Contact mechanics modeling of pull-off measurements: effect of solvent, probe radius, and chemical binding probability on the detection of single-bond rupture forces by atomic force microscopy

Pull-off forces for chemically modified atomic force microscopy tips in contact with flat substrates coated with receptor molecules are calculated using a Johnson, Kendall, and Roberts contact mechanics model. The expression for the work of adhesion is modified to account for the formation of discrete numbers of chemical bonds ([n.sub.Bonds]) between the tip and substrate. The model predicts that the pull-off force scales as [n.sub.Bonds.sup.1/2], which differs from a common assumption that the pull-off force scales linearly with [n.sub.Bonds]. Periodic peak progressions are observed in histograms generated from hundreds of computed pull-off forces. The histogram periodicity is the signature of discrete chemical interactions between the tip and substrate and allows estimation of single-bond rupture forces. The effects of solvent, probe tip radius, and chemical binding probability on the detection of single-bond forces are examined systematically. A dimensionless parameter, the effective force resolution, is introduced that serves as a quantitative predictor for determining when periodicity in force histograms can occur. The output of model is compared to recent experimental results involving tips and substrates modified with self-assembled monolayers. An advantage of this contact mechanics approach is that it allows straightforward estimation of solvent effects on pull-off forces.