors are triggered through straightforward cyclic (un)loading or stretch-and-sonication processes (Fig. IB), in which hydrogen-bonded a-CD-based crystalline domains within the polyrotaxane hydrogels act as mechanically reconfigurable noncovalent crosslinkers. When the hydrogels are stretched, the crystalline domains are mechanically reorganized from large, randomly oriented, and highly connected crosslinkers into small, directional, and less connected ones (Fig. IB). The reconfigured small crystalline domains slide along the polymeric axles upon mechanical loading, similar to slide-ring crosslinkers. When free dangling polyethylene glycol (d-PEG) chains were additionally introduced to the polyrotaxane networks (d-PN, Fig. 1C), a-CDs provided in an aqueous bath threaded onto the dangling chains and co-crystallized to reinforce the existing crystalline domains, mimicking a scar formation process. This hydrogel reinforcement process becomes significantly more effective when the hydrogels are simultaneously trained and strengthened, demonstrating an out-of-equilibrium adaptive growth behavior.

[0257] Polyrotaxane hydrogels featuring a-CD-based crystalline domains exhibit remarkable mechanical reconfigurability and adaptive strengthening capabilities. Upon cyclic (un)loading or stretch-and-sonication, the a-CD-based crystalline domains are disrupted, allowing the a-CDs to shuttle, redistribute, and recrystallize along the stretched PEGs. These processes led to the reconfiguration of polymer networks with 5~6-fold enhanced strength, 8~25-fold enhanced fracture energy, and 15~27-foldDocket No.: 021343 / WOenhanced fatigue threshold. Moreover, we observed further growth of these crystalline domains by threading free a-CDs to the dangling chains of the polyrotaxane networks. Specifically, the mechanically trained networks demonstrated an out-of-equilibrium growth, mimicking the adaptive growth in scar formation and muscle training. This integrated crystalline domain growth allows the hydrogel to actively reinforce its network under mechanical stress, which offers a new perspective on the design of hydrogels with adaptive strengthening features, opening up exciting possibilities for creating smart materials that can adaptively toughen themselves to the environment, much like biological tissues.

[0258] In various aspects, the disclosed adapt-ring networks (ARNs) exhibit mechanically driven learning and network remodeling. ARNs comprise a dense a-CD crystalline-domain-based network interlaced with a sparse covalently crosslinked PEG network. Unlike conventional hydrogels, ARNs undergo mechanically guided adaptive learning, reorganizing their crystalline-domain networks into strain-prescribed states that are kinetically stable yet fully reversible. Mechanical training, via cyclic (un)loadings or stretch-and-sonication, transforms initially large, randomly oriented crystalline domains into smaller, evenly distributed, strain-aligned crystalline domains that dramatically increase modulus, strength, toughness, and fatigue resistance. Solvent annealing erases the learned architecture, enabling the network to repeatedly learn, erase, and reprogram under different mechanical regimes.

[0259] ARNs also demonstrate spatially resolved adaptive learning, recording local strain patterns and autonomously evolving from a homogeneous network into a gradient architecture. This capability has not previously been demonstrated in synthetic polymer networks. Incorporating dangling PEG chains further enables environment-fed, mechanically guided network growth, allowing ARNs to take up external a-CDs and regrow their crystalline domains under out-of-equilibrium conditions. This process yields spatiotemporally patterned, strain-directed reinforcement with nonlocal strengthening, which is another capability not previously observed in hydrogels.Together, these advances establish ARNs as tough, strong, kinetically stable, reversible, spatially reconfigurable materials that communicate with their mechanical and chemical environment, providing a blueprint for soft matter systems that adapt, remember, and improve with use.

[0260] Non-limiting examples of polyrotaxane (PN) hydrogel compositions areDocket No.: 021343 / WOdescribed herein.

[0261] In various aspects, the PN hydrogel compositions include a plurality of cross-linked diamino-polyethylene glycol (ax-PEG) chains threaded with a plurality of a-cyclodextrin moieties, in which the ax-PEG chains are cross-linked using 1,3,5-triformylphloroglucinol (Tp) crosslinkers. In various aspects, the ax-PEG chains may vary in length as expressed by molar masses ranging from about 4 kg / mol to about 20 kg / mol. The ax-PEGs comprise the chemical structure illustrated below:(1)

[0262] In various aspects, the a-cyclodextrin moeties each comprise chemical structure (2) as illustrated below:

[0263] In various aspects, the Tp crosslinker comprises chemical structure (3) as illustrated below:

[0264] In various aspects, the PN network hydrogel comprises chemical structure (4) as illustrated below:Docket No.: 021343 / WO(4)

[0265] In various aspects, the PN hydrogel network may be further functionalized with dangling PEG (d-PEG) chains to form a d-PN network hydrogel.

[0266] In various aspects, the d-PEG chain comprises chemical structure (5) as illustrated below:

[0267] In various aspects, the d-PN network hydrogel comprises chemical structure (6) as illustrated below:

[0268] In various other aspects, at least a portion of the d-PEG chains of the d- PN network hydrogel may be threaded with a plurality of additional a-cyclodextrin moieties as illustrated by chemical structure (7) below:

[0269] Methods of synthesizing the PN network hydrogels, d-PN network hydrogels, and variations thereof as disclosed herein are described in Appendices A andDocket No.: 021343 / WOB, the contents of which are incorporated by reference in their entirety.

[0270] In various other aspects, R groups can be optionally substituted with one or more groups independently selected from the group consisting of hydroxyl; Cl-lOalkyl hydroxyl; amine; Cl-lOcarboxylic acid; Cl-lOcarboxyl; straight chain or branched Cl-lOalkyl, optionally containing unsaturation; a C2-10cycloalkyl optionally containing unsaturation or one oxygen or nitrogen atom; straight chain or branched Cl-lOalkyl amine; heterocyclyl; heterocyclic amine; and aryl comprising a phenyl; heteroaryl containing from 1 to 4 N, O, or S atoms; unsubstituted phenyl ring; substituted phenyl ring; unsubstituted heterocyclyl; and substituted heterocyclyl, wherein the unsubstituted phenyl ring or substituted phenyl ring can be optionally substituted with one or more groups independently selected from the group consisting of hydroxyl; Cl-lOalkyl hydroxyl; amine; Cl-lOcarboxylic acid; Cl-lOcarboxyl; straight chain or branched Cl-lOalkyl, optionally containing unsaturation; straight chain or branched Cl-lOalkyl amine, optionally containing unsaturation; a C2-10cycloalkyl optionally containing unsaturation or one oxygen or nitrogen atom; straight chain or branched Cl-lOalkyl amine; heterocyclyl; heterocyclic amine; aryl comprising a phenyl; and heteroaryl containing from 1 to 4 N, O, or S atoms; and the unsubstituted heterocyclyl or substituted heterocyclyl can be optionally substituted with one or more groups independently selected from the group consisting of hydroxyl; Cl-lOalkyl hydroxyl; amine; Cl-lOcarboxylic acid; Cl-lOcarboxyl; straight chain or branched Cl-lOalkyl, optionally containing unsaturation; straight chain or branched Cl-lOalkyl amine, optionally containing unsaturation; a C2-10cycloalkyl optionally containing unsaturation or one oxygen or nitrogen atom; heterocyclyl; straight chain or branched Cl-lOalkyl amine; heterocyclic amine; and aryl comprising a phenyl; and heteroaryl containing from 1 to 4 N, O, or S atoms. Any of the above can be further optionally substituted.

[0271] The term “imine” or “imino”, as used herein, unless otherwise indicated, can include a functional group or chemical compound containing a carbon-nitrogen double bond. The expression “imino compound”, as used herein, unless otherwise indicated, refers to a compound that includes an “imine” or an “imino” group as defined herein. The “imine” or “imino” group can be optionally substituted.

[0272] The term “hydroxyl”, as used herein, unless otherwise indicated, can include -OH. The “hydroxyl” can be optionally substituted.Docket No.: 021343 / WO

[0273] The terms “halogen” and “halo”, as used herein, unless otherwise indicated, include chlorine, chloro, Cl; fluorine, fluoro, F; bromine, bromo, Br; or iodine, iodo, or I.

[0274] The term “acetamide”, as used herein, is an organic compound with the formula CH₃CONH₂. The “acetamide” can be optionally substituted.

[0275] The term “aryl”, as used herein, unless otherwise indicated, include a carbocyclic aromatic group. Examples of aryl groups include, but are not limited to, phenyl, benzyl, naphthyl, or anthracenyl. The “aryl” can be optionally substituted.

[0276] The terms “amine” and “amino”, as used herein, unless otherwise indicated, include a functional group that contains a nitrogen atom with a lone pair of electrons and wherein one or more hydrogen atoms have been replaced by a substituent such as, but not limited to, an alkyl group or an aryl group. The “amine” or “amino” group can be optionally substituted.

[0277] The term “alkyl”, as used herein, unless otherwise indicated, can include saturated monovalent hydrocarbon radicals having straight or branched moieties, such as but not limited to, methyl, ethyl, propyl, butyl, pentyl, hexyl, octyl groups, etc.Representative straight-chain lower alkyl groups include, but are not limited to, -methyl, -ethyl, -n-propyl, -n-butyl, -n-pentyl, -n-hexyl, -n-heptyl and -n-octyl; while branched lower alkyl groups include, but are not limited to, -isopropyl, -sec-butyl, -isobutyl, -tert-butyl, -isopentyl, 2-methylbutyl, 2-methylpentyl, 3 -methylpentyl, 2,2-dimethylbutyl, 2,3-dimethylbutyl, 2,2-dimethylpentyl, 2,3-dimethylpentyl, 3, 3 -dimethylpentyl, 2,3,4-trimethylpentyl, 3 -methylhexyl, 2,2-dimethylhexyl, 2,4-dimethylhexyl, 2,5-dimethylhexyl, 3,5-dimethylhexyl, 2,4-dimethylpentyl, 2-methylheptyl, 3 -methylheptyl, unsaturated Cl-10 alkyls include, but are not limited to, -vinyl, -allyl, -1-butenyl, -2-butenyl, -isobutylenyl, -1-pentenyl, -2-pentenyl, -3 -methyl- 1-butenyl, -2-methyl-2-butenyl, -2,3-dimethyl-2-butenyl, 1-hexyl, 2-hexyl, 3-hexyl, -acetylenyl, -propynyl, -1-butynyl, -2-butynyl, -1 -pentynyl, -2-pentynyl, or -3 -methyl- 1 butynyl. An alkyl can be saturated, partially saturated, or unsaturated. The “alkyl” can be optionally substituted.

[0278] The term “carboxyl”, as used herein, unless otherwise indicated, can include a functional group consisting of a carbon atom double bonded to an oxygen atom and single bonded to a hydroxyl group (-COOH). The “carboxyl” can be optionally substituted.Docket No.: 021343 / WO

[0279] The term “alkenyl”, as used herein, unless otherwise indicated, can include alkyl moieties having at least one carbon-carbon double bond wherein alkyl is as defined above and including E and Z isomers of said alkenyl moiety. An alkenyl can be partially saturated or unsaturated. The “alkenyl” can be optionally substituted.

[0280] The term “alkynyl”, as used herein, unless otherwise indicated, can include alkyl moieties having at least one carbon-carbon triple bond wherein alkyl is as defined above. An alkynyl can be partially saturated or unsaturated. The “alkynyl” can be optionally substituted.

[0281] The term “acyl”, as used herein, unless otherwise indicated, can include a functional group derived from an aliphatic carboxylic acid, by removal of the hydroxyl (–OH) group. The “acyl” can be optionally substituted.

