Quantitative Connection between Macroscopic Stress and Bond-Breaking Force Enabled by Time-Stamped Mechanochemical Fluorescence

Quantitative Connection between Macroscopic Stress and Bond-Breaking Force Enabled by Time-Stamped Mechanochemical Fluorescence | 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 Quantitative Connection between Macroscopic Stress and Bond-Breaking Force Enabled by Time-Stamped Mechanochemical Fluorescence Junpeng Wang, Zeyu Wang, Devavrat Sathe, Ming-Chi Wang, Junfeng Zhou, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5205619/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 Mechanical stress is ubiquitous in materials, and it is well accepted that stress causes material wear and failure—which, at the molecular level, results from force-induced bond breakage. Understanding the mechanical behavior of materials at the molecular level requires a quantitative relationship between macroscopic stress and bond-breaking force, a connection that remains largely unexplored. Here we report that the macroscopic stress and the bond-breaking force are quantitatively connected through the kinetics of mechanically activated retro-Diels–Alder reaction of an anthracene–maleimide adduct mechanophore, which is embedded within the crosslink of a double-network elastomer. We find that the force required for bond breakage is largely insensitive to the strain applied to the elastomer but increases linearly with the logarithm of the strain rate. These findings provide insights into the mechanical behavior of polymeric materials and offer valuable guidance for the design of mechanically responsive materials. Physical sciences/Materials science/Soft materials/Polymers Physical sciences/Chemistry/Materials chemistry Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 One-Sentence Summary The effect of macroscopic loading on the bond-breaking force in a polymer network is quantified, advancing the understanding of the mechanical responses of materials at the molecular level. Main Text Materials are commonly subjected to mechanical stress, which is widely recognized as a driving force behind wear and eventual failure through force-activated bond breaking at the molecular level.( 1 ) Establishing a quantitative relationship between macroscopic stress and molecular bond-breaking forces is essential to unravel the molecular mechanisms of material deformation and failure.( 2, 3 ) Such insights lay the foundation for predictive molecular models that accurately describe the mechanical behavior of materials. The field of polymer mechanochemistry has been transformed by the incorporation of force-responsive functional groups, known as mechanophores.( 4 ) By strategically designing mechanophores, mechanical forces can be harnessed to realize constructive responses, such as controlled molecular release,( 5–8 ) gated polymer degradation,( 9–11 ) mechanocatalysis,( 12, 13 ) and self-strengthening.( 14, 15 ) Developing a quantitative link between macroscopic stress and molecular bond-breaking force would facilitate the efficient utilization of force for mechanochemical transduction. Mechanophores have been incorporated into bulk materials to leverage the stress within the materials for mechanochemical transformations.( 16–22 ) Since force accelerates the bond-breaking reaction by lowering the activation barrier,( 23 ) in principle, the bond-breaking force can be derived from the force-coupled reaction rate constant; however, quantitative measurements of the kinetics under macroscopic stress have been rare.( 24–26 ) The scarcity of kinetic studies of bulk mechanochemical activation is partially due to the limited degree of mechanochemical activation in bulk materials. While a high percentage of mechanophore activation (up to complete activation) has been achieved through the ultrasonication of polymer solutions ( 27–32 ), mechanophores in bulk materials often exhibit low activation levels (< 5%) ( 33, 34 ), which can be attributed to the inhomogeneity of force distribution in a polymer network under load, where the percentage of stress-bearing strands is low. Significant efforts have been dedicated to improving the efficiency of mechanophore activation in bulk materials.( 22 ) A particularly effective approach involves embedding mechanophores within double-network systems. Key contributions in this area include the works of Creton ( 35–38 ), Craig ( 39–41 ), and Otsuka( 42 ). In these studies, mechanophores are incorporated into the first network of the double-network system. The double-network system benefits mechanophore activation in two main ways. First, the first network is pre-stretched while it is swollen in the monomer of the second network, and curing of the second network fixes the stretched length. Thus, the force distribution in the first network is more homogeneous than that in a regular polymer network. Second, as demonstrated by Gong ( 43–45 ) and Suo ( 46, 47 ), the double-network design significantly enhances the material’s strength, allowing it to withstand levels of deformation that a single-network material cannot. Mechanophores that generate chromic or fluorescent responses upon activation, known as mechanochromophores, provide opportunities to conveniently detect and quantify the forces experienced by the polymer at the molecular level ( 48–53 ). Compared with other mechanochromophores, anthracene–maleimide adduct (AM) is attractive for its facile synthesis and excellent thermal stability ( 32, 33, 54 ). Moreover, the product of the mechanically activated retro-Diels–Alder reaction (rDA), anthracene, is stable under ambient conditions and emits a strong fluorescence signal, which facilitates convenient ex situ characterization. We therefore synthesized a double-network elastomer where AM is incorporated in the crosslink of the first network (AM-DN, Fig. 1 A). In comparison to a single network where AM is used as the crosslinker (AM-SN), the AM-DN system enables significantly more efficient activation of AM, as manifested by the significantly stronger fluorescence signal (Fig. S2). In addition, uniaxial compression resulted in much higher activation than uniaxial extension (Fig. S3); thus, we focused on compression studies for this work. A representative stress–strain curve obtained from the compression study is shown in Fig. 1 B. When a certain level of strain was reached, the strain was maintained for a period to allow the activation product (anthracene) to accumulate. The compressed specimen was then subjected to solid-state fluorescence spectroscopy at an excitation wavelength of 365 nm (Fig. 1 C). Initially, we set the strain rate to 0.5 min − 1 and the compression ratio H 0 / H to 16:1. The fluorescence signal increased with the hold time and reached a plateau at 10 min (Fig. 2 A). The rate of increase in fluorescence was found to be close to first-order kinetics (Fig. 2 B), corresponding to a rate constant, k rDA , of 4 × 10 − 3 s − 1 . The rate constant reflects the acceleration of the rDA reaction by molecular forces. In addition, during this period, stress relaxation remained below 20% (Fig. 2 C). Encouraged by this initial success in capturing the kinetics of mechanochemical fluorescence, we set out to investigate how the loading conditions affect the kinetics. A range of strain rates was applied (2.5 min − 1 , 12.5 min − 1 , 62.5 min − 1 , and 312.5 min − 1 ) while the compression ratio was kept at 16:1. The stress (before relaxation) showed a logarithmic dependence on the strain rate (Fig. 3 A). The stress applied to the sample was also held for 10 min (Fig. S4), allowing for the kinetics of the fluorescence build-up to be measured. The kinetics of the rDA at different strain rates, as measured with fluorescence spectroscopy, are shown in Fig. 3 B. The logarithmic rate of mechanochemical fluorescence was found to increase linearly with stress in the range of 115–180 MPa, with no further increase in the rate observed beyond this range (Fig. 3 C). In another set of experiments, we kept the strain rate at 0.5 min − 1 but changed the strain, i.e., the compression ratio. Compression ratios of H 0 / H were set at 4, 8, 16, and 32, corresponding to the stress values (before relaxation) of 25 MPa, 81 MPa, 114 MPa, and 153 MPa, respectively (Fig. 3 D). The time-stamped mechanochemical fluorescence of the corresponding sample under each stress was also measured (Fig. 3 E). The ultimate percentages of mechanophore activation were below 3% when compression ratios were at or below 16. When the compression ratio was increased to 32, 11% mechanophore activation was achieved. Despite the substantial increase in the percentage of activation (from < 3–11%) when the compression ratio was increased from 16 to 32, the rate constant k rDA only increased from 4 × 10 − 3 s − 1 to 6 × 10 − 3 s − 1 . To relate the rate constant to the molecular force, we