Molecular self-organization: Predicting the pattern diversity and lowest energy state of competing ordering motifs

Self-organized monolayers of highly flexible Fréchet dendrons were deposited on graphite surfaces by solution casting. Scanning tunneling microscopy (STM) reveals an unprecedented variety of patterns with up to seven stable hierarchical ordering motifs allowing us to use these molecules as a versatile model system. The essential molecular properties determined by molecular mechanics simulations are condensed to a coarse grained interaction-site model of various chain configurations. In a Monte Carlo approach with random starting configurations, the experimental pattern diversity can be reproduced in all facets of the local and global ordering. Based on an energy analysis of the Monte Carlo and molecular mechanics modeling, the thermodynamically most stable pattern is predicted and shown to coincide with the pattern which dominates the STM images after several hours or upon moderate heating.

Figure 1

(Color online) A single molecule of the dodecyl/octyl terminated Fréchet dendron is highlighted. One of seven different ordering patterns on HOPG is exemplified. Middle: STM image of a jigsaw pattern of the Fréchet dendron $\left(7.5\text{nm}\times 12.5\text{nm},U_{Bias}=-800\text{mV},\left|I_T\right|=8\text{pA}\right)$. Left: atomistic modeling by an energy minimized MM simulation (see text). Right: simulation of the LDOS by DFT calculations based on the input of the geometry determined by MM.

Figure 2

(Color online) [(a)–(d)] STM results and corresponding [(e)–(f)] molecular mechanics modeling (see text) of four experimentally found patterns of Fréchet dendrons: (a) sawtooth, (b) honeycomb, (c) jigsaw, and (d) tiretrack. The molecular backbones (highlighted) indicate the local ordering motif. ($10\text{nm}\times 10\text{nm}$, $U_{Bias}=-700$ to $-800\text{mV}$, and $\left|I_T\right|=5–30\text{pA}$)

Figure 3

(Color online) Top: angle configuration for conformer $\alpha$. The box displays the six possible orientations on a fixed lattice of hexagonal symmetry. Bottom: conformers $\beta$, $\gamma$, and $\delta$ with the respective internal angles indicated.

Figure 4

(Color online) MC simulations (i)–(iv). (0) Random starting configurations allowing discrete $\pi /3$ rotations of the coarse grained molecules. Upon slow cooling the following patterns formed from random state (0) indicated with red arrows: (i) sawtooth pattern for conformer $\beta$ and for conformer $\alpha$, (ii) trimer honeycomb pattern for conformer $\delta$, (iii) jigsaw pattern for conformer $\alpha$, and (iv) tiretrack pattern for conformers $\alpha$, $\beta$, and $\gamma$. All phases were stable upon heating to $300°\text{C}$.

Figure 5

(Color online) Alternative phases, that have been predicted, condensed from random starting configurations by the Monte Carlo approach: (v) honeycomb pattern of conformer $\alpha$ and $\gamma$, and (vi) inverted honeycomb pattern of conformer $\gamma$. Both the inverted honeycomb and honeycomb MC patterns proved unstable upon simulating a finite temperature and, thus, cannot be considered as likely patterns; these patterns find no close resemblance in the experimental data.

Figure 6

(Color online) conformer $\beta$, coarse grained model with angles $180°$ and $60°$ between the long and short chains. (a) Zero-temperature energy analysis for determining the associated lowest energy state. The experimentally relevant regime corresponds to $3.2a/\sigma$. (b) The pattern of lowest energy in the zero-temperature analysis for conformations $\gamma$ and $\delta$. At the experimentally relevant regime of $3.2a/\sigma$, the sawtooth pattern for conformer $\gamma$ and jigsaw pattern for conformer $\delta$, did not prove stable upon heating and hence cannot represent the thermodynamically most stable pattern.

Figure 7

(Color online) (a) Another local ordering motif of the MC simulation [Fig. 4(iv)] that was subsequently identified experimentally; (b) STM measurement of the rarely found fifth pattern with corresponding; and (c) MM modeling. $\left(12.5\text{nm}\times 12.5\text{nm},U_{Bias}=-800\text{mV},\left|I_T\right|=8\text{pA}\right)$