A universal strategy for decoupling stiffness and extensibility of polymer networks

Abstract

Since the invention of polymer networks such as cross-linked natural rubber in the 19th century, it has been a dogma that stiffer networks are less stretchable. We report a universal strategy for decoupling the stiffness and extensibility of single-network elastomers. Instead of using linear polymers as network strands, we use 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 network strand mass and is determined by the side chains. We validate this concept by creating single-network elastomers with nearly constant Young’s modulus (30 kilopascals) while increasing tensile breaking strain by 40-fold, from 20 to 800%. We show that this strategy applies to networks of different polymer species and topologies. Our discovery opens an avenue for developing polymeric materials with extraordinary mechanical properties.

Foldable bottlebrush polymer network strands release stored length to decouple stiffness-extensibility trade-off of elastomers.

INTRODUCTION

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 k_BT per volume V of a network strand, E ≈ 3k_BT/V (1, 2). By contrast, the extensibility ε_max, or the maximum strain the network strand can be stretched to, increases with the network strand size (Fig. 1A). Thus, the network stiffness and extensibility are correlated: E∝(ε_max)^−α, where α = 2 for a flexible linear network strand, α > 2 if the network strand is pre-strained (3, 4), or α < 2 if the network strand is a semiflexible brush-like polymer (5) (Fig. 1B; supplementary text, note 1, eqs. S4, S18, and S28). Nevertheless, α must be positive for single-network elastomers.

Fig. 1. Concept of fBB polymer network strands.

(A) A conventional single-network elastomer consists of cross-linked linear polymers without solvents. The network extensibility is limited by the ratio of the maximum length, L_max, to the initial size, R, of the network strand: ε_max = L_max/R − 1 ~ N^1/2, where R = bN^1/2 represents the random walk of N Kuhn monomers of size b per network strand and L_max = bN is the network strand contour length. The network Young’s modulus is E ≈ 3k_BT/V ~ 1/N, where k_B is Boltzmann constant, T is the absolute temperature, and V ≈ Nb³ is the network strand volume. Thus, the network stiffness and extensibility are negatively correlated: E∝(ε_max)⁻². (B) Using conventional bottlebrush polymers increases the network strand MW and, therefore, reduces network stiffness but does not break the inherent stiffness-extensibility trade-off: E∝(ε_max)^−α, where α is 2, 1, or >2 if the bottlebrush polymer is flexible, semiflexible, or pre-strained, respectively (supplementary text, note 1). (C) A foldable bottlebrush (fBB) polymer consists of many linear side chains (n_sc) randomly separated by small spacer monomers at a molar ratio of r_sp. (i) The design criteria are that the side chain has a relatively high MW (DP N_sc) and a low glass transition temperature (T_g), whereas the spacer monomer has a low MW and is highly incompatible with the side chains (relatively large Flory-Huggins interaction parameter χ). (ii) 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 overlapping side chains in both the folded and unfolded states. The fBB polymer remains elastic because of its low T_g side chains. (iii) Upon stretching, the collapsed bottlebrush backbone unfolds to release the stored length. By contrast, the MW of the fBB polymer is dominated by the side chains. Thus, using fBB polymers as network strands is expected to decouple network stiffness and extensibility (α = 0).

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 rubber (6, 7), reversible bonds in dual-cross-linked polymer networks (8–11), and brittle networks in interpenetrating-network hydrogels (12–14) and elastomers (15). When subjected to deformation, the weak structure undergoes fracture to prevent localized, amplified stress near network defects (16) or along network strands, avoiding premature failure of the strong network (17). An alternative strategy to prevent premature network fracture is introducing mobile cross-linkers such as entanglements (18–20) and slide rings (21), which move along network strands to redistribute stress throughout the polymer network. These two strategies, however, do not change the stretching limit of the network strand between two neighboring permanent cross-links 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 constituents (22, 23). 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 single-network elastomers.

