Quantifying Rate- and Temperature-Dependent Molecular Damage in Elastomer Fracture

Elastomers are highly valued soft materials finding many applications in the engineering and biomedical fields for their ability to stretch reversibly to large deformations. Yet their maximum extensibility is limited by the occurrence of fracture, which is currently still poorly understood. Because of a lack of experimental evidence, current physical models of elastomer fracture describe the rate and temperature dependence of the fracture energy as being solely due to viscoelastic friction, with chemical bond scission at the crack tip assumed to remain constant. Here, by coupling new fluorogenic mechanochemistry with quantitative confocal microscopy mapping, we are able to quantitatively detect, with high spatial resolution and sensitivity, the scission of covalent bonds as ordinary elastomers fracture at different strain rates and temperatures. Our measurements reveal that, in simple networks, bond scission, far from being restricted to a constant level near the crack plane, can both be delocalized over up to hundreds of micrometers and increase by a factor of 100, depending on the temperature and stretch rate. These observations, permitted by the high fluorescence and stability of the mechanophore, point to an intricate coupling between strain-rate-dependent viscous dissipation and strain-dependent irreversible network scission. These findings paint an entirely novel picture of fracture in soft materials, where energy dissipated by covalent bond scission accounts for a much larger fraction of the total fracture energy than previously believed. Our results pioneer the sensitive, quantitative, and spatially resolved detection of bond scission to assess material damage in a variety of soft materials and their applications.


I. INTRODUCTION
Many new soft but tough rubbery materials have been recently discovered [1][2][3][4], and new applications such as flexible prosthetics [5], stretchable electrodes [6], or soft robotics [7] continuously emerge. Yet, a credible multiscale quantitative picture of damage and fracture of these materials has still not emerged, in particular, due to our fundamental inability to disentangle the irreversible scission of chemical bonds along the fracture path from dissipation by internal molecular friction [8].
The failure and fracture of soft materials is indeed an inherently multiscale process: The propagation of a macroscopic crack in the material couples molecular covalent bond scission processes at the crack tip, with deformation and energy dissipation in the bulk [9,10]. Elastomers, a representative class of soft materials, are networks of connected flexible polymer chains, which do not display a well-defined localized yielding behavior, such as metals, ceramics, or polymer glasses. When a crack propagates in an elastomer, it is thus impossible to detect when and where bonds break with conventional methods, and the "process zone" (the mechanically damaged region) is treated for lack of information as an energy sink [11][12][13] or a cohesive zone of zero thickness [14,15].
Within the field of mechanochemistry, synthetic chemists have recently developed new molecules that can respond optically to forces and bond scission processes when suitably incorporated in polymer networks [16][17][18]. These mechanosensitive molecules have been incorporated into multiple network elastomers and in filled elastomers and have given important new insights into sacrificial bond scission during the fracture process [19][20][21]. However, the dioxetane-based mechanophore previously used by Ducrot et al. emits light only upon bond scission, cannot be calibrated easily to compare different materials in absolute terms, and gives a very low signal (approximately one emitted photon every 1000 broken bonds). As a result, the first generation of mechanophores could detect bond scission only in reinforced elastomers containing sacrificial bonds in the bulk by design, and quantitative comparisons between different materials were not possible. Furthermore, the low sensitivity and real time emission upon crack propagation made it challenging to address dynamic problems like crack propagation at different rates with a high spatial resolution. No signal was detected, for example, upon fracture of simple unfilled elastomers [19], making it impossible to address the questions of the current paper. It should be noted also that, while the importance of breaking covalent sacrificial bonds to toughen soft materials, and elastomers, in particular, has been amply demonstrated in several materials [19,20,22], the strain rate and/or temperature dependence of bond breakage of covalent (not dynamic) bonds has never been addressed. Yet this rate and T dependence of the fracture energy in elastomers has major technological consequences in applications [8] and is a long-standing and still open scientific question [8,9,12].
Recently, Göstl, Sijbesma, and co-workers reported a new fluorogenic mechanophore based on a Diels-Alder (DA) adduct of π-extended anthracene [18,23] that fluoresces stably and sensitively upon force-induced bond scission, making it an ideal candidate for quantitative studies on simple elastomers. This high sensitivity and stability make it possible to label simple networks of classical unfilled elastomers, which are at the heart of all molecular fracture theories.
We incorporate this mechanophore as a chain scissionreporting cross-linker into a series of acrylate elastomers prepared by photoinitiated free radical polymerization (Tables I and II and Appendix A). By fracturing these labeled elastomers at different temperatures and strain rates and performing postmortem fluorescence imaging, we could improve sensitivity by at least 2 orders of magnitude with respect to our previous strategy [19] and obtain unprecedented spatially resolved quantitative insight into the coupling between molecular bond scission processes at the crack tip and bulk viscoelastic dissipation in these soft materials.

