Polymers, polmer networks, and methods of making polymer networks

Abstract

The present disclosure provides for foldable bottlebrush polymers, foldable bottlebrush polymer networks and methods of making foldable bottlebrush polymers and foldable bottlebrush polymer networks. The present disclosure provides a general method for decoupling stiffness and extensibility of polymer networks. Instead of using classical linear polymers as network strands, an aspect of the present disclosure provides for methods using foldable bottlebrush polymers, which feature a collapsed backbone grafted with many linear side chains. Upon elongation, the collapsed backbone unfolds to release stored length, enabling remarkable extensibility. By contrast, the network elastic modulus is inversely proportional to the network strand mass and is determined by the side chains.

Description

[0001] POLYMERS, POLMER NETWORKS, AND METHODS OF MAKING POLYMER NETWORKS

[0002] CROSS-REFERENCE TO RELATED APPLICATION

[0003] This application claims priority to U.S. provisional application entitled “Universal Strategy for Decoupling Stiffness and Extensibility of Polymer Networks” having serial number 63 / 517,846 filed on August 4, 2023, which is entirely incorporated herein by reference.

[0004] STATEMENT ON FUNDING PROVIDED BY THE U.S. GOVERNMENT

[0005] This invention was made with Government support under contract DMR-1944625 awarded by the National Science Foundation. The Government has certain rights in the invention.

[0006] BACKGROUND

[0007] Stiffness and extensibility are two fundamental mechanical properties of polymer networks. Although these properties seem distinct, they share a common microscopic origin. As a result, stiffer polymer networks are less extensible. There is a need to control both the stiffness and extensibility independently.

[0008] SUMMARY

[0009] The present disclosure provides for foldable bottlebrush polymers, foldable bottlebrush polymer networks and methods of making foldable bottlebrush polymers and foldable bottlebrush polymer networks. The present disclosure provides a general method for decoupling stiffness and extensibility of polymer networks. Instead of using classical linear polymers as network strands, an aspect of the present disclosure provides for methods using foldable bottlebrush polymers, which feature a collapsed backbone grafted with many linear side chains. Upon elongation, the collapsed backbone unfolds to release stored length, enabling remarkable extensibility. By contrast, the network elastic modulus is inversely proportional to the network strand mass and is determined by the side chains. The developed strategy applies to polymers of different species and networks of different topologies such as end-crosslinked and randomly crosslinked networks.

