Introduction

Polydiene elastomers, owing to their elasticity and flexibility, are essential materials for humans because of their critical applications in tires, seals, and shock absorbers [1, 2]. Polydienes without crosslinks exhibit low mechanical strength, which limits their performance in practical use [3]. Vulcanization, i.e., the introduction of covalent crosslinks, has been the primary method for enhancing the mechanical properties of polydiene elastomers, significantly improving their strength and toughness [4,5,6]. However, there is a trade-off between the stretchability and stiffness of covalently crosslinked elastomers. Higher crosslink densities lead to greater stiffness but lower stretchability, whereas lower crosslink densities increase stretchability at the cost of stiffness. This trade-off restricts the overall toughness of the material [7, 8]. Additionally, the irreversible nature of covalent bonds reduces the ability of a material to recover after deformation, leading to nonrecoverable fatigue [9, 10].

To address the limitations of traditional covalent crosslinks, dynamic bonds, which are relatively weak and reversible interactions, have been introduced into polymer networks as dynamic crosslinks [11,12,13,14]. When an external force is applied, the dynamic crosslinks break prior to the rupture of covalent bonds, serving as sacrificial bonds to protect the material integrity14. The dissociation and association of dynamic crosslinks make the network structure capable of dissipating energy effectively, thus increasing stretchability while maintaining stiffness. Additionally, the reversible nature of dynamic bonds contributes to the recovery of mechanical properties [15]. Various types of dynamic bonds, including hydrogen bonds [16, 17], metal–ligand coordination [18], host–guest interactions [19], ionic interactions [20], and electrostatic interactions [21], have been explored for their ability to enhance mechanical properties. However, the inherently reversible nature of dynamic bonds often compromises the long-term mechanical integrity of the material [13].

The combination of dynamic and covalent (static) crosslinking is a promising way to simultaneously improve stretchability, strength, and recoverability [22, 23]. Polymer networks with both dynamic and static crosslinks are referred to as dual-crosslinked networks. Great efforts have been made in researching the mechanical properties [24,25,26,27,28], fracture behavior [29], and energy dissipation [30,31,32,33,34] of dual-crosslinked hydrogels. There are also some studies on dual-crosslinked elastomers [35,36,37,38,39,40,41]. Weitz et al. developed an elastomer by integrating hydrogen bonds into a covalently crosslinked network, achieving high toughness and self-healing capabilities [42]. Liu et al. incorporated metal‒ligand coordination bonds as dynamic crosslinks into vulcanized styrene‒butadiene rubber to improve its mechanical properties and shape-memory ability [37]. Despite these efforts, the individual and collective influences of static and dynamic crosslinks on mechanical properties remain incompletely understood. It is necessary to establish a systematic framework for understanding and predicting the effects of varying static and dynamic crosslink densities on mechanical behavior. This knowledge provides valuable guidance for designing high-performance elastomers with tailored properties.

In this study, we systematically investigated the influence of static and dynamic crosslink densities on the mechanical properties of dual-crosslinked elastomers. We utilized styrene−butadiene rubber (SBR) as a matrix and metal‒ligand coordination complexes as dynamic crosslinks. Zinc salt was added to SBR containing pyridine ligands (poly(styrene-co-butadiene-co-4-vinylpyridine), SBPy) to form pyridine–Zn2+ complexes as dynamic crosslinks. We discovered that simple thermal treatment of the coordinated SBPy in air could induce the formation of static crosslinks. Both the static and dynamic crosslink densities could be easily controlled by changing the zinc content and heating time. The static crosslinks significantly increased the mechanical strength of the elastomer because of their rigidity, complementing the energy-dissipating properties of the dynamic bonds. By integrating both types of crosslinks, we can explore the effects of dynamic crosslinking and static crosslinking on critical properties such as mechanical strength, energy dissipation, and recoverability.

Experimental

Materials

Poly(styrene-co-butadiene-co-4-vinylpyridine) (SBPy) synthesized by emulsion polymerization was obtained from ENEOS Materials Corp. The mole fractions of styrene, 1,4-butadiene, 1,2-butadiene, and 4-vinylpyridine were 9.43%, 70.55%, 13.46%, and 6.56%, respectively, as determined by 1H NMR (Fig. S1). Zn(II) trifluoromethanesulfonate (Zn(OTf)2) was purchased from Tokyo Chemical Industry Co., Ltd. (Japan). 2,6-Di-tert-butyl-4-methylphenol (BHT), triethylamine (TEA), dehydrated tetrahydrofuran (THF), pyridine, and methanol were purchased from FUJIFILM Wako Pure Chemical Corp. (Japan). SBPy was purified by precipitating the THF solution in methanol twice, followed by vacuum drying. Other chemicals were used as received.

