Designing network heterogeneity for anti-fatigue elastomers

Designing network heterogeneity for anti-fatigue elastomers | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Designing network heterogeneity for anti-fatigue elastomers Ming-Chao Luo, Yu Zhou, Hao-Jia Guo, Junqi Zhang, Lingmin Kong, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4973429/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract 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 Figures Figure 1 Figure 2 Figure 3 Figure 4 1. INTRODUCTION 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 ( Γ 0 ) characterizes a material’s resistance to crack propagation, below which crack propagation does not occur. 4 Regular networks usually exhibit low Γ 0 values, typically around 50 J/m 2 . 5 This low Γ 0 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 ( Γ 0 ~ 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 Γ 0 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 Γ 0 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. 2. EXPERIMENTAL SECTION 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 o C 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 - t 0 , where M H was the maximum torque, M t was the torque at vulcanization time t , and t 0 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 o C 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 o C 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, V 0 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 o C/min. From − 80 to 40 o C, 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. RESULTS AND DISCUSSION 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. 1 a. 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 Zn 2+ 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 Zn 2+ , while D only contains nucleophiles (Fig. 1 b). 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. 31 Crosslinking 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. 1 b, 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 re s (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. 1 c. The D re s /2π distribution in Fig. 1 c 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. 1 d. 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. 1 e. In the case of the same average crosslinking density, all samples have the similar tensile strength in Fig. 1 f and T g in Figure S11 . Compared to regular networks, the inhomogeneous networks exhibit longer the strain at break in Fig. 1 f. 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. 1 g, 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. 2 a and Fig. 2 b. 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. 2 a, 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 2 b 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. 2 c. 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. 2 d. 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. 2 e. 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 H 0 is the initial samples height. Under the G of approximately 800 J/m 2 , a camera records the crack length of IR and IR -ZDC-D under cyclic loads in Fig. 3 a and Fig. 3 b. For IR, cracks propagate obviously with the increase in the number of cycles in Fig. 3 a. For IR-ZDC-D, we hardly observe the crack propagation after 100000th cycle in Fig. 3 b. Also, SEM is used to investigate the surface of fatigue fracture samples in Fig. 3 c. 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 (d c /d NC ) 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, d c /d NC versus G curves are plotted in Fig. 4a , allowing us to approximately determine Γ 0 below which the fatigue crack does not propagate under infinite cycles of loads. In Fig. 4c , the Γ 0 of IR (regular networks) is around 67 J/m 2 , 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 Γ 0 . 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 Γ 0 . 50 In Fig. 4c and Fig. 4d , both G c and Γ 0 increase with the formation of inhomogeneous networks. It is worth noting that IR-ZDC-D has achieved a high threshold of 1200 J/m 2 , 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) d c /d NC versus G curves of IR and IR-ZDC-D samples. (b) Cyclic stress-stretch curves for IR-ZDC-D with no precut cracks. (c) Γ 0 of IR and IR-ZDC-D samples. (d) G c of IR and IR-ZDC-D samples. (e) Γ 0 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 4. CONCLUSIONS 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/m 2 . 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. Declarations ACKNOWLEDGEMENTS This work was supported by National Natural Science Foundation of China (Grant No. 52173058 and Grant No. 52363007). 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Macromolecules 47:5815–5824 Long R, Hui C-Y, Gong JP, Bouchbinder E (2021) The Fracture of Highly Deformable Soft Materials: A Tale of Two Length Scales. Annu Rev Condens Matter Phys 12:71–94 Zhou Y, Hu J, Zhao P, Zhang W, Suo Z, Lu T (2021) Flaw-Sensitivity of a Tough Hydrogel under Monotonic and Cyclic Loads. J Mech Phys Solids 153:104483–104495 Yang C, Yin T, Suo Z (2019) Polyacrylamide Hydrogels. I. Network Imperfection. J Mech Phys Solids 131:43–55 Chen C, Wang Z, Suo Z (2017) Flaw Sensitivity of Highly Stretchable Materials. Extreme Mech Lett 10:50–57 Zeng L, Liu F, Yu Q, Jin C, Yang J, Suo Z, Tang J (2023) Flaw-Insensitive Fatigue Resistance of Chemically Fixed Collagenous Soft Tissues. Sci Adv 9:eade7375 Li X, Gong JP (2022) Role of Dynamic Bonds on Fatigue