Chemical reactions modulated by mechanical stress: Extended Bell theory

Charge Redistribution in Mechanochemical Reactions for Solid Interfaces

Mechanochemical strategies are widely used in various fields, ranging from friction and wear to mechanosynthesis, yet how the mechanical stress activates the chemical reactions at the electronic level is still open. We used first-principles density functional theory to study the rule of the stress-modified electronic states in transmitting mechanical energy to trigger chemical responses for different mechanochemical systems. The electron density redistribution among initial, transition, and final configurations is defined to correlate the energy evolution during reactions. We found that stress-induced changes in electron density redistribution are linearly related to activation energy and reaction energy, indicating the transition from mechanical work to chemical reactivity. The correlation coefficient is defined as the term "interface reactivity coefficient" to evaluate the susceptibility of chemical reactivity to mechanical action for material interfaces. The study may shed light on the electronic mechanism of the mechanochemical reactions behind the fundamental model as well as the mechanochemical phenomena.

Activation volume and quantum tunneling in the hydrogen transfer reaction between methyl radical and methane: A first computational study

We present a theory of the effect of quantum tunneling on the basic parameter that characterizes the effect of pressure on the rate constant of chemical reactions in a dense phase, the activation volume. This theory results in combining, on the one hand, the extreme pressure polarizable continuum model, a quantum chemical method to describe the effect of pressure on the reaction energy profile in a dense medium, and, on the other hand, the semiclassical version of the transition state theory, which includes the effect of quantum tunneling through a transmission coefficient. The theory has been applied to the study of the activation volume of the model reaction of hydrogen transfer between methyl radical and methane, including the primary isotope substitution of hydrogen with deuterium (H/D). The analysis of the numerical results offers, for the first time, a clear insight into the effect of quantum tunneling on the activation volume for this hydrogen transfer reaction: this effect results from the different influences that pressure has on the competing thermal and tunneling reaction mechanisms. Furthermore, the computed kinetic isotope effect (H/D) on the activation volume for this model hydrogen transfer correlates well with the experimental data for more complex hydrogen transfer reactions.

Interactions and reactivity in crystalline intermediates of mechanochemical cyclorhodation reactions

There is experimental evidence that solid mixtures of the rhodium dimer [Cp*RhCl2]2 and benzo[h] quinoline (BHQ) produce two different polymorphic molecular cocrystals called 4α and 4β under ball milling conditions. The addition of NaOAc to the mixture leads to the formation of the rhodacycle [Cp*Rh-(BHQ)Cl], where the central Rh atom retains its tetracoordinate character. Isolate 4β reacts with NaOAc leading to the same rhodacycle while isolate 4α does not under the same conditions. We show that the puzzling difference in reactivity between the two cocrystals can be traced back to fundamental aspects of the intermolecular interactions between the BHQ and [Cp*RhCl2]2 fragments in the crystalline environment. To support this view, we report a number of descriptors of the nature and strength of chemical bonds and intermolecular interactions in the extended solids and in a cluster model. We calculate formal quantum mechanical descriptors based on electronic structure, electron density, and binding and interaction energies including an energy decomposition analysis. Without exception, all descriptors point to 4β being a transient structure higher in energy than 4α with larger local and global electrophilic and nucleophilic powers, a more favorable spatial and energetic distribution of the frontier orbitals, and a more fragile crystal structure.

Dynamically tuning friction at the graphene interface using the field effect

Dynamically controlling friction in micro- and nanoscale devices is possible using applied electrical bias between contacting surfaces, but this can also induce unwanted reactions which can affect device performance. External electric fields provide a way around this limitation by removing the need to apply bias directly between the contacting surfaces. 2D materials are promising candidates for this approach as their properties can be easily tuned by electric fields and they can be straightforwardly used as surface coatings. This work investigates the friction between single layer graphene and an atomic force microscope tip under the influence of external electric fields. While the primary effect in most systems is electrostatically controllable adhesion, graphene in contact with semiconducting tips exhibits a regime of unexpectedly enhanced and highly tunable friction. The origins of this phenomenon are discussed in the context of fundamental frictional dissipation mechanisms considering stick slip behavior, electron-phonon coupling and viscous electronic flow.

Inferring equilibrium transition rates from nonequilibrium protocols

We develop a theory for inferring equilibrium transition rates from trajectories driven by a time-dependent force using results from stochastic thermodynamics. Applying the Kawasaki relation to approximate the nonequilibrium distribution function in terms of the equilibrium distribution function and the excess dissipation, we formulate a nonequilibrium transition state theory to estimate the rate enhancement over the equilibrium rate due to the nonequilibrium protocol. We demonstrate the utility of our theory in examples of pulling of harmonically trapped particles in one and two dimensions, as well as a semiflexible polymer with a reactive linker in three dimensions. We expect our purely thermodynamic approach will find use in both molecular simulation and force spectroscopy experiments.

