Mesoscopic theory for systems with competing interactions near a confining wall

Statics and dynamics of a finite two-dimensional colloidal system with competing attractive critical Casimir and repulsive magnetic dipole interactions

We continue our theoretical study of a recently proposed two-dimensional colloidal system with attractive critical Casimir and repulsive magnetic dipole forces that can be tuned easily and independently from each other via the temperature and the strength of an external magnetic field, respectively [K. Marolt, M. Zimmermann, and R. Roth, Phys. Rev. E 100, 052602 (2019)2470-004510.1103/PhysRevE.100.052602]. Using this freedom, it is possible to construct a competing interaction potential that causes microphase separation featuring spatially inhomogeneous cluster, stripe, and bubble phases in the bulk, i.e., in an infinite system without an external potential. In the present work, we demonstrate by means of density functional theory that microphase separation can also occur in finite geometries. In a square cell with a side length of 20 or 30 colloid diameters, we observe the emergence of highly structured cluster and ring phases at intermediate bulk densities in addition to almost uniform fluid phases for lower and higher bulk densities. We then employ dynamic density functional theory to determine how the system reacts when the temperature and the magnetic field are altered over time, and we show how to induce a transition from the liquid to the cluster/ring phase and also from the cluster directly to the ring phase. We find that often a slowly varying and nontrivial path in parameter space is required to reach a stable state, whereas abrupt changes are prone to lead to metastable configurations.