Threshold of Tough Hydrogels. Proc. Natl. Acad. Sci. U.S.A. 119 , e2200678119 Heinrich G, Vilgis TA (1993) Contribution of entanglements to the mechanical properties of carbon black-filled polymer networks. Macromolecules 26:1109–1119 Zhong D, Wang Z, Xu J, Liu J, Xiao R, Qu S, Yang W (2024) A Strategy for Tough and Fatigue-Resistant Hydrogels via Loose Cross-Linking and Dense Dehydration-Induced Entanglements. Nat Commun 15:5896 Zeng X, Xu L, Xia X, Bai X, Zhong C, Fan J, Ren L, Sun R, Zeng X (2023) The Synergy of Hydrogen Bond and Entanglement of Elastomer Captures Unprecedented Flaw Insensitivity Rate. Small 19:2207409 Wang Z, Yang F, Liu X, Han X, Li X, Huyan C, Liu D, Chen F (2024) Hydrogen Bonds-Pinned Entanglement Blunting the Interfacial Crack of Hydrogel–Elastomer Hybrids. Adv Mater 36:2313177 Zheng D, Lin S, Ni J, Zhao X (2022) Fracture and Fatigue of Entangled and Unentangled Polymer Networks. Extreme Mech Lett 51:101608–101617 Ma J, Zhang X, Yin D, Cai Y, Shen Z, Sheng Z, Bai J, Qu S, Zhu S, Jia Z (2024) Designing Ultratough Single-Network Hydrogels with Centimeter-Scale Fractocohesive Lengths via Inelastic Crack Blunting. Adv Mater 36:2311795 Yanyo LC (1989) Effect of Crosslink Type on the Fracture of Natural Rubber Vulcanizates. Int J Fract 39:103–110 Lake GJ, Lindley PB (1965) The Mechanical Fatigue Limit for Rubber. J Appl Polym Sci 9:1233–1251 Gent AN, Tobias RH (1982) Threshold Tear Strength of Elastomers. J Polym Sci Polym Phys Ed 20:2051–2058 Xiang C, Wang Z, Yang C, Yao X, Wang Y, Suo Z (2020) Stretchable and Fatigue-Resistant Materials. Mater Today 34:7–16 Liu B, Yin T, Zhu J, Zhao D, Yu H, Qu S, Yang W (2023) Tough and Fatigue-Resistant Polymer Networks by Crack Tip Softening. Proc. Natl. Acad. Sci. U.S.A 120 , e2217781120 Li P, Gu B, Wang F, Zhang J, Li X, Han D, Liu L, Li F (2024) Self-Heating and Fatigue Crack Growth Behavior of Reinforced NR/BR Nanocomposites with Different Blending Ratio. Int J Fatigue 183:108238–108249 Yin T, Wu T, Liu J, Qu S, Yang W (2021) Essential Work of Fracture of Soft Elastomers. J Mech Phys Solids 156:104616–104626 Sanoja GE, Morelle XP, Comtet J, Yeh CJ, Ciccotti M, Creton C (2021) Why is Mechanical Fatigue Different from Toughness in Elastomers? The Role of Damage by Polymer Chain Scission. Sci Adv 7:eabg9410 Zheng Y, Kiyama R, Matsuda T, Cui K, Li X, Cui W, Guo Y, Nakajima T, Kurokawa T, Gong JP (2021) Nanophase Separation in Immiscible Double Network Elastomers Induces Synergetic Strengthening, Toughening, and Fatigue Resistance. Chem Mater 33:3321–3334 Li C, Yang H, Suo Z, Tang J (2020) Fatigue-Resistant Elastomers. J Mech Phys Solids 134:103751–103762 Steck J, Kim J, Kutsovsky Y, Suo Z (2023) Multiscale Stress Deconcentration Amplifies Fatigue Resistance of Rubber. Nature 624:303–308 Chen Z, Zhang G, Luo Y, Suo Z (2024) Rubber-Glass Nanocomposites Fabricated Using Mixed Emulsions. Proc. Natl. Acad. Sci. U.S.A 121 , e2322684121 Additional Declarations There is NO Competing Interest. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4973429","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":348442674,"identity":"f3bed6fb-65b1-4eac-ada7-e9e7eb288e07","order_by":0,"name":"Ming-Chao Luo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2ElEQVRIiWNgGAWjYFACHsYDDAw2CQzMMIEDhLWA1KSRruVwAkKAkBbd9rMHDvNUnM/jb+c9+LmwjUGO70YC4+cCPFrMzuQlHOY5c7tY4jBfsvTMNgZjyRsJzNIz8Gm5wWNwmLftdmLDYR4Dad42hsQNNxLYmHkIazmXOP8wj/FvoJZ6YrUcSNxwmMcMZEuCAUEtZ3IMDs45k5y4EajFmuechOHMMw+bpfFqOX7G8MGbCrvEeefPGN/mKbOR5zuefPAzPi3oQAKIGRtI0DAKRsEoGAWjABsAAJQBTIjK2lGPAAAAAElFTkSuQmCC","orcid":"","institution":"Hainan University","correspondingAuthor":true,"prefix":"","firstName":"Ming-Chao","middleName":"","lastName":"Luo","suffix":""},{"id":348442675,"identity":"57fef779-b382-49a8-9530-9065252f6859","order_by":1,"name":"Yu Zhou","email":"","orcid":"","institution":"Hainan University","correspondingAuthor":false,"prefix":"","firstName":"Yu","middleName":"","lastName":"Zhou","suffix":""},{"id":348442676,"identity":"27341d26-20e3-4942-bd32-eb799d7a90ac","order_by":2,"name":"Hao-Jia Guo","email":"","orcid":"","institution":"Hainan University","correspondingAuthor":false,"prefix":"","firstName":"Hao-Jia","middleName":"","lastName":"Guo","suffix":""},{"id":348442677,"identity":"cefe8955-2d64-4f33-9d2f-9ff2e6b909bb","order_by":3,"name":"Junqi Zhang","email":"","orcid":"","institution":"Sichuan University","correspondingAuthor":false,"prefix":"","firstName":"Junqi","middleName":"","lastName":"Zhang","suffix":""},{"id":348442678,"identity":"53448e10-9c6d-43a9-b5ac-57e65e56a026","order_by":4,"name":"Lingmin Kong","email":"","orcid":"","institution":"Sichuan University","correspondingAuthor":false,"prefix":"","firstName":"Lingmin","middleName":"","lastName":"Kong","suffix":""},{"id":348442679,"identity":"d7da6c35-b887-4977-b634-162ca6229d81","order_by":5,"name":"Shuangquan Liao","email":"","orcid":"","institution":"Hainan University","correspondingAuthor":false,"prefix":"","firstName":"Shuangquan","middleName":"","lastName":"Liao","suffix":""},{"id":348442680,"identity":"825222f0-59f0-4a5c-a6a0-b80f159bcaf8","order_by":6,"name":"Jinrong Wu","email":"","orcid":"https://orcid.org/0000-0002-5329-5522","institution":"Sichuan University","correspondingAuthor":false,"prefix":"","firstName":"Jinrong","middleName":"","lastName":"Wu","suffix":""}],"badges":[],"createdAt":"2024-08-25 