calculated the force-coupled energy barrier of the retro-Diels–Alder reaction of AM using the B3LYP/6-31G(d) level of theory. Consistent with previous study by Boulatov and co-workers ( 55 ), the rDA reaction can proceed through either a concerted pathway or a stepwise pathway, with the latter involving two transition states (Fig. 4 A). The concerted mechanism is preferred when the force is below 485 pN. Above 485 pN, the stepwise pathway is favored, with the breakage of the first C-C bond being the rate-determining step. While the concerted pathway is insensitive to force, the energy barriers for the stepwise C-C bond breakage decrease significantly as the applied force increases. By combining the energy barriers of the favored pathways below and above 485 pN, we obtained a complete force-coupled energy barrier for the rDA reaction (Fig. 4 B). Using these energy barriers, we calculated the corresponding rate constants with the Eyring Eq. (5 6 ). The rate constants observed in the uniaxial compression study are within the range of 10 − 3 –10 − 1 s − 1 , corresponding to the range of forces of 1520–1620 pN. The above data therefore provide a rare opportunity to illustrate how molecular bond-breaking force F changes with the macroscopic stress σ (Fig. 5 A). Figure 5 B shows the molecular force as a function of stress under two different conditions: varying strain while keeping strain rate constant, and varying strain rate while keeping strain constant. At a constant strain rate of 0.5 min − 1 , F remained unchanged at 1525 pN as σ increased from 25 MPa to 81 MPa. A slight increase occurred on F (from 1525 pN to 1530 pN) as σ increased from 81 MPa to 114 pN. Further increasing σ to 153 MPa resulted F rising to 1545 pN. This minimal increase in F indicates that F is insensitive to strain, particularly at lower strain levels. The increase in stress with higher strain is mainly due to the increased number of stress-bearing strands, which is also evidenced by the increased fraction of mechanophore activation. On the other hand, when the strain rate was varied while maintaining a compression ratio of 16, F increased linearly with σ . Since σ also increased linearly with the logarithm of strain rate (Fig. 3 A), a linear relationship between bond-breaking force F and the logarithm of strain rate is expected. This finding aligns with the Bell–Evans model ( 57 ), which captures the relationship between bond-breaking force F and the loading rate r F (Eq. 1 ). $$\:F=\frac{{k}_{B}T}{\varDelta\:{x}^{‡}}\text{ln}\left(\frac{{r}_{F}\varDelta\:{x}^{‡}}{{k}_{0}{k}_{B}T}\right)$$ 1 In Eq. 1 , Δ x ‡ represents the extension in the polymer chain as the reaction progresses from the ground state to the transition state; k B is Boltzmann’s constant; T is the temperature; and k 0 is the force-free rate constant. Since compression can be viewed as biaxial stretching in the perpendicular direction, the corresponding stretching strain ε s should be the square root of the compressing strain ε c . Under a constant strain rate, the stretching strain rate \(\:\dot{{\epsilon\:}_{s}}\) can be expressed as a function of the compressing strain rate \(\:\dot{{\epsilon\:}_{c}}\) (Eq. 2 ). $$\:\dot{{\epsilon\:}_{s}}=\sqrt{\frac{\dot{{\epsilon\:}_{c}}}{{t}_{0}}}$$ 2 In Eq. 2 , t 0 represents the unit time interval, which is set to 1 s for standard units. Assuming that the loading rate in the polymer strands scales with the stretching strain rate, we have Eq. 3 : $$\:{r}_{F}=C\dot{{\epsilon\:}_{s}}$$ 3 Based on Equations 1 – 3 , the relationship between the molecular force F and the compressive strain rate \(\:\dot{{\epsilon\:}_{c}}\) is given by Eq. 4 : $$\:F=\frac{{k}_{B}T}{2\varDelta\:{x}^{‡}}ln\left(\frac{C\varDelta\:{x}^{‡}\dot{{\epsilon\:}_{c}}}{{k}_{0}{t}_{0}{k}_{B}T}\right)$$ 4 We fit the plot of F vs. \(\:\dot{{\epsilon\:}_{c}}\) to Eq. 4 , which provides a slope of 17.7 pN, corresponding to a Δ x ‡ of 1.16 Å. This is comparable to the calculated Δ x ‡ for the stepwise pathway, where Δ x ‡ is 1.29 Å at 130 pN. We were unable to obtain an optimized transition state structure TS1 (Fig. 4 A) for the stepwise pathway at forces below 130 pN as the concerted pathway becomes dominant. Nevertheless, it is expected that the force-free Δ x ‡ to be close to 1.29 Å. Overall, the self-consistency of the framework supports the validity of the quantitative connection between the macroscopic stress and the molecular bond-breaking force. Conclusions Having the anthracene–maleimide mechanophore installed in the first network of a double-network elastomer enables up to 20% mechanophore activation when the elastomer is compressed. The kinetic responses of the mechanochemical retro-Diels–Alder reaction provide a rare opportunity to analyze the dependence of the bond-breaking force on the loading conditions. Notably, while both strain and strain rate can influence the macroscopic stress, their effects on bond-breaking forces differ: the bond breaking force is largely insensitive to strain but shows a logarithmic dependence on strain rate. This quantitative connection between the molecular bond-breaking force and the strain rate can be viewed as a “macroscopic dynamic force-spectroscopy”, which allows us to interrogate the structures of the transition states that regulate the reaction. The relationship demonstrated here highlights the robustness of the chemomechanical framework for understanding reactivity across various scales. Looking ahead, we expect that mechanochemical kinetics will be further leveraged to unveil the mechanical behavior of materials. Declarations Acknowledgments: The authors thank S-Q Wang for helpful discussion. Funding: The following funding sources are gratefully acknowledged: National Science Foundation CHE-2204079 (JW) Alfred P. Sloan Foundation FG-2023-20341 (JW) Camille and Henry Dreyfus Foundation TC-24-087 (JW) Author contributions: Conceptualization: ZW, QZ, JW Methodology: ZW, QZ, JW Investigation: ZW, DS, MCW, JZ, QZ, JW Project administration: QZ, JW Writing – original draft: ZW Writing – review & editing: ZW, QZ, JW Competing interests: Authors declare that they have no competing interests. Data and materials availability: All data are available in the main text or the supplementary materials. References M. K. Beyer, H. Clausen-Schaumann, Mechanochemistry: The Mechanical Activation of Covalent Bonds. Chem. Rev. 105 , 2921-2948 (2005). S. Wang, S. Panyukov, M. Rubinstein, S. L. Craig, Quantitative Adjustment to the Molecular Energy Parameter in the Lake–Thomas Theory of Polymer Fracture Energy. Macromolecules , (2019). S.-Q. Wang, Z. Fan, C. Gupta, A. Siavoshani, T. Smith, Fracture Behavior of Polymers in Plastic and Elastomeric States. Macromolecules 57 , 3875-3900 (2024). M. M. Caruso et al. , Mechanically-Induced Chemical Changes in Polymeric Materials. Chem. Rev. 109 , 5755-5798 (2009). M. B. Larsen, A. J. Boydston, “Flex-Activated” Mechanophores: Using Polymer Mechanochemistry To Direct Bond Bending Activation. J. Am. Chem. Soc. 135 , 8189-8192 (2013). X. Hu, T. Zeng, C. C. Husic, M. J. Robb, Mechanically Triggered Small Molecule Release from a Masked Furfuryl Carbonate. J. Am. Chem. Soc. 141 , 15018-15023 (2019). S. Huo et al. , Mechanochemical bond scission for the activation of drugs. Nat. Chem. 13 , 131-139 (2021). Y. Yao et al. , Remote control of mechanochemical reactions under physiological conditions using biocompatible focused ultrasound. Proc. Natl. Acad. Sci. U. S. A. 120 , e2309822120 (2023). T.-G. Hsu et al. , A Polymer with “Locked” Degradability: Superior Backbone Stability and Accessible Degradability Enabled by Mechanophore Installation. J. Am. Chem. Soc. 142 , 2100-2104 (2020). Y. Lin, T. B. Kouznetsova, S. L. Craig, Mechanically Gated Degradable Polymers. J. Am. Chem. Soc. 142 , 2105-2109 (2020). J. Yang, Y. Xia, Mechanochemical generation of acid-degradable poly(enol ether)s. Chem. Sci. 12 , 4389-4394 (2021). A. Piermattei, S. Karthikeyan, R. P. Sijbesma, Activating catalysts with mechanical force. Nat. Chem. 1 , 133-137 (2009). Y. Yu, X. Zheng, C. Duan, S. L. Craig, R. A. Widenhoefer, Force-Modulated Selectivity of the Rhodium-Catalyzed Hydroformylation of 1-Alkenes. ACS Catalysis 12 , 13941-13950 (2022). A. L. B. Ramirez et al. , Mechanochemical strengthening of a synthetic polymer in response to typically destructive shear forces. Nat. Chem. 5 , 757 (2013). H. Zhang et al. , Mechanochromism and Mechanical-Force-Triggered Cross-Linking from a Single Reactive Moiety Incorporated into Polymer Chains. Angew. Chem. Int. Ed. 55 , 3040-3044 (2016). A. L. Black, J. M. Lenhardt, S. L. Craig, From molecular mechanochemistry to stress-responsive materials. J. Mater. Chem. 21 , 1655-1663 (2011). J. Li, C. Nagamani, J. S. Moore, Polymer Mechanochemistry: From Destructive to Productive. Acc. Chem. Res. 48 , 2181-2190 (2015). N. Willis-Fox, E. Rognin, T. A. Aljohani, R. Daly, Polymer Mechanochemistry: Manufacturing Is Now a Force to Be Reckoned With. Chem 4 , 2499-2537 (2018). M. Stratigaki, R. Göstl, Methods for Exerting and Sensing Force in Polymer Materials Using Mechanophores. ChemPlusChem 85 , 1095-1103 (2020). A. J. Boydston et al. , The role of polymer mechanochemistry in responsive materials and additive manufacturing. Nat. Rev. Mater. 