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.
more »
« less
This content will become publicly available on December 1, 2024
A Molecular-Scale Analysis of Pressure-Dependent Sliding Shear Stresses
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.
more »
« less
- Award ID(s):
- 2020525
- NSF-PAR ID:
- 10535335
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Tribology Letters
- Volume:
- 71
- Issue:
- 4
- ISSN:
- 1023-8883
- Page Range / eLocation ID:
- 121
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
more » « less
Abstract Mechanical stress can directly activate chemical reactions by reducing the reaction energy barrier. A possible mechanism of such mechanochemical activation is structural deformation of the reactant species. However, the effect of deformation on the reaction energetics is unclear, especially, for shear stress-driven reactions. Here, we investigated shear stress-driven oligomerization reactions of cyclohexene on silica using a combination of reactive molecular dynamics simulations and ball-on-flat tribometer experiments. Both simulations and experiments captured an exponential increase in reaction yield with shear stress. Elemental analysis of ball-on-flat reaction products revealed the presence of oxygen in the polymers, a trend corroborated by the simulations, highlighting the critical role of surface oxygen atoms in oligomerization reactions. Structural analysis of the reacting molecules in simulations indicated the reactants were deformed just before a reaction occurred. Quantitative evidence of shear-induced deformation was established by comparing bond lengths in cyclohexene molecules in equilibrium and prior to reactions. Nudged elastic band calculations showed that the deformation had a small effect on the transition state energy but notably increased the reactant state energy, ultimately leading to a reduction in the energy barrier. Finally, a quantitative relationship was developed between molecular deformation and energy barrier reduction by mechanical stress.
-
more » « less
Abstract Localized frictional sliding on faults in the continental crust transitions at depth to distributed deformation in viscous shear zones. This brittle‐ductile transition (BDT), and/or the transition from velocity‐weakening (VW) to velocity‐strengthening (VS) friction, are controlled by the lithospheric thermal structure and composition. Here, we investigate these transitions, and their effect on the depth extent of earthquakes, using 2D antiplane shear simulations of a strike‐slip fault with rate‐and‐state friction. The off‐fault material is viscoelastic, with temperature‐dependent dislocation creep. We solve the heat equation for temperature, accounting for frictional and viscous shear heating that creates a thermal anomaly relative to the ambient geotherm which reduces viscosity and facilitates viscous flow. We explore several geotherms and effective normal stress distributions (by changing pore pressure), quantifying the thermal anomaly, seismic and aseismic slip, and the transition from frictional sliding to viscous flow. The thermal anomaly can reach several hundred degrees below the seismogenic zone in models with hydrostatic pressure but is smaller for higher pressure (and these high‐pressure models are most consistent with San Andreas Fault heat flow constraints). Shear heating raises the BDT, sometimes to where it limits rupture depth rather than the frictional VW‐to‐VS transition. Our thermomechanical modeling framework can be used to evaluate lithospheric rheology and thermal models through predictions of earthquake ruptures, postseismic and interseismic crustal deformation, heat flow, and the geological structures that reflect the complex deformation beneath faults.
-
null (Ed.)A bstract We quantify the effect of gauge bosons from a weakly coupled lepton flavor dependent U(1) ′ interaction on the matter background in the evolution of solar, atmospheric, reactor and long-baseline accelerator neutrinos in the global analysis of oscillation data. The analysis is performed for interaction lengths ranging from the Sun-Earth distance to effective contact neutrino interactions. We survey ∼ 10000 set of models characterized by the six relevant fermion U(1) ′ charges and find that in all cases, constraints on the coupling and mass of the Z′ can be derived. We also find that about 5% of the U(1) ′ model charges lead to a viable LMA-D solution but this is only possible in the contact interaction limit. We explicitly quantify the constraints for a variety of models including $$ \mathrm{U}{(1)}_{B-3{L}_e} $$ U 1 B − 3 L e , $$ \mathrm{U}{(1)}_{B-3{L}_{\mu }} $$ U 1 B − 3 L μ , $$ \mathrm{U}{(1)}_{B-3{L}_{\tau }} $$ U 1 B − 3 L τ , $$ \mathrm{U}{(1)}_{B-\frac{3}{2}\left({L}_{\mu }+{L}_{\tau}\right)} $$ U 1 B − 3 2 L μ + L τ , $$ \mathrm{U}{(1)}_{L_e-{L}_{\mu }} $$ U 1 L e − L μ , $$ \mathrm{U}{(1)}_{L_e-{L}_{\tau }} $$ U 1 L e − L τ , $$ \mathrm{U}{(1)}_{L_e-\frac{1}{2}\left({L}_{\mu }+{L}_{\tau}\right)} $$ U 1 L e − 1 2 L μ + L τ . We compare the constraints imposed by our oscillation analysis with the strongest bounds from fifth force searches, violation of equivalence principle as well as bounds from scattering experiments and white dwarf cooling. Our results show that generically, the oscillation analysis improves over the existing bounds from gravity tests for Z′ lighter than ∼ 10 − 8 → 10 − 11 eV depending on the specific couplings. In the contact interaction limit, we find that for most models listed above there are values of g′ and M Z′ for which the oscillation analysis provides constraints beyond those imposed by laboratory experiments. Finally we illustrate the range of Z′ and couplings leading to a viable LMA-D solution for two sets of models.more » « less
