Multi-modal mechanophores based on cinnamate dimers

Mechanochemistry offers exciting opportunities for molecular-level engineering of stress-responsive properties of polymers. Reactive sites, sometimes called mechanophores, have been reported to increase the material toughness, to make the material mechanochromic or optically healable. Here we show that macrocyclic cinnamate dimers combine these productive stress-responsive modes. The highly thermally stable dimers dissociate on the sub-second timescale when subject to a stretching force of 1–2 nN (depending on isomer). Stretching a polymer of the dimers above this force more than doubles its contour length and increases the strain energy that the chain absorbs before fragmenting by at least 600 kcal per mole of monomer. The dissociation produces a chromophore and dimers are reformed upon irradiation, thus allowing optical healing of mechanically degraded parts of the material. The mechanochemical kinetics, single-chain extensibility, toughness and potentially optical properties of the dissociation products are tunable by synthetic modifications.

Computed forcedependent free energies of activation of homolysis of backbone bonds in models of polymers of cinnamate dimers before and after dissociation of cinnamate dimers. Each line corresponds to G ‡ for homolysis of the bond of the same color highlighted in bold: dashed lines refer to homolysis of bonds in diethyl (1R,2S,3R,4S)-3,4-dimethylcyclobutane-1,2-dicarboxylate (left structure), solid lines to ethyl E-3-(4-(propionyloxy)phenyl)acrylate (right structure). Force was applied to the C atoms of the Me groups (as illustrated by arrows). G t ‡ (f) for dissociation of the cinnamate dimers studied in this work are contained in the grey area. All calculations were at the uMPW1K/6-31+G* level in vacuum. Figure 6. Force-dependent barriers of dissociation of 3. Energies of individual kinetic barriers (left graphs, solid and dashed lines represent barriers to dissociation of the 1 st and 2 nd scissile bonds, respectively) of the M2 mechanism and the total activation free energy of dissociation, G t ‡ (right graphs) of anti-3 (a) and syn-3 (b) macrocycles compared with the same energies for nonmacrocyclic cinnamate dimers. Note that at force <0.5 nN (anti-1, anti-3a and syn-3) or <0.8 nN (syn-1) the dimers dissociate by M1 mechanism whose barriers are omitted for clarity from the left-side graphs. Above these forces, the dissociation mechanism is M2 ( Fig. 1b and Supplementary Figs. 1, 3c-d). The graphs' colors match those of the reactions on the right. The pulling axes are defined by black arrows (force is applied at the C atoms of the Me groups). We didn't calculate the activation energies of anti-3b (n=1, Fig. 1a) because its reactant was calculated to be 32 kcal mol -1 less stable than the syn-3a analog, making it synthetically inaccessible.

Supplementary Figure 7. Mechanistic origin of isomerization of 3 during dissociation.
Mechanochemical dissociation of series 3 dimers produces either EE or EZ dienes, depending on the applied force and the length of the linker. (a) The relationship between various rotational conformers of Int' and TS2' along the M2 dissociation path; the pulling axis is defined by the red arrows; Ph' = pphenoxy. (b) The free energy of the TS2' EZ conformational ensemble (leading to EZ dienes) relative to the EE-generating transition states (TS2' EE + TS2r' EE in a). Negative values mean that the TS2' EZ is more stable than the TS2' EE analogs with the dissociation producing EZ dienes. Mechanochemical dissociation of series 3 dimers is calculated to produce EZ dienes over practically relevant forces (force is applied at the C atoms of the Me groups). Figure 8. Synthesis of precursors to 2a.   Supplementary Fig. 19). Irradiation of P2 prior to mechanical loading doesn't change its solubility.     H NMR and 13 C NMR spectra were recorded in either CDCl 3 or DMSO and referenced to the residual solvent signals on a 500 MHz Brucker Avance II spectrometer at 25 °C. All chemical shifts were given in ppm (δ) as singlet (d), triplet (t), quartet (q), multiplet (m), or broad (br).

Supplementary
Gel permeation chromatography (GPC) data were calibrated on two in series columns (7.8 × 300 mm, 2 GMHHRM17932 and 1 GMHHRH17360) with THF (HPLC grade) as eluent at 40 o C with a LC-20AD pump.
The facility was equipped with two detectors (RID-10A refractive index detector; SPD-20A UV detector) and the molecular weight was calibrated against polystyrene standards.
Silicon nitride AFM tips (Veeco Instruments, now Bruker Nano, Santa Barbara, CA, MLCT) were used in the SMFS experiments. Before modification, the AFM tips were treated with piranha solution (H 2 SO 4 (98%)/H 2 O 2 (30%) = 7:3 in volume), and thoroughly rinsed with deionized water, followed by drying in an oven at 115 o C for 90 min to remove any remaining water.