15:40:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4973429/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4973429/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":63966979,"identity":"d594a502-a2f3-4932-80a3-16df7dc7b4a9","added_by":"auto","created_at":"2024-09-04 09:55:53","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":167209,"visible":true,"origin":"","legend":"\u003cp\u003eDesign strategies for heterogeneous networks incorporating both short and long strands. (a) Schematic depiction of network structure resulting from a single catalyst versus two catalysts. Utilizing two catalysts yields a broad distribution of chain lengths, ranging from long coiled strands to comparatively short strands, whereas a single catalyst results in exclusively short strands. (b) Molecular structure of ZDC and D, and their influence on the crosslinking \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e. (c) \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ere\u003c/em\u003e\u003c/sub\u003e\u003csub\u003es\u003c/sub\u003e/2π distributions of IR and IR-ZDC-D. (d) Melting peaks of the cyclohexane entrapped in the network for IR and IR-ZDC-D. (e) Crosslinking density of IR and IR-ZDC-D. At the same crosslinking density, ZDC and D are employed to modulate long and short strands for subsequent studies. (f) Stress-strain curves of IR and IR-ZDC-D samples. (g) Elastic modulus of IR and IR-ZDC -D samples.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-4973429/v1/93b53034045c2af978dcc173.png"},{"id":63967601,"identity":"4f801072-0108-49d4-8f69-edea7a2cf04d","added_by":"auto","created_at":"2024-09-04 10:03:55","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":5912205,"visible":true,"origin":"","legend":"\u003cp\u003eStress deconcentration capabilities. (a) Stress-strain curves of IR with varying notch length, indicating that IR is sensitive to flaws. (b) Stress-strain curves of IR-ZDC-D with varying notch length, indicating that IR-ZDC-D is insensitive to flaws. (c) The \u003cem\u003el\u003c/em\u003e\u003csub\u003e\u003cem\u003eT\u003c/em\u003e\u003c/sub\u003e of IR and IR-ZDC-D samples. (d) DIC images of regular networks (IR) and inhomogeneous networks (IR-ZDC-D) for comparison. The scale bar from purple to red indicates that the stress concentration varies from low to high. (e) Illustration of stress deconcentration by long strands. When inhomogeneous networks are stretched, entanglements readily slip and enable tension to transmit in strands along their length.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-4973429/v1/6d5847ccdf47b8dcefe69c83.png"},{"id":63966982,"identity":"6f389c88-ac0b-4d95-974e-fc6dc348eb31","added_by":"auto","created_at":"2024-09-04 09:55:53","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":4785542,"visible":true,"origin":"","legend":"\u003cp\u003eCrack propagation behaviors of IR and IR-ZDC-D samples. (a) Snapshots show the crack propagation of IR during fatigue tests. (b) Snapshots show the crack propagation of IR-ZDC-D during fatigue tests. (c) SEM show photographs of IR and IR-ZDC-D. The above all experiments of precut samples are operated at various numbers of cycles under the \u003cem\u003eG\u003c/em\u003e of about 800 J/m\u003csup\u003e2\u003c/sup\u003e.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-4973429/v1/a393cb06db6ce742e2d9665a.png"},{"id":63967595,"identity":"1dbec354-fe7f-4c7c-bbd7-a916e545d823","added_by":"auto","created_at":"2024-09-04 10:03:53","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":97400,"visible":true,"origin":"","legend":"\u003cp\u003eTough and fatigue-resistant inhomogeneous networks. (a) d\u003cem\u003ec\u003c/em\u003e/d\u003cem\u003eNC\u003c/em\u003e versus \u003cem\u003eG\u003c/em\u003e curves of IR and IR-ZDC-D samples. (b) Cyclic stress-stretch curves for IR-ZDC-D with no precut cracks. (c) \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e of IR and IR-ZDC-D samples. (d) \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e of IR and IR-ZDC-D samples. (e) \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e of various elastomers. Elastomers with inhomogeneous networks in the current work are compared with other elastomers, such as regular elastomers by single network design,\u003csup\u003e5,17,18,51-53\u003c/sup\u003e double elastomers,\u003csup\u003e54,55\u003c/sup\u003e and reinforced elastomers.\u003csup\u003e56-58\u003c/sup\u003e\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-4973429/v1/a734fc9e429f7e02fa50b54d.png"},{"id":66157080,"identity":"d95e0594-15ba-452b-8e4d-e12a04291050","added_by":"auto","created_at":"2024-10-08 08:44:25","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":11968498,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4973429/v1/2b0579a9-c1bd-4b26-90ff-a8b5a67b92e5.pdf"},{"id":63966983,"identity":"4a29f8c8-dad2-4c14-bb7a-a8a12143085a","added_by":"auto","created_at":"2024-09-04 09:55:53","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":943391,"visible":true,"origin":"","legend":"","description":"","filename":"SI.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4973429/v1/36d28c2dad43e803c846ea4e.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Designing network heterogeneity for anti-fatigue elastomers","fulltext":[{"header":"1. INTRODUCTION","content":"\u003cp\u003ePolymer networks, being molecular scaffolds for superior properties, are ubiquitous in both common and highly specialized applications.