RESULTS

We seek to develop a strategy to split the inherent stiffness-extensibility trade-off of 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 monomers (24). The design criteria require that the side chains have a relatively high molecular weight (MW) and a low glass transition temperature (T_g); by contrast, the spacer monomer is low MW and highly incompatible with the side chains (Fig. 1C, i). Reminiscent of oil droplets in water, the spacer monomers are prone to aggregate to minimize interfacial free energy. However, because of chain connectivity and relatively high grafting density of side chains, 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 T_g 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 (fBB) polymer, 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 χ ≈ 0.2 and have markedly different T_g of 54°C and −100°C, respectively (25). We fix the degree of polymerization (DP) (N_sc = 14) of the PDMS side chain (MW ~ 1000 g/mol) while changing the number of side chains (n_sc) and the number ratio between spacers and side chains (r_sp) within the bottlebrush polymer. This approach allows us to reduce the four design parameters of fBB polymers, [n_sc, r_sp, N_sc, χ], to two, [n_sc, r_sp].

Fig. 2. Design and synthesis of fBB networks.

(A) A proof-of-concept design of fBB polymer networks exploiting the classical triblock copolymer self-assembly. Side chain, linear PDMS of 1000 g/mol; spacer, BnMA or MMA; linear blocks, PBnMA with DP N_l . Because the side chain MW is constant, this triblock copolymer has three design parameters [n_sc, N_l, r_sp]. (B) Transmission electron microscopy (TEM) images of (left) the control polymer without spacers, [550, 176, 0], and (right) the polymer with spacer, [534, 177, 0.84]. Dark dots represent spherical nodules aggregated by linear end blocks. The average inter-domain distances are d = 75.7 ± 13.1 nm (r_sp = 0) and 85.2 ± 10.8 nm (r_sp = 0.84). Scale bars, 200 nm. (C) Dependence of small-angle x-ray scattering (SAXS)/wide-angle x-ray scattering (WAXS) intensity on the magnitude of wave vector, q, for the self-assembled networks. (D) A schematic illustrating two characteristic lengths in the self-assembled networks: (i) the average inter-domain distance, d = 2π/q*, and (ii) the inter-backbone distance, D_bb = 2π/q_bb, of fBB polymers [noted by arrows in (C)]. (E) Large amplitude oscillatory shear measurements reveal that introducing spacer monomers increases the shear yield strain (γ_y) 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′, storage modulus; G″, loss modulus. (F and G) Characteristic lengths (d, L_max, D_bb) of fBB polymer networks with various BnMA spacer ratios, [~200, ~33, 0 to 3.46]. (F) As the average DP of the spacer segment (N_g = r_sp + 1) increases, d remains nearly the same, but L_max increases markedly. (G) D_bb increases with the decrease of grafting density (1/N_g) in both melts (squares) and self-assembled networks (circles). This behavior contradicts the understanding of conventional bottlebrush polymers (dashed line, D_bb∝N_sc^1/2N_g^−1/2, supplementary text, note 1, eq. S10). However, it can be well explained by our recent molecular theory, which accounts for the incompatibility between spacer monomers and side chains within fBB polymers (solid line, D_bb∝N_sc^1/2N_g^1/6 + N_g^2/3; supplementary text, note 2, eq. S39).

We exploit the self-assembly of ABA triblock copolymers (26) to cross-link the fBB polymers to create networks. We synthesize an fBB polymer (24) and then grow onto its two ends a high T_g linear polymer (PBnMA) (25), forming a linear-fBB-linear triblock copolymer (Fig. 2A). We start with two fBB polymers consisting of nearly the same number of side chains (n_sc ≈ 550) but different spacer ratios (r_sp = 0, 0.84) (table S1). Simultaneously, we fix the DP of a linear end block (N_l ≈ 0.3n_sc ≈ 175) to reach a volume fraction of 10% (supplementary data set 1, 1.3). At RT, the linear blocks aggregate into spherical glassy nodules that cross-link 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 = 2π/q* (left arrow, Fig. 2, C and D). These results demonstrate the formation of end-cross-linked fBB polymer networks encoded by three molecular architecture parameters [n_sc, N_l, r_sp] (Fig. 2D).

