Analytical modeling of the junction evolution in single-molecule break junctions: towards quantitative characterization of the time-dependent process

The conductance through single-molecule junctions characterized by the break junction techniques consists of the through-space tunneling and through-molecule tunneling conductance, and the existence of through-space tunneling between the electrodes makes the quantitative extraction of the intrinsic molecular signals of single-molecule junctions challenging. Here, we established an analytic model to describe the evolution of the conductance of a single molecule in break junction measurements. The experimental data for a series of oligo(aryleneethynylene) derivatives validate the proposed model, which provides a modeling insight into the conductance evolution for the opening process in a "real" break junction experiment. Further modulations revealed that the junction formation probability and rupture distance of the molecular junction, which reflect the junction stability, will significantly influence the amplitude and position of the obtained conductance peak. We further extend our model to a diffusion and a chemical reaction process, for which the simulation results show that the break junction technique offers a quantitative understanding of these time-dependent systems, suggesting the potential of break junction techniques in the quantitative characterization of physical and chemical processes at the single-molecule scale.