Pulling on bonds counterintuitively
Experimental mechanochemistry has largely focused on the application of force along chemical bonds to accelerate their cleavage. Akbulatov et al. now demonstrate that force can also play a more subtle role. They generated strained macrocyclic rings photochemically and then studied the influence of that strain on the rates of reactions that cleaved either phosphorus-oxygen or silicon-oxygen bonds. P-O cleavage was accelerated by force orthogonal to the bond axis, whereas the Si-O cleavage was inhibited by force along the bond. Both results were consistent with the respective transition states predicted by theory.
Science, this issue p. 299
Abstract
Stretching polymer chains accelerates dissociation of a variety of internal covalent bonds, to an extent that correlates well with the force experienced by the scissile bond. Recent theory has also predicted scenarios in which applied force accelerates dissociation of unloaded bonds and kinetically strengthens strained bonds. We report here unambiguous experimental validation of this hypothesis: Detailed kinetic measurements demonstrate that stretching phosphotriesters accelerates dissociation of the unloaded phosphorus-oxygen bond orthogonal to the pulling axis, whereas stretching organosiloxanes inhibits dissociation of the aligned loaded silicon-oxygen bonds. Qualitatively, the outcome is determined by phosphoester elongation and siloxane contraction along the pulling axis in the respective rate-determining transition states. Quantitatively, the results agree with a simple mechanochemical kinetics model.
The chemical responses of polymers to mechanical loads play an important role in polymer applications and the prospective design of new stress-responsive and energy-transducing materials (1–4). Thus far, only one type of covalent mechanochemical response has been demonstrated experimentally: accelerated dissociation of loaded (i.e., strained by applied force) bonds. Density functional theory (DFT) calculations indicate that the activation free energies, ΔG‡, of mechanistically diverse organic reactions reported to date (5–13) decrease approximately proportionally to the restoring force of the scissile bond, 
, with the slope averaged over 0 to 1.5 nN ranging from 0.18 to 1.1 Å [average: 0.7 ± 0.2 Å, corresponding to (6 ± 3)–fold acceleration per 0.1 nN of 
at 300 K (fig. S1 and table S1)]. Yet theory (14–16) and computations (17–21) suggest that stretching force can inhibit rather than accelerate dissociation of strained covalent bonds and accelerate dissociation of unloaded versus loaded bonds. Experimental evidence for such unconventional mechanochemistry has been elusive. Contradictory, often irreproducible reports from the 1970s and 1980s of load-inhibited reactions in bulk polymers are now considered erroneous (22, 23). A more recent claim (24) contradicts quantum-chemical computations (fig. S2) and awaits validation. Dissociation of certain biological adducts is weakly inhibited by force <0.1 nN (25), but the small magnitude and complex underlying molecular mechanisms limit the effect of such examples on polymer mechanochemistry.
The lack of experimental validation of such unconventional mechanochemistry bears out the considerable challenges of designing synthetically accessible molecules that can be strained along the necessary molecular axis, induced to react at suitable rates, and monitored to reliably quantify these rates. Here we show that force accelerates dissociation of the unloaded P–O bond of phosphotriesters [Fig. 1, reactions 1a to 1c (1a-c)] and accelerates or inhibits dissociation of loaded Si–O bonds of organosiloxanes, depending on force magnitude and solution acidity [Fig. 1, reactions 2a and 2b (2a-b)].
The gray double-headed arrows specify the internal molecular coordinate, 
, whose restoring force is useful for rationalization and prediction of the mechanochemical kinetics. p-AcOC6H4O– is p-acetylphenoxide. Ph, phenyl.