As the spacer ratio increases from 0 to 0.84, the network shear storage modulus G′, measured at 1 rad/s, remains nearly constant at 3 kPa. By contrast, the yield strain increases by more than threefold from 161 to 515%, as shown by large amplitude oscillatory shear measurements in Fig. 2E. At large deformations, the control network (r_sp = 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. Unexpectedly, for the network with spacer monomers (r_sp = 0.84), the strain stiffening occurs after a remarkable strain-softening regime with a reduction of 14% in shear modulus (left arrow, Fig. 2E). Consistent with this observation, prestressing the network results in the decrease of modulus (fig. S1A). This strain softening diminishes for fBB polymer networks with fewer side chains (n_sc < 360) (fig. S1, B to D). 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 ([n_sc, N_l, r_sp]) within which fBB polymer networks allow for decoupled stiffness and extensibility, we fix the number of side chains (n_sc ≈ 200) while increasing the spacer ratio within a wide range (r_sp = 0 to 3.46) (table S1; fig. S2, A and C; supplementary data set 1). Simultaneously, we fix the end block volume fraction relative to the side chains at ~6% (N_l ≈ 33). All polymers self-assemble to end–cross-linked networks, as confirmed by the presence of primary SAXS scattering peaks (fig. S3A). As the average DP of the spacer segment, N_g = r_sp + 1, increases from 1 to 4.46, d increases less than twice from ~30 to ~50 nm (green circles, Fig. 2F). By contrast, the contour length of the fBB polymer L_max = N_gn_scl [l = 2.56 Å is the main-chain length of a chemical monomer (24)], the maximum extent to which the fBB polymer can be stretched increases by more than four times from ~50 to ~220 nm (red squares, Fig. 2F). The marked difference between the values of d and L_max highlights 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 backbone (3) (supplementary text, 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, q_bb, associated with the inter-backbone distance between two neighboring fBB polymers, D_bb = 2π/q_bb (right arrow, Fig. 2C; fig. S3A). As N_g increases from 1 to 4.46, D_bb monotonically increases by 60% from 3.54 to 5.51 nm (circles, Fig. 2G). Notably, in the self-assembled networks, the dependence of D_bb on N_g quantitatively 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 D_bb with N_g contradicts the understanding of conventional bottlebrush polymer melts (dashed line, Fig. 2G; supplementary text, note 1, eq. S10) (27–29). However, this discrepancy is well explained by our recent theory that accounts for the incompatibility between side chains and backbone within a bottlebrush polymer (24). 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 in grafting density (solid lines, Fig. 2G; supplementary text, 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 (movies S1 to S5). The stress-strain curves exhibit three distinct behaviors depending on the spacer ratio. For low spacer ratios (regime I, 0 < r_sp < r_sp,l ≈ 1.5), the stress-strain curves nearly overlap at low strains, yet the networks with more spacers become more stretchable (Fig. 3A, i, and fig. S4A, i). Moreover, the tensile breaking strain, ε_b, is the same as ε_max, 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, ε_max increases by a remarkable 20-fold from (21 ± 6)% to (428 ± 59)% (light green regions, Fig. 3, C and D). The Young’s moduli are consistent with network shear moduli, G, following the classic relation E = 3G (fig. S5) (1). Moreover, the dependence of network modulus on the spacer ratio can be well explained by the theoretical prediction for unentangled single-network elastomers (fig. S5E). These results show that using fBB polymers as network strands enables truly decoupled network stiffness and extensibility [E∝(ε_max)^−α, α = 0] (light green region, Fig. 3E).

Fig. 3. Using fBB polymers as network strands provides a universal strategy for decoupling stiffness and extensibility of single-network elastomers.

(A and B) Nominal stress-strain curves of networks with (A) BnMA and (B) MMA as spacers. ε_b, tensile breaking strain; ε_max, critical strain at which the nominal stress is maximum. At either (i) low or (iii) high spacer ratios, ε_b = ε_max. By contrast, at intermediate spacer ratios, ε_max < ε_b and the networks exhibit plastic deformation under large deformations, at which the nominal stress decreases markedly with strain. The plastic deformation is attributed to pulling the linear end blocks out from the relatively weak glassy nodules (fig. S6). Thus, we use ε_max to denote the extensibility attributed to fBB polymer network strands. All measurements are performed at RT and a fixed tensile strain rate of 0.02/s. (C and D) Dependencies of (C) network extensibility (ε_max) and (D) Young’s modulus (E) on the spacer ratio. (E) At relatively small spacer ratios, the network stiffness and extensibility are truly decoupled, where ε_max can be increased from ~20 to 800% while keeping E constant at ~30 kPa (α = 0). There exists a small window (intermediate spacer ratios), in which stiffness and extensibility are positively correlated (α < 0). At high spacer ratios, the folded bottlebrush itself has an elevated T_g and becomes stiff (fig. S7), such that the network stiffness and extensibility resume the classical negative correlation (α > 0). Error bar, SD for n = 3 to 5.

