Supplementary Information for "Diffusion of point defects in two-dimensional colloidal crystals"
Nature, V413, 147

 

The hopping of the defects proceeds through thermal activation over some energy barrier separating two neighbor configurations. The diffusion rate, D/a2, with D the diffusion constant, contains contributions from all the possible processes, of the form n oexp(-Eb/kBT), where n o is an attempt frequency and Eb is the energy barrier of a specific process1,2. The time-scale of fluctuations n o is a characteristic time-scale for short wavelength lattice distortions. In colloidal crystals, the short wavelength phonons are highly over-damped3, due to the viscosity of the water and hydrodynamic friction from the confining plates. Spectral analysis of the fluctuations of the displacements of the particles gives estimates for relaxation rates at the edge of the Brillouin zone of about 50 Hz (A.P., unpublished data). These figures combine to give estimates for the energy barriers Eb» 2-3 kBT. The elastic energy ka2 of the colloidal crystal is of order 100 kBT, ref. 4, therefore Eb~ O(10-2 ka2) or a few percent of the formation energy of the defects.

  1. Kramers, H.A. Brownian motion in a field of force and the diffusion model of chemical reactions, Physica 7, 284 (1940).
  2. Chandrasekhar, S. Stochastic problems in Physics and Astronomy, Rev. Mod. Phys. 15, 1 (1943).
  3. Hurd, A.J., Clark, N.A, Mockler, R.C. & O'Sullivan, W.J Lattice dynamics of colloidal crystals, Phys. Rev. A 26, 2869-2881 (1982).
  4. Weiss, J.A., Larsen, A.E. & Grier, D.G. Interactions, dynamics, and elasticity in charge-stabilized colloidal crystals, J. Chem. Phys. 109, 8659-8666 (1998).

Video Clips

The two files "Pertsinidis_di_creation" (1,270 K) and "Pertsinidis_mono_creation" (1,921 K) are the initial video data and show the creation of point defects bymanipulation with optical tweezers. Time is slowed down by a factor of 2.

The two files "Pertsinidis_Mono_Triangle" (7,428 K), and "Pertsinidis_Di_Triangle" (5,240 K) show the triangulation of the position of the particles in every frame.The mis-coordinated particles in the cores of the defects are shown withcolored circles, using the following color scheme:
Green 5-fold
Violet 7-fold
Magenta 8-fold
Red 9-fold.

The inset in every video clip shows a two-dimensional gray-scale plot ofthe coordination number. The uniform background is comprised of 6-foldcoordinated particles and constitutes the perfect lattice. Darker pointsare the 5-fold coordinated particles and brighter the 7,8 or 9-foldcoordinated particles. Time is slowed down by a factor of 6.

The files "Pertsinidis_Mono_Trajectory" (1,199 K) and "Pertsinidis_Di_Trajectory" 1,237 K) show the trajectories of the defects. The current position of the defectis specified by the open square symbol and the previous points visited areshown by small dots. The insets are the same as the insets in thetriangulation files. Again, time is slowed down by a factor of 6.Neighboring "clumps" of dots are separated by roughly half lattice spacingand correspond to the defect being in a configuration near a lattice pointand to a split configuration between two lattice points.