Microscopic approach to the kinetics of pattern formation of charged molecules on surfaces

A microscopic formalism based on computing many-particle densities is applied to the analysis of the diffusion-controlled kinetics of pattern formation in oppositely charged molecules on surfaces or adsorbed at interfaces with competing long-range Coulomb and short-range Lennard-Jones interactions. Particular attention is paid to the proper molecular treatment of energetic interactions driving pattern formation in inhomogeneous systems. The reverse Monte Carlo method is used to visualize the spatial molecular distribution based on the calculated radial distribution functions (joint correlation functions). We show the formation of charge domains for certain combinations of temperature and dynamical interaction parameters. The charge segregation evolves into quasicrystalline clusters of charges, due to the competing long- and short-range interactions. The clusters initially co-exist with a gas phase of charges that eventually add to the clusters, generating ”fingers” or line of charges of the same sign, very different than the nanopatterns expected by molecular dynamics in systems with competing interactions in two dimensions, such as strain or dipolar versus van der Waals interactions.

Figure 1

(Color online) The correlation functions calculated for parameter set $\eta =0.4$, $\theta =0.35$, $\delta =0.35$, and $\mu =0.5$; the observation time $t$: (1) $2^{12}$, (2) $2^{14}$, (3) $2^{16}$, and (4) $2^{18}$.

Figure 2

The calculated correlation functions (full curves), and their RMC approximation (circles). The time $t$: (a) $2^{12}$, (b) $2^{14}$, (c) $2^{16}$, and (d) $2^{18}$. Parameters: $\eta =0.4$, $\theta =0.35$, $\delta =0.35$, and $\mu =0.5$.

Figure 3

(Color online) Fragments of the characteristic snapshots obtained using the RMC for the correlation functions in Fig. 2. The snapshots numbering corresponds to (a)-(d) in Fig. 2. Parameters: $\eta =0.4$, $\theta =0.35$, $\delta =0.35$, and $\mu =0.5$.