[0282] The term “alkoxyl”, as used herein, unless otherwise indicated, can include O-alkyl groups wherein alkyl is as defined above, and O represents oxygen. Representative alkoxyl groups include, but are not limited to, -O-methyl, -O-ethyl, -O-n-propyl, -O-n-butyl, -O-n-pentyl, -O-n-hexyl, -O-n-heptyl, -O-n-octyl, -O-isopropyl, -O-sec-butyl, -O-isobutyl, -O-tert-butyl, -O-isopentyl, -O-2-methylbutyl, -O-2-methylpentyl, -O-3 -methylpentyl, -0-2,2-dimethylbutyl, -0-2,3 -dimethylbutyl, -0-2,2-dimethylpentyl, -0-2,3-dimethylpentyl, -0-3, 3 -dimethylpentyl, -0-2, 3,4-trimethylpentyl, -0-3 -methylhexyl, -0-2,2-dimethylhexyl, -0-2,4-dimethylhexyl, -O-2,5-dimethylhexyl, -0-3,5-dimethylhexyl, -O-2,4dimethylpentyl, -0-2-methylheptyl, -0-3 -methylheptyl, -0-vinyl, -O-allyl, -0-1-butenyl, -0-2-butenyl, -O-isobutylenyl, -O-1-pentenyl, -0-2-pentenyl, -0-3 -methyl- 1-butenyl, -O-2-methyl-2-butenyl, -0-2,3-dimethyl-2-butenyl, -0-1 -hexyl, -0-2 -hexyl, -0-3-hexyl, -O-acetylenyl, -O-propynyl, -0-1-butynyl, -0-2-butynyl, -0-1 -pentynyl, -0-2-pentynyl and -0-3 -methyl- 1-butynyl, -O-cyclopropyl, -O-cyclobutyl, -O-cyclopentyl, -O-cyclohexyl, -O-cycloheptyl, -O-cyclooctyl, -O-cyclononyl and -O-cyclodecyl, -O-CH2-cyclopropyl, -0-CH2-cyclobutyl, -O-CH2-cyclopentyl, -O-CH2-cyclohexyl, -O-CH2-cycloheptyl, -0-CH2-cyclooctyl, -O- CH2-cyclononyl, -O-CH2-cyclodecyl, -O-(CH2)2-cyclopropyl, -O-(CH2)2-cyclobutyl, -O-(CH2)2-cyclopentyl, -O-(CH2)2-cyclohexyl, -O-(CH2)2-cycloheptyl, -O-(CH2)2-cyclooctyl, -O-(CH2)2-cyclononyl, or -O-(CH2)2-cyclodecyl. An alkoxyl can be saturated, partially saturated, or unsaturated. The “alkoxyl” can be optionally substituted.Docket No.: 021343 / WO

[0283] The term “cycloalkyl”, as used herein, unless otherwise indicated, can include an aromatic, non-aromatic, saturated, partially saturated, or unsaturated, monocyclic or fused, spiro or unfused bicyclic or tricyclic hydrocarbon referred to herein containing a total of from 1 to 10 carbon atoms (e.g., 1 or 2 carbon atoms if there are other heteroatoms in the ring), preferably 3 to 8 ring carbon atoms. Examples of cycloalkyls include, but are not limited to, C3-10 cycloalkyl groups include, but are not limited to, -cyclopropyl, -cyclobutyl, -cyclopentyl, -cyclopentadienyl, -cyclohexyl, -cyclohexenyl, -1,3-cyclohexadienyl, -1,4-cyclohexadienyl, -cycloheptyl, -1,3-cycloheptadienyl, -1,3,5-cycloheptatrienyl, -cyclooctyl, and -cyclooctadienyl. The term “cycloalkyl” also can include -lower alkyl-cycloalkyl, wherein lower alkyl and cycloalkyl are as defined herein. Examples of -lower alkyl-cycloalkyl groups include, but are not limited to, -CH2-cyclopropyl, -CH2-cyclobutyl, -CH2-cyclopentyl, -CH2-cyclopentadienyl, -CH2-cyclohexyl, -CH2-cycloheptyl, or -CH2-cyclooctyl. The “cycloalkyl” can be optionally substituted. A “cycloheteroalkyl”, as used herein, unless otherwise indicated, can include any of the above with a carbon substituted with a heteroatom (e.g., O, S, N).

[0284] The term “heterocyclic” or “heteroaryl”, as used herein, unless otherwise indicated, can include an aromatic or non-aromatic cycloalkyl in which one to four of the ring carbon atoms are independently replaced with a heteroatom from the group consisting of O, S and N. Representative examples of a heterocycle include, but are not limited to, benzofuranyl, benzothiophene, indolyl, benzopyrazolyl, coumarinyl, isoquinolinyl, pyrrolyl, pyrrolidinyl, thiophenyl, furanyl, thiazolyl, imidazolyl, pyrazolyl, triazolyl, quinolinyl, pyrimidinyl, pyridinyl, pyridonyl, pyrazinyl, pyridazinyl, isothiazolyl, isoxazolyl, (l,4)-di oxane, (l,3)-dioxolane, 4, 5 -dihydro- 1H-imidazolyl, or tetrazolyl. Heterocycles can be substituted or unsubstituted. Heterocycles can also be bonded at any ring atom (i.e., at any carbon atom or heteroatom of the heterocyclic ring). A heterocyclic can be saturated, partially saturated, or unsaturated. The “hetreocyclic” can be optionally substituted.

[0285] The term “indole”, as used herein, is an aromatic heterocyclic organic compound with the formula C₈H₇N. It has a bicyclic structure, consisting of a sixmembered benzene ring fused to a five-membered nitrogen-containing pyrrole ring. The “indole” can be optionally substituted.

[0286] The term “cyano”, as used herein, unless otherwise indicated, can includeDocket No.: 021343 / WOa -CN group. The “cyano” can be optionally substituted.

[0287] The term “alcohol”, as used herein, unless otherwise indicated, can include a compound in which the hydroxyl functional group (–OH) is bound to a carbon atom. In particular, this carbon center should be saturated, having single bonds to three other atoms. The “alcohol” can be optionally substituted.

[0288] The term “solvate” is intended to mean a solvate form of a specified compound that retains the effectiveness of such compound. Examples of solvates include compounds of the invention in combination with, for example: water, isopropanol, ethanol, methanol, dimethylsulfoxide (DMSO), ethyl acetate, acetic acid, or ethanolamine.

[0289] The term “mmol”, as used herein, is intended to mean millimole. The term “equiv”, as used herein, is intended to mean equivalent. The term “mL”, as used herein, is intended to mean milliliter. The term “g”, as used herein, is intended to mean gram. The term “kg”, as used herein, is intended to mean kilogram. The term “pg”, as used herein, is intended to mean micrograms. The term “h”, as used herein, is intended to mean hour. The term “min”, as used herein, is intended to mean minute. The term “M”, as used herein, is intended to mean molar. The term "pL", as used herein, is intended to mean microliter. The term “pM”, as used herein, is intended to mean micromolar. The term “nM”, as used herein, is intended to mean nanomolar. The term “N”, as used herein, is intended to mean normal. The term “amu”, as used herein, is intended to mean atomic mass unit. The term “°C”, as used herein, is intended to mean degree Celsius. The term “wt / wt”, as used herein, is intended to mean weight / weight. The term “N / N”, as used herein, is intended to mean volume / volume. The term “MS”, as used herein, is intended to mean mass spectroscopy. The term “HPLC”, as used herein, is intended to mean high performance liquid chromatography. The term “RT”, as used herein, is intended to mean room temperature. The term "e.g.", as used herein, is intended to mean example. The term “N / A”, as used herein, is intended to mean not tested.

[0290] As used herein, the expression “pharmaceutically acceptable salt” refers to pharmaceutically acceptable organic or inorganic salts of a compound of the invention. Preferred salts include, but are not limited, to sulfate, citrate, acetate, oxalate, chloride, bromide, iodide, nitrate, bisulfate, phosphate, acid phosphate, isonicotinate,Docket No.: 021343 / WOlactate, salicylate, acid citrate, tartrate, oleate, tannate, pantothenate, bitartrate, ascorbate, succinate, maleate, gentisinate, fumarate, gluconate, glucaronate, saccharate, formate, benzoate, glutamate, methanesulfonate, ethanesulfonate, benzenesulfonate, p- toluenesulfonate, or pamoate (i.e., l,l'-methylene-bis-(2-hydroxy-3-naphthoate)) salts. A pharmaceutically acceptable salt may involve the inclusion of another molecule such as an acetate ion, a succinate ion, or other counterion. The counterion may be any organic or inorganic moiety that stabilizes the charge on the parent compound.Furthermore, a pharmaceutically acceptable salt may have more than one charged atom in its structure. Instances where multiple charged atoms are part of the pharmaceutically acceptable salt can have multiple counterions. Hence, a pharmaceutically acceptable salt can have one or more charged atoms and / or one or more counterion. As used herein, the expression “pharmaceutically acceptable solvate” refers to an association of one or more solvent molecules and a compound of the invention. Examples of solvents that form pharmaceutically acceptable solvates include, but are not limited to, water, isopropanol, ethanol, methanol, DMSO, ethyl acetate, acetic acid, and ethanolamine. As used herein, the expression “pharmaceutically acceptable hydrate” refers to a compound of the invention, or a salt thereof, that further can include a stoichiometric or non- stoichiometric amount of water bound by non-covalent intermolecular forces.

[0291] A "stable" formulation or composition can refer to a composition having sufficient stability to allow storage at a convenient temperature, such as between about 0 °C and about 60 °C, for a commercially reasonable period of time, such as at least about one day, at least about one week, at least about one month, at least about three months, at least about six months, at least about one year, or at least about two years.I. KITS

[0292] Also provided are kits. Such kits can include an agent or composition described herein and, in certain embodiments, instructions for administration. Such kits can facilitate performance of the methods described herein. When supplied as a kit, the different components of the composition can be packaged in separate containers and admixed immediately before use. Components include, but are not limited to, various reagents used to produce the disclosed PN hydrogels and / or d-PN hydrogels including diamino-polyethylene glycol (ax-PEG) chains, dangling PEG (d-PEG) chains, a- cyclodextrins, and 1,3,5-triformylphloroglucinol (Tp) crosslinkers. Such packaging of the components separately can, if desired, be presented in a pack or dispenser device,Docket No.: 021343 / WOwhich may contain one or more unit dosage forms containing the composition. The pack may, for example, comprise metal or plastic foil such as a blister pack. Such packaging of the components separately can also, in certain instances, permit long-term storage without losing activity of the components.

[0293] Kits may also include reagents in separate containers such as, for example, sterile water or saline to be added to a lyophilized active component packaged separately. For example, sealed glass ampules may contain a lyophilized component and in a separate ampule, sterile water, or sterile saline, each of which has been packaged under a neutral non-reacting gas, such as nitrogen. Ampules may consist of any suitable material, such as glass, organic polymers, such as polycarbonate, polystyrene, ceramic, metal, or any other material typically employed to hold reagents. Other examples of suitable containers include bottles that may be fabricated from similar substances as ampules, and envelopes that may consist of foil-lined interiors, such as aluminum or an alloy. Other containers include test tubes, vials, flasks, bottles, syringes, and the like. Containers may have a sterile access port, such as a bottle having a stopper that can be pierced by a hypodermic injection needle. Other containers may have two compartments that are separated by a readily removable membrane that upon removal permits the components to mix. Removable membranes may be glass, plastic, rubber, and the like.

[0294] In certain embodiments, kits can be supplied with instructional materials. Instructions may be printed on paper or other substrate, and / or may be supplied as an electronic-readable medium, such as a floppy disc, mini-CD-ROM, CD-ROM, DVD-ROM, Zip disc, videotape, audio tape, and the like. Detailed instructions may not be physically associated with the kit; instead, a user may be directed to an Internet website specified by the manufacturer or distributor of the kit.

[0295] Compositions and methods described herein utilizing molecular biology protocols can be according to a variety of standard techniques known to the art (see, e.g., Sambrook and Russel (2006) Condensed Protocols from Molecular Cloning: A Laboratory Manual, Cold Spring Harbor Laboratory Press, ISBN-10: 0879697717; Ausubel et al. (2002) Short Protocols in Molecular Biology, 5th ed., Current Protocols, ISBN-10: 0471250929; Sambrook and Russel (2001) Molecular Cloning: A Laboratory Manual, 3d ed., Cold Spring Harbor Laboratory Press, ISBN-10: 0879695773; Green and Sambrook 2012 Molecular Cloning: A Laboratory Manual, 4th ed., Cold SpringDocket No.: 021343 / WOHarbor Laboratory Press, ISBN-10: 1605500569; Elhai, J. and Wolk, C. P. 1988.Methods in Enzymology 167, 747-754; Studier (2005) Protein Expr Purif. 41(1), 207-234; Gellissen, ed. (2005) Production of Recombinant Proteins: Novel Microbial and Eukaryotic Expression Systems, Wiley-VCH, ISBN-10: 3527310363; Baneyx (2004) Protein Expression Technologies, Taylor & Francis, ISBN-10: 0954523253).

[0296] Definitions and methods described herein are provided to better define the present disclosure and to guide those of ordinary skill in the art in the practice of the present disclosure. Unless otherwise noted, terms are to be understood according to conventional usage by those of ordinary skill in the relevant art.

[0297] In some embodiments, numbers expressing quantities of ingredients, properties such as molecular weight, reaction conditions, and so forth, used to describe and claim certain embodiments of the present disclosure are to be understood as being modified in some instances by the term “about.” In some embodiments, the term “about” is used to indicate that a value includes the standard deviation of the mean for the device or method being employed to determine the value. In some embodiments, the numerical parameters set forth in the written description and attached claims are approximations that can vary depending upon the desired properties sought to be obtained by a particular embodiment. In some embodiments, the numerical parameters should be construed in light of the number of reported significant digits and by applying ordinary rounding techniques. Notwithstanding that the numerical ranges and parameters setting forth the broad scope of some embodiments of the present disclosure are approximations, the numerical values set forth in the specific examples are reported as precisely as practicable. The numerical values presented in some embodiments of the present disclosure may contain certain errors necessarily resulting from the standard deviation found in their respective testing measurements. The recitation of ranges of values herein is merely intended to serve as a shorthand method of referring individually to each separate value falling within the range. Unless otherwise indicated herein, each individual value is incorporated into the specification as if it were individually recited herein. The recitation of discrete values is understood to include ranges between each value.

[0298] In some embodiments, the terms “a” and “an” and “the” and similar references used in the context of describing a particular embodiment (especially in the context of certain of the following claims) can be construed to cover both the singularDocket No.: 021343 / WOand the plural, unless specifically noted otherwise. In some embodiments, the term “or” as used herein, including the claims, is used to mean “and / or” unless explicitly indicated to refer to alternatives only or the alternatives are mutually exclusive.

[0299] The terms “comprise,” “have” and “include” are open-ended linking verbs. Any forms or tenses of one or more of these verbs, such as “comprises,” “comprising,” “has,” “having,” “includes” and “including,” are also open-ended. For example, any method that “comprises,” “has” or “includes” one or more steps is not limited to possessing only those one or more steps and can also cover other unlisted steps. Similarly, any composition or device that “comprises,” “has” or “includes” one or more features is not limited to possessing only those one or more features and can cover other unlisted features.

[0300] All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g. “such as”) provided with respect to certain embodiments herein is intended merely to better illuminate the present disclosure and does not pose a limitation on the scope of the present disclosure otherwise claimed. No language in the specification should be construed as indicating any non-claimed element essential to the practice of the present disclosure.

