Theoretical Approaches for Understanding the Interplay Between Stress and Chemical Reactivity

JEDI: A versatile code for strain analysis of molecular and periodic systems under deformation

Stretching or compression can induce significant energetic, geometric, and spectroscopic changes in materials. To fully exploit these effects in the design of mechano- or piezo-chromic materials, self-healing polymers, and other mechanoresponsive devices, a detailed knowledge about the distribution of mechanical strain in the material is essential. Within the past decade, Judgement of Energy DIstribution (JEDI) analysis has emerged as a useful tool for this purpose. Based on the harmonic approximation, the strain energy in each bond length, bond angle, and dihedral angle of the deformed system is calculated using quantum chemical methods. This allows the identification of the force-bearing scaffold of the system, leading to an understanding of mechanochemical processes at the most fundamental level. Here, we present a publicly available code that generalizes the JEDI analysis, which has previously only been available for isolated molecules. Now, the code has been extended to two- and three-dimensional periodic systems, supramolecular clusters, and substructures of chemical systems under various types of deformation. Due to the implementation of JEDI into the Atomic Simulation Environment, the JEDI analysis can be interfaced with a plethora of program packages that allow the calculation of electronic energies for molecular systems and systems with periodic boundary conditions. The automated generation of a color-coded three-dimensional structure via the Visual Molecular Dynamics program allows insightful visual analyses of the force-bearing scaffold of the strained system.

Experimental quantitation of molecular conditions responsible for flow-induced polymer mechanochemistry

Fragmentation of macromolecular solutes in rapid flows is of considerable fundamental and practical importance. The sequence of molecular events preceding chain fracture is poorly understood, because such events cannot be visualized directly but must be inferred from changes in the bulk composition of the flowing solution. Here we describe how analysis of same-chain competition between fracture of a polystyrene chain and isomerization of a chromophore embedded in its backbone yields detailed characterization of the distribution of molecular geometries of mechanochemically reacting chains in sonicated solutions. In our experiments the overstretched (mechanically loaded) chain segment grew and drifted along the backbone on the same timescale as, and in competition with, the mechanochemical reactions. Consequently, only <30% of the backbone of a fragmenting chain is overstretched, with both the maximum force and the maximum reaction probabilities located away from the chain centre. We argue that quantifying intrachain competition is likely to be mechanistically informative for any flow fast enough to fracture polymer chains.

Allosteric control of olefin isomerization kinetics via remote metal binding and its mechanochemical analysis

Allosteric control of reaction thermodynamics is well understood, but the mechanisms by which changes in local geometries of receptor sites lower activation reaction barriers in electronically uncoupled, remote reaction moieties remain relatively unexplored. Here we report a molecular scaffold in which the rate of thermal E-to-Z isomerization of an alkene increases by a factor of as much as 104 in response to fast binding of a metal ion to a remote receptor site. A mechanochemical model of the olefin coupled to a compressive harmonic spring reproduces the observed acceleration quantitatively, adding the studied isomerization to the very few reactions demonstrated to be sensitive to extrinsic compressive force. The work validates experimentally the generalization of mechanochemical kinetics to compressive loads and demonstrates that the formalism of force-coupled reactivity offers a productive framework for the quantitative analysis of the molecular basis of allosteric control of reaction kinetics. Important differences in the effects of compressive vs. tensile force on the kinetic stabilities of molecules are discussed.

