Colloidal Lock-and-Key Dimerization Reactions of Hard Annular Sector Particles Controlled by Osmotic Pressure

Colloidal annular sectors are a broad class of shapes that offer the interesting possibility of dimerization when osmotically compressed to high densities while undergoing Brownian motion in two dimensions (2D). Here, we lithographically create and form a stable aqueous dispersion of many microscale prismatic 270° annular sectors, and we explore their near-equilibrium behavior in a tilted 2D gravitational column. Near the top of the column where the 2D gravitational osmotic pressure Π(2D) is low, we observe a gas-like phase composed almost entirely of monomers. However, below the surface and deeper into the column where Π(2D) is higher, we observe a reaction zone where monomers and dimers coexist, followed by an arrested region containing a very high percentage of interpenetrating, lock-and-key dimers that are a racemic mixture of positive and negative chiralities. We determine particle area fractions of monomers and dimers as a function of depth and use these to obtain the system's 2D osmotic equation of state. In the reaction zone, where dimers transiently form and break up, we also use these to calculate the equilibrium constant K associated with the monomer-dimer reaction, which increases exponentially with Π(2D). This dependence can be attributed the reduction in number of accessible microstates for dimers as they become more tightly compressed.