Energetics and Order Parameters of Driven Dissipative Colloidal Crystals

Empirical studies demonstrate that driven dissipative colloidal crystals can form and stabilize in various configurations, from simple Bravais lattices to complex superpositions like Moiré patterns, particularly under highly nonlinear and strongly stochastic conditions [1]. Their lifelike behaviors suggest a dynamic phase space in which both internal and external dynamics influence the potential energy surfaces.

To investigate these phenomena, we developed a simulator replicating these conditions to quantify the energetics of such systems and identify order parameters that gauge the degree of structural organization. In our hard-sphere model, Brownian particles are driven by a Gaussian potential to facilitate the aggregation of a diverse range of crystal structures. We define and calculate order parameters based on system geometry, particle density, potential strength, and external forces. This approach allows us to explore the conditions necessary for the emergence of stable crystals, quantify their formation energies, entropies, and assess their transition probabilities.

[1] Ilday, S., Makey, G., Akguc, G. et al. Rich complex behaviour of self-assembled nanoparticles far from equilibrium. Nat Commun 8, 14942 (2017).