The development of advanced functional materials frequently involves the formation of patterns and structures on multiple scales. The ability to predict, prototype, and optimize these multi-scale functional materials is a key enabler for many next-generation technologies ranging from microelectronics to catalytic materials. Recently developed mesoscopic models have enabled multi-scale hierarchical stochastic (Monte Carlo) and continuum simulation of the complex surface pattern formation processes involved in the manufacture of these functional materials.
In this work, pattern formation on a surface is simulated using a deterministic mesoscopic diffusion model where short-range attractive and long-range repulsive interactions are present. The transition mechanisms and pattern structure are studied using different dynamics (Metropolis and Arrhenius) and particle-particle interaction potentials (Guassian and Yukawa). The pattern evolution mechanisms predicted by this model are compared to relevant experimental systems, including recent observations of surface self-assembly in block copolymer and colloidal systems. Online/concurrent order reconstruction techniques are used to quantify the evolution of pattern quality (feature size, variation, and long-range order) during simulation.