Buckling instabilities of a confined colloid crystal layer

Abstract

A model predicting the structure of repulsive, spherically symmetric, monodisperse particles confined between two walls is presented. When plate separations are small, only one layer of particles can be confined; however, when the plate separation is increased, multiple layers will eventually form.We study the buckling transition of a single flat layer as the double layer state develops. Experimental realizations of this model are suspensions of stabilized colloidal particles squeezed between glass plates. By expanding the thermodynamic potential about a flat state of N confined colloidal particles, we derive a free energy as a functional of in-plane and out-of-plane displacements. As the gap separation increases, certain out-of-plane modes soften. The wavevectors of these first buckling instabilities correspond to three different ordered structures. Landau theory predicts that the symmetry of these phases allows for second order phase transitions. This possibility exists even in the presence of gravity or plate asymmetry. These transitions lead to critical behavior and phases with the symmetry of the three-state and four-state Potts models, the X-Y model with 6-fold anisotropy, and the Heisenberg model with cubic interactions. Experimental detection of these structures is discussed.

Finite-Size Effects on the Closest Packing of Hard Spheres

“…Additionally, the model proposed a smooth transition between 2ᮀ and 2᭝ via a phase with rhombic symmetry. Evidence for both features was found experimentally [13][14][15] as well as in Monte Carlo simulations [16] and in a stability analysis [17] of the 2D hexagonal lattice. However, although the buckling principle turns out to be an important mechanism to maximize F during the transition from n 1 to n 2, only little is known about its extension to the transitions with higher n.…”

Hydrodynamic fluctuation forces

“…In Ref. [20] buckling instabilities in a confined colloidal crystals were analyzed. An interesting behavior of colloids in external fields were reported in Ref.…”

Zigzag transitions and nonequilibrium pattern formation in colloidal chains

“…Accordingly, the threshold value b c is obtained from Eq. (12) at h * = 0, which gives b c = 8 93 ζ (5) ≈ 0.288 (13) as the maximum field at which h * is a stable solution. Here, we have taken into account that ∞ m=1 p m m −5 = ∞ n=1 (2n − 1) −5 = (31/32)ζ (5).…”

“…11 On the one hand, a simple system can be built by confining colloidal particles between two walls or placing them on a spatially confined surface and inducing repulsive interactions between the particles. [12][13][14] On the other hand, optical trapping techniques can be used to localize each colloid in an individual optical trap, leading to a one-dimensional colloidal chain of hydrodynamically coupled particles in the form of a line 5,6 or a ring. 7 In this study, we focus on the interplay of both these ingredients to create an initially linear chain of colloids.…”