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This paper shows how the effect of combined normal and shear stresses on the rates of tribochemical reactions can be calculated using Evans-Polanyi (E-P) perturbation theory. The E-P approach is based on transition-state theory, where the rate of reaction is taken to be proportional to the concentration of activated complex. The equilibrium constant depends on the molar Gibbs free energy change between the initial- and transition-states, which, in turn, depends on the stresses. E-P theory has been used previously to successfully calculate the effects of normal stresses on reaction rates. In this case, ln(Rate) varies linearly with stress with a slope given by an activation volume, which broadly corresponds to the volume difference between the reactant and activated complex. An advantage of E-P theory is that it can calculate the influence of several perturbations, for example, the normal stress dependence of the shear stress during sliding. In this paper, E-P theory is used to calculate shear-induced, tribochemical reaction rates. The results depend on four elementary activation volumes for different contributions to the Gibbs free energy: two of them due to normal and shear stresses for sliding over the surface and two more for the surface reaction. The results of the calculations show that there is a linear dependence of ln(Rate) on the normal stress but that the coefficient of proportionality between the ln(Rate) and the normal stress now has contributions from all elementary-step activation volumes. Counterintuitively, the analysis predicts that the ln(Rate)-normal stress evolution tends, at zero normal stress, to an asymptotic rate constant that depends on sliding velocity and differs from the thermal reaction rate. The theoretical prediction is verified for the shear-induced decomposition of ethyl thiolate species adsorbed on a Cu(100) single crystal substrate that decomposes by C‒S bond cleavage. The theoretical analyses show that tribochemical reactions can be influenced by either just normal stresses or by a combination of normal and shear stresses, but that the latter effect is much greater. Finally, it is predicted that there should be a linear relationship between the activation energy and the logarithm of the pre-exponential factor of the asymptotic rate constant. 

We analyze the effect of pressure on the Diels–Alder (D–A) dimerization reactions using Evans–Polanyi (E–P) theory, a thermodynamic analysis of the way in which a perturbation, in this case a hydrostatic pressure, modifies a reaction rate. 

Stress-modified activated processes are analyzed using a model first proposed by Evans and Polanyi that uses transition-state theory to calculate the effect of some perturbation, described by an intensive variable, \(I\), on the reaction rate. They suggested that the rate constant depended primarily on the equilibrium between the transition state and the reactant, which, in turn, depends on the effect of the perturbation \(I\) on the Gibbs free energy, \(G=U-TS+IC\), where \(C\) is a variable conjugate to \(I\). For example, in the case of a hydrostatic pressure \(P\), the conjugate variable is the volume, \(-V\). This allows a pressure-dependent rate to be calculated from the equilibrium constant between the reactant and transition state. Advantages to this approach are that the analysis is independent of the pathway between the two states and can simultaneously include the effect of multiple perturbations. These ideas are applied to the Prandtl–Tomlinson model, which analyses the force-induced transition rate over a surface energy barrier. The Evans–Polanyi analysis is independent of the shape of the sliding potential and merely requires the locations of the initial and transition states. It also allows the effects of both normal and shear stresses to be analyzed to identify the molecular origins of the well-known pressure-dependent shear stress: \(\tau ={\tau }_{0}+{\mu }_{L}P\), where \({\tau }_{0}\) is a pressure-independent stress. The analysis reveals that \({\mu }_{L}\) depends on the molecular corrugation of the potential and that \({\tau }_{0}\) is velocity dependent, in accord with an empirical equation proposed by Briscoe and Evans. 

Mechanochemical reaction pathways are conventionally obtained from force-displaced stationary points on the potential energy surface of the reaction. This work tests a postulate that the steepest-descent pathway (SDP) from the transition state to reactants can be reasonably accurately used instead to investigate mechanochemical reaction kinetics. This method is much simpler because the SDP and the associated reactant and transition-state structures can be obtained relatively routinely. Experiment and theory are compared for the normal-stress-induced decomposition of methyl thiolate species on Cu(100). The mechanochemical reaction rate was calculated by compressing the initial- and transition-state structures by a stiff copper counter-slab to obtain the plots of energy versus slab displacement for both structures. The reaction rate was also measured experimentally under compression using a nanomechanochemical reactor comprising an atomic-force-microscopy (AFM) instrument tip compressing a methyl thiolate overlayer on Cu(100) (the same system for which the calculations were carried out). The rate was measured from the indent created on a defect-free region of the methyl thiolate overlayer, which also enabled the contact area to be measured. Knowing the force applied by the AFM tip yields the reaction rate as a function of the contact stress. The result agrees well with the theoretical prediction without the use of adjustable parameters. This confirms that the postulate is correct and will facilitate the calculation of the rates of more complex mechanochemical reactions. An advantage of this approach, in addition to the results agreeing with the experiment, is that it provides insights into the effects that control mechanochemical reactivity that will assist in the targeted design of new mechanochemical syntheses. 

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–CH 3 bond. In contrast, no critical stress is found for ethyl thiolate with an almost horizontal C–CH 3 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.