Designing network heterogeneity for anti-fatigue elastomers

doi:10.21203/rs.3.rs-4973429/v1

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Designing network heterogeneity for anti-fatigue elastomers

https://doi.org/10.21203/rs.3.rs-4973429/v1

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Polymer networks provide essential elasticity and strength for elastomers, yet the intrinsic fracture energy or fatigue threshold of regular networks has remained relatively low, around 50–100 J/m². In this study, we introduce the concept of an inhomogeneous network design to enhance the intrinsic fracture energy or fatigue threshold of single-network polymers. By utilizing catalysts with varying catalytic abilities, we create an inhomogeneous network consisting of both long and short strands. This network structure simultaneously improves the fracture toughness and fatigue threshold. Specifically, compared with regular networks, the inhomogeneous network achieves a remarkable fatigue threshold of approximately 1200 J/m². This substantial improvement is attributed to stress deconcentration and increased stored elastic energy from the long strands in the inhomogeneous network. This innovative approach is broadly applicable to soft matter systems, presenting opportunities to enhance the crack propagation resistance of polymer networks.

Physical sciences/Materials science/Soft materials/Polymers

Physical sciences/Materials science/Structural materials/Mechanical properties

Polymer networks, being molecular scaffolds for superior properties, are ubiquitous in both common and highly specialized applications.^1–3 However, polymers are susceptible to crack propagation under deformation, which affects the safety and longevity of these materials. Therefore, the enhancement of crack propagation resistance has been a focal topic in the field of advanced elastomers. The intrinsic fracture energy or fatigue threshold (Γ₀) characterizes a material’s resistance to crack propagation, below which crack propagation does not occur.⁴ Regular networks usually exhibit low Γ₀ values, typically around 50 J/m².⁵ This low Γ₀ of regular networks is understood according to the classical model of Lake and Thomas which postulates that the energy needed to break an individual strand is directly proportional to the number of Kuhn monomers of strands (Γ₀ ~ N, where N is the number of Kuhn monomers per strands).⁶ When networks break at the crack tip, the stored energy in strands is dissipated. Longer strands tend to store higher elastic energy, resulting in greater energy dissipation upon chain breakage. However, the crosslinking process usually lead to short chain strands with reduced stored elastic energy, thus weakening the material's resistance to crack propagation. As a consequence, enhancing the Γ₀ of networks has become a long-standing challenge.

In principle, improvements in the energy required to propagate a crack or an inherent flaw per newly created surface area can enhance the crack propagation resistance. Energy dissipation strategies have been proven to be effective to improve the crack propagation resistance under monotonic loads. Recently, sacrificial bond networks, such as prestretched networks in double-network hydrogels,^7–9 hydrogen bonds,¹⁰ and coordination bonds,¹¹ have been developed to dissipate a large amount of energy upon deformation, leading to improved crack-propagation resistance and higher facture toughness (G_c) under monotonic loads. However, due to the irreversible nature of energy dissipation from irreversible networks or the inability to promptly recover energy dissipation from reversible networks, such energy dissipation is usually exhausted under cyclic loads, rendering it ineffective for resisting fatigue crack propagation in subsequent loading cycles.^4,12,13 Therefore, it is clear that the energy, which is required to rupture a single layer of polymer strands, cannot be depleted under cyclic loads for the design of the crack propagation-resistant networks.

The stored elastic energy in strands, which is available under cyclic loads, contributes to crack propagation resistance. As the long strands have high elastic energy, Suo’s group pioneers a crack propagation-resistant strategy through constructing a network with long strands.^14–17 Thereby, they can achieve a balance between high modulus and Γ₀ in hydrogels through designing low water content and low crosslinker content, which forms long strands and dense entanglements.^18,19 However, for most industrial elastomers, such as natural rubber and synthetic elastomers, regular short strands, rather than entanglements or long strands, are dominating their mechanical performance. How to enable networks with regular short strands with superior crack propagation resistance still needs our further investigations.