[0010] In an aspect, the present disclosure provides for a composition, comprising: a foldable bottlebrush polymer having spacer monomer groups and side chains, wherein the side chains are bonded to a portion of the monomer groups, wherein the monomer group are about 5 to 50% of the foldable bottlebrush polymer, wherein the portion of the monomer with the side chains is about 50 to 95% of the foldable bottlebrush polymer, wherein the spacer monomer groups and side chains are incompatible as defined by a Flory-Huggins interaction parameter ( ^ ^ of about 0.05 or more while in the dry state without solvent. BRIEF DESCRIPTION OF DRAWINGS Further aspects of the present disclosure will be more readily appreciated upon review of the detailed description of its various embodiments, described below, when taken in conjunction with the accompanying drawings. Figures 1A to 1C illustrate the concept of foldable bottlebrush (fBB) polymer network strands. Figure 1A illustrate a conventional single-network elastomer is comprised of crosslinked flexible linear polymers without solvents. The network extensibility is limited by the ratio of the maximum length, Lmax, to the initial size, R, of the network strand: emax=Lmax / R-1~N1 / 2, where R=bN1 / 2is the random walk of N Kuhn monomers of size b per network strand, and Lmax=bN is the contour length of the network strand. The network Young’s modulus is E≈3kBT / V~1 / N, where kBis Boltzmann constant, T is the absolute temperature, and V≈Nb3is the volume of a network strand. Thus, the network stiffness and extensibility are negatively correlated: E∝(emax)-2. Figure 1B illustrates using conventional bottlebrush polymers increases the network strand molecular weight and, therefore, reduces network stiffness, but does not break the inherent stiffness-extensibility trade-off: E∝(emax)-a, where the value of a is 2, 1, or >2 if the bottlebrush polymer is flexible, semiflexible, or pre- strained (Supplementary Note 1). Figure 1C illustrates a fBB polymer consists of many linear side chains (nsc) randomly separated by small spacer monomers at a molar ratio of rsp. Figure 1C(i) illustrates the design criteria are that the side chain has a relatively high MW (DP Nsc) and a low glass transition temperature (Tg), whereas the spacer monomer has a low MW and is highly incompatible with the side chains (relatively large Flory-Huggins interaction parameter Figure 1C(ii) illustrates that to minimize interfacial free energy, the backbone collapses into a cylindrical core with its surface densely grafted with side chains, despite the strong steric repulsion among the overlapped side chains in both the folded and unfolded states. The fBB polymer remains elastic because of its low Tgside chains. Figure 1C(iii) illustrates that upon stretching, the collapsed bottlebrush backbone unfolds to release the stored length. By contrast, the molecular weight of this fBB polymer is dominated by the side chains. Thus, it is expected that using fBB polymers as network strands enables decoupling network stiffness and extensibility (a=0). Figures 2A-2G illustrate the design and synthesis of foldable bottlebrush polymer networks. Figure 2A illustrates a proof-of-concept design of fBB polymer networks by exploiting the classical ABA triblock copolymer self-assembly. Side chain: linear poly(dimethyl siloxane) (PDMS) of 1,000 g / mol; spacer: benzyl methacrylate (BnMA) of 176 g / mol or methyl methacrylate (MMA) of 100 g / mol; linear blocks: poly(benzyl methacrylate) (PBnMA) with DP Nl;. Since the side chain MW is constant, this linear-fBB-linear triblock copolymer has three design parameters [nsc, Nl, rsp]. Figure 2B illustrates hollow-cone dark- field TEM images of the microstructures self-assembled by two triblock copolymers. Left: control polymer without spacers, [550, 176, 0]; right: polymer with spacers, [534, 177, 0.84]. The dark dots are the spherical nodules aggregated by linear PBnMA end blocks. The average inter-domain distances are d=75.7±13.1 nm (rsp=0) and 85.2±10.8 nm (rsp=0.84). Scale bars, 200 nm. Figure 2C illustrates the dependence of SAXS / WAXS intensity on the magnitude of wavevector, q, for the self-assembled networks. Figure 2D illustrates a schematic illustrating two characteristic lengths in the self-assembled networks: (1) the average inter-domain distance, d=2p / q*, and (2) the inter-backbone distance, Dbb=2p / qbb, of fBB polymers, as noted by the arrows in (c). Figure 2E illustrates large amplitude oscillatory shear (LAOS) measurements reveal that introducing spacer monomers increases the shear yield strain (gy) but nearly does not alter network stiffness. The network with spacers exhibits a remarkable strain-softening regime, with a reduction of 14% in shear modulus, followed by the classical strain-stiffening. G’ and G’’ are, respectively, shear storage and loss moduli measured at 1 rad / sec at 20 °C. Figure 2F and 2G illustrate characteristic length scales (d, Lmax, Dbb) of fBB polymer networks with various BnMA spacer ratios, [~200, ~33, 0-3.46]. (f) As the average DP of the spacer segment (Ng=rsp+1) increases, the inter-domain distance (d) remains nearly the same, but the bottlebrush backbone contour length (Lmax=nsclNg) increases dramatically. Here, l is the main-chain bond length of a repeating unit in the backbone. Figure 2G illustrates the inter-backbone distance (Dbb) increases with the decrease of grafting density (1 / Ng) in both melts (squares) and self-assembled networks (circles). This behavior contradicts the understanding of conventional bottlebrush polymers (dashed line, Supplementary Note 1, eq. S10). Yet, it can be well-explained by our recent molecular theory that accounts for the incompatibility between spacer monomers and side chains within fBB polymers (solid line, Supplementary Note 2, eq. S39). Figures 3A-3E illustrate using fBB polymers as network strands provides a universal strategy for decoupling network stiffness and extensibility. a, b, Nominal stress-strain curves of networks with (Figure 3A) BnMA and (Figure 3B) MMA as spacers. ef, tensile fracture strain; emax, critical strain at which the nominal stress is maximum. At either (i) low or (iii) high spacer ratios, ef= emax. By contrast, at intermediate spacer ratios, emax< efand the networks exhibit plastic deformation under large deformations, at which the nominal stress decreases dramatically with strain. All measurements are performed at RT and a fixed tensile strain rate of 0.02 / sec. Figure 3C and 3D illustrate the dependencies of (Figure 3C) network extensibility (emax) and (Figure 3D) Young’s modulus (E) on the spacer ratio. Figure 3E illustrates at relatively small spacer ratios, the network stiffness and extensibility are truly decoupled, where emaxcan be increased from ~20% to 800% while keeping E constant at ~30 kPa (a=0). There exists a small window (intermediate spacer ratios) in which stiffness and extensibility are positively correlated (a<0). At high spacer ratios, the folded bottlebrush itself has an elevated Tgand becomes stiff (Extended Data Figures 10A-10G), such that the network stiffness and extensibility resume the classical negative correlation (a>0). Error bar, standard deviation for n=3-5. Figures 4A-4G illustrate unfolding of a collapsed bottlebrush network strand under extension. Figure 4A illustrates an illustration of in situ SAXS / WAXS measurements for a fBB elastomer with BnMA as the spacer monomer ([200, 33, 2.9]) under uniaxial tensile test at a strain rate of 0.01 / sec. Figure 4B illustrates two-dimensional (2D) (i) SAXS and (ii) WAXS patterns at various strains. Figure 4C and 4D illustrates that along the elongation direction, the inter-domain distance (d) increases linearly with strain (e). Figures 4E and 4F illustrate perpendicular to the elongation direction, the inter-backbone distance (Dbb) decreases with the increase of strain because of the strain-triggered unfolding of a collapsed bottlebrush backbone. g, For WAXS, the orientation factor is negative and decreases with the increase of strain (eq.2, Methods). This behavior indicates that the bottlebrush backbones become more aligned along the stretching direction, and therefore, the orientation of inter-backbone spacing becomes more ordered perpendicular to the stretching direction (Extended Data Figures 12A to 12D). Figures 5A-5C, extended Data for Figure 1, illustrates the strain-softening of fBB polymer networks. Figure 5A illustrates LAOS measurements of fBB polymer networks are performed at 20 °C and 1 rad / sec. All networks have nearly the same spacer ratio (rsp) but different numbers of side chains (nsc). The DP of each linear end block is about 30% of the number of side chains (Nl≈ 0.3nsc); this ensures that the volume fraction of the end linear blocks is nearly the same at ~10%. All networks exhibit a remarkable strain-softening followed by classical strain-stiffening attributed to stretching the network strand to its length limit. To describe the dynamic mechanical properties of a network under LAOS measurement, we introduce three parameters: yield strain (gy), the strain (gmin) at which the shear storage modulus is minimum (G’min), and shear storage modulus at the lowest strain 1% (G’0). Figure 5B illustrates that remarkably, as nscdecreases from 534 to 360, the strain- softening behavior nearly vanishes, as evidenced by the increase of the ratio G’min / G’0from 86.6% to 98.2% (northwest pointing arrow). The width of the strain-softening regime, gs, defined as the critical strain above which the strain-softening regime ends (G’ / G’0>1), increases with the number of side chains. Additionally, the network shear modulus is inversely proportional to the number of side chains or the volume of the fBB polymer network strand (inset). Figure 5C illustrates that all the characteristic shear strains, gmin, gs, and gy, increase linearly with the number of side chains. These results suggest that for a fBB polymer network, a relatively large number of side chains is needed to exhibit pronounced strain-softening. Figures 6A-6C, extended data for Fig.2, illustrates GPC profiles of linear-fBB-linear triblock copolymers. Figures 6A and 6B illustrates GPC profiles of polymers with (Figure 6A) BnMA and (Figure 6B) MMA as spacers. Figure 6C illustrate the logarithmic MW, M, of all triblock polymers decreases linearly with the increase of peak retention time, t. These results demonstrate controlled synthesis of linear-fBB-linear polymers with desired molecular architecture parameters ([nsc, Nl, rsp]). Figures 7A and 7B, extended data for Figure 3, illustrate microstructure of self- assembled fBB polymer networks. Figures 7A and 7B illustrate radially averaged one- dimensional (1D) SAXS / WAXS intensity profiles as a function of the magnitude of the wavevector (q) for the self-assembled fBB polymer networks with (Figure 7A) BnMA and (Figure 7B) MMA as spacer monomers. All polymers form an end-crosslinked network, in which the fBB polymers are crosslinked by glassy nodules aggregated by linear end blocks (inset, b). For both series of polymers, the inter-backbone distance (Dbb) increases with the spacer ratio (rsp). These results confirm that fBB polymer network strands remain folded in the self-assembled networks. Figures 8A to 8D, extended data for Figure 4, illustrates dynamic mechanical properties of fBB polymer networks. Figures 8A and 8B illustrate the frequency dependencies of the storage (solid symbols, G’) and loss (open symbols, G’’) moduli of fBB polymer networks with (Figure 8A) BnMA and (Figure 8B) MMA as spacer monomers. All measurements are performed at 20 °C with a fixed strain of 5%. At low spacer ratios (Regime I), G’ exhibits a weak dependence on frequency and reaches a plateau at low frequency. By contrast, as the spacer ratio becomes relatively high (Regimes II & III), G’ increases rapidly with frequency, indicating enhanced dissipative behavior in the polymer networks. Figure 8C and 8D illustrate consistent with this understanding, the loss factor, tanδ=G’’ / G’, increases with the spacer ratio. Yet, all polymers are a solid network with G’ greater than G’’ (tanδ<1). Figure 8E illustrates that the network shear modulus G (G’ at the lowest frequency 0.1 rad / sec) remains nearly a constant at low spacer ratios (symbols in the light green region). The experimental measurements can be well-explained by the theory that the shear modulus of an unentangled network is kBT per volume of the network strand: G=kBTNAvr / M. Here, T=293 K, NAvis Avogadro number, r≈1 g / cm3is polymer density, and M=(nscMsc+rspnscMsp) is the molar mass of the fBB polymer (with Msc≈1000 g / mol and Mspbeing the side chain and spacer molecular weight, respectively). Black dashed line: G≈11 kPa for the control network (rsp=0); red solid line: networks with BnMA spacer; blue solid line: networks with MMA spacer. Note that the predicted shear modulus is nearly independent of the spacer ratio, as the molecular weight of the fBB polymer is dominated by the side chains. At relatively high spacer ratios (light red and gray regions), G increases exponentially with the spacer ratio (dashed lines). The dependence of shear modulus G on the spacer ratio aligns well with the network Young’s moduli E, following the classical relation E=3G (Figure 3D). Figure 9, extended data for figure 5, illustrates that the plastic deformation disappears for stronger glassy nodules. At intermediate spacer ratios, fBB polymer networks exhibit plastic deformation under large deformation, at which the nominal stress decreases dramatically with the increase of tensile strain (Fig.3A,iii & B,ii). We propose that the plastic deformation is because of the end-chain pullout from the glassy nodules. During this process, the network continues to stretch without breaking, but the network strands cannot efficiently sustain stress, resulting in an apparent decrease in nominal stress. We test this hypothesis by synthesizing two networks with the same fBB polymer network strand but different end block volume fractions. As the end block volume fraction increases, the glassy nodules increase in size and strength, preventing the end-chain pullout from the glassy nodules. Consistent with this understanding, the plastic deformation disappears as the end block volume fraction increases from 6% to 13%, a value close to the upper limit for sphere morphology. Moreover, the network Young’s moduli remain the same, as shown by the overlap of strain-stress curves at low strains. These results demonstrate that the plastic deformation occurs only for relatively weak glassy nodules, as illustrated in Extended Data Figure 8E. Thus, we use emax, the strain at which the nominal stress is maximum, to describe the network extensibility attributed to the fBB polymer network strands. Figures 10A-10G, extended data for Figure 6 illustrates that th melts of fBB polymers are viscoelastic solids at high spacer ratios. Figures 10A and 10B illustrate that the dependence of shear moduli on temperature for the melts of fBB polymers with (Figures 10A) BnMA and (Figure 10B) MMA as spacer monomers. All measurements are performed at 1 rad / sec with a fixed oscillatory shear strain of 5%. Figures 10C and 10D illustrate that the dynamic mechanical analysis (DMA) reveals that at relatively high spacer ratios, the loss factor of fBB polymer melts exhibits a pronounced peak at the glass transition temperature Tgassociated with the collapsed bottlebrush backbone. Figure 10E illustrates that the Tg,of fBB polymers, measured by DMA, increases with the spacer ratio (empty symbols). Figure 10F illustrates that, in parallel, we use differential scanning calorimetry (DSC) to measure the Tgof fBB polymers. The curves for the heat capacity Cpof fBB polymers are shifted vertically for clarity. The values of Tgmeasured by DSC (filled symbols in (Figure 10E)) are consistent with those measured by DMA (empty symbols in (Figure 10E)). At low spacer ratios, the volume fraction of the backbone within the fBB polymer is relatively small (<20%). Consequently, the Tgof fBB polymers is much below RT, such that the fBB polymers remain elastic at RT. However, at relatively high spacer ratios, the Tgof fBB polymers becomes close to and even higher than RT, such that the fBB polymers become a viscoelastic solid at RT. Figure 10G illustrate the shear storage modulus G’ (measured at 1 rad / sec and 20 °C) of fBB polymers increases with the spacer ratio. At relatively high spacer ratios (rsp>2), the fBB polymers themselves become stiff, with G’ increasing exponentially with the spacer ratio (dashed red and blue lines for BnMA and MMA spacers, respectively). Moreover, the stiffness of fBB polymers becomes greater than the elastic contribution of the fBB polymers as a network strand (~11 kPa, horizontal dashed line). As a result, the stiffness of fBB polymer networks is dominated by the fBB polymer and increases exponentially with the spacer ratio (Figure 10D). Figure 11A and 11C, extended data for Fig.7, illustrates in situ SAXS / WAXS scattering of a fBB polymer network under uniaxial tension. Figure 11A illustrates a 2D WAXS pattern of a fBB polymer network (spacer: BnMA; [200, 33, 2.9]) at a tensile strain of 1.94. To determine the azimuthal spread of the peak intensity associated with the inter- backbone spacing, we choose the region with q values from 0.8 nm-1to 2 nm-1(the ring between two dashed circles). This range is sufficient to cover the width of the characteristic scattering peak located at 1.2 nm-1, as illustrated in (Figure 11C). An example of the scattering intensity as a function of the azimuthal angle is shown by the lower panel. Figure 11B illustrates, without deformation, the scattering intensity exhibits no preference for the azimuthal angle, indicating no preference for the orientation of the inter-backbone spacing. As the strain increases, the scattering intensity becomes more pronounced at 90°, indicating that the orientation of inter-backbone spacing becomes more ordered perpendicular to the stretching direction. Figure 11C, along the stretching direction, the 1D scattering intensity profiles exhibit a characteristic peak associated with the inter-backbone distance, as illustrated in extended data Fig.8C. Remarkably, as the strain increases, the peak location does not change, yet the peak intensity decreases. This behavior is consistent with the understanding that the fBB polymer network strands are compressed perpendicular to the stretching direction, such that along the stretching direction, the inter-backbone distance does not change, yet the orientation of inter-backbone spacing becomes less ordered (Extended Data Figure 8C). Figure 12A to 12D, extended data for Fig.8, is an illustration of molecular mechanisms for stretching fBB polymer networks. Figure 12A illustrates a network self- assembled by linear-fBB-linear triblock copolymers, the end blocks aggregate into spherical glassy domains (green spheres) that crosslink the fBB polymer network strands. Without deformation, the backbone of fBB network strands remains folded (thick red line, lower panel). Moreover, the glassy nodules and the orientation of the collapsed bottlebrush backbone are randomly distributed. Consequently, the 2D SAXS / WAXS intensity profiles are independent of the azimuthal angle and exhibit symmetric, circular patterns (Figure 4B). Figure 12B illustrates, upon elongation, the inter-domain distance (d) increases along the elongation direction but decreases perpendicular to the elongation direction (Figure 4C, 4D). Figure 12C, along the elongation direction, the backbone of the fBB polymer network strands becomes more aligned, resulting in more ordered inter-backbone spacing perpendicular to the elongation direction. Consequently, as the strain increases, the characteristic WAXS scattering peaks exhibit increased intensity (Figure 4E, Extended Data Figure 7B) and enhanced orientation function (Figure 4G). Figure 12D illustrates, simultaneously, along the elongation direction, the collapsed backbone unfolds, resulting in reduced side chain grafting density. Thus, both the side chain size and the bottlebrush backbone diameter decrease, resulting in reduced inter-backbone distance (Dbb) perpendicular to the stretching direction (Figure 4F). By contrast, the fBB polymer network strands are not stretched but compressed, resulting in negligible change in inter-backbone distance along the stretching direction (Extended Data Figure 7C). Figure 12E illustrates that in some cases, when the glassy nodules are relatively weak, it is possible to pull the linear end blocks out from the glassy nodules. This process enables extremely stretchable networks. However, as the end-chain is being pullout, the network strands cannot efficiently sustain stress. Thus, the network exhibits plastic deformation with the nominal stress decreasing dramatically with the increase of tensile strain (Figures.3A and 3B, ii). However, this plastic deformation disappears when the glassy nodules become relatively strong (Extended Data Figure 5) or the crosslinkers become permanent covalent bonds (Extended Data Figure 9). Figure 13A-13C, extended data Figure 9, illustrates randomly crosslinked fBB polymer networks. Figure 13A illustrates that we create randomly crosslinked fBB polymer networks by copolymerizing three precursor monomers: (i) a mono-functional linear PDMS polymer (MCR-M11, ~1000 g / mol) as the side chain, (ii) a di-functional linear PDMS polymer (DMS-R18, ~5000 g / mol) as the crosslinking chain, and (iii) BnMA as the spacer monomer. Figure 13B illustrates that ee denote a randomly crosslinked fBB polymer network using two parameters, [nsc, rsp], where nscis the average number of side chains per crosslinking chain. Using the same method for synthesizing fBB polymers, we fix the side chain / crosslinking chain molar ratio at 100:1 (ns=100) and only change the spacer ratio (rsp). For a polymer network, we use a mixed solvent, DMF and THF at a volume ratio of 1:1, to wash away any unreacted monomers and catalyst. The polymer networks are dried under vacuum before mechanical test. Figure 13C illustrates compared to the control network (rsp=0), which fractures at a tensile strain ef=200% (thin red line), the network with a low spacer ratio (rsp=1.0) has nearly the same Young’s modulus of 46 kPa but a significantly higher tensile breaking strain ef=416% (intermediate thick black line). At an intermediate spacer ratio (rsp=2.0), the network has a higher Young’s modulus of 58 kPa and a large extensibility of ef=578% (thick green line). As expected, unlike the self-assembled fBB polymer networks that exhibit plastic deformation at intermediate spacer ratios (ef>emax), the randomly crosslinked fBB polymer networks do not exhibit plastic deformation (ef=emax). These results demonstrate that our strategy of using fBB polymers as network strands to decouple the stiffness and extensibility of unentangled single-network elastomers applies to randomly crosslinked networks. All tensile tests are performed at RT and a fixed strain rate of 0.02 / sec. Figure 14, extended data Figure 10, illustrates a comparison between fBB polymer networks and conventional bottlebrush polymer networks. Our fBB polymer networks allow for truly decoupled stiffness and extensibility (empty circles and squares, light green region). By contrast, the stiffness and extensibility of conventional bottlebrush polymer networks are negatively correlated (Supplementary Table S1). Because the backbone is strained by the steric repulsion among overlapping side chains, conventional bottlebrush polymers networks (BNPs) are often brittle with low extensibility unless using bottlebrush network strands of extremely high molecular weight (when the networks become very soft). By contrast, our fBB polymer networks can exhibit remarkable extensibility while maintaining constant stiffness. Filled symbols represent the tensile fracture strain effor fBB polymer networks with intermediate spacer ratios. Figure 15, extended data Table 1, provides the molecular architecture parameters, microstructure, and mechanical properties of fBB polymer networks. number of side chains per bottlebrush polymer; DP of each end linear blocks; ^^ spacer / side chain number ratio; volume fraction of the end blocks; PDI, polydispersity index; G, shear modulus (G’ at 0.1 rad / sec and 20 °C); E, Young’s modulus measured by tensile tests; the strain at which the nominal tensile stress is maximum tensile fracture strain; d, inter-domain distance of glassy nodules; Dbb, inter-backbone distance for fBB polymers in both the melt and the self-assembled networks. S1 and S3: samples with BnMA as the spacer; S2: samples with MMA as the spacer. The side chains are linear PDMS of 1000 g / mol and the linear end blocks are PBnMA. NA: not applicable or not measured. DETAILED DESCRIPTION In general, the present disclosure provides for foldable bottlebrush polymers, methods of making foldable bottlebrush polymers, and the like. Additional details are provided herein and in the Examples. This disclosure is not limited to particular embodiments described, and as such may, of course, vary. The terminology used herein serves the purpose of describing particular embodiments only, and is not intended to be limiting, since the scope of the present disclosure will be limited only by the appended claims. Where a range of values is provided, each intervening value, to the tenth of the unit of the lower limit unless the context clearly dictates otherwise, between the upper and lower limit of that range and any other stated or intervening value in that stated range, is encompassed within the disclosure. The upper and lower limits of these smaller ranges may independently be included in the smaller ranges and are also encompassed within the disclosure, subject to any specifically excluded limit in the stated range. Where the stated range includes one or both of the limits, ranges excluding either or both of those included limits are also included in the disclosure.

