Optimized Interactions for Targeted Self-Assembly: Application to a Honeycomb Lattice

We devise an inverse statistical-mechanical methodology to find optimized interaction potentials that lead spontaneously to a target many-particle configuration. Target structures can possess varying degrees of disorder, thus extending the traditional idea of self-assembly to incorporate both amorphous and crystalline structures as well as quasicrystals. For illustration purposes, our computational technique is applied to yield an optimized isotropic (nondirectional) pair potential that spontaneously yields the three-coordinated honeycomb lattice as the ground state structure in two dimensions. This target choice is motivated by its three-dimensional analog, the diamond lattice, which is known to possess desirable photonic band gap properties.

Figure 1

500-particle annealed MC results at specific area $\alpha =1.45$ for a potential with parameters displaced from those given by Eq. (5).

Figure 2

The optimized pair potential $V(r)$ specified by Eq. (6) for honeycomb-lattice self-assembly.

Figure 3

Phonon spectrum (frequency squared) for the optimized honeycomb potential depicted in Fig. 2 at specific area $\alpha =1.45$.

Figure 4

500-particle MC results for the optimized potential annealed depicted in Fig. 2 from $k_{B}T=0.22$ to $k_{B}T=0$ at specific area $\alpha =1.45$.