Preparation of the dual-crosslinked elastomer

A total of 200 mg of SBPy (pyridine content: 0.211 mmol) was dissolved in dry THF (19 mL). The required amount of Zn(OTf)2 was separately dissolved in 1 mL of methanol. The amount of Zn(OTf)2 was varied so that the molar ratio of Zn2+ to the pyridine group in SBPy, defined as x, was 10%, 20%, and 30%. The Zn(OTf)2/methanol solution was added dropwise to the SBPy/THF solution under vigorous stirring. For x = 20% and 30%, 1 equivalent of pyridine against Zn(OTf)2 was added to prevent gelation. The mixed solution was vacuum filtered to remove possible undissolved impurities. The homogeneous solution was cast on a Teflon dish, dried in a nitrogen atmosphere for 24 h and then dried in vacuo for 12 h at room temperature to obtain a sample with dynamic crosslinks. This process completely removed the added free pyridine for x = 20% and 30%, as confirmed by 1H NMR (Fig. S2). To introduce static crosslinks, the sample with dynamic crosslinks was subjected to heating cycles in air with a hydraulic heat press. Each cycle was performed at 80 °C and 20 MPa for 15 min. We have found that this simple treatment without any additional crosslinking reagents can induce static crosslinking, as discussed later. The degree of static crosslinking was adjusted by the number of heating cycles, y (y = 0−4). The samples are hereafter called “SBPy-Zn(x,y)”, where x refers to the content of Zn2+, and y refers to the number of heating cycles applied.

Preparation of the control elastomer without dynamic crosslinks

The control sample was prepared by conventional vulcanization of SBPy. SBPy (100 g), tetrabenzylthiuram disulfide (6.8 g), and varying amounts of sulfur were compounded by using a roll mill. The loading of sulfur per 100 g SBPy was varied from 0.3 g to 1.0 g to achieve varying densities of static crosslinks. The compound was hot pressed using a hydraulic heat press at 160 °C and 20 MPa for 30 min. These samples are coded as SBPy-S(z), where z refers to the sulfur loading in grams per 100 g SBPy.

Characterizations

1H NMR spectra were recorded on a JNM-ECZ 600 R spectrometer (JEOL, Japan) in CDCl3. The solvent signal at 7.26 ppm was chosen as the internal standard signal. Temperature-resolved infrared (IR) spectroscopy measurements were performed on an IRAffinity-1S spectrometer (Shimadzu, Japan). A polymer solution droplet was cast on a potassium bromide plate and dried under a nitrogen purge. The dried film was subsequently sandwiched between two plates of potassium bromide and mounted onto a THMS600 hot stage (Linkam Scientific Instrument Ltd., UK) fitted in the IR test chamber to record in situ spectra. Polarized optical microscopy (POM) was performed on a BX51 polarized optical microscope (Olympus Co., Japan) equipped with a digital camera. The film sample (thickness ∼0.1 mm) sandwiched between glass slides was mounted on a Linkam THMS600 hot stage and observed under crossed polarization. Tensile tests were performed using an AGS-X tensile tester (Shimadzu, Japan) equipped with a 100 N load cell. A dumbbell-shaped sample (thickness ∼ 0.1 mm) conforming to JIS K6251-7 (scaled down by a 2/3 ratio, with an initial parallel section length of 8 mm) was punched out of the sample film. In a simple tensile test, the test piece was stretched at a constant speed until it ruptured. Five crosshead speeds of 5, 25, 50, 250, and 500 mm/min were used, which corresponded to nominal strain rates of 0.0104, 0.0521, 0.104, 0.521, and 1.04 s−1, respectively. Tensile tests at 50 mm/min (strain rate = 0.104 s−1) were repeated for 3 pieces, whereas one or two test pieces were used for the other rates. In the cyclic tensile tests, a test piece was stretched to a prescribed strain and then unloaded to zero strain at a constant crosshead speed of 50 mm/min (nominal strain rate = 0.104 s−1). For the recoverability tests, the cycle was repeated 7 times in total, with time intervals of 0, 1, 30, 60, 180, and 360 min before the 2nd, 3rd, 4th, 5th, 6th, and 7th cycles, respectively. The stress and strain reported in this study were engineering stress and nominal strain, respectively. The engineering stress was calculated by dividing the recorded force by the initial cross-section of the parallel section of the test piece. The nominal strain was calculated by dividing the crosshead displacement by the initial length of the parallel section of the test piece (8 mm). Young’s modulus was obtained as the slope of the initial straight section of the strain‒stress curve by linear fitting.