[0301] Groupings of alternative elements or embodiments of the present disclosure disclosed herein are not to be construed as limitations. Each group member can be referred to and claimed individually or in any combination with other members of the group or other elements found herein. One or more members of a group can be included in, or deleted from, a group for reasons of convenience or patentability. When any such inclusion or deletion occurs, the specification is herein deemed to contain the group as modified thus fulfilling the written description of all Markush groups used in the appended claims.

[0302] Any publications, patents, patent applications, and other references cited in this application are incorporated herein by reference in their entirety for all purposes to the same extent as if each individual publication, patent, patent application, or other reference was specifically and individually indicated to be incorporated by reference in its entirety for all purposes. Citation of a reference herein shall not be construed as an admission that such is prior art to the present disclosure.Docket No.: 021343 / WO

[0303] Having described the present disclosure in detail, it will be apparent that modifications, variations, and equivalent embodiments are possible without departing from the scope of the present disclosure defined in the appended claims. Furthermore, it should be appreciated that all examples in the present disclosure are provided as nonlimiting examples.EXAMPLES

[0304] The following examples illustrate various aspects of the disclosure.Methods

[0305] Chemicals were commercially available and used directly without further purification unless otherwise noted. a-Cyclodextrin (a-CD) was generously provided by Wacker Chemical Corporation. All polyethylene glycols (PEG-(OH)2) and a-methoxy, co-amino-polyethylene glycol (MeO-PEG-NH2, named as d-PEG) with molecular weights of Ik, 2k, 5k and 10k Da were obtained from Thermo Scientific Chemicals.

[0306] Nuclear magnetic resonance (NMR) spectra were obtained on Bruker Avance III™ HD 400 MHz spectrometers, with the working frequencies of 400 MHz for 1H nuclei. Unless otherwise specified, chemical shifts in ppm relative to solvent residual signals were referenced as follows: (1H) CDC13, 7.26 ppm; (1H) D2O, 4.79 ppm; (1H) DMSO-d6, 2.50 ppm.

[0307] A consumer-grade camera was used to record optical images.

[0308] THINKY mixer AR-100 was used for hydrogel preparations.

[0309] The tensile tests, fracture energy, hysteresis measurements, mechanical training, and fatigue threshold measurements were performed on CellScale UniVert with a load cell of 10 N and / or 100 N.

[0310] Bonvoisin handheld ultrasonic probes (D = 8 mm, Frequency = 30 kHz, direct current (DC) =12~24 V with DC = 14 V) were used for stretch-and-sonication training of the PN network. Small- and wide-angle X-ray scattering (S / WAXS) experiments were carried out at beamline SMI of NSLS-II at 16.1 keV photon energy with a beam size of 200 pm x 25 pm. Scattering data were collected using a Pilatus2M detector at 9 m downstream of the sample. The form factor was analyzed employing the Sas View 5.0.6 program package (http: / / www.sasview.org / ). The experimental SAXS profiles of PN(20k), PN(20k)MT, PN(20k)ST, d-PN(20k, 4k, 0 mM) and d-PN(20k, 4k,Docket No.: 021343 / WO0 mM)MT were fitted by the combined model of Debye–Anderson–Brumberger (DAB)( 0.005 < q < 0.012) and the cylinder form factor (0.008 < q < 0.110). The experimental SAXS profiles of d-PN(20k, 4k, 35 mM), d-PN(20k, 4k, 35 mM)MT, d-PN(20k, 4k, 50 mM) and d-PN(20k, 4k, 50 mM)MT were fitted by the combined model of lamellar (0.005 < q < 0.030) and cylinder model (0.030 < q < 0.110) (1).

[0311] Environmental scanning electron microscope (ESEM) experiments were conducted using a Thermofisher Quattro S ESEM. The CO2 supercritical point drier of samdri-795 (tousimis, USA) was used for drying ESEM samples.

[0312] The tensile tests, fracture energy, hysteresis measurements, mechanical training, and fatigue threshold measurements were performed on CellScale UniVert with a load cell of 10 N and / or 100 N.

[0313] Cyclic (un)loading experiment. The mechanical training of PN hydrogels was performed through a multi-cyclic loading-unloading process in silicon oil to prevent water loss. The strain is set to a = 300% with a tensile rate of 100 mm / min for 1000 cycles. The measured stress values at different strains in each cycle were recorded. After training, the trained samples were unloaded from the tensile tester. Their dimensions were remeasured before reloading onto the tensile tester to measure their nominal stress-strain curves and fracture energy.

[0314] Stretch-and-sonication experiment. The sonication training was performed by loading PN hydrogel samples onto a tensile tester in an oil bath. Each specimen was stretched to εpre= 1000% at a tensile rate of 100 mm / min. After that, the sample was held at the specific strain in the oil bath, and one ultrasonic probe was placed at the center of the stretched specimen. Four ultrasonic probes were placed near each comer of the thicker samples. Pulsed sonication was applied to the sample for 3 h with cycles of 10 s ON and 30 s OFF. The oil bath was kept in an ice-water bath to maintain its temperature at 18-23 °C during the stretch-and-sonication training process. Afterward, the specimen was unloaded to recover its shape. The dimensions of the stretch-and-sonication trained sample were re-measured for further mechanical tests.

[0315] Tensile tests. The samples for tensile tests were prepared using dog-bone molds. The tensile tests were typically performed on CellScale Univert with a 10 N or 100 N maximum load cell. Unless otherwise specified, specimens were manually mounted onto the tensile grips and then stretched at a speed of 100 mm / min until ruptureDocket No.: 021343 / WOto obtain the nominal stress-strain curves. Strain (a) was measured by the extension of the gauge length, while nominal stress (G) was calculated by dividing the applied force by the original cross-sectional area of the specimen. The Young’s modulus (E) was determined from the initial slope of the nominal stress-strain curve, and the work of rupture (W) was calculated by integrating the nominal stress-strain curve.

[0316] Fracture energy. In this work, the single-notch method was used to characterize the fracture energy, following the previously reported method9,27. Notched and unnotched samples were prepared with identical dimensions. The notched samples were cut with an initial notch (c, one-fifth to one-fourth of the width) under a microscope using a razor blade. Both notched and unnotched samples were stretched at a constant speed of 100 mm / min until rupture occurred. The fracture energy (T) of the samples was calculated by Γ = 2kc ∫0εσdε, k = 3 / √(εm+ 1), where εmwas the critical strain obtained from the notched sample at which steady-state crack propagation occurs, and σ was the stress of the unnotched samples.

[0317] Fatigue threshold measurements. The fatigue threshold was measured following the single-notch and pure-shear method9,27,37. Specifically, PN hydrogels were applied for single-notch tests, while d-PN hydrogels with rectangular shapes were applied for pure-shear tests. For each single-notch test, both notched and unnotched samples were subjected to cyclic loading and unloading for 1000 cycles in an oil bath to prevent water loss. First, we recorded the cyclic loading-unloading curves at different maximum applied strain (EA) from the unnotched sample to calculate the strain energy density (W) at the Nth cycle. The strain energy density was calculated using W(εA, N) = ∫0εσ(N)dε, where G refers to the nominal stress and £ represents strain. Next, the notched samples were cyclically stretched to the same εAfor 1000 cycles. The crack length was recorded during these cycles and the crack extension rate dc / dN was subsequently calculated to evaluate the propagation of the crack as a function of the cycle number N. For the single-notch tests, the applied energy release rate G in the notched sample under the Nth cycle at the applied strain EAwas calculated using G(εA, N) = 2k(εA) · c(N) · W(εA, N), where k was a slowly varying function of the applied stretch expressed as k = 3 / √(εA+ 1), c(N) was the crack length at the Nth cycle, and W(εA, N) is the strain energy density measured from the unnotched sample. For pure-shear tests, the applied energy release rate G was calculated using G(εA, N) = H ·Docket No.: 021343 / WOW(εA, N), in which H is the initial gauge length of the pure-shear sample. A plot of crack extension per cycle (dc / dN) versus the applied energy release rate (G) was obtained. The critical energy release rate Gcwas determined by linearly extrapolating the dc / dN – G curve to the intercept with the abscissa. By definition, the fatigue threshold is equal to the critical energy release rate Gc, below which the fatigue crack would not propagate under an infinite number of loading cycles.

[0318] Photoelasticity experiments. The design of photoelasticity experiments follows the established protocol in literature59. The setup consists of a light source, two linear polarizers, two quarter-wave plates, a universal tensile tester, and a camera. The samples are stretched by the mechanical tester with the linear polarizers and quarterwave plates positioned sequentially on either side. The light source and camera are placed in front and behind the samples, respectively. When stress is applied, the PN hydrogels exhibit distinct fringe patterns, known as a photoelastic response, providing a clear visual representation of the internal stress distribution. The video camera captures the shape and photoelastic fringe pattern images of the hydrogels during the tensile test.

[0319] Punching experiment. The d-PN(20k, 4k) hydrogels were synthesized by molding the pre-crosslinked hydrogel as round disks (50 mm in diameter, 2.0 mm in thickness) and then subjected to extensive crosslinking and solvent exchanges as described in Section 2. The obtained d-PN(20k, 4k) hydrogels were measured with a diameter of -45 mm and a thickness of ~1.2 mm. The sample was fixed in a customized 3D-printed holder (46 mm outer diameter, 40 mm inner diameter). A customized 3D-printed puncher was applied to the specimen to a depth of 12 mm with a retraction distance of 6 mm, at a speed of 600 mm / min, for a total of 500 cycles in open air, and then for another 30,000 cycles in a-CD solutions of different concentrations (with 1.0 M Na2SO4).

[0320] Knee-joint model training for ARN(20k) and d-ARN(20k, 4k):Rectangular-shaped hydrogels were prepared by molding, and they are measured as 180 x 20 x 1.5 mm after DMSO wash and rehydration in the IM Na2SO4solution. Both ends of the specimen were adhered to a knee-joint bone model using super glue. The setup was mounted to the tensile tester, immersed in a silicon oil bath, and subjected to 12,000 cycles of bending motion (rate: 600 mm / min) by fixing the two ends of the knee joint to the tensile tester clamps. The sample was detached from the knee-joint model and sprayed with black paint before loading onto the CellScale for tensile tests. TheDocket No.: 021343 / WOgradient reinforcement was characterized by using the digital image correlation (DIC) method. For the d-ARN(20k, 4k) sample, an a-CD patch (a polyester-based drycleaning cloth, 20 x 165 mm, soaked in a 35 mM a-CD 1.0 M Na2SO4aqueous solution) was wrapped around the center of the knee-joint model and secured with plastic wrap. The assembly was then either kept in a sealed tube for 24 h or subjected to 12,000 bending cycles in a silicon oil bath.Example 1: Design and Synthesis of ARN Hydrogels

[0321] ARNs and control networks (CNs) were synthesized by reacting different lengths of diamino-PEG (ax-PEG, Mn= 4, 6, 10, to 20 kg / mol) with 1,3,5- triformylphloroglucinol (Tp) in a 3:2 molecular ratio in the presence and absence of a- CDs, respectively26. The weight percentages of ax-PEGs and a-CD were kept at 4 wt% and 20 wt%, respectively, to ensure a constant repeating unit EG to a-CD molar ratio of 4.4: 1. These ARN(xk), where ‘x’ refers to the molecular weight of an ax-PEG in kg / mol, were thoroughly washed and hydrolyzed in NaOD / D2O to reveal the average number of threaded a-CDs as 10 to 33 a-CDs as the ax-PEG increased from 4 to 20 kg / mol, as summarized in Table 1 below:TABLE 1: Compositions of PN Hydrogelsfed ax-PEG fed Tp fed a-CD IJ-CU: a.v-PEG water samples content wt% mM mM wt% itiM fed found coverage (%)’ (wt%) PN(4k) 10 6.7 20.6 1£> ± 1 22.2 ±2.2 63 PN(6k) 4 6.7 101 20 206 30.7 11 ± 1 16.2 ± 1.5 59 PN(10k) 4? 7 51.5 21 ± 1 18.5 ± 0.8 58 PN(20k)-i 12 123 61.7 23 ± I 101 ±0.4 65 PN(20k)-ii 15 154 77.0 24 ± 2 10.6 ± 0.4 60 PN(20k)-iii 17 175 87.5 27 ± 1 119 ±0.4 584 2 1.3PN(20k)-iv 20 206 103.0 33 ± 2 14.5 ± 1.3 60 PN(20k)-v 22 226 113.0 43 ± 2 18.9 ± 0.9 60PN(20k)-vi 25 256 128.0 47 ± 2 20.7 ± 0.9 561coverage percentage is calculated by dividing the threaded a-CD numbers by the maximum threaded number of each ax-PEG. The maximum number of threaded a-CDs (N^) was calculated based on the threading ratio of EG / a-CD = 2:1. The repeating unit of EG in ax-PEG4k, ax-PEG6k, ax-PEG10k, and ax- PEGiatareSO, 136, 227 and 454 respectively, and the maximum threading numbers are 45, 68, 114 and 227 respectively.Example 2: Mechanical Reconfiguration of ARN Hydrogels

[0322] To evaluate and characterize the mechanical reconfiguration of the disclosed ARN hydrogels in response to external loads, the following experiment were conducted.Docket No.: 021343 / WO

[0323] Tensile tests: The samples for tensile tests were prepared using dog-bone molds. The tensile tests were typically performed on CellScale Univert with a 10 N or 100 N maximum load cell. Unless otherwise specified, specimens were manually mounted onto the tensile grips and then stretched at a speed of 100 mm / min until rupture to obtain the nominal stress-strain curves. Strain (a) was measured by the extension of the gauge length, while nominal stress (G) was calculated by dividing the applied force by the original cross-sectional area of the specimen. The Young’s modulus (E) was determined from the initial slope of the nominal stress-strain curve, and the work of rupture (W) was calculated by integrating the nominal stress-strain curve.