Mechanochemical Felkin-Anh Model: Achieving Forbidden Reaction Outcomes with Mechanical Force

Anti-Felkin-Anh diastereoselectivity can be achieved for nucleophilic additions to α-chiral ketones upon stretching the ketone with a mechanical pulling force. Herein, a mechanochemical Felkin-Anh model is proposed for predicting the outcome of a nucleophilic addition to an α-chiral ketone. Essentially, the fully stretched chiral ketone has one substituent shielding each side of the carbonyl, in contrast to the Felkin-Anh model, in which free rotation around a bond is required to achieve the two rotamers of the ketone. Depending on the pulling scenario, either Felkin-Anh or anti-Felkin-Anh diastereoselectivity is obtained. The model is entirely based on the distance between the pulling points, which is maximized in the anti-periplanar arrangement. The major diastereomer is associated with the approach with the least steric interactions. The intuitive model is validated by means of mechanochemical density functional theory calculations. Importantly, the ketone is fully stretched in the sub 1 nN force regime, thus minimizing the risk of undesired homolytic bond rupture. Moreover, the mechanical force is not used for lowering the reaction barriers associated with the nucleophilic addition; instead, it is solely applied for locking the conformation of a molecule and provoking otherwise inaccessible reaction pathways on the force-modified potential energy surface.

Competitive Activation Experiments Reveal Significantly Different Mechanochemical Reactivity of Furan–Maleimide and Anthracene–Maleimide Mechanophores

During the past two decades, our understanding of mechanochemical reactivity has advanced considerably. Nevertheless, an incomplete knowledge of structure-activity relationships and the principles that govern mechanochemical transformations limits molecular design. The experimental development of mechanophores has thus benefited from simple computational tools like CoGEF, from which quantitative metrics like rupture force can be extracted to estimate reactivity. Furan-maleimide (FM) and anthracene-maleimide (AM) Diels-Alder adducts are widely studied mechanophores that undergo retro-Diels-Alder reactions upon mechanical activation in polymers. Despite possessing significantly different thermal stability, similar rupture forces predicted by CoGEF calculations suggest that these compounds exhibit similar mechanochemical reactivity. Here, we directly probe the relative mechanochemical reactivity of FM and AM adducts through competitive activation experiments. Ultrasound-induced mechanochemical activation of bis-adduct mechanophores comprising covalently tethered FM and AM subunits reveals pronounced selectivity-as high as ∼13:1-for reaction of the FM adduct compared to the AM adduct. Computational models provide insight into the greater reactivity of the FM mechanophore, indicating a more efficient mechanochemical coupling for the FM adduct compared to the AM adduct. The methodology employed here to directly interrogate the relative reactivity of two different mechanophores using a tethered bis-adduct configuration may be useful for other systems where more common sonication-based approaches are limited by poor sensitivity.

Critical stresses in mechanochemical reactions

The rates of mechanochemical reactions are generally found to increase exponentially with applied stress. However, a buckling theory analysis of the effect of a normal stress on an adsorbate that is oriented perpendicularly to the surface that reacts by tilting suggests that a critical value of the stress should be required to initiate a mechanochemical reaction. This concept is verified by using density functional theory calculations to simulate the effect of compressing a homologous series of alkyl thiolate species on copper by a hydrogen-terminated copper counter-face. This predicts that a critical stress is indeed needed to initiate methyl thiolate decomposition, which has a perpendicular C-CH3 bond. In contrast, no critical stress is found for ethyl thiolate with an almost horizontal C-CH3 bond, while a critical stress is required to isomerize propyl thiolate from a trans to a cis configuration. These predictions are tested by measuring the mechanochemical reaction rates of these alkyl thiolates on a Cu(100) substrate by sliding an atomic force microscope tip over the surface and finding a critical stress of ∼0.43 GPa for methyl thiolate, ∼0.33 GPa for propyl thiolate, but no evidence of a critical stress for ethyl thiolate, in accord with the predictions. These results provide insights not only into mechanochemical reaction mechanisms on surfaces, but also on the origin of critical phenomena in stress-induced processes in general. It also suggests novel approaches to designing robust surface films that can resist wear and damage.

Force Dependent Barriers from Analytic Potentials within Elastic Environments

Bond rupture under the action of external forces is usually induced by temperature fluctuations, where the key quantity is the force dependent barrier that needs to be overcome. Using analytic potentials we find that these barriers are fully determined by the dissociation energy and the maximal force the potential can withstand. The barrier shows a simple dependence on these two quantities that allows for a re-interpretation of the Eyring-Zhurkov-Bell length Δ x ‡ and the expressions in theories going beyond that. It is shown that solely elastic environments do not change this barrier in contrast to the predictions of constraint geometry simulate external force (COGEF) strategies. The findings are confirmed by explicit calculations of bond rupture in a polydimethylsiloxane model.

Assessing models of force-dependent unbinding rates via infrequent metadynamics

Protein–ligand interactions are crucial for a wide range of physiological processes. Many cellular functions result in these non-covalent “bonds” being mechanically strained, and this can be integral to proper cellular function. Broadly, two classes of force dependence have been observed—slip bonds, where the unbinding rate increases, and catch bonds, where the unbinding rate decreases. Despite much theoretical work, we cannot predict for which protein–ligand pairs, pulling coordinates, and forces a particular rate dependence will appear. Here, we assess the ability of MD simulations combined with enhanced sampling techniques to probe the force dependence of unbinding rates. We show that the infrequent metadynamics technique correctly produces both catch and slip bonding kinetics for model potentials. We then apply it to the well-studied case of a buckyball in a hydrophobic cavity, which appears to exhibit an ideal slip bond. Finally, we compute the force-dependent unbinding rate of biotin–streptavidin. Here, the complex nature of the unbinding process causes the infrequent metadynamics method to begin to break down due to the presence of unbinding intermediates, despite the use of a previously optimized sampling coordinate. Allowing for this limitation, a combination of kinetic and free energy computations predicts an overall slip bond for larger forces consistent with prior experimental results although there are substantial deviations at small forces that require further investigation. This work demonstrates the promise of predicting force-dependent unbinding rates using enhanced sampling MD techniques while also revealing the methodological barriers that must be overcome to tackle more complex targets in the future.

