Modeling of directed particle assembly in two-dimensional structures based on constructal law

While two-dimensional (2D) structural photonic materials have led to many new innovations in the field of optics, the preferential alignment and assembly of colloidal particle arrays over large areas remains a challenge. Here, we develop a theoretical model based on the constructal law in order to describe this particle assembly behavior. The constructal model was then used to predict and tune the resulting particle alignment with and without the presence of an external driving force. Ultimately, this model provides a generalized framework that could be expanded upon to predict the self/directed-assembly of colloidal particles in a range of dynamically tunable and reconfigurable systems.