The many flavours of mechanochemistry and its plausible conceptual underpinnings

Mechanochemistry describes diverse phenomena in which mechanical load affects chemical reactivity. The fuzziness of this definition means that it includes processes as seemingly disparate as motor protein function, organic synthesis in a ball mill, reactions at a propagating crack, chemical actuation, and polymer fragmentation in fast solvent flows and in mastication. In chemistry, the rate of a reaction in a flask does not depend on how fast the flask moves in space. In mechanochemistry, the rate at which a material is deformed affects which and how many bonds break. In other words, in some manifestations of mechanochemistry, macroscopic motion powers otherwise endergonic reactions. In others, spontaneous chemical reactions drive mechanical motion. Neither requires thermal or electrostatic gradients. Distinct manifestations of mechanochemistry are conventionally treated as being conceptually independent, which slows the field in its transformation from being a collection of observations to a rigorous discipline. In this Review, we highlight observations suggesting that the unifying feature of mechanochemical phenomena may be the coupling between inertial motion at the microscale to macroscale and changes in chemical bonding enabled by transient build-up and relaxation of strains, from macroscopic to molecular. This dynamic coupling across multiple length scales and timescales also greatly complicates the conceptual understanding of mechanochemistry.

The Mechanism of Flex-Activation in Mechanophores Revealed By Quantum Chemistry

Flex-activated mechanophores can be used for small-molecule release in polymers under tension by rupture of covalent bonds that are orthogonal to the polymer main chain. Using static and dynamic quantum chemical methods, we here juxtapose three different mechanical deformation modes in flex-activated mechanophores (end-to-end stretching, direct pulling of the scissile bonds, bond angle bendings) with the aim of proposing ways to optimize the efficiency of flex-activation in experiments. It is found that end-to-end stretching, which is a traditional approach to activate mechanophores in polymers, does not trigger flex-activation, whereas direct pulling of the scissile bonds or displacement of adjacent bond angles are efficient methods to achieve this goal. Based on the structural, energetic and electronic effects responsible for these observations, we propose ways of weakening the scissile bonds experimentally to increase the efficiency of flex-activation.

A Polymer with Mechanochemically Active Hidden Length

Incorporating hidden length into polymer chains can improve their mechanical properties, because release of the hidden length under mechanical loads enables localized strain relief without chain fracture. To date, the design of hidden length has focused primarily on the choice of the sacrificial bonds holding the hidden length together. Here we demonstrate the advantages of adding mechanochemical reactivity to hidden length itself, using a new mechanophore that integrates (Z)-2,3-diphenylcyclobutene-1,4-dicarboxylate, with hitherto unknown mechanochemistry, into macrocyclic cinnamate dimers. Stretching a polymer of this mechanophore more than doubles the chain contour length without fracture. DFT calculations indicate that the sequential dissociation of the dimer, followed by cyclobutene isomerization at higher forces yields a chain fracture energy 11 times that of a simple polyester of the same initial contour length and preserves high energy-dissipating capacity up to ∼3 nN. In sonicated solutions cyclobutene isomerizes to two distinct products by competing reaction paths, validating the computed mechanochemical mechanism and suggesting an experimental approach to quantifying the distribution of single-chain forces under diverse loading scenarios.

A mechanochemical model for the simulation of molecules and molecular crystals under hydrostatic pressure

A novel mechanochemical method for the simulation of molecules and molecular crystals under hydrostatic pressure, the eXtended Hydrostatic Compression Force Field (X-HCFF) approach, is introduced. In contrast to comparable methods, the desired pressure can be adjusted non-iteratively and molecules of general shape retain chemically reasonable geometries even at high pressure. The implementation of the X-HCFF approach is straightforward, and the computational cost is practically the same as for regular geometry optimization. Pressure can be applied by using any desired electronic structure method for which a nuclear gradient is available. The results of the X-HCFF for pressure-dependent intramolecular structural changes in the investigated molecules and molecular crystals as well as a simple pressure-induced dimerization reaction are chemically intuitive and fall within the range of other established computational methods. Experimental spectroscopic data of a molecular crystal under pressure are reproduced accurately.

Experimentally realized mechanochemistry distinct from force-accelerated scission of loaded bonds

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.

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.

