Inhomogeneous Relaxation of a Molecular Layer on an Insulator due to Compressive Stress

We discuss the inhomogeneous stress relaxation of a monolayer of hexahydroxytriphenylene (HHTP) which adopts the rare line-on-line (LOL) coincidence on KCl(001) and forms moiré patterns. The fact that the hexagonal HHTP layer is uniaxially compressed along the LOL makes this system an ideal candidate to discuss the influence of inhomogeneous stress relaxation. Our work is a combination of noncontact atomic force microscopy experiments, density functional theory and potential energy calculations, and a thorough interpretation by means of the Frenkel-Kontorova model. We show that the assumption of a homogeneous molecular layer is not valid for this organic-inorganic heteroepitaxial system since the best calculated energy configuration correlates with the experimental data only if inhomogeneous relaxations of the layer are taken into account.

Figure 1

(a) Molecular domains of HHTP on KCl(001) ($300\times 300{\mathrm{nm}}^2$, normalized $\Delta f$: $\gamma =-0.03\mathrm{nN}·\sqrt{\mathrm{nm}}$). The domains consist of fringes forming a moiré pattern with a periodicity of 45.5 Å. Three distinct orientations are visible (numbered arrows). Insets: HHTP molecule (left) and zoom on a type 3 domain showing both the fringes orientation and a molecular axis (right, $40\times 40{\mathrm{nm}}^2$, $\gamma =-0.12\mathrm{nN}·\sqrt{\mathrm{nm}}$). (b) Zoom on a molecular domain ($25\times 25{\mathrm{nm}}^2$, $\gamma =-0.27\mathrm{nN}·\sqrt{\mathrm{nm}}$). Upper part: acquired topography signal. Lower part: topography signal autocorrelation showing the molecular hexagonal arrangement in a LOL epitaxy ($⟨10{⟩}_m$ and $⟨2\overline{1}{⟩}_s$ are parallel). Inset: KCl imaged close to the molecular domain ($2.2\times 2.2{\mathrm{nm}}^2$, $\gamma =-0.33\mathrm{nN}·\sqrt{\mathrm{nm}}$). (c) FFT showing both the diffraction spots of HHTP and of KCl (green and white circles, respectively): raw data in Fig. S1 of Supplemental Material 16. (d) Sketch illustrating the correspondence between real and reciprocal space. The LOL results from a coincidence of the ends of molecular and substrate reciprocal vectors: $5{\mathbf{a}}_{\mathbf{2}\mathbf{m}}^{*}=2{\mathbf{a}}_{\mathbf{2}\mathbf{s}}^{*}+{\mathbf{a}}_{\mathbf{1}\mathbf{s}}^{*}$.

Figure 2

(a) Autocorrelation image of a molecular domain showing moiré fringes and periodic bright spots. The orientation of the fringes with respect to $⟨10{⟩}_m$ is $(100\pm 3)°$. (b) Simulated moiré pattern which reproduces both the experimental fringes and the bright spots, respectively.

Figure 3

(a) Unit cell of the HHTP freestanding layer as calculated by DFT. A H-bonded (dotted green lines) hexagonal structure with $\Vert {\mathbf{a}}_{\mathbf{1}\mathbf{m},\mathbf{2}\mathbf{m}}^{\mathrm{DFT}}\Vert =11.62\AA$ is found. (b) Evolution of the cohesion energy per molecule as a function of $a_{1m}^{\mathrm{DFT}}$ (uniaxial stress), from which the uniaxial stiffness $k_{\mathrm{DFT}}=15.3\mathrm{N}/\mathrm{m}$ of the layer is derived. (c) Adhesion energy of a single HHTP adsorbed on KCl(001), as calculated by PE calculations. The constant background of $-0.76\mathrm{eV}$ (mainly vdW interaction) is laterally corrugated due to ES molecule-substrate interaction. (d) Adsorption energy per molecule for a cluster of 3600 molecules when translated with fixed angular orientation. The remaining 1D potential is 4 meV deep and carries the LOL epitaxy direction.

Figure 4

Nine molecules are forced within the distance of ten minima of the ES energy profile along the $⟨2\overline{1}{⟩}_s$ for a single molecule [see Fig. 3c]. The adsorption energy of the molecules with even number is significantly larger when the molecules are spaced according to the FK model (lower ones) compared to the equally spaced molecules (upper ones, homogeneous chain).