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
This content will become publicly available on September 1, 2025
An Analysis of Shear-Dependent Mechanochemical Reaction Kinetics
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
- Award ID(s):
- 2020525
- NSF-PAR ID:
- 10535337
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Tribology Letters
- Volume:
- 72
- Issue:
- 3
- ISSN:
- 1023-8883
- Page Range / eLocation ID:
- 76
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Zinc dialkyldithiophosphate (ZDDP), the most widely used antiwear additive in engine oils, has been extensively studied over the last few decades to help understand the origin of its effectiveness. Glassy phosphate-based tribofilms, approximately 100 nm thick, are often formed on surfaces sliding in ZDDP-containing oils, which help to prevent or reduce wear. Recent studies reveal that a combination of applied shear and compressive stresses drive mechanochemical reactions that promote tribofilm growth, and that growth is further accelerated by increased temperature. While recent work has shown that compressive stress alone is insufficient to form tribofilms, the individual effects of the shear stress and compressive stress are not fully understood. Here, shear and compressive stresses are studied separately by using different ratios of high-viscosity, high-traction fluids for testing. This allows the areal mean compressive and shear stresses in the fluid when confined at a loaded sliding interface, to be independently controlled while driving tribofilm growth, which is a system we refer to as a stress-controlled mechanochemical reactor. Tribofilms derived from a secondary ZDDP were generated using a tungsten carbide/tungsten carbide ball-on-disk contact in the full elastohydrodynamic lubrication (EHL) regime using a mini-traction machine (MTM), meaning that solid–solid contact is avoided. The MTM was equipped with a spacer layer imaging (SLIM) capability, permitting in situ measurement of the tribofilm thickness during its growth. The well-separated sliding surfaces generated by the high-viscosity fluids confirm that solid–solid contact is not required for tribofilm formation. Under these full fluid film EHL conditions, shear stress and temperature promote tribofilm growth in accordance with stress-augmented thermal activation. In contrast, under constant shear stress and temperature, compressive stress has the opposite effect, inhibiting tribofilm growth. Using the extended Eyring model for shear- and hydrostatic pressure-affected reaction kinetics, an activation energy of 0.54 ± 0.04 eV is found, consistent with prior studies of ZDDPs. The activation volume for shear stress is found to be 0.18 ± 0.06 nm 3 , while that for the compressive stress component is much smaller, at 0.010 ± 0.004 nm 3 . This not only confirms prior work supporting that shear stress drives tribofilm growth, but demonstrates and quantifies how compressive stress inhibits growth, consistent with the rate-limiting step in tribofilm growth involving a bond-breaking reaction. Implications of these findings are discussed.more » « less
-
more » « less
Abstract At seismic slip rates, flash‐weakening can significantly reduce the coefficient of friction, and the magnitude of weakening increases with surface temperature. To quantify the distribution of flash temperature, high‐speed double‐direct shear experiments were conducted on Westerly granite blocks using velocity steps from 1 mm/s to 900 mm/s at 9 MPa normal stress. We employed a high‐speed infrared camera to measure surface temperatures on the moving block during sliding, and utilized a novel sliding‐surface geometry to control the mm‐scale contact history. Following the initial weakening upon the velocity step, the blocks slide at a constant coefficient of friction. Surface temperatures are inhomogeneously distributed across the sliding surface, and increase with displacement. To determine the local normal stress distribution at the mm‐scale, we combine a one‐dimensional thermal model with conventional flash‐weakening models that incorporate a surface temperature‐dependence informed by the controlled, mm‐scale contact history. Early contacts experience local normal stress exceeding 40 times the applied normal stress. As sliding progresses, the local normal stress at the hottest contacts decreases as contact area increases, leading to local normal stresses ranging from 2 to 6 times the applied normal stress on most contacts by 30 mm of slip. Increases in surface temperature, which would decrease the coefficient of friction, are buffered by wear processes that increase contact area and decrease the local normal stress. Treatments of flash heating are advanced by incorporating improved characterization of the state of the sliding surface at the mm and larger scales during sliding.
-
Mechano- or tribochemical processes are often induced by the large pressures, of the order of 1 GPa, exerted at contacting asperities at the solid–solid interface. These tribochemical process are not very well understood because of the difficulties of probing surface-chemical reaction pathways occurring at buried interfaces. Here, strategies for following surface reaction pathways in detail are illustrated for the tribochemical decomposition of 7-octenoic and octanoic acid adsorbed on copper. The chemistry was measured in ultrahigh vacuum by sliding either a tungsten carbide ball or a silicon atomic force microscope (AFM) tip over the surface to test a previous proposal that the nature of the terminal group in the carboxylic acid, vinyl versus alkyl, could influence its binding to the counterface, and therefore the reaction rate. The carboxylic acids bind strongly to the copper substrate as carboxylates to expose the hydrocarbon terminus. The tribochemical reaction rate was found to be independent of the nature of the hydrocarbon terminus, although the pull-off and friction forces measured by the AFM were different. The tribochemical reaction is initiated in the same way as the thermal reaction, by the carboxylate group tilting to eliminate carbon dioxide and deposit alkyl species onto the surface. This reaction occurs thermally at ∼640 K, but tribochemically at room temperature, producing significant differences in the rates and selectivities of the subsequent decomposition pathways of the adsorbed products.more » « less
-
Mechanochemical activation has created new opportunities for applications such as solvent-free chemical synthesis, polymer processing, and lubrication. However, mechanistic understanding of these processes is still limited because the mechanochemical response of a system is a complex function of many variables, including the direction of applied stress and the chemical features of the reactants in non-equilibrium conditions. Here, we studied shear-activated reactions of simple cyclic organic molecules to isolate the effect of chemical structure on reaction yield and pathway. Reactive molecular dynamics simulations were used to model methylcyclopentane, cyclohexane, and cyclohexene subject to pressure and shear stress between silica surfaces. Cyclohexene was found to be more susceptible to mechanochemical activation of oxidative chemisorption and subsequent oligomerization reactions than either methylcyclopentane or cyclohexane. The oligomerization trend was consistent with shear-driven polymerization yield measured in ball-on-flat sliding experiments. Analysis of the simulations showed the distribution of carbon atom sites at which oxidative chemisorption occurred and identified the double bond in cyclohexene as being the origin of its shear susceptibility. Lastly, the most common reaction pathways for association were identified, providing insight into how the chemical structures of the precursor molecules determined their response to mechanochemical activation.more » « less
