Modeling single molecule junction mechanics as a probe of interface bonding
Using the atomic force microscope based break junction approach, applicable to metal point contacts and single molecule junctions, measurements can be repeated thousands of times resulting in rich data sets characterizing the properties of an ensemble of nanoscale junction structures. This paper focuses on the relationship between the measured force extension characteristics including bond rupture and the properties of the interface bonds in the junction. We analyzed a set of exemplary model junction structures using density functional theory based calculations to simulate the adiabatic potential surface that governs the junction elongation. The junction structures include representative molecules that bond to the electrodes through amine, methylsulfide, and pyridine links. The force extension characteristics are shown to be most effectively analyzed in a scaled form with maximum sustainable force and the distance between the force zero and force maximum as scale factors. Widely used, two parameter models for chemical bond potential energy versus bond length are found to be nearly identical in scaled form. Furthermore, they fit well to the present calculations of N–Au and S–Au donor-acceptor bonds, provided no other degrees of freedom are allowed to relax. Examination of the reduced problem of a single interface, but including relaxation of atoms proximal to the interface bond, shows that a single-bond potential form renormalized by an effective harmonic potential in series fits well to the calculated results. This, then, allows relatively accurate extraction of the interface bond energy. Analysis of full junction models shows cooperative effects that go beyond the mechanical series inclusion of the second bond in the junction, the spectator bond that does not rupture. Calculations for a series of diaminoalkanes as a function of molecule length indicate that the most important cooperative effect is due to the interactions between the dipoles induced by the donor-acceptor bond formation at the junction interfaces. The force extension characteristic of longer molecules such as diaminooctane, where the dipole interaction effects drop to a negligible level, accurately fit to the renormalized single-bond potential form. Our results suggest that measured force extension characteristics for single molecule junctions could be analyzed with a modified potential form that accounts for the energy stored in deformable mechanical components in series.