Interplay Between Applied Force and Radical Attack in the Mechanochemical Chain Scission of Poly(acrylic acid)

Sonication and radical attack are both known to contribute to breaking down polymers. Quantum chemical models show how the two can operate together, where radical attack is shown to reduce the effective tensile strength of the material. Using poly(acrylic acid) (PAA) as a model, hydrogen atom abstraction in PAA was found to improve the thermodynamics and kinetics of bond scission. The force needed for bond rupture was estimated to decrease from 4.7 to 2.5 nN. This occurs because hydrogen atom abstraction drastically alters the potential energy surface of the scissile bond. Bond activation was also found to decrease the magnitude of the changes in bond scission geometries and energetics in response to the applied force. While radical abstraction is overall beneficial for mechanical bond scission, the polymer also becomes less responsive to force than the unactivated polymer. This finding places upper limits on the efficacy of the synergy between radical attack and applied force. In addition, the importance of reaction pathway optimization is also shown, where comparisons to the COGEF method show the latter to be qualitatively incapable of describing chain scission after radical activation.

Molecular Paradigms for Biological Mechanosensing

Many proteins in living cells are subject to mechanical forces, which can be generated internally by molecular machines, or externally, e.g., by pressure gradients. In general, these forces fall in the piconewton range, which is similar in magnitude to forces experienced by a molecule due to thermal fluctuations. While we would naively expect such moderate forces to produce only minimal changes, a wide variety of "mechanosensing" proteins have evolved with functions that are responsive to forces in this regime. The goal of this article is to provide a physical chemistry perspective on protein-based molecular mechanosensing paradigms used in living systems, and how these paradigms can be explored using novel computational methods.

Ab initio molecular dynamics modeling of single polyethylene chains: Scission kinetics and influence of radical under mechanical strain

Ab initio molecular dynamics was used to estimate the response to constant imposed strain on a short polyethylene (PE) chain and a radical chain with a removed hydrogen atom. Two independent types of simulations were run. In the first case, the chains were strained by expanding a periodic cell, restraining the length but allowing the internal degrees of freedom to reach equilibrium. From these simulations, the average force on the chain was computed, and the resulting force was integrated to determine the Helmholtz free energy for chain stretching. In the second set of simulations, chains were constrained to various lengths, while a bond was restrained at various bond lengths using umbrella sampling. This provided free energy of bond scission for various chain strains. The sum of the two free energy functions results in an approximation of the free energy of chain scission under various strains and gives a realistic and new picture of the effect of chain strain on bond breaking. Unimolecular scission rates for each chain type were examined as a function of chain strain. The scission rate for the radical chain is several orders of magnitude larger than that of the pristine chain at smaller strains and at equilibrium. This highlights the importance of radical formation in PE rupture and is consistent with experiments. Constant strain results were used to derive a constant-force model for the radical chain that demonstrates a roll over in rate similar to the "catch-bond" behavior observed in protein membrane detachment experiments.

A Hotspot's Better Half: Non-Equilibrium Intra-Molecular Strain in Shock Physics

Shockwave interactions with a material's microstructure localizes energy into hotspots, which act as nucleation sites for complex processes such as phase transformations and chemical reactions. To date, hotspots have been described via their temperature fields. Nonreactive, all-atom molecular dynamics simulations of shock-induced pore collapse in a molecular crystal show that more energy is localized as potential energy (PE) than can be inferred from the temperature field and that PE localization persists beyond thermal diffusion. The origin of the PE hotspot is traced to large intramolecular strains, storing energy in modes readily available for chemical decomposition.

Substituent Effects in Mechanochemical Allowed and Forbidden Cyclobutene Ring-Opening Reactions

Woodward and Hoffman once jested that a very powerful Maxwell demon could seize a molecule of cyclobutene at its methylene groups and tear it open in a disrotatory fashion to obtain butadiene (Woodward, R. B.; Hoffmann, R. The Conservation of Orbital Symmetry. Angew. Chem., Int. Ed. 1969, 8, 781-853). Nearly 40 years later, that demon was discovered, and the field of covalent polymer mechanochemistry was born. In the decade since our demon was befriended, many fundamental investigations have been undertaken to build up our understanding of force-modified pathways for electrocyclic ring-opening reactions. Here, we seek to extend that fundamental understanding by exploring substituent effects in allowed and forbidden ring-opening reactions of cyclobutene (CBE) and benzocyclobutene (BCB) using a combination of single-molecule force spectroscopy (SMFS) and computation. We show that, while the forbidden ring-opening of cis-BCB occurs at a lower force than the allowed ring-opening of trans-BCB on the time scale of the SMFS experiment, the opposite is true for cis- and trans-CBE. Such a reactivity flip is explained through computational analysis and discussion of the so-called allowed/forbidden gap.