6 , 84-98 (2021). S. L. Craig, Concluding remarks: Fundamentals, applications and future of mechanochemistry. Faraday Discuss. 241 , 485-491 (2023). E. M. Lloyd, J. R. Vakil, Y. Yao, N. R. Sottos, S. L. Craig, Covalent Mechanochemistry and Contemporary Polymer Network Chemistry: A Marriage in the Making. J. Am. Chem. Soc. 145 , 751-770 (2023). G. I. Bell, Models for the specific adhesion of cells to cells: a theoretical framework for adhesion mediated by reversible bonds between cell surface molecules. Science 200 , 618-627 (1978). C. K. Lee et al. , Force-induced redistribution of a chemical equilibrium. J. Am. Chem. Soc. 132 , 16107-16111 (2010). T. A. Kim, M. J. Robb, J. S. Moore, S. R. White, N. R. Sottos, Mechanical Reactivity of Two Different Spiropyran Mechanophores in Polydimethylsiloxane. Macromolecules 51 , 9177-9183 (2018). Y. Vidavsky et al. , Enabling Room-Temperature Mechanochromic Activation in a Glassy Polymer: Synthesis and Characterization of Spiropyran Polycarbonate. J. Am. Chem. Soc. 141 , 10060-10067 (2019). T.-G. Hsu et al. , A Polymer with "locked" Degradability: Superior Backbone Stability and Accessible Degradability Enabled by Mechanophore Installation. J. Am. Chem. Soc. 142 , 2100-2104 (2020). Y. Lin, T. B. Kouznetsova, C. C. Chang, S. L. Craig, Enhanced polymer mechanical degradation through mechanochemically unveiled lactonization. Nat. Commun. 11 , 4987 (2020). P. A. May, N. F. Munaretto, M. B. Hamoy, M. J. Robb, J. S. Moore, Is Molecular Weight or Degree of Polymerization a Better Descriptor of Ultrasound-Induced Mechanochemical Transduction? ACS Macro Lett. 5 , 177-180 (2016). J. M. Lenhardt, A. L. Black, S. L. Craig, gem-Dichlorocyclopropanes as Abundant and Efficient Mechanophores in Polybutadiene Copolymers under Mechanical Stress. J. Am. Chem. Soc. 131 , 10818-10819 (2009). H. Zhang, C. E. Diesendruck, Linear versus Helical Side Chains in Bottlebrush Polymers: Morphology and Mechanochemistry. Macromolecules 57 , 3664-3670 (2024). S. M. Luo, R. W. Barber, A. C. Overholts, M. J. Robb, Competitive Activation Experiments Reveal Significantly Different Mechanochemical Reactivity of Furan–Maleimide and Anthracene–Maleimide Mechanophores. ACS Polymers Au 3 , 202-208 (2023). C. P. Kabb, C. S. O'Bryan, C. D. Morley, T. E. Angelini, B. S. Sumerlin, Anthracene-based mechanophores for compression-activated fluorescence in polymeric networks. Chem. Sci. 10 , 7702-7708 (2019). J. M. Lenhardt et al. , Characterizing the mechanochemically active domains in gem-dihalocyclopropanated polybutadiene under compression and tension. J. Mater. Chem. 21 , 8454-8459 (2011). Y. Chen, C. Joshua Yeh, Y. Qi, R. Long, C. Creton, From force-responsive molecules to quantifying and mapping stresses in soft materials. Sci. Adv. 6 , 1-9 (2020). P. Millereau et al. , Mechanics of elastomeric molecular composites. Proc. Natl. Acad. Sci. U. S. A. 115 , 9110-9115 (2018). J. Slootman, C. J. Yeh, P. Millereau, J. Comtet, C. Creton, A molecular interpretation of the toughness of multiple network elastomers at high temperature. Proc. Natl. Acad. Sci. U. S. A. 119 , 1-11 (2022). E. Ducrot, Y. Chen, M. Bulters, R. P. Sijbesma, C. Creton, Toughening elastomers with sacrificial bonds and watching them break. Science 344 , 186-189 (2014). Z. Wang et al. , Toughening hydrogels through force-triggered chemical reactions that lengthen polymer strands. Science 374 , 193-193 (2021). T. Ouchi, B. H. Bowser, T. B. Kouznetsova, X. Zheng, S. L. Craig, Strain-triggered acidification in a double-network hydrogel enabled by multi-functional transduction of molecular mechanochemistry. Materials Horizons 10 , 585-593 (2023). Z. J. Wang et al. , Effect of the Activation Force of Mechanophore on Its Activation Selectivity and Efficiency in Polymer Networks. J. Am. Chem. Soc. 146 , 13336−13346 (2024). T. Watabe, D. Aoki, H. Otsuka, Polymer-Network Toughening and Highly Sensitive Mechanochromism via a Dynamic Covalent Mechanophore and a Multinetwork Strategy. Macromolecules 55 , 5795-5802 (2022). J. P. Gong, Y. Katsuyama, T. Kurokawa, Y. Osada, Double-Network Hydrogels with Extremely High Mechanical Strength. Adv. Mater. 15 , 1155-1158 (2003). J. P. Gong, Why are double network hydrogels so tough? Soft Matter 6 , 2583-2590 (2010). J. P. Gong, Materials both Tough and Soft. Science 344 , 161-162 (2014). R. Bai et al. , Fatigue fracture of tough hydrogels. Extreme Mechanics Letters 15 , 91-96 (2017). Y. Zhou et al. , The Stiffness-Threshold Conflict in Polymer Networks and a Resolution. Journal of Applied Mechanics 87 , 031002 (2019). D. A. Davis et al. , Force-induced activation of covalent bonds in mechanoresponsive polymeric materials. Nature 459 , 68-72 (2009). H. Sakai et al. , Visualization and Quantitative Evaluation of Toughening Polymer Networks by a Sacrificial Dynamic Cross-Linker with Mechanochromic Properties. ACS Macro Lett. 9 , 1108-1113 (2020). Z. Wang et al. , A Novel Mechanochromic and Photochromic Polymer Film: When Rhodamine Joins Polyurethane. Adv. Mater. 27 , 6469-6474 (2015). Z. Chen et al. , Stress-Dependent Multicolor Mechanochromism in Epoxy Thermosets Based on Rhodamine and Diaminodiphenylmethane Mechanophores. Macromolecules 55 , 2310-2319 (2022). Z. S. Kean, G. R. Gossweiler, T. B. Kouznetsova, G. B. Hewage, S. L. Craig, A coumarin dimer probe of mechanochemical scission efficiency in the sonochemical activation of chain-centered mechanophore polymers. Chem. Commun. 51 , 9157-9160 (2015). J. Sung, M. J. Robb, S. R. White, J. S. Moore, N. R. Sottos, Interfacial mechanophore activation using laser-induced stress waves. J. Am. Chem. Soc. 140 , 5000-5003 (2018). J. Li et al. , Mechanophore Activation at Heterointerfaces. J. Am. Chem. Soc 136 , 15925−15928 (2014). S. Akbulatov et al. , Experimentally realized mechanochemistry distinct from force-accelerated scission of loaded bonds. Science 357 , 299-303 (2017). H. Eyring, The Activated Complex in Chemical Reactions. J. Chem. Phys. 3 , 107-115 (1935). E. Evans, K. Ritchie, Dynamic strength of molecular adhesion bonds. Biophys. J. 72 , 1541-1555 (1997). 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-5205619","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":398814934,"identity":"7a573abe-b97f-41ec-9b2b-6b41c6a7c6ae","order_by":0,"name":"Junpeng Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyUlEQVRIiWNgGAWjYBACxgYQWWHDwMCDLEBYy5k0ErRAlLUcJkEL84zkZw+/NpxP7O85+/BxAYON7IYDhCyYkWZuLLvjduKMs+3GxjMY0owJa5mdYCYteeZ2YsN5NjZpHobDiURoSf8mLdl2LnE+RMt/YrTkmEl+bDuQuOFsG0jLASK0zH9TJs1wJtl445ljzMY8BsnGMwlpMew5vk3yR4Wd7LwzaYyPeYCMPoJaGoABzQPnGhBQDgLyIMf9IELhKBgFo2AUjGAAAAwsRUUZXZlRAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-4503-5026","institution":"University of Akron","correspondingAuthor":true,"prefix":"","firstName":"Junpeng","middleName":"","lastName":"Wang","suffix":""},{"id":398814935,"identity":"9dc4fa5e-6ed3-4b03-9e37-1d302793e7bf","order_by":1,"name":"Zeyu Wang","email":"","orcid":"https://orcid.org/0000-0002-6343-0548","institution":"University of Akron","correspondingAuthor":false,"prefix":"","firstName":"Zeyu","middleName":"","lastName":"Wang","suffix":""},{"id":398814936,"identity":"bd415a61-4b4c-4c93-ae04-a254261a8d38","order_by":2,"name":"Devavrat Sathe","email":"","orcid":"https://orcid.org/0000-0003-0481-3466","institution":"University of Akron","correspondingAuthor":false,"prefix":"","firstName":"Devavrat","middleName":"","lastName":"Sathe","suffix":""},{"id":398814937,"identity":"a4eca36b-3cd0-4c58-bbf1-39c460147812","order_by":3,"name":"Ming-Chi Wang","email":"","orcid":"","institution":"University of Akron","correspondingAuthor":false,"prefix":"","firstName":"Ming-Chi","middleName":"","lastName":"Wang","suffix":""},{"id":398814938,"identity":"04d4d955-8ba3-43d6-a197-a5f975159e02","order_by":4,"name":"Junfeng Zhou","email":"","orcid":"","institution":"University of Akron","correspondingAuthor":false,"prefix":"","firstName":"Junfeng","middleName":"","lastName":"Zhou","suffix":""},{"id":398814939,"identity":"8acac19e-03ef-4d2d-8b99-e376b6d5fe61","order_by":5,"name":"Zichen Ling","email":"","orcid":"","institution":"University of Akron","correspondingAuthor":false,"prefix":"","firstName":"Zichen","middleName":"","lastName":"Ling","suffix":""},{"id":398814940,"identity":"d06d2264-6173-43b9-891f-93ae88b51fcf","order_by":6,"name":"Qixin Zhou","email":"","orcid":"https://orcid.org/0000-0003-1022-780X","institution":"University of Akron","correspondingAuthor":false,"prefix":"","firstName":"Qixin","middleName":"","lastName":"Zhou","suffix":""}],"badges":[],"createdAt":"2024-10-04 