We first demonstrate that mechanochemistry of reactions 1 and 2 deviates from the conventional pattern of accelerated dissociation of a loaded bond by quantum-chemical calculations at B3LYP/6-311+G(d) with the SMD model to account for the reaction solvent. Although the performance of B3LYP in calculating reaction barriers is mixed, in our benchmarking of nine functionals, B3LYP reproduced all available experimental ΔG‡ for reactions 1 and 2 with the smallest mean error (0.7 kcal/mol) (tables S3 and S4). Because solvation affects nucleophilic-displacement mechanisms and kinetics, we calculated ΔG‡ for multiple microsolvation patterns (figs. S6 to S8 and table S2). We obtained the best agreement between experimental and calculated ΔG‡ with singly microsolvated nucleophiles (
and 
) for reactions 1a to 1c and 2a, and with two molecules of methanol as an H+-transfer bridge from the nucleophile (CH3OH) to the leaving alkoxide for reaction 2b. Our calculations reproduced the accepted mechanisms of reactions 1a to 1c (single-barrier associative interchange) (fig. S3) and 2a (two-barrier associative interchange) (fig. S4) (26). Methanolysis of siloxanes (reaction 2b), whose mechanism was not reported, was calculated to proceed by two competing associative paths, with the nucleophile entering adjacent to the leaving group (26) (fig. S5). To establish that the computed results reflect mechanochemistry of phosphate- and siloxane-containing macromolecules, we calculated complete conformational ensembles of three increasingly large homologs of each molecule (n = 0 to 2) (Fig. 1), as recommended previously (27).
To understand how force affects the reaction kinetics and mechanisms, we repeated these calculations with a stretching force of up to 2 nN applied between the terminal C atoms of the alkoxy substituents, using the method validated theoretically (16) and experimentally (13, 28) and reviewed (18, 29). These calculations indicate that although the mechanism of reactions 1a to 1c is insensitive to force (fig. S3), force causes mechanistic crossover in reactions 2a and 2b (fig. S9) by destabilizing the strain-free minimum-energy paths and stabilizing the higher-energy alternatives. As a result, these alternative mechanisms become dominant at 1.5 nN (reaction 2a) or 0.5 nN (reaction 2b), yielding complex nonmonotonic dependence of the activation energies on force, 
(Fig. 2 and fig. S10). For each reaction, the two largest homologs manifested comparable 
values (fig. S10), which suggests that they are representative of arbitrarily large analogs, including polymers (27).
.The energy difference is plotted as a function of the restoring force of the (A) scissile P–O or Si–O bond, 
, or of the (B) 
coordinate (defined by the arrows in Figs. 1 and 3), 
. 
is the strain-free activation free energy. Circles represent the experimental data, with 
for each E/Z pair of macrocycles (see below). Error bars define the 68% confidence intervals calculated according to eqs. S22 to S25. See data S1 and tables S5, S6, and S14 for the plotted data. 
signifies ensemble averaging. The lines are averages of the two largest homologs.
Figure 2 illustrates how 
correlates with the restoring force of the scissile bond, 
, and that of the 
nonbonding distance (gray arrows in Fig. 1), 
. These restoring forces quantify a fraction of molecular strain (imposed either externally by stretching a macrochain or internally in strained macrocycles described below) distributed over different parts of the molecule (12, 15, 18, 27, 29, 30). Of several proposed (31, 32) force-based schemes to quantify strain and its distribution, we used one based on molecular compliance (16, 33) because it is theoretically sound; depends only on atoms defining the coordinate, which allows comparisons across structurally distinct reactants; and, unlike the alternatives (34), is experimentally validated (28).
The 
versus 
correlation (Fig. 2A) illustrates the extent to which the mechanochemical kinetics of reactions 1a to 1c and 2a and 2b deviates from the previously established pattern (dashed line): Whereas the previously reported reactions are accelerated (6 ± 3)–fold per 0.1 nN of 
(fig. S1), P–O bond scission in reactions 1a to 1c is accelerated >104-fold. Conversely, scission of the loaded Si–O bond in reaction 2a is inhibited approximately twofold per 0.1 nN. The nonmonotonic 
of reaction 2b results from a competition between a reaction mechanism that is destabilized by a factor of ~150 per 0.1 nN and the alternative that is stabilized by a factor of 4 (fig. S8). Our calculations suggest that such competition is common for Si–O bond dissociations in a neutral or acidic medium (figs. S14 to S16), explaining the reported (35) accelerated failure of siloxane bridges at ≥0.8 nN in acid. Although any force accelerates nucleophile-free Si–O bond heterolysis, its barrier is too high to be relevant (fig. S17).