Our research presents an innovative inhomogeneous network design that integrates short strands and long strands. This combination is engineered to increase the stored elastic energy from long strands and modulus from short strands, which in turn improves the crack propagation resistance under monotonic or cyclic loads. We select polyisoprene rubber (IR) as the soft matrix and employ catalysts with varying catalytic activities. Specifically, zinc diethyldithiocarbamate (ZDC), a catalyst with a high catalytic efficiency, is used to form short strands, while diphenylguanidine (D), a catalyst with a lower catalytic efficiency, is responsible for forming long strands. Through different catalytic activities from ZDC and D, the resulting crosslinked elastomers possess an inhomogeneous network with a broad range of strands from long strands to short strands. When the samples are stretched, the high elastic energy and entanglements from long strands improve crack propagation resistance. Our findings allow us to establish a clear correlation between the network structural characteristics and the resultant enhancement in both toughness and fatigue-resistant properties. Ultimately, this research provides an inhomogeneous network concept for the fabrication of more durable polymer-based systems.

Materials. Isoprene rubber (IR70) was purchased from FuShun Yikesi New Material Co., Ltd. ZDC (98%) and D (97%) were purchased from Aladdin. Zinc oxide (ZnO, 99%) was purchased from Adamas. Stearic acid (99%) was obtained from Macklin. Sulfur and N-Cyclohexyl-2-benzothiazoly lsulfenamide (CZ) were industrial grade.

Synthesis of Regular Networks. According to conventional crosslinking reactions of rubbers,²⁰ IR (100 g), sulfur (1.5 g), stearic acid (2 g), ZnO (5 g), and CZ (1.5 g) were blended on a two-roll mill. Once mixed, these compounds were subjected to compression at 145 ^oC to initiate the crosslinking reaction. The reaction duration was determined using a vulcameter.

Synthesis of Inhomogeneous Networks. Catalysts were crucial in facilitating crosslinking reactions to form networks in this study.²¹ Utilizing a combination of catalysts with varying catalytic efficiencies, researchers were able to manipulate the lengths of strands within a single soft matrix, resulting in the creation of heterogeneous networks. ZDC, known for its high catalytic capacity, was responsible for generating short strands, while D, with a lower catalytic capacity, contributed to the formation of long strands. The experimental setup involved mixing IR (100 g), sulfur (1.5 g), stearic acid (2 g), and ZnO (5 g) on an open mill with 1 mm roller space, along with different proportions of ZDC and D. A one-step radical reaction at 145°C facilitated crosslinking for all components, with the reaction time determined using a vulcameter. We denoted IR with ZDC and D as IR-ZDC-x-D-y, where x was the weight fraction of ZDC and y was the weight fraction of D. The IR-ZDC-2.5-D-0.5 contained IR (100 g), sulfur (1.5 g), stearic acid (2 g), ZnO (5 g), ZDC (2.5 g), and D (0.5 g). The IR-ZDC-2-D-1 contained IR (100 g), sulfur (1.5 g), stearic acid (2 g), ZnO (5 g), ZDC (2 g), and D (1 g). The IR-ZDC-1.5-D-1.5 contained IR (100 g), sulfur (1.5 g), stearic acid (2 g), ZnO (5 g), ZDC (1.5 g), and D (1.5 g).

Crosslinking Researches. According to the previous work,²² time dependence of torque curves for samples were analyzed at various temperatures by a GOTECH M-3000 AU vulcameter. We plotted curves of ln(M_H-M_t) versus t-t₀, where M_H was the maximum torque, M_t was the torque at vulcanization time t, and t₀ was the time for minimum torque. The reaction rate constant (k) was determined by fitting the following equation

$$\:{ln}\left({M}_{H}-{M}_{t}\right)=A-k{(t-{t}_{0})}^{\alpha\:}$$

where A was constant, k was reaction rate constant, and α was a modified coefficient. Through Arrhenius equation fitting, we obtained activation energy (E_a) of crosslinking reactions.