[0324] Hysteresis ratio measurements: Loading-unloading tests were performed with a controlled maximum applied strain (sA) to examine the hysteresis behavior of samples. The hysteresis ratio h is determined by the ratio of the area enclosed by the hysteresis loop to the area under the loading curves, as defined below:h = (∫loading dε - ∫unloading dε) / ∫loading dε

[0325] The strain-dependent hysteresis ratio was assessed by evaluating the stress-strain curves from cyclic loading and unloading tests, with increasing strain levels applied progressively.

[0326] Fracture energy (T) measurements: In this work, the single-notch method was used to characterize the fracture energy, following the previously reported method (4, 5). Notched and unnotched samples were prepared with identical dimensions. The notched samples were cut with an initial notch (c, one-fifth to one-fourth of the width) under a microscope using a razor blade. Both notched and unnotched samples were stretched at a constant speed of 100 mm / min until rupture occurred. The fracture energy (T) of the samples was calculated by Γ =k = 3 / √(εm+ 1), where am was the critical strain obtained from the notched sample at which steady-state crack propagation occurs, and G was the stress of the unnotched samples.

[0327] Tensile tests on PN hydrogels with different ax-PEG: To investigate the impact of ax-PEG molecular weight on the mechanical performance, a PN network with varying ax-PEG chain lengths was prepared (See Table 1). Their tensile tests wereDocket No.: 021343 / WOperformed at 100 mm / min. The fracture energy was measured by the single-notch method.

[0328] Comparison of the PN(20k) and CN(20k) hydrogels: The tensile profiles of PN(20k) and CN(20k) were measured with a tensile rate of 100 mm / min. The hysteresis of the hydrogel was measured by cyclic (un)loading experiments. PN(20k) and CN(20k) hydrogels were strained to 20%, 60%, 80%, 100%, 200%, 300%, 400%, 500%, 600% and relaxed to their original states at 100 mm / min.

[0329] Tensile rate dependence studies on PN(20k) hydrogel: To examine ratedependent behavior, tensile and loading-unloading tests were performed at 60 mm / min, 100 mm / min, 150 mm / min, and 200 mm / min. The hysteresis of the hydrogel was measured by cyclic (un)loading experiments. PN(20k) and CN(20k) hydrogels were strained to 20%, 60%, 80%, 100%, 200%, 300%, 400%, 500%, 600% and relaxed to their original states at 100 mm / min.

[0330] Number of threaded a-CDs on the PN(20k) hydrogel: The number of threaded a-CDs is well correlated with the fed amount of a-CDs during the hydrogel preparation (Table S3). Hence, we used the fed a-CD amount to label the corresponding PN(20k) hydrogel. PN hydrogels synthesized with different amounts of fed a-CDs were prepared according to Section 2. Their tensile tests were performed at 100 mm / min. The fracture energy was measured by the single-notch method. As shown in Table S3 and Figure S14, when the a-CD fed amount of PN(20k) is 20 wt%, the mechanical property of PN(20k) is the toughest. Thus, PN(20k) fed with 20 wt% a-CDs was chosen for further mechanical training study.Table S3. Summary of the measured mechanical parameters of PN(20k) hydrogels synthesized at different fed a-CD concentrations.fed a-CD CD: PEG E 45 £ W - E Samplesfed found (MPa: (MPa) (%) (XU ffi i (kJ / nf) 12 61.? 23 ± 1 0.167 1.78 2478 IB.69 0.72 ± 0.15 15 77.5 24 ±2 0.290 1.41 2100 13 27 1.10 ±0.07 17 S7. S 27 ± 1 0.276 1.40 1950 12.21 1.27 ± 0.20 PN(20fc)20 W3.0 33 ± 3 0299 127 1470 926 159 ± 006 22 113.8 43 ± 2 0309 0.78 1120 495 1 49 ±0 1625 128.0 47 ± 2 0.591 0.47 829 2.74 1.08 ± 0.17Mechanical training of the PN and d-PN hydrogels

[0331] Cyclic (un)loading training method of cyclic strain screening: TheDocket No.: 021343 / WOmechanical training of PN hydrogels was performed through a multi-cyclic loadingunloading process in silicon oil to prevent water loss. The strain is set to a = 100%, 300%, and 500% with a tensile rate of 100 mm / min for 1000 cycles, respectively. The measured stress values at different strains in each cycle were recorded. After training, the trained samples were unloaded from the tensile tester. Their dimensions were remeasured before reloading onto the tensile tester to measure their nominal stressstrain curves and fracture energy.

[0332] Cyclic (un)loading training at various tensile speeds: The mechanical training of PN(20k) hydrogels was performed through a multi-cyclic loading-unloading process in silicon oil to prevent water loss. The strain is set to a = 300% with a tensile rate of 60, 100, and 150 mm / min for 1000 cycles, respectively. After training, the trained samples were unloaded from the tensile tester. Their dimensions were remeasured before reloading onto the tensile tester to measure their nominal stressstrain curves and fracture energy.

[0333] Cyclic (un)loading training at different total cycles: The mechanical training of PN(20k) hydrogels was performed at different total cycle numbers (N = 250, 500, 1000 cycles) at a strain a = 300% and a tensile / recovery speeds of 100 mm / min. After training, their tensile profiles were measured as described previously.

[0334] Optimized cyclic (un)loading method: The mechanical training of PN hydrogels synthesized using various ax-PEG (Mn = 4, 6, 10, 20 kg / mol) was performed through the multi-cyclic loading-unloading process in silicon oil to prevent water loss. The strain is set to a = 300% with tensile and recovery rates of 100 mm / min for 1000 cycles. After training, the trained samples were unloaded from the tensile tester. Their dimensions were remeasured before reloading onto the tensile tester to measure their nominal stress-strain curves and fracture energy (See below). For d-PN hydrogels, the training was conducted by immersing the samples in silicon oil or different concentrations of a-CD solutions (with Na2SO4, 1.0 M), and their results will be summarized below.Table S4. Summary of the measured mechanical parameters of PN and PNMT hydrogels.Docket No.: 021343 / WOE r Samples(MPa) (MPa) (MJ / sr) (kJ / tir) PN(4k) 0.36 073 577 193 0.60 PV-lkW:51 16 1 19 305 1 41 1 16? N%k> 8.45 0.72 713 2.73 0.62202 1.29 506 4.75 357 PN(lflk) 0.27 0.66 748 2.46 0.913.48 0.66 271 0.91 2.46 PN(20k) 0.30 1.27 1570 926 15.10PN(20k)?>n <32 8.40 450 15.6 13.21 ’P (4k) was trained at 200% steam for 1000 cycles, and all the other PN samples were trained at 300% strain for 1000 cycles.

[0335] Recovery of the PN hydrogel from the PNMT hydrogel: PN(20k)MT hydrogels trained following the above mentioned method were swelled in DMSO until they turned transparent. The swelled DMSO-gel was then immersed in 1.0 M Na2SO4 aqueous solution for 1~2 days to generate PN(20k)restored before the tensile test.

[0336] Composition analysis of PN(20k), PN(20k)MT, PN(20k)restored: To examine whether the ketoenamine covalent network has been partially degraded during the cyclic (un)loading training and training-restoring processes, we measured the water contents of these hydrogels. These hydrogels were also hydrolyzed for 1H NMR analysis.

[0337] To measure the water contents of PN(20k)MT and PN(20k)restored samples, these samples (ml) were dried at 70 °C with measured mass m2. The mass reduction ratios (ml-m2) / ml revealed the water content of the hydrogel listed in Table S5.

[0338] If the ketoenamine covalent crosslinked network is damaged, some of the previously threaded a-CDs will be dethreaded in DMSO and washed away, which will show an a-CD / PEG ratio reduction. To measure a-CD / PEG ratios in the PN(20k)MT and PN(20k)restored samples, they were first immersed and washed extensively in DMSO to remove any dethreaded a-CDs. These DMSO-gels were deswelled in acetone and dried to remove any residual solvent. The dried samples were hydrolyzed in NaOD / D2O (5% w / v) at 70 °C until fully dissolved. The results are summarized in Table S5. The a-CD / PEG ratios in these samples are consistent, indicating the ketoenamine network damage is negligible in these processes.Docket No.: 021343 / WOTable S5. Comparison of mechanical properties and composition of PN(20k), PN(20k)MT and PN(20k)restoredCompasitioiiSamples N«-cs on eachWater contest {%)33-FEG20kPN(20kl 60 ±3 33 ± 245 ± 3 34 i 2{20k 56 ± 1 34 ± 1

[0339] Stretch-and-sonication training of PN hydrogels: The sonication training was performed by loading PN hydrogel samples onto a tensile tester in an oil bath. Each specimen was stretched to spre = 600%, 800%, and 1000% at a tensile rate of 100 mm / min. After that, the sample was held at the specific strain in the oil bath, and one ultrasonic probe was placed at the center of the stretched specimen. For thicker samples, four ultrasonic probes were placed near each corner of the sample (see the setup illustration and image below). Pulsed sonication was applied to the sample for 1.5-3 h. The oil bath was kept in an ice-water bath to maintain its temperature at 18-23 °C during the stretch-and-sonication training process. Afterward, the specimen was unloaded to recover its shape. The dimensions of the stretch-and-sonication trained sample were re-measured for further mechanical tests. We chose spre = 1000% at a tensile rate of 100 mm / min and 3 h sonication with 10 s ON and 30 s OFF as the optimized experimental setup parameters. Note: we observed that the effectiveness of the stretch-and-sonication is sample size-dependent. Larger-sized samples will require longer sonication time and more ultrasonic probes.

[0340] ARN hydrogels are opaque due to the presence of large a-CD-based crystalline domains. When ARN hydrogels with varying ax-PEG lengths (Fig. 2a) were subjected to tensile tests, from ARN(4k) to ARN(lOk), the strengths (omax, or stress-at-break) of the hydrogels are comparable, while their stretchability (smax, %) increased slightly (Fig. 2b). When the ax-PEG reached 20 kg / mol, the ARN(20k) showed dramatically increased strength (omax = 1.26 MPa) and stretchability (smax = 1,560%, Fig. 2b). At a fixed EG-to-a-CD molar ratio, increasing the chain length progressively lowers the covalent crosslinking density, thereby amplifying the disparity between the covalent and a-CD-crystalline-domain-based physical networks. This network feature could enable preferential force transduction to the a-CD crystalline domains. TheDocket No.: 021343 / WOhysteresis of ARN(20k) at different strains grew rapidly up to 300% strain, then increased marginally (Supplementary Fig. 12). In comparison, CN(20k) hydrogels without a-CD exhibited small hysteresis with negligible strain-dependent variations, confirming that crystalline domain disruption dominates in ARN(20k) at lower strains.

[0341] We next varied the fed EG-to-a-CD molar ratios of ARN(20k) hydrogels to tune the density of the crystalline domain-based physical network and modulate energy dissipation (Fig. 2c). Increasing the a-CD feed from 12 to 25 wt% reduced both stretchability and work of rupture (Wrupture, MJ / m3), consistent with the formation of denser crystalline domains that limit ax-PEG mobility (Supplementary Fig. 14). To identify the optimal balance between covalent to physical crosslinks, we measured the fracture energy (T, kJ / m2) of pre-notched samples (Fig. 2c), finding that ARN(20k) synthesized with 20 wt% fed a-CD exhibited the highest (1.59 kJ / m2).

[0342] With the network composition optimized, we next tested whether mechanical loading could reorganize these crystalline domains in a strain-directed manner (Fig. 2d). We applied cyclic (un)loading method across a range of strains, tensile rates, and cycle numbers (Supplementary Fig. 16-20). Optimal training conditions (a tensile / recovery rate of 100 mm / min for 1,000 cycles) produced a steady mechanical state characterized by low hysteresis and moderate plastic elongation along the loading direction (Supplementary Fig. 16, and 24).

[0343] The tensile behaviors of ARN(20)MT hydrogels exhibit a strong dependence on training strain (Fig. 2e). As the training strain increased, the Young’s modulus rose from 0.3 MPa to 7.1 MPa, and tensile strength from 1.3 MPa to 11.5 MPa (600% training strain), while the strain-at-break decreased from 1570% to 241%. The work-of-rupture peaks at 15.7-15.8 MJ / m3fortraining strains of 300-400%, indicating the optimum strain regime for energy dissipation and load transfer. Composition analysis after DMSO washing and hydrolysis confirmed no change in chemical composition (Supplementary Table 6), demonstrating that reinforcement arises from reversible network reconfiguration and no covalent network damage. Notably, ARN hydrogels represents the first system in which tensile profiles (modulus and strength) can be fine-tuned over more than an order of magnitude solely by varying training strain9,27,28.

[0344] The strong training-strain dependence reflects strain-inducedDocket No.: 021343 / WOreorganization into kinetically trapped network topologies. ARN(20)MT hydrogels trained at 300% strain were used to assess these kinetically trapped network stabilities and showed no change in tensile behavior after 1-7 days at room temperature (Supplementary Fig. 23). Heating at 70 °C for 1-3 days partially relaxed the network, while full restoration was achieved through DMSO / H2O exchange, which enabled a-CD dissociation, translocation, and recrystallization (Fig. 3f). This network reconfiguration is also highly reversible. ARN(20)MT samples subjected to repeated cycles of solventexchange restoration followed by mechanical retraining consistently “erased” and “relearned” their network architectures. After each cycle, the tensile profiles closely matched those of the initially trained state (Fig. 3g), demonstrating the reproducibility and full reversibility of the crystalline-domain network reconfiguration.