[0011] Embodiments of the present disclosure will employ, unless otherwise indicated, techniques of chemistry, polymer chemistry, organic chemistry, and the like, which are within the skill of the art. Such techniques are explained fully in the literature.

[0012] The following examples are put forth so as to provide those of ordinary skill in the art with a complete disclosure and description of how to perform the methods and use the compositions and compounds disclosed and claimed herein. Efforts have been made to ensure accuracy with respect to numbers (e.g., amounts, temperature, etc.), but some errors and deviations should be accounted for. Unless indicated otherwise, parts are parts by weight, temperature is in °C, and pressure is at or near atmospheric. Standard temperature and pressure are defined as 20 °C and 1 atmosphere.

[0013] Before the embodiments of the present disclosure are described in detail, it is to be understood that, unless otherwise indicated, the present disclosure is not limited to particular materials, reagents, reaction materials, manufacturing processes, dimensions, frequency ranges, applications, or the like, as such can vary. It is also to be understood that the terminology used herein is for purposes of describing particular embodiments only, and is not intended to be limiting. It is also possible in the present disclosure that steps can be executed in different sequence, where this is logically possible. It is also possible that the embodiments of the present disclosure can be applied to additional embodiments involving measurements beyond the examples described herein, which are not intended to be limiting. It is furthermore possible that the embodiments of the present disclosure can be combined or integrated with other measurement techniques beyond the examples described herein, which are not intended to be limiting.

[0014] It should be noted that, as used in the specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a support” includes a plurality of supports. In this specification and in the claims that follow, reference will be made to a number of terms that shall be defined to have the following meanings unless a contrary intention is apparent.

[0015] Prior to describing the various embodiments, the following definitions are provided and should be used unless otherwise indicated. Definitions It is understood that “substitution” or “substituted” includes the implicit proviso that such substitution is in accordance with permitted valence of the substituted atom and the substituent, and that the substitution results in a stable compound, i.e., a compound that does not spontaneously undergo transformation such as by rearrangement, cyclization, elimination, etc. It will be understood by those skilled in the art that the moieties substituted can themselves be substituted, if appropriate. For instance, the substituents of a substituted alkyl may include halogen, hydroxy, nitro, thiols, amino, azido, imino, amido, phosphoryl (including phosphonate and phosphinate), sulfonyl (including sulfate, sulfonamido, sulfamoyl and sulfonate), and silyl groups, as well as ethers, alkylthios, carbonyls (including ketones, aldehydes, carboxylates, and esters), -CF3, -CN and the like. Cycloalkyls can be substituted in the same manner. The term "composition" as used herein refers to a product comprising the specified ingredients in the specified amounts, as well as any product which results, directly or indirectly, from combination of the specified ingredients in the specified amounts. “Polymers” are understood to include, but are not limited to, homopolymers, copolymers, such as for example, block, graft, random and alternating copolymers, terpolymers, etc. and blends and modifications thereof. The term "alkyl", as used herein, means a monovalent, saturated hydrocarbon radical which may be a straight chain (i.e. linear) or a branched chain. An alkyl radical for use in the present disclosure generally comprises from about 1 to 20 carbon atoms, particularly from about 1 to 12, 1 to 10, 1 to 8 or 1 to 7, more particularly about 1 to 6 carbon atoms, or 3 to 6. Illustrative alkyl radicals include methyl, ethyl, n-propyl, n-butyl, n-pentyl, n-hexyl, isopropyl, isobutyl, isopentyl, amyl, sec-butyl, tert-butyl, tert-pentyl, n-heptyl, n-actyl, n-nonyl, n-decyl, undecyl, n-dodecyl, n-tetradecyl, pentadecyl, n-hexadecyl, heptadecyl, n-octadecyl, nonadecyl, eicosyl, dosyl, n-tetracosyl, and the like, along with branched variations thereof. In certain aspects of the disclosure an alkyl radical is a C1-C6lower alkyl comprising or selected from the group consisting of methyl, ethyl, n-propyl, n-butyl, n-pentyl, n-hexyl, isopropyl, isobutyl, isopentyl, amyl, tributyl, sec-butyl, tert-butyl, tert-pentyl, and n-hexyl. An alkyl radical may be optionally substituted with substituents as defined herein at positions that do not significantly interfere with the preparation of compounds of the disclosure and do not significantly reduce the efficacy of the compounds. In certain aspects of the disclosure, an alkyl radical is substituted with one to five substituents including halo, lower alkoxy, lower aliphatic, a substituted lower aliphatic, hydroxy, cyano, nitro, thio, amino, keto, aldehyde, ester, amide, substituted amino, carboxyl, sulfonyl, sulfuryl, sulfenyl, sulfate, sulfoxide, substituted carboxyl, halogenated lower alkyl (e.g. CF3), halogenated lower alkoxy, hydroxycarbonyl, lower alkoxycarbonyl, lower alkylcarbonyloxy, lower alkylcarbonylamino, cycloaliphatic, substituted cycloaliphatic, or aryl (e.g., phenylmethyl benzyl)), heteroaryl (e.g., pyridyl), and heterocyclic (e.g., piperidinyl, morpholinyl). Substituents on an alkyl group may themselves be substituted. The term “cycloalkyl” as used herein is a non-aromatic carbon-based ring composed of at least three carbon atoms. Examples of cycloalkyl groups include, but are not limited to, cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl, norbornyl, and the like. The term “heterocycloalkyl” is a type of cycloalkyl group as defined above, and is included within the meaning of the term “cycloalkyl,” where at least one of the carbon atoms of the ring is replaced with a heteroatom such as, but not limited to, nitrogen, oxygen, sulfur, or phosphorus. The cycloalkyl group and heterocycloalkyl group can be substituted or unsubstituted. The cycloalkyl group and heterocycloalkyl group can be substituted with one or more groups including, but not limited to, alkyl, cycloalkyl, alkoxy, amino, ether, halide, hydroxy, nitro, silyl, sulfo-oxo, or thiol as described herein The terms "alkoxyl" or "alkoxyalkyl" as used herein refer to an alkyl-O- group wherein alkyl is as previously described. The term "alkoxyl" as used herein can refer to C1-20inclusive, linear, branched, or cyclic, saturated or unsaturated oxo-hydrocarbon chains, including, for example, methoxyl, ethoxyl, propoxyl, isopropoxyl, butoxyl, t-butoxyl, and pentoxyl. The term “alkenyl” as used herein is a hydrocarbon group of from 2 to 24 carbon atoms or 2 to 8 carbon atoms or 2 to 6 carbon atoms with a structural formula containing at least one carbon-carbon double bond. Asymmetric structures such as (R1R2)C=C(R3R4) are intended to include both the E and Z isomers. This can be presumed in structural formulae herein wherein an asymmetric alkene is present, or it can be explicitly indicated by the bond symbol C=C. The alkenyl group can be substituted with one or more groups including, but not limited to, alkyl, cycloalkyl, alkoxy, alkenyl, cycloalkenyl, alkynyl, cycloalkynyl, aryl, heteroaryl, aldehyde, amino, carboxylic acid, ester, ether, halide, hydroxy, ketone, azide, nitro, silyl, sulfo-oxo, or thiol, as described herein. The term “cycloalkenyl” as used herein is a non-aromatic carbon-based ring composed of at least three carbon atoms and containing at least one carbon-carbon double bound, i.e., C=C. Examples of cycloalkenyl groups include, but are not limited to, cyclopropenyl, cyclobutenyl, cyclopentenyl, cyclopentadienyl, cyclohexenyl, cyclohexadienyl, norbornenyl, and the like. The term “heterocycloalkenyl” is a type of cycloalkenyl group as defined above and is included within the meaning of the term “cycloalkenyl,” where at least one of the carbon atoms of the ring is replaced with a heteroatom such as, but not limited to, nitrogen, oxygen, sulfur, or phosphorus. The cycloalkenyl group and heterocycloalkenyl group can be substituted or unsubstituted. The cycloalkenyl group and heterocycloalkenyl group can be substituted with one or more groups including, but not limited to, alkyl, cycloalkyl, alkoxy, alkenyl, cycloalkenyl, alkynyl, cycloalkynyl, aryl, heteroaryl, aldehyde, amino, carboxylic acid, ester, ether, halide, hydroxy, ketone, azide, nitro, silyl, sulfo-oxo, or thiol as described herein. As used herein, "alkynyl" or “alkynyl group” refers to straight or branched chain hydrocarbon groups having 2 to 40, 2 to 20, 2 to 10, or 2 to 5 carbon atoms and at least one triple carbon to carbon bond, such as ethynyl. Reference to "alkynyl" or “alkynyl group” includes unsubstituted and substituted forms of the hydrocarbon moiety. The Ar (e.g., Ar1, Ar2, etc) group is an aromatic system or group such as an aryl group. “Aryl”, as used herein, refers to C5-C20-membered aromatic, heterocyclic, fused aromatic, fused heterocyclic, biaromatic, or bihetereocyclic ring systems. In an aspect, “aryl”, can include 5-, 6-, 7-, 8-, 9-, and 10-membered single-ring aromatic groups that may include from zero to four heteroatoms, for example, functional groups that correspond to benzene, pyrrole, furan, thiophene, imidazole, oxazole, thiazole, triazole, pyrazole, pyridine, pyrazine, pyridazine and pyrimidine, and the like. Those aryl groups having heteroatoms in the ring structure may also be referred to as “aryl heterocycles” or “heteroaromatics”. The aromatic ring can be substituted at one or more ring positions with one or more substituents including, but not limited to, halogen, azide, alkyl, aralkyl, alkenyl, alkynyl, cycloalkyl, hydroxyl, alkoxyl, amino (or quaternized amino), nitro, sulfhydryl, imino, amido, phosphonate, phosphinate, carbonyl, carboxyl, silyl, ether, alkylthio, sulfonyl, sulfonamido, ketone, aldehyde, ester, heterocyclyl, aromatic or heteroaromatic moieties, -CF3, -CN; and combinations thereof. The term “aryl” also includes polycyclic ring systems (C5-C30) having two or more cyclic rings in which two or more carbons are common to two adjoining rings (i.e., “fused rings”) wherein at least one of the rings is aromatic, e.g., the other cyclic ring or rings can be cycloalkyls, cycloalkenyls, cycloalkynyls, aryls and / or heterocycles. Examples of heterocyclic rings include, but are not limited to, benzimidazolyl, benzofuranyl, benzothiofuranyl, benzothiophenyl, benzoxazolyl, benzoxazolinyl, benzthiazolyl, benztriazolyl, benztetrazolyl, benzisoxazolyl, benzisothiazolyl, benzimidazolinyl, carbazolyl, 4aH carbazolyl, carbolinyl, chromanyl, chromenyl, cinnolinyl, decahydroquinolinyl, 2H,6H- 1,5,2-dithiazinyl, dihydrofuro[2,3 b]tetrahydrofuran, furanyl, furazanyl, imidazolidinyl, imidazolinyl, imidazolyl, 1H-indazolyl, indolenyl, indolinyl, indolizinyl, indolyl, 3H-indolyl, isatinoyl, isobenzofuranyl, isochromanyl, isoindazolyl, isoindolinyl, isoindolyl, isoquinolinyl, isothiazolyl, isoxazolyl, methylenedioxyphenyl, morpholinyl, naphthyridinyl, octahydroisoquinolinyl, oxadiazolyl, 1,2,3-oxadiazolyl, 1,2,4-oxadiazolyl, 1,2,5-oxadiazolyl, 1,3,4-oxadiazolyl, oxazolidinyl, oxazolyl, oxindolyl, pyrimidinyl, phenanthridinyl, phenanthrolinyl, phenazinyl, phenothiazinyl, phenoxathinyl, phenoxazinyl, phthalazinyl, piperazinyl, piperidinyl, piperidonyl, 4-piperidonyl, piperonyl, pteridinyl, purinyl, pyranyl, pyrazinyl, pyrazolidinyl, pyrazolinyl, pyrazolyl, pyridazinyl, pyridooxazole, pyridoimidazole, pyridothiazole, pyridinyl, pyridyl, pyrimidinyl, pyrrolidinyl, pyrrolinyl, 2H-pyrrolyl, pyrrolyl, quinazolinyl, quinolinyl, 4H-quinolizinyl, quinoxalinyl, quinuclidinyl, tetrahydrofuranyl, tetrahydroisoquinolinyl, tetrahydroquinolinyl, tetrazolyl, 6H-1,2,5-thiadiazinyl, 1,2,3- thiadiazolyl, 1,2,4-thiadiazolyl, 1,2,5-thiadiazolyl, 1,3,4-thiadiazolyl, thianthrenyl, thiazolyl, thienyl, thienothiazolyl, thienooxazolyl, thienoimidazolyl, thiophenyl and xanthenyl. One or more of the rings can be substituted as defined above for “aryl”. Discussion The present disclosure provides for foldable bottlebrush polymers, foldable bottlebrush polymer networks and methods of making foldable bottlebrush polymers and foldable bottlebrush polymer networks. Since polymer networks were discovered in the 19thcentury, it has been a dogma that stiffer networks are less stretchable, a trade-off inherent to the molecular nature of polymer network strands. However, the present disclosure provides for foldable bottlebrush polymers that stiff polymer networks and are stretchable (e.g., extensibility). The present disclosure provides for a strategy for decoupling the stiffness and extensibility of single-network elastomers. In an aspect, this can be accomplished using foldable bottlebrush polymers, which feature a collapsed backbone (spacer monomers) grafted with many linear side chains. Upon elongation, the collapsed backbone unfolds to release stored length, enabling remarkable extensibility. By contrast, the network elastic modulus is inversely proportional to the network strand mass and is determined by the side chains. In an aspect, the present disclosure provides for the creation of a series of unentangled single-network elastomers with nearly constant Young’s modulus (about 30 kPa) while increasing tensile breaking strain by 40-fold, from 20% to 800%. This has been shown to apply to polymer networks of different polymer species and topologies. In general, the foldable bottlebrush polymers have spacer monomers and monomers having side chains. The foldable bottlebrush polymers can be crosslinked to form foldable bottlebrush polymers networks. In an aspect, the side chains have a relatively high molecular weight (MW) and relatively low glass transition temperature, whereas the spacer monomers are of low MW and a relatively high glass transition temperature. In addition, the side chains and spacer monomers are highly incompatible (e.g., based on the Flory-Huggins interaction parameter). Additional details are provided herein and in Example 1. Now having described the present disclosure in general, additional details are provided. In an aspect, the present disclosure provides for a composition that includes a foldable bottlebrush polymer and a foldable bottlebrush polymer network. The foldable bottlebrush polymer can be an end-crosslinked foldable bottlebrush polymer or a randomly crosslinked foldable bottlebrush polymer. In an aspect, the foldable bottlebrush polymer network can be solvent free (or stated differently, free of solvent). In another aspect, the foldable bottlebrush polymer network can include a solvent, such water, an organic solvent, and an ionic liquid. The foldable bottlebrush polymer network has the characteristic of being able to reversibly unfold when a stress is applied and fold back to the original foldable bottlebrush polymer or substantially to the foldable bottlebrush polymer network. For example, foldable bottlebrush polymer network has the characteristic of being able to reversibly unfold in about 0.01 - 20 sec, and the polymer network can experience consecutive loading-unloading for more than 500 times with less than 1 % change in stiffness and extensibility.