II. FRACTURE PROPAGATION IN ELASTOMERS
We propagate cracks by stretching single-edged notched samples of elastomeric networks in uniaxial extension at different stretch rates _ λ and temperatures T [ Fig. 1(a) and Appendix B]. The networks are synthesized from ethyl acrylate (EA) or methyl acrylate (MA) monomers and 1,4-butanediol diacrylate (BDA) as nonmechanoresponsive cross-linker and are labeled with additional 0.02 mol% (relative to monomer) of the mechanophore diacrylate cross-linker (see Tables I and II and synthesis details in Appendix A and in Supplemental Material [24]). The total cross-link density is of the order of ν x ∼ 10 25 m −3 . These mechanical measurements [ Fig. 1(b)] are used to extract the macroscopic fracture energy Γ c [J · m −2 ] (energy necessary to propagate a unit area of crack), using a fracture mechanics method [25], as well as the crack propagation speed v crack (see Appendix B). For the poly(methyl acrylate) elastomer (PMA-DA-0.4, see Table I), we observe a decrease in fracture energy for an increasing temperature and for decreasing crack propagation speed v crack (obtained by varying the stretch rate) (Fig. S5 in Supplemental Material [24]), a typical observation in elastomers [26].
As shown in Fig. 1(c), following classical timetemperature superposition of the data [12], this macroscopic fracture energy obtained for various temperatures (square) and stretch rates (circles) can be plotted as a sole function of a reduced crack speed a T · v crack . The factor a T is a decreasing function of the temperature, characterizing viscoelastic dissipation in the sample, and is measured from linear rheology (reported in Fig. S7 in Supplemental Material [24]). This overall rescaling leads to a powerlaw increase in the fracture energy with crack propagation speed [dashed line, Fig. 1(c)], characterizing the importance of viscoelastic processes during fracture propagation.
For a lack of molecular insights on the actual dissipative processes occurring at the crack tip, this rate-dependent behavior has always been described by the phenomenological expression Γ c ¼ Γ 0 · ½1 þ fða T :v crack Þ, decoupling the rate-independent bond scission processes in the network Γ 0 , occurring strictly in the fracture plane [27], from bulk rate-dependent viscoelastic dissipation [characterized by the function fða T :v crack Þ with fðv → 0Þ ¼ 0], predicted from the linear viscoelastic properties of the material [11,28,29] or simply correlated with mechanical hysteresis [30]. This picture is clearly oversimplified: Assuming Γ 0 to be velocity independent is in contradiction with the general expectation for rate-dependent materials [31], and quantitative agreement with data if a constant Γ 0 is assumed requires the introduction of arbitrary length or energy scales [8,32] or predicts viscoelastic dissipation to take place down to typically unphysically small molecular distances at the crack tip [12]. Here, we tackle the inconsistencies in the current models by quantifying for the first time molecular bond breakage at the crack tip during fracture propagation in these materials.

