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Figure 19. (a) The continuous curve shows the probability distribution of the local normal loads, P(1), for rough adhesive surfaces with a total normal load of L = 307 nN. The dotted curve is the result of a simulation for adhesive atomically smooth crystalline gold (111) surfaces. (b) Simulation results of the local friction force, f, as a function of the local normal load, 1. The dashed line corresponds to a fit to the data by a Weibull cumulative distribution function.

Figure 19 (a) The continuous curve shows the probability distribution of the local normal loads, P(1), for rough adhesive surfaces with a total normal load of L = 307 nN. The dotted curve is the result of a simulation for adhesive atomically smooth crystalline gold (111) surfaces. (b) Simulation results of the local friction force, f, as a function of the local normal load, 1. The dashed line corresponds to a fit to the data by a Weibull cumulative distribution function.

Related Figures (20)

Figure 1. FFM measurements in ethanol of the friction force F between bare template-stripped gold surfaces and two unfunctionalized Si tips of different radii and spring constants. Main figure: R = 33 nm, uw = 0.42 4 + 0.01. Inset: R = 11 nm, w = 0.49 4 t 0.02. Sliding velocity: V = 0.15 wm/s. Adapted from Ruths, M. Langmuir 2003, 19, 6788. Copyright 2003 American Chemical Society.
Figure 1. FFM measurements in ethanol of the friction force F between bare template-stripped gold surfaces and two unfunctionalized Si tips of different radii and spring constants. Main figure: R = 33 nm, uw = 0.42 4 + 0.01. Inset: R = 11 nm, w = 0.49 4 t 0.02. Sliding velocity: V = 0.15 wm/s. Adapted from Ruths, M. Langmuir 2003, 19, 6788. Copyright 2003 American Chemical Society.
Figure 2. Friction force between benzyltrichlorosilane monolayers chemically bound to glass or Si in ethanol (y < 1 mJ/m’). (a) SFA measurements where both glass surfaces were covered with a mono- layer. Circles and squares show two different experiments: one with R = 2.6 cm, V = 0.15 um/s, giving w = 0.33 + 0.01; the other with R = 1.6 cm, V = 0.5 um/s, giving w = 0.30 + 0.01. (b) FFM measurements of the same monolayer-functionalized Si tip (R = 11 nm) sliding on a monolayer-covered glass surface at V = 0.15 wm/s, giving uw = 0.30 4 Israelachvili, J. N. + 0.01. Adapted from Ruths, M.; Alcantar, N. A.; J. Phys. Chem. 2003, 107, 11149. Copyright 2003 American Chemical Society.
Figure 2. Friction force between benzyltrichlorosilane monolayers chemically bound to glass or Si in ethanol (y < 1 mJ/m’). (a) SFA measurements where both glass surfaces were covered with a mono- layer. Circles and squares show two different experiments: one with R = 2.6 cm, V = 0.15 um/s, giving w = 0.33 + 0.01; the other with R = 1.6 cm, V = 0.5 um/s, giving w = 0.30 + 0.01. (b) FFM measurements of the same monolayer-functionalized Si tip (R = 11 nm) sliding on a monolayer-covered glass surface at V = 0.15 wm/s, giving uw = 0.30 4 Israelachvili, J. N. + 0.01. Adapted from Ruths, M.; Alcantar, N. A.; J. Phys. Chem. 2003, 107, 11149. Copyright 2003 American Chemical Society.
Figure 3. SFA measurements on untreated alumina surfaces: smooth, undamaged surfaces (curve a); and rough, damaged surfaces after continuous sliding (curve b). Smooth surfaces coated with a monolayer of octadecyl phosphonic acid (curve c) slide with a higher friction at low loads than untreated alumina but remain undamaged even after prolonged sliding, keeping the friction substantially lower than rough surfaces at high loads. Experimental conditions: sliding velocity V = 0.05—0.5 wm/s, undeformed surface radii R ~ 1 cm, temperature T = 25 °C, contact pressure range P = 1-10 MPa, relative humidity RH = 0% (curves a and c) and RH = 100% (curve b). Additional points measured on damaged alumina surfaces at RH = 0% also fell on curve b (not shown). Reprinted from Berman et al. Tribol. Lett. 1998, 4, 43— 48, with permission from Kluwer Academic Publishers.
