Buckling instabilities of a confined colloid crystal layer

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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 wave vectors 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 sixfold anistropy, and the Heisenberg model with cubic interactions. The experimental detection of these structures is discussed.
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