III. MECHANOPHORES QUANTITATIVELY REPORT STRAND SCISSION
As shown in Fig. 2, by incorporating DA adduct mechanophores as cross-linkers in the network, we can quantify chain scission during elastomer failure [ Fig. 2(a); typically, 5%-10% of overall cross-links are mechanophores]. In its native form, the mechanophore is nonfluorescent [ Fig. 2(b)(i)]. If a sufficient force is applied to the bond, it can undergo cycloelimination (a retro DA reaction), which is irreversible at low temperature [18], leading to the release of a fluorescent π-extended anthracene moiety [ Fig. 2 reported [33,34], the retro DA reaction is greatly accelerated under force with a significantly higher mechanochemical scission rate compared to homolytic C─C bond scission. When connected to the mechanophore, a stressed polymer strand under extension, thus, fails more likely through scission of this mechanochemically weaker bond [ Fig. 2(b)(ii)], leading to the activation of fluorescence.
Since the mechanophore bond is weaker than the C─C bond, an important question is its ability to quantitatively and reliably report for strand breakage. The key aspect to understand here is that, in a 3D network of entangled and cross-linked polymer chains, the forces on bonds along the chain and at cross-link points are not homogeneous, since the strands between cross-links have a distribution of lengths (number of monomers) and conformations (some are more coiled than others). In elastomers, cross-link points deform affinely with macroscopic deformation. In a mean-field representation neglecting interactions between strands, only the strands that are close to their maximum extension see forces of the order of the scission force as discussed in detail by Vernerey et al. [35].
Of course, the breakage force of a strand containing a mechanophore will be lower than that of a C─C bond. However, because of the strong nonlinearity of the forceextension curve of the strands [35,36], a C─C bond would have broken anyway at only a slightly larger macroscopic extension than the mechanophore. As a result, the fluorescence should, in principle, report broken strands quantitatively but simply at a slightly lower value of stretch than what C─C bonds would break at. In this work, we hypothesize that the fraction ϕ of cleaved chains in the overall material, a characteristic of local damage of the network, is equal to the fraction of cleaved mechanophores. To validate this important hypothesis, we verify that the number of activated mechanophores during mechanical testing varies indeed linearly with the initial fraction of DA adduct used as cross-linker ( Fig. 8 in Appendix C) and that the mechanophore-labeled networks have nearly identical mechanical properties as the pristine ones within the reproducibility of the experiment (Fig. S6 in Supplemental Material [24]). We add a simple quantitative argument rationalizing this result in Appendix C.
The extent of strand failure and damage in the material can now be quantified postmortem by measuring the activation of fluorescent mechanophores following crack propagation in various conditions. We use confocal mapping to quantify strand scission in the material normal to the crack surface through the measurement of the local fluorescence intensity due to mechanophore activation [ Fig. 3(b)]. Confocal mapping reduces out-of-focus light and allows the measurement of intensity in local volumes x × z × y ("voxels") of typically 1.8 × 1.8 × 12 μm 3 inside of the material (see Appendix C). Figure 3(a) shows 500 × 500 μm 2 maps of the fluorescence intensity in planes normal to the crack surface, in two PMA-DA-0.4 samples fractured at stretch rates _ λ ¼ 3.10 −3 s −1 and temperature (i) T ¼ 80°C and (ii) T ¼ 25°C, conditions where (i) low and (ii) high bulk viscoelastic dissipation is active [ Fig. S7(d) [24]]. We observe in these 2D maps a maximum in fluorescence intensity at the crack surface and an intensity profile relatively invariant along the directions of crack propagation [vertical x direction in Fig. 3(a)]. Remarkably, large differences in the fluorescence profile are observed when comparing these two fracture conditions. For the first sample, fractured at T ¼ 80°C, bulk viscoelastic dissipation is low, and fluorescence activation (and, hence, network scission) is spatially confined to a region a few micrometers wide at the crack surface. When the sample is fractured at T ¼ 25°C, where bulk viscoelastic dissipation is much higher, we observe both an increase in intensity, revealing a larger local density of broken bonds, as well as a much larger spatial extension of the damage, with strand scission progressively decreasing toward the bulk of the material over a hundred micrometers. As similar damage maps are observed along the sample thickness [z direction, Fig. 3(b)], we restrict all further quantitative analysis to a constant depth of 100 μm in our samples (see Appendix C). Note that a significant thermal contribution to the retro DA fluorescence activation can be ruled out, as it would lead to increasing fluorescence with increasing temperature (Appendix C).
For quantification, the local fluorescence intensity is then compared to calibration samples with known amounts of 9-((4-anisyl)ethynyl)anthracene reference fluorophore [18] [equivalent to the activated anthracene, Fig. 2(b)(ii)] (Appendix C). As shown in Fig. 3(c), we extract from these raw confocal images the spatial profile of the fraction ϕ of activated mechanophores, equivalent to the fraction of broken strands [ Fig. 3(c), averaged spatial profile shown, respectively, in red (i) and blue (ii)]. As already shown in Fig. 3(a), the damage profile varies strongly with the fracture temperature. We define a damage length L, characterizing the spatial extension of strand scission in the material down to the detection threshold concentration of ð4 × 10 −3 Þ% and equal, respectively, to L ðiÞ ¼ 25 μm and L ðiiÞ ¼ 250 μm at 80°C and 25°C, respectively To quantify further the extent of damage in the network in each condition, we compute the density Σ of cleaved strands per unit area of crack surface created. This quantity Σ ¼ 2ν x R ϕðzÞdz (with ν x the volume density of crosslinks) is obtained by integrating the damage ϕðzÞ normal to the crack surface and is found to be, respectively, Σ ðiÞ ≈ 1.2 × 10 18 m −2 and Σ ðiiÞ ¼ 2.2 × 10 19 m −2 for, respectively, 80°C and 25°C. The factor 2 in the expression of Σ accounts for the fact that each crack surface includes only half of the total damage per unit area. Σ can be conveniently normalized by Σ LT , the minimum number of strands that need to be broken for a crack to propagate in the material [27]. Σ LT can be estimated as 1=2 × v x hR 2 0 i 1=2 , with ν x the volume density of cross-linking points and hR 2 0 i 1=2 the average distance between cross-links. Following Gaussian statistics, Σ LT can be expressed as a function of material parameters [37] (Appendix C) and is found to be of the order of 10 17 strands per m −2 (Table I). For the two conditions in Fig. 3, we find, respectively, Σ ðiÞ =Σ LT ≈ 6 and Σ ðiiÞ =Σ LT ≈ 110, a very large value demonstrating that, in this condition, crack propagation in the material involves the failure of many more bonds than a single molecular plane and extends over distances in the material that are more than 4 orders of magnitude larger than the network mesh size.