Network Structure Characterizations. The equilibrium swelling method was used to measure the molecular weight between crosslinks (M_c) in toluene solutions which characterized the crosslinking density of networks. IR and IR-ZDC-D samples were swollen in toluene at 25 ^oC for 7 days. After the removal of toluene on the surface of samples, the swollen IR and IR-ZDC-D samples were immediately weighed and dried in a vacuum oven at 80 ^oC until constant weight. We got M_c according to the following equation: $\:-{ln}\left(1-{}_{r}\right)-{}_{r}-{}_{r}{{}_{r}}^{2}=n{V}_{0}\left({}_{r}^{1/3}-\frac{1}{2}{}_{r}\right)$ and $\:{\:M}_{c}=\frac{}{{n}_{c}}$ (φ_r was the polymer volume fraction in the swollen network, V₀ was 106.2 mL/mol for toluene, χ_r was 0.393 for IR/toluene, n_c was the average number of movable chain segments per unit volume, and ρ was 0.94 g/mL for IR). To characterize the heterogeneity of networks, flow heat curves of cyclohexane-swollen samples were obtained by a TA Q250 differential scanning calorimeter (DSC) at a heating rate of 10 ^oC/min. From − 80 to 40 ^oC, DSC was also used to obtain glass transition temperature. According to the previous work,²³ a double-quantum nuclear magnetic resonance (DQ NMR, Bruker mq20) was used to investigate distributions of crosslinking density. DQ build-up curve (I_DQ) and a reference intensity decay curve (I_ref) were first obtained. Then we acquired the normalized DQ build-up (I_nDQ) function which can reach a relative amplitude of 0.5 in the long-time limit. Residual dipolar couplings (D_res) were directly related to crosslinking density and distributions of D_res can represent distributions of networks. We got distributions of D_res, according to the following equation: $\:{I}_{nDQ}\left({\tau\:}_{DQ}\right)=\int\:P\left(\text{ln}\left({D}_{res}\right)\right){I}_{nDQ}\left({\tau\:}_{DQ},{D}_{res}\right)d\text{ln}\left({D}_{res}\right)$, where τ_DQ was DQ evolution time.

Uniaxial Tensile Tests. The samples for uniaxial tensile tests were the dumbbell strip with 25 mm length, 6 mm width, and 1 mm thickness. A GOTECH AI-3000 mechanical instrument with an extension rate of 500 mm/min was operated to characterize stress-strain curves under room temperature.

Measurements of G_c. According to the classical single edge notch experiment,²⁴ fracture tests were performed using a GOTECH AI-3000 mechanical instrument at a strain rate of 6 mm/min under room temperature. A 1 mm notch was introduced at the center of a rectangular specimen, the dimension of which was 20 mm length, 5 mm width, and 1 mm thickness. The G_c is calculated by the following equation:$\:{G}_{c}=\frac{6Wc}{\sqrt{{\lambda\:}_{c}}}$, where c was the notch length, λ_c was the strain at break of notched samples, and W was the strain energy density.

Flaw Sensitivity Tests of Samples. To test the flaw sensitivity of IR and IR-ZDC-D samples, we fabricated samples with dimensions of 100 mm in length, 15 mm in width, and 1 mm in thickness. The precut notches had lengths of 1.5 mm, 2 mm, and 2.5 mm, respectively. Both unnotched and notched samples were subjected to testing on a testing machine at a loading rate of 500 mm/min.

Fatigue Resistance Experiments. Fatigue tests were conducted using an electro-dynamic mechanical test system (M-3000, CARE Measurement & Control Co., Ltd.). The samples had dimensions of 100 mm in length, 20 mm in width, and 1 mm in thickness. The precut notches had lengths of 20 mm. A camera was used to record changes in the crack length during fatigue processes.

Morphologies at the Crack Tip. A scanning electron microscope (SEM, Verios G4 UC, Thermo Fisher Technology Brno Co., Ltd.) was used to observe morphologies of fatigue fracture surface at the crack tip.

Digital Image Correlation (DIC). We applied black paint to the sample surfaces to create random speckles and then used the DIC system, XTDIC-CONST 12M, from XTOP 3D TECHNOLOGY (SHENZHEN) Co., Ltd., to measure the strain field distributions at the crack tips.