18:00:51","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5205619/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5205619/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":73240679,"identity":"ce596a8e-efb0-4f75-82b9-90ebf88ff549","added_by":"auto","created_at":"2025-01-08 06:00:51","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":248849,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMechanochemical fluorescence of a mechanophore-containing double-network elastomer. \u003c/strong\u003e(\u003cstrong\u003eA\u003c/strong\u003e) Synthetic scheme of a double network: copolymerization of methyl acrylate and a diacrylate containing anthracene–maleimide adduct (AM) affords the first network, or single network AM-SN. AM-SN is then swollen in a mixture of ethyl acrylate, butanediol diacrylate and Irgacure 819 prior, and polymerization of the mixture leads to the formation of the double network elastomer AM-DN. (\u003cstrong\u003eB\u003c/strong\u003e) A representative stress-strain curve of an AM-DN sample (strain rate = 0.5 min\u003csup\u003e-1\u003c/sup\u003e). The insert shows a picture with the Instron compression head and the sample; scale bar = 5 mm. (\u003cstrong\u003eC\u003c/strong\u003e) Solid-state fluorescence spectra (\u003cem\u003eλ\u003c/em\u003e\u003csub\u003eex\u003c/sub\u003e = 365 nm) of a virgin sample (black) and a sample that was compressed to \u003cem\u003eH\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eH\u003c/em\u003e = 16 at a strain rate of 0.5 min\u003csup\u003e-1\u003c/sup\u003e and then held for 10 min (purple). The inset shows pictures of a virgin sample (left) and a sample compressed to \u003cem\u003eH\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eH\u003c/em\u003e = 16 at a strain rate of 0.5 min\u003csup\u003e-1\u003c/sup\u003e and then held for 10 min (right); scale bar = 5 mm.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-5205619/v1/af9139d16f6d4003652bb094.png"},{"id":73240684,"identity":"a6afe50e-da67-4b0e-acec-ef507a354cb7","added_by":"auto","created_at":"2025-01-08 06:00:51","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":92543,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTime-stamped mechanochemical fluorescence. \u003c/strong\u003e(\u003cstrong\u003eA\u003c/strong\u003e) Fluorescence spectra of AM-DN samples that had been compressed to \u003cem\u003eH\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eH\u003c/em\u003e = 16 at a strain rate of 0.5 min\u003csup\u003e-1 \u003c/sup\u003eand then held for various durations of time. (\u003cstrong\u003eB\u003c/strong\u003e) Fluorescence intensity (left y-axis) at 414 nm and the percentage of mechanophore activation (right y-axis) vs. hold time.\u0026nbsp; (\u003cstrong\u003eC\u003c/strong\u003e) Stress relaxation profile of a sample during constantstrain compression (\u003cem\u003eH\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eH\u003c/em\u003e = 16).\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-5205619/v1/93235539f1f1802ac98af72c.png"},{"id":73240686,"identity":"727a272d-249e-4224-b5af-ca4dab8bb7b6","added_by":"auto","created_at":"2025-01-08 06:00:52","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":204181,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTime-stamped mechanochemical fluorescence under different loading conditions. \u003c/strong\u003e(\u003cstrong\u003eA\u003c/strong\u003e) Compressive stress achieved at compression ratio \u003cem\u003eH\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eH\u003c/em\u003e = 16 when different strain rates are applied. (\u003cstrong\u003eB\u003c/strong\u003e) Fluorescence intensity (left y-axis) at 414 nm and the percentage of mechanophore activation (right y-axis) vs. hold time when different strain rates are applied. (\u003cstrong\u003eC\u003c/strong\u003e) Rate constant of the time-stamped fluorescence from (\u003cstrong\u003eB\u003c/strong\u003e) as a function of compressive stress from (\u003cstrong\u003eA\u003c/strong\u003e)\u003cem\u003e. \u003c/em\u003e\u003cstrong\u003e(D) \u003c/strong\u003eCompressive stress achieved at different compression ratios under a strain rate of 0.5 min\u003csup\u003e-1\u003c/sup\u003e. (\u003cstrong\u003eE\u003c/strong\u003e) Fluorescence intensity (left y-axis) at 414 nm and the percentage of mechanophore activation (right y-axis) vs. hold time for different compression ratios. (\u003cstrong\u003eF\u003c/strong\u003e) Rate constant of the time-stamped fluorescence from (\u003cstrong\u003eE\u003c/strong\u003e) as a function of compressive stress from (\u003cstrong\u003eD\u003c/strong\u003e)\u003cem\u003e.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-5205619/v1/08bb0995198468866f6fdf63.png"},{"id":73240689,"identity":"b5634671-f7c5-4d28-a40e-3818fbca7381","added_by":"auto","created_at":"2025-01-08 06:00:52","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":258121,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCalculation of the force-coupled retro Diels–Alder reaction of anthracene–maleimide adduct. \u003c/strong\u003e\u0026nbsp;(\u003cstrong\u003eA\u003c/strong\u003e) Optimized geometries for the ground state (GS), the transition state of the concerted pathway (TSc), and the transition states of the stepwise pathway (TS1 and TS2). (\u003cstrong\u003eB\u003c/strong\u003e) Free energy barrier and rate constant vs. force for the force coupled retro Diels–Alder reaction of anthracene–maleimide adduct.\u003cstrong\u003e \u003c/strong\u003eFree energy barriers were calculated from ground state and transition state structures coupled with soft pair potentials to simulate tension, optimized at the B3LYP/6-31G(d) level. Rate constants were calculated from the free energy barriers using the Eyring equation. For further details, see SI.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-5205619/v1/bc53fb86f1b22ab78cd504f1.png"},{"id":73240690,"identity":"4c9e5467-4a22-4127-96a5-5b9155950a7c","added_by":"auto","created_at":"2025-01-08 06:00:52","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":98480,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eQuantitative connection between the macroscopic stress and the molecular force \u003c/strong\u003e\u003cem\u003e\u003cstrong\u003eF\u003c/strong\u003e\u003c/em\u003e\u003cstrong\u003e. \u003c/strong\u003e\u0026nbsp;(\u003cstrong\u003eA\u003c/strong\u003e) Compressive stress applied to the polymer network is manifested at the molecular level, causing the retro-Diels–Alder reaction of the anthracene–maleimide adduct. (\u003cstrong\u003eB\u003c/strong\u003e) Bond-breaking force \u003cem\u003eF\u003c/em\u003e as a function of compressive stress at varying strains (black circle) and varying strain rates (red square). (\u003cstrong\u003eC\u003c/strong\u003e) Bond-breaking force \u003cem\u003eF\u003c/em\u003e as a function of the logarithm of the strain rate. Since the plot of \u003cem\u003eF\u003c/em\u003e vs. ln(r) is meant to capture the linear region, the data point at 312.5 min\u003csup\u003e-1\u003c/sup\u003e is not included.\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-5205619/v1/5289a0fc212e76442027c80f.png"},{"id":91448552,"identity":"f09d9fff-7ee5-4d93-8d4b-24925fbba93a","added_by":"auto","created_at":"2025-09-16 15:04:17","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1603148,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5205619/v1/0197d224-8222-4fb0-ba68-13cd83119ec4.pdf"},{"id":73240680,"identity":"92564284-e44d-4c13-8d2d-fadbe26e2ef1","added_by":"auto","created_at":"2025-01-08 06:00:51","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1427316,"visible":true,"origin":"","legend":"Supplementary Information","description":"","filename":"SIMacroscopicStressvs.MolecularForce.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5205619/v1/e52744078d580f4c231fe1f5.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Quantitative Connection between Macroscopic Stress and Bond-Breaking Force Enabled by Time-Stamped Mechanochemical Fluorescence","fulltext":[{"header":"One-Sentence Summary","content":"\u003cp\u003eThe effect of macroscopic loading on the bond-breaking force in a polymer network is quantified, advancing the understanding of the mechanical responses of materials at the molecular level.\u003c/p\u003e"},{"header":"Main Text","content":"\u003cp\u003eMaterials are commonly subjected to mechanical stress, which is widely recognized as a driving force behind wear and eventual failure through force-activated bond breaking at the molecular level.(\u003cem\u003e1\u003c/em\u003e) Establishing a quantitative relationship between macroscopic stress and molecular bond-breaking forces is essential to unravel the molecular mechanisms of material deformation and failure.