\u003csup\u003e\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e 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 (\u003cem\u003eΓ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e) characterizes a material\u0026rsquo;s resistance to crack propagation, below which crack propagation does not occur.\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e Regular networks usually exhibit low \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e values, typically around 50 J/m\u003csup\u003e2\u003c/sup\u003e.\u003csup\u003e5\u003c/sup\u003e This low \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e 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 (\u003cem\u003eΓ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;~\u0026thinsp;\u003cem\u003eN\u003c/em\u003e, where \u003cem\u003eN\u003c/em\u003e is the number of Kuhn monomers per strands).\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e 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 \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e of networks has become a long-standing challenge.\u003c/p\u003e\u003cp\u003eIn 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,\u003csup\u003e\u003cspan additionalcitationids=\"CR8\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e hydrogen bonds,\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e and coordination bonds,\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e have been developed to dissipate a large amount of energy upon deformation, leading to improved crack-propagation resistance and higher facture toughness (\u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e) 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.\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e 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.\u003c/p\u003e\u003cp\u003eThe 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\u0026rsquo;s group pioneers a crack propagation-resistant strategy through constructing a network with long strands.\u003csup\u003e\u003cspan additionalcitationids=\"CR15 CR16\" citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e Thereby, they can achieve a balance between high modulus and \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e in hydrogels through designing low water content and low crosslinker content, which forms long strands and dense entanglements.\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e,\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e 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.\u003c/p\u003e\u003cp\u003eOur 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.\u003c/p\u003e"},{"header":"2. EXPERIMENTAL SECTION","content":"\u003cp\u003e \u003cb\u003eMaterials.\u003c/b\u003e 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 \u003cem\u003eN\u003c/em\u003e-Cyclohexyl-2-benzothiazoly lsulfenamide (CZ) were industrial grade.\u003c/p\u003e \u003cp\u003e \u003cb\u003eSynthesis of Regular Networks.\u003c/b\u003e According to conventional crosslinking reactions of rubbers,\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e 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 \u003csup\u003eo\u003c/sup\u003eC to initiate the crosslinking reaction. The reaction duration was determined using a vulcameter.\u003c/p\u003e \u003cp\u003e \u003cb\u003eSynthesis of Inhomogeneous Networks.\u003c/b\u003e Catalysts were crucial in facilitating crosslinking reactions to form networks in this study.\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e 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\u0026deg;C facilitated crosslinking for all components, with the reaction time determined using a vulcameter. We denoted IR with ZDC and D as IR-ZDC-\u003cem\u003ex\u003c/em\u003e-D-\u003cem\u003ey\u003c/em\u003e, where \u003cem\u003ex\u003c/em\u003e was the weight fraction of ZDC and \u003cem\u003ey\u003c/em\u003e 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).\u003c/p\u003e \u003cp\u003e \u003cb\u003eCrosslinking Researches.\u003c/b\u003e According to the previous work,\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e time dependence of torque curves for samples were analyzed at various temperatures by a GOTECH M-3000 AU vulcameter. We plotted curves of ln(\u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e-\u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e) versus \u003cem\u003et\u003c/em\u003e-\u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e, where \u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e was the maximum torque, \u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e was the torque at vulcanization time \u003cem\u003et\u003c/em\u003e, and \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e was the time for minimum torque. The reaction rate constant (\u003cem\u003ek\u003c/em\u003e) was determined by fitting the following equation\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{ln}\\left({M}_{H}-{M}_{t}\\right)=A-k{(t-{t}_{0})}^{\\alpha\\:}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eA\u003c/em\u003e was constant, \u003cem\u003ek\u003c/em\u003e was reaction rate constant, and \u003cem\u003eα\u003c/em\u003e was a modified coefficient. Through Arrhenius equation fitting, we obtained activation energy (\u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e) of crosslinking reactions.\u003c/p\u003e \u003cp\u003e \u003cb\u003eNetwork Structure Characterizations.