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.

Microphase separation in a two-dimensional colloidal system with competing attractive critical Casimir and repulsive magnetic dipole interactions.

We propose and study theoretically a colloidal system in two dimensions with attractive critical Casimir and repulsive magnetic dipole forces, wherein the strength of attraction and repulsion can be easily and independently tuned by adjusting the temperature and an external magnetic field, respectively. We expect this setup to be experimentally accessible and are confident that it can serve to deepen our understanding of the mechanisms behind microphase separation due to competing interactions. We develop a density functional theory for our model and present first results of our calculations in the form of a phase diagram for fixed temperature, but varying magnetic fields and bulk densities. For certain values of these parameters, we are able to confirm the existence of thermodynamically stable inhomogeneous density profiles in the bulk, such as parallel lamellar stripes, as well as clusters and voids on a hexagonal lattice.

Modeling diffusion in colloidal suspensions by dynamical density functional theory using fundamental measure theory of hard spheres.

We study the dynamics of colloidal suspensions of hard spheres that are subject to Brownian motion in the overdamped limit. We obtain the time evolution of the self- and distinct parts of the van Hove function by means of dynamical density functional theory. The free-energy model for the hard-sphere fluid that we use is the very accurate White Bear II version of Rosenfeld's fundamental measure theory. However, in order to remove interactions within the self-part of the van Hove function, a nontrivial modification has to be applied to the free-energy functional. We compare our theoretical results with data that we obtain from dynamical Monte Carlo simulations, and we find that the latter are well described by our approach even for colloid packing fractions as large as 40%.