(\u003cem\u003e2, 3\u003c/em\u003e) Such insights lay the foundation for predictive molecular models that accurately describe the mechanical behavior of materials. The field of polymer mechanochemistry has been transformed by the incorporation of force-responsive functional groups, known as mechanophores.(\u003cem\u003e4\u003c/em\u003e) By strategically designing mechanophores, mechanical forces can be harnessed to realize constructive responses, such as controlled molecular release,(\u003cem\u003e5\u0026ndash;8\u003c/em\u003e) gated polymer degradation,(\u003cem\u003e9\u0026ndash;11\u003c/em\u003e) mechanocatalysis,(\u003cem\u003e12, 13\u003c/em\u003e) and self-strengthening.(\u003cem\u003e14, 15\u003c/em\u003e) Developing a quantitative link between macroscopic stress and molecular bond-breaking force would facilitate the efficient utilization of force for mechanochemical transduction.\u003c/p\u003e \u003cp\u003eMechanophores have been incorporated into bulk materials to leverage the stress within the materials for mechanochemical transformations.(\u003cem\u003e16\u0026ndash;22\u003c/em\u003e) Since force accelerates the bond-breaking reaction by lowering the activation barrier,(\u003cem\u003e23\u003c/em\u003e) in principle, the bond-breaking force can be derived from the force-coupled reaction rate constant; however, quantitative measurements of the kinetics under macroscopic stress have been rare.(\u003cem\u003e24\u0026ndash;26\u003c/em\u003e) The scarcity of kinetic studies of bulk mechanochemical activation is partially due to the limited degree of mechanochemical activation in bulk materials. While a high percentage of mechanophore activation (up to complete activation) has been achieved through the ultrasonication of polymer solutions (\u003cem\u003e27\u0026ndash;32\u003c/em\u003e), mechanophores in bulk materials often exhibit low activation levels (\u0026lt;\u0026thinsp;5%) (\u003cem\u003e33, 34\u003c/em\u003e), which can be attributed to the inhomogeneity of force distribution in a polymer network under load, where the percentage of stress-bearing strands is low.\u003c/p\u003e \u003cp\u003eSignificant efforts have been dedicated to improving the efficiency of mechanophore activation in bulk materials.(\u003cem\u003e22\u003c/em\u003e) A particularly effective approach involves embedding mechanophores within double-network systems. Key contributions in this area include the works of Creton (\u003cem\u003e35\u0026ndash;38\u003c/em\u003e), Craig (\u003cem\u003e39\u0026ndash;41\u003c/em\u003e), and Otsuka(\u003cem\u003e42\u003c/em\u003e). In these studies, mechanophores are incorporated into the first network of the double-network system. The double-network system benefits mechanophore activation in two main ways. First, the first network is pre-stretched while it is swollen in the monomer of the second network, and curing of the second network fixes the stretched length. Thus, the force distribution in the first network is more homogeneous than that in a regular polymer network. Second, as demonstrated by Gong (\u003cem\u003e43\u0026ndash;45\u003c/em\u003e) and Suo (\u003cem\u003e46, 47\u003c/em\u003e), the double-network design significantly enhances the material\u0026rsquo;s strength, allowing it to withstand levels of deformation that a single-network material cannot.\u003c/p\u003e \u003cp\u003eMechanophores that generate chromic or fluorescent responses upon activation, known as mechanochromophores, provide opportunities to conveniently detect and quantify the forces experienced by the polymer at the molecular level (\u003cem\u003e48\u0026ndash;53\u003c/em\u003e). Compared with other mechanochromophores, anthracene\u0026ndash;maleimide adduct (AM) is attractive for its facile synthesis and excellent thermal stability (\u003cem\u003e32, 33, 54\u003c/em\u003e). Moreover, the product of the mechanically activated retro-Diels\u0026ndash;Alder reaction (rDA), anthracene, is stable under ambient conditions and emits a strong fluorescence signal, which facilitates convenient \u003cem\u003eex situ\u003c/em\u003e characterization. We therefore synthesized a double-network elastomer where AM is incorporated in the crosslink of the first network (AM-DN, Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eA). In comparison to a single network where AM is used as the crosslinker (AM-SN), the AM-DN system enables significantly more efficient activation of AM, as manifested by the significantly stronger fluorescence signal (Fig. S2). In addition, uniaxial compression resulted in much higher activation than uniaxial extension (Fig. S3); thus, we focused on compression studies for this work. A representative stress\u0026ndash;strain curve obtained from the compression study is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eB. When a certain level of strain was reached, the strain was maintained for a period to allow the activation product (anthracene) to accumulate. The compressed specimen was then subjected to solid-state fluorescence spectroscopy at an excitation wavelength of 365 nm (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eC).\u003c/p\u003e \u003cp\u003eInitially, we set the strain rate to 0.5 min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and the compression ratio \u003cem\u003eH\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eH\u003c/em\u003e to 16:1. The fluorescence signal increased with the hold time and reached a plateau at 10 min (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eA). The rate of increase in fluorescence was found to be close to first-order kinetics (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eB), corresponding to a rate constant, \u003cem\u003ek\u003c/em\u003e\u003csub\u003erDA\u003c/sub\u003e, of 4 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. The rate constant reflects the acceleration of the rDA reaction by molecular forces. In addition, during this period, stress relaxation remained below 20% (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eC).\u003c/p\u003e\u003cp\u003eEncouraged by this initial success in capturing the kinetics of mechanochemical fluorescence, we set out to investigate how the loading conditions affect the kinetics. A range of strain rates was applied (2.5 min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, 12.5 min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, 62.5 min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, and 312.5 min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) while the compression ratio was kept at 16:1. The stress (before relaxation) showed a logarithmic dependence on the strain rate (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA). The stress applied to the sample was also held for 10 min (Fig. S4), allowing for the kinetics of the fluorescence build-up to be measured. The kinetics of the rDA at different strain rates, as measured with fluorescence spectroscopy, are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB. The logarithmic rate of mechanochemical fluorescence was found to increase linearly with stress in the range of 115\u0026ndash;180 MPa, with no further increase in the rate observed beyond this range (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eC).\u003c/p\u003e \u003cp\u003eIn another set of experiments, we kept the strain rate at 0.5 min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e but changed the strain, i.e., the compression ratio. Compression ratios of \u003cem\u003eH\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e/\u003cem\u003eH\u003c/em\u003e were set at 4, 8, 16, and 32, corresponding to the stress values (before relaxation) of 25 MPa, 81 MPa, 114 MPa, and 153 MPa, respectively (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eD). The time-stamped mechanochemical fluorescence of the corresponding sample under each stress was also measured (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eE). The ultimate percentages of mechanophore activation were below 3% when compression ratios were at or below 16. When the compression ratio was increased to 32, 11% mechanophore activation was achieved. Despite the substantial increase in the percentage of activation (from \u0026lt;\u0026thinsp;3\u0026ndash;11%) when the compression ratio was increased from 16 to 32, the rate constant \u003cem\u003ek\u003c/em\u003e\u003csub\u003erDA\u003c/sub\u003e only increased from 4 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e to 6 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eTo relate the rate constant to the molecular force, we calculated the force-coupled energy barrier of the retro-Diels\u0026ndash;Alder reaction of AM using the B3LYP/6-31G(d) level of theory. Consistent with previous study by Boulatov and co-workers (\u003cem\u003e55\u003c/em\u003e), the rDA reaction can proceed through either a concerted pathway or a stepwise pathway, with the latter involving two transition states (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eA). The concerted mechanism is preferred when the force is below 485 pN. Above 485 pN, the stepwise pathway is favored, with the breakage of the first C-C bond being the rate-determining step. While the concerted pathway is insensitive to force, the energy barriers for the stepwise C-C bond breakage decrease significantly as the applied force increases. By combining the energy barriers of the favored pathways below and above 485 pN, we obtained a complete force-coupled energy barrier for the rDA reaction (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eB). Using these energy barriers, we calculated the corresponding rate constants with the Eyring Eq.