Directed Self-Assembly of Spheres into a Two-Dimensional Colloidal Crystal by Viscoelastic Stresses

Abstract

Ordering induced by shear flow can be used to direct the assembly of particles in suspensions. Flow-induced ordering is determined by the balance between a range of forces, such as direct interparticle, Brownian, and hydrodynamic forces. The latter are modified when dealing with viscoelastic rather than Newtonian matrices. In particular, 1D stringlike structures of spherical particles have been observed to form along the flow direction in shear thinning viscoelastic fluids, a phenomenon not observed in Newtonian fluids at similar particle volume fractions. Here we report on the formation of freestanding crystalline patches in planes parallel to the shearing surfaces. The novel microstructure is formed when particles are suspended in viscoelastic, wormlike micellar solutions and only when the applied shear rate exceeds a critical value. In spite of the very low volume fraction (less than 0.01), particles arrange themselves in 2D crystalline patches along the flow direction. This is a bulk phenomenon because 2D crystals form throughout the whole gap between plates, with the gap thickness being much larger than the particle size. Shear flow may hence be an easy method to drive particles into crystalline order in suspensions with viscoelastic properties. The crystalline structure reported here could be used to design new materials with special mechanical, optical, thermal, or electric properties.

Alignment of particles in sheared viscoelastic fluids

“…2(a) of Ref. 6 suggests similar behavior under experimental conditions, as the photographed strings of colloids resemble trains running along the same track. The order of the colloids along the flow line typically stays the same, though we have seen occasions where a colloid briefly left a string and was overtaken by (part of) the string before returning to the flow line.…”

“…6 In all simulations of the micellar fluid, with and without colloids, the velocity profile V (y) of the flowing fluid was virtually linear, indicating that colloidal alignment does not require shear banding. This observation is also in agreement with experiments, 6 which indicate that shear-banding can promote alignment but is not a prerequisite.…”

“…III were used to suspend spherical colloids, with colloidal radii equal to the radius of gyration of the polymer and micellar chains, R col = R g = 40 nm. These colloids are much smaller than the colloids used in the recent experiments with dispersions in the same fluids by Pasquino et al, 6 since the experimental radius would have led to prohibitively large simulation boxes. Because of the smaller size, Brownian displacements play a more important role in the simulations than in the experiments.…”

“…6 In this and all subsequent simulations, the colloids were immersed in a rectangular simulation box measuring 24 × 16 × 12R 3 g . To facilitate the formation of colloidal strings, in the expectation that they would occur, the 30 colloids of the initial box were placed in a plane spanned by the shear velocity and the velocity-gradient, i.e., the xy-plane, taking care to prevent any significant overlap while randomly placing the colloids.…”

“…4,5 Instead, these authors suggested that shear-thinning is a necessary condition for shear-induced alignment of spherical particles. The recent work of Pasquino et al 6 on dilute suspensions of hard spheres in a worm-like micellar solution showed the formation of string-like structures at low shear rates and 2D crystals at high shear rates. For a review on flow-induced ordering in complex fluids, we refer the reader to Malkin et al 7 The Vermant group 8 has recently shown that alignment typically occurs at the walls of the rheometer, following colloidal migration from the bulk towards these walls.…”