Primary cilium: a paradigm for integrating mathematical modeling with experiments and numerical simulations in mechanobiology

Primary cilia are non-motile, solitary (one per cell) microtubule-based organelles that emerge from the mother centriole after cells have exited the mitotic cycle. Identified as a mechanosensing organelle that responds to both mechanical and chemical stimuli, the primary cilium provides a fertile ground for integrative investigations of mathematical modeling, numerical simulations, and experiments. Recent experimental findings revealed considerable complexity to the underlying mechanosensory mechanisms that transmit extracellular stimuli to intracellular signaling many of which include primary cilia. In this invited review, we provide a brief survey of experimental findings on primary cilia and how these results lead to various mathematical models of the mechanics of the primary cilium bent under an external forcing such as a fluid flow or a trap. Mathematical modeling of the primary cilium as a fluid-structure interaction problem highlights the importance of basal anchorage and the anisotropic moduli of the microtubules. As theoretical modeling and numerical simulations progress, along with improved state-of-the-art experiments on primary cilia, we hope that details of ciliary regulated mechano-chemical signaling dynamics in cellular physiology will be understood in the near future.

Universal G' ∼ L-3 Law for the Low-Frequency Shear Modulus of Confined Liquids

Liquids confined to sub-millimeter scales have remained poorly understood. One of the most striking effects is the large elasticity revealed using good wetting conditions, which grows upon further decreasing the confinement length, L. These systems display a low-frequency shear modulus in the order of 1-10³ Pa, contrary to our everyday experience of liquids as bodies with a zero low-frequency shear modulus. While early experimental evidence of this effect was met with skepticism and abandoned, further experimental results and, most recently, a new atomistic theoretical framework have confirmed that liquids indeed possess a finite low-frequency shear modulus G', which scales with the inverse cubic power of confinement length L. We show that this law is universal and valid for a wide range of materials (liquid water, glycerol, ionic liquids, non-entangled polymer liquids, isotropic liquids crystals). Open questions and potential applications in microfluidics mechanochemistry, energy, and other fields are highlighted.

Unraveling the Friction Evolution Mechanism of Diamond-Like Carbon Film during Nanoscale Running-In Process toward Superlubricity

Diamond-like carbon (DLC) films are capable of achieving superlubricity at sliding interfaces by a rapid running-in process. However, fundamental mechanisms governing the friction evolution during this running-in processes remain elusive especially at the nanoscale, which hinders strategic tailoring of tribosystems for minimizing friction and wear. Here, it is revealed that the running-in governing superlubricity of DLC demonstrates two sub-stages in single-asperity nanocontacts. The first stage, mechanical removal of a thin oxide layer, is described quantitatively by a stress-activated Arrhenius model. In the second stage, a large friction decrease occurs due to a structural ordering transformation, with the kinetics well described by the Johnson-Mehl-Avrami-Kolmogorov model with a modified load dependence of the activation energy. The direct observation of a graphitic-layered transfer film formation together with the measured Avrami exponent reveal the primary mechanism of the ordering transformation. The findings provide fundamental insights into friction evolution mechanisms, and design criteria for superlubricity.

Tribochemistry as an Alternative Synthesis Pathway

While reactions driven by mechanical force or stress can be labeled mechanochemical, those specifically occurring at a sliding interface inherit the name tribochemical, which stems from the study of friction and wear: tribology. Increased perception of tribochemical reactions has been gained through technological advancement, and the development of new applications remains on-going. This surprising physico-kinetic process offers great potential in novel reaction pathways for synthesis techniques and nanoparticle interactions, and it could prove to be a powerful cross-disciplinary research area among chemists, engineers, and physicists. In this review article, a survey of the history and recent usage of tribochemical reaction pathways is presented, with a focus on forging new compounds and materials with this sustainable synthesis methodology. In addition, an overview of tribochemistry’s current utility as a synthesis pathway is given and compared to that of traditional mechanochemistry.

Polymer mechanochemistry-enabled pericyclic reactions

Polymer mechanochemical pericyclic reactions are reviewed with regard to their structural features and substitution prerequisites to the polymer framework.

Measuring and modelling mechanochemical reaction kinetics

Quasi-static quantum calculations of the mechanochemical decomposition rate of methyl thiolate species on Cu(100) accurately reproduce the experimental kinetics measured in ultrahigh vacuum by an atomic force microscopy tip.

Mechanical unfolding of spectrin reveals a super-exponential dependence of unfolding rate on force

We investigated the mechanical unfolding of single spectrin molecules over a broad range of loading rates and thus unfolding forces by combining magnetic tweezers with atomic force microscopy. We find that the mean unfolding force increases logarithmically with loading rate at low loading rates, but the increase slows at loading rates above 1pN/s. This behavior indicates an unfolding rate that increases exponentially with the applied force at low forces, as expected on the basis of one-dimensional models of protein unfolding. At higher forces, however, the increase of the unfolding rate with the force becomes faster than exponential, which may indicate anti-Hammond behavior where the structures of the folded and transition states become more different as their free energies become more similar. Such behavior is rarely observed and can be explained by either a change in the unfolding pathway or as a reflection of a multidimensional energy landscape of proteins under force.