Figure 3. SFA measurements on untreated alumina surfaces: smooth, undamaged surfaces (curve a); and rough, damaged surfaces after continuous sliding (curve b). Smooth surfaces coated with a monolayer of octadecyl phosphonic acid (curve c) slide with a higher friction at low loads than untreated alumina but remain undamaged even after prolonged sliding, keeping the friction substantially lower than rough surfaces at high loads. Experimental conditions: sliding velocity V = 0.05—0.5 wm/s, undeformed surface radii R ~ 1 cm, temperature T = 25 °C, contact pressure range P = 1-10 MPa, relative humidity RH = 0% (curves a and c) and RH = 100% (curve b). Additional points measured on damaged alumina surfaces at RH = 0% also fell on curve b (not shown). Reprinted from Berman et al. Tribol. Lett. 1998, 4, 43— 48, with permission from Kluwer Academic Publishers.
Figure 4. Friction force F and measured “real” contact area A vs load L for two undamaged mica surfaces sliding in adhesive contact in dry air (A, O). The area A between these molecularly smooth surfaces is well described by the JKR theory even during sliding, and F is found to be directly proportional to A (©). The vertical dashed line and downward- pointing arrow show the transition from interfacial (wearless) friction to friction with wear (@). The sliding velocity was 0.2 wm/s. The two lowest curves show two mica surfaces sliding past each other while immersed in a 0.01 M KCI solution (nonadhesive conditions). The water film is molecularly thin, D = 0.25—0.5 nm, and the interfacial friction force is very low for smooth, undamaged surfaces (1). A fter the surfaces have become damaged, shown by the vertical arrow (mM), the friction coefficient is ~0.3, which is similar to that for damaged surfaces in air (@). Adapted from Homola et al., 1989, 1990, with permission from ASME publishers.
Figure 4. Friction force F and measured “real” contact area A vs load L for two undamaged mica surfaces sliding in adhesive contact in dry air (A, O). The area A between these molecularly smooth surfaces is well described by the JKR theory even during sliding, and F is found to be directly proportional to A (©). The vertical dashed line and downward- pointing arrow show the transition from interfacial (wearless) friction to friction with wear (@). The sliding velocity was 0.2 wm/s. The two lowest curves show two mica surfaces sliding past each other while immersed in a 0.01 M KCI solution (nonadhesive conditions). The water film is molecularly thin, D = 0.25—0.5 nm, and the interfacial friction force is very low for smooth, undamaged surfaces (1). A fter the surfaces have become damaged, shown by the vertical arrow (mM), the friction coefficient is ~0.3, which is similar to that for damaged surfaces in air (@). Adapted from Homola et al., 1989, 1990, with permission from ASME publishers.
Figure 5. Measured friction force F (©) and real contact area A (@) as a function of load L between two molecularly smooth mica surfaces sliding in 0.5 M KCl solution at T = 22 °C where the intersurface forces are short ranged and repulsive (providing a nonadhering system). The sliding velocity was V = 0.12 wm/s. The dashed curve through the data points for A vs L (@) is the theoretical fit to the Hertz equation, using the measured undeformed radius of the surfaces R = 0.95 cm and K = 4.0 x 10'° N/m? for the effective elastic modulus of the substrate materials. Figure adapted from Berman et al. Trib. Lett. 1998, 4, 95-101, reprinted with permission from Kluwer Academic Publish- ers.
Figure 5. Measured friction force F (©) and real contact area A (@) as a function of load L between two molecularly smooth mica surfaces sliding in 0.5 M KCl solution at T = 22 °C where the intersurface forces are short ranged and repulsive (providing a nonadhering system). The sliding velocity was V = 0.12 wm/s. The dashed curve through the data points for A vs L (@) is the theoretical fit to the Hertz equation, using the measured undeformed radius of the surfaces R = 0.95 cm and K = 4.0 x 10'° N/m? for the effective elastic modulus of the substrate materials. Figure adapted from Berman et al. Trib. Lett. 1998, 4, 95-101, reprinted with permission from Kluwer Academic Publish- ers.
Figure 6. Steady-state friction forces F (@,O,m™,0) and contact areas A (©) vs load L measured with the SFA on a confined squalane film between two undamaged mica surfaces at two different velocities in the smooth (non stick-slip) sliding regime. Open symbols (0,0) show friction force data obtained on loading (increasing L); filled symbols (@,™) show unloading, all four of which are straight lines passing through the origin, one of which is shown by the thick line passing through the (O,@) points. The thin line is a fit of the Hertz equation to the A vs L data (©) using K = 1 x 10!° N/m?2, R = 2 cm. The thickness D varies monotonically from D = 2.5 to 1.7 nm as the load increases from L = 0 to 10 mN. Adapted from Gourdon and Israelachvili, Phys. Rev. E 2003, 68, 021602/1—10. Copyright 2003 American Physical Society.