Results and discussion

Formation of dynamic and static crosslinks

The preparation of the dual-crosslinked elastomer is schematically illustrated in Fig. 1. Starting from SBPy with a monomer molar composition of styrene (a = 9.43%), 1,4-butadiene (b = 70.55%), 1,2-butadiene (c = 13.46%), and 4-vinylpyridine (d = 6.56%) (Fig. 1a), dynamic crosslinks were first introduced by the addition of Zn(OTf)2 (Fig. 1b). Zn was selected as the metal species in this study because the oxidation state of Zn2+ is generally very stable and because pyridine is known to coordinate strongly to Zn2+ [43]. Therefore, the ratio of Zn2+ ions to pyridine side groups in SBPy is expected to correspond to the density of dynamic crosslinks. Solubility tests were conducted on a cast film of SBPy containing Zn(OTf)2. The 20% Zn2+ sample did not dissolve in THF, whereas it did dissolve in THF containing excess pyridine (Fig. S3a). This observation suggests that crosslinking occurs by dynamic pyridine−Zn2+ coordination bonds. In the presence of free pyridine molecules, the crosslink density decreased, leading to the dissolution of the polymer.

Fig. 1
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Schematic illustrations showing the preparation of the dual-crosslinked elastomers. a SBPy. b SBPy-Zn(x,0) sample with dynamic crosslinks prepared by the addition of Zn(OTf)2 to the solution, followed by drying. c SBPy-Zn(x,y) sample with dynamic and static crosslinks prepared by multiple heating cycles at 80 °C, where x is the molar ratio of Zn2+ to pyridine side groups in SBPy and controls the dynamic crosslink density, and y is the number of heating cycles, which affects the static crosslink density

We discovered that simple heating of SBPy containing Zn(OTf)2 led to the formation of static crosslinks (Fig. 1c). When the 20% Zn2+ sample was heated at 80 °C for 48 h, it became insoluble in THF, even in the presence of excess pyridine (Fig. S3c), indicating the formation of static crosslinks. We found that both Zn(OTf)2 and heating were necessary to induce static crosslinks, as heating SBPy without Zn(OTf)2 did not yield an insoluble component. We speculate that Zn2+ facilitated radical crosslinking by thermally induced radicals and/or oxidation by atmospheric oxygen. The detailed mechanism of the observed heat-induced crosslinking remains unknown.

We optimized the heat treatment protocol for tuning the static crosslink density. The protocol involved successive cycles of heating, each consisting of 15 min of heating at 80 °C in air. The number of heat cycles controlled the density of static crosslinks (Fig. 1c). Hereafter, the sample is denoted SBPy-Zn(x,y), where x and y represent the ratio of Zn2+ ions to the pyridine side groups in SBPy and the number of heat cycles, respectively. The appearances of the samples with varying Zn2+ contents (x) and numbers of heat cycles (y) are displayed in Fig. S4. All the samples were flexible and transparent. The solubility of these compounds in THF with excess pyridine decreased with increasing y. At x = 20%, the sample with y = 2 remained mostly soluble, whereas the sample with y = 4 only swelled and did not dissolve (Fig. S4b).

The coordination between Zn2+ and the pyridine side groups was confirmed by IR spectroscopy. In the C=C and C=N region (1600–1650 cm−1), SBPy without Zn(OTf)2 showed two absorption peaks at 1639 cm−1 and 1597 cm⁻1 (Fig. S5a, b). The peak at 1639 cm−1 can be assigned to the C=C stretching vibration of the polybutadiene repeat units, and the peak at 1597 cm⁻1 can be attributed to the C‒N stretching vibration of the noncoordinated pyridine group [44]. The alkene in the polybutadiene repeat units also gave rise to two strong peaks attributed to the out-of-plane C‒H bending vibration in 900–1000 cm−1 (Fig. S5c). The enlarged spectra around the C‒N stretching peak for SBPy with and without Zn(OTf)2 are shown in Fig. 2a. Upon the addition of Zn(OTf)2, the 1597 cm⁻1 peak weakened, and a new peak appeared at 1616 cm⁻1. The new peak is attributed to the C‒N stretching vibration of a coordinated pyridine group [44]. Thus, the formation of a coordination bond between Zn²⁺ and pyridine was confirmed. In Fig. 2a, the variation in the ratio of the two peaks is strongly correlated with x, indicating that the added Zn2+ ions coordinate with the pyridine groups efficiently in SBPy.

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IR spectra of a SBPy-Zn(x,0) with x = 0–30% and b SBPy-Zn(20,y) with y = 0–4. The absorbance was normalized to the value of the 2950 cm−1 peak (saturated C–H stretching vibration) as an internal reference and was vertically shifted for clarity. The dashed lines indicate the position of the C‒N stretching vibration peak attributed to noncoordinated and coordinated pyridine groups

The stability of this coordination bond against heating was also investigated. The IR spectra of SBPy-Zn(20,y) with y = 0−4 are shown in Fig. 2b. No significant changes are observed in the peaks at 1597 cm⁻¹ and 1616 cm⁻¹ after four heating cycles, which suggests that the coordination bond is not disturbed by the introduction of static crosslinks. Therefore, we can assume that the samples with the same x (≤ 20%) but different y values possess an identical dynamic crosslink density.

