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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. 

Recent website fingerprinting attacks have been shown to achieve very high performance against traffic through Tor. These attacks allow an adversary to deduce the website a Tor user has visited by simply eavesdropping on the encrypted communication. This has consequently motivated the development of many defense strategies that obfuscate traffic through the addition of dummy packets and/or delays. The efficacy and practicality of many of these recent proposals have yet to be scrutinized in detail. In this study, we re-evaluate nine recent defense proposals that claim to provide adequate security with low-overheads using the latest Deep Learning-based attacks. Furthermore, we assess the feasibility of implementing these defenses within the current confines of Tor. To this end, we additionally provide the first on-network implementation of the DynaFlow defense to better assess its real-world utility. 

Recent website fingerprinting attacks have been shown to achieve very high performance against traffic through Tor. These attacks allow an adversary to deduce the website a Tor user has visited by simply eavesdropping on the encrypted communication. This has consequently motivated the development of many defense strategies that obfuscate traffic through the addition of dummy packets and/or delays. The efficacy and practicality of many of these recent proposals have yet to be scrutinized in detail. In this study, we re-evaluate nine recent defense proposals that claim to provide adequate security with low-overheads using the latest Deep Learning-based attacks. Furthermore, we assess the feasibility of implementing these defenses within the current confines of Tor. To this end, we additionally provide the first on-network implementation of the DynaFlow defense to better assess its real-world utility.