[0016] In an embodiment, the foldable bottlebrush polymer includes spacer monomer groups and side chains. In an aspect, the side chain can be hydrophilic and the spacer monomer group can be hydrophobic. The side chains are bonded to a portion of the monomer groups. The monomer group are about 5-50% of the foldable bottlebrush polymer and the portion of the monomer with the side chains is about 50% to 95% the foldable bottlebrush polymer. In an aspect, the spacer monomer group and side chains are incompatible as defined by a Flory-Huggins interaction parameter (χ) of about 0.05 or more, 0.1 or more, or about 0.15 or more, about 0.2 or more, about 0.1 to 0.3, about 0.1 to 0.25, or about 0.1 to 0.2, while in the dry state without solvent.

[0017] In an aspect, while in the presence of a solvent such as water, the side chains are highly soluble (e.g., about 100 g / L or more), whereas the spacer monomers have low solubility (e.g., about 10 g / L or less) in water.

[0018] The side chains have a relatively higher (e.g., about 90% or more, about 95% or more, or about 98% or more) molecular weight than the spacer monomer groups so that the molecular weight is substantially (e.g., about 90% or more, about 95% or more, about 98% or more, about 90% to 98% or about 95% to 98%) defined by the side chains. In an aspect, the side chains can have a molecular weight of about 500 to 100,000 g / mol, about 1000 to 100,000 g / mol, about 10,000 to 100,000 g / mol, about 25,000 to 100,000 g / mol, about 500 to 50,000, about 500 to 10,000 g / mol, or about 500 to 1000 g / mol. In an aspect, the spacer monomer can have a molecular weight of about 20 to 500 g / mol or about 40-400 g / mol.

[0019] In an aspect, the side chain can a glass transition temperature (Tg) of about -100°C to 0°C. In an aspect, the spacer monomer group can have a glass transition temperature (Tg) of about 40°C to 300°C.

[0020] In an embodiment of the present disclosure, the side chain can be a linear poly(dimethyl siloxane (PDMS), a linear polyethylene glycol (PEG), or a linear cis- 1 ,4- polyisoprene. The side chain can be bonded to the backbone of the foldable bottlebrush polymer. For example, PDMS can be bonded to an O group for a methacrylate-based monomer (See Fig.2A). In an aspect, the linear PDMS can have a molecular weight of about 500 to 100,000 g / mol, about 1000 to 100,000 g / mol, about 10,000 to 100,000 g / mol, about 25,000 to 100,000 g / mol, about 500 to 50,000, about 500 to 10,000 g / mol, or about 500 to 1000 g / mol. In an aspect, the linear PEG can have a molecular weight of about 500 to 100,000 g / mol, about 1000 to 100,000 g / mol, about 10,000 to 100,000 g / mol, about 25,000 to 100,000 g / mol, about 500 to 50,000, about 500 to 10,000 g / mol, or about 500 to 1000 g / mol. In an aspect, the linear cis-1,4-polyisoprene can have a molecular weight of about 500 to 100,000 g / mol, about 1000 to 100,000 g / mol, about 10,000 to 100,000 g / mol, about 25,000 to 100,000 g / mol, about 500 to 50,000, about 500 to 10,000 g / mol, or about 500 to 1000 g / mol. In an aspect, the spacer monomer group can be a methacrylate-based monomer, an acrylate-based monomer, an acrylamide-based monomers, or a vinyl-based monomer. The acrylate-based monomer can have a molecular weight of about 40 to 400 g / mol. The acrylamide-based monomer can have a molecular weight of about 40 to 400 g / mol. The vinyl-based monomer can have a molecular weight of about 40_ to 400 g / mol. In an aspect, the foldable bottlebrush polymer can have any one of the following structures as part of the polymer: [ ( ) ( ) ] [( )( ) ] ( ) ( ) [ ] ( ) ( ) and [ ] , where each of these can be an end-crosslinked foldable bottlebrush polymer or a randomly crosslinked foldable bottlebrush polymer. In an aspect, R1 can be an alkyl group (linear or branched C1 to C18 hydrocarbon), an aryl group, a phenyl group, a vinyl group, an alkoxyl group, a cycloalkyl group, a cycloalkenyl, group, an alkynyl group, or a heterocyclic group, each of these groups can be substituted or unsubstituted. In an aspect Q can be a linear poly(dimethyl siloxane (PDMS), a linear polyethylene glycol (PEG), or a linear cis-1,4-polyisoprene. In an aspect, rsp is defined as the molar ratio of spacer monomers to side chains. In an aspect, rspcan be about 0.1 to 10 or about 0.5 to 5. In an aspect, nsccan be about 10 to 5000 or about 50 to 1000. In an aspect, the foldable bottlebrush polymer can include a linear PDMS and one or more of a methacrylate-based monomer, an acrylate-based monomer, an acrylamide-based monomers, or a vinyl-based monomer. The tables below provide for various specific combinations. In an aspect, the foldable bottlebrush polymer can include a linear PEG and one or more of a methacrylate-based monomer, an acrylate-based monomer, an acrylamide-based monomers, or a vinyl-based monomer. The tables below provide for various specific combinations.

[0021] In an aspect, the foldable bottlebrush polymer can include a linear cis- 1 ,4- polyisoprene and one or more of a methacrylate-based monomer, an acrylate-based monomer, an acrylamide-based monomers, or a vinyl-based monomer. The tables below provide for various specific combinations.

