Accelerated annealing of colloidal crystal monolayers by means of cyclically applied electric fields

External fields are commonly applied to accelerate colloidal crystallization; however, accelerated self-assembly kinetics can negatively impact the quality of crystal structures. We show that cyclically applied electric fields can produce high quality colloidal crystals by annealing local disorder. We find that the optimal off-duration for maximum annealing is approximately one-half of the characteristic melting half lifetime of the crystalline phase. Local six-fold bond orientational order grows more rapidly than global scattering peaks, indicating that local restructuring leads global annealing. Molecular dynamics simulations of cyclically activated systems show that the ratio of optimal off-duration for maximum annealing and crystal melting time is insensitive to particle interaction details. This research provides a quantitative relationship describing how the cyclic application of fields produces high quality colloidal crystals by cycling at the fundamental time scale for local defect rearrangements; such understanding of dynamics and kinetics can be applied for reconfigurable colloidal assembly.


List of Supplemental Figures
. MD model parameter variations 3

Area fraction of assembled structures
The area fraction of spheres (d2D) value represents how many colloidal particles assembled in the characterized region. A completer comparison of d2D changes as time progresses with !"" = 0, 0.5 #$ , and 10 #$ is reported. Figure S1. The change of area fraction of the colloids as time progresses. (a) Confocal laser scanning micrographs with calculated % value and area fraction of spheres (d2D) value for !"" = 0, 0.5 #$ , and 10 #$ at the first, third, and last cycle, respectively. (b) Time evolution of d2D for !"" = 0, 0.5 #$ , and 10 #$ . Scale bars in images are 10 μm.

First Cycle
Last Cycle 3 rd Cycle

Diffusion of particles during the field-off time
Under the best annealing performance condition !"" = 0.5 #$ , there are about 6% of the particles diffused at a distance greater than 1μm during each field-off period (which is only half of the particle radius).

Voronoi defect evolution
We track sample-wide changes to the number and area belonging to Voronoi defects for experiment and simulation. Defect area ( &'"'() ) is defined as the summed area of all non-sixsided Voronoi cells. Additionally, the average area of all six-sided Voronoi cells is found ( *+' ). The excess area belonging to defective particles is then approximated as: then approximates the number of additional particles which could be added to the system if defective particles occupied the same area as non-defective particles.
Expressed as a fraction of total snapshot particles, the quantity '- Figure S3 (row a) for simulation (column i) and experiment (column ii). Simulations begin with a smaller fraction of excess area belonging to defective particles than experiments, and that area does not change much over the course of annealing. In contrast, experimental samples begin with a larger defect area and experience a reduction in defect area for annealing protocols which also improve the other measures (SALS, % ) measured in this study. Together these results indicate that the proposed annealing strategy is effective at accelerating the approach of the system to a baseline defect concentration. The value of the baseline concentration is controlled by the thermodynamics of the crystalline state, and therefore we do not expect it to be modified by the annealing procedure. Figure S3

Local ordering in MD simulation
Time evolution of % data for a simulated system showing twenty cycles of cyclic field annealing with nine different durations of !"" . For long !"" , little or no improvement in % is seen over twenty cycles. As the !"" is decreased, the maximum improvement of % is found for !"" = 0.5 #$ . As the !"" is further decreased, the linear growth rate decreases and the % improvement from zero to twenty cycles also decreases. Model parameter choice has some effect on peak shape, but for all models considered optimal annealing was found at !"" / #$ = 0.5.

Local and global ordering in MD simulation
Unlike in the experimental measurements, only negligible differences are present in the growth rate of SALS and % curves in MD simulation. We attribute this difference to the comparatively smaller size of the simulated system, which is 250 μm x 500 μm as compared to 250 μm x 5000 μm for the experimental system. With fewer particles, the local and global re-arrangements are strongly coupled and have minimal differences in their rate of change.

AC electric field device
The AC electric field device was prepared by first depositing 2.5 nm of titanium followed by 25 nm of gold onto a glass substrate. The gap between the two Ti/Au electrodes is 250 μm wide. The colloidal suspension was injected into the spacer, which is 1 mm in height. The inner diameter of the spacer is 5 mm. Figure S7. Illustration of the coplanar AC electric field device.

Colloidal Suspension
Ti/Au Electrode units. The screening length for particle interactions is two particle diameters in all cases.