IV. VISCOELASTIC DISSIPATION AND CHAIN DAMAGE
The strong coupling between damage and viscoelastic dissipation in the sample uncovered in Fig. 3 and the large amount of molecular damage following crack propagation is an unexpected and novel result, never incorporated in any fracture model for lack of experimental insight. Using the same quantification technique, we carry out coupled mechanical measurements and postmortem damage mapping and quantification, systematically varying the stretch rates and temperature during fracture propagation. In order to increase the range of probed viscoelastic dissipation regimes, we furthermore compare the two PMA and PEA networks of respective glass transition T MA g ¼ 18°C and T EA g ¼ −18°C but similar cross-link density (Table I). Rescaling between the EA and MA data is obtained by adjusting the viscoelastic shift factor aðTÞ based on the onset of the glass transition in the storage modulus (Fig. S7 [24]). As shown in Fig. 4(a), we observe for these two materials a power-law increase in the fracture energy with crack propagation speed [dashed lines, Fig. 4(a)]. Because of the low glass transition temperature of the PEA network, we reach for this sample a low-velocity regime for which Γ c becomes less dependent on the crack speed, here for a T · v crack < 10 −10 m · s −1 [ Fig. 4(a), dashed arrow]. As discussed above, this overall rescaling of Γ c with reduced crack speed a T · v crack has been classically accounted for by spatially decoupling rate-independent processes at the crack tip with bulk viscoelastic dissipation. Our methodology developed in Figs. 2 and 3 allows us to revisit this oversimplified picture, as we can now quantify for each of these experimental conditions the density of strands broken per unit area of crack. To compare the two materials, we plot the normalized damage Σ=Σ LT as a function of a T · v crack . As shown in Fig. 4(b), this normalized areal density of broken strands shows a similar trend as that of the fracture energy Γ c , with a power-law increase in the density of broken bonds with increasing reduced crack velocity [dashed line in Fig. 4(b)]. This significant increase in covalent bond scission with crack speed contradicts the classical picture of fracture propagation, which assumes strand breakage to be independent or weakly dependent on crack velocity [11,27,38]. At very low crack velocities, we do recover a limiting behavior for which damage appears (within our experimental spatial resolution) indeed solely confined to a molecular plane, as characterized by Σ=Σ LT ≈ 1 [ Fig. 4(b), horizontal dashed line]. We also observe a saturation in damage due to bond scission for the PMA sample in the limit of high crack velocities (a T :v crack > 10 −3 m · s −1 ). Finally, as shown in Fig. 4(c), the damage length L characterizing the extension of damage in the material shows a similar trend as the normalized bond breakage Σ=Σ LT . Viscoelasticity, strand failure, and fracture energy appear here strongly coupled.
We rationalize this coupling between viscoelastic dissipation and bond scission in the network as due to an increase of the elastoadhesive length scale [9] at propagation Γ c =E with increasing reduced crack velocity. In viscoelastic materials, propagating the crack at a faster speed leads to more dissipation (the dissipative modulus E 00 increases with the strain rate) and requires higher values of the energy release rate G, leading to higher strains far from the crack. As discussed in a recent review [9], the elastoadhesive length at propagation Γ c =E sets the size of the crack tip opening displacement δ and the scale for the onset of nonlinear behaviors at the crack tip. As shown schematically in Fig. 5(e), this increase of δ ∼ Γ c =E with increased crack speed increases all local strains around the crack tip and, hence, the local probability of strand scission. Over the range of stretch rates and temperatures probed here, the reduced stretch rate is of the order of a T _ λ ∼ 2 × 10 −9 − 5 × 10 −4 s −1 , for which the elastic component of the modulus E 0 ≈ 1 MPa varies only little with the strain rate (Fig. S7 in Supplemental Material [24]). Given this nearly constant elastic modulus E', the crack tip displacement δ ∼ Γ c =E 0 should then scale with the reduced crack speed like Γ c . Since the strain field around the crack tip is directly dependent on δ, the associated areal damage density Σ should increase with δ and, we indeed, observe an  Table I . Note that the saturation of damage for the largest crack velocity could be due to the onset of stiffening of the material (increase in E) for the largest stretch rates (Fig. S7 [24]). In essence, this coupling means that a small increase in viscoelastic dissipation per unit volume far from the tip can cause a commensurable amount of dissipated energy close to the crack tip by bond scission and by the dissipative processes associated with bond scission.