[0022] In an aspect, the present disclosure provides for various combinations of side chains and spacer monomers. The following tables provide for various combinations as well as for some combinations the Flory-Huggins parameter (χ). The present disclosure provides for methods of making the foldable bottlebrush polymer. Selection of Monomers: Choose appropriate monomers for the side chains and spacer groups. For example, the side chains can have a high molecular weight and low glass transition temperature, while the spacer monomers have a low molecular weight and high glass transition temperature. Examples of monomers that can be selected are provided herein (e.g., the monomers can be determined based on the polymers provided herein). Polymerization: Use controlled polymerization techniques such as atom transfer radical polymerization (ATRP) or reversible addition-fragmentation chain transfer (RAFT) polymerization to graft the side chains onto the backbone. This step ensures uniform grafting and precise control over the molecular architecture of the polymer. Or one can use free radical polymerization if the reaction kinetics of the spacer monomers and side chains can be adjusted to be similar with <15% difference. Formation of Foldable Bottlebrush Structure: Introduce spacer monomers to the polymer backbone. The incompatibility between side chains and spacer monomers leads to the collapse of the backbone into a cylindrical core with side chains densely grafted on the surface. This folded structure allows for the unique mechanical properties of the polymer. Crosslinking: Crosslink the polymer chains to form a network. This can be achieved through chemical crosslinkers or physical methods such as UV irradiation or heat. The crosslinking density is controlled to achieve the desired mechanical properties. Example 1 illustrates methods of making the foldable bottlebrush polymer. While embodiments of the present disclosure are described in connection with the Examples and the corresponding text and figures, there is no intent to limit the disclosure to the embodiments in these descriptions. On the contrary, the intent is to cover all alternatives, modifications, and equivalents included within the spirit and scope of embodiments of the present disclosure. EXAMPLE 1 Stiffness and extensibility are two fundamental mechanical properties of polymer networks. Although these properties seem distinct, they share a common microscopic origin. For an unentangled single-network elastomer, the basic component of all kinds of polymer networks, the stiffness (Young’s modulus E) is about the thermal energy kBT per volume V of a network strand, E≈3kBT / V.1By contrast, the extensibility emax, or tensile strain at break, increases with the network strand size (Fig.1A). Thus, the network stiffness and extensibility are correlated: E∝(emax)-a, where a=2 for a flexible linear network strand, a>2 if the network strand is pre-strained2,3, or a<2 if the network strand is a semiflexible brush-like polymer4(Fig.1B; Supplementary Note 1, eqs. S4, S18, and S28). Nevertheless, a must be positive for single-network elastomers. A widely accepted strategy to mitigate the stiffness-extensibility trade-off is incorporating a weak structure within a strong network; examples include clusters of nanoparticles in filled rubber5,6, reversible bonds in dual-crosslinked polymer networks7–10, and brittle networks in interpenetrating-network hydrogels11–13and elastomers14. When subjected to deformation, the weak structure undergoes fracture to prevent localized, amplified stress near network defects15or along network strands, avoiding premature failure of the strong network16. An alternative strategy to prevent premature network facture is introducing mobile crosslinkers such as entanglements17–19and slide-rings20, which move along network strands to redistribute stress throughout the polymer network. These two strategies, however, do not change the nature of network strands and cannot break the inherent stiffness-extensibility trade-off of single-network elastomers. An emerging strategy to extend a network strand beyond its nominal stretching limit is through mechanochemistry, where mechano-sensitive monomers release stored length upon force-triggered cycloreversion, which converts a cyclic compound to its acyclic constituents21,22. However, this process is irreversible and often results in impaired network mechanical properties. Nevertheless, it represents a fundamental challenge to decouple the stiffness and extensibility of unentangled single-network elastomers. We seek to develop a strategy to split the inherent stiffness-extensibility trade-off of unentangled single-network elastomers. Instead of using linear polymers as network strands, we propose to use our recently discovered hybrid bottlebrush polymers, which consist of many linear side chains randomly separated by small spacer monomers23. The design criteria require that the side chains have a relatively high molecular weight (MW) and a low glass transition temperature (Tg); by contrast, the spacer monomer is low MW and highly incompatible with the side chains (Fig.1C, 1I). Reminiscent of oil droplets in water, the spacer monomers are prone to aggregate to minimize interfacial free energy. However, because of chain connectivity, the spacer monomers cannot form spherical droplets; instead, they collapse into a cylindrical core with its surface densely grafted with side chains (Fig.1C, ii). Yet the folded bottlebrush polymer remains elastic at room temperature (RT) because of its low Tg side chains. Upon elongation, the collapsed backbone unfolds to release the stored length, enabling remarkable network extensibility (Fig.1C, iii). By contrast, the network stiffness, or the MW of this so-called foldable bottlebrush polymer (fBB), is not much affected by the backbone but is determined by the side chains. Thus, we hypothesize that using fBB as network strands enables independent control over polymer stiffness and extensibility. To test this hypothesis, we design a fBB polymer using linear poly(dimethyl siloxane) (PDMS) as the side chain and benzyl methacrylate (BnMA) as the spacer monomer (Fig. 2A). Poly(benzyl methacrylate) (PBnMA) and PDMS are highly incompatible with the Flory- Huggins interaction parameter c≈0.2, and have dramatically different Tgof 54oC and -100oC, respectively24. We fix the degree of polymerization (DP) (Nsc=14) of the PDMS side chain (MW~1000 g / mol) while changing the number of side chains (nsc) and the number ratio between spacers and side chains (rsp) within the bottlebrush polymer. This approach allows us to reduce the four design parameters of fBB polymers, [nsc, rsp, Nsc, c], to two, [nsc, rsp]. We exploit the self-assembly of ABA triblock copolymers25to crosslink the fBB polymers to create networks. We synthesize an fBB polymer23and then grow onto its two ends a high Tglinear polymer (PBnMA)24, forming a linear-fBB-linear triblock copolymer (Fig. 2A). We start with two fBB polymers consisting of nearly the same number of side chains (nsc≈550) but different spacer ratios (rsp=0, 0.84) (Extended Data Table 1, FIG.15). Simultaneously, we fix the DP of a linear end block (Nl≈0.3nsc≈175) to reach a volume fraction of 10% (Supplementary Data Set 1). At RT, the linear blocks aggregate into spherical glassy nodules that crosslink the fBB polymers, as evidenced by the hollow-cone dark-field transmission electron microscopy (TEM) (Fig.2B). This microstructure is further confirmed by small-angle X-ray scattering (SAXS), which reveals a pronounced primary scattering peak, q*, that corresponds to the average inter-domain distance, d=2p / q*(left arrow, Fig.2C; Fig.2D). These results demonstrate the formation of end-crosslinked fBB polymer networks encoded by three molecular architecture parameters [nsc, Nl, rsp] (Fig.2D). As the spacer ratio increases from 0 to 0.84, the network shear storage modulus G’, measured at 1 rad / sec, remains nearly constant at 3 kPa. By contrast, the yield strain increases by more than three-fold from 161% to 515% (Fig.2E). At large deformations, the control network (rsp=0) exhibits strain-stiffening characterized by a rapid increase of G’ with strain (solid circles, Fig.2E). This phenomenon is classical to unentangled polymer networks, attributed to extending the network strand to its stretching limit. Surprisingly, for the network with spacer monomers (rsp=0.84) the strain-stiffening occurs after a remarkable strain-softening regime with a reduction of 14% in shear modulus (left arrow, Fig.2E). This strain-softening diminishes for fBB polymer networks with fewer side chains (nsc<360) (Fig. 5). Nevertheless, it has never been observed in any existing unentangled single-network elastomers. The remarkable strain-softening strongly suggests the strain-triggered unfolding of the collapsed bottlebrush backbone: As the fBB polymer unfolds, it becomes unable to sustain stress efficiently, resulting in reduced network stiffness (Fig.1C). These results indicate the potential of using fBB polymers as network strands to increase network extensibility without altering stiffness. To identify the parameter space ([nsc, Nl, rsp]) within which fBB polymer networks allow for decoupled stiffness and extensibility, we fix the number of side chains (nsc≈200) while increasing the spacer ratio within a wide range (rsp=0 to 3.46) (Extended Data Table 1, Fig.15; Fig.6A, C; Supplementary Data Set 1). Simultaneously, we fix the end block volume fraction relative to the side chains at ~6% (Nl≈33). All polymers self-assemble to end- crosslinked networks, as confirmed by the presence of primary SAXS scattering peaks (Fig. 7A). As the average DP of the spacer segment, Ng=rsp+1, increases from 1 to 4.46, d increases less than twice from ~30 nm to ~50 nm (green circles, Fig.2F). By contrast, the contour length of the fBB polymer Lmax=Ngnscl (l=2.56 Å is the main-chain length of a chemical monomer23), the maximum extent to which the fBB polymer can be stretched, increases by more than four times from ~50 nm to ~220 nm (red squares, Fig.2F). The dramatic difference between the values of d and Lmaxhighlights the ability of fBB polymers to store length as network strands. In the self-assembled polymer networks, however, the glassy nodules are incompatible with the elastic bottlebrush network strands, resulting in interfacial repulsion that generates tension along the bottlebrush backbone2(Supplementary Note 1.2.3). To determine whether the tension unfolds the collapsed bottlebrush backbone, we compare the molecular structure of unperturbed fBB polymers in the melt to that in the self-assembled networks. Using wide-angle X-ray scattering (WAXS), we observe a characteristic peak, qbb, associated with the inter-backbone distance between two neighboring fBB polymers, Dbb=2π / qbb(right arrow, Fig.2C; Fig.7A). As Ngincreases from 1 to 4.46, Dbbmonotonically increases by 60% from 3.54 nm to 5.51 nm (circles, Fig.2G). Notably, in the self-assembled networks, the dependence of Dbbon Ngquantitatively agrees with that observed in the melt (filled squares in Fig.2G). These findings show that the fBB polymers remain folded in the self-assembled networks. We emphasize that the observed increase of Dbbwith Ngcontradicts the understanding of conventional bottlebrush polymer melts (dashed line, Fig.2G; Supplementary Note 1, eq. S10)26–28. However, this discrepancy is well-explained by our recent theory that accounts for the incompatibility between side chains and backbone within a bottlebrush polymer23. The theory predicts that the backbone folds into a cylindrical core, with all grafting sites located on its surface, to minimize the interfacial free energy between the side chains and the bottlebrush backbone (Fig.1C). As the grafting density decreases, the backbone polymer collapses, leading to an increase in the cylindrical core diameter. Simultaneously, the distance between grafting sites in space reduces, enhancing steric repulsion among the side chains that further extends the side chains. Consequently, the bottlebrush diameter increases with the decrease of grafting density (solid lines, Fig.2G; Supplementary Note 2, eq. S39). After confirming that fBB polymers remain folded in the self-assembled networks, we quantify the network mechanical properties using uniaxial tensile tests. The stress-strain curves exhibit three distinct behaviors depending on the spacer ratio. For low spacer ratios (Regime I, 0<rsp<rsp,l≈1.5), the stress-strain curves nearly overlap at low strains, yet the networks with more spacers become more stretchable (Fig.3A, i). Moreover, the tensile fracture strain, ef, is the same as emax, the strain at which the nominal stress is maximum. Quantitatively, the network Young’s moduli E remain nearly the same of ~30 kPa; by contrast, emaxincreases by a remarkable 20-fold from (21±6)% to (428±59)% (light green regions, Figs.3C, D). The Young’s moduli are consistent with network shear moduli, G, following the classic relation E=3G (Fig.8).1Moreover, the dependence of network modulus on the spacer ratio can be well explained by the theoretical prediction for unentangled single-network elastomers (Fig.8E). These results show that using fBB polymers as network strands enables truly decoupled network stiffness and extensibility a=0) (light green region, Fig.3E). Remarkably, for intermediate spacer ratios (Regime II, rsp,l<rsp<rsp,m≈2.3), the networks are extremely stretchable with efup to ~2800% (grey line, Fig.3A, ii). Yet, these networks exhibit plastic deformation above a critical strain (emax~900%) with the nominal stress decreasing dramatically with strain (Fig.3A, ii). This plastic deformation is likely because of pulling the linear block out from the glassy nodules, which occurs for relatively weak ones. Consistent with this understanding, the plastic deformation disappears if glassy nodules become strong (Fig.9) or the crosslinkers are permanent covalent bonds (Fig.13). At high spacer ratios (Regime III, rsp>rsp,m), there is no plastic deformation and ef=emax. (Fig. 3A, iii). Thus, we use emaxto describe the extensibility attributed to fBB polymer network strands (arrow, Fig.3A, ii). Plotting E against emaxreveals two distinct correlations at relatively high spacer ratios (rsp>rsp,l). There exists a small window (rsp,l<rsp<rsp,m) in which stiffer networks are more stretchable (a<0) (light red region, Fig.3E). This behavior highlights the potential of exploiting fBB polymers to simultaneously enhance network stiffness and extensibility, a capability inaccessible by conventional single-network elastomers. At high spacer ratios (rsp>rsp,m), the networks resume the classical stiffness-extensibility trade-off (a>0) yet remain quite stretchable (emax>400%) (light grey region, Fig.3E). Notably, the network stiffness increases exponentially with the spacer ratio (red dashed line, Fig.3D). This polymer stiffening is caused by elevated Tg of fBB polymers, such that the fBB polymers themselves become viscoelastic solids (Fig.10A-F). Indeed, at RT, the shear modulus of fBB polymers with high spacer ratios dominates the elastic contribution of fBB polymers as network strands and increases exponentially with the spacer ratio (Fig.10G). These results highlight the importance of keeping fBB polymers elastic (of low Tg) to increase network extensibility without altering stiffness. Despite macroscopic evidence from the remarkable strain-softening (Fig.2E) and truly decoupled network stiffness and extensibility (light green region, Fig.3E), it has yet to be microscopically validated the unfolding of a collapsed bottlebrush backbone upon elongation (Fig.1C). We perform in situ SAXS / WAXS measurements on a network undergoing uniaxial extension (Fig.4A). We choose the network with a relatively high spacer ratio (rsp=2.9), so that the inter-backbone distance (Dbb=5.39 nm) is 50% greater than that of the control network (Fig.4B). Along the stretching direction, the inter-domain distance increases linearly with strain (Fig.4C, D), yet the inter-backbone distance remains constant (Fig.11C). Remarkably, perpendicular to the stretching direction, the inter-backbone distance decreases with strain (Fig.4E, F). These contrasting behaviors originate from two distinct phenomena that resulted from unfolding the collapsed bottlebrush backbone. First, along the stretching direction, the network strand unfolds, resulting in an increased inter-domain distance (Fig.12A, B) and more aligned bottlebrush backbone (Fig.12C). Second, the unfolding process reduces the diameter of the cylindrical core of the collapsed bottlebrush backbone. Simultaneously, it decreases the grafting distance of side chains in space, such that the side chains become less crowded and their size decreases (Fig.12Dd). Consequently, as the strain increases, perpendicular to the stretching direction, not only the value of inter-backbone spacing decreases but also its orientation is more ordered, as evidenced by the enhanced orientation factor (Fig.4G, Fig.7A, B). Collectively, our results show that a collapsed bottlebrush backbone unfolds upon extension. Finally, we examine the universality of our design strategy by using another spacer monomer methyl methacrylate (MMA). MMA fulfills the design criteria as it has a low MW (100 g / mol) and is highly incompatible with PDMS29. We synthesize a series of fBB polymer networks with a wide range of MMA spacer ratios, [~200, ~60, 0-3.62] (Extended Data Table 1, Fig.15; Fig.2B, C; Supplementary Data Set 2). We observe similar behavior from the network microstructure (Fig.7B) to the mechanical properties (Fig.3B; blue squares, Fig. 3C, D; Figs.4, 6). Moreover, for both MMA and BnMA spacers, E versus emaxcollapses to a universal relation, where emaxcan be increased by nearly 40-fold, from ~20% to ~800% while keeping E constant of ~30 kPa (a=0) (light green region, Fig.3E). In summary, we have discovered that employing fBB polymers as network strands offers a general strategy to decouple the inherent stiffness-extensibility tradeoff of single- network elastomers. The unfolding of a fBB polymer is a reversible physical process, reminiscent of unzipping titin protein in muscle30. Importantly, our design approach is not limited to network topology; it applies to both end-crosslinked (Fig.3) and randomly crosslinked single-network elastomers (Fig.13). Moreover, the extensibility of fBB polymer networks is significantly larger than that of conventional bottlebrush polymer networks2–4,28,31(Fig.14; Supplementary Table S1). Given that single-network polymers are the fundamental component of all kinds of networks, the universality of our design strategy and the resulting extremely stretchable polymer networks, our discovery opens an avenue for the development of polymer networks with extraordinary mechanical properties. Methods 1. Materials. Monomethacryloxypropyl-terminated poly(dimethyl siloxane) (MCR-M11, MW~1000 g / mol) and methacryloxypropyl terminated poly(dimethyl siloxane) (DMS-R18, MW~5000 g / mol) are purchased from Gelest and purified using basic alumina columns to remove inhibitors. Benzyl methacrylate (BnMA, 98%) and methyl methacrylate (MMA, 98%) are purchased from Sigma Aldrich and purified using basic alumina columns to remove inhibitors. Copper (II) chloride (CuCl2, 99.999%), tris[2-(dimethylamino)ethyl]amine (Me6TREN), ethylene bis(2-bromoisobutyrate (2f-BiB, 97%), Tin(II) 2-ethylhexanoate (Sn(EH)2, 92.5–100%), anisole (≥99.7%) and p-xylene (≥99.7%) are purchased from Sigma Aldrich and used as received. Tetrahydrofuran (THF, analytical reagent (AR)), purchased from Macron Fine Chemicals, and THF (High-performance liquid chromatography (HPLC) grade), methanol (Certified ACS), dichloromethane (DCM, Certified ACS), dimethylformamide (DMF, Certified ACS), purchased from Fisher, are used as received. 2. Polymer synthesis and characterization. In a fBB polymer, the side chains are randomly separated by spacer monomers. However, the side chains and the spacer monomers have different reactivity unless in a well-controlled condition. To this end, we use our previously established methods23,31,32to synthesize end-crosslinked and randomly crosslinked fBB polymer networks. 2.1 End-crosslinked fBB polymer networks. We present a detailed synthesis procedure using a sample with BnMA as the spacer ([195, 40, 1.08]) as an illustrative example. Step I. Synthesis of a fBB middle block. A 50 mL Schlenk flask is charged with ethylene bis(2-bromoisobutyrate) (2f-BiB, 4.3 mg, 0.012 mmol), MCR-M11 (6g, 6 mmol), BnMA (705 mg, 4mmol), p-xylene (4 mL) and anisole (4 mL). Me6TREN (46 mg, 0.2 mmol) and CuCl2(4.5 mg, 0.02 mmol) are dissolved in 1 mL DMF to prepare a catalyst solution. Then, 30 µL catalyst solution is added to the mixture. Followed by a 60-minute bubbling of the mixture with nitrogen, Sn(EH)2(14.6 mg, 0.036 mmol) in 100 µL p-xylene is quickly added into the reaction mixture while bubbling. The flask is then sealed with a rubber stopper and immersed in an oil bath at 60 °C. The reaction is monitored by proton nuclear magnetic resonance spectroscopy (1H NMR) and stopped at 39% conversion. The reaction mixture is diluted with THF and passed through a neutral alumina column to remove the catalyst. The collected solution is concentrated using a rotary evaporator (Buchi R-205). To remove unreacted monomers and other impurities, the concentrated polymer solution is precipitated in methanol three times. After purification, the number of BnMA spacers is determined using1H NMR, which is 211 for this fBB polymer. Additionally, the polymer contains 195 PDMS side chains, corresponding to a spacer / side chain ratio of rsp=1.08. Step II. Synthesis of a linear-fBB-linear triblock copolymer. A 25 mL Schlenk flask is charged with BnMA (282 mg, 1.6 mmol), macroinitiator (fBB PDMS, 232 kg / mol, 470 mg, 2 × 10–3mmol), p-xylene (1.3 mL), and anisole (1.3 mL). Me6TREN (46 mg, 0.2 mmol) and CuCl2(2.7 mg, 0.02 mmol) are dissolved in 1 mL of DMF to prepare a catalyst solution. Then, 85 μL of the catalyst solution containing 1.7 × 10–2mmol Me6TREN and 1.7 × 10–3mmol CuCl2is added to the mixture, and the resulting mixture is bubbled with nitrogen for 45 min to remove oxygen. Subsequently, the reducing agent, Sn(EH)2(27.5 mg, 6.8 × 10–2mmol) in 200 μL of p-xylene, is quickly added to the reaction mixture using a glass syringe. The flask is sealed and immersed in an oil bath at 60 °C. We stop the reaction at 10% conversion, purify the polymers following the same procedure as that in Step I, and use1H NMR to confirm the DP of BnMA is 40 per end block. Finally, the sample is dried in a vacuum oven (Thermo Fisher, Model 6258) at RT for 24 hours. The polymer is a transparent solid at RT. 2.2. Randomly crosslinked fBB polymer networks. These networks are synthesized following the procedure in Step I (Methods, Section 2.1) with the only difference that a di-functional crosslinking chain (DMS-R18) is added to the reaction mixture at a molar ratio 1:100 to the side chains (Fig.13A, B). Thus, the average number of side chains per network strand is nsc=100. For each network, we use a co-solvent, DMF and THF with a volume ratio of 1:1, to remove unreacted monomers and catalyst, and then use THF to wash the network three times to remove DMF. The polymer networks are dried in a vacuum oven at RT overnight before being subjected to mechanical measurements. 3.1H NMR characterization. We use1H NMR to determine the average number of side chains per bottlebrush, the average number of spacer monomers, and the DP of each end block in a triblock copolymer polymer. The first one is calculated based on the conversion of linear PDMS macromonomers to bottlebrush PDMS. The number of spacer monomers is determined based on the NMR spectra of a purified bottlebrush polymer. The DP of each end block is determined based on the NMR spectra of purified triblock polymers. Chemical shifts for1H NMR spectra are reported in parts per million compared to a singlet at 7.26 ppm in CDCl3. 4. Gel permeation chromatography (GPC). GPC measurements are conducted using the TOSOH EcoSEC HLC-8320 GPC system equipped with two TOSOH Bioscience TSKgel GMHHR-M 5 µm columns in series. The GPC system includes a refractive index detector and operates at a temperature of 40 °C. HPLC grade THF is used as the eluent, and it is delivered at a flow rate of 1 mL / min. The samples for analysis are prepared by dissolving them in THF at a concentration of approximately 5 mg / mL. 5. SAXS / WAXS measurements. To prepare a sample for SAXS / WAXS characterization, we dissolve a triblock copolymer in toluene at a concentration of 100 mg / mL with a total volume of 3 mL in a glass vial and allow the solvent to slowly evaporate for 24 hours. Because toluene is a solvent close to being equally good for PBnMA and PDMS, it avoids the effects of solvent selectivity on the self-assembly process. Subsequently, we subject the sample to thermal annealing in a vacuum oven for 6 hours at 180 °C. Following the thermal annealing step, we slowly cool down the sample to RT at a rate of 0.5 °C / min. Throughout this cooling process, the microstructure of the self-assembled polymers does not change. We use the Soft Matter Interfaces (12-ID) beamline at the Brookhaven National Laboratory to conduct SAXS / WAXS measurements on fBB polymers and networks. We perform measurements at multiple locations, thereby ensuring the consistency of the acquired two-dimensional (2D) scattering patterns. The distance between the sample and the detector is 8.3 meters, and the radiation wavelength used is The scattered X- rays are captured using an in-vacuum Pilatus 1M detector, which consists of an array of 0.172 mm square pixels in a 941x1043 configuration. The raw SAXS images are converted into q-space, visualized in Xi-CAM software, and then radially integrated using customized Python code. The resulting one-dimensional intensity profile, denoted as is plotted as a function of the scattering wave vector, where represents the scattering angle. We perform in situ tensile tests using a Linkam TST-350 tensile stage equipped with a 2.5 N load cell. The Linkam stage is positioned in front of the X-ray beam with a horizontal orientation relative to the X-ray detector. To prepare the sample, we cut an annealed polymer into a rectangular shape with typical dimensions of 5-8 mm in length, 2-4 mm in width, and 0.5-1.0 mm in thickness. We load the sample to the Linkham tensile stage and stretch the elastomer at a strain rate of 0.01 / sec while using SAXS / WAXS to characterize the microstructure of the network. Because long-time exposure to X-ray may damage the elastomer, we limit the number of SAXS / WAXS measurements to 10 during target tensile strain. For each sample, data acquisition is conducted at a rate of one point per 35 seconds. Additionally, throughout the experiment, the beamline is maintained consistently passing through the central region of the sample. SAXS and WAXS patterns are recorded with a Pilatus 1M detector and a Pilatus 9K, respectively, with a pixel size of 0.172 mm. The distance between the sample and the WAXS detector is 2.5 meters, and the radiation wavelength used is In WAXS, the characteristic scattering peak corresponds to the inter-backbone distance of fBB polymers. The orientation of inter-backbone spacing, not the bottlebrush backbone, is determined from the azimuthal spread of the peak intensity from a 2D WAXS pattern: Here, ^^ is the azimuthal angle and ^^^ ^^^ is the intensity for the characteristic peak, as outlined by the region between two dashed circles in Fig.11A. The Herman’s orientation parameter S is defined as: The value of S is 0 if the inter-backbone spacing exhibits no preferred direction, 1 when aligned parallel to the stretching direction, and -0.5 when aligned perpendicular to the stretching direction. Note that WAXS does not measure the alignment of the bottlebrush backbone but the inter-backbone spacing. Thus, when the bottlebrush backbones are more aligned on the stretching direction, the orientation of inter-backbone spacing is more ordered perpendicular to the stretching direction, resulting in the decrease of S. Consistent with this understanding, as the tensile strain increases from 0 to ~6, the value of S decreases from 0 to ~-0.1 (Fig.4G). 6. Transmission electron microscopy (TEM). We use our previously established method to prepare the samples for TEM imaging24,33. We use hollow-cone dark-field TEM (FEI Titan 80-300) at the electron energy of 300 keV with a tilt angle of 0.805º to characterize the annealed samples. This tilt angle allows for sharp contrast between PDMS and PBnMA domains without staining. The size of spherical domains is calculated using ImageJ, and >200 domains are used to ensure sufficiently powered statistics. 7. Rheological characterization. Rheological measurements are performed using a stress- controlled rheometer (Anton Paar MCR 302) with a plate-plate geometry of 8 mm in diameter. We exploit the solvent reprocessability of our polymers to prepare samples in situ. Specifically, we dissolve a polymer in DCM at a volume ratio of 1:2 to make a homogenous mixture. Approximately 1 mL of the solution is pipetted onto the bottom plate of the rheometer and allowed to dry in ambient air at RT for one hour. Subsequently, the bottom plate is heated to 40 °C for 20 minutes. These procedures allow us to prepare a relatively thick film, ~0.3 mm, without the occurrence of cavities resulting from solvent evaporation. Then, we lower the upper plate and trim the excess sample at the edge of the geometry. For frequency sweep, we fix the temperature at 20 °C and the oscillatory shear strain at 0.5% while varying the shear frequency from 0.1 rad / sec to 100 rad / sec. For strain sweep, we fix the temperature at 20 °C and the oscillatory shear frequency at 1 rad / sec while increasing the shear strain from 1% to 1000%. For the temperature sweep, we fix the oscillatory frequency at 1 rad / s and the shear strain at 5% while increasing the temperature from –20 °C to 80 °C, well above the Tg=54 °C of PBnMA34. As detailed in our previous work32, we use a slow temperature ramping rate, 1 °C / minute, and wait for 20 minutes at each temperature point before collecting data; this ensures that the self-assembled microstructure is in equilibrium at each temperature point. 8. Tensile test. We prepare the self-assembled fBB polymer networks using a Teflon model described above (Methods, Section 5). We use a normalized cutter to cut the elastomers into dumbbell-shaped samples, which have a central part of 13 mm in length, 3 mm in width, and 0.5-1.0 mm in thickness. To load a sample, we use epoxy to glue the two ends of a sample to a hard cardboard, which is clamped to a tensile grip to avoid possible damage to the elastomers. For uniaxial tensile test, use a Mark-10 ESM303 Motorized Test Stand equipped with a 2.5 N load cell or an Instron (6800-SC) equipped with a 10 N load cell. Nominal stress is defined as the tensile force per unit of the initial cross-section area of the central part. During the tensile test, we use a camera to record the strain by tracking the displacement of the central part of a dumbbell-shaped sample. Each measurement is performed at RT at a strain rate of 0.02 / sec and repeated at least three times on parallel samples. 