Two caveats of the static and dynamic crosslinks in our dual-crosslinked elastomers should be mentioned. The first caveat is that samples with the same y and different x values do not necessarily share the same static crosslink density. Although the addition of Zn(OTf)2 was a requirement for heat-induced static crosslinking, different concentrations of Zn(OTf)2 can lead to different degrees of static crosslinking, even among samples with the same number of heat cycles (y). Therefore, it would be difficult to draw meaningful conclusions on crosslink density from a comparison among samples with the same y and different x. The second caveat is the potential effects of the noncoordinated ligands. Increasing x leads not only to an increase in the amount of coordinated pyridine but also to a corresponding decrease in the amount of noncoordinated pyridine. The concentration of the noncoordinated ligand could affect ligand exchange kinetics [45].

We confirmed the dispersion of Zn2+ ions in the elastomers by POM. The POM images of SBPy-Zn(x,y) with x = 10–50% and y = 1–4 under cross-polarization are shown in Fig. S6. No brightness was detected for samples with x ≤ 30%, indicating the absence of crystal formation during heating. This suggests a uniform dispersion of Zn(OTf)2 at the ~100 μm scale. After the second heat treatment, the sample with x = 50% presented bright spots, suggesting the formation of crystals, presumably Zn(OTf)2. The amount of Zn(OTf)2 that could dissolve uniformly in SBPy was limited, leading to the precipitation of Zn(OTf)2 crystals. On the basis of these results, we set the highest Zn2+ content to x = 30%.

Tensile behavior

The stress‒strain curves of the dual-crosslinked elastomers are presented in Fig. 3, and the tensile properties are summarized in Table S1. As a reference, the results of the control samples without dynamic crosslinks are also displayed.

Fig. 3
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Stress‒strain curves of the dual-crosslinked elastomers and the control samples. a Control samples, SBPy-S(z), with static crosslinks only. Dual-crosslinked elastomers, SBPy-Zn(x,y), with b x = 10%, c x = 20%, and d x = 30%. The curve of SBPy is replicated in each panel as a reference. All tests were performed at a nominal strain rate of 0.104 s−1 at room temperature

The stress‒strain curves of the uncrosslinked SBPy and control samples with static crosslinks but without dynamic crosslinks (sulfur-vulcanized SBPy, SBPy-S(z), where z is the grams of sulfur per 100 g SBPy) are compared in Fig. 3a. The SBPy without any crosslinks has a Young’s modulus of 0.65 MPa and a strain at break of ca. 500%. Compared with the SBPy control samples, SBPy-S(z) samples had higher moduli, strains at break, and strengths. With increasing sulfur loading (z), the modulus increases, whereas the strain at break decreases. This is a manifestation of the trade-off between stiffness and stretchability that is typical for static crosslinking.

The stress‒strain curves of the dual-crosslinked elastomers with a fixed Zn2+ content (x) and a varying number of heat cycles (y) are shown in Fig. 3b−d. Each series with the same x can be considered to have the same dynamic crosslink density. For each x, increasing y leads to a decrease in the strain at break and an increase in the modulus. This trend qualitatively agrees with that of the control SBPy-S(z) samples with only static crosslinks, demonstrating the trade-off between stiffness and stretchability caused by static crosslinks.

The effect of y on the static crosslink density can be confirmed by comparing the values with the Young’s modulus (E). The affine network model in the classical rubber elasticity theory shows that E = 3νRT, where ν is the number density of elastically effective chains (EECs) in the network, R is the gas constant, and T is the temperature. Assuming that both static and dynamic crosslinks contribute to ν, E can be recognized as a measure of the total crosslink density, including both static and dynamic crosslinks. Because samples with the same x could be considered to have the same dynamic crosslink density, the difference in E for the same x but different y should be due to the difference in the static crosslink density. E against y for each series with the same x is shown in Fig. S7. E increased monotonously with increasing y, further confirming that the repeated heating treatment generated static crosslinks.