Temperature-Dependent Mechanochemical Wear of Silicon in Water: The Role of Si-OH Surfacial Groups

Mechanochemical wear has attracted much attention due to its critical role in micro/nanodevice applications, reliable microscopy, and ultraprecision manufacturing. As a process of stress-associated chemical reactions, mechanochemical wear strongly depends on temperature; however, the impact mechanism is not fully understood at any length scale. Here, we reported different water-temperature dependence of mechanochemical wear on two typical single crystal silicon (Si) surfaces, involving oxide-covered Si partially terminated with Si-OH groups and oxide-free Si fully terminated with Si-H groups. As the water temperature increased from 10 to 80 °C, the mechanochemical wear of the oxide-covered Si underwent a process from no obvious surface damage to significant material removal but that occurring at all temperatures decreased gradually on the oxide-free Si surface. The opposite temperature-dependence was found to have a strong relation to the growth or degeneration of the Si-OH surfacial groups. The mechanochemical wear on the both Si surfaces decreased with the Si-OH coverage rising, which facilitated the growth of strongly hydrogen-bonded ordered water and then suppressed the chemical reaction between the sliding interfaces. These results can provide new insight into the mechanism of the surrounding temperature affecting the reliable micro/nanodevices, manufacturing, and microscopy.

Force-conductance spectroscopy of a single-molecule reaction

We demonstrate how simultaneous measurements of conductance and force can be used to monitor the step-by-step progress of a mechanically-activated cis-to-trans isomerization single-molecule reaction, including events that cannot be distinguished using force or conductance alone. To do so, we simulated the force-conductance profile of cyclopropane oligomers connected to graphene nanoribbon electrodes that undergo a cis-to-trans isomerization during mechanical elongation. This was done using a combination of classical molecular dynamics simulation of the pulling using a reactive force field, and Landauer transport computations of the conductance with nonequilibrium Green's function methods. The isomerization events can be distinguished in both force and conductance profiles. However, the conductance profile during the mechanical elongation distinguishes between reaction intermediates that cannot be resolved using force. In turn, the force signals non-reactive deformations in the molecular backbone which are not visible in the conductance profile. These observations are shown to be robust to the choice of electrode and Hamiltonian model. The computations exemplify the potential of the integration of covalent mechanochemistry with molecular conductance to investigate chemical reactivity at the single-entity limit.

Implementing the mechanical force into the conceptual DFT framework: understanding and predicting molecular mechanochemical properties

Studying mechanochemical properties through the implementation of the mechanical force into the conceptual DFT framework (E = E[N,v,F_ext]).

Nanoscale Functionalized Particles with Rotation-Controlled Capture in Shear Flow

Important processes in nature and technology involve the adhesive capture of flowing particles or cells on the walls of a conduit. This paper introduces engineered spherical microparticles whose capture rates are limited by their near surface motions in flow. Specifically, these microparticles are sparsely functionalized with nanoscopic regions ("patches") of adhesive functionality, without which they would be nonadhesive. Not only is particle capture on the wall of a shear-chamber limited by surface chemistry as opposed to transport, but also the capture rates depend specifically on particle rotations that result from the vorticity of the shear flow field. These particle rotations continually expose new particle surface to the opposing chamber wall, sampling the particle surface for an adhesive region and controlling the capture rate. Control studies with the same patchy functionality on the chamber wall rather than the particles reveal a related signature of particle capture but substantially faster (still surface limited) particle capture rates. Thus, when the same functionality is placed on the wall rather than the particles, the capture is faster because it depends on the particle translation past a functionalized wall rather than on the particle rotations. The dependence of particle capture on functionalization of the particles versus the wall is consistent with the faster near-wall particle translation in shearing flow compared with the velocity of the rotating particle surface near the wall. These findings, in addition to providing a new class of nanoscopically patchy engineered particles, provide insight into the capture and detection of cells presenting sparse distinguishing surface features and the design of delivery packages for highly targeted pharmaceutical delivery.

Ab initio simulations of bond breaking in sulfur crosslinked isoprene oligomer units

Sulfur crosslinked polyisoprene (rubber) is used in important material components for a number of technical tasks (e.g., in tires and sealings). If mechanical stress, like tension or shear, is applied on these material components, the sulfur crosslinks suffer from homolytic bond breaking. In this work, we have simulated the bond breaking mechanism of sulfur crosslinks between polyisoprene chains using Car-Parrinello molecular dynamic simulations and investigated the maximum forces which can be resisted by the crosslinks. Small model systems with crosslinks formed by chains of N = 1 to N = 6 sulfur atoms have been simulated with the slow growth-technique, known from the literature. The maximum force can be thereby determined from the calculated energies as a function of strain (elongation). The stability of the crosslink under strain is quantified in terms of the maximum force that can be resisted by the system before the crosslink breaks. As shown by our simulations, this maximum force decreases with the sulfur crosslink length N in a step like manner. Our findings indicate that in bridges with N = 1, 2, and 3 sulfur atoms predominantly, carbon-sulfur bonds break, while in crosslinks with N > 3, the breaking of a sulfur-sulfur bond is the dominant failure mechanism. The results are explained within a simple chemical bond model, which describes how the delocalization of the electrons in the generated radicals can lower their electronic energy and decrease the activation barriers. It is described which of the double bonds in the isoprene units are involved in the mechanochemistry of crosslinked rubber.