[0345] To achieve more uniform network reorganization, we developed a complementary stretch-and-sonication strategy that couples mechanical alignment with pulsed ultrasonication (Supplementary Fig. 29-30).29In this method, ARN(20k) hydrogels were stretched to 600-1,000% strain in an oil bath while subjected to pulsed sonication (30 kHz, 10 s on, 30 s off, 1-3 h). The optimized ARN(20k)sr hydrogel, trained at 1,000% strain for 3 h, exhibited exceptional performance (Fig. 2h), combining high stretchability (1,050%) with a remarkable work-of-rupture (58.8 MJ / m3).Importantly, its tensile profile was fully restored after DMSO / H2O exchange, underscoring that even this large reconfiguration remains entirely reversible through adaptive learning.

[0346] The a-CD-based crystalline-domain network in ARN hydrogels can be systematically reorganized by external force, transitioning from opaque to translucent due to reduced domain size and diminished light scattering. To elucidate molecular-scale network evolution in ARN(20k)MT and ARN(20k)sr, we conducted wide- and small-angle X-ray scattering (WAXS / SAXS) analyses. While pristine ARN(20k) showed isotropic scattering, trained samples exhibited strong anisotropy in WAXS patterns (Fig. 3a), indicating alignment of a-CD crystalline domains along the stretching direction. Notably, the overall degree of crystallinity remained unchanged before and after training (Supplementary Fig. 35; Table S8)32, confirming that mechanical reconfiguration fragments and aligns crystalline domains without altering total crystalline content.

[0347] SAXS measurements showed similar anisotropy (Fig. 3b). The scatteringDocket No.: 021343 / WOfringes were fitted using the Debye- Anderson-Brumberger and polydispersed cylinder models (Supplementary Table 9)33. The crystalline-domain dimensions decreased from d* 1 = 6.6 x 13.7 nm in pristine ARN(20k) to 6.0 x 7.3 nm in ARN(20k)MT and 5.8 x 6.6 nm in ARN(20k)sT. These findings indicate that mechanical reconfiguration both aligns and fragments the crystalline domains into smaller, more uniform structures, enhancing network anisotropy and mechanical robustness.

[0348] We used molecular dynamics (MD) simulations to elucidate the crystalline domain reconfiguration in ARNs. A coarse-grained model34with a three- connected covalent network and 34 threaded a-CDs per strand was constructed (Supplementary Section S4). Under quiescent conditions, Langevin dynamics yielded a pristine network resembling ARN(20k), featuring large, randomly oriented crystalline domains (Fig. 3c). Intrachain a-CD crystallization also generated loop-like aggregates alongside interchain stem-like domains, consistent with hierarchical motifs reported for a-CD / PEG polypseudorotaxanes35’36. Under simulated cyclic (un)loading, repeated uniaxial extension ( E < 500%) and recovery resulted in the fragmentation of these crystalline domains and their alignment along the stretch direction (Fig. 3 d-f). To approximate stretch-and-sonication, the model was held at 1,000% strain while switching on / ff a-CD attractive interactions intermittently. This in silico sonication fully disrupted the crystalline domains, yielding networks with smaller domains and orientational order (Supplementary Fig. 42) comparable to ARN(20k)MT, in agreement with WAXS / SAXS experiments.

[0349] Mechanical network reconfiguration also eliminates the looped defects (Fig. 3g). In pristine ARN(20k), looped PEG segments restrict crystalline-domain sliding, whereas loop-to-stem reconfiguration allows a-CD clusters to slide along aligned ax-PEG chains. Sliding-dynamics analysis shows that reconfigured crystalline domains sustain much larger displacements before rupture than those in pristine networks (Fig. 3h). Together, the WAXS / SAXS and MD results provide a coherent mechanistic picture: external force converts large, randomly oriented crystalline domains into numerous smaller, highly aligned ones while removing looped defects, generating kinetically trapped architectures that encode mechanical history and enable the adaptive learning behavior of ARN hydrogels.Example 3: Suppression of Crack Growth and Fatigue in ARN HydrogelsDocket No.: 021343 / WO

[0350] To evaluate and characterize suppression of crack growth and fatigue within the disclosed ARN hydrogels, the following experiments were conducted.Fatigue threshold (TO) measurements.

[0351] The fatigue threshold was measured following the single-notch and pure- shear method (4-6). Specifically, PN hydrogels were applied for single-notch tests, while d-PN hydrogels with rectangular shapes were applied for pure-shear tests. For each single-notch test, both notched and unnotched samples were subjected to cyclic loading and unloading for 1000 cycles in an oil bath to prevent water loss. First, we recorded the cyclic loading-unloading curves at different maximum applied strain (aA) from the unnotched sample to calculate the strain energy density (W) at the Nth cycle. The strain energy density was calculated using0, where c refers to the nominal stress and a represents strain. Next, the notched samples were cyclically stretched to the same aA for 1000 cycles. The crack length was recorded during these cycles and the crack extension rate dc / dN was subsequently calculated to evaluate the propagation of the crack as a function of the cycle number N. For the single-notch tests, the applied energy release rate G in the notched sample under the Nth cycle at the applied strain eA was calculated using G(EA, ) = 2kfg4l -N) *where k was a slowly varying function of the applied stretch expressed as-'•Ea 1;,c(N) was the crack length at the Nth cycle, and W(SA, N) is the strain energy density measured from the unnotched sample.

[0352] The strain-induced network reconfiguration in ARN hydrogels leads to large enhancements in fracture and fatigue resistance (Fig. 4a). Notched samples of ARN(20k)MT and ARN(20k)sr hydrogels exhibited significant resistance to crack propagation, unlike the rapid crack propagation observed in pristine ARN(20k) hydrogel (Supplementary Fig. 46). Correspondingly, the fracture energy (T) increased from 1.6 kJ / m2in pristine ARN(20k) to 13.2 kJ / m2in ARN(20k)MT, and 40.8 kJ / m2in ARN(20k)sr (Fig. 4b). Remarkably, the fatigue thresholds (To) of ARN(20k)MT and ARN(20k)sr hydrogels were measured at 770 and 1,366 J / m2, respectively (Fig. 4c), rendering 15-fold and 27-fold enhancements compared to the pristine ARN(20k).

[0353] We used photoelasticity to probe the toughening mechanism during crack propagation (Supplementary Videos 1-2). Pristine ARN(20k) displayed a classical butterfly-shaped birefringence pattern near the crack tip at low strain (a = 50%, Fig. 4d),Docket No.: 021343 / WOwhich rapidly localized as the crack propagated (a > 100%). In contrast, ARN(20k)MT exhibited a delocalized, diffuse birefringence pattern extending along the stretching direction up to 200% strain, demonstrating effective redistribution of stress away from the crack tip (Fig. 4e). This delocalization originates from the reconfigured ARN(20k)MT, whose smaller, more uniformly dispersed crystalline domains slide along aligned ax-PEG chains to dissipate energy. Such dynamic stress redistribution results in enhanced fracture energy and fatigue resistance.

[0354] These significant gains in fatigue resistance do not compromise their stiffness (Fig. 4f). The fatigue threshold To of ARN(20k)MT and ARN(20k)sr deviates from the typical inverse scaling (To ~ E| / 2) observed in conventional hydrogels4,10,57, revealing a rare decoupling of toughness and modulus. The combination of high fracture energy, high fatigue threshold, and preserved modulus places these trained ARNs among the toughest hydrogels reported (Fig. 4f)9,10, 27, 37'56. Moreover, the magnitude of performance enhancement achieved through mechanical reconfigurations (Fig.4g)9,1047,37-56, together with reversible leaming-and-erasing behavior, fundamentally distinguishes them from traditional polymer networks.Example 4: Spatially Resolved Mechanical Learning in ARN Hydrogels

[0355] To evaluate and characterize strain-dependent mechanical training within the disclosed ARN hydrogels, the following experiments were conducted.

[0356] Strain-dependent mechanical training reorganizes ARN network architectures to enable localized adaptation under heterogeneous strain fields. When a pristine ARN(20k) hydrogel is exposed to nonuniform deformation, different regions “learn” their mechanical history by reorganizing crystalline-domain networks and adaptively reinforcing high-strain zones, autonomously transforming a homogeneous material into a gradient network without external patterning (Fig. 5). To demonstrate this behavior, a rectangular ARN(20k) hydrogel (120 x 11 x 1.5 mm mm) was mounted on a model knee joint and subjected to 12,000 bending cycles (Fig. 5a, Supplementary Video S3). During these motions, the central region experienced the highest cyclic strain (Fig. 5d), while the fixed ends remained largely undeformed. After training, the hydrogel displayed heterogeneous translucency, wherein the center became translucent while both ends remained opaque, indicating spatially selective reinforcement.Docket No.: 021343 / WO

[0357] Strain distributions of pristine and adaptively learned samples were quantified by digital image correlation (DIC, Fig. 5b-c, Supplementary Video S4)9. Upon stretching, pristine ARN(20k) showed a uniform strain field matching the bulk strain, confirming a homogeneous internal network. In contrast, the adaptively learned ARN(20k)AL exhibited a strain gradient across the sample (Fig. 5c). At a global strain of 206%, the central region showed a reduced local strain of 172%. The strain gradient of ARN(20k)AL closely matches the simulated pre-set strain distribution of the model knee joint (Fig. 5d, Supplementary Video S5), demonstrating that ARN hydrogels record and interpret their mechanical histories, autonomously reorganizing their crystalline-domain networks to reinforce regions according to local strain demand. Unlike conventional gradient materials that rely on preset designs and fixed gradients58, ARNs achieve sitespecific reinforcement solely through the mechanical stimuli they experience, enabling spatially precise, self-directed material adaptation.Example 5: Out-of-equilibrium, Environment-fed Growth Driven by Adaptive Mechanical Learning in ARN Hydrogels

[0358] To evaluate and characterize out-of-equilibrium, environment-fed growth driven by adaptive mechanical learning within the disclosed ARN hydrogels, the following experiments were conducted.

[0359] Small- and wide-angle X-ray scattering (SAXS and WAXS) of PN(20k), PN(20k)MT, PN(20k)ST: S / WAXS experiments were carried out at beamline SMI of NSLS-II at 16.1 keV photon energy with a beam size of 200 pm x 25 pm. Scattering data was collected using a Pilatus2M detector at 9 m downstream of the sample. To avoid blockage of scattering signals at 0° and 90° by the masking grids, the samples were kept at a 45°-angle to the vertical plane as shown below.

[0360] For SAXS profile fitting, the form factor was analyzed employing the Sas View 5.0.6 program package (http: / / www.sasview.org / ), and for all the SAXS profiles, the sector circular scattering profiles were used for fitting. The experimental SAXS profiles of PN(20k), PN(20k)MT, and PN(20k)ST were fitted by the combined model of Debye- Anderson-Brumberger (DAB) ( 0.005 < q < 0.012) and the cylinder form factor (0.008 < q < 0.110) (1).Docket No.: 021343 / WOTable S9. Summary of SAXS model fitting results of PN(20k), PN(20k)MT, and PN(20k)ST network.Samples Medel DAB cere Cylinder Cylinder length length (ijm) diamerer (am) (am) PN(20k) 567 66 137 PN(2Gk)^ DAB +cylinder 45.0 60 7.330.2 5.8 6.6

[0361] ARNs are intrinsically closed systems. To enable molecular exchange with the environment, we introduced dangling PEG chains to create d-ARNs capable of threading free a-CDs from solution (Fig. 6a). This modification allows additional a- CDs to co-crystallize with the existing mechanically interlocked a-CDs during network reorganization. d-ARN(xk, yk) hydrogels were synthesized by mixing ax-PEG (4 wt%, 2 mM) with a-amino-co-methoxy-PEGs (d-PEGs, Mn= 1-10 kg / mol; 1 mM) in the presence of a-CDs (23 wt%, 236 mM) and Tp (1.67 mM), where x and j' denote the molecular weights of ax-PEG and d-PEG, respectively.

[0362] Environmental scanning electron microscope (ESEM) images: ESEM experiments were carried out on the samples of PN(20k), PN(20k)MT, and PN(20k)ST. To prepare the samples, each hydrogel was dried using a CO2 supercritical point drier. Each hydrogel was immersed in acetone to perform a solvent exchange. The acetonecontaining sample was transferred to the chamber of the supercritical drier to remove any residual solvent. The samples were dissected using a sharp blade along the tensile direction, and the cross-section of the dissected areas was imaged.

[0363] Photoelasticity experiments: To visually observe the stress distribution during deformation and fracture behavior in PN hydrogels and compare the differences between pristine and mechanically trained PN hydrogels, we setup a photoelasticity measurement to analyze the internal stress in PN(20k) and PN(20k)MT hydrogels. The experiment leverages color changes that occur when hydrogels are under stress. The setup consists of a light source, two linear polarizers, two quarter-wave plates, a universal tensile tester, and a camera. As shown in Figure S35, the samples are stretched by the mechanical tester with the linear polarizers and quarter-wave plates positioned sequentially on either side. The light source and camera are placed in front and behind the samples, respectively. When stress is applied, the PN hydrogels exhibit distinct fringe patterns, known as a photoelastic response, providing a clear visual representation of the internal stress distribution. The video camera captures the shapeDocket No.: 021343 / WOand photoelastic fringe pattern images of the hydrogels during the tensile test.