The 
versus 
correlation (Fig. 2B) allows the computed force-dependent kinetics to be validated experimentally using series of increasingly strained macrocyclic phosphoesters and siloxanes (Fig. 3), in which (E)-1,1′-biindanylidene (E stiff stilbene) exerts a well-defined stretching force on the reactive moiety with magnitude controlled by the macrocyclic size. We previously demonstrated (28) that 
values derived from such macrocycles predict quantitatively mechanochemical kinetics in polymers in single-molecule force spectroscopy (SMFS). We used macrocycles because reactions 1a to 1c and 2a and 2b cannot be studied by SMFS, which is limited to reactions that increase the macrochain contour length by several nanometers or break it and are either accelerated or only very weakly inhibited by force.
The scissile bonds are shown in bold. Macrocycles 2, 3, 6, and 7 exist as diastereomers due to point chirality of P and axial chirality of stiff stilbene (tables S7 and S8). The kinetics was measured on diastereomeric mixtures. In Z15 and E19, the two nonequivalent Si–O bonds dissociated in parallel (fig. S23 and tables S10, S12, and S13). The gray double-headed arrows define the 
distance whose restoring force is used to compare the computed and measured mechanochemical kinetics (Fig. 2B). kZ and kE are rate constants. Me, methyl.
We synthesized strain-free Z isomers of macrocycles 1 through 19 in four to six steps and 5 to 17% overall yields (fig. S18). Irradiating solutions of Z macrocycles yielded strained E analogs in up to 80% yield (fig. S19 and tables S7 and S8). All compounds were fully characterized by nuclear magnetic resonance (NMR), high-resolution mass spectrometry (HRMS), and ultraviolet-visible spectroscopy (tables S7, S8, and S10). We measured the kinetics of reactions 1a to 1c in H2O:CH3OH (2:1 molar ratio) by monitoring the absorbance of generated p-nitrophenolate (table S11 and figs. S20 to S22). Reactions 2a and 2b were measured in CH3OH and monitored by high-performance liquid chromatography (HPLC) (tables S12 and S13 and fig. S23). We performed all kinetic measurements in the dark to avoid photoisomerizing stiff stilbene and under pseudo–first-order conditions in the nucleophile. The reactions were first order in the macrocycle and in the nucleophile, consistent with the literature (the order of reaction 2b in the nucleophile could not be determined because it was the solvent). The reaction products were confirmed by NMR, HPLC, and HRMS (tables S15 and S16).
All E macrocyclic phosphates (reactions 1a to 1c) reacted faster than their Z analogs, with competition experiments yielding rate constant ratios, kE/kZ, of 2 to 12, 4 to 210, and 4 to 50 for OH–, PhO–, and p-acetylphenoxide, respectively, at 25°C (tables S11 to S14). Methanolysis of Z siloxane macrocycles proceeded in two steps (Fig. 3 and tables S12 and S13), with statistical ratios of the sequential rate constants in symmetrical Z macrocycles, 
. Conversely, we observed no intermediates in the methanolysis of E8 to E12 and of E15 to E16, consistent with slower dissociation of the first (strained) Si–O bond—which breaks the macrocycle to relax the distorted E stiff stilbene and the siloxane moiety (Fig. 3)—versus the second (strain-free) Si–O bond (i.e., 
). The conclusion that E stiff stilbene inhibits the first Si–O bond dissociation primarily by straining it is also consistent with the identical dissociation rates of the second (strain-free) Si–O bond in E and Z siloxanes 
. Conversely, the ratios of the rate constants for methanolysis of strained (E) and strain-free (Z) Si–O bonds 
were 0.01 to 0.1 in reaction 2a and 0.03 to 1.9 in reaction 2b. Rate constants measured at three or five temperatures over 25° to 60°C (6° to 25°C for E1) yielded activation entropies between –70 and 220 J K−1 mol−1 (average: 117 ± 29 J K−1 mol−1) (tables S5 to S7), consistent with the calculated associative mechanisms (26).