\u0026nbsp;(5\u003cem\u003e6\u003c/em\u003e). The rate constants observed in the uniaxial compression study are within the range of 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u0026ndash;10\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, corresponding to the range of forces of 1520\u0026ndash;1620 pN.\u003c/p\u003e \u003cp\u003eThe above data therefore provide a rare opportunity to illustrate how molecular bond-breaking force \u003cem\u003eF\u003c/em\u003e changes with the macroscopic stress \u003cem\u003eσ\u003c/em\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eA). Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eB shows the molecular force as a function of stress under two different conditions: varying strain while keeping strain rate constant, and varying strain rate while keeping strain constant. At a constant strain rate of 0.5 min\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, \u003cem\u003eF\u003c/em\u003e remained unchanged at 1525 pN as \u003cem\u003eσ\u003c/em\u003e increased from 25 MPa to 81 MPa. A slight increase occurred on \u003cem\u003eF\u003c/em\u003e (from 1525 pN to 1530 pN) as \u003cem\u003eσ\u003c/em\u003e increased from 81 MPa to 114 pN. Further increasing \u003cem\u003eσ\u003c/em\u003e to 153 MPa resulted \u003cem\u003eF\u003c/em\u003e rising to 1545 pN. This minimal increase in \u003cem\u003eF\u003c/em\u003e indicates that \u003cem\u003eF\u003c/em\u003e is insensitive to strain, particularly at lower strain levels. The increase in stress with higher strain is mainly due to the increased number of stress-bearing strands, which is also evidenced by the increased fraction of mechanophore activation. On the other hand, when the strain rate was varied while maintaining a compression ratio of 16, \u003cem\u003eF\u003c/em\u003e increased linearly with \u003cem\u003eσ\u003c/em\u003e. Since \u003cem\u003eσ\u003c/em\u003e also increased linearly with the logarithm of strain rate (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA), a linear relationship between bond-breaking force \u003cem\u003eF\u003c/em\u003e and the logarithm of strain rate is expected. This finding aligns with the Bell\u0026ndash;Evans model (\u003cem\u003e57\u003c/em\u003e), which captures the relationship between bond-breaking force \u003cem\u003eF\u003c/em\u003e and the loading rate \u003cem\u003er\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e (Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:F=\\frac{{k}_{B}T}{\\varDelta\\:{x}^{\u0026Dagger;}}\\text{ln}\\left(\\frac{{r}_{F}\\varDelta\\:{x}^{\u0026Dagger;}}{{k}_{0}{k}_{B}T}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, Δ\u003cem\u003ex\u003c/em\u003e\u003csup\u003e\u0026Dagger;\u003c/sup\u003e represents the extension in the polymer chain as the reaction progresses from the ground state to the transition state; \u003cem\u003ek\u003c/em\u003e\u003csub\u003eB\u003c/sub\u003e is Boltzmann\u0026rsquo;s constant; \u003cem\u003eT\u003c/em\u003e is the temperature; and \u003cem\u003ek\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e is the force-free rate constant. Since compression can be viewed as biaxial stretching in the perpendicular direction, the corresponding stretching strain \u003cem\u003eε\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e should be the square root of the compressing strain \u003cem\u003eε\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e. Under a constant strain rate, the stretching strain rate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\dot{{\\epsilon\\:}_{s}}\\)\u003c/span\u003e\u003c/span\u003e can be expressed as a function of the compressing strain rate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\dot{{\\epsilon\\:}_{c}}\\)\u003c/span\u003e\u003c/span\u003e (Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\dot{{\\epsilon\\:}_{s}}=\\sqrt{\\frac{\\dot{{\\epsilon\\:}_{c}}}{{t}_{0}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, \u003cem\u003et\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e represents the unit time interval, which is set to 1 s for standard units. Assuming that the loading rate in the polymer strands scales with the stretching strain rate, we have Eq.\u0026nbsp;\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{r}_{F}=C\\dot{{\\epsilon\\:}_{s}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eBased on Equations \u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the relationship between the molecular force \u003cem\u003eF\u003c/em\u003e and the compressive strain rate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\dot{{\\epsilon\\:}_{c}}\\)\u003c/span\u003e\u003c/span\u003e is given by Eq.\u0026nbsp;\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:F=\\frac{{k}_{B}T}{2\\varDelta\\:{x}^{\u0026Dagger;}}ln\\left(\\frac{C\\varDelta\\:{x}^{\u0026Dagger;}\\dot{{\\epsilon\\:}_{c}}}{{k}_{0}{t}_{0}{k}_{B}T}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWe fit the plot of \u003cem\u003eF\u003c/em\u003e vs. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\dot{{\\epsilon\\:}_{c}}\\)\u003c/span\u003e\u003c/span\u003e to Eq.\u0026nbsp;\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, which provides a slope of 17.7 pN, corresponding to a Δ\u003cem\u003ex\u003c/em\u003e\u003csup\u003e\u0026Dagger;\u003c/sup\u003e of 1.16 \u0026Aring;. This is comparable to the calculated Δ\u003cem\u003ex\u003c/em\u003e\u003csup\u003e\u0026Dagger;\u003c/sup\u003e for the stepwise pathway, where Δ\u003cem\u003ex\u003c/em\u003e\u003csup\u003e\u0026Dagger;\u003c/sup\u003e is 1.29 \u0026Aring; at 130 pN. We were unable to obtain an optimized transition state structure TS1 (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eA) for the stepwise pathway at forces below 130 pN as the concerted pathway becomes dominant. Nevertheless, it is expected that the force-free Δ\u003cem\u003ex\u003c/em\u003e\u003csup\u003e\u0026Dagger;\u003c/sup\u003e to be close to 1.29 \u0026Aring;. Overall, the self-consistency of the framework supports the validity of the quantitative connection between the macroscopic stress and the molecular bond-breaking force.\u003c/p\u003e "},{"header":"Conclusions","content":"\u003cp\u003eHaving the anthracene\u0026ndash;maleimide mechanophore installed in the first network of a double-network elastomer enables up to 20% mechanophore activation when the elastomer is compressed. The kinetic responses of the mechanochemical retro-Diels\u0026ndash;Alder reaction provide a rare opportunity to analyze the dependence of the bond-breaking force on the loading conditions. Notably, while both strain and strain rate can influence the macroscopic stress, their effects on bond-breaking forces differ: the bond breaking force is largely insensitive to strain but shows a logarithmic dependence on strain rate. This quantitative connection between the molecular bond-breaking force and the strain rate can be viewed as a \u0026ldquo;macroscopic dynamic force-spectroscopy\u0026rdquo;, which allows us to interrogate the structures of the transition states that regulate the reaction. The relationship demonstrated here highlights the robustness of the chemomechanical framework for understanding reactivity across various scales. Looking ahead, we expect that mechanochemical kinetics will be further leveraged to unveil the mechanical behavior of materials.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgments:\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe authors thank S-Q Wang for helpful discussion.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding:\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe following funding sources are gratefully acknowledged:\u003c/p\u003e\n\u003cp\u003eNational Science Foundation CHE-2204079 (JW)\u003c/p\u003e\n\u003cp\u003eAlfred P. Sloan Foundation FG-2023-20341 (JW)\u003c/p\u003e\n\u003cp\u003eCamille and Henry Dreyfus Foundation TC-24-087 (JW)\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eConceptualization: ZW, QZ, JW\u003c/p\u003e\n\u003cp\u003eMethodology: ZW, QZ, JW\u003c/p\u003e\n\u003cp\u003eInvestigation: ZW, DS, MCW, JZ, QZ, JW\u003c/p\u003e\n\u003cp\u003eProject administration: QZ, JW\u003c/p\u003e\n\u003cp\u003eWriting \u0026ndash; original draft: ZW\u003c/p\u003e\n\u003cp\u003eWriting \u0026ndash; review \u0026amp; editing: ZW, QZ, JW\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests:\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAuthors declare that they have no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData and materials availability:\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAll data are available in the main text or the supplementary materials.