For intermediate spacer ratios (regime II, r_sp,l < r_sp < r_sp,m ≈ 2.3), the networks are extremely stretchable with ε_b up to ~2800% (gray line, Fig. 3A, ii; movie S3). However, the nominal stress at ε_b is not maximum. Instead, the maximum stress occurs at a critical yield strain (ε_max ~ 900%), above which the network exhibits plastic deformation with the nominal stress decreasing markedly with strain (Fig. 3A, ii, and fig. S4A, 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 the glassy nodules become strong (fig. S6). At high spacer ratios (regime III, r_sp > r_sp,m), there is no plastic deformation at large deformations and the nominal stress reaches maximum at the tensile breaking strain (Fig. 3A, iii, and fig. S4A, iii). Thus, we use ε_max to describe the extensibility attributed to fBB polymer network strands, which corresponds to tensile breaking strain (ε_b) for low and high spacer ratios and yield strain for intermediate spacer ratios (arrow, Fig. 3A, ii).

The correlation between E and ε_max exhibits two distinct behaviors at relatively high spacer ratios (r_sp > r_sp,l). There exists a small window (r_sp,l < r_sp < r_sp,m) in which stiffer networks are more stretchable (α < 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 (r_sp > r_sp,m), the networks resume the classical stiffness-extensibility trade-off (α > 0) yet remain quite stretchable (ε_max > 400%) (light gray 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 T_g of fBB polymers, such that the fBB polymers themselves become viscoelastic solids (fig. S7, A to F). 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. S7G). These results highlight the importance of keeping fBB polymers elastic (of low T_g) 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). To this end, 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 (r_sp = 2.9), so that the inter-backbone distance (D_bb = 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. 4, C and D), yet the inter-backbone distance remains constant (fig. S8C). Perpendicular to the stretching direction, the inter-backbone distance decreases with strain (Fig. 4, E and F).

Fig. 4. Unfolding of a collapsed bottlebrush network strand under extension.

(A) 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/s. (B) Two-dimensional (2D) (i) SAXS and (ii) WAXS patterns at various strains. (C and D) Along the elongation direction, the inter-domain distance (d) increases linearly with strain (ε). (E and F) Perpendicular to the elongation direction, the inter-backbone distance (D_bb) 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 (Materials and 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 (fig. S9, B to D).

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. S9, A and B) and a more aligned bottlebrush backbone (fig. S9C). 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. S9D). 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 and fig. S8, A and B). Collectively, our results show that a collapsed bottlebrush backbone unfolds upon extension.

Last, we confirm that our design strategy applies to networks of different topologies and polymer species. We synthesize randomly cross-linked fBB polymer networks using BnMA as the spacer monomer (fig. S10, A and B). We fix the average number of side chains per network strand (n_sc = 100) and increase the spacer ratio to intermediate values (r_sp = 0, 1.0, and 2.0). The network Young’s moduli remain nearly constant at ~50 kPa while the tensile breaking strain increases by nearly three times (fig. S10C and movies S6 and S7). Unlike the self-assembled networks that are end–cross-linked by glassy nodules, the random networks are cross-linked by permanent covalent bonds and do not exhibit plastic deformation at an intermediate spacer ratio (r_sp = 2.0; green line, fig. S10C). This result further supports that the plastic deformation for the self-assembled networks is due to the chain-pullout of the end blocks (Fig. 3A, ii, and fig. S9E).

