Molecular Stripe Patterns on Surfaces in the Presence of Long-Range Repulsive Electrostatic Interactions: Monte Carlo Simulations and Mean-Field Theory

Abstract

Mobile molecules on surfaces can arrange into stripes due to directional attractive interactions such as π−π stacking, hydrogen, or covalent bonding. The structural arrangement of the stripes depends on the underlying substrate lattice and omnipresent long-range electrostatic interactions. To model the impact of the interplay of short-range attractive and long-range interactions on the molecular arrangements, we study a coarsegrained theoretical approach, where the attractive interaction is described by an anisotropic Ising model. As for the long-range electrostatic interaction, we focus on repulsive dipole−dipole interactions. An efficient Monte Carlo algorithm is developed by which even stripe patterns with very long stripes can be equilibrated. Using this algorithm, we assess the limits of a previously developed mean-field theory, which provides analytical predictions for stripe-to-stripe distance and stripe length distributions. This theory allows one to extract interaction parameters by fitting respective distributions to experimental data. We determine the limits of the applicability of the mean-field theory and beyond its limits suggest a combined approach of mean-field analysis and simulations. The power of this approach is demonstrated by applying it to experimental observed stripe pattern of 3hydroxybenzoic acid (3-HBA) on the calcite (10.4) surface.

Improved Random Batch Ewald Method in Molecular Dynamics Simulations

“…Whereas, the nonbonded forces are the computational bottleneck as the electrostatic forces must be calculated between all pairs of particles, and the van der Waals forces need to calculate the pair interactions less than some cutoff radius (0.9–1.5 nm), remaining a broad interest for algorithm development and optimization. Particularly, electrostatic interactions are ubiquitous in biomolecular and material systems such as DNA aggregation, protein folding/unfolding, − the form of surface pattern, ion adsorption, and polyelectrolyte complexation . An efficient and accurate electrostatic solver plays an essential role for the simulations of these systems.…”

Improved random batch Ewald method in molecular dynamics simulations

“…Whereas, the non-bonded forces are the computational bottleneck as the electrostatic forces must be calculated between all pairs of particles, and the van der Waals forces need to calculate the pair interactions less than some cutoff radius (0.9 ∼ 1.5nm), remaining a broad interest for algorithm development and optimization. Particularly, electrostatic interactions are ubiquitous in biomolecular and material systems such as DNA aggregation [7], protein folding/unfolding [8,9,10], the form of surface pattern [11], ion adsorption [12], and polyelectrolyte complexation [13]. An efficient and accurate electrostatic solver plays essential role for the simulations of these systems.…”