\u003c/b\u003e The equilibrium swelling method was used to measure the molecular weight between crosslinks (\u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e) in toluene solutions which characterized the crosslinking density of networks. IR and IR-ZDC-D samples were swollen in toluene at 25 \u003csup\u003eo\u003c/sup\u003eC 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 \u003csup\u003eo\u003c/sup\u003eC until constant weight. We got \u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e according to the following equation: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:-{ln}\\left(1-{}_{r}\\right)-{}_{r}-{}_{r}{{}_{r}}^{2}=n{V}_{0}\\left({}_{r}^{1/3}-\\frac{1}{2}{}_{r}\\right)\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\:M}_{c}=\\frac{}{{n}_{c}}\\)\u003c/span\u003e\u003c/span\u003e (\u003cem\u003eφ\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e was the polymer volume fraction in the swollen network, \u003cem\u003eV\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e was 106.2 mL/mol for toluene, \u003cem\u003eχ\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e was 0.393 for IR/toluene, \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e was the average number of movable chain segments per unit volume, and \u003cem\u003eρ\u003c/em\u003e 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 \u003csup\u003eo\u003c/sup\u003eC/min. From \u0026minus;\u0026thinsp;80 to 40 \u003csup\u003eo\u003c/sup\u003eC, DSC was also used to obtain glass transition temperature. According to the previous work,\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e a double-quantum nuclear magnetic resonance (DQ NMR, Bruker mq20) was used to investigate distributions of crosslinking density. DQ build-up curve (\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003eDQ\u003c/em\u003e\u003c/sub\u003e) and a reference intensity decay curve (\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003eref\u003c/em\u003e\u003c/sub\u003e) were first obtained. Then we acquired the normalized DQ build-up (\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003enDQ\u003c/em\u003e\u003c/sub\u003e) function which can reach a relative amplitude of 0.5 in the long-time limit. Residual dipolar couplings (\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003eres\u003c/em\u003e\u003c/sub\u003e) were directly related to crosslinking density and distributions of \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003eres\u003c/em\u003e\u003c/sub\u003e can represent distributions of networks. We got distributions of \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003eres\u003c/em\u003e\u003c/sub\u003e, according to the following equation: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{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)\\)\u003c/span\u003e\u003c/span\u003e, where \u003cem\u003eτ\u003c/em\u003e\u003csub\u003e\u003cem\u003eDQ\u003c/em\u003e\u003c/sub\u003e was DQ evolution time.\u003c/p\u003e \u003cp\u003e \u003cb\u003eUniaxial Tensile Tests.\u003c/b\u003e 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.\u003c/p\u003e \u003cp\u003e \u003cb\u003eMeasurements of\u003c/b\u003e \u003cb\u003eG\u003c/b\u003e\u003csub\u003e\u003cb\u003ec\u003c/b\u003e\u003c/sub\u003e. According to the classical single edge notch experiment,\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e 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 \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e is calculated by the following equation:\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{G}_{c}=\\frac{6Wc}{\\sqrt{{\\lambda\\:}_{c}}}\\)\u003c/span\u003e\u003c/span\u003e, where \u003cem\u003ec\u003c/em\u003e was the notch length, \u003cem\u003eλ\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e was the strain at break of notched samples, and \u003cem\u003eW\u003c/em\u003e was the strain energy density.\u003c/p\u003e \u003cp\u003e \u003cb\u003eFlaw Sensitivity Tests of Samples.\u003c/b\u003e 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.\u003c/p\u003e \u003cp\u003e \u003cb\u003eFatigue Resistance Experiments.\u003c/b\u003e Fatigue tests were conducted using an electro-dynamic mechanical test system (M-3000, CARE Measurement \u0026amp; 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.\u003c/p\u003e \u003cp\u003e \u003cb\u003eMorphologies at the Crack Tip.\u003c/b\u003e 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.\u003c/p\u003e \u003cp\u003e \u003cb\u003eDigital Image Correlation (DIC).\u003c/b\u003e 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.\u003c/p\u003e"},{"header":"3. RESULTS AND DISCUSSION","content":"\u003cp\u003e \u003cb\u003e3.1. Design Strategies of Inhomogeneous Networks.\u003c/b\u003e Typical crosslinking generates short strands, while the use of two catalysts results in a combination of short and long strands, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea. 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.\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan additionalcitationids=\"CR26\" citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e Zn\u003csup\u003e2+\u003c/sup\u003e from ZnO withdraws electrons from sulfur, while nucleophiles provide electrons for sulfur, both contributing to the sulfur ring-opening, as illustrated in \u003cb\u003eFigure \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e\u003c/b\u003e.\u003csup\u003e\u003cspan additionalcitationids=\"CR29\" citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e In our study, ZDC and D are used as catalysts for crosslinking. Molecular structure analysis reveals that ZDC contains both nucleophiles and Zn\u003csup\u003e2+\u003c/sup\u003e, while D only contains nucleophiles (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb). 