3.1. Design Strategies of Inhomogeneous Networks. Typical crosslinking generates short strands, while the use of two catalysts results in a combination of short and long strands, as illustrated in Fig. 1a. In this study, designing catalysts with different catalytic activities is crucial for creating heterogeneous networks. IR is selected as the soft matrix. The primary factor in forming crosslinked networks in rubber matrices is the sulfur ring-opening.^20,25–27 Zn²⁺ from ZnO withdraws electrons from sulfur, while nucleophiles provide electrons for sulfur, both contributing to the sulfur ring-opening, as illustrated in Figure S1.^28–30 In our study, ZDC and D are used as catalysts for crosslinking. Molecular structure analysis reveals that ZDC contains both nucleophiles and Zn²⁺, while D only contains nucleophiles (Fig. 1b). We denote IR with ZDC as IR-ZDC and IR with D as IR-D. To track the crosslinking process, we used a GOTECH M-3000 AU vulcameter to monitor the torque as a function of time.³¹Crosslinking enhances interactions among polymer chains, leading to the higher torque value of polymer matrixes. Torque versus time plots at various temperatures (Figure S2 and Figure S5), ln(MH-Mt) versus (t-t0) plots (Figure S3 and Figure S6), and fitting curves (Figure S4 and Figure S7) are obtained in Supporting Information. From these plots, the activation energy (Ea) of IR-ZDC is 85 kJ/mol and that of IR-D is 137 kJ/mol in Fig. 1b, revealing that ZDC exhibits higher catalytic activity than D. As a result, D with low catalytic activities leads to low crosslinking density (long strands) in IR-D and ZDC with high catalytic activities induces high crosslinking density (short strands) in IR-ZDC, as shown in Figure S8. These results suggest that using two catalysts, ZDC and D, creates an inhomogeneous network with both short and long strands.

To examine the features of inhomogeneous networks, we conduct DQ NMR and DSC analyses after crosslinking. DQ NMR has been proved to be an effective method to explore the structure of crosslinking networks.^27,32,33 D_res (residual dipolar couplings) is sensitive to topological constraints and closely related to the number of Kuhn segments. The molecular weight between crosslinks, abbreviated as M_c, can be estimated from D_res (D_res ~ M_c⁻¹). The normalized DQ curves of IR and IR-ZDC-D are shown in Figure S9 and Figure S10, respectively. The distribution curve of D_res, corresponding to the distribution of crosslinking density, is depicted in Fig. 1c. The D_res/2π distribution in Fig. 1c becomes wider with the use of two catalysts. Additionally, the results of thermoporosimetry are similar to those from DQ NMR. The melting behavior of the cyclohexane entrapped in networks can be used to characterize the heterogeneity of networks in Fig. 1d. The broad distribution of cyclohexane melting temperature corresponds to the broad distribution of crosslinking density.³⁴ The addition of two catalysts results in a wide melting peak distribution for IR-ZDC-D, indicating a broad distribution of crosslinking density. This broad distribution is ascribed to the combination of long strands and short strands within a single crosslinking network.

To investigate the effect of networks heterogeneities, rather than crosslinking density, on properties, this work designs all samples with the same average crosslinking density of approximately 7500 g/mol calculated by the equilibrium swelling method, as shown in Fig. 1e. In the case of the same average crosslinking density, all samples have the similar tensile strength in Fig. 1f and T_g in Figure S11. Compared to regular networks, the inhomogeneous networks exhibit longer the strain at break in Fig. 1f. The stretch limit of strands (λ_lim) is calculated as $\:{\lambda\:}_{lim}=\frac{Nb}{\sqrt{N}b}=\sqrt{N}$, where b is the length of each Kuhn monomer and N is the number of Kuhn monomers per strands. Long strands in inhomogeneous networks increase N, thus enlarging λ_lim of inhomogeneous networks. The presence of only one transition temperature in each DSC heat flow curve indicates that the formation of long strands and short strands does not lead to microphase separation. Long strands are expected to have low modulus, while short strands contribute to high modulus. In Fig. 1g, IR and IR-ZDC-D have the similar modulus, demonstrating that the modulus of samples is not compromised by long strands.