(Caution: Piranha solution that may result in explosion or skin burns is a very hazardous oxidant. This solution must be handled with extreme care.)
The vapor-phase deposition method was used for the silanization of clean AFM tips by placing them in the atmosphere of the APDMMS in a dry nitrogen-purged desiccator for 1.5 h at 25℃. Immediately after being taken out, the silanized tips were rinsed three times with methanol and then placed in a 110 o C oven for 10 min for activation.

Synthesis
All chemical structures and NMR spectra are shown in Supplementary Figs. 24-28.

Quantum-chemical calculations
All calculations were performed with the Gaussian09.E01 10 software package. The Berny algorithm was used to locate stationary points. Very tight convergence criteria and ultrafine integration grids were used in all optimizations. Thermodynamic corrections to electronic energies of individual conformers were calculated statistical-mechanically in the harmonic oscillator/rigid rotor/ideal gas approximations, as 3RT +ZPE +U vib -TS, where ZPE is the zero-point energy, U vib is the vibrational component of the internal energy and S is the total entropy. Vibrational frequencies below 500 cm -1 were replaced with 500 cm -1 as previously recommended 11 , to avoid the artifactually large contribution of such lowfrequency modes to vibrational entropy. The calculations of analytical frequencies on converged constrained molecules is valid because the molecule plus its infinitely-compliant constraining potential is a stationary point. 12,13 The free energies of ensembles were calculated as − ln ∑ −∆ / , where G min is the free energy of the conformational minimum, G i is the excess free energy of conformer i relative to this minimum, and g i is its degeneracy. The energy barriers separating individual strain-free conformers were <4 kcal/mol, justifying the use of Boltzmann statistics in calculating properties of ground and transition states and energies of activation. Ensemble averaging was done as , where  is the quantity of interest (e.g., end-to-end distance) and the remaining terms are defined above.
The converged wavefunctions were stable as determined by outcome of the testing with the "stable" key word in Gaussian. All converged conformers of the reactant or intermediate states had 0 imaginary frequencies and all converged conformers of the transition states had a single imaginary frequency with the nuclear motion consistent with dissociation/rotation as appropriate. Unconstrained conformational ensembles of 1-3 were built systematically as previously described. 14,15 All unique conformers of every stationary state of 1 were fully optimized at the uMPW1K/6-31+G(d) level. For macrocycles 2-3, conformers of the reactant, TS1, TS2, TS1', TS2', Int and Int' (with one or both scissile bonds constrained for all species other than the reactant) were first generated at the MM3 level, followed by constrained optimization at uBLYP/6-31+G(d), and constrained reoptimization of the unique BLYP conformers within 1.5 kcal mol -1 from each conformational minima at the uMPW1K/6-31+G(d) level. Of these, all conformers of the transition states and intermediates within 1 kcal mol -1 from the conformational minima were fully reoptimized (analytical frequencies were calculated before and after optimization of all transition state conformers and some intermediates, where initial optimization converged to a reactant because of a poor initial estimate of the Hessian). Force-dependent properties of individual conformers and the conformational ensembles were calculated following the described procedures. 14, 15

