Force-modified Potential Energy Surface Research Articles

Mechanoresponsive Metal-Organic Cage-Crosslinked Polymer Hydrogels.

We report the formation of metal-organic cage-crosslinked polymer hydrogels. To enable crosslinking of the cages and subsequent network formation, we used homodifunctionalized poly(ethylene glycol) (PEG) chains terminally substituted with bipyridines as ligands for the Pd6 L4 corners. The encapsulation of guest molecules into supramolecular self-assembled metal-organic cage-crosslinked hydrogels, as well as ultrasound-induced disassembly of the cages with release of their cargo, is presented in addition to their characterization by nuclear magnetic resonance (NMR) techniques, rheology, and comprehensive small-angle X-ray scattering (SAXS) experiments. The constrained geometries simulating external force (CoGEF) method and barriers using a force-modified potential energy surface (FMPES) suggest that the cage-opening mechanism starts with the dissociation of one pyridine ligand at around 0.5 nN. We show the efficient sonochemical activation of the hydrogels HG3 -6 , increasing the non-covalent guest-loading of completely unmodified drugs available for release by a factor of ten in comparison to non-crosslinked, star-shaped assemblies in solution.

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.

Understanding the Mechanochemistry of Ladder-Type Cyclobutane Mechanophores by Single Molecule Force Spectroscopy.

We have recently reported a series of ladder-type cyclobutane mechanophores, polymers of which can transform from nonconjugated structures to conjugated structures and change many properties at once. These multicyclic mechanophores, namely, exo-ladderane/ene, endo-benzoladderene, and exo-bicyclohexene-peri-naphthalene, have different ring structures fused to the first cyclobutane, significantly different free energy changes for ring-opening, and different stereochemistry. To better understand their mechanochemistry, we used single molecule force spectroscopy (SMFS) to characterize their force-extension behavior and measure the threshold forces. The threshold forces correlate with the activation energy of the first bond, but not with the strain of the fused rings distal to the polymer main chain, suggesting that the activation of these ladder-type mechanophores occurs with similar early transition states, which is supported by force-modified potential energy surface calculations. We further determined the stereochemistry of the mechanically generated dienes and observed significant and variable contour length elongation for these mechanophores both experimentally and computationally. The fundamental understanding of ladder-type mechanophores will facilitate future design of multicyclic mechanophores with amplified force-response and their applications as mechanically responsive materials.

On the Electronic Structure Origin of Mechanochemically Induced Selectivity in Acid-Catalyzed Chitin Hydrolysis.

Recently, mechanical ball milling was applied to chitin depolymerization. The mechanical activation afforded higher selectivity toward glycosidic bond cleavage over amide bond breakage. Hence, the bioactive N-acetylglucosamine (GlcNAc) monomer was preferentially produced over glucosamine. In this regard, the force-dependent mechanochemical activation-deactivation process in the relaxed and pulled GlcNAc dimer undergoing deacetylation and depolymerization reactions was studied. For the relaxed case, the activation energies of the rate-determining steps (RDS) proved that the two reactions could occur simultaneously. Mechanical forces associated with ball milling were approximated with linear pulling and were introduced explicitly in the RDS of both reactions through force-modified potential energy surface (FMPES) formalism. In general, as the applied pulling force increases, the activation energy of the RDS of deacetylation shows no meaningful change, while that of depolymerization decreases. This result is consistent with the selectivity exhibited in the experiment. Energy and structural analyses for the depolymerization showed that the activation can be attributed to a significant change in the glycosidic dihedral at the reactant state. A lone pair of the neighboring pyranose ring O adopts a syn-periplanar conformation relative to the glycosidic bond. This promotes electron donation to the σ*-orbital of the glycosidic bond, leading to activation. Consequently, the Brønsted-Lowry basicity of the glycosidic oxygen also increases, which can facilitate acid catalysis.

Isotope Effect in the Activation of a Mechanophore.

In mechanochemistry, molecules under tension can react in unexpected ways. The reactivity of mechanophores (mechanosensitive molecules) can be controlled using various geometric or electronic factors. Often these factors affect the rate of mechanical activation but sometimes give rise to alternative reaction pathways. Here we show that a simple isotope substitution (H to D) leads to a reversal of selectivity in the activation of a mechanophore. Remarkably this isotope effect is not kinetic in nature but emerges from dynamic effects in which deuteration reduces the ability of the reactant to follow a post-transition-state concerted trajectory on the bifurcated force-modified potential energy surface. These results give a new insight into the reactivity of molecules under tension.

The cascade unzipping of ladderane reveals dynamic effects in mechanochemistry.

Force can induce remarkable non-destructive transformations along a polymer, but we have a limited understanding of the energy transduction and product distribution in tandem mechanochemical reactions. Ladderanes consist of multiple fused cyclobutane rings and have recently been used as monomeric motifs to develop polymers that drastically change their properties in response to force. Here we show that [4]-ladderane always exhibits 'all-or-none' cascade mechanoactivations and the same stereochemical distribution of the generated dienes under various conditions and within different polymer backbones. Transition state theory fails to capture the reaction kinetics and explain the observed stereochemical distributions. Ab initio steered molecular dynamics reveals unique non-equilibrium dynamic effects: energy transduction from the first cycloreversion substantially accelerates the second cycloreversion, and bifurcation on the force-modified potential energy surface leads to the product distributions. Our findings illustrate the rich chemistry in closely coupled multi-mechanophores and an exciting potential for effective energy transduction in tandem mechanochemical reactions.