V. EFFECT OF MOLECULAR STRUCTURE
Our methodology allows us to further investigate the effects of the molecular architecture of the material, such as the cross-link density, on bond scission at the crack tip. As shown in Fig. 5(a), when plotting the fracture energy as a function of the rescaled velocity for the two PMA samples with different cross-link densities, we observe that Γ c is larger for the sample with the lowest cross-link density ν x [ Fig. 5(a), comparing red and blue points] but follows the same power law with a T :v crack . Intriguingly, as shown in Fig. 5(b), the density Σ of strands cleaved during crack propagation shows a similar scaling; the broken strand density is actually slightly smaller for the PMA-DA-0.2 sample, with the smaller cross-link density and the larger Γ c [ Fig. 5(b), comparing red and blue points].
We can interpret these trends in the molecular framework set by Lake and Thomas [27]. The classical Lake-Thomas model makes two important claims. First, in the absence of viscoelastic dissipation (in threshold conditions), the fracture energy Γ c is expected to be proportional to the areal density of strands crossing the interface Σ LT . Second, each broken strand dissipates an energy N x · U B , with N x the number of backbone bonds in the strand and U B the rupture energy of a single bond. While these claims are reasonable in threshold conditions (in the absence of viscoelastic dissipation), where they have been checked experimentally [39][40][41], there are no obvious reasons for the extension of this coupling between strand scission and fracture energy, when additional viscoelastic dissipative processes are at stake in the material. Our measurements nevertheless demonstrate that a network of lower cross-link density leads to more total dissipated energy for fewer broken strands not only in threshold conditions but also for a wider range of crack propagation speeds.

VI. BOND SCISSION AND FRACTURE ENERGY
Since a significant level of bond scission occurs in our material during crack propagation, an important question is the relative contribution of viscoelastic dissipation Γ visco and bond scission Γ damage to the measured fracture energy, expressed as Γ c ¼ Γ damage þ Γ visco . Extrapolating the argument of Lake and Thomas on strand failure to strands in the bulk, we approximate the energy dissipated per unit area due to bond breakage as Γ damage ¼ Σ · U strand ¼ Σ · N x · U B . The original Lake-Thomas model proposed a value U B of 350 kJ·mol −1 or 3.6 eV for a carbon-carbon bond [27]. A recent analysis of the statistical aspect associated with strand failure based on single molecule stretching experiments provides a more realistic value of 60 kJ·mol −1 or 0.6 eV=bond as a sounder estimate [42] for the average energy lost by each C─C bond when the polymer strand breaks. Regardless of the exact value associated with this bond scission energy, we plot in Fig. 5(c) the quantity Γ damage =U b ¼ N x · Σ (directly proportional to the energy dissipated by bond scission) as a function of the macroscopic fracture energy Γ c of the material.
Whereas the energy Γ damage dissipated due to bond scission is classically assumed to be constant and proportional to Σ LT :N x [horizontal gray domain, Fig. 5(c)], we find in Fig. 5(c) a strong correlation between Γ damage =U b and Γ c (dashed lines are power-law fits). Bond scission thus contributes to the total fracture energy to a much larger extent than previously thought.
Γ damage can accordingly reach values of 100 times the Lake-Thomas Γ 0 threshold [ Fig. 5(c)], i.e., for the PMA-DA-0.4 network, more than 1 kJ=m 2 , dissipated over a volume with dimensions of the order of 100 μm near the crack tip. This new experimental insight highlights the so far neglected influence of molecular bond scission at the crack tip on fracture energies and explains why, as already pointed out by Gent [12], purely linear viscoelastic theories typically require viscoelastic dissipation to take place down to unphysically small molecular distances to the crack tip to account for experimentally measured fracture energy.
Our measurements allow us to further compare specifically the behavior of the different networks [Figs. 5(c) and 5(d)]. In Fig. 5(c), we approximate the coupling between bond scission and fracture energies as power laws, with Γ damage ∼ Γ β c with β ¼ 0.95, 0.72, and 0.54, respectively, for the three networks. The fraction of energy dissipated through molecular damage and viscoelasticity can be expressed, respectively, as . The scaling coefficient β e < 1 for all three networks suggests a slow and progressive transition from a strand scissiondominated regime to a viscoelasticity-dominated regime, without any simple decoupling between Γ damage and Γ visco . Figure 5(d) additionally shows the ratio Γ damage =Γ c as a function of a T V (taking the value U B ¼ 60 kJ:mol −1 for the bond breakage energy). Interestingly, this ratio varies from 0.8 to 0.2 as a T V increases, and, while the trend is clear, the relative importance of chain scission and viscoelastic dissipation does seem to depend both on the crosslinking ratio and on the nature of the polymer itself.
In summary, and as schematically represented in