If we assume the validity of the affine network model, we can estimate the ν values by ν = E/(3RT). Moreover, if we assume that all Zn2+ ions bind with pyridine side groups, we can estimate the number density of EECs due to dynamic crosslinks (νdyn). We further assume that two pyridine groups bind to one Zn2+ ion; this is the simplest form of a complex that can act as a crosslink. One such complex adds two EECs to the system. Therefore, νdyn is approximately 2x[L]0, where [L]0 is the concentration of pyridine ligands in the bulk SBPy ( ~ 1.05×103 mol m−3, assuming that the polymer density is 1 g cm−3). The values of νtot and νdyn thus estimated are listed in Table S2 for each sample. Note that these values are very rough estimations based on multiple assumptions. The estimated νtot ranged from 213 mol m−3 (SBPy-Zn(10,1)) to 827 mol m−3 (SBPy-Zn(30,4)), whereas νdyn was 210, 420, and 630 mol m−3 for x = 10, 20, and 30%, respectively. Several samples showed an unnatural relation of νdyn > νtot. Perhaps the above assumption that all Zn2+ formed elastically effective crosslinks overestimates νdyn. Nevertheless, these calculations suggest that the densities of static and dynamic crosslinks were of a comparable order.

Let us turn our attention again to the stress‒strain curves (Fig. 3a–d). In addition to the comparison among the samples with the same x, it is also tempting to compare the curves with the same y but different x to verify the effects of the dynamic crosslink density. However, as previously discussed with respect to the IR spectra, the static crosslink density can depend on both x and y. Therefore, we discuss the effect of the dynamic crosslink density alone by organizing the data of all the samples on the basis of the Young’s modulus (E) as a measure of the total crosslink density, including both static and dynamic crosslinks [46].

The plots of each tensile parameter against E for the dual-crosslinked elastomers and the control samples are shown in Fig. 4. In Fig. 4a, the strain at break (εb) is plotted against E for SBPy-Zn(x,y) and SBPy-S(z). The points of SBPy-Zn(x,y) are organized into three series, each having the same x but different y. In all four series, εb decreases with increasing E. This finding reaffirms the trade-off between stiffness and stretchability at the same dynamic crosslink density, as discussed in Fig. 3b–d. On the other hand, comparisons between the data with different values of x reveal different trends. The series with x = 20% is shifted to the upper right compared with that with x = 10%. This finding demonstrates that increasing the density of dynamic crosslinks increases the stiffness without compromising the stretchability, breaking the stiffness‒stretchability trade-off. A further increase in x to 30% causes the series to shift slightly to the lower right. Too many dynamic crosslinks make the material rigid but brittle, resulting in reduced stretchability. The stress at break (σb) against E for SBPy-Zn(x,y) and SBPy-S(z) is shown in Fig. 4b. For each series with the same x, E and σb are positively correlated: a higher modulus leads to a higher strength. With increasing x from 10% to 20%, σb drastically increases when compared at the same E. Figure 4c shows the toughness, which is the area under the stress‒strain curve, against E. Toughness depends on both stiffness and stretchability. As a result, the toughness of each series with the same x changes only slightly with y because of the conflicting effects of the increased modulus and reduced stretchability with increasing static crosslink density. In contrast, increasing x from 10% to 20% leads to a significant increase in toughness at the same E because dynamic crosslinking enhances both the stiffness and stretchability. This observation clearly demonstrates the breaking of the stiffness‒stretchability trade-off.

Fig. 4
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Tensile properties as a function of the Young’s modulus (E). a Strain at break (εb). b Stress at break (σb). c Toughness. The error bars represent the standard deviation of replicated tests (N = 3). The dashed lines serve as guides to the eye

Strain rate dependence of the tensile behavior

To gain a deeper understanding of the dynamic crosslinks in the network, we performed tensile tests at different strain rates ranging from 0.0104 s−1 to 1.04 s−1. All the stress‒strain curves are shown in Figs. S8−S10. The typical stress‒strain curve of SBPy-Zn(20,1) is shown in Fig. 5a. At a constant strain, the stress increases with increasing strain rate. Furthermore, as the strain increases, the changes in stress become more significant, which is a commonly observed trend in viscoelastic materials. All the samples showed qualitatively similar tendencies (Figs. S8−S10).

Fig. 5
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Strain rate dependence of the tensile behavior of the dual-crosslinked elastomer SBPy-Zn(x,y). a Stress‒strain curves of SBPy-Zn(20,1) at different strain rates. b Stress of SBPy-Zn(20,1) at selected strains plotted against the strain rate. The dashed lines indicate the power-law fitting results. Each series is vertically shifted by the indicated factor for the sake of legibility. c Strain rate dependence α as a function of strain for SBPy-Zn(20,y) with y = 1−4. d Strain rate dependence α at a strain of 200% plotted against the Young’s modulus measured at a strain rate of 0.104 s−1. The dashed lines serve as guides to the eye