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.\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003eCrosslinking enhances interactions among polymer chains, leading to the higher torque value of polymer matrixes. Torque \u003cem\u003eversus\u003c/em\u003e time plots at various temperatures (\u003cb\u003eFigure S2\u003c/b\u003e and \u003cb\u003eFigure S5\u003c/b\u003e), ln(\u003cem\u003eMH\u003c/em\u003e-\u003cem\u003eMt\u003c/em\u003e) \u003cem\u003eversus\u003c/em\u003e (\u003cem\u003et\u003c/em\u003e-\u003cem\u003et0\u003c/em\u003e) plots (\u003cb\u003eFigure S3\u003c/b\u003e and \u003cb\u003eFigure S6\u003c/b\u003e), and fitting curves (\u003cb\u003eFigure S4\u003c/b\u003e and \u003cb\u003eFigure S7\u003c/b\u003e) are obtained in Supporting Information. From these plots, the activation energy (\u003cem\u003eEa\u003c/em\u003e) of IR-ZDC is 85 kJ/mol and that of IR-D is 137 kJ/mol in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb, 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 \u003cb\u003eFigure S8\u003c/b\u003e. These results suggest that using two catalysts, ZDC and D, creates an inhomogeneous network with both short and long strands.\u003c/p\u003e \u003cp\u003eTo 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.\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e,\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e,\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ere\u003c/em\u003es\u003c/sub\u003e (residual dipolar couplings) is sensitive to topological constraints and closely related to the number of Kuhn segments. The molecular weight between crosslinks, abbreviated as \u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e, can be estimated from \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003eres\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003eres\u003c/em\u003e\u003c/sub\u003e ~ \u003cem\u003eM\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e\u003csup\u003e\u003cem\u003e\u0026minus;1\u003c/em\u003e\u003c/sup\u003e). The normalized DQ curves of IR and IR-ZDC-D are shown in \u003cb\u003eFigure S9\u003c/b\u003e and \u003cb\u003eFigure S10\u003c/b\u003e, respectively. The distribution curve of \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003eres\u003c/em\u003e\u003c/sub\u003e, corresponding to the distribution of crosslinking density, is depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec. The \u003cem\u003eD\u003c/em\u003e\u003csub\u003e\u003cem\u003ere\u003c/em\u003es\u003c/sub\u003e/2π distribution in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec 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.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed. The broad distribution of cyclohexane melting temperature corresponds to the broad distribution of crosslinking density.\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e 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.\u003c/p\u003e \u003cp\u003eTo 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.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee. In the case of the same average crosslinking density, all samples have the similar tensile strength in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ef and \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e in \u003cb\u003eFigure S11\u003c/b\u003e. Compared to regular networks, the inhomogeneous networks exhibit longer the strain at break in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ef. The stretch limit of strands (\u003cem\u003eλ\u003c/em\u003e\u003csub\u003e\u003cem\u003elim\u003c/em\u003e\u003c/sub\u003e) is calculated as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\lambda\\:}_{lim}=\\frac{Nb}{\\sqrt{N}b}=\\sqrt{N}\\)\u003c/span\u003e\u003c/span\u003e, where \u003cem\u003eb\u003c/em\u003e is the length of each Kuhn monomer and \u003cem\u003eN\u003c/em\u003e is the number of Kuhn monomers per strands. Long strands in inhomogeneous networks increase \u003cem\u003eN\u003c/em\u003e, thus enlarging \u003cem\u003eλ\u003c/em\u003e\u003csub\u003e\u003cem\u003elim\u003c/em\u003e\u003c/sub\u003e 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.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eg, IR and IR-ZDC-D have the similar modulus, demonstrating that the modulus of samples is not compromised by long strands.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003e3.2. Flaw Insensitivity of Inhomogeneous Networks.\u003c/b\u003e The flaw sensitivity of networks is intricately linked to its crack propagation resistance.\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e,\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e 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.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea and Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb. 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.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea, 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 \u003cb\u003eFigure S12\u003c/b\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb 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 \u003cb\u003eFigure S13\u003c/b\u003e. The flaw sensitivity of materials is strongly correlated with the fractocohesive length (\u003cem\u003el\u003c/em\u003e\u003csub\u003e\u003cem\u003eT\u003c/em\u003e\u003c/sub\u003e) which is defined as the ratio of \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e to the work of fracture.