For the self-assembled end–cross-linked networks, we use another spacer monomer methyl methacrylate (MMA), which fulfills the design criteria as it has a low MW (100 g/mol) and is highly incompatible with PDMS (30). We synthesize a series of fBB polymer networks with a wide range of MMA spacer ratios, [~200, ~60, 0 to 3.62] (table S1; fig. S2, B and C; and supplementary data set 2). We observe similar behavior from the network microstructure (fig. S3B) to the mechanical properties (Fig. 3B; blue squares, Fig. 3, C and D; figs. S4B, S5, and S7). Moreover, for both MMA and BnMA spacers, E versus ε_max collapses to a universal relation, where ε_max can be increased by nearly 40-fold, from ~20 to ~800% while keeping E constant of ~30 kPa (α = 0) (light green region, Fig. 3E).

DISCUSSION

In summary, we have discovered a general strategy for decoupling stiffness and extensibility of single-network elastomers. The underlying concept is to use fBB polymers as network strands. The sole criterion for creating fBB polymers is the high incompatibility between the backbone and the side chains, which leads to the collapse of the backbone despite strong steric repulsion among highly overlapped side chains (supplementary text, note 2). This behavior contrasts with conventional bottlebrush polymers, in which the bottlebrush backbone is pre-strained. Consequently, the extensibility of fBB polymer networks is substantially larger than that of conventional bottlebrush polymer networks (fig. S11 and table S2) (3–5, 29, 31–36). A characteristic feature attributed to the unfolding of fBB polymers is delayed strain stiffening after a remarkable strain softening, which is noticeable for networks with a relatively large number of side chains (fig. S1) or high spacer ratios (fig. S4). Unlike mechanophores that release the stored length via irreversible chemical reactions (22, 23), the unfolding of fBB polymers is a reversible physical process (fig. S12), reminiscent of unzipping titin protein in muscle (37). Because the bottlebrush molecular architecture prevents the formation of entanglements, the modulus of conventional bottlebrush polymer networks is often much lower than ~1 MPa, the entanglement modulus of their linear counterpart (27). By contrast, the modulus of fBB polymer networks can be markedly increased using high T_g spacer monomers to reach MPa (gray region, fig. S5E) without substantially compromising extensibility (Fig. 3, A, iii, and B, iii). It would be worthwhile to explore whether the concept of fBB polymer networks can be applied to create structural polymers of both high modulus and high extensibility. Nevertheless, 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 developing polymeric materials with extraordinary mechanical properties.

MATERIALS AND METHODS

Materials

Monomethacryloxypropyl-terminated PDMS (MCR-M11, MW ~ 1000 g/mol) and methacryloxypropyl-terminated PDMS (DMS-R18, MW ~ 5000 g/mol) are purchased from Gelest and purified using basic alumina columns to remove inhibitors. BnMA (98%) and 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 to 100%], anisole (≥99.7%), and p-xylene (≥99.7%) are purchased from Sigma-Aldrich and used as received. Tetrahydrofuran (THF; analytical reagent), purchased from Macron Fine Chemicals, and THF [high-performance liquid chromatography (HPLC) grade], methanol (Certified ACS), dichloromethane (DCM; Certified ACS), and dimethylformamide (DMF; Certified ACS), purchased from Thermo Fisher Scientific, are used as received.

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 methods (24, 31, 38) to synthesize end–cross-linked and randomly cross-linked fBB polymer networks.

End–cross-linked 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 2f-BiB (4.3 mg, 0.012 mmol), MCR-M11 (6 g, 6 mmol), BnMA (705 mg, 4 mmol), 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 of DMF to prepare a catalyst solution. Then, 30 μl of catalyst solution is added to the mixture. Followed by a 60-min bubbling of the mixture with nitrogen, Sn(EH)₂ (14.6 mg, 0.036 mmol) in 100 μl of 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 using ¹H NMR, which is 211 for this fBB polymer. In addition, the polymer contains 195 PDMS side chains, corresponding to a spacer/side chain ratio of r_sp = 1.08 (supplementary data and fig. S16).

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 × 10⁻³ mmol), 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 × 10⁻² mmol Me₆TREN and 1.7 × 10⁻³ mmol CuCl₂ is 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 × 10⁻² mmol) 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 use ¹H NMR to confirm that the DP of BnMA is 40 per end block (supplementary data and fig. S33). Last, the sample is dried in a vacuum oven (Thermo Fisher Scientific, Model 6258) at RT for 24 hours. The polymer is a transparent solid at RT.