VII. CONCLUSION
The labeling of elastomeric networks with fluorogenic mechanophores that become fluorescent upon scission gives unprecedented insights in the bond scission processes occurring at the crack tip as the material breaks. Our measurements unveil that, contrary to previous belief, bond scission in these simple networks can extend over more than 100 μm from the crack plane and is strongly dependent on the bulk viscoelastic properties of the network. These observations contradict classical models assuming spatial decoupling between strain-rate-independent damage processes at the crack tip and bulk viscoelastic dissipation. These new experimental insights suggest, instead, the occurrence of intrinsically coupled processes between strand scission and viscoelastic relaxation, mediated by an increase in local strains at the crack tip. Bond scission accordingly accounts for a much larger amount of the fracture energy than anticipated, especially in conditions of large viscoelasticity, and is an overlooked key factor to understand and model fracture toughness from molecular structure.
Our methodology and measurements on model networks open far-reaching and diverse paths. It can be used to quantitatively reevaluate a number of damage processes as, e.g., occurring during soft material long-term failure and reveal previously invisible damage in a nondestructive way. Our study should further guide the engineering and control of dissipative bond scission processes in complex tough soft materials such as engineering elastomers or tough hydrogels and stimulate the development of new multiscale models and simulations of elastomer fracture, coupling bond scission and viscoelastic behavior.
All data needed to evaluate the conclusions in the paper are present in the paper and/or Supplemental Material [24]. Additional data available from authors upon request. The authors declare that they have no competing interests.
The project was planned by C. C. and J. S. The samples were synthesized by J. S. and V. W. The mechanophore molecules were synthesized by J. S. and C. B. with advice from R. G. The mechanical testing was done by J. S. and V. W. The optical analysis of the data was carried out by C. J. Y. and J. C. The data was analyzed by J. S., J. C., and V. W., and the paper was written by C. C. and J. C., with input from all authors. The synthesis part was written by R. G. C. C. supervised the project. Purity and exact mass of the synthesized compounds are determined using an LCQ Fleet (Thermo Finnigan) ion-trap mass spectrometer equipped with a Surveyor autosampler and Surveyor PDA detector (Thermo Finnigan). Solvents are pumped with a flow of 0.2 mL·min −1 using a highpressure gradient system using two LC-10AD pumps (Shimadzu). Before mass analysis, the crude is run over a reverse phase C 18 column (GraceSmart 2 × 50 mm, Grace) using a 2%-90% MeCN linear gradient in H 2 O with 0.1% formic acid.

Diels-Alder adduct mechanophore synthesis
The synthetic procedure of the Diels-Alder adduct mechanophore is adapted from the procedure developed by the groups of Göstl and Sijbesma [18,23]. The five-step synthesis is described in Supplemental Material [24], Sec. S1 and Figs. S1-S4. The final product is noted DACL (for Diels-Alder adduct cross-linker). Intermediate species are noted DACL1-4.

Network synthesis
Samples are prepared through photoinduced free radical polymerization following a previously published general procedure [19,21]. 2-Hydroxy-2-methylpropiophenone (HMP) is used as an UV initiator. The standard crosslinker used is 1,4-butanediol diacrylate (BDA). Monomer, cross-linker, and initiator (1.16 mol% relative to monomer) are mixed, and the solution is cast in a mold. The latter is composed of two glass plates covered with transparent PET films (with a hydrophobic surface), with a silicone spacer QUANTIFYING RATE-AND TEMPERATURE-DEPENDENT … PHYS. REV. X 10, 041045 (2020) 041045-9 to control the sample thickness (0.7 mm) and two metal frames to seal the mold. The mold is placed under UV (λ ¼ 365 nm) for 2 h. The UV power is kept low (below 10 μW cm −2 ) to induce a slow polymerization in order to decrease the number of simultaneous growing chains and the number of termination reactions. After polymerization, the sample was dried overnight in vacuo (without heating) to remove unreacted volatile monomer. The sample is weighed before and after drying. The weight loss is less than 0.2%.
The cross-linker concentration is adjusted to tune the properties of the various materials (see Table II). For each material, up to three samples are obtained from one polymerization batch. For each polymerization, run on the same day, the reactive medium is taken from the same stock solution (monomer, cross-linkers), and the initiator is added prior to each polymerization.