\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e,\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e Such fractocohesive length can represent the stress transfer abilities of materials.\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e,\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e To obtain the \u003cem\u003el\u003c/em\u003e\u003csub\u003e\u003cem\u003eT\u003c/em\u003e\u003c/sub\u003e 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 \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e. \u003cem\u003el\u003c/em\u003e\u003csub\u003e\u003cem\u003eT\u003c/em\u003e\u003c/sub\u003e data of IR and IR-ZDC-D samples are exhibited in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec. The \u003cem\u003el\u003c/em\u003e\u003csub\u003e\u003cem\u003eT\u003c/em\u003e\u003c/sub\u003e of inhomogeneous networks (1.73 mm) is 1.7 times more than that of regular networks (1 mm).\u003c/p\u003e \u003cp\u003eMooney-Rivlin equation are used to perform an in-depth analysis of stress-strain curves for investigating the changes in entanglements (details in \u003cb\u003eSupporting Information\u003c/b\u003e),\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{\\sigma\\:}{\\lambda\\:-{\\lambda\\:}^{-2}}={E}_{c}+{E}_{e}f\\left(\\lambda\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e, where \u003cem\u003eσ\u003c/em\u003e is the engineering stress of materials, \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e represents the contribution from chemical crosslinking, and \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e is associated to physical topological constraints. Mooney-Rivlin curves of IR and IR-ZDC-D samples are shown in \u003cb\u003eFigure S14\u003c/b\u003e-\u003cb\u003eFigure S17\u003c/b\u003e and then we further calculate \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e (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.\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e Thus, inhomogeneous networks exhibit higher \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e than regular networks in \u003cb\u003eFigure S18\u003c/b\u003e. More entanglements of inhomogeneous networks are beneficial for transmitting tensions upon stretching.\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e,\u003cspan additionalcitationids=\"CR44\" citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eDIC techniques demonstrate the effective stress deconcentration of elastomers with long strands at the crack tip in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed. 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.\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e,\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e,\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e When encountering cracks, long strands contribute to the stress deconcentration, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ee.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAdditionally, 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 (\u003cem\u003eG\u003c/em\u003e) is calculated from the stress-stretch curves of unnotched samples of first cycle according to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:G=W\\left(\\lambda\\:\\right)\u0026middot;{H}_{0}\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:W\\left(\\lambda\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e is the stored elastic energy and \u003cem\u003eH\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e is the initial samples height. Under the \u003cem\u003eG\u003c/em\u003e of approximately 800 J/m\u003csup\u003e2\u003c/sup\u003e, a camera records the crack length of IR and IR -ZDC-D under cyclic loads in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea and Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb. For IR, cracks propagate obviously with the increase in the number of cycles in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea. For IR-ZDC-D, we hardly observe the crack propagation after 100000th cycle in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb. Also, SEM is used to investigate the surface of fatigue fracture samples in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec. 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.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003e3.3. Tough and Fatigue-Resistant Inhomogeneous Networks.\u003c/b\u003e This part demonstrates that inhomogeneous networks hinder the crack propagation under monotonic loads or cyclic loads in \u003cb\u003eFig.\u0026nbsp;4\u003c/b\u003e. These inhomogeneous networks exhibit near-perfect elasticity in \u003cb\u003eFig.\u0026nbsp;4b\u003c/b\u003e. 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 (\u003cem\u003eΔc\u003c/em\u003e) versus number of cycles (\u003cem\u003eNC\u003c/em\u003e) in steady state and further get the crack propagation rate (d\u003cem\u003ec\u003c/em\u003e/d\u003cem\u003eNC\u003c/em\u003e) of samples by calculating the slope of plots of \u003cem\u003eΔc\u003c/em\u003e versus \u003cem\u003eNC\u003c/em\u003e, as shown in \u003cb\u003eFigure S19\u003c/b\u003e-\u003cb\u003eFigure S22\u003c/b\u003e. The \u003cem\u003eG\u003c/em\u003e is obtained from stress-strain curves of unnotched samples when the cyclic loading reaches the steady state at the corresponding strain. Subsequently, d\u003cem\u003ec\u003c/em\u003e/d\u003cem\u003eNC\u003c/em\u003e versus \u003cem\u003eG\u003c/em\u003e curves are plotted in \u003cb\u003eFig.