To enable comparisons between the measured kinetics of reactions 1a to 1c and 2a and 2b in macrocycles 1 through 19 and the computational models of stretched polymers (Fig. 2B), we quantified the excess molecular strain responsible for the difference in the reactivity of the E and Z isomers of each macrocycle 
(table S14) as the ensemble-averaged restoring force of the 
distance (arrows in Fig. 3), 
(eq. S1). We chose the 
distance because it is one of the two coordinates common for all macrocycles and because the negligible restoring force of the other common coordinate (scissile bond) in E1 through E7 precludes its use for comparisons among the macrocycles. We suggest that 
values correctly reflect the stereoelectronic factors responsible for the variation of the kinetics of reactions 1a to 1c and 2a and 2b across the macrocycles because 
values were derived from the same calculations that accurately reproduced measured ΔG‡ (table S8: mean error of 1.8 kcal/mol).
Qualitatively, mechanochemistry of reactions 1a to 1c and 2a and 2b is consistent with the conventional understanding of how force affects reaction rates: Transition states that are longer along the pulling axis than the corresponding reactants are stabilized by stretching force and vice versa (36). While in the transition states of reactions 1a to 1c both the scissile P–O bond and the molecule elongate along the pulling axis (Fig. 4A), in reactions 2a and 2b the molecule contracts in the rate-determining transition states, despite the simultaneous elongation of the scissile Si–O bond. The structural origin of this difference is the preference of the leaving group in nucleophilic displacements for an axial position of the trigonal-bipyramidal transition state. In phosphates, force acts across the termini of the spectator alkoxy moieties. The movement of these moieties in the equatorial plane of the trigonal-bipyramidal transition state requires the O–P–O angle to increase, and the molecule elongates monotonically as it progresses along the reaction path (dashed arrows in Fig. 4A), regardless of what happens to the scissile bond length. In contrast, the departure of an equivalent alkoxide group in siloxanes is energetically preferable from an axial position, so that the formation of the rate-determining transition state requires a contraction of the analogous O–Si–O angle, which shortens the terminal 
separation to a greater extent that the elongating scissile Si–O bond increases it. As a result, a siloxane first contracts along the pulling axis, which destabilizes the molecule when tensile force is acting on it, before elongating and eventually breaking.
(A) Overlay of the strain-free minimum-energy conformers of the reactant (magenta) and the rate-determining transition state (blue) for reactions 1a and 2a, omitting H atoms and phenyl moieties. Dashed arrows define the pulling axes. (B) Comparison of 
from DFT calculations (black) and extrapolations of strain-free kinetics using three internuclear distances: scissile bond (green), 
[red, solid arrows in (A)], and 
[magenta, dashed arrows in (A)]. Blue dotted lines are extrapolated 
values for the two competing paths of reaction 2b, using the 
distance; the resulting difference in the reaction activation energy 
is denoted by the blue dotted line with red overlap. For the other coordinates, only 
values are shown.
A major challenge in polymer mechanochemistry is to develop practical means of estimating kinetic stabilities of monomers under mechanical load. The simplest approach is to approximate 
by the product of applied force, f, and the difference of a single internuclear distance between the strain-free rate-determining transition and reactant states, ΔqO. The accuracy of such estimates depends strongly on the choice of this internuclear distance, as illustrated in Fig. 4B, where quantum-chemically calculated 
of reactions 2a and 2b (black) are compared with the estimates based on the elongation or contraction of two coordinates routinely used to rationalize mechanochemical reactivity [defined by the C atoms of the terminal methyl groups, 
, as well as by the scissile bond, 
, and that of the 
separation, 
(all illustrated in Fig. 4A)].
