Compatibility waves drive crystal growth on patterned substrates

Abstract

We explore the crystallization in a colloidal monolayer on a structured template starting from a few-particle nucleus. The competition between the substrate structure and that of the growing crystal induces a new crystal growth scenario. Unlike with the crystal growth in the bulk where a welldefined and connected crystal-fluid interface grows into the fluid, we identify a mechanism where a 'compatibility wave' of the prescribed nucleus with the underlying substrate structure dictates the growth direction and efficiency. The growth process is strongly anisotropic and proceeds via transient island formation in front of an initial solid-fluid interface. We demonstrate the validity of this compatibility wave concept for a large class of substrate structures including a square lattice and a quasicrystalline pattern. Dynamical density functional theory that provides a microscopic approach to the crystallization process is employed for colloidal hard spheres. Our predictions can be verified in experiments on confined colloids and also bear consequences for molecular crystal growth on structured substrates.

Solid phase properties and crystallization in simple model systems

“…2.2, the connection to an actual system remains unclear). Very recently, an FMT-type density functional has been employed to study the nucleation of hard disks on a patterned substrate [78]. The nucleation on the surface follows a so-called compatibility wave scenario with preferred growth directions that give the least mismatch between the 2d substrate and the 2d crystal lattices.…”

Dynamical density functional theory for circle swimmers

“…Microscopic here means that the description is based and operates on the length scales of the individual agents. Thus, for instance, when classical density functional theory (DFT) or its variants are used to describe the properties of crystalline structures [67][68][69][70][71][72][73][74][75][76][77][78][79][80], individual crystal peaks can be resolved in the statistical density field.…”

“…It can be extended to overdamped relaxational dynamics in terms of DDFT [85][86][87][88] by assuming at each instant an effective equilibrium situation to evaluate the involved potential interactions. For example, solidification processes are addressed in this way [71,72,74,78]. Since microswimmers by construction operate at low Reynolds numbers [89], their dynamics is overdamped.…”

Dynamical density functional theory for the diffusion of injected Brownian particles

“…As one can easily verify from Eq. (20) or from the ideal gas result, the function ε C (r) diverges logarithmically to infinity when the limit r → 0 is taken. In fact, the ideal gas result diverges to infinity at every point r, in the limit g → 0 of vanishing external drive.…”

“…One could in principle use more accurate approximations for the excess free energy functional, like fundamental measure theory for non-overlapping particles [15][16][17][18][19][20]. Nevertheless, in order to allow for straightforward analytic progress, we choose the simpler Ramakrishnan-Yussouff scheme in the present work.…”