Randomly cross-linked fBB polymer networks

These networks are synthesized following the procedure in Step I (see the “End–cross-linked fBB polymer networks” section) with the only difference that a di-functional cross-linking chain (DMS-R18) is added to the reaction mixture at a molar ratio 1:100 to the side chains (fig. S10, A and B). Thus, the average number of side chains per network strand is n_sc = 100. For each network, we use a cosolvent, 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.

¹H NMR characterization

We use ¹H 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 on the basis of the conversion of linear PDMS macromonomers to bottlebrush PDMS. The number of spacer monomers is determined on the basis of the NMR spectra of a purified bottlebrush polymer. The DP of each end block is determined on the basis of the NMR spectra of purified triblock polymers. Chemical shifts for ¹H NMR spectra are reported in parts per million compared to a singlet at 7.26 parts per million in CDCl₃.

Gel permeation chromatography

Gel permeation chromatography (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.

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 m, and the radiation wavelength used is λ = 0.77 Å. The scattered x-rays are captured using an in-vacuum Pilatus 1 M detector, which consists of an array of 0.172-mm square pixels in a 941 × 1043 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 1D intensity profile, denoted as I(q), is plotted as a function of the scattering wave vector, $\mid \overrightarrow{q}\mid =q=4\mathrm{\pi }{\mathrm{\lambda }}^{-1}\text{sin}(\mathrm{\theta }/2)$, where θ 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 to 8 mm in length, 2 to 4 mm in width, and 0.5 to 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/s 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 s. In addition, 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 1 M detector and a Pilatus 9 K, respectively, with a pixel size of 0.172 mm. The distance between the sample and the WAXS detector is 2.5 m, and the radiation wavelength used is λ = 0.77 Å.

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: $\langle {\text{cos}}^2\mathrm{\varphi }\rangle =\frac{{\int }_0^{\mathrm{\pi }/2}I(\mathrm{\varphi }){\text{cos}}^2\mathrm{\varphi }\text{sin}\mathrm{\varphi }d\mathrm{\varphi }}{{\int }_0^{\mathrm{\pi }/2}I(\mathrm{\varphi })\text{sin}\mathrm{\varphi }d\mathrm{\varphi }}$. Here, ϕ is the azimuthal angle, and I(ϕ) is the intensity for the characteristic peak, as outlined by the region between two dashed circles in fig. S8A.

Herman’s orientation parameter S is defined as $S=\frac{3\langle {\text{cos}}^2\mathrm{\varphi }\rangle -1}{2}$. 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).

Transmission electron microscopy

We use our previously established method to prepare the samples for TEM imaging (25, 39). We use hollow-cone dark-field TEM (FEI Titan 80-300) at the electron energy of 300 keV with a tilt angle of 0.805° 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.

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 1 hour. Subsequently, the bottom plate is heated to 40°C for 20 min. 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 to 100 rad/s. For strain sweep, we fix the temperature at 20°C and the oscillatory shear frequency at 1 rad/s while increasing the shear strain from 1 to 10,000%. 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° to 80°C, well above the T_g = 54°C of PBnMA (40). As detailed in our previous work (38), we use a slow temperature ramping rate, 1°C/min, and wait for 20 min at each temperature point before collecting data; this ensures that the self-assembled microstructure is in equilibrium at each temperature point.

Tensile test

We prepare the self-assembled fBB polymer networks using a Teflon model described above (see the “SAXS/WAXS measurements” section). 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 to 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-sectional 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/s and repeated at least three times on parallel samples.

Differential scanning calorimetry

We determine the T_g of fBB polymers using a differential scanning calorimeter (DSC Q20, TA Instruments). All the samples are prepared using a combination of solvent and thermal annealing (see the “SAXS/WAXS measurements” section) to ensure an 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 393 K 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. The specific heat capacity, C_p, is determined following the second heating cycle. The T_g values are determined as the midpoint of the specific heat capacity jump; these values are also consistent with those determined by the inflection point of the heat capacity under temperature sweep.

Supplementary Materials

The PDF file includes:

Figs. S1 to S68

Tables S1 and S2

Supplementary Text

Legends for movies S1 to S7

Supplementary Data

Other Supplementary Material for this manuscript includes the following:

Movies S1 to S7