[0364] We conducted photoelasticity tests on pristine and mechanically trained PN hydrogels, examining unnotched and notched samples. We applied a constant tensile rate of 100 mm / min, as used in other tests in this study, and observed and recorded the color changes. As shown in Figure S36(a) and Video SI, the pristine PN hydrogel exhibited a gradual color change at increased strains, transitioning from bright yellow to orange, purple, blue, green, and finally yellowish-green. Correspondingly, in the notched sample shown in Figure S36(b) and Video S2, a butterfly-shaped birefringence pattern was observed around the crack tip, following the same color change sequence, indicating stress concentration at the crack tip.

[0365] In Figure S36(c) and Video SI, the PN(20k)MT hydrogel exhibited a different sequence of color changes during the loading process, transitioning from bright white to bright yellow, purplish-red, blueish-purple, and eventually blue as the strain increased. The different color variations in the mechanically trained sample, compared to the pristine hydrogel, are attributed to the different thicknesses of the hydrogel before and after mechanical training. In the notched sample, as shown in Figure S36(d) and Video S2, unlike the pristine hydrogel, where stress was concentrated solely around the crack tip, the longitudinal direction near the crack first exhibited a reddish-orange color. As the stretch increased, stress concentration became more apparent near the crack tip, following the color change sequence in unnotched PN(20k)MT hydrogel. This difference in the first stage is due to the anisotropy introduced by mechanical training, which created aligned a-CD crystalline domains in the vertical direction. The stress was deconcentrated along these longitudinal fibers, resulting in slower crack propagation compared to PN(20k), thereby enhancing both fracture and fatigue resistance.S5. Molecular dynamics simulations

[0366] We performed coarse-grained (CG) Langevin dynamics simulations using LAMMPS (32). Similar CG simulations have successfully been implemented in the study of the ring-sliding dynamics in polyrotaxane systems, of which the macrocycles cannot crystallize (33, 34). In our simulations, the polymer axles and a-CDs were described by a generic bead-spring model and water was treated as an implicit good solvent. Our percolated polymer network consists of 96 flexible bead-spring chains as the network strands (ax-PEGs). Each strand comprises 150 beads, which are connected by covalent bonds modeled as harmonic springs:Docket No.: 021343 / WO

[0367] where Kbond is the spring constant, rij is the bond length between neighboring beads, and rO is the equilibrium bond length. We set rO to c and Kbond to a constant of30& sin which c andE;are the reduced units of length and energy, respectively. Using the reduced mass m, we define the characteristic time in our simulations as~. The timestep in our CG simulations was O. OITZJ. The polymer ends were attached to crosslinking junctions with a functionality of three, resulting in 64 crosslinking points. Because each polymer bead represents a Kuhn segment of PEG (about three PEG monomers), our generic bead-spring network strands mimic the experimental ax-PEG20k.

[0368] Our a-CDs consisted of six beads bonded by the harmonic potential Ubond. To retain the shape of a-CD, a harmonic angle potential:

[0369] as used. Here, Kangle is the bending constant, Dijk is the angle between three successive macrocycle beads, and DO is the equilibrium angle. We set Kangle to 100 > / rad2 and Dijk to 120°. A dihedral potential was used to preserve the planarity of the macrocycle through:

[0370] where is the dihedral angle between four successive macrocycle beads,A> = 2u eanc[ As = -20 z,an(j A2 = A4 = A5 = 0. Each chain contained 34 macrocycles, which were mechanically interlocked on the polymer but maintained the ability to slide along the backbone. The number of a-CDs per chain was chosen to match the experimental sample PN(20k). The polymer-polymer and polymer-macrocycle interactions were modeled as purely repulsive using the Weeks-Chandler- Anderson (WCA) potential (35).Docket No.: 021343 / WO

[0371] Macrocycle-macrocycle interactions were also modeled with a WCA potential to generate random initial configurations and to mimic sonication treatment. A shifted and truncated 12-6 Lennard- Jones (LJ) potential withs= 0.6 and cut-off (rc) at 2.5 o was applied to allow a-CDs to crystallize in the hydrogels.

[0372] System equilibration: We initially created a regular lattice network where each node is connected to the three earest network strands of length 150 beads, creating a percolated network with functionality of three (see Figure S37). The polymer network was equilibrated in a cubic box with side lengths of 600 c and periodic boundary conditions were applied in all directions before the system was compressed to form a cubic box with side lengths of 62.5 c, resulting in a number density of approximately 0.14 σ-3.

[0373] a-CD mobility: The coarse-grained a-CDs can slide along the polymer backbones in equilibrium simulations and during in-silico tensile tests. To characterize the mobility of an individual a-CD on the polymer backbone, which depends on the polymer-CD interactions, we placed an a-CD on the center bead of each chain. We varied the a-CD-ax-PEG interaction c from 0.9 to 1.0 and observed tunable mobility of the a-CDs along the ax-PEG. Each system was sampled using a Langevin integrator for a total time of 1 × 103at a temperature (T*) of 1, where= T s f s. We recorded the ax-PEG bead (or index) nearest to the center of mass of each a-CD ring as they diffused along the polymer network. The one-dimensional mean squared displacement MSD(t)' = - i(t + At))2)(MSD) was obtained using:

[0374] where i(t) is the index position of a-CD along the polymer at time t and At is the time lag.

[0375] Mechanical training: To prepare the pristine hydrogels, we first simulated the bead-spring networks at T* = 1 using a Langevin integrator for a total time of 1 x 104. A WCA potential was applied for the a-CD-a-CD interactions to provide independent initial configurations with no crystalline domains. We set the a-CD-ax-Docket No.: 021343 / WOPEG interaction c = 0.9 to increase the mobility of the a-CDs along the ax-PEG and facilitate faster equilibration (see Figure S38a). The initial configurations with noncrystalline a-CDs represent the polyrotaxane networks in DMSO. To mimic the DMSO-water solvent exchange and deswelling in IM Na2SO4 aqueous solution, the attractiveLJ potential of = 0.6 between macrocycle beads was enabled and the system wasallowed to equilibrate for 5 x 105τLJunder NVT conditions before the box was compressed at a rate of -7.5 x 10-4σ / τLJ / in all directions to form a cubic box with side lengths of 55 o. This resulted in a density of approximately 0.2 o-3, corresponding to a water content of approximately 75 wt%. The system was further equilibrated for 5 x 105τLJunder NVT conditions until crystallization finished and the number of crystals and crystal size plateaued (see Figure S38b and c).

[0376] To mimic the experimental mechanical training for PN(20k)MT, we applied cyclic uniaxial deformation to the polyrotaxane network in simulations. We increased the a-CD-ax-PEG interaction c = 0.975 to mimic the intra-chain diffusion of a-CD on a PEG axle observed in all-atom simulations (36, 37). The polymer network was subjected to an affine uniaxial strain of 500 % at a velocity of 5 x 10-3 o / on the polymer network, with lateral directions shrunk accordingly to maintain a constant system volume. The macrocycles were allowed to slide and rearrange along polymer axles during training. At the terminus of the strain, the direction of the deformation was reversed, and the system was compressed to the original dimensions at a velocity of -1 x 10-3 o / . The cyclic loading was performed three times on three initial configurations.

[0377] Separate simulations were performed for extension along the x, y, and z-axis on each system to ascertain the relationship between crystal orientation and extension direction. Iterative stress-strain curves of the complete uniaxial loading treatment are shown in Figure S38(d-f). We observe a large hysteresis in the first cycle, which reduces in the subsequent cycles. Interestingly, the stress is essentially negligible in the strain range of 0-150 % which matches the experimental stress-strain data after 1000 cyclic loads (Figure 2f). We attributed this to the plastic deformation of the sample and repeated the cyclic loading at the same velocities, this time only compressing to a strain of 150 % (Figure S38g-i), to better mimic the experimental treatment.Docket No.: 021343 / WO

[0378] We retain a large hysteresis in the initial cycle followed by a significant decrease in the subsequent cycles and observe the stress reaching zero in this deformed state. The cyclic loading with recovery to 150 % strain was performed three times in different directions (x, y, and z) on five initial configurations, giving a total of 15 independent simulations. The subsequent crystalline analyses were performed on the 150 % stain samples to prevent excessive compression. Figure S39 shows snapshots of the network at a strain of 150 % after the completion of the final recovery cycle.

[0379] Sonication training: To mimic the sonication of PN(20k)ST, we first deformed the equilibrated gels uniaxially under constant volume to a strain of 1000%. We prepared three initial configurations for in silico “sonication” by extending the simulation boxes along the x, y, and z-axis. Once the stretched polymer networks were prepared, we set the nonbonded interactions between macrocycles to be purely repulsive (WCA potential) to randomize the distribution of macrocycles. The macrocyclebackbone interaction was set to c = 0.9 to increase the mobility of the a-CDs along the ax-PEG. Each system underwent randomization in the deformed state using a Langevinintegrator for a total time of 1 x 104. The inter-macrocycle attraction of = 0.6 was enabled to facilitate crystal growth, and the system was equilibrated or a total of 10 x 105 (Figure S40a and b). The randomization of macrocycles predicts the upper bound of the sonication effect, where the CD crystals are completely disrupted, and individual macrocycles recrystallize once the sonication is stopped. Finally, each equilibrated system was subjected to an affine deformation in the strain direction at a velocity of -1.0 x 10-3 c / DLJ on the polymer network, with lateral directions coupled to maintain a constant system volume. Figure S40(c) shows the stress decay to zero at a strain of approximately 400 %. We analyze the crystalline domains at this partially extended state to account for the plastic deformation observed in Figure S24 and prevent over-compression. Three randomized configurations were created for each extended network, resulting in a total of nine independent simulations. Figure S41 shows snapshots of the network at an extension of 400 %, where the stress becomes negligible.

[0380] Characterization of crystalline domain aggregates: Using the center of mass and the normal vector U to the face of each macrocycle, the local nematic order ofDocket No.: 021343 / WOa-CD aggregates was used to determine the presence of crystalline domains in the system. A neighbor list for each a-CD in the system was created with a cylindrical cutoff scheme with a center of mass displacement cutoff of 1.25 c normal to the macrocycle ace and 3.0 o in the radial direction. Macrocycles pack into a hexagonal lattice when forming crystals, matching experimental single crystal data (31), giving a total of 20 neighboring sites within the cut-off distances per macrocycle. To search for crystalline a-CDs, we only focused on rings that with more than 50 % neighbor site occupancy. For these a-CDs, we quantify their orientational (nematic) order parameter using the second Legendre polynomial:3C c>a( B — 1S = - ■ -2

[0381] where is the deflection angle between the orientational vector t of the macrocycle and local nematic director (»). To quantify the orientational order with regards to the uniaxial extension, the unit vector » represents the stretching direction. To determine local crystalline order, we considered AT as the eigenvector corresponding to the largest eigenvalue of the local nematic tensor Q:>. 1Q = {t ® t) --I

[0382] where () denotes averaging over all the local orientations of a-CDs, and I is the identity matrix. The value of S ranges from -0.5 to 1, indicating alignment perpendicular (-0.5) or parallel (1) to AT. A local group of a-CDs with S > 0.9 are considered crystalline and only crystalline macrocycles are used to determine the orientational order with respect to the direction of uniaxial extension.

[0383] Figure S42 shows the effect of training methods on the orientation of crystalline domains in the hydrogel. We see the initially isotropic orientation of crystalline domains ((S) = 0) in the pristine gel become highly anisotropic upon mechanical deformation. The crystalline domains retain this high degree of alignment, parallel to the stretching direction, plateauing at (S) ~ 0.6 after each recovery cycle. The sonication treatment also results in the highly anisotropic crystal alignment with (S) ~ 0.5.

