Paper TR+AS+NS+SS-MoA8
The Relationship Between Molecular Contact Thermodynamics and Surface Contact Mechanics

Monday, October 28, 2013, 4:20 pm, Room 203 C

The atomic force microscope (AFM) has been used widely to study nanoscale tribological phenomena, but a unified model for the mechanics of the tip-sample interaction is lacking. Experimental data show that nanoscale friction depends strongly on interfacial chemistry, but these correlations are not explained adequately by existing models. Here we report measurements of interactions between hydrogen bond-forming molecules adsorbed onto solid surfaces and AFM tips. By making measurements in liquid mixtures, we demonstrate a quantitative correlation between the surface shear strength in a nanoscale contact and the free energy of solution-phase hydrogen bonding interactions, uniting classical contact mechanics with equilibrium thermodynamics. We demonstrate that the thermodynamics of intermolecular interactions may be determined quantitatively from nanoscale friction measurements. It has been found that the contact mechanics are best modeled by treating the friction force as the sum of a load-dependent term (attributed to “molecular plowing”) and an area-dependent term attributed to shearing (adhesion). The relative contributions of plowing and shearing are determined by the coefficient of friction, µ, and the surface shear strength τ. The transition from adhesion- to load-determined friction is controlled by the solvation state of the surface: solvated surfaces represent a limiting case in which the shear term approaches zero, and the friction-load relationship is linear, while in other circumstances, the friction-load relationship is non-linear and consistent with Derjaguin-Muller-Toporov (DMT) mechanics. A striking correlation has been observed between the concentration-dependence of the association constant (K_a) for the formation of 1:1 hydrogen-bonded complexes and the pull-off force F_a and surface shear strength τ for the same molecules when one partner is immobilized by attachment to an AFM probe and the other is adsorbed to a surface. Analysis of the concentration-dependence of F_a and τ enables the prediction of K_S with remarkably high precision, indicating that for these hydrogen bonding systems, the tip-sample adhesion is dominated by the H-bond thermodynamics. For hydrocarbon surfaces, we have found that friction-load relationships are also fitted by DMT mechanics, and experimentally determined works of adhesion correlate closely with predictions from Lifshitz theory. For polymer brushes, a broader range of behavior is observed, but this may also be understood if the contact mechanics are modeled by treating the friction force as the sum of a load-dependent term and an area-dependent term attributed to shearing.