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eM. K. Beyer, H. Clausen-Schaumann, Mechanochemistry:\u0026thinsp; The Mechanical Activation of Covalent Bonds. \u003cem\u003eChem. Rev.\u003c/em\u003e \u003cstrong\u003e105\u003c/strong\u003e, 2921-2948 (2005).\u003c/li\u003e\n\u003cli\u003eS. Wang, S. Panyukov, M. Rubinstein, S. L. Craig, Quantitative Adjustment to the Molecular Energy Parameter in the Lake\u0026ndash;Thomas Theory of Polymer Fracture Energy. \u003cem\u003eMacromolecules\u003c/em\u003e, (2019).\u003c/li\u003e\n\u003cli\u003eS.-Q. Wang, Z. Fan, C. Gupta, A. Siavoshani, T. Smith, Fracture Behavior of Polymers in Plastic and Elastomeric States. \u003cem\u003eMacromolecules\u003c/em\u003e \u003cstrong\u003e57\u003c/strong\u003e, 3875-3900 (2024).\u003c/li\u003e\n\u003cli\u003eM. M. Caruso\u003cem\u003e et al.\u003c/em\u003e, Mechanically-Induced Chemical Changes in Polymeric Materials. \u003cem\u003eChem. Rev.\u003c/em\u003e \u003cstrong\u003e109\u003c/strong\u003e, 5755-5798 (2009).\u003c/li\u003e\n\u003cli\u003eM. B. Larsen, A. J. Boydston, \u0026ldquo;Flex-Activated\u0026rdquo; Mechanophores: Using Polymer Mechanochemistry To Direct Bond Bending Activation. \u003cem\u003eJ. Am. Chem. Soc.\u003c/em\u003e \u003cstrong\u003e135\u003c/strong\u003e, 8189-8192 (2013).\u003c/li\u003e\n\u003cli\u003eX. Hu, T. Zeng, C. C. Husic, M. J. Robb, Mechanically Triggered Small Molecule Release from a Masked Furfuryl Carbonate. \u003cem\u003eJ. Am. Chem. Soc.\u003c/em\u003e \u003cstrong\u003e141\u003c/strong\u003e, 15018-15023 (2019).\u003c/li\u003e\n\u003cli\u003eS. Huo\u003cem\u003e et al.\u003c/em\u003e, Mechanochemical bond scission for the activation of drugs. \u003cem\u003eNat. Chem.\u003c/em\u003e \u003cstrong\u003e13\u003c/strong\u003e, 131-139 (2021).\u003c/li\u003e\n\u003cli\u003eY. Yao\u003cem\u003e et al.\u003c/em\u003e, Remote control of mechanochemical reactions under physiological conditions using biocompatible focused ultrasound. \u003cem\u003eProc. Natl. Acad. Sci. U. S. A.\u003c/em\u003e \u003cstrong\u003e120\u003c/strong\u003e, e2309822120 (2023).\u003c/li\u003e\n\u003cli\u003eT.-G. Hsu\u003cem\u003e et al.\u003c/em\u003e, A Polymer with \u0026ldquo;Locked\u0026rdquo; Degradability: Superior Backbone Stability and Accessible Degradability Enabled by Mechanophore Installation. \u003cem\u003eJ. Am. Chem. Soc.\u003c/em\u003e \u003cstrong\u003e142\u003c/strong\u003e, 2100-2104 (2020).\u003c/li\u003e\n\u003cli\u003eY. Lin, T. B. Kouznetsova, S. L. Craig, Mechanically Gated Degradable Polymers. \u003cem\u003eJ. Am. Chem. Soc.\u003c/em\u003e \u003cstrong\u003e142\u003c/strong\u003e, 2105-2109 (2020).\u003c/li\u003e\n\u003cli\u003eJ. Yang, Y. Xia, Mechanochemical generation of acid-degradable poly(enol ether)s. \u003cem\u003eChem. Sci.\u003c/em\u003e \u003cstrong\u003e12\u003c/strong\u003e, 4389-4394 (2021).\u003c/li\u003e\n\u003cli\u003eA. Piermattei, S. Karthikeyan, R. P. Sijbesma, Activating catalysts with mechanical force. \u003cem\u003eNat. Chem.\u003c/em\u003e \u003cstrong\u003e1\u003c/strong\u003e, 133-137 (2009).\u003c/li\u003e\n\u003cli\u003eY. Yu, X. Zheng, C. Duan, S. L. Craig, R. A. Widenhoefer, Force-Modulated Selectivity of the Rhodium-Catalyzed Hydroformylation of 1-Alkenes. \u003cem\u003eACS Catalysis\u003c/em\u003e \u003cstrong\u003e12\u003c/strong\u003e, 13941-13950 (2022).\u003c/li\u003e\n\u003cli\u003eA. L. B. Ramirez\u003cem\u003e et al.\u003c/em\u003e, Mechanochemical strengthening of a synthetic polymer in response to typically destructive shear forces. \u003cem\u003eNat. Chem.\u003c/em\u003e \u003cstrong\u003e5\u003c/strong\u003e, 757 (2013).\u003c/li\u003e\n\u003cli\u003eH. Zhang\u003cem\u003e et al.\u003c/em\u003e, Mechanochromism and Mechanical-Force-Triggered Cross-Linking from a Single Reactive Moiety Incorporated into Polymer Chains. \u003cem\u003eAngew. Chem. Int. Ed.\u003c/em\u003e \u003cstrong\u003e55\u003c/strong\u003e, 3040-3044 (2016).\u003c/li\u003e\n\u003cli\u003eA. L. Black, J. M. Lenhardt, S. L. Craig, From molecular mechanochemistry to stress-responsive materials. \u003cem\u003eJ. Mater. Chem.\u003c/em\u003e \u003cstrong\u003e21\u003c/strong\u003e, 1655-1663 (2011).\u003c/li\u003e\n\u003cli\u003eJ. Li, C. Nagamani, J. S. Moore, Polymer Mechanochemistry: From Destructive to Productive. \u003cem\u003eAcc. Chem. Res.\u003c/em\u003e \u003cstrong\u003e48\u003c/strong\u003e, 2181-2190 (2015).\u003c/li\u003e\n\u003cli\u003eN. Willis-Fox, E. Rognin, T. A. Aljohani, R. Daly, Polymer Mechanochemistry: Manufacturing Is Now a Force to Be Reckoned With. \u003cem\u003eChem\u003c/em\u003e \u003cstrong\u003e4\u003c/strong\u003e, 2499-2537 (2018).\u003c/li\u003e\n\u003cli\u003eM. Stratigaki, R. G\u0026ouml;stl, Methods for Exerting and Sensing Force in Polymer Materials Using Mechanophores. \u003cem\u003eChemPlusChem\u003c/em\u003e \u003cstrong\u003e85\u003c/strong\u003e, 1095-1103 (2020).\u003c/li\u003e\n\u003cli\u003eA. J. Boydston\u003cem\u003e et al.\u003c/em\u003e, The role of polymer mechanochemistry in responsive materials and additive manufacturing. \u003cem\u003eNat. Rev. Mater.\u003c/em\u003e \u003cstrong\u003e6\u003c/strong\u003e, 84-98 (2021).\u003c/li\u003e\n\u003cli\u003eS. L. Craig, Concluding remarks: Fundamentals, applications and future of mechanochemistry. \u003cem\u003eFaraday Discuss.\u003c/em\u003e \u003cstrong\u003e241\u003c/strong\u003e, 485-491 (2023).\u003c/li\u003e\n\u003cli\u003eE. M. Lloyd, J. R. Vakil, Y. Yao, N. R. Sottos, S. L. Craig, Covalent Mechanochemistry and Contemporary Polymer Network Chemistry: A Marriage in the Making. \u003cem\u003eJ. Am. Chem. Soc.\u003c/em\u003e \u003cstrong\u003e145\u003c/strong\u003e, 751-770 (2023).\u003c/li\u003e\n\u003cli\u003eG. I. Bell, Models for the specific adhesion of cells to cells: a theoretical framework for adhesion mediated by reversible bonds between cell surface molecules. \u003cem\u003eScience\u003c/em\u003e \u003cstrong\u003e200\u003c/strong\u003e, 618-627 (1978).\u003c/li\u003e\n\u003cli\u003eC. K. Lee\u003cem\u003e et al.\u003c/em\u003e, Force-induced redistribution of a chemical equilibrium. \u003cem\u003eJ. Am. Chem. Soc.\u003c/em\u003e \u003cstrong\u003e132\u003c/strong\u003e, 16107-16111 (2010).\u003c/li\u003e\n\u003cli\u003eT. A. Kim, M. J. Robb, J. S. Moore, S. R. White, N. R. Sottos, Mechanical Reactivity of Two Different Spiropyran Mechanophores in Polydimethylsiloxane. \u003cem\u003eMacromolecules\u003c/em\u003e \u003cstrong\u003e51\u003c/strong\u003e, 9177-9183 (2018).\u003c/li\u003e\n\u003cli\u003eY. Vidavsky\u003cem\u003e et al.\u003c/em\u003e, Enabling Room-Temperature Mechanochromic Activation in a Glassy Polymer: Synthesis and Characterization of Spiropyran Polycarbonate. \u003cem\u003eJ. Am. Chem. Soc.\u003c/em\u003e \u003cstrong\u003e141\u003c/strong\u003e, 10060-10067 (2019).\u003c/li\u003e\n\u003cli\u003eT.-G. Hsu\u003cem\u003e et al.\u003c/em\u003e, A Polymer with \u0026quot;locked\u0026quot; Degradability: Superior Backbone Stability and Accessible Degradability Enabled by Mechanophore Installation. \u003cem\u003eJ. Am. Chem. Soc.\u003c/em\u003e \u003cstrong\u003e142\u003c/strong\u003e, 2100-2104 (2020).\u003c/li\u003e\n\u003cli\u003eY. Lin, T. B. Kouznetsova, C. C. Chang, S. L. Craig, Enhanced polymer mechanical degradation through mechanochemically unveiled lactonization. \u003cem\u003eNat. Commun.\u003c/em\u003e \u003cstrong\u003e11\u003c/strong\u003e, 4987 (2020).\u003c/li\u003e\n\u003cli\u003eP. A. May, N. F. Munaretto, M. B. Hamoy, M. J. Robb, J. S. Moore, Is Molecular Weight or Degree of Polymerization a Better Descriptor of Ultrasound-Induced Mechanochemical Transduction? \u003cem\u003eACS Macro Lett.\u003c/em\u003e \u003cstrong\u003e5\u003c/strong\u003e, 177-180 (2016).\u003c/li\u003e\n\u003cli\u003eJ. M. Lenhardt, A. L. Black, S. L. Craig, gem-Dichlorocyclopropanes as Abundant and Efficient Mechanophores in Polybutadiene Copolymers under Mechanical Stress. \u003cem\u003eJ. Am. Chem. Soc.\u003c/em\u003e \u003cstrong\u003e131\u003c/strong\u003e, 10818-10819 (2009).\u003c/li\u003e\n\u003cli\u003eH. Zhang, C. E. Diesendruck, Linear versus Helical Side Chains in Bottlebrush Polymers: Morphology and Mechanochemistry. \u003cem\u003eMacromolecules\u003c/em\u003e \u003cstrong\u003e57\u003c/strong\u003e, 3664-3670 (2024).\u003c/li\u003e\n\u003cli\u003eS. M. Luo, R. W. Barber, A. C. Overholts, M. J. Robb, Competitive Activation Experiments Reveal Significantly Different Mechanochemical Reactivity of Furan\u0026ndash;Maleimide and Anthracene\u0026ndash;Maleimide Mechanophores. \u003cem\u003eACS Polymers Au\u003c/em\u003e \u003cstrong\u003e3\u003c/strong\u003e, 202-208 (2023).