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.

The effect of external forces on the initial dissociation of RDX (1,3,5-trinitro-1,3,5-triazine): A mechanochemical study

Experimental and theoretical studies have proposed different initiation reactions for the decomposition of hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX). Three primary reactions are considered to start RDX decomposition: homolytic NN bond fission, HONO elimination, and concerted fission of CN bonds. The focus of this article is to study the effect of external forces on the energy barrier and reaction energies of all three mechanisms. We used the Nudged Elastic Band method along with ab initio Density Functional Theory within the framework of a generalized force-modified potential energy surface (G-FMPES) to calculate the minimum energy paths at different compressive (corresponding to pressure between approximately 6 and 294 MPa) and expansive force values (between 10 and 264 pN). For all three reactions, the application of an expansive force increases the exothermicity and lowers the energy barriers to different extents, while a compressive force decreases the exothermicity and raises the energy barrier to different extents.

A generalized force-modified potential energy surface for mechanochemical simulations.

We describe the modifications that a spatially varying external load produces on a Born-Oppenheimer potential energy surface (PES) by calculating static quantities of interest. The effects of the external loads are exemplified using electronic structure calculations (at the HF/6-31G(∗∗) level) of two different molecules: ethane and hexahydro-1,3,5-trinitro-s-triazine (RDX). The calculated transition states and Hessian matrices of stationary points show that spatially varying external loads shift the stationary points and modify the curvature of the PES, thereby affecting the harmonic transition rates by altering both the energy barrier as well as the prefactor. The harmonic spectra of both molecules are blueshifted with increasing compressive "pressure." Some stationary points on the RDX-PES disappear under application of the external load, indicating the merging of an energy minimum with a saddle point.

Theoretical Approaches for Understanding the Interplay Between Stress and Chemical Reactivity.

The use of mechanical stresses to induce chemical reactions has attracted significant interest in recent years. Computational modeling can play a significant role in developing a comprehensive understanding of the interplay between stresses and chemical reactivity. In this review, we discuss techniques for simulating chemical reactions occurring under mechanochemical conditions. The methods described are broadly divided into techniques that are appropriate for studying molecular mechanochemistry and those suited to modeling bulk mechanochemistry. In both cases, several different approaches are described and compared. Methods for examining molecular mechanochemistry are based on exploring the force-modified potential energy surface on which a molecule subjected to an external force moves. Meanwhile, it is suggested that condensed phase simulation methods typically used to study tribochemical reactions, i.e., those occurring in sliding contacts, can be adapted to study bulk mechanochemistry.

Modeling mechanophore activation within a crosslinked glassy matrix

Mechanically induced reactivity is a promising means for designing self-reporting materials. Mechanically sensitive chemical groups called mechanophores are covalently linked into polymers in order to trigger specific chemical reactions upon mechanical loading. These mechanophores can be linked either within the backbone or as crosslinks between backbone segments. Mechanophore response is sensitive to both the matrix properties and placement within the matrix, providing two avenues for material design. A model framework is developed to describe reactivity of mechanophores located as crosslinks in a glassy polymer matrix. Simulations are conducted at the molecular and macromolecular scales in order to develop macroscale constitutive relations. The model is developed specifically for the case of spiropyran (SP) in lightly crosslinked polymethylmethacrylate (PMMA). This optically trackable mechanophore (fluorescent when activated) allows the model to be assessed in terms of observed experimental behavior. The force modified potential energy surface (FMPES) framework is used in conjunction with ab initio steered molecular dynamics (MD) simulations of SP to determine the mechanophore kinetics. MD simulations of the crosslinked PMMA structure under shear deformation are used to determine the relationship between macroscale stress and local force on the crosslinks. A continuum model implemented in a finite element framework synthesizes these mechanochemical relations with the mechanical behavior. The continuum model with parameters taken directly from the FMPES and MD analyses under predicts stress-driven activation relative to experimental data. The continuum model, with the physically motivated modification of force fluctuations, provides an accurate prediction for monotonic loading across three decades of strain rate and creep loading, suggesting that the fundamental physics are captured.

First Principles Dynamics and Minimum Energy Pathways for Mechanochemical Ring Opening of Cyclobutene

We use ab initio steered molecular dynamics to investigate the mechanically induced ring opening of cyclobutene. We show that the dynamical results can be considered in terms of a force-modified potential energy surface (FMPES). We show how the minimal energy paths for the two possible competing conrotatory and disrotatory ring-opening reactions are affected by external force. We also locate minimal energy pathways in the presence of applied external force and show that the reactant, product, and transition state geometries are altered by the application of external force. The largest effects are on the transition state geometries and barrier heights. Our results provide a framework for future investigations of the role of external force on chemical reactivity.