3.2. Flaw Insensitivity of Inhomogeneous Networks. The flaw sensitivity of networks is intricately linked to its crack propagation resistance.^35,36 This work investigates the flaw sensitivity of inhomogeneous networks by uniaxially stretching IR and IR-ZDC-D samples with various precut notch width in Fig. 2a and Fig. 2b. In this part, all tested samples have overall dimensions of 100 mm in length, 15 mm in width, and 1 mm in thickness. In Fig. 2a, IR samples exhibit susceptibility to the propagation of existing flaws. As the flaw length increases, the stress at rupture decreases significantly from 11.3 MPa to 6.6 MPa, as shown in Figure S12. Figure 2b reveals that IR-ZDC-D samples are flaw-insensitive. For IR-ZDC-D with inhomogeneous networks, the strength of notched samples is comparable with that of unnotched samples in Figure S13. The flaw sensitivity of materials is strongly correlated with the fractocohesive length (l_T) which is defined as the ratio of G_c to the work of fracture.^37,38 Such fractocohesive length can represent the stress transfer abilities of materials.^39,40 To obtain the l_T of IR and IR-ZDC-D samples, this work first measures the energy density of the unnotched samples stretched up to catastrophic failure (the work of fracture) and G_c. l_T data of IR and IR-ZDC-D samples are exhibited in Fig. 2c. The l_T of inhomogeneous networks (1.73 mm) is 1.7 times more than that of regular networks (1 mm).

Mooney-Rivlin equation are used to perform an in-depth analysis of stress-strain curves for investigating the changes in entanglements (details in Supporting Information),⁴¹ $\:\frac{\sigma\:}{\lambda\:-{\lambda\:}^{-2}}={E}_{c}+{E}_{e}f\left(\lambda\:\right)$, where σ is the engineering stress of materials, E_c represents the contribution from chemical crosslinking, and E_e is associated to physical topological constraints. Mooney-Rivlin curves of IR and IR-ZDC-D samples are shown in Figure S14-Figure S17 and then we further calculate E_e (the contribution from physical topological constraints). Compared with regular networks, inhomogeneous networks have much more long strands. Long strands are often accompanied by much more entanglements.⁴² Thus, inhomogeneous networks exhibit higher E_e than regular networks in Figure S18. More entanglements of inhomogeneous networks are beneficial for transmitting tensions upon stretching.^18,43–45

DIC techniques demonstrate the effective stress deconcentration of elastomers with long strands at the crack tip in Fig. 2d. For comparison, DIC techniques are also used to investigate the strain distribution of IR around crack tip. The apparent stress concentration phenomenon of IR appears at the crack tip. Therefore, compared with regular short strands, inhomogeneous networks are beneficial to transmitting tension. Such result is similar to the hydrogels with the unusually low amount of crosslinkers.^18,19,46 When encountering cracks, long strands contribute to the stress deconcentration, as illustrated in Fig. 2e.

Additionally, we examine the impact of long strands and short strands on the crack propagation behaviors. Typically, crack propagation is driven by the release of stored elastic energy. The energy release rate (G) is calculated from the stress-stretch curves of unnotched samples of first cycle according to $\:G=W\left(\lambda\:\right)·{H}_{0}$, where $\:W\left(\lambda\:\right)$ is the stored elastic energy and H₀ is the initial samples height. Under the G of approximately 800 J/m², a camera records the crack length of IR and IR -ZDC-D under cyclic loads in Fig. 3a and Fig. 3b. For IR, cracks propagate obviously with the increase in the number of cycles in Fig. 3a. For IR-ZDC-D, we hardly observe the crack propagation after 100000th cycle in Fig. 3b. Also, SEM is used to investigate the surface of fatigue fracture samples in Fig. 3c. The fatigue fracture surface of IR is smooth, while that of IR-ZDC-D is rough. This rough fracture surface is ascribed to superior stress transfer capabilities from long strands.