We quantified the strain rate dependence by a simple method based on nonlinear viscoelasticity theory. This method was originally developed by Smith [47] and was applied to rubber materials [48, 49]. A detailed description of the theory can be found in our previous report [50]. Briefly, assuming time‒strain separability, the stress decay \(\sigma (t)\) after the application of step strain \({\varepsilon }_{0}\) can be written as a product of a time-dependent linear stress relaxation modulus \(E(t)\) and a strain-dependent damping function \(g(\varepsilon )\), i.e., \(\sigma (t)=E(t)g({\varepsilon }_{0}){\varepsilon }_{0}\). Additionally, assuming that \(E(t)\) decays as \(E(t)\propto {t}^{-\alpha }\) in the time scale of interest, for uniaxial tensile tests with a constant strain rate, the stress \(\sigma\) at a prescribed strain is expected to scale with the strain rate \(\dot{\varepsilon }\) as \(\sigma \propto {\dot{\varepsilon }}^{\alpha }\). The exponent α reflects the rate at which stress decays over time, which is correlated with the dynamicity of the polymer network. The α ranges from 0 for a perfect elastic body (no time dependence) to 1 for a perfect Newtonian fluid: real materials fall between these two extremes.

The double-logarithmic plot of stress at selected strains against strain rate is shown in Fig. 5b, with the data in Fig. 5a used as a representative example. The data points at each strain exhibit a linear relationship, from which α can be estimated. The α values for the remaining datasets were similarly estimated and are displayed in Figs. S8−S10. At high strain rates, slight deviations from linear scaling and saturation are observed for SBPy-Zn(10,y). The origin of this behavior is not fully understood at present; it might be due to more complex dynamics than those assumed in the current power-law analysis. The value of α as a function of strain for SBPy-Zn(20,y) at varying values of y is plotted in Fig. 5c. The value of α is greater at higher strain levels for all samples, suggesting that strain promotes the dissociation of dynamic bonds and makes the network structure more dynamic. The α decreases significantly and becomes less sensitive to the strain level with increasing heat cycle number y. Although the number of dynamic crosslinks in the unstretched state remains unchanged during the heating cycles (Fig. 2b), the introduction of static crosslinks reduces the dynamicity of the entire network structure at large strains. For a comprehensive comparison of the effects of static and dynamic crosslinking on the dynamicity, we extract the α value at 200% strain for each sample and plot it against E in Fig. 5d. When compared at the same modulus (i.e., the same total crosslink density), series with higher x (i.e., larger number of dynamic crosslinks) exhibit higher α. Overall, an increase in the number of dynamic crosslinks increases the dynamicity of the network structure.

Energy dissipation and recoverability

Dynamic crosslinks enable a network to dissipate energy upon deformation42. We performed single-cycle tensile tests to quantify the energy dissipation efficiency. In each test, a fresh test piece was stretched to a prescribed maximum strain and unloaded to zero strain at a fixed strain rate of 0.104 s−1. The typical stress‒strain curves of the cyclic tests with varying maximum strains for SBPy-Zn(20,2) are shown in Fig. 6a. The loading curves overlap well with each other, indicating that the measurements are consistent and reproducible across the samples. There is a large hysteresis during the loading and unloading processes, indicating energy dissipation due to disruption of the network structure during loading. With increasing maximum strain, the hysteresis becomes more significant. The results of single-cycle tests for all samples (SBPy-Zn(x,y) with x = 10−30% and y = 1−4) are presented in Figs. S11, S13, and S15. These data qualitatively follow the trend described in Fig. 6a.

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Effect of static and dynamic crosslinking on energy dissipation behavior. a Stress‒strain curves of cyclic tensile tests for SBPy-Zn(20,2) are shown as representative examples. b Hysteresis area (H) and c efficiency of energy dissipation (H/W) plotted against the work of loading (W) for SBPy-Zn(20,y) with y = 1−4 and various maximum applied strains. d H/W plotted against W for all samples and all maximum strains tested. The points for SBPy-Zn(20,y) are the same as those in (c). The dashed curves serve as guides to the eye

The key quantities of the cyclic test results were further analyzed. The work of loading (W), defined as the area under the loading curve, represents the work required to deform the sample to a given maximum strain. The hysteresis area (H), defined as the area between the loading and unloading curves, represents the energy dissipated during the cycle. The energy dissipation efficiency is defined as H/W, i.e., the ratio of the mechanical energy consumed in the cycle to the energy applied to stretch the sample.