[0384] Crystal stability upon deformation: To monitor the stability of the crystals in the trained samples during deformation, we exposed the PN(20k), PN(20k)MT and PN(20k)ST network strands to uniaxial extension at a constant velocity of 5 * 10-3 o / Docket No.: 021343 / WOin the direction of training while the lateral directions were shrunk to

[0385] maintain a constant volume. We monitored the size of the crystalline domains during the deformation and tracked the center of mass of the a-CD as it diffused along the polymer backbone. Only a-CD present in a stem portion of the crystal rings were recorded. We only tracked crystals with sizes around 600 ± 50, 400 ± 50, and 200 ± 50 rings, which represent the characteristic crystal sizes in PN(20k), PN(20k)MT and PN(20k)ST samples, respectively.S6. Active growth of polyrotaxane networks using d-PN hydrogels

[0386] Threading of a-CDs to d-PN network without mechanical training. To prepare the a-CD-threaded d-PN hydrogel samples, d-PN(20k, yk) hydrogels were soaked in the aqueous solutions of a-CD (50 mL) and 1.0 M Na2SO4for 1~2 d. The concentrations of a-CD solutions were fixed at 0, 10, 15, 25, 35, 50, 75, 100 mM. The total amounts of the free a-CD in the solution are in large excess to the number of a- CDs that could potentially thread on the dangling PEG axle. Hence, the concentration of the a-CD could be considered constant during the threading process.Table S10. Mechanical properties of d-PN(20k, Ik) hydrogel in different concentrations of a-CDa-CDE r conceiitratioH(MPa) (MPa) (%} (MlW) (klW) iEM)0 mM 0.® 0.49 777 1.30 1.1010 mM &. S2 0.76 332 4.05 1.2415 BLM 0.87 0.56 648 2.56 1.3425 mM 1 71 068 700 567 1.6135 ffiM 1 63 0.67 395 207 1 7050 BLM 2.01 0.67 319 1.74 1.7875 mM 1.81 0.61 1.68 1.69100 mM 1.90 0.64 338 1.79 1.55Docket No.: 021343 / WOTable Sil. Mechanical properties of d-PN(20k, 2k) hydrogel in different cenceiitations of a-CD.e-CDE < Sai32 Vk I concent ration (MPa) (MPa) (%) (MJ / m-) (kJ / m2) (mM)0 mM 0.43 042 686 1 82 0.70 10 mM 0.52 0.58 825 3.02 1.15 15 mM 0.87 0.56 648 2.54 1 21.25 HIM 1.18 061 348 1 96 1.36 35 mM 1.26 734 319 1.98 1.38 50 mM 1.59 0.66 286 2.94 1 52 75 rn. M 1 53 0.70 176 250 1 80 100 mM 2.20 0.63 271 2.92 1.50Table SI 2. Mechanical piuperties of <i-PN(20k;4k) hydrogel in different concentrations of a-CD a-CDc one esiti atian E r (MPa) (MPa) (%) W (Wirt) (mM)O rnM 044 0.42 1050 2 S0 1.12 10 mM 0.54 0.55 1050 3.60 1.28 15 mM 0.30 0.70 1020 4.77 1 44 25 mM 1 15 0.66 620 3.05 1.63 35 mM 1.54 0.70 453 2.50 1.70 50 niM 2.61 0.72 445 2.64 2.02 75 mM 236 0.73 ■419 2.62 2.56 100 niM 2.34 0.66 327 1.88 2.40Table SIS. Mechanical properties of d-PN(20k. 5k) hydrogel in different concentrstians of a-CD.e-CDc»ii cent rattan E restore r (MPa) (MPa) (%) (MJ. W) (kl / m2) (mM)0 mM 0.25 0.353 620 1.39 0.70 10 mM 0.29 Q.303 472 0.92 0.76 15 mM 0.69 0.428 429 1.32 1.02 25 mM 093 0372 295 0.84 1 14 35 mM 1 45 0.479 2S6 1.14 1 40 50 mM 1.81 0.577 310 1.51 1.89 75 mM 1.97 0.543 214 099 1 67 106 mM 2.27 0.551 138 0.66 0.88Docket No.: 021343 / WOTable S14. Mechanical jxopeities of d-PN(20k, 10k) hydrogel in different co centeiroas of a-CD. o-CDE r concentration(MPa) (MPa) (MJZnr) ■kJ-’sf) 0 mM 0.28 0.321 825 1.71 0.6310 mM 0.44 0 356 550 1.38 0.9815 mM 1 18 0367 467 1 59 1 0625 mM 1.27 0.512 496 2.06 1.1735 n: M 2.06 0.662 319 1.80 1 5750 mM 1.98 0.696 238 1.43 2.2175 mM: 3.58 0.696 200 1.26 1.85100 mM 2.83 0.712 205 1.47 1 40Tabie S15. Summary of the tnechsnsea! properties of d-PN(20, 4k) in different concentrations of «-CD.[CDJMI / E Wl n eqzte* r EB(MPa) (MPa) (%) (MJ / m3) AJ / nv.) (XW)(%) d-PN(20k, 4k, d iriMJto 072 1,47 561 530 325 256 100 d-PN(20k, 4k, 78 1.05 1.60 440 4.74 3 36 N G 118 d-PN(20k, 4k, 15 mMhi? 1.38 2.19 447 6.75 365 J 73 126 d-PN(2(Jk. 4k, 25 ndffte 1.48 2.07 367 5.50 396 134 d-PN(20k, 4k, 35 3.25 3.08 309 6.50 4.42 546 184 d-PN(20k, 4k, 5& SBM)MT 2.84 3.58 261 6.73 4.01 355 160 d-PN(20k,4k, IQS 3.53 1.89 127 6.52 2.38 226 146Table S16. Sv.mmsiy of the absorbed nCD rates of PN(20k) trained arid immersed in different concentrations of ct-CD aqneous soiution.a CL) ca-acaatatioii(mM) (%)10 03%50 106%100 97%

[0387] Fatigue threshold of d-PN(20k, 4k, a mM) and d-PN(20k, 4k, a mM)MT: Pure-shear tests were conducted to measure the fatigue threshold of d-PN(20k, 4k, a mM) and d-PN(20k, 4k, a mM)MT (6). The applied energy release rate G was calculated using G(sA, N) = H • W(sA, N), in which H is the initial gauge length of the pure-shear sample. A plot of crack extension per cycle (dc / dN) versus the applied energy release rate (G) was obtained. The critical energy release rate Gc was determinedDocket No.: 021343 / WOby linearly extrapolating the dc / dN - G curve to the intercept with the abscissa. By definition, the fatigue threshold is equal to the critical energy release rate Gc, below which the fatigue crack would not propagate under an infinite number of loading cycles.

[0388] SAXS of d-PN(20k, 4k, a mM) and (20k, 4k, a mM): The experimental SAXS profiles of d-PN(20k, 4k, 0 mM) and d-PN(20k, 4k, 0 mM)MT were fitted by the combined model of Debye- Anderson-Brumberger (DAB) (0.005 < q < 0.012) and the cylinder form factor (0.008 < q < 0.110). The experimental SAXS profiles of d-PN(20k, 4k, 35 mM), d-PN(20k, 4k, 35 mM)MT, d-PN(20k, 4k, 50 mM) and d-PN(20k, 4k, 50 mM)MT were fitted by the combined model of lamellar (0.005 < q < 0.030) and cylinder model (0.030 < q < 0.110)(l).Table S17. Ss miary of the fitted parameters of d-P {2SL 4k a toM) and d-PN(20k, 4k, a mMjwr in the SXAS analysisCylinderDAB core lengthSamples Model Diameter Length(SUB)(nm) (ism) d-PN(20k.4k, SnLM) 109.0 7.6 15.7DAB •d-PN(2Qk.4k, 8 cylinder 59,4 57 101Lamellar thickness Diameter Length Samples(ism) (um) (nisi) d-PN(20k, 4k, M. S 63 14.5Lamellar+d-PN(20k, 4k, 5’5 SBM'IMT 21.3 5.4 19.5cylinderd PK'.'ftk. 4k, 50 mM) 23.0 5.9 239 d-PN(20k. 4k, 50mM)«r 33.4 55 276

[0389] Punching experiment of d-PN hydrogels: The d-PN(20k, 4k) hydrogels were synthesized by molding the pre-crosslinked hydrogel as round disks (50 mm in diameter, 2.0 mm in thickness) and then subjected to extensive crosslinking and solvent exchanges as described in Section 2. The obtained d-PN(20k, 4k) hydrogels were measured with a diameter of -45 mm and a thickness of ~1.2 mm. The sample was fixed in a customized 3D-printed holder (46 mm outer diameter, 40 mm inner diameter). A customized 3D-printed puncher was applied to the specimen to a depth of 12 mm with a retraction distance of 6 mm, at a speed of 600 mm / min, for a total of 500 cycles in open air, and then for another 30,000 cycles in a-CD solutions of differentDocket No.: 021343 / WOconcentrations (with 1.0 M Na2SO4).

[0390] Post-punching analysis: Nine sections of the punched hydrogels were dissected from the central and surrounding area (gradient distance is around 5 mm), respectively. These hydrogel samples were dried and weighed as mO. Next, they were swelled in 500 pL DMSO-d6 with 1 pL / mL acetonitrile as an internal reference. The absorbed a-CD amounts were calculated by measuring the dissolved a-CD in the 1H NMR analysis against the internal reference.

[0391] Simulation details: We conducted finite element analysis (FEA) using ABAQUS (ABAQUS 2024, ABAQUS Inc.) to simulate stress distribution in the d-PN(20k, 4k) hydrogel during the punching test. The one term Ogden model was employed to describe the stress-strain behavior of the hydrogel. The free energy density function is expressed as:^=50I + ^2 +M - 3)

[0392] where p represents the shear modulus, a is a fitting parameter, and i represents the ith principal stretch (i = 1, 2, 3). By fitting Equation (1) to the experimental stress-strain curve of the d-PN(20k, 4k) hydrogel, we determined the fitting parameters p and a to be 9.56 kPa and 1.49, respectively. Using the conditions from the punching experiment, we simulated the impact of a vertical punch applied at the center of a circular d-PN(20k, 4k) hydrogel with a diameter of 40 mm, subjected to a vertical displacement of 12 mm. The results, shown in Figure S69(a), visualize the stress distribution in the circular hydrogel. The stress decreases as the distance from the center of the hydrogel increases. This enhanced stress concentration in the center correlates with a more effective reconfiguration of the hydrogel network, corresponding to the higher absorbed a-CD ratios (Figure S69(b)).

[0393] When d-ARN hydrogels were immersed in a-CD baths (0-100 mM), their elastic moduli and strength increased while stretchability decreased (Fig. 6b), consistent with newly threaded a-CDs co-crystallizing with existing crystalline domains (Fig. 6a, top right). This behavior aligns with the moderate increase in overall crystallinity observed by WAXS (Supplementary Table 18). Among them, d-ARN(20k, 4k) hydrogels displayed the greatest tunability and were further subjected to 1,200 cyclic (un)loading in a-CD baths. After training, d-ARN(20k, 4k, a IIM)MT hydrogels exhibited significantly higher modulus, strength, and fracture energy compared withDocket No.: 021343 / WOuntrained samples (Fig. 6c).

[0394] Both 'HNMR and W / SAXS analyses (Supplementary Tables 17-19) revealed that d-ARN(20k, 4k)MT incorporated significantly more a-CDs than untrained samples at the same bath concentration, resulting in higher crystallinity and larger crystalline domain sizes. This effect peaked in a 35 mM a-CD bath (Fig. 6d), demonstrating that mechanical training drives cooperative, out-of-equilibrium crystalline-domain growth through coupled a-CD threading and mechanically guided network reorganization.

[0395] Notably, this out-of-equilibrium network growth enabled active tuning of fatigue thresholds (Fig. 6e), a capability rarely observed in synthetic hydrogels. The fatigue threshold increased from 256 J / m2for d-ARN(20k, 4k, 0 IIIM)MT to 546 J / m2at 35 mM a-CD, before decreasing at higher concentrations. This result represents the first demonstration of out-of-equilibrium, environment-fed growth that actively increases fatigue threshold in a synthetic polymer hydrogel.

[0396] Mechanically guided out-of-equilibrium growth also enabled omnidirectional, strain-dependent strengthening. In a punching test (Fig. 6f), d-ARN(20k, 4k) hydrogels in 10-100 mM a-CD baths exhibited rapid increases in resisting force (Supplementary Fig. 84). After 30,000 cycles,NMR analysis revealed a spatial gradient of a-CD uptake that closely followed the local strain distribution (Fig.6g and Supplementary Fig. 85), confirming strain-controlled crystalline-domain growth and spatially targeted reinforcement.

[0397] Beyond uniform a-CD exposure, d-ARN hydrogels exhibit nonlocal network growth enabled by molecular exchange with their environment. Rectangular d-ARN(20k, 4k) hydrogels were mounted on a model knee joint and attached with a 35 mM a-CD patch, either statically or under 12,000 bending cycles (Fig. 6h). DIC strain mapping revealed that static patching produced a sharp, localized reinforcement confined to the patch region and dictated solely by a-CD concentration (Fig. 6i, Supplementary Video S6). In contrast, patching combined with mechanical learning generated a smooth strain gradient that extended well beyond the patched zone and closely matched the simulated strain distribution. This emergent behavior arises from two integrated processes: bending-induced shear promotes long-range a-CD diffusion, while mechanical loading actively drives a-CD incorporation into growing crystallineDocketNo.: 021343 / WOdomain networks. Together, these effects produce a spatiotemporally patterned, out-of- equilibrium remodeling process in which the material autonomously grows and reinforces regions of tailored mechanical demand. To our knowledge, no synthetic hydrogel has previously demonstrated such remote mechanochemical reinforcement, establishing d-ARNs as the first polymer networks capable of tissue-like, environment- fed, mechanically guided growth.Example 5: Synthesis of ARN Hydrogels

[0398] 1,3,5-Triformylphloroglucinol (Tp) was synthesized according to previously reported methods (2). All dihydroxyl -polyethylene glycols (PEG-(OH)2) were refluxed in toluene with a Dean- Stark apparatus to remove the water azeotropically from the starting material.Scheme S1. Synthesis of ax-PEGs and d-PEGs.

[0399] PEG-(OTs)2: In a 250-mL round bottom flask, anhydrous PEG-(OH)2 (10 g, 1.0 equiv.) was dissolved in CH2C12 (60-100 mL) in an ice bath before 4- dimethylaminopyridine (DMAP, 0.4 equiv.) and triethylamine (NEt3, 20.0 equiv.) were added. A solution of 4-toluenesulfonyl chloride (TsCl, 10.0 equiv.) in CH2C12 (30 mL) was added to the reaction dropwise over 10 min. The solution was allowed to warm to room temperature and stirred overnight. The reaction was washed with saturated NaCl aqueous solution three times, and the organic layer was collected and dried over anhydrous Na2SO4. A white crude product was obtained after the solvent was removed under the reduced pressure. The crude product was re-dissolved in CH2C12 and precipitated in an excess of diethyl ether. The product was collected by filtration and dried at 40 °C under vacuum for 24 h, affording PEG-(OTs)2 as a white powder.

