From Chaos to Order: Chain-Length Dependence of the Free Energy of Formation of Meso-tetraalkylporphyrin Self-Assembled Monolayer Polymorphs

Abstract

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.

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“…[368,369] The molecular structures determined from modelling of large areas of the L and M polymorphs are shown, as is how they seamlessly meld together to form the interface layers. The L polymorph is observed for all odd-length chain molecules studied (lengths m from 11 to 19) [253,363,366,368] but not for the even chain Free-electron gas, exact description n molecule studied, 2H-C 12 P, [364,365] while three M polymorphs [253,364,365,368] of quite different form named M a , M b , and M c are observed for 2H-C 11 P, 2H-C 12 P, and 2H-C 13 P, respectively. The L structures have all four alkyl chains lying flat on the surface while the M polymorphs have two such chains with the other two somehow oriented into the solution.…”

“…Our work has focussed on the self-assembly of tetraalkylporphyrin molecules synthesized by Max Crossley on highly ordered pyrolytic graphite (HOPG) surfaces from solution in 1-phenyloctane, octanoic acid, or n-tetradecane. [253,[363][364][365][366][367][368] This involved measurement of STM images and the simulation [253,363,369] of the Gibbs free-energy of formation for a wide range of possible atomic structures for each image. The molecules considered are shown in Chart 2.…”

“…A high density polymorph with only one chain on the surface is also known for 2H-C 11 P. [368] Atomic structures for the SAMs are determined by comparing calculated and observed structures. The calculated structures were obtained by optimizing five possible structures for the L polymorphs [363,366] and 40 possibilities for the M polymorphs. [363,369] These possibilities were obtained by considering various conformations of the chain kinks that occur as the alkyl chains come away from the porphyrin at an angle near 608 and must subsequently be bent back in order to lie flat on the surface.…”

“…The calculated structures were obtained by optimizing five possible structures for the L polymorphs [363,366] and 40 possibilities for the M polymorphs. [363,369] These possibilities were obtained by considering various conformations of the chain kinks that occur as the alkyl chains come away from the porphyrin at an angle near 608 and must subsequently be bent back in order to lie flat on the surface. The 40 possibilities for the M polymorphs were obtained by varying kink-structure conformers and macrocycle rotation angles, first eliminating possibilities that cannot be shaped into a valid SAM.…”

“…After optimization, only at most 22 stable SAMs were realised, named Ma to Mv. Structure assignment was made by comparing these structures to experiment, considering: [253,363,366,369] -Agreement of observed and calculated lattice parameters. To do this, new experimental techniques based on internal calibration and repeated measurements were developed to significantly reduce the experimental uncertainties in the lattice parameters, allowing for discrimination between the calculated structures.…”