An algorithm to locate optimal bond breaking points on a potential energy surface for applications in mechanochemistry and catalysis

The reaction path of a mechanically induced chemical transformation changes under stress. It is well established that the force-induced structural changes of minima and saddle points, i.e., the movement of the stationary points on the original or stress-free potential energy surface, can be described by a Newton Trajectory (NT). Given a reactive molecular system, a well-fitted pulling direction, and a sufficiently large value of the force, the minimum configuration of the reactant and the saddle point configuration of a transition state collapse at a point on the corresponding NT trajectory. This point is called barrier breakdown point or bond breaking point (BBP). The Hessian matrix at the BBP has a zero eigenvector which coincides with the gradient. It indicates which force (both in magnitude and direction) should be applied to the system to induce the reaction in a barrierless process. Within the manifold of BBPs, there exist optimal BBPs which indicate what is the optimal pulling direction and what is the minimal magnitude of the force to be applied for a given mechanochemical transformation. Since these special points are very important in the context of mechanochemistry and catalysis, it is crucial to develop efficient algorithms for their location. Here, we propose a Gauss-Newton algorithm that is based on the minimization of a positively defined function (the so-called σ-function). The behavior and efficiency of the new algorithm are shown for 2D test functions and for a real chemical example.

Theoretical simulation of the infrared signature of mechanically stressed polymer solids

Mechanical stress leads to deformation of strands in polymer solids, including elongation of covalent bonds and widening of bond angles, which changes the infrared spectrum. Here, the infrared spectrum of solid polymer samples exposed to mechanical stress is simulated by density functional theory calculations. Mechanical stress is described with the external force explicitly included (EFEI) method. The uneven distribution of the external stress on individual polymer strands is accounted for by a convolution of simulated spectra with a realistic force distribution. N-Propylpropanamide and propyl propanoate are chosen as model molecules for polyamide and polyester, respectively. The effect of a specific force on the polymer backbone is a redshift of vibrational modes involving the C-N and C-O bonds in the backbone, while the free C-O stretching mode perpendicular to the backbone is largely unaffected. The convolution with a realistic force distribution shows that the dominant effect on the strongest infrared bands is not a shift of the peak position, but rather peak broadening and a characteristic change in the relative intensities of the strongest bands, which may serve for the identification and quantification of mechanical stress in polymer solids.

Modeling Mechanochemical Reaction Mechanisms

The mechanochemical reaction between copper and dimethyl disulfide is studied under well-controlled conditions in ultrahigh vacuum (UHV). Reaction is initiated by fast S-S bond scission to form adsorbed methyl thiolate species, and the reaction kinetics are reproduced by two subsequent elementary mechanochemical reaction steps, namely a mechanochemical decomposition of methyl thiolate to deposit sulfur on the surface and evolve small, gas-phase hydrocarbons, and sliding-induced oxidation of the copper by sulfur that regenerates vacant reaction sites. The steady-state reaction kinetics are monitored in situ from the variation in the friction force as the reaction proceeds and modeled using the elementary-step reaction rate constants found for monolayer adsorbates. The analysis yields excellent agreement between the experiment and the kinetic model, as well as correctly predicting the total amount of subsurface sulfur in the film measured using Auger spectroscopy and the sulfur depth distribution measured by angle-resolved X-ray photoelectron spectroscopy.

Franck-Condon Theory of Quantum Mechanochemistry

The spectroscopic Franck-Condon (FC) principle is extended to mechanochemistry. If the external force is applied rapidly (the sudden-force regime), then the transition between the potential energy surface and the force-modified potential energy surface is analogous to the optical electronic transition. Such a transition produces a nonequilibrium ensemble of vibrationally excited molecules. This excess of vibrational energy is another activation source in addition to the well-known reaction barrier modulation by the external force. In the same time, the nonequilibrium vibrational distribution implies nonstatistical kinetics of a mechanochemical transformation. Mechanochemical FC principle thus provides a conceptual picture for the sudden-force mechanochemistry and opens possibilities for quantitative calculations of the mechanochemical rates and mechanisms. Here we use it to compute the dissociation rates of a model diatomic molecule and to explain the selectivity in mechanochemical bond breaking in n-butane. The approach is predicted to be relevant for large-magnitude external forces, applied instantaneously. Otherwise, the excess vibrational energy will dissipate due to intramolecular vibrational redistribution and interaction with environment.

Force-induced retro-click reaction of triazoles competes with adjacent single-bond rupture

The highly controversial force-induced cycloreversion of 1,2,3-triazole, its well-known retro-click reaction, is shown to be possible only for 1,5-substituted triazoles, but competes with rupture of an adjacent single-bond. We draw this conclusion from both static and dynamic calculations under external mechanical forces applied to unsubstituted and 1,4- and 1,5-substituted triazoles. The JEDI (Judgement of Energy DIstribution) analysis, a quantum chemical tool quantifying the distribution of strain energy in mechanically deformed molecules, is employed to identify the key factors facilitating the force-induced retro-click reaction in these systems. For 1,4-substituted triazoles it is shown to be impossible, but the parallel alignment of the scissile bond in 1,5-substituted triazoles with the acting force makes it generally feasible. However, the weakness of the carbon-nitrogen bond connecting the triazole ring to the linker prevents selective cycloreversion.

