From chaos to order: Chain-length dependence of the free energy of formation of meso-tetraalkylporphyrin self-assembled monolayer polymorphs

We demonstrate that systematic errors can be reduced and physical insight gained through investigation of the dependence of free energies for meso-tetraalkylporphyrin self-assembled monolayers (SAMs) polymorphism on the alkyl chain length m. These SAMs form on highly ordered pyrolytic graphite (HOPG) from organic solution, displaying manifold densities and atomic structures. SAMs with m = 11-19 are investigated experimentally while those with m = 6-28 are simulated using density-functional theory (DFT). It is shown that, for m = 15 or more, the alkyl chains crystallize to dominate SAM structure. Meso-tetraalkylporphyrin SAMs of length less than 11 have never been observed, a presumed effect of inadequate surface attraction. Instead, we show that free energies of SAM formation actually enhance as the chain length decreases. The inability to image regular SAMs stems from the appearance of many polymorphic forms of similar free energy, preventing SAM ordering. We also demonstrate a significant odd/even effect in SAM structure arising from packing anomalies. Comparison of the chain-length dependence of formation free energies allows the critical dispersion interactions between molecules, solvent, and substrate to be directly examined. Interpretation of the STM data combined with measured enthalpies indicates that Grimme's D3 explicit-dispersion correction and the implicit solvent correction of Floris, Tomasi and Pascual Ahuir are both quantitatively accurate and very well balanced to each other.