Directed self-assembly of spherical caps via confinement

Abstract

In this work we use Monte Carlo simulations to study the phase behavior of spherical caps confined between two parallel hard walls separated by a distance H. The particle model consists of a hard sphere of diameter σ cut off by a plane at a height χ, and it is loosely based on mushroom cap-shaped particles whose phase behavior was recently studied experimentally [E. K. Riley and C. M. Liddell, Langmuir, 26, 2010, 11648]. The geometry of the particles is characterized by the reduced height χ* = χ/σ, such that the model extrapolates between hard spheres for χ* → 1 and infinitely thin hard spherical caps for χ* → 0. Three different particle shapes are investigated: (a) three-quarter height spherical caps (χ* = ¾), (b) one-half height spherical caps or hemispheres (χ* = ½), and (c) one-quarter height spherical caps (χ* = ¼). These three models are used to rationalize the effect of particle shape on the entropy-driven self-assembly of the particles under strong confinements; i.e., for 1 < H/χ < 2.5. As H is varied, a sequence of crystal structures is observed, including some having similar symmetry as that of the structures observed in confined hard spheres on account of the remaining spherical surface in the particles, but with additional features on account of the particle shapes having intrinsic anisotropy and orientational degrees of freedom. The χ* = ¾ system is found to exhibit a phase diagram that is most similar to the one obtained experimentally for the confined mushroom cap-shaped colloidal particles under confinement; however, simulations also reveal six other phases that occur on approaching the close-packing conditions for a given H. A qualitative global phase diagram is constructed that helps reveal the interrelations among different phases for all the particle shapes and confinements studied.