Role of Interaction Anisotropy in the Formation and Stability of Molecular Templates

Surface templating via self-assembly of hydrogen-bonded molecular networks is a rapidly developing bottom-up approach in nanotechnology. Using the melamine-PTCDI molecular system as an example we show theoretically that the network stability in the parameter space of temperature versus molecular coupling anisotropy is highly restricted. Our kinetic Monte Carlo simulations predict a structural stability diagram that contains domains of stability of an open honeycomb network, a compact phase, and a high-temperature disordered phase. The results are in agreement with recent experiments, and reveal a relationship between the molecular size and the network stability, which may be used to predict an upper limit on pore-cavity sizes.

Figure 1

(a) Molecules on hexagonal grid illustrating anisotropic (hydrogen bonds) molecular bonding. Rodlike (PTCDI) molecules are shown as elongated rectangles, while vertexlike (melamine) molecules are triangles. Hydrogen-bond-generating functional groups are indicated by line segments; hydrogen bonds are shown by dotted line segments. (b)–(d) Phases of stoichiometric mixture of 180 rodlike and 120 vertexlike molecules observed in different regions of parameter space during KMC simulations: (b) network structure at $E^I=0\mathrm{eV}$ and $T=0.08\mathrm{eV}$; (c) compact structure at $E^I=-0.16\mathrm{eV}$ and $T=0.1\mathrm{eV}$; magnified is main structural unit; (d) disordered structure at $E^I=-0.1\mathrm{eV}$ and $T=0.24\mathrm{eV}$.

Figure 2

Structural stability diagram of system shown in Fig. 1 in parameter space of normalized temperature $k_{B}T/E_{12}^A$ versus ratio of isotropic (van der Waals) to anisotropic (hydrogen-bond) energies $E^I/E_{12}^A$. Solid curves indicate structural transitions between three domains identified as network, close-packed or compact, and disordered phases. Shaded region indicates likely region of parameters corresponding to melamine-PTCDI molecular system. Lines AA’ and BB’ indicate directions for obtaining heat capacity $C_V$ and generalized susceptibility ${\chi }_E$ in Fig. 3. The open square symbol at $k_{B}T/E_{12}^A=-0.108$ and $E^I/E_{12}^A=0.135$ indicates parameters of simulated system displayed in Fig. 4. We use elevated temperatures in our simulations to reach equilibration within a reasonable time. Therefore structural defects are also more likely to be observed.

Figure 3

Heat capacity $C_V$ (curve 1) and generalized susceptibility ${\chi }_E$ (curve 2) of system in Fig. 1 indicating structural transition between compact and disordered phases at point C in Fig. 2 with coordinates $k_{B}T/E_{12}^A=-0.16$ and $E^I/E_{12}^A=0.11$. Functions are scaled to have the same peak value. The origin of the curve is in both cases at the maximum of the function.

Figure 4

PTCDI-melamine molecular structures with PTCDI molecules appearing as bright double lines and melamine molecules not resolved. (a) STM image of on the $\mathrm{Ag}/\mathrm{Si}(111)\mathrm{\text{−}}(\sqrt{3}\times \sqrt{3}R30°)$ surface at room temperature; (b) simulated structure obtained for the parameter values corresponding to the open square symbol in Fig. 2. White bars indicate the positions of PTCDI molecules and white triangles those of the melamine molecules. Hexagons in both (a) and (b) represent structural unit of the equilibrium structures, while the clusters of the compacted structures outlined by white dashed lines represent typical defects. The compact structures in (a) and (b) are not identical, as illustrated by white symbols inside outlined areas. However, they consist of the same zigzag motif with a different side shift that is likely to be stabilized by an additional hydrogen bond between PTCDI (1) and melamine (2), as labeled in (a).