[0400] PEG4k-(OTs)2: Yield 74%. 1H NMR (400 MHz, CDC13, ppm) 8 = 7.80 (d, J = 8.4 Hz, 4H), 7.34 (d, J = 8.2 Hz, 4H), 4.18 - 4.12 (m, 4H), 3.64 (s, 364H), 2.45 (s, 6H) (3).

[0401] PEG6k-(OTs)2: Yield 87%. 1H NMR (400 MHz, CDC13, ppm) δ 7.80Docket No.: 021343 / WO(d, J = 8.4 Hz, 4H), 7.38 - 7.31 (m, 4H), 4.20 -4.12 (m, 4H), 3.64 (s, 612H), 2.45 (s, 6H).

[0402] PEG10k-(OTs)2: Yield 80%. 1H NMR (400 MHz, CDC13, ppm) δ 7.82 (d, J = 8.0 Hz, 4H), 7.37 (d, J = 8.0 Hz, 4H), 4.18 (t, J = 4.9 Hz, 5H), 3.67 (d, J = 0.9 Hz, 920H), 2.47 (s, 5H).

[0403] PEG20k-(OTs)2: Yield 89%. 1H NMR (400 MHz, CDC13, ppm) δ 7.79 (d, J = 8.1 Hz, 4H), 7.34 (d, J = 8.0 Hz, 4H), 4.15 (s, 4H), 3.64 (s, 2120H), 2.45 (s, 6H).

[0404] MeO-PEG4k-OTs: Yield 83%. 1H NMR (400 MHz, CDC13, ppm) δ 7.80 (d, J = 8.1 Hz, 2H), 7.34 (d, J = 8.0 Hz, 2H), 4.16 (t, J = 4.9 Hz, 2H), 3.64 (s, 382H), 3.38 (s, 3H), 2.45 (s, 3H).

[0405] ax-PEG: PEG-(OTs)2 (1.0 equiv.) was dissolved in an ammonium hydroxide solution (5 w / v%, 70-100 mL) in a 250-mL round bottom flask connected with a condenser. The reaction was stirred at 70 °C for 24 h in open air. After cooling down, the solution was extracted using CH2C12 (50 mL x 3). The organic layer was collected and washed with saturated NaCl aqueous solution three times. The crude product was obtained after the solvent was removed under reduced pressure, which was subsequently re-dissolved in CH2C12 and precipitated in an excess of diethyl ether. The final product was collected by filtration and dried at 40 °C under vacuum for 24 h, affording ax-PEG as a white powder.

[0406] ax-PEG4k: Yield 83%. 1H NMR (400 MHz, CDC13, ppm) δ = 3.52 – 3.79 (m, 364H) (3).ax-PEG6k: Yield 81%. 1H NMR (400 MHz, CDC13, ppm) δ 3.64 (bs, 546H).

[0407] ax-PEGlOk: Yield 60%. 1H NMR (400 MHz, CDC13, ppm) δ 3.63 (bs, 1H).

[0408] ax-PEG20k: Yield 78%. 1H NMR (400 MHz, CDC13, ppm) δ 3.66 (bs, 1818H).

[0409] d-PEG4k: Yield 74%. 1H NMR (400 MHz, CDC13, ppm) δ 3.57 (bs, 364H), 3.31 (s, 3H).Example 7: Preparation of the polyrotaxane-based hydrogelsDocket No.: 021343 / WO2.5. r ry*-;: cwest. <:?»?■<■>•:■? 5. S& W> viasS-J'g wWrtte VY-V {cos) YSciww $2. Synthesis of the PN hy<fcogels.

[0410] Synthesis of PN hydrogels: PN hydrogels were prepared similarly to our previously reported method (3). For PN(20k), ax-PEG20k (400 mg, 0.2 mmol, 1.0 equiv.) was dissolved in 4 mL deionized water before Tp (2.8 mg, 0.013 mmol, 0.67 equiv.) was added at room temperature. The suspension was sonicated for 2~3 min until the complete dissolution of Tp. An aqueous solution of a-CD (2.0 g, 205.6 mmol in 6 mL water) was added to the reaction, and the mixture was stirred at 60 °C for 2 h. The hot suspension was transferred to a dog-bone-shaped mold. After cooling down, the hydrogel was formed and kept at room temperature in a humid chamber for 15 h. Next, the hydrogel was heated at 70 °C for 3~5 h in open-air to allow for extensive crosslinking (dehydration of the hydrogel also occurred). The crosslinked sample was swelled in DMSO to remove any unreacted species. The DMSO-gel was washed by soaking it in fresh DMSO three times. The DMSO-gel was converted to hydrogel by immersing the sample in an aqueous Na2SO4 (1 M) solution three times over a period of 1-2 days to remove any residual DMSO.

[0411] For specific hydrogel synthesis, the amounts of reactants were listed in Table SI. The introduction of aqueous Na2SO4 (1 M) solutions for hydrogel regeneration allowed us to keep the water contents of the PN hydrogels consistently at ca. 60 wt%.a, fSS' ‘ '' r cf T «Scheme S3. Synthesis of d-PN hydrogels.

[0412] Synthesis of d-PN hydrogels: For d-PN(20k, 4k), ax-PEG20k (400 mg, 0.2 mmol, 1.0 equiv.), and d-PEG4k (40 mg, 0.1 mmol, 0.5 equiv.) were dissolved in 4Docket No.: 021343 / WOmL deionized water, and then Tp (3.5 mg, 0.017 mmol, 0.83 equiv.) was added to the reaction at room temperature. The suspension was then sonicated for 2~3 min until the complete dissolution of Tp. An aqueous solution of a-CD (2.3 g, 236 mmol in 6 mL water) was added to the reaction, and the mixture was stirred at 60 °C for 2 h. The suspension was then transferred to a dog-bone-shaped mold. After cooling down, the hydrogel was formed and kept at room temperature in a humid chamber for 15 h. Next, the hydrogel was heated at 70 °C for 3~5 h in open-air to allow for extensive crosslinking (dehydration of the hydrogel also occurred). The crosslinked sample was swelled in DMSO to remove any unreacted species. The DMSO-gel was washed by soaking it in fresh DMSO three times. The DMSO-gel was converted to hydrogel by immersing the sample in an aqueous Na2SO4 (1 M) solution three times over a period of 1-2 days to remove any residual DMSO. For specific hydrogel synthesis, the amounts of reactants were listed in Table S2.Scheme S4, HyA ysss <sf the crosshnfcgd P and d-P hydrogels.

[0413] The PN and d-PN hydrogels were hydrolyzed for 1H NMR analysis to reveal the average threaded a-CDs and a-CD-to-PEG ratios. Experimentally, hydrogels with measured mass ml were dried at 70 °C with measured mass m2. The mass reduction ratios (ml-m2) / ml revealed the water content of the hydrogel listed in Table SI -2. The dried samples were hydrolyzed in NaOD / D2O (5% w / v) at 70 °C until fully dissolved. The averaged numbers of threaded a-CDs were calculated based on the proton integrations attributed to a-CDs and PEG. The theoretical maximum numbers of allowable threaded a-CDs (Nmax) were calculated by assuming an EG / a-CD = 2:1.Table S2. Composition of d-PN hydrogels in this work. The fed ax-PEG20k is kept at the concentration of 2 mM or 4 wt% for all d-PN samples.Docket No.: 021343 / WOFed d-PEG Tp Feci s-CD CD: PEG Water Samples coverage on content wt% mM EiM wt% Fed Foundax-PEG (%)‘ (wt%) d-PN(20k, Ik) 0.1 1 79 >3 I 23.3 58 d-PN(20k, 2k) 0.2 1 79 51 i 1 79 65 d-PN(20k, 4k) 0.4 1 1.7 23 236 79 50= 1 22.0 Sg d-PN(20k, 5k) 05 1 79 50 i 1 220 66d-PN(20k, 10k) 1.0 1 79 44 ± 2 19.4 64 ’‘ calculated with the integration of proton resonances of s.-CD and fee -CH2CH3O- of ax-PEG and d-PEG Coverage percentage is calculated by dividing the threaded &-CD number by the maximum threaded number of ax-PEG^1 H h X-H 2. 70c,c.4. DJ wate; washing as-PESTPCN hydrogelsScheme S5. Synthesis of CN hydrogels

[0414] Synthesis CN(20k) hydrogel: ax-PEG20k (400 mg, 0.2 mmol, 1.0 equiv.) were dissolved in 10 mL DMSO with Tp (2.8 mg, 0.013 mmol, 0.67 equiv.). The mixture was placed in THINKY mixer AR100 and mixed for 2 min at 2000 rpm to remove bubbles. A clear solution was formed, and it was transferred to a dog-bone- shaped mold. The sample was kept at room temperature in a humid chamber and then heated at 70 °C for 3~5 h in open air for extensive crosslinking until complete evaporation of DMSO. The sample was swelled in water to remove unreacted species and then soaked in an aqueous Na2SO4 (1.0 M) solution for 24-48 h. The water content was measured as 78 wt%. The sample was hydrolyzed in NaOD / D2O, and the ratio of the ax-PEG20k to Tp was measured as 1:0.79 (fed ratio 1:0.67) calculated from their integration ratio of protons.

Claims

Docket No.: 021343 / WOClaimsWhat is claimed is:

1. An adapt-ring network hydrogel composition comprising:a. a first amount of diamino-polyethylene glycol (ax-PEG), each ax-PEG comprising a first and a second amino moiety covalently bonded at opposite ends of a PEG chain;b. a second amount of 1,3,5-triformylphloroglucinol (Tp) comprising three carbaldehyde moieties;c. a third amount of a-cyclodextrin (a-CD), each a-CD defining a central lumen passing therethrough; andd. a fourth amount of a IM Na2SO4 solution;wherein at least a portion of the first and second amino moieties of the ax-PEGs are each covalently bound to one of the three carbaldehyde moieties of the Tp’s, and the central lumens of the third amount of a-CDs are threaded over the PEG chains of the first amount of ax-PEG.

2. The composition of claim 1, wherein the ax-PEG further comprises a molecular mass ranging from about 4 kg / mol to about 20 kg / mol.

3. The composition of any one of claims 1 -2, wherein the first amount ax-PEG comprises about 4 wt% of the composition.

4. The composition of any one of claims 1 - 3, wherein the third amount of a-CD comprises about 8 wt% of the composition.

5. The composition of any one of claims 1 -4, wherein the composition further comprises a unit ethylene glycol (EG) to a-CD ratio of about 4.4:1.

6. The composition of any one of claims 1 - 5, wherein the composition further comprises ax-PEGS with a molecular mass of about 4 kg / mol and an average of about 10 a-CDs threaded on each ax-PEG.

7. The composition of any one of claims 1 - 6, wherein the composition further comprises ax-PEGS with a molecular mass about 20 kg / mol and of an average of about 33 a-CDs threaded on each ax-PEG.

8. The composition of any one of claims 1 - 6, wherein the third amount of a-CDs are configured to freely slide over the PEG chains of the first amount ax-PEG threaded through the central lumens.Docket No.: 021343 / WO9. The composition of any one of claims 1 - 8, wherein the third amount of a-CDs are configured to spontaneously form a plurality of dense crystalline domains, each dense crystalline domain comprising a dense array of a-CDs from a portion of the third amount of a-CDs.

10. The composition of any one of claims 1 - 9, wherein the plurality of dense crystalline domains are configured to spontaneously reform into a plurality of stress-directed crystalline domains in response to a mechanical loading, wherein the plurality of stress-directed crystalline domains are at least one of fragmented, translocated, and aligned relative to the plurality of dense crystalline domains.

11. The composition of any one of claims 1 - 10, wherein the mechanical loading comprises at least one of cyclic loading and unloading, and stretch-and- sonication.

12. The composition of any one of claims 1 - 11, wherein the plurality of stress- directed crystalline domains are configured to spontaneously reform into a plurality of dense crystalline domains in response to a solvent annealing.

13. The composition of any one of claims 1 - 12, wherein the solvent annealing comprises a DMSO / H2O exchange.

14. The composition of any one of claims 1 - 13, further comprising:a. a fifth amount of dangling PEG (d-PEG) comprising a third amino moiety covalently bonded at one end of a dangling PEG chain, wherein the third amino moieties of the d-PEG are covalently bonded to free carbaldehyde moi eties of the second amount of Tp; andb. a sixth amount of free a-CDs.

15. The composition of any one of claims 1 - 14, wherein the fifth amount of dangling PEG (d-PEG) further comprises a molecular mass ranging from about 1 kg / mol to about 10 kg / mol.

16. The composition of any one of claims 1 - 15, wherein the fifth amount of dangling PEG (d-PEG) is configured to thread through the free central lumens of the free a-CDs.

17. The composition of any one of claims 1 - 16, wherein the threaded free a-CDs are configured to spontaneously form a plurality of enlarged dense crystalline domains comprising an enlarged array of a-CDs from a portion of the third amount of a-CDs and a portion of the free a-CDs.Docket No.: 021343 / WO18. The composition of any one of claims 1 - 17, wherein the plurality of enlarged dense crystalline domains are configured to spontaneously reform into a plurality of stress-directed integrated crystalline domains in response to a mechanical loading, wherein the plurality of stress-directed integrated crystalline domains are at least one of fragmented, translocated, and aligned relative to the plurality of dense crystalline domains.

19. The composition of any one of claims 1 - 18, wherein the composition is configured to autonomously generate spatially self-organized, strain-dependent reinforcement.

20. The composition of any one of claims 1 - 19, wherein the spatially selforganized, strain-dependent reinforcement comprises strain-dependent reinforcement.

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