Analysis of the Acting Forces in a Theory of Catalysis and Mechanochemistry

The theoretical description of a chemical process resulting from the application of mechanical or catalytical stress to a molecule is performed by the generation of an effective potential energy surface (PES). Changes for minima and saddle points by the stress are described by Newton trajectories (NTs) on the original PES. From the analysis of the acting forces we postulate the existence of pulling corridors built by families of NTs that connect the same stationary points. For different exit saddles of different height we discuss the corresponding pulling corridors; mainly by simple two-dimensional surface models. If there are different exit saddles then there can exist saddles of index two, at least, between. Then the case that a full pulling corridor crosses a saddle of index two is the normal case. It leads to an intrinsic hysteresis of such pullings for the forward or the backward reaction. Assuming such relations we can explain some results in the literature. A new finding is the existence of roundabout corridors that can switch between different saddle points by a reversion of the direction. The findings concern the mechanochemistry of molecular systems under a mechanical load as well as the electrostatic force and can be extended to catalytic and enzymatic accelerated reactions. The basic and ground ansatz includes both kinds of forces in a natural way without an extra modification.

Driving Surface Chemistry at the Nanometer Scale Using Localized Heat and Stress

Driving and measuring chemical reactions at the nanoscale is crucial for developing safer, more efficient, and environment-friendly reactors and for surface engineering. Quantitative understanding of surface chemical reactions in real operating environments is challenging due to resolution and environmental limitations of existing techniques. Here we report an atomic force microscope technique that can measure reaction kinetics driven at the nanoscale by multiphysical stimuli in an ambient environment. We demonstrate the technique by measuring local reduction of graphene oxide as a function of both temperature and force at the sliding contact. Kinetic parameters measured with this technique reveal alternative reaction pathways of graphene oxide reduction previously unexplored with bulk processing techniques. This technique can be extended to understand and precisely tailor the nanoscale surface chemistry of any two-dimensional material in response to a wide range of external, multiphysical stimuli.

Mechanochemical Kinetics in Elastomeric Polymer Networks: Heterogeneity of Local Forces Results in Nonexponential Kinetics

A common approach to inducing selective mechanochemical transformations relies on embedding the target molecules (called mechanophores) within elastomeric polymer networks. Mechanical properties of such elastomers can also be modulated through the mechanochemical response of the constituent polymer chains. The inherent randomness in the molecular structure of such materials leads to heterogeneity of the local forces exerted on individual mechanophores. Here we use coarse-grained simulations to study the force distributions within random elastomeric networks and show that those distributions are close to exponential regardless of the applied macroscopic load, entanglement effects, or network parameters. Exponential form of the distribution allows one to completely characterize the mechanophore kinetics in terms of the mean value of the force. At the same time, heterogeneity of the local force affects the kinetics qualitatively: While a narrow force distribution around the mean would lead to exponential kinetics, exponential force distribution results in highly nonexponential kinetics, with a fast kinetic phase involving highly loaded molecules, followed by a slow phase dominated by unloaded molecules.

Mechanical gating of a mechanochemical reaction cascade

Covalent polymer mechanochemistry offers promising opportunities for the control and engineering of reactivity. To date, covalent mechanochemistry has largely been limited to individual reactions, but it also presents potential for intricate reaction systems and feedback loops. Here we report a molecular architecture, in which a cyclobutane mechanophore functions as a gate to regulate the activation of a second mechanophore, dichlorocyclopropane, resulting in a mechanochemical cascade reaction. Single-molecule force spectroscopy, pulsed ultrasonication experiments and DFT-level calculations support gating and indicate that extra force of >0.5 nN needs to be applied to a polymer of gated gDCC than of free gDCC for the mechanochemical isomerization gDCC to proceed at equal rate. The gating concept provides a mechanism by which to regulate stress-responsive behaviours, such as load-strengthening and mechanochromism, in future materials designs.

Perspective: Mechanochemistry of biological and synthetic molecules

Coupling of mechanical forces and chemical transformations is central to the biophysics of molecular machines, polymer chemistry, fracture mechanics, tribology, and other disciplines. As a consequence, the same physical principles and theoretical models should be applicable in all of those fields; in fact, similar models have been invoked (and often repeatedly reinvented) to describe, for example, cell adhesion, dry and wet friction, propagation of cracks, and action of molecular motors. This perspective offers a unified view of these phenomena, described in terms of chemical kinetics with rates of elementary steps that are force dependent. The central question is then to describe how the rate of a chemical transformation (and its other measurable properties such as the transition path) depends on the applied force. I will describe physical models used to answer this question and compare them with experimental measurements, which employ single-molecule force spectroscopy and which become increasingly common. Multidimensionality of the underlying molecular energy landscapes and the ensuing frequent misalignment between chemical and mechanical coordinates result in a number of distinct scenarios, each showing a nontrivial force dependence of the reaction rate. I will discuss these scenarios, their commonness (or its lack), and the prospects for their experimental validation. Finally, I will discuss open issues in the field.

Advances in Quantum Mechanochemistry: Electronic Structure Methods and Force Analysis

In quantum mechanochemistry, quantum chemical methods are used to describe molecules under the influence of an external force. The calculation of geometries, energies, transition states, reaction rates, and spectroscopic properties of molecules on the force-modified potential energy surfaces is the key to gain an in-depth understanding of mechanochemical processes at the molecular level. In this review, we present recent advances in the field of quantum mechanochemistry and introduce the quantum chemical methods used to calculate the properties of molecules under an external force. We place special emphasis on quantum chemical force analysis tools, which can be used to identify the mechanochemically relevant degrees of freedom in a deformed molecule, and spotlight selected applications of quantum mechanochemical methods to point out their synergistic relationship with experiments.

