Ordering of Rods near Surfaces: Concentration Effects

We study the orientation of rods in the neighborhood of a surface. A semi-infinite region in two different situations is considered: (i) the rods are located close to a flat wall and (ii) the rods occupy the space that surrounds a sphere. In a recent paper we investigated a similar problem: the interior of a sphere, with a fixed concentration of rods. Here, we allow for varying concentration, the rods are driven from a reservoir to the neighborhood of the surface by means of a tunable chemical potential. In the planar case, the particle dimensions are irrelevant. In the curved case, we consider cylinders with dimensions comparable to the radius of curvature of the sphere; as they come close to the surface, they have to accommodate to fill the available space, leading to a rich orientational profile. These systems are studied by a mapping onto a three-state Potts model with annealed disorder on a semi-infinite lattice; two order parameters describe the system: the occupancy and the orientation. The Hamiltonian is solved using a mean-field approach producing recurrence relations that are iterated numerically and we obtain various interesting results: the system undergoes a first order transition just as in the bulk case; the profiles do not have a smooth decay but may present a step and we search for the factors that determine their shape. The prediction of such steps may be relevant in the field of self-assembly of colloids and nanotechnology.

Abstract licence: CC BY

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