The behavior of W, H, and H/W is first discussed for SBPy-Zn(20,y) (Figs. 6 and S14). W increases with increasing maximum strain and number of heat cycles (Fig. S14b). The relationship between H and W for SBPy-Zn(20,y) samples subjected to varying maximum strains and varying y values is shown in Fig. 6b. Interestingly, all the H data, irrespective of the number of heat cycles and applied maximum strain, decrease on a single master curve that monotonically increases with W. This observation indicates that the increase in the static crosslink density is equivalent to applying greater strain in terms of the effect on H. Figure 6c shows the energy dissipation efficiency (H/W) against W. All the SBPy-Zn(20,y) samples with different numbers of heat cycles and applied maximum strains fall on a single master curve again. H/W is initially relatively small when W approaches 0 and increases rapidly to reach a plateau at approximately 0.8. This behavior suggests that static crosslinks, as well as larger strains, help facilitate the reorganization of dynamic crosslink networks. Static crosslinking has a positive effect on the efficiency of energy dissipation. We hypothesize that a certain W is required to destroy dynamic crosslink networks sufficiently so that the energy is efficiently dissipated. The final value of H/W corresponds to the extent to which the dynamic bonds break during loading. Once this threshold is reached, further increasing the number of heat cycles or maximum strains has no effect on H/W. The samples with different dynamic crosslink densities (SBPy-Zn(x,y) with x = 10 and 30) showed qualitatively similar tendencies to those of SBPy-Zn(20,y) (Figs. S12 and S16).

We then investigated the effect of the dynamic crosslink density on energy dissipation. H/W for all the samples as a function of W is plotted in Fig. 6d. Points with the same x are plotted in the same color. As we have seen earlier in Fig. 6c, the data points with the same x value follow a single master curve. Compared with that at a fixed W, H/W decreases with increasing x. This suggests that a higher content of dynamic crosslinks results in a lower energy dissipation efficiency.

The ability of dynamic bonds to associate and dissociate enables a material to recover its structure after stretching [51]. To explore this behavior, successive cyclic tests were conducted with a waiting time between cycles. The sample was stretched to 200% strain, unloaded to zero strain, and held for a prescribed waiting time. This process was repeated 6 times with waiting times of 0, 1, 30, 60, 180 and 360 min. Figure 7a shows the cyclic stress‒strain curves for SBPy-Zn(20,2) as a representative example. The maximum stress and hysteresis area of the second cycle are significantly lower than those of the first cycle. As the waiting time between cycles increases, the maximum stress and the hysteresis area gradually recover and approach the values in the first cycle. This trend was qualitatively similar in all the samples (Figs. S17−S19). We use the hysteresis area as a measure of recoverability. Hn represents the hysteresis area of the nth cycle. Hn for SBPy-Zn(20,y) with y = 1−4 is shown in Fig. 7b. From the second cycle, Hn increases with increasing waiting time, suggesting a gradual recovery of the network structure. The samples recovered sufficiently after 60 min, as Hn almost plateaued after the 5th cycle. The results for the other x values are provided in Fig. S20.

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Fig. 7The alternative text for this image may have been generated using AI.
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a Stress‒strain curves of successive cyclic tests for SBPy-Zn(20,2). The waiting time before each cycle is indicated in the parentheses in the legend. b Hysteresis areas (Hn) and c recovery rates (Hn/H7) plotted against the number of tensile cycles (n) for SBPy-Zn(20,y) with y = 1−4. d Recovery ratio H7/H1 for SBPy-Zn(x,y) with x = 10−30% and y = 1−4 plotted as a function of the work of loading of the first cycle (W1). The dashed lines serve as guides to the eye

The rate of recovery for each sample was analyzed by plotting the Hn/H7 ratio (n = 2−7), as shown in Fig. 7c for SBPy-Zn(20,y) as representative data and in Fig. S21 for the other samples. No significant difference was observed in the recovery rate between the samples with different y values, suggesting similar recoveries of the coordination bond after stress removal. The maximum recoverability that a sample could attain was evaluated by taking the H7/H1 ratio. H1 and H7/H1 are plotted against E in Fig. S22. According to previous assumptions, E is proportional to the total crosslink density, including both static and dynamic crosslinks. At the same x, an increase in y results in a decrease in H7/H1, suggesting the irreversible rupture of static crosslinks during mechanical loading. H7/H1 is shown as a function of the work of loading of the first cycle (W1) in Fig. 7d. At the same x, an increase in y, which was equivalent to an increase in W1, led to a decrease in H7/H1. Denser static crosslinks led to higher stress and greater input energy in the loading process. While some of this large input energy is dissipated by the dissociation of dynamic crosslinks, irreversible damage to the covalent network structure occurs. During the recovery process after stress is released, the dissociated dynamic bonds reassociate randomly, rebuilding a network. When compared at a fixed W1, an increase in x significantly enhanced the recoverability (Fig. 7d). That is, at the same input energy level, more dynamic crosslinks lead to greater recoverability. These findings demonstrate the positive role of dynamic crosslinks in restoring network structure. While static crosslinks contribute to material stiffness, their irreversible nature limits their recoverability. In contrast, dynamic crosslinks facilitate network recovery, highlighting their complementary role.

The observations from the cyclic tensile tests are summarized as follows. At a constant dynamic crosslink density (constant x), both increasing the static crosslink density and applying larger strains can facilitate the reorganization of the dynamic crosslinks and increase the energy dissipation efficiency (Fig. 6c). Compared with loading W, dynamic crosslinking reduces the energy dissipation efficiency (Fig. 6d). At constant W1, the introduction of dynamic crosslinks leads to increased recoverability, whereas static crosslinks diminish it (Fig. 7d).

