Cooperation, competition and emergence of hierarchy: reconfigurable assembly of active colloids under combined electric and magnetic fields

TL;DR

The paper addresses how to achieve reconfigurable, multi-scale assembly of isotropic colloids using combined AC electric and DC magnetic fields. It demonstrates three dynamical modes—cooperation, competition, and hierarchical reorganization—by tuning field strength, frequency, direction, and sequence, with imaging and FFT analysis linking field parameters to emergent structures. A key advance is showing that crossed fields yield double hierarchy with domains composed of chains, whose architecture can be reversibly reconfigured, and that binary mixtures add further structural richness. The findings offer a versatile route toward programmable bottom-up materials, switchable photonic crystals, and modular microswimmers for applications in drug delivery and environmental remediation.

Abstract

Field induced assembly of reconfigurable structures with complex hierarchical configurations has recently become an area of intense research with the promise for exciting applications in programmable self-assembly and nano/microstructure fabrication. While a wide variety of structures, from crystals to glasses, to chains and oligomers have been produced by activating colloidal particles with electric and magnetic fields, a combined approach utilizing the capabilities of multiple field types offers a richer parameter space, enabling precise structural control and a higher degree of reconfigurability. Here we demonstrate the assembly of complex hierarchical colloidal superstructures using an electric field (AC) and magnetic field (DC) combination. In our chosen frequency regime, dipolar (magnetic and electric) and electrohydrodynamic interactions are comparable, leading to a rich phase space with a wide number of configurations which are tunable by relatively small changes of the field parameters. This is in contrast to the existing small number of studies on multi-field induced assembly that work in size and frequency regimes where the dominant mechanism is dipolar interaction induced assembly. We show that depending upon the direction and frequency of the applied fields, there can be three possibilities in structure formation: a) a cooperation among the fields b) a competition among the fields and c) hierarchical reorganization in which micrometer-sized particles form chains that are part of larger clusters or 'domains' spanning tens of micrometers. This versatile, easy to set up and fully reconfigurable approach of multi-field induced structure formation opens up new opportunities for bottom-up fabrication of smart materials, switchable photonic crystals, and modular microswimmers for targeted drug delivery and environmental remediation.

Figures (9)

• Figure 1: Structures produced from purely electric (E) and magnetic field (B) and one specific E field-B field combination: (a) The experimental setup showing the sample chamber, Cu contacts for applying the E field and Helmholtz coil configurations for applying in-plane and out-of-plane magnetic fields. (b) Under an out-of-plane electric field (AC) of frequency 10 kHz and peak-to-peak voltage (Vpp) 12 V, formation of quasi-planar, non close-packed clusters is observed. (b) A DC in-plane magnetic field of 0.62 mT produces linear chains due to the magnetic dipolar interactions between superparamagnetic polystyrene particles in the direction of the applied field. (c) A combination of an out-of-plane AC electric field and an in-plane magnetic field produces a double-hierarchical structure with large quasi-planar non close-packed clustered regions ('domains'), individually composed of linear chains. The schematic diagrams on the right of each picture bring out the structural variation across the three cases.
• Figure 2: Cooperation and competition in structure formation under parallel electric and magnetic fields. (a)-(c) In the electric field frequency regime of 100 kHz-1 MHz, E and B fields act in cooperation. (a) Randomly dispersed particles in the bulk in the absence of any applied field. (b) Partial stacking of particles induced by an out-of-plane magnetic field of 0.62 mT. (c) The subsequent application of a 1 MHz AC electric field at peak-to-peak voltage (Vpp) of 20 V enhances the stacking process, incorporating all loose particles into longer columnar stacks. The red and the blue colors represent the particles in focus and out of focus on the viewing plane, respectively. The schematic diagrams representing the three cases are shown below the figures. (d) A plot showing the number of tracked objects (both red and blue, over an area of 6912 $\mu$m$^2$) plotted as a function of the number of fields acting on the particles. The total number of objects observed in each case is normalized with the maximum number of objects as seen in Fig. 2a (no field condition). The decreasing trend indicates a reinforced stacking of the particles under combined E and B fields. (e) Number of particles in each stack ($N_s$) plotted as a function of the number of fields in cooperation, showing a gradual increase from (a) to (c). In the lower frequency regime (5-20 kHz), the E and B fields compete with each other in structure formation as shown in (f)-(h). (f) Randomly dispersed particles in the absence of any applied field. (g) Partial stacking of particles induced by an out-of-plane magnetic field of 0.62 mT. (h) The subsequent application of a 5 kHz AC electric field at Vpp = 20 V breaks the stacks to form smaller stacks (shown in blue) and singlet particles (shown in red), both of which are part of a large local cluster. The schematics are given below the figures. (i) