To quantify charge transport through molecular junctions fabricated using the conducting probe atomic force microscopy (CP-AFM) platform, information on the number of molecules $N$ per junction is absolutely necessary. $N$ can be currently obtained only via contact mechanics, and the Youngs modulus $E$ of the self-assembled monolayer (SAM) utilized in the key quantity for this approach. The experimental determination of $E$ for SAMs of CP-AFM junctions fabricated using oligophenylene dithiols (OPDn, $1 leq n leq 4$) and gold electrodes turned out to be too challenging. Recent measurements (Z. Xie et al, J. Am. Chem. Soc. 139 (2017) 5696) merely succeeded to provide a low bound estimate ($E approx 58,$GPa). It is this state of affairs that motivated the present theoretical investigation. Our microscopic calculations yield values $E approx 240 pm 6,$GPa for the OPDn SAMs of the aforementioned experimental study, which are larger than those of steel ($ E approx 180 - 200,$GPa) and silicon ($E approx 130 - 185,$GPa). The fact that the presently computed $E$ is much larger than the aforementioned experimental lower bound explain why experimentally measuring $E$ of OPDn SAMs is so challenging. Having $E approx 337 pm 8,$GPa, OPDn SAMs with herringbone arrangement adsorbed on fcc (111)Au are even stiffer than Si$_3$N$_4$ ($E approx 160 - 290,$GPa).
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