9. Differential scanning calorimetry. We determine the Tgof fBB polymers using a differential scanning calorimeter (DSC Q20, TA instruments). All the samples are prepared using a combination of solvent and thermal annealing (Methods, Section 5) to ensure equilibrated state. Before characterization, the samples are further dried at RT (~293 K) under vacuum (30 mbar) for at least 24 hours. A standard aluminum DSC pan is used for all the measurements with approximately 10 mg of sample loaded. All the samples were annealed at 393K for 2 min to erase the thermal history, followed by cooling at 10 K / min to 213 K and then heating at 10 K / min to 393 K. 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Inherent stiffness-extensibility trade-off of conventional unentangled single-network elastomers For an unentangled single-network elastomer, the stiffness is about per volume of a network strand: Here, is the network shear modulus, which is 1 / 3 of the network bulk modulus (Young’s modulus The network extensibility, or tensile strain at break is determined by the network strand size, where are the contour length and unperturbed end-to-end distance of the network strand, respectively. The relations for network stiffness [eq. (S1)] and extensibility [eq. (S2)] apply to unentangled single-network elastomers regardless of the type of network strands. The correlation between network stiffness and extensibility follows a power law relation: For conventional single-network elastomers, must be positive. However, the value of depends on the type of network strands. Below we derive the value of for network strands made of classical flexible linear polymers and emerging bottlebrush polymers. 1.1. Flexible linear polymers For a network strand made of a flexible linear polymer with Kuhn monomers of size Substituting these relations to eqs. (S1) and (S2) and considering one obtains the stiffness-extensibility relation: flexible linear network strand (S4) 1.2. Conventional bottlebrush polymers A bottlebrush polymer consists of a long, linear backbone grafted with many relatively short linear side chains. The degree of polymerization (DP) of the side chain is and the average DP of the backbone section between two neighboring grafting points is The number of side chains per bottlebrush polymer, is much larger than the DP of the side chain, such that the effects of extra space near the two ends of a grafted polymer on the polymer conformation can be ignored. We use respectively, to denote the length of a main-chain bond and the volume of a chemical monomers. Throughout the theory, we denote the side chains and the bottlebrush backbone with ‘sc’ and ‘bb’ as subscripts or superscripts, respectively. Additionally, we provide simplified expressions that disregard the difference in polymer physics parameters between the side chains and the bottlebrush backbone polymer. This simplification aids in distilling the essential physical pictures for the bottlebrush polymers. In a conventional bottlebrush polymer, the side chains and the backbone are assumed to be compatible. An example is a poly(dimethyl siloxane) (PDMS) bottlebrush in which the bottlebrush backbone and the side chains are both linear PDMS1. The molecular structure of a conventional bottlebrush polymer is largely determined by how to pack the densely grafted side chains into the limited space surrounding the bottlebrush backbone. In brief, at relatively low grafting density when the side chains are far apart from each other, the side chain adopts an unperturbed Gaussian conformation. The mean-square end-to-end distance of an unperturbed side chain is: As the grafting density (1 / ^^^) increases, the side chains from the same bottlebrush polymer can overlap. Yet, they will not completely fill the volume pervaded by one side chain of unperturbed size, until a crossover grafting density, 1 / ^^∗: ^ Here, ^^ is the number of monomers in a backbone section passing through the pervaded volume, and corresponds to the number of side chains within At the side chains are not crowded and there is no steric repulsion among the side chains. Thus, the backbone polymer is not extended and adopts an unperturbed Gaussian conformation. Because the size of the backbone section with ^^ monomers is about that of the side chain, eq. (S6) can be rewritten as: As the grafting density further increases the space near the bottlebrush backbone is not enough to accommodate all the side chains from the same bottlebrush polymer if the backbone remains an unperturbed Gaussian conformation. To avoid the crowding of side chains, the backbone polymer must extend. This process ensures a constant distance in space between two neighboring grafting sites. In doing so, the side chains remain an unperturbed Gaussian conformation of size [eq. (S5)]. By contrast, the backbone polymer continues to extend as the grafting density increases. However, the extension of the backbone cannot continue forever; instead, it will stop at certain grafting density at which the spacer segment between two neighboring grafting sites is stretched to its maximum contour length. At very high grafting density there is no other way for the side chains to avoid crowding except by radially extending away from the backbone polymer. The side chain size ^^^^is determined by volume conservation: a side chain of volume fills the cylindrical space surrounding the backbone polymer: This gives: for a densely grafted bottlebrush And is the crossover grafting density above which the side chains start to extend: Assuming the backbone and the side chains are compatible with the Flory Huggins parameter the value of for PDMS bottlebrush polymers with 1000 g / mol side chains and a methacrylate-based backbone is approximately 1.5.21.2.1. Inter-backbone distance In the melt, a bottlebrush molecule is effectively a ‘fat’ linear polymer with a cross-section about twice the side chain size. The diameter of a bottlebrush polymer approximately equals the inter-backbone distance ^^^^between neighboring bottlebrush polymers: Thus, for the melt of conventional bottlebrush polymers, decreases with decrease of grafting density by a power of 1 / 2 (black dashed line, Fig.2G). This understanding has been pointed out in pioneering experimental works1,3, confirmed by simulations4, and detailed in a seminal work by Rubinstein Lab5. 1.2.2. Unperturbed bottlebrush network strands The network stiffness is inversely proportional to the volume of a network strand. The contribution to the volume of the bottlebrush polymer is predominately from the side chains, and therefore: where the molar mass of a side chain is much larger than that of backbone or spacer monomers is the density of the polymer, and is the Avogadro number. As a result, the number of side chains per bottlebrush polymer is related to the network shear modulus by: To understand the network extensibility, one needs to determine the relation between the size and the molecular architecture parameters of a bottlebrush network strand. The contour length of the bottlebrush backbone is: The bottlebrush polymer is effectively a ‘fat’ semiflexible polymer, the end-to-end distance of which can be determined using the worm-like-chain model6: in which ^^^^ ^^^^is the persistence length of the bottlebrush polymer. The end-to-end distance of the bottlebrush polymer can be simplified into two cases depending on flexibility of a bottlebrush, which is defined as7: For a relatively stiff bottlebrush with ^^ ^ 1, eq. (S13) can be approximated as: For a flexible bottlebrush with ^^ ≫ 1, eq. (S13) can be approximated as: Thus, the network extensibility [eq. (S2)]: Recalling the network stiffness [eq. (S11)], the stiffness-extensibility tradeoff of conventional bottlebrush polymer networks is: These relationships were demonstrated both experimentally and theoretically in our previous work8. 1.2.3. Pre-strained bottlebrush network strands In a network self-assembled by linear-bottlebrush-linear (LBBL) triblock copolymers, the bottlebrush backbone is pre-strained to balance interfacial repulsion between incompatible bottlebrush and end block domains. To understand the stiffness-extensibility trade-off of networks with pre-strained bottlebrush polymer network strands, we consider a sphere microstructure self-assembled by a LBBL triblock copolymer. The volume fraction of end blocks is the radius of a spherical domain is and the distance between the centers of two neighboring spherical domains is The interfacial free energy density is the product of interfacial tension and the interfacial area per unit volume, Here, the interfacial area per unit volume is the product of the number density of spherical domains, and the surface area of a spherical domain, Considering that the density of different blocks is nearly the same, the domain radius and distance is related by the volume fraction, Thus, the interfacial free energy density can be rewritten as: which increases linearly with ^^ but is inverse to the radius of the spherical domain. The entropic free energy is associated with stretching the bottlebrush backbone. For a semiflexible bottlebrush polymer at unperturbed state the bottlebrush backbone is already stretched close to its contour length. As a result, the corresponding bottlebrush polymer networks are very brittle with low fracture strain. Therefore, we consider a flexible bottlebrush whose entropic free energy obeys the same form as Gaussian coil. The end-to-end distance of the bottlebrush polymer is: The entropic free energy associated with stretching one bottlebrush polymer is: The volume of a bottlebrush polymer is [eq. (S16)], where is the packing length of the bottlebrush polymer. Thus, the entropic free energy density due to the stretching of the bottlebrush backbone is: Using eqs. (S20) and (S23), the density of total free energy is: Minimizing the density of total free energy by setting gives the radius of the spherical domain in equilibrium: where is related to the interfacial thickness and has the scale of a monomer length. The effective Kuhn monomer of a bottlebrush is nearly spherical, such that the packing length is comparable to the persistence length Thus, the equilibrium size of the bottlebrush polymer in the self-assembled network is: The above scaling theory was documented in our previous work9. A similar scaling theory was also documented in the supplementary information of a previous publication10. Recalling the definition of ^^ [eq. (S14)], the network extensibility can be rewritten as: Recalling that the network shear modulus is inversely proportional to the number side chains per bottlebrush polymer [eq. (S11)], one obtains the stiffness-extensibility relation for conventional bottlebrush polymer networks self-assembled by LBBL triblock polymers: pre-strained conventional bottlebrush network strand (S28) Supplementary Note 2. Inter-backbone distance of foldable bottlebrush polymers in melts The theory for the inter-backbone distance of foldable bottlebrush polymers in melts has been documented in our previous publication2. Here, we briefly review the theory and describe essential physical pictures associated with foldable bottlebrush polymers. We consider the strongly segregated case characterized by sharp interface between distinct domains. To achieve this, it is necessary for all the grafting sites to reside on the surface rather than the interior of the cylindrical core formed by the folded backbone polymer. To determine the diameter of the bottlebrush polymer, we consider the free energy associated with its folded structure. The steric repulsion among the strongly overlapping side chains tends to elongate the cylindrical core. Conversely, the backbone polymer tends to collapse into a cylinder of a larger diameter to minimize the interfacial area between the side chains and the backbone polymer (Fig.1C). Thus, the total free energy of a bottlebrush polymer can be expressed as: Here, represents the interfacial free energy between the incompatible backbone and side chains. correspond to the entropic free energies resulting from the stretching of the side chains and the backbone polymer, respectively. However, even in a densely grafted conventional bottlebrush polymer, the stretching of the bottlebrush backbone is comparable to that of one side chain, as detailed in our previous publication2and by others5. Moreover, there are many side chains in each bottlebrush polymer. Thus, compared to ^^^^, ^^^^is much smaller and can be neglected. The interfacial free energy between the side chains and the bottlebrush backbone is: Here, is the total surface area of the cylindrical core, and is the interfacial free energy per contact area ^^^of a Kuhn segment. The length ^^^of the cylinder is given by the volume conservation of the backbone polymer: Thus, eq. (S30) can be re-written as: To calculate the entropic free energy of side chains, we consider a section of the cylindrical core with the length of ^^^^. The number of side chains grafted to this cylindrical section is in which is the volume of the section of the cylindrical core, and ^^ ^^ is the volume of backbone section between two neighboring grafting sites. Surrounding the cylindrical core, these side chains fill the space with a volume of Assuming that the side chain size is much larger than the diameter of the cylindrical core, the effects of cylindrical core on the volume available to the side chains can be neglected: Re-writing eq. (S32) gives the side chain size: The entropic free energy due to the stretching of side chains of the bottlebrush polymer is: Using eqs. (S29), (S31), and (S35), one obtains the total free energy of the bottlebrush polymer: Minimizing the total free energy gives the equilibrium cross-section size of the cylindrical core: ^ in which is a length scale determined by the Flory-Huggins interaction parameter Substituting eq. (S37) into eq. (S34) gives the equilibrium size of the side chain: భ Here, is the number of chemical monomers per Kuhn segment of the bottlebrush backbone. Consequently, the inter-backbone distance becomes [eqs. (S37) and (S38)]: Note that our theory is based on the minimization of free energy for individual foldable bottlebrush polymers, which requires that the polymers are in a thermodynamic equilibrium. This would not be an issue for foldable bottlebrush polymers with relatively low spacer ratios at which the glass transition temperature of the foldable bottlebrush polymers is below room temperature (RT) (Fig.10). At relatively high spacer ratios the of the foldable bottlebrush polymers is higher than RT, such that the conformation of a foldable bottlebrush polymer may be trapped in a metastable state at RT. To this end, we use a combination of solvent and thermal annealing to prepare both foldable bottlebrush polymer melts and networks to ensure that they are in an equilibrated state. Our theory [eq. (S39)] predicts that the inter-backbone distance increases with the decrease of grafting density At very high grafting density (small or with long side chains (large the scales with by a power of 1 / 6: However, the window for this regime is very small, because the diameter of the cylindrical core becomes noticeable at relatively large this makes the approximation in eq. (S33) inappropriate. Nevertheless, is expected to increase with but with an exponent intermediate between 1 / 6 and 2 / 3. These predications were verified by experiments in our previous work for the melt of foldable bottlebrush polymers (filled squares, Fig.2G)2. Supplementary Tables Table S1. Mechanical properties of conventional bottlebrush polymer networks.

