Field-Pulse-Induced Annealing of 2D Colloidal Polycrystals

Abstract

Two-dimensional colloidal crystals are of considerable fundamental and practical importance. However, their quality is often low due to the widespread presence of domain walls and defects. In this work, we explored the annealing process undergone by monolayers of superparamagnetic colloids adsorbed onto fluid interfaces in the presence of magnetic field pulses. These systems present the extraordinary peculiarity that both the extent and the character of interparticle interactions can be adjusted at will by simply varying the strength and orientation of the applied field so that the application of field pulses results in a sudden input of energy. Specifically, we have studied the effect of polycrystal size, pulse duration, slope and frequency on the efficiency of the annealing process and found that (i) this strategy is only effective when the polycrystal consists of less than approximately 10 domains; (ii) that the pulse duration should be of the order of magnitude of the time required for the outer particles to travel one diameter during the heating step; (iii) that the quality of larger polycrystals can be slightly improved by applying tilted pulses. The experimental results were corroborated by Brownian dynamics simulations.

Keywords: 2D confined systems; colloidal annealing; dynamic self-assembly; fluid interface; superparamagnetic particles.

Figure 1

(a) Magnetic particles are attracted to a water/decane interface with the help of a magnet to facilitate the adsorption process. After the magnet is moved away, the non-adsorbed particles fall into the aqueous sub-phase, while the adsorbed particles remain in the plane of the fluid interfaces due to the relatively high value of the trapping energy. To reduce the drift motion generated by convention effects, the laden water/decane interface is confined by a hollow, non-magnetic glass cylinder. Finally, the adsorbed magnetic particles are magnetized by the field generated by a pair of coils connected in series, aligned along the X and Y axes and a fifth coil aligned along Z, the optical axis of the microscope. (b) The image sequence shows how the application of the high-frequency rotating field, $f_x=f_y=20 \mathrm{Hz}$, at the interface plane promotes a crystallization process, which, at relatively high particle densities, occurs in the range of tens of seconds. From t = 120 s, the rotating field is replaced by the combination of two fields with different frequencies, which still promotes isotropic attraction between the particles but prevents rotation of both the constituent particles and the resulting polycrystals (please, compare the images taken at t = 120 s and 130 s). Scale bar: 20 microns. (c) Diagram of configurations showing the regions where crystal formation is observed after application of the in-plane rotating field. The white area represents the conditions where the attraction between colloids causes the particles to form a polycrystal composed of different domains with hexagonal order. In the blue zone, the colloidal particles form linear aggregates or are scattered by the thermal noise itself, and the green zone represents the onset of the premelting zone, a transition zone between the two previous configurations. Here, the continuous lines represent constant field values.

Figure 2

(a) Series of pulses are applied outside the planar interface to induce the restructuring of the formed 2D polycrystals and to explore the possibility of improving their spatial and orientational order. The pulses, applied perpendicular to the fluid interface, are determined by the square wave amplitude $A_z$, the field offset $H_z^0$, the pulse duration${\tau }_p$ and the period of the square wave T. (b) In the first method, the degree of alteration of the hexagonal order during the annealing process is evaluated by following the change in the slope of the linear fit at the first 7 maxima of $g_6\left(r,t\right)$ after each pulse. (c) In an alternative strategy, the degree of alteration of the hexagonal order during the annealing process is evaluated by following the change in the area of the predominant crystalline domain after each pulse, defining this area as the surface covered by the largest region (area colored in orange) composed of connected particles having ${\phi }_{6,k}>0.8$ (particles colored in yellow). (d) The upper plot shows the time evolution of ${\phi }_6\left(t\right)$, while the lower graph shows the time evolution of both, ${\xi }_i$ and the fraction of area covered by the predominant domain. Here, ${\xi }_i$ is the relative change in the slope of the line fitted to the first maxima of $g_6\left(r,t\right)$ after each pulse i. The measured data, corresponding to the polycrystal presented in c, show that the system reaches a stable conformation after 10 pulses (red dashed line).

Figure 3

(a) The sequence of microscope images shows how the application of a consecutive series of field pulses oriented perpendicular to the fluid interface, where particles are adsorbed, allows the melting of grain boundaries and defects, thus improving crystallinity. (b) In small polycrystals composed of between 100 and 500 particles, the pulse application can alter the values taken by the parameters ξ, α and ε, which evaluate the degree of enhancement of the hexagonal order and are defined throughout the text. These parameters take positive values when the pulse duration is close to the time it takes for the outer particles to travel a radius of distance under the action of the pulses, τ_c. ${\mu }_0{H}_{total}^{ext}={\mu }_0\sqrt{H_0^2+{(H_z^{max})}^2}=$ 2.0 and 8.0 mT for the black circles and the red squares, respectively.

Figure 4

(a) In big polycrystals composed of more than 500 particles, the application of field pulses oriented perpendicularly to the fluid interface barely alter the values of ξ. (b) A sequence of microscope images showing how the application of tilted pulses, resulting from the simultaneous application of pulses along the Z and X axes, favors the growth of domains oriented along the X direction. (c) As $\beta$decreases, there is a slight enhancement in the hexagonal order, due to the formation of the privileged direction in the polycrystal. ${\mu }_0{H}_{total}^{ext}={\mu }_0\sqrt{H_0^2+{(H_z^{max})}^2}=$ 2.0, 5.5 and 8.0 mT for the black circles, green triangles and red squares, respectively.

Figure 5

(a) Time evolution of ${\phi }_6\left(t\right)$ along the Brownian dynamics simulation, during the application of three different pulses, alongside snapshots representing the system at the beginning of the simulations, at $4 \mathrm{s}$ (black), $9 \mathrm{s}$ (blue) and $14 \mathrm{s}$ (red). (b) Hexagonal order correlation function for the following three different times: $4 \mathrm{s}$ (black), $9 \mathrm{s}$ (blue) and $14 \mathrm{s}$ (red) that correspond with the snapshots of the system shown in panel (a). The simulation has been run for ${\tau }_p=0.15 \mathrm{s}$, ${\mu }_0{H}_{total}^{ext}=5.5 \mathrm{mT}$, ${\mu }_0{H}_0=3 \mathrm{mT}$, $T=2\pi /{\omega }_{pulse}=5 \mathrm{s}$, $f_x=20 \mathrm{Hz}$ and $f_y=60 \mathrm{Hz}$.