Alignment of cylindrical colloids near chemically patterned substrates induced by critical Casimir torques.

Recent experiments have demonstrated a fluctuation-induced lateral trapping of spherical colloidal particles immersed in a binary liquid mixture near its critical demixing point and exposed to chemically patterned substrates. Inspired by these experiments, we study this kind of effective interaction, known as the critical Casimir effect, for elongated colloids of cylindrical shape. This adds orientational degrees of freedom. When the colloidal particles are close to a chemically structured substrate, a critical Casimir torque acting on the colloids emerges. We calculate this torque on the basis of the Derjaguin approximation. The range of validity of the latter is assessed via mean-field theory. This assessment shows that the Derjaguin approximation is reliable in experimentally relevant regimes, so that we extend it to Janus particles endowed with opposing adsorption preferences. Our analysis indicates that critical Casimir interactions are capable of achieving well-defined, reversible alignments both of chemically homogeneous and of Janus cylinders.

Effective interaction between a colloid and a soft interface near criticality.

Within mean-field theory we determine the universal scaling function for the effective force acting on a single colloid located near the interface between two coexisting liquid phases of a binary liquid mixture close to its critical consolute point. This is the first study of critical Casimir forces emerging from the confinement of a fluctuating medium by at least one shape responsive, soft interface, instead of by rigid walls only as studied previously. For this specific system, our semi-analytical calculation illustrates that knowledge of the colloid-induced, deformed shape of the interface allows one to accurately describe the effective interaction potential between the colloid and the interface. Moreover, our analysis demonstrates that the critical Casimir force involving a deformable interface is accurately described by a universal scaling function, the shape of which differs from that one for rigid walls.

Critical Casimir effect for colloids close to chemically patterned substrates.

Colloids immersed in a critical or near-critical binary liquid mixture and close to a chemically patterned substrate are subject to normal and lateral critical Casimir forces of dominating strength. For a single colloid, we calculate these attractive or repulsive forces and the corresponding critical Casimir potentials within mean-field theory. Within this approach we also discuss the quality of the Derjaguin approximation and apply it to Monte Carlo simulation data available for the system under study. We find that the range of validity of the Derjaguin approximation is rather large and that it fails only for surface structures which are very small compared to the geometric mean of the size of the colloid and its distance from the substrate. For certain chemical structures of the substrate, the critical Casimir force acting on the colloid can change sign as a function of the distance between the particle and the substrate; this provides a mechanism for stable levitation at a certain distance which can be strongly tuned by temperature, i.e., with a sensitivity of more than 200 nm/K.

Critical adsorption and critical Casimir forces for geometrically structured confinements.

We study the behavior of fluids, confined by geometrically structured substrates, upon approaching a critical point at T=T(c) in their bulk phase diagram. As generic substrate structures periodic arrays of wedges and ridges are considered. Based on general renormalization group arguments we calculate, within mean field approximation, the universal scaling functions for order parameter profiles of a fluid close to a single structured substrate and discuss the decay of its spatial variation into the bulk. We compare the excess adsorption at corrugated substrates to the one at planar walls. The confinement of a critical fluid by two walls generates effective critical Casimir forces between them. We calculate corresponding universal scaling functions for the normal critical Casimir force between a flat and a geometrically structured substrate as well as the lateral critical Casimir force between two identically patterned substrates.

Critical Casimir forces between planar and crenellated surfaces.

We study critical Casimir forces between planar walls and geometrically structured substrates within mean-field theory. As substrate structures, crenellated surfaces consisting of periodic arrays of rectangular crenels and merlons are considered. Within the widely used proximity force approximation, both the top surfaces of the merlons and the bottom surfaces of the crenels contribute to the critical Casimir force. However, for such systems the full, numerically determined critical Casimir forces deviate significantly from the pairwise addition formalism underlying the proximity force approximation. A first-order correction to the proximity force approximation is presented in terms of a step contribution arising from the critical Casimir interaction between a planar substrate and the right-angled steps of the merlons consisting of their upper and lower edges as well as their sidewalls.