The scissile bond performs poorly (even predicting acceleration instead of inhibition of reaction 2a, green line in Fig. 4B) because it is too local, i.e., it fails to account for structural changes elsewhere in the molecule that are required for bond breaking (37, 38). The strain-free separation of C atoms of the methyl groups across which force is applied vastly overestimates the force effect (either inhibition or acceleration) because 
varies so much with force that its strain-free value poorly reflects structural differences of force-coupled states responsible for changes in reaction kinetics (fig. S11). Contrary to previous speculations (11, 14–19, 24, 27, 29, 39, 40), assuming that the coordinate is harmonically force-dependent only worsens the extrapolations (fig. S12). The 
distance outperforms the conventional coordinates, as it does in other nucleophilic displacements (6, 11, 12, 17, 37), reproducing the exact results within a factor of 2 (red line in Fig. 4B). It is also the only coordinate that correctly predicts force-dependent mechanistic crossover in reaction 2b and the resulting nonmonotonic 
correlation, thus illustrating that the minimum of the fΔqO products for individual reaction paths well approximates the net 
value of a reaction with competing mechanisms (dotted lines in Fig. 4B and fig. S13). Such competition is likely common in force-inhibited reactions, and properly quantifying the contributions of individual paths to the reaction activation energy is necessary to obtain realistic predictions of force-coupled reactivity.
The 
separation in reactions 1 and 2 exemplifies a previously suggested (6, 11, 12, 14–17, 37) universal coordinate for estimating force-dependent activation energies of nucleophilic displacements. This coordinate is defined by the two atoms that connect the electrophilic atom (i.e., P in reactions 1a to 1c and Si in reactions 2a and 2b) to the molecular moieties that transmit the external load to the reactive site, which are backbones in polymers and the linkers connecting the phosphate or siloxane sites to E stiff stilbene in macrocycles 1 through 19. The computational and experimental data on reactions 1a to 1c and 2a and 2b confirm that this universal coordinate performs well across the whole range of mechanochemical responses—that is, accelerated and inhibited dissociation of loaded bonds and accelerated dissociation of unloaded bonds. The universal coordinate renders predictable the mechanochemical kinetics of reactions not studied previously by allowing force-dependent kinetics to be estimated from strain-free geometries and obviating the need for demanding computations of strained geometries.
Our work confirms the existence of two mechanochemical phenomena distinct from force-accelerated scission of a loaded bond: accelerated dissociation of an unloaded bond, which is not perturbed by the applied force, and inhibited dissociation of a loaded (and weakened) bond. Quantum-chemical calculations suggest that the force-dependent kinetics measured in nonpolymeric models quantitatively reflect the reactions in polymers, where analogous measurements are not yet possible.
Supplementary Materials
www.sciencemag.org/content/357/6348/299/suppl/DC1
Materials and Methods
Supplementary Text
Figs. S1 to S23
Tables S1 to S17
Equations S1 to S25
NMR Spectra
Data S1
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References and Notes
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- Acknowledgments: The work was supported by the U.K. Engineering and Physical Sciences Research Council (Early Career Fellowship) and the U.S. NSF (CAREER Award); computational resources were provided by XSEDE (Extreme Science and Engineering Discovery Environment), supported by the NSF. S.A. synthesized the compounds and contributed to data analysis and writing of the manuscript; Y.T. performed the quantum-chemical computations and contributed to data analysis; Z.H. measured the kinetics of reactions 1a to 1c; T.J.K. measured the kinetics of reactions 2a and 2b and contributed to synthesis; Q.-Z.Y. developed stiff-stilbene syntheses; and R.B. conceived of and supervised the project, analyzed the data, and prepared the manuscript. Data supporting the results and conclusions in the manuscript are available as supplementary materials.
