Monolayer-to-thin-film transition in supramolecular assemblies: the role of topological protection

An innovative combination of TEM and STM sheds new insight into the growth of organic layers and reveals the importance of topology in controlling the transition from two- to three-dimensional structure.

The topography of TMA and TPA films was studied using AFM. Figure S1a shows tapping mode images of 6 minute deposition films for TMA (a,c) and TPA (c,d). The TMA and TPA films themselves appear in stark contrast to each other; TMA shows a flat, continuous thinfilm whereas TPA appears to grow in small lozenge-shaped crystallites. This is in agreement with the structures studied using TEM. 3 The thicknesses of TMA and TPA films were also measured using AFM. Figure S1b shows measurements of film thickness for the TMA and TPA depositions onto graphene on copper. Panel (a) is a tapping mode AFM topography image of an 18 minute-deposition film of TPA on graphene on copper after a trench has been scratched through the film. The trench is scratched by repeatedly scanning a small region in contact mode. Panel (b) is an averaged lineprofile from the white dashed rectangle in (a), from which the film thickness was measured.   Analysis of STM images from TMA on Gr-Cu shows two distinct orientations of the chicken-wire superstructure with respect to the underlying graphene lattice. Figure S2b  images were drift-corrected by using the graphene atomic lattice as a reference. In particular, the acquisition of STM images with both molecular and substrate atomic resolution allows the images to be rescaled based on the known lattice periodicity of graphene. Once the correct unit cell of the molecular assembly has been determined, other images showing only molecular resolution can be rescaled accordingly.

S4: Measuring the characteristic dose of TMA on graphene
The use of electron microscopy to study organic thin films is restricted by the lifetime of the organic molecules, and their supramolecular structure, under the electron beam. To quantify this lifetime, diffraction patterns from organic thin films can be analyzed to find the characteristic dose -defined as the dose after which the diffraction spot intensity has been reduced by a factor 1/e, and after which the structure is believed to have been significantly where is the electron dosing rate of the electron beam at the sample plane and is the time after which the diffraction spot intensity has been reduced by a factor 1/e (characteristic time).    The simulated image assuming direct stacking (AA stacking) is clearly more consistent with the reconstructed one, than the simulated image based on an offset model (AB stacking).
acTEM imaging thus proves that the TMA is stacking in a direct (AA) fashion, creating nanopores.

TEM image reconstruction background
For an electron wavefunction propagating through a unit cell with atoms located at positions , where = 1, … , , the electrostatic potential ( ) felt by the electron at a point may be determined through a summation of all potentials at point : Here, are the individual potentials of each atom. The potential ( ) is a continuous realspace function. The Fourier components ( ) of potential ( ) are related by: These ( ) are related to the structure factor F( ) by a scaling factor: where the structure factor ( ) is defined as a discrete sum of structure factor amplitudes | ( )| and phases 2 ( • ) for each atom in the unit cell: .
Individual structure factor amplitudes and phases are measured in a Fourier transform (power spectrum) of an image of a unit cell or multiple unit cells (these appear as the lattice spots in the power spectrum). The original unit cell potential ( ) is therefore related to the structure factor ( ) for the unit cell through a scaled inverse Fourier transform: .
Truncating this series to some finite order of gives an approximation to the unit cell potential    Table