Quantum Chemical Strain Analysis For Mechanochemical Processes

The use of mechanical force to initiate a chemical reaction is an efficient alternative to the conventional sources of activation energy, i.e., heat, light, and electricity. Applications of mechanochemistry in academic and industrial laboratories are diverse, ranging from chemical syntheses in ball mills and ultrasound baths to direct activation of covalent bonds using an atomic force microscope. The vectorial nature of force is advantageous because specific covalent bonds can be preconditioned for rupture by selective stretching. However, the influence of mechanical force on single molecules is still not understood at a fundamental level, which limits the applicability of mechanochemistry. As a result, many chemists still resort to rules of thumb when it comes to conducting mechanochemical syntheses. In this Account, we show that comprehension of mechanochemistry at the molecular level can be tremendously advanced by quantum chemistry, in particular by using quantum chemical force analysis tools. One such tool is the JEDI (Judgement of Energy DIstribution) analysis, which provides a convenient approach to analyze the distribution of strain energy in a mechanically deformed molecule. Based on the harmonic approximation, the strain energy contribution is calculated for each bond length, bond angle and dihedral angle, thus providing a comprehensive picture of how force affects molecules. This Account examines the theoretical foundations of quantum chemical force analysis and provides a critical overview of the performance of the JEDI analysis in various mechanochemical applications. We explain in detail how this analysis tool is to be used to identify the "force-bearing scaffold" of a distorted molecule, which allows both the rationalization and the optimization of diverse mechanochemical processes. More precisely, we show that the inclusion of every bond, bending and torsion of a molecule allows a particularly insightful discussion of the distribution of mechanical strain in deformed molecules. We illustrate the usefulness of the JEDI analysis by rationalizing the finding that a knot tremendously weakens a polymer strand via a "choking" motion of the torsions in the curved part of the knot, thus leading to facilitated bond rupture in the immediate vicinity of the knot. Moreover, we demonstrate that the JEDI analysis can be exploited to devise methods for the stabilization of inherently strained molecules. In addition to applications in the electronic ground state, the JEDI analysis can also be used in the electronically excited state to determine the mechanical energy that a molecular photoswitch can release into its environment during photoisomerization. This approach allows the quantification of the mechanical efficiency of a photoswitch, i.e., the part of the energy that becomes available for the motion into a specific direction, which enables us to judge whether a photoswitch is capable of performing a desired switching function.

Experimental Polymer Mechanochemistry and its Interpretational Frameworks

Polymer mechanochemistry is an emerging field at the interface of chemistry, materials science, physics and engineering. It aims at understanding and exploiting unique reactivities of polymer chains confined to highly non-equilibrium stretched geometries by interactions with their surroundings. Macromolecular chains or their segments become stretched in bulk polymers under mechanical loads or when polymer solutions are sonicated or flow rapidly through abrupt contractions. An increasing amount of empirical data suggests that mechanochemical phenomena are widespread wherever polymers are used. In the past decade, empirical mechanochemistry has progressed enormously, from studying fragmentations of commodity polymers by simple backbone homolysis to demonstrations of self-strengthening and stress-reporting materials and mechanochemical cascades using purposefully designed monomers. This progress has not yet been matched by the development of conceptual frameworks within which to rationalize, systematize and generalize empirical mechanochemical observations. As a result, mechanistic and/or quantitative understanding of mechanochemical phenomena remains, with few exceptions, tentative. In this review we aim at systematizing reported macroscopic manifestations of polymer mechanochemistry, and critically assessing the interpretational framework that underlies their molecular rationalizations from a physical chemist's perspective. We propose a hierarchy of mechanochemical phenomena which may guide the development of multiscale models of mechanochemical reactivity to match the breadth and utility of the Eyring equation of chemical kinetics. We discuss the limitations of the approaches to quantifying and validating mechanochemical reactivity, with particular focus on sonicated polymer solutions, in order to identify outstanding questions that need to be solved for polymer mechanochemistry to become a rigorous, quantitative field. We conclude by proposing 7 problems whose solution may have a disproportionate impact on the development of polymer mechanochemistry.

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.

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.