\u0026nbsp;4a\u003c/b\u003e, allowing us to approximately determine \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e below which the fatigue crack does not propagate under infinite cycles of loads. In \u003cb\u003eFig.\u0026nbsp;4c\u003c/b\u003e, the \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e of IR (regular networks) is around 67 J/m\u003csup\u003e2\u003c/sup\u003e, which is comparable to other elastomers such as chloroprene rubber, butadiene rubber, and polydimethylsiloxane.\u003csup\u003e\u003cspan additionalcitationids=\"CR48\" citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e In terms of the classical Lake-Thomas model,\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e 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 \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e. 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.\u003c/p\u003e \u003cp\u003eConsequently, 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 \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e and the ability to resist the crack propagation under cyclic loads is characterized by \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e.\u003csup\u003e\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e In \u003cb\u003eFig.\u0026nbsp;4c\u003c/b\u003e and \u003cb\u003eFig.\u0026nbsp;4d\u003c/b\u003e, both \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e increase with the formation of inhomogeneous networks. It is worth noting that IR-ZDC-D has achieved a high threshold of 1200 J/m\u003csup\u003e2\u003c/sup\u003e, one order of magnitude higher than existing elastomers in \u003cb\u003eFig.\u0026nbsp;4e\u003c/b\u003e. 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.\u003c/p\u003e \u003cp\u003e \u003cb\u003eFigure 4.\u003c/b\u003e Tough and fatigue-resistant inhomogeneous networks. (a) d\u003cem\u003ec\u003c/em\u003e/d\u003cem\u003eNC\u003c/em\u003e versus \u003cem\u003eG\u003c/em\u003e curves of IR and IR-ZDC-D samples. (b) Cyclic stress-stretch curves for IR-ZDC-D with no precut cracks. (c) \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e of IR and IR-ZDC-D samples. (d) \u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e of IR and IR-ZDC-D samples. (e) \u003cem\u003eΓ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e of various elastomers. Elastomers with inhomogeneous networks in the current work are compared with other elastomers, such as regular elastomers by single network design,\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e,\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e,\u003cspan additionalcitationids=\"CR52\" citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e double elastomers,\u003csup\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e,\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e\u003c/sup\u003e and reinforced elastomers.\u003csup\u003e\u003cspan additionalcitationids=\"CR57\" citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e"},{"header":"4. CONCLUSIONS","content":"\u003cp\u003eThis 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/m\u003csup\u003e2\u003c/sup\u003e. 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.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eACKNOWLEDGEMENTS\u003c/h2\u003e \u003cp\u003eThis work was supported by National Natural Science Foundation of China (Grant No. 52173058 and Grant No. 52363007).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eDanielsen SPO, Beech HK, Wang S, El-Zaatari BM, Wang X, Sapir L, Ouchi T, Wang Z, Johnson PN, Hu Y, Lundberg DJ, Stoychev G, Craig SL, Johnson JA, Kalow JA, Olsen BD, Rubinstein M (2021) Molecular Characterization of Polymer Networks. Chem Rev 121:5042\u0026ndash;5092\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGu Y, Zhao J, Johnson JA (2020) Polymer Networks: From Plastics and Gels to Porous Frameworks. 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U.S.A 121\u003c/em\u003e, e2322684121\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":false,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4973429/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4973429/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePolymer 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\u0026ndash;100 J/m\u0026sup2;. 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/m\u0026sup2;. 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.\u003c/p\u003e","manuscriptTitle":"Designing network heterogeneity for anti-fatigue elastomers","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-09-04 09:55:48","doi":"10.21203/rs.3.rs-4973429/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"b9e0e79e-7eaa-439e-aa97-4d437de3be1e","owner":[],"postedDate":"September 4th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":36968348,"name":"Physical sciences/Materials science/Soft materials/Polymers"},{"id":36968349,"name":"Physical sciences/Materials science/Structural materials/Mechanical properties"}],"tags":[],"updatedAt":"2025-11-14T09:17:15+00:00","versionOfRecord":[],"versionCreatedAt":"2024-09-04 09:55:48","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4973429","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4973429","identity":"rs-4973429","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}