The energy dissipation and recoverability of the dual-crosslinked elastomers can be explained by the degree of breaking and restoration of the network structure, as shown in Fig. 8. First, we compared samples with the same dynamic crosslink density but different static crosslink densities (Fig. 8a, b). As shown in Fig. 7d, a higher W resulting from a higher static crosslink density imparts greater irreversible damage to the structure, resulting in greater H1 than that in the case of a lower static crosslink density. These findings are illustrated in the stress‒strain curves, as shown by the black curves in the rightmost part of Figure 8ab. Even after a sufficiently long waiting time, the structure remains unrecoverable because of the irreversible nature of the damage, resulting in a reduced Hn with a large n, as illustrated by the red curve in the same figure. Conversely, networks with fewer static crosslinks (Fig. 8b), which experience less W at the same applied strain because of lower apparent crosslink density, suffer less dynamic crosslink breakage. Consequently, minimal network rearrangement occurs during the cycle, resulting in a reduced H1 in the stress‒strain curve.

Fig. 8
Fig. 8The alternative text for this image may have been generated using AI.
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Schematic illustration of energy dissipation and recovery for the dual-crosslinked elastomer during cyclic deformation: a, b same x but different y; b, c same overall crosslink density; c more static crosslinks. The solid black line and dashed red line in the rightmost parts of the figure represent the stress‒strain curves of the first cycle and recovered cycle after a sufficiently long waiting time, respectively. The same level of strain is applied upon loading in all three cases

Next, dual-crosslinked elastomers with the same overall crosslink density but different ratios of static and dynamic crosslinks are compared (Fig. 8b, c). When subjected to applied strain, networks with higher static crosslink density (Fig. 8b) exhibit greater rupture of static crosslinks during deformation. The irreversible nature of static crosslinks causes a substantial decrease in the crosslink density after loading, resulting in large hysteresis, as illustrated by the schematic stress‒strain curve in Fig. 8b. These broken static crosslinks cannot reform, causing reduced hysteresis in subsequent cycles after a sufficient recovery time (red dashed curve). Networks dominated by dynamic crosslinks (Fig. 8c) exhibit different behaviors under stress. During stretching, fewer static crosslinks break, with dynamic crosslinks primarily dissociating. After the force is released, these dynamic networks can partially reassociate over time, leading to less network disruption; as a result, the hysteresis area and energy dissipation efficiency decrease. The reversible nature of dynamic crosslinking enables network recovery given sufficient time, leading to significantly greater material recoverability than that of static crosslink-dominated networks.

Before concluding, we comment on some limitations of the outcome of this study. First, the present study focused only on a particular metal–ligand pair. These results are affected by the characteristics of metal‒ligand coordination bonds, which depend on the choice of the metal and the ligand. Second, the roles of noncoordinated free pyridine groups may require further attention. As we have commented earlier, an excess amount of free pyridine can potentially influence the exchange kinetics of dynamic crosslinks [45]. While the mechanical properties are considered to be governed mainly by bond dissociation kinetics [52], experiments on samples with different numbers of ligands will be necessary to clarify this point.

Conclusion

We systematically investigated the mechanical properties of dual-crosslinked elastomers that had both dynamic and static crosslinks. Dynamic crosslinks were formed by the coordination of pyridine moieties in SBPy to the added Zn2+ ions, whereas static crosslinks could be introduced simply by subsequent heat treatments. Uniaxial tensile tests, including tests with varying strain rates and cyclic tests, clearly revealed the effects of the two crosslink types on the mechanical properties. More static crosslinks helped maintain the network structure under deformation, making the elastomer stiffer and more solid-like, whereas more dynamic crosslinks allowed the network structure to adapt dynamically and reversibly to external forces, leading to efficient dissipation of applied mechanical energy and subsequent recovery after unloading. These roles of static and dynamic crosslinking were in line with what has been hypothesized in previous studies: We successfully provided quantitative evidence of these roles. Furthermore, we demonstrated that the trade-off between stiffness and stretchability caused by static crosslink networks could be overcome by dynamic crosslinks, which increased both the stiffness and stretchability at the same time. Another striking discovery was that the energy dissipation efficiency depended on only two factors: the work of loading and the dynamic crosslink density. That is, at a constant dynamic crosslink density, the increase in the static crosslink density and the increase in the applied strain had an indistinguishable effect on the energy dissipation efficiency. The knowledge obtained with the model dual-crosslinked elastomer system with Zn2+-pyridine coordination bonds in this study will offer a rational pathway for materials with controlled toughness, strain rate dependence, and recoverability.