Calculation of single-chain force/extension curves of P2
No analytical solution describes the force/extension curve or the evolution of the composition of the chain during a dynamic single-molecule force experiment. 14,16 Consequently, force/extension curves were calculated by incrementing the value of the stretching time, t, and control parameter, L, (figure on the right) and calculating all other parameters determining the behavior of the chain (chain length, l, restoring force of the chain, f, chain composition, x; bending force of the cantilever, F and the survival probability, s) for each sequential value of t and L as described below. Force/extension curves for dissociation of syn dimers were calculated independently from those for anti dimers (in the former case, the simulation stopped when the final syn dimer dissociated; in the latter case, the simulations started with copolymer of EE diene and anti dimer). Because isomerization of each monomer is a stochastic process, for a chain containing n dimers we calculated ~10 5 n 3/2 (or 10 8 , whichever was smaller) individual force/extension curves. In each simulation a unique combination of n monotonically decreasing random numbers from 0.9999 to 10 -4 was used to define at which simulation step each dimer dissociated (below we call this set of n numbers probability vector, S). These sets of random numbers were generated and converted to the total relative probability that each calculated force/extension curve would appear among all generated curves as described below.
The force-extension curve of a chain comprised of a syn dimers, b anti dimers and c E,E dienes was calculated as l(f)=a(l(A n=2 )+l(A n=4 )/2+l(A n=6 )/3)/6+ b(l(B n=2 )+l(B n=4 )/2+l(B n=6 )/3)/6 + c(l(C n=1 )+l(C n=2 )/2)/2, where l(X n=y ) is the ensemble average separation of the C atoms of the terminal Me groups (i.e., Me C … C Me ) as a function of the externally applied force for one of the compounds shown above, which are repeat units of copolymer P2 before or after dimer dissociation. In other words, our calculations of the measured force/extension curves used scaled Me C … C Me distances extrapolated from ensemble-averaged Me C … C Me distances of repeat units of polymer P2 before and after mechanochemical reactions calculated at the BLYP/6-31+G* level in vacuum. Some of the force/extension curves for the extreme cases (e.g., c=0 or a=0) are illustrated in Supplementary Fig. 11 as dashed red, blue and green curves).
At the i th step of the calculation L i = L i-1 + vt i (v = 1 m/s is the experimental stretching rate and t i is the time increment of the i th step) and the composition of the chain was x i (which defines the number of syn, anti and E,E monomers, i.e., x i =[a i ,b i ,c i ] using the notations above). If the condition of mechanical equilibrium was satisfied (|f i | = |F i |, see below), the end-to-end separation of the chain was found numerically be solving the equation l i = L i -f(l i ,x i )/, where f(l,x) is the force-extension curve for a chain of composition x derived from quantum-chemical calculations as described above and  is the harmonic compliance of the cantilever. From l i , f i (the restoring force of the chain) was found using the f(l,x) correlation. From f i , the expectation value of the survival probability of the dimer by time t i from the start of the experiment, s i , is found as s i = s i-1 (1-k(f i )t i ), where ( ) = ℎ −∆ ‡ ( )/ is the rate constant of dissociation at the restoring force f i and G ‡ t (f i ) are plotted as green curves on the right panel of Supplementary Fig. 5. If s i exceeded a predefined value, the simulation progressed to the (i+1) th step. Otherwise, the composition of the chain was changed by reducing the number of the appropriate isomer of the dimer by one and increasing the number of the E,E dienes by 1. Because a large object such as an AFM tip moves much slower than the rate at which the chain reaches internal mechanical equilibrium after one of its monomers reacted, for a few steps immediately after dimer dissociation the absolute value of the restoring force of the chain, |f i | is less than the force corresponding to the instantaneous deflection of the cantilever, |F i | which is evidenced in the experiments by short segments of force/extension curves where the extension increases while the force decreases. Consequently, for a few steps following the dissociation the force of the cantilever was calculated as |F i |=|F i-1 |-t i (|F i-1 |-|f(l i ,x i )|), where  is a coefficient whose value was adjusted to reproduce the rate at which mechanical equilibrium between the cantilever and the stretched chain re-establishes. This formula was applied as long |f(L i ,x i )|<|F i-1 |+10 pN, after which the mechanical equilibrium was assumed to have re-established. A comparison of an experimental force extension curve (blue) and a calculated L(F) curve (red) for an experimentally studied chain comprised of 32 syn dimers and 308 anti dimers is shown below (in this simulation, only syn dimers were reacted).
In each simulation the step at which a dimer was dissociated was determined by comparing the expectation value of the survival probability with the corresponding number from the probability vector. For each chain containing n syn dimers or n anti dimers we generated ~10 5 n 3/2 unique vectors (i.e., sets of n monotonically decreasing random numbers selected between 0.9999 and 10 -4 ). The example above corresponds to the highest-probability L(F) curve and was generated using the following set of random numbers to define the survival probabilities at which each subsequent dimer dissociated (for space, only (1) where s j,i is the i th number from the vector above. Physically, this relative weight corresponds to the probability of the j th curve to be observed if the experiment were repeated under identical conditions 10 5 n 3/2 times. The curve illustrated above had the calculated relative probability of 3.13×10 -7 .
For chains with fewer than 15 reactive dimers, the set of probability vectors were generated using the rand function of Matlab. After calculating their absolute weights (the numerator of the equation above), the generated vectors were sorted and only those vectors with the largest absolute weights that together accounted for 95% of the sum in the denominator of the above equation were retained. As the n increases, the fraction of randomly generated probability vectors accounting for 95% of the denominator decreases very rapidly making this approach to generating probability vectors impractical for simulating force/extension curves with 15 or more equivalent reactive sites. Consequently, for chains with more than 14 reactive dimers we used a different strategy in which we first found the probability vector corresponding to the largest possible value of the numerator by funding the roots of the system of n-1 polynomials generated by differentiating the numerator with respect to each s i . We then used these values to limit the range over which each corresponding survival probability value could vary across the whole set of probability vectors. For example, the set of survival probabilities that determine when the first isomerization would occur was generated by applying the rand function to the range [0.9999:(s m,1 -s m,2 )/2], where m signifies the highest-probability vector described above and 1 and 2 corresponds to the 1 st and 2 nd element of this vector. We established that the two methods produce equivalent distributions of dissociation forces by generated two sets of probability vectors (one by each method) for a chain with 10 syn (and 53 anti) and 15 syn (and 40 anti) dimers.
In calculating the distribution of single-chain forces for dissociation of anti dimers for comparison with the experiment, only the dissociation of the first m dimers was considered, where m is the number of experimentally observed dissociations.