Reproducing morphologies of disorderly self-assembling planar molecules with static and dynamic simulation methods by matching density

Monte Carlo and molecular dynamics simulations are the two main numerical approaches to modeling molecular self-assembly and ordering. Conceptually, however, each method explores different paths through the thermodynamic landscape. Molecular dynamics depends on the position and momentum terms. Monte Carlo is a static set, and thus the momentum term is replaced with an energy term that is dependent on the volume and entropy. Until now, it was unclear if a stochastic process of densifying particles would have the same internal structure as morphologies produced from classical mechanics. This paper provides a systematic (i.e., statistical) analysis of the outcomes of 4032 simulations for hard-core circular objects as a function of the number of molecules and the boundary conditions. Structural classification of the resultant ensembles (averaged pair correlation function, bond-order parameter, translational order parameter, and Voronoi diagrams) shows that stochastic and dynamic approaches do not alter the morphology of the steric molecules. We conclude that when the probability density of covering area fractions are matched, the ensembles produced from the two methods will show the same level of structural disorder and positional patterns. The resultant morphology from both models, therefore, is not a product of dynamic unrest, but that of the relaxation of entropic frustration from macromolecular crowding. Although statistically the two methods produce similar configurations, nuances arise from the static and dynamic nature of modeling. As a result, Monte Carlo is slightly better suited to modeling systems when the desired morphology is represented by a metastable state; molecular dynamics on the other hand is more suited to finding defects that can arise in morphologies. Regardless, a fixed density will result in similar morphologies from both techniques, driven by similar configurational entropy.