Incorporation of the mechanophore into the network
To label the samples with mechanophores, the Diels-Alder adduct mechanophore diacrylate cross-linker (DACL) is covalently incorporated. The DACL is used in combination with the mechanochemically nonresponsive cross-linker BDA. The mechanophore cross-linker is introduced at a concentration of 0.02 mol%. This small quantity is sufficient for damage detection by fluorescence.

APPENDIX B: NETWORK PROPERTIES AND CHARACTERIZATION
The glass transition temperature T g of PMA and PEA networks is measured from dynamic mechanical analysis, based on an estimation of the inflection point of the storage modulus. We find T g of −18°C and 18°C for the PMA and PEA networks, respectively.

Evaluation of network cross-link density for the Lake-Thomas model
To properly characterize the density of cross-links and entanglements in our materials, we fit the stress-strain curve of the notched samples, with the network elasticity model proposed by Rubinstein and Panyukov [43]. Stress-strain curves are corrected for notch opening. We use measurements at _ λ ¼ 3.10 −3 s −1 and T ¼ −5°C and T ¼ 25°C for the PEA and PMA samples, respectively, allowing us to fit the stress-strain curves up to λ ¼ 2.6. This fit allows us to extract the contribution of cross-links E x and entanglements E e , from The average number N x of monomer between crosslinks is then estimated from E x as We find E x ¼ ½0.6; 0.35; 0.5 and E e ¼ ½0.7; 0.7; 0.5 for, respectively, PMA-DA-0.4 at 25°C, PMA-DA-0.2 at 25°C, and PEA-DA-0.5 at −5°C (values are averaged over two samples for PMA). As expected, the contribution of entanglements E e is the same for the two PMA samples. The fact that the ratio between cross-link contribution E x is not exactly two between PMA-DA-0.4 and PMA-DA-0.2 is probably due to the difference in reactivity between monomer and cross-linker leading to a different efficiency in the incorporation of the cross-linker in the network.

Lake-Thomas chain density
From Gaussian statistics, we can express Σ LT , the areal density of polymer strand crossing an arbitrary plane, as [37] with ν x the bulk density of cross-linking points, hR 2 0 i 1=2 the average distance between cross-links, l 0 the length of a C─C bond, E x the modulus due to cross-linking, ρ the density of the monomer, M 0 the molar mass of the monomer, T the temperature, and k B the Boltzmann constant. The parameters used for EA and MA network are reported in Table III.  We use an excitation wavelength λ ¼ 405 nm and recorded emission from 450 to 550 nm.

Confocal image collection
Crack propagation occurs throughout most of our experiments in a well-defined plane. In cases where few crack bifurcations appear (e.g., PEA at 40°C and 60°C), we restrict our image analysis to the regions of planar cracks. In all samples, the signal is homogenous throughout the thickness, and the 3D nature of the process can, thus, be simplified to a 2D analysis.
For systematic analysis, single optical sections are recorded in the area where the crack propagates. The images are taken perpendicular to the crack surface. Samples are immersed in glycerol to avoid refractive index mismatch at the crack surface (refractive index of PEA, PMA [45], and glycerol are, respectively, 1.464, 1.479, and 1.4722). The top of the sample is identified as the plane of maximal intensity. The focal plane is then displaced at 100 μm depth from the top of the sample for all quantification. Laser and gain are adapted for each set of experiments.
The sample is broken in two pieces following the crack propagation test. Two images at the beginning and end of the crack length are recorded for each side (four pictures per sample). Error bars in the main text [Figs. 4(b), 4(c), and 5(a)-5(c)] characterize standard deviation due to this spatial variability.

Vignetting and flat-field correction
During imaging with the AZ-100/C2+ confocal macroscope, the low magnification of the optical system results in vignetting (inhomogeneous illumination and gradual intensity darkening toward the corners). To correct for vignetting, we measure the intensity I FlatField in a calibration sample with a homogeneous concentration of fluorescent calibration molecule. The corrected image of the crack surface I corr is taken as I corr ¼ I original =I FlatField . We furthermore restrict all quantitative analysis of damage to a distance of 500 μm along the crack profile (see main text, Fig. 3).