Figure 6. Steady-state friction forces F (@,O,m™,0) and contact areas A (©) vs load L measured with the SFA on a confined squalane film between two undamaged mica surfaces at two different velocities in the smooth (non stick-slip) sliding regime. Open symbols (0,0) show friction force data obtained on loading (increasing L); filled symbols (@,™) show unloading, all four of which are straight lines passing through the origin, one of which is shown by the thick line passing through the (O,@) points. The thin line is a fit of the Hertz equation to the A vs L data (©) using K = 1 x 10!° N/m?2, R = 2 cm. The thickness D varies monotonically from D = 2.5 to 1.7 nm as the load increases from L = 0 to 10 mN. Adapted from Gourdon and Israelachvili, Phys. Rev. E 2003, 68, 021602/1—10. Copyright 2003 American Physical Society.
Figure 7. Scanning-induced reduction of adhesion and friction forces in FFM measurements with a Pt-coated tip in contact with a mica surface in UHV. After each run, the pull-off force also decreased in magnitude (not shown), implying a scanning-induced decrease in the adhesion energy from an initial value of y = 404 mJ/m? on the first scan (not shown) to y = 19 mJ/m? on the last scan (lowest curve) that paralleled the decrease in F shown here. The sliding in this system proceeded by stick-slip with a periodicity of the atomic spacing, and the friction force shown is the average “critical” or “static” friction force necessary to induce the slips. Reproduced with permission from Carpick et al. Langmuir 1996, 12, 3334-3340. Copyright 1996 American Chemical Society.
Figure 7. Scanning-induced reduction of adhesion and friction forces in FFM measurements with a Pt-coated tip in contact with a mica surface in UHV. After each run, the pull-off force also decreased in magnitude (not shown), implying a scanning-induced decrease in the adhesion energy from an initial value of y = 404 mJ/m? on the first scan (not shown) to y = 19 mJ/m? on the last scan (lowest curve) that paralleled the decrease in F shown here. The sliding in this system proceeded by stick-slip with a periodicity of the atomic spacing, and the friction force shown is the average “critical” or “static” friction force necessary to induce the slips. Reproduced with permission from Carpick et al. Langmuir 1996, 12, 3334-3340. Copyright 1996 American Chemical Society.
Figure 8. Rough gold surfaces separated by (a) vacuum and (b) hexadecane molecules.
Figure 8. Rough gold surfaces separated by (a) vacuum and (b) hexadecane molecules.
Figure 9. Hexadecane segmental density profiles, plotted as a function of distance along the axis normal to the solid planes (z) for selected value of the applied normal load. The left panel corresponds to the case of nonadhesive rough surfaces. The middle and right panels correspond, respectively to adhesive rough and adhesive flat surfaces.
Figure 9. Hexadecane segmental density profiles, plotted as a function of distance along the axis normal to the solid planes (z) for selected value of the applied normal load. The left panel corresponds to the case of nonadhesive rough surfaces. The middle and right panels correspond, respectively to adhesive rough and adhesive flat surfaces.
Figure 10. Top view of molecular arrangement in the interfacial region in contact with the solid surface. The top panel corresponds to the rough surface junction, and the bottom panel shows ordered domains corresponding to the flat surface junction. In both cases, the results are for adhesive interaction between the hexadecane molecules and the gold atoms.
Figure 10. Top view of molecular arrangement in the interfacial region in contact with the solid surface. The top panel corresponds to the rough surface junction, and the bottom panel shows ordered domains corresponding to the flat surface junction. In both cases, the results are for adhesive interaction between the hexadecane molecules and the gold atoms.
Figure 12. Total “macroscopic” friction force, F, plotted as a function of the total normal load, L, for rough nonadhesive surfaces lubricated by hexadecane molecules as shown in Figure 8b. For both temperatures, T = 300 and 350 K, the sliding velocity is V = 1.0 m/s. The quoted friction coefficients « are defined by the slopes of the lines.
Figure 12. Total “macroscopic” friction force, F, plotted as a function of the total normal load, L, for rough nonadhesive surfaces lubricated by hexadecane molecules as shown in Figure 8b. For both temperatures, T = 300 and 350 K, the sliding velocity is V = 1.0 m/s. The quoted friction coefficients « are defined by the slopes of the lines.
Figure 15. Similar to Figure 12 but for atomically smooth (crystalline) surfaces. Results for an adhesive junction are shown in (a), and those for a nonadhesive junction are shown in (b).
Figure 15. Similar to Figure 12 but for atomically smooth (crystalline) surfaces. Results for an adhesive junction are shown in (a), and those for a nonadhesive junction are shown in (b).
Figure 13. Similar to Figure 12 but for rough adhesive surfaces.
Figure 13. Similar to Figure 12 but for rough adhesive surfaces.