[0040] Supplementary References

[0041] 1. Cai, L.-H. et al. Soft Poly(dimethylsiloxane) elastomers from architecture-driven entanglement free design. Adv Mater 27, 5132-5140 (2015).

[0042] 2. Nian, S., Huang, B., Freychet, G., Zhernenkov, M. & Cai, L.-H. H. Unexpected folding of bottlebrush polymers in melts. Macromolecules 56, 2551-2559 (2023).

[0043] 3. Daniel, W. F. M. M. et al. Solvent-free, supersoft and superelastic bottlebrush melts and networks. Nat Mater 15, 183-189 (2016). 4. Sarapas, J. M., Martin, T. B., Chremos, A., Douglas, J. F. & Beers, K. L. Bottlebrush polymers in the melt and polyelectrolytes in solution share common structural features. Proc Natl Acad Sei USA 117, 5168-5175 (2020). 5. Paturej, J. J., Sheiko, S. S., Panyukov, S. & Rubinstein, M. Molecular structure of bottlebrush polymers in melts. Sci Adv 2, e1601478 (2016).

[0044] 6. Rubinstein, M. & Colby, R. H. Polymer Physics. (Oxford University Press, 2003).

[0045] 7. Nian, S. et al. Self-assembly of flexible linear-semiflexible bottlebrush-flexible linear triblock copolymers. Macromolecules 54, 9361-9371 (2021).

[0046] 8. Cai, L. H. Molecular understanding for large deformations of soft bottlebrush polymer networks. Soft Matter 16, 6259-6264 (2020).

[0047] 9. Nian, S. et al. Molecular architecture directs linear-bottlebrush-linear triblock copolymers to self-assemble to soft reprocessable elastomers. ACS Macro Lett 8, 1528-1534 (2019).

[0048] 10. Vatankhah-Varnosfaderani, M. et al. Mimicking biological stress-strain behaviour with synthetic elastomers. Nature 549, 497-501 (2017).

[0049] 11 . Vatankhah-Varnosfaderani, M. et al. Chameleon-like elastomers with molecularly encoded strain-adaptive stiffening and coloration. Science 359, 1509-1513 (2018).

[0050] 12. Nian, S. et al. Three-dimensional printable, extremely soft, stretchable, and reversible elastomers from molecular architecture-directed assembly. Chem Mater 33, 2436- 2445 (2021).

[0051] 13. Keith, A. N. et al. Bottlebrush bridge between soft gels and firm tissues. ACS Cent Sci 6, 413-419 (2020).

[0052] 14. Dobrynin, A. V. et al. Forensics of polymer networks. Nat Mater 22, 1394-1400 (2023).

[0053] 15. Self, J. L. et al. Dynamic bottlebrush polymer networks: Self-healing in super-soft materials. J Am Chem Soc 142, 7567-7573 (2020).

[0054] 16. Yu, X. et al. Self-healable, stretchable, and super-soft bottlebrush polyester elastomers for highly sensitive flexible sensors. ACS Appl Polym Mater 5, 2750-2759 (2023).

[0055] 17. Maw, M. et al. Brush architecture and network elasticity: Path to the design of mechanically diverse elastomers. Macromolecules 55, 2940-2951 (2022).

[0056] It should be noted that ratios, concentrations, amounts, and other numerical data may be expressed herein in a range format. It is to be understood that such a range format is used for convenience and brevity, and thus, should be interpreted in a flexible manner to include not only the numerical values explicitly recited as the limits of the range, but also to include all the individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly recited. To illustrate, a concentration range of “about 0.1 percent to about 5 percent” should be interpreted to include not only the explicitly recited concentration of about 0.1 weight percent to about 5 weight percent but also include individual concentrations (e.g., 1 percent, 2 percent, 3 percent, and 4 percent) and the sub-ranges (e.g., 0.5 percent, 1.1 percent, 2.2 percent, 3.3 percent, and 4.4 percent) within the indicated range. The term “about” can include traditional rounding according to significant figures of the numerical value. In addition, the phrase “about ‘x’ to ‘y’” includes “about ‘x’ to about ‘y’”. Many variations and modifications may be made to the above-described aspects. All such modifications and variations are intended to be included herein within the scope of this disclosure and protected by the following claims.

Claims

CLAIMSWhat is claimed:

1. A composition, comprising: a foldable bottlebrush polymer having spacer monomer groups and side chains, wherein the side chains are bonded to a portion of the monomer groups, wherein the monomer group are about 5 to 50% of the foldable bottlebrush polymer, wherein the portion of the monomer with the side chains is about 50 to 95% of the foldable bottlebrush polymer, wherein the spacer monomer groups and side chains are incompatible as defined by a Flory- Huggins interaction parameter (χ) of about 0.05 or more while in the dry state without solvent.

2. The composition of claim 1 , wherein the side chains have a relatively higher molecular weight than the spacer monomer groups so that the molecular weight is substantially defined by the side chains, wherein the side chain has a molecular weight of about 500 to 100,000 g / mol.

3. The composition of claim 1 or 2, wherein the side chain has a glass transition temperature (Tg) of about -100°C to 0°C, wherein the spacer monomer group has a glass transition temperature (Tg) of about 40°C to 300°C.

4. The composition of any one of claims 1 to 3, wherein the side chain is hydrophilic and wherein the spacer monomer group is hydrophobic.

5. The composition of claims 1 to 4, wherein the foldable bottlebrush polymer is an end- crosslinked foldable bottlebrush polymer.

6. The composition of claims 1 to 4, wherein the foldable bottlebrush polymer is randomly crosslinked foldable bottlebrush polymer.

7. The composition of claims 1-6, wherein the foldable bottlebrush polymer is solvent free.

8. The composition of claims 1-6, wherein the foldable bottlebrush polymer comprises a solvent.

9. The composition of claim 8, wherein the solvent is selected from the group consistingof: water, an organic solvent, and an ionic liquid.

10. The composition of claims 1 to 9, wherein the side chain is selected from the group consisting of: a linear poly(dimethyl siloxane (PDMS), a linear polyethylene glycol (PEG), and a linear cis-1 ,4-polyisoprene.11 . The composition of claim 10, wherein the spacer monomer group is selected from the group consisting of: a methacrylate-based monomer, an acrylate-based monomer, an acrylamide-based monomers, and a vinyl-based monomer.

12. The composition of claims 1 to 9, wherein the side chain is linear poly(dimethyl siloxane (PDMS) having a molecular weight of about 500 to 100,000 g / mol.

13. The composition of claim 12, wherein the spacer monomer group is selected from the group consisting of: a methacrylate-based monomer, an acrylate-based monomer, an acrylamide-based monomers, and a vinyl-based monomer.

14. The composition of claims 1 to 9, wherein the side chain is the linear polyethylene glycol (PEG) having a molecular weight of about 500 to 100,000 g / mol.

15. The composition of claim 14, wherein the spacer monomer group is selected from the group consisting of: a methacrylate-based monomer, an acrylate-based monomer, an acrylamide-based monomers, and a vinyl-based monomer.

16. The composition of claims 1 to 9, wherein the side chain is the linear cis-1 ,4- polyisoprene having a molecular weight of about 500 to 100,000 g / mol.

17. The composition of claim 16, wherein the spacer monomer group is selected from the group consisting of: a methacrylate-based monomer, an acrylate-based monomer, an acrylamide-based monomers, and a vinyl-based monomer.

18. The composition of claims 1 to 17, wherein the foldable bottlebrush polymer is an ABA block copolymer.

19. The composition of claims 1 to 18, wherein the foldable bottlebrush polymer has the characteristic of being able to reversibly unfold.

20. The composition of claims 1 to 9, wherein the foldable bottlebrush polymer has one of the following structures as part of the polymer:wherein R1 is selected from the group consisting of: an alkyl group, an aryl group, a phenyl group, a vinyl group, an alkoxyl group, a cycloalkyl group, a cycloalkenyl, group, an alkynyl group, and a heterocyclic group, where each of these groups are able to be substituted or unsubstituted; wherein Q is selected from a linear poly(dimethyl siloxane (PDMS), a linear polyethylene glycol (PEG), or a linear cis-1,4- polyisoprene; wherein r is the molar ratio of spacer monomers to side chains; wherein rspis about 0.1 to 10; and wherein nscis about 10 to 5000.

21. The composition of claims 1 or 20, wherein the side chains have a solubility in the presence of water of about 100 g / L or more and the spacer monomers have a solubility in the presence of water of about 10 g / L or less.

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