Calibration of fluorescence intensity
To convert fluorescence intensity to a concentration of activated molecules, we use calibration samples. The calibration molecule [9-((4-anisyl)ethynyl)anthracene] [18] is solution blended directly with linear PEA chains (M w ∼ 95 kg·mol −1 in toluene from Sigma-Aldrich). The solvent is evaporated under a fume hood for one day and in vacuo overnight, leading to calibration samples with a homogeneous and known concentration of fluorescent molecules.
As fluorescence originates from the π-extended anthracene moiety, which is present both in the calibration molecule and in the activated mechanophore and because the environment is similar (PEA chains), the calibration molecule is assumed to have the same fluorescence properties as the activated mechanophore. Phase separation is not present at the optical scale, as verified by confocal fluorescence microscopy. The concentration of activated mechanophores can, thus, be measured based on the intensity of the calibration molecule. By varying the concentration of the calibration molecule, a calibration curve of fluorescence intensity vs activated mechanophore concentration (mol · m −3 ) is constructed as shown in Fig. 6. This calibration procedure is repeated each time a new set of optical measurements is taken.

Quantitative image analysis
We measure the intensity profile IðxÞ perpendicular to the crack edge and define the background intensity I bkg (Fig. 7). The concentration profile cðxÞ [and the fraction of activated mechanophore ϕðxÞ] is calculated as cðxÞ ¼ α½IðxÞ − I bkg with α the coefficient obtained from the calibration curve (Fig. 6).

Representativity of mechanophore activation for chain damage
To verify that mechanophore activation and fluorescence intensity are indeed representative of chain scission, we synthetize four samples with different concentrations of DACL while keeping the overall cross-linker concentration constant (0.41 mol%, corresponding to PMA-DA-04, Table II). We propagate cracks at a stretch rate of _ λ ¼ 3 × 10 −3 s −1 in these samples and quantify the fraction of activated mechanophore per unit area of crack. As shown in Fig. 8(a), we observe a nearly linear relation between activated mechanophore concentration and the molar fraction of mechanophore in the first network, indicating that the activation of mechanophores in the network is indeed representative of chain scission. Additionally, Fig. 8(b) shows that the damage profiles for the four different DACL concentration are indeed independent of the initial molar fraction of mechanophore incorporated in the network. In terms of mechanical properties, replacing ϕ ¼ 5% of the cross-linkers by a weaker mechanophore cross-linker is in the worst case equivalent to diluting the effective number of mechanically active chains per volume by ϕ (assuming the mechanophore link as infinitely weak), leading to ν eff x ¼ ð1 − ϕÞν 0 x . The areal density of nonmechanophore chains can then be expressed as Σ ∼ ðν eff x Þ 2=3 ∼ ð1 − ϕÞ 2=3 Σ 0 . Expressing the fracture energy as Γ ¼ N x ΣU, it has then only a weak scaling with ϕ (a 10% change in ϕ leads to a 7% change in fracture energy assuming that N does not change) that is within experimental error.

Intrinsic activation of mechanophore as a function of stretch rate and temperature
Mechanophore activation via the retro Diels-Alder reaction (see Fig. 2) could be intrinsically biased by the temperature or strain rate. To probe this effect, we synthetize a multiple network elastomer network of PMA as previously described in detail [19,21,37] with the first network containing the DACL mechanophore. This multiple network structure (obtained by swelling and polymerization steps) leads to an isotropic prestretch λ 0 ¼ 2.3 of the network synthesized first and allows us to apply large strains to this mechanophore-labeled network without macroscopically breaking the material. We can thus probe the intrinsic activation of the mechanophore under various conditions of strain and temperature. As shown in Fig. 9, we stretch this sample to various λ, leading to a stretch λ · λ 0 on the first network, and measure the bulk activation ϕ of the mechanophore. As reported in Fig. 9(a), within our experimental reproducibility, bulk mechanophore activation appears independent of the strain rate. We measure a slight increase in mechanophore activation at higher temperatures [ Fig. 9(b)], which could be an indication of thermally biased scission of the DACL bond. This effect could lead to the overestimation of damage at a large temperature. However, as shown in Figs. 4 and 5, we observe a large decrease in mechanophore activation at the fracture surface for an increasing temperature. Such a slight damage overestimation at a larger temperature does not affect our conclusion.