Combined Constant-Force and Constant-Velocity Single-Molecule Force Spectroscopy of the Conrotatory Ring Opening Reaction of Benzocyclobutene

Single-molecule force spectroscopy (SMFS) of multi-mechanophore polymers has been used to provide kinetic and mechanistic insights into mechanochemical reactions. Whereas biological systems have benefitted from force clamp spectroscopy, synthetic polymers have been studied primarily with constant-velocity methods. Here, force clamp SMFS is applied to the mechanically accelerated conrotatory ring opening of benzocyclobutene, and a comparison with constant-velocity SMFS extends the range of available rate-versus-force data and corroborates the use of constant-velocity SMFS to extract force dependencies.

Theoretical Modeling of Tribochemical Reaction on Pt and Au Contacts: Mechanical Load and Catalysis

Microelectromechanical system and nanoelectromechanical system (MEMS and NEMS) transistors are considered promising for size-reducing and power-maximizing electronic devices. However, the tribopolymer which forms due to the mechanical load to the contacts affects the conductivity dramatically. This is one of the challenging problems that prevents the widespread practical use of these otherwise promising devices. Here, we use density functional theory (DFT) to investigate the mechanisms of tribopolymer formation, including normal mechanical load and the catalytic effect, as well as the electrochemical effect of the metal contacts. We select benzene as the background gas, because it is one of the most common and severe hydrocarbon contaminants. Two adsorption cases are considered: one is benzene on the reactive metal surface, Pt(111), and the other is benzene on the noble metal, Au(111). We demonstrate that the formation of tribopolymer is induced by both the mechanical load and the catalytic effect of the contact. First, benzene molecules are adsorbed on the Pt surfaces. Then, due to the closure of the Pt contacts, stress is applied to the adsorbates, making the C-H bonds more fragile. As the stress increases further, H atoms are pressed close to the Pt substrate and begin to bond with Pt atoms. Thus, Pt acts as a catalyst, accelerating the dehydrogenation process. When there is voltage applied across the contacts, the catalytic effect is enhanced by electrochemistry. Finally, due to the loss of H atoms, C atoms become more reactive and link together or pile up to form tribopolymer. By understanding these mechanisms, we provide guidance on designing strategies for suppressing tribopolymer formation.

Differences in the Abilities to Mechanically Eliminate Activation Energies for Unimolecular and Bimolecular Reactions

Mechanochemistry, i.e. the application of forces, F, at the molecular level, has attracted significant interest as a means of controlling chemical reactions. The present study uses quantum chemical calculations to explore the abilities to mechanically eliminate activation energies, ΔE^‡, for unimolecular and bimolecular reactions. The results demonstrate that ΔE^‡ can be eliminated for unimolecular reactions by applying sufficiently large F along directions that move the reactant and/or transition state (TS) structures parallel to the zero-F reaction coordinate, S₀. In contrast, eliminating ΔE^‡ for bimolecular reactions requires the reactant to undergo a force-induced shift parallel to S₀ irrespective of changes in the TS. Meeting this requirement depends upon the coupling between F and S₀ in the reactant. The insights regarding the differences in eliminating ΔE^‡ for unimolecular and bimolecular reactions, and the requirements for eliminating ΔE^‡, may be useful in practical efforts to control reactions mechanochemically.

Force-dependent switch in protein unfolding pathways and transition-state movements

Although it is known that single-domain proteins fold and unfold by parallel pathways, demonstration of this expectation has been difficult to establish in experiments. Unfolding rate, [Formula: see text], as a function of force f, obtained in single-molecule pulling experiments on src SH3 domain, exhibits upward curvature on a [Formula: see text] plot. Similar observations were reported for other proteins for the unfolding rate [Formula: see text]. These findings imply unfolding in these single-domain proteins involves a switch in the pathway as f or [Formula: see text] is increased from a low to a high value. We provide a unified theory demonstrating that if [Formula: see text] as a function of a perturbation (f or [Formula: see text]) exhibits upward curvature then the underlying energy landscape must be strongly multidimensional. Using molecular simulations we provide a structural basis for the switch in the pathways and dramatic shifts in the transition-state ensemble (TSE) in src SH3 domain as f is increased. We show that a single-point mutation shifts the upward curvature in [Formula: see text] to a lower force, thus establishing the malleability of the underlying folding landscape. Our theory, applicable to any perturbation that affects the free energy of the protein linearly, readily explains movement in the TSE in a β-sandwich (I27) protein and single-chain monellin as the denaturant concentration is varied. We predict that in the force range accessible in laser optical tweezer experiments there should be a switch in the unfolding pathways in I27 or its mutants.

Reaction Coordinates and Pathways of Mechanochemical Transformations

The notions of a reaction path and a reaction coordinate are central to chemistry as they provide low-dimensional descriptions of complex molecular processes. Here we discuss how to define, compute, and use the reaction paths for chemical transformations in molecules that are subjected to mechanical stress and thus driven toward regions of conformational space that are otherwise inaccessible both in computational studies and in reality. We further show that the circuitous nature of mechanochemical pathways often makes their one-dimensional description impossible and describe how multidimensional effects can be detected experimentally.