Figure 14. Dependence of the friction force on the sliding velocity, obtained from MD simulations of a hexadecane film lubricating the junction between nonadhesive rough surfaces at 300 K, under a load of 615 nN.
Figure 14. Dependence of the friction force on the sliding velocity, obtained from MD simulations of a hexadecane film lubricating the junction between nonadhesive rough surfaces at 300 K, under a load of 615 nN.
Figure 16. Average segmental displacements, A, for the two interfacial regions of the confined hexadecane film (one near the upper surface and the other near the bottom surface), plotted vs time during shear simulations of rough-surface junctions. Results are displayed (a) for the nonadhesive junction at the three indicated loads and (b) for the adhesive junction at three load values. The confining solid blocks move at a constant relative velocity of 1 m/s, and the solid straight lines correspond to the displacements of the top and bottom confining solid blocks which move in opposite directions.
Figure 16. Average segmental displacements, A, for the two interfacial regions of the confined hexadecane film (one near the upper surface and the other near the bottom surface), plotted vs time during shear simulations of rough-surface junctions. Results are displayed (a) for the nonadhesive junction at the three indicated loads and (b) for the adhesive junction at three load values. The confining solid blocks move at a constant relative velocity of 1 m/s, and the solid straight lines correspond to the displacements of the top and bottom confining solid blocks which move in opposite directions.
Figure 17. (a) Probability density P(l) of the local normal load, |, for rough nonadhesive surfaces at a total normal applied load of L = 513 nN. The solid lines were recorded in MD simulations, and the dashed line is a gamma function fit to the data. The simulation was done at 300 K. (b) The local friction force f, as a function of the local normal load |. The dashed line is a fit to the data using the Weibull cumulative distribution function. The results for other values of the total applied load are of similar form as those shown here for the particular chosen normal load value.
Figure 17. (a) Probability density P(l) of the local normal load, |, for rough nonadhesive surfaces at a total normal applied load of L = 513 nN. The solid lines were recorded in MD simulations, and the dashed line is a gamma function fit to the data. The simulation was done at 300 K. (b) The local friction force f, as a function of the local normal load |. The dashed line is a fit to the data using the Weibull cumulative distribution function. The results for other values of the total applied load are of similar form as those shown here for the particular chosen normal load value.
Figure 18. Averaged (spatially and temporally) local friction force f for nonadhesive rough surfaces plotted as a function of the average local normal load |, calculated as described in the text. The circles are the simulation results. The stars are fits of the Weibull cumulative distribution function. The solid line gives a linear fit to the simulation results with a slope (friction coefficient) of 0.10.
Figure 18. Averaged (spatially and temporally) local friction force f for nonadhesive rough surfaces plotted as a function of the average local normal load |, calculated as described in the text. The circles are the simulation results. The stars are fits of the Weibull cumulative distribution function. The solid line gives a linear fit to the simulation results with a slope (friction coefficient) of 0.10.
Figure 21. Difference in the local distribution of the external total applied load or normal adhesive force between load-controlled non- adhering surfaces (A) and adhesion-controlled surfaces (B). In the former case, the total friction force F is given either by F = wL for one contact point (left side) or by F = '3uL + YauL + '/guL = wL for three contact points (right side). Thus the load-controlled friction is always proportional to the applied load, independent of the number of contacts and of their geometry. In the case of adhering surfaces (B), the effective “intemal” load is given by kA, where A is the real local contact area, which is proportional to the number of intermolecular bonds being made and broken across each single contact point. The total friction force is now given by F = wkA for one contact point (left side), and F = wkA; + wkA2 + wkA3) = wkAtot for three contact points (right side). Thus, for adhesion-controlled friction, the friction is proportional to the real contact area, at least when no additional extemal load is applied to the system.
Figure 21. Difference in the local distribution of the external total applied load or normal adhesive force between load-controlled non- adhering surfaces (A) and adhesion-controlled surfaces (B). In the former case, the total friction force F is given either by F = wL for one contact point (left side) or by F = '3uL + YauL + '/guL = wL for three contact points (right side). Thus the load-controlled friction is always proportional to the applied load, independent of the number of contacts and of their geometry. In the case of adhering surfaces (B), the effective “intemal” load is given by kA, where A is the real local contact area, which is proportional to the number of intermolecular bonds being made and broken across each single contact point. The total friction force is now given by F = wkA for one contact point (left side), and F = wkA; + wkA2 + wkA3) = wkAtot for three contact points (right side). Thus, for adhesion-controlled friction, the friction is proportional to the real contact area, at least when no additional extemal load is applied to the system.
Related topics:
EngineeringThermodynamicsFundamental ParametersWeibull distributionMD SimulationMolecular Dynamic SimulationBoltzmann distribution
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