\u003c/li\u003e\n\u003cli\u003eC. P. Kabb, C. S. O\u0026apos;Bryan, C. D. Morley, T. E. Angelini, B. S. Sumerlin, Anthracene-based mechanophores for compression-activated fluorescence in polymeric networks. \u003cem\u003eChem. Sci.\u003c/em\u003e \u003cstrong\u003e10\u003c/strong\u003e, 7702-7708 (2019).\u003c/li\u003e\n\u003cli\u003eJ. M. Lenhardt\u003cem\u003e et al.\u003c/em\u003e, Characterizing the mechanochemically active domains in gem-dihalocyclopropanated polybutadiene under compression and tension. \u003cem\u003eJ. Mater. Chem.\u003c/em\u003e \u003cstrong\u003e21\u003c/strong\u003e, 8454-8459 (2011).\u003c/li\u003e\n\u003cli\u003eY. Chen, C. Joshua Yeh, Y. Qi, R. Long, C. Creton, From force-responsive molecules to quantifying and mapping stresses in soft materials. \u003cem\u003eSci. Adv.\u003c/em\u003e \u003cstrong\u003e6\u003c/strong\u003e, 1-9 (2020).\u003c/li\u003e\n\u003cli\u003eP. Millereau\u003cem\u003e et al.\u003c/em\u003e, Mechanics of elastomeric molecular composites. \u003cem\u003eProc. Natl. Acad. Sci. U. S. A.\u003c/em\u003e \u003cstrong\u003e115\u003c/strong\u003e, 9110-9115 (2018).\u003c/li\u003e\n\u003cli\u003eJ. Slootman, C. J. Yeh, P. Millereau, J. Comtet, C. Creton, A molecular interpretation of the toughness of multiple network elastomers at high temperature. \u003cem\u003eProc. Natl. Acad. Sci. U. S. A.\u003c/em\u003e \u003cstrong\u003e119\u003c/strong\u003e, 1-11 (2022).\u003c/li\u003e\n\u003cli\u003eE. Ducrot, Y. Chen, M. Bulters, R. P. Sijbesma, C. Creton, Toughening elastomers with sacrificial bonds and watching them break. \u003cem\u003eScience\u003c/em\u003e \u003cstrong\u003e344\u003c/strong\u003e, 186-189 (2014).\u003c/li\u003e\n\u003cli\u003eZ. Wang\u003cem\u003e et al.\u003c/em\u003e, Toughening hydrogels through force-triggered chemical reactions that lengthen polymer strands. \u003cem\u003eScience\u003c/em\u003e \u003cstrong\u003e374\u003c/strong\u003e, 193-193 (2021).\u003c/li\u003e\n\u003cli\u003eT. Ouchi, B. H. Bowser, T. B. Kouznetsova, X. Zheng, S. L. Craig, Strain-triggered acidification in a double-network hydrogel enabled by multi-functional transduction of molecular mechanochemistry. \u003cem\u003eMaterials Horizons\u003c/em\u003e \u003cstrong\u003e10\u003c/strong\u003e, 585-593 (2023).\u003c/li\u003e\n\u003cli\u003eZ. J. Wang\u003cem\u003e et al.\u003c/em\u003e, Effect of the Activation Force of Mechanophore on Its Activation Selectivity and Efficiency in Polymer Networks. \u003cem\u003eJ. Am. Chem. Soc.\u003c/em\u003e \u003cstrong\u003e146\u003c/strong\u003e, 13336\u0026minus;13346 (2024).\u003c/li\u003e\n\u003cli\u003eT. Watabe, D. Aoki, H. Otsuka, Polymer-Network Toughening and Highly Sensitive Mechanochromism via a Dynamic Covalent Mechanophore and a Multinetwork Strategy. \u003cem\u003eMacromolecules\u003c/em\u003e \u003cstrong\u003e55\u003c/strong\u003e, 5795-5802 (2022).\u003c/li\u003e\n\u003cli\u003eJ. P. Gong, Y. Katsuyama, T. Kurokawa, Y. Osada, Double-Network Hydrogels with Extremely High Mechanical Strength. \u003cem\u003eAdv. Mater.\u003c/em\u003e \u003cstrong\u003e15\u003c/strong\u003e, 1155-1158 (2003).\u003c/li\u003e\n\u003cli\u003eJ. P. Gong, Why are double network hydrogels so tough? \u003cem\u003eSoft Matter\u003c/em\u003e \u003cstrong\u003e6\u003c/strong\u003e, 2583-2590 (2010).\u003c/li\u003e\n\u003cli\u003eJ. P. Gong, Materials both Tough and Soft. \u003cem\u003eScience\u003c/em\u003e \u003cstrong\u003e344\u003c/strong\u003e, 161-162 (2014).\u003c/li\u003e\n\u003cli\u003eR. Bai\u003cem\u003e et al.\u003c/em\u003e, Fatigue fracture of tough hydrogels. \u003cem\u003eExtreme Mechanics Letters\u003c/em\u003e \u003cstrong\u003e15\u003c/strong\u003e, 91-96 (2017).\u003c/li\u003e\n\u003cli\u003eY. Zhou\u003cem\u003e et al.\u003c/em\u003e, The Stiffness-Threshold Conflict in Polymer Networks and a Resolution. \u003cem\u003eJournal of Applied Mechanics\u003c/em\u003e \u003cstrong\u003e87\u003c/strong\u003e, 031002 (2019).\u003c/li\u003e\n\u003cli\u003eD. A. Davis\u003cem\u003e et al.\u003c/em\u003e, Force-induced activation of covalent bonds in mechanoresponsive polymeric materials. \u003cem\u003eNature\u003c/em\u003e \u003cstrong\u003e459\u003c/strong\u003e, 68-72 (2009).\u003c/li\u003e\n\u003cli\u003eH. Sakai\u003cem\u003e et al.\u003c/em\u003e, Visualization and Quantitative Evaluation of Toughening Polymer Networks by a Sacrificial Dynamic Cross-Linker with Mechanochromic Properties. \u003cem\u003eACS Macro Lett.\u003c/em\u003e \u003cstrong\u003e9\u003c/strong\u003e, 1108-1113 (2020).\u003c/li\u003e\n\u003cli\u003eZ. Wang\u003cem\u003e et al.\u003c/em\u003e, A Novel Mechanochromic and Photochromic Polymer Film: When Rhodamine Joins Polyurethane. \u003cem\u003eAdv. Mater.\u003c/em\u003e \u003cstrong\u003e27\u003c/strong\u003e, 6469-6474 (2015).\u003c/li\u003e\n\u003cli\u003eZ. Chen\u003cem\u003e et al.\u003c/em\u003e, Stress-Dependent Multicolor Mechanochromism in Epoxy Thermosets Based on Rhodamine and Diaminodiphenylmethane Mechanophores. \u003cem\u003eMacromolecules\u003c/em\u003e \u003cstrong\u003e55\u003c/strong\u003e, 2310-2319 (2022).\u003c/li\u003e\n\u003cli\u003eZ. S. Kean, G. R. Gossweiler, T. B. Kouznetsova, G. B. Hewage, S. L. Craig, A coumarin dimer probe of mechanochemical scission efficiency in the sonochemical activation of chain-centered mechanophore polymers. \u003cem\u003eChem. Commun.\u003c/em\u003e \u003cstrong\u003e51\u003c/strong\u003e, 9157-9160 (2015).\u003c/li\u003e\n\u003cli\u003eJ. Sung, M. J. Robb, S. R. White, J. S. Moore, N. R. Sottos, Interfacial mechanophore activation using laser-induced stress waves. \u003cem\u003eJ. Am. Chem. Soc.\u003c/em\u003e \u003cstrong\u003e140\u003c/strong\u003e, 5000-5003 (2018).\u003c/li\u003e\n\u003cli\u003eJ. Li\u003cem\u003e et al.\u003c/em\u003e, Mechanophore Activation at Heterointerfaces. \u003cem\u003eJ. Am. Chem. Soc\u003c/em\u003e \u003cstrong\u003e136\u003c/strong\u003e, 15925\u0026minus;15928 (2014).\u003c/li\u003e\n\u003cli\u003eS. Akbulatov\u003cem\u003e et al.\u003c/em\u003e, Experimentally realized mechanochemistry distinct from force-accelerated scission of loaded bonds. \u003cem\u003eScience\u003c/em\u003e \u003cstrong\u003e357\u003c/strong\u003e, 299-303 (2017).\u003c/li\u003e\n\u003cli\u003eH. Eyring, The Activated Complex in Chemical Reactions. \u003cem\u003eJ. Chem. Phys.\u003c/em\u003e \u003cstrong\u003e3\u003c/strong\u003e, 107-115 (1935).\u003c/li\u003e\n\u003cli\u003eE. Evans, K. Ritchie, Dynamic strength of molecular adhesion bonds. \u003cem\u003eBiophys. J.\u003c/em\u003e \u003cstrong\u003e72\u003c/strong\u003e, 1541-1555 (1997).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"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-5205619/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5205619/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMechanical stress is ubiquitous in materials, and it is well accepted that stress causes material wear and failure—which, at the molecular level, results from force-induced bond breakage. Understanding the mechanical behavior of materials at the molecular level requires a quantitative relationship between macroscopic stress and bond-breaking force, a connection that remains largely unexplored. Here we report that the macroscopic stress and the bond-breaking force are quantitatively connected through the kinetics of mechanically activated retro-Diels–Alder reaction of an anthracene–maleimide adduct mechanophore, which is embedded within the crosslink of a double-network elastomer. We find that the force required for bond breakage is largely insensitive to the strain applied to the elastomer but increases linearly with the logarithm of the strain rate. These findings provide insights into the mechanical behavior of polymeric materials and offer valuable guidance for the design of mechanically responsive materials.\u003c/p\u003e","manuscriptTitle":"Quantitative Connection between Macroscopic Stress and Bond-Breaking Force Enabled by Time-Stamped Mechanochemical Fluorescence","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-08 06:00:46","doi":"10.21203/rs.3.rs-5205619/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":"9bf8504b-b30d-4376-8863-57058aad2507","owner":[],"postedDate":"January 8th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":42488237,"name":"Physical sciences/Materials science/Soft materials/Polymers"},{"id":42488238,"name":"Physical sciences/Chemistry/Materials chemistry"}],"tags":[],"updatedAt":"2025-09-16T14:56:09+00:00","versionOfRecord":[],"versionCreatedAt":"2025-01-08 06:00:46","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5205619","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5205619","identity":"rs-5205619","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}