3.3. Tough and Fatigue-Resistant Inhomogeneous Networks. This part demonstrates that inhomogeneous networks hinder the crack propagation under monotonic loads or cyclic loads in Fig. 4. These inhomogeneous networks exhibit near-perfect elasticity in Fig. 4b. Stress-strain curves have negligible hysteresis, indicating the absence of sacrificial bonds in inhomogeneous networks. The near-perfect elasticity is ascribed to short strands in the matrix. For fatigue experiments on notched samples, a pre-crack is cut using a razor blade. During fatigue experiments, we obtain crack length (Δc) versus number of cycles (NC) in steady state and further get the crack propagation rate (dc/dNC) of samples by calculating the slope of plots of Δc versus NC, as shown in Figure S19-Figure S22. The G is obtained from stress-strain curves of unnotched samples when the cyclic loading reaches the steady state at the corresponding strain. Subsequently, dc/dNC versus G curves are plotted in Fig. 4a, allowing us to approximately determine Γ₀ below which the fatigue crack does not propagate under infinite cycles of loads. In Fig. 4c, the Γ₀ of IR (regular networks) is around 67 J/m², which is comparable to other elastomers such as chloroprene rubber, butadiene rubber, and polydimethylsiloxane.^47–49 In terms of the classical Lake-Thomas model,⁵ the energy required to fracture a single layer of strands per unit area is directly proportional to the monomer number of strands in polymer physics. Regular networks with short strands have low Γ₀. With the formation of long strands in inhomogeneous networks, the stored elastic energy in strands increases and the energy required to fracture strands also increases, improving the crack propagation resistance under monotonic or cyclic loads.

Consequently, our proposed inhomogeneous networks enhance the crack propagation resistance by reducing stress concentration and enhancing stored elastic energy, which is fundamentally different from energy dissipation toughening networks. When a crack propagates, a single layer of strands based on the Lake-Thomas model should be ruptured. Long strands in inhomogeneous networks can effectively deconcentrate the stress around the crack tip and provide more elastic energy for the matrix, contributing to the crack propagation resistance. The ability to resist the crack propagation under monotonic loads is characterized by G_c and the ability to resist the crack propagation under cyclic loads is characterized by Γ₀.⁵⁰ In Fig. 4c and Fig. 4d, both G_c and Γ₀ increase with the formation of inhomogeneous networks. It is worth noting that IR-ZDC-D has achieved a high threshold of 1200 J/m², one order of magnitude higher than existing elastomers in Fig. 4e. The concept of inhomogeneous networks is generic to soft matter systems. In fact, the present applied crosslinked elastomers typically feature a single crosslinking network, such as natural rubber and synthetic elastomers. Through the regulation of long strands and short strands, single crosslinking networks become crack propagation-resistant structure under external loads, which is widely applicable to network designs for various applications.

Figure 4. Tough and fatigue-resistant inhomogeneous networks. (a) dc/dNC versus G curves of IR and IR-ZDC-D samples. (b) Cyclic stress-stretch curves for IR-ZDC-D with no precut cracks. (c) Γ₀ of IR and IR-ZDC-D samples. (d) G_c of IR and IR-ZDC-D samples. (e) Γ₀ of various elastomers. Elastomers with inhomogeneous networks in the current work are compared with other elastomers, such as regular elastomers by single network design,^{5,17,18,51–53} double elastomers,^54,55 and reinforced elastomers.^56–58

This work designs an inhomogeneous network to enhance the crack propagation resistance. By using catalysts with varying catalytic abilities, we create an inhomogeneous network composed of both long and short strands. Under monotonic loads and cyclic loads, mechanical properties are investigated. Experimental results show that inhomogeneous networks enhance both toughness and fatigue threshold, achieving a notable fatigue threshold of 1200 J/m². These improvements in the crack propagation resistance are ascribed to stress deconcentration and improved stored elastic energy from inhomogeneous networks. This study presents a straightforward, general construction strategy for inhomogeneous networks that can be applied to other elastomers.

ACKNOWLEDGEMENTS

This work was supported by National Natural Science Foundation of China (Grant No. 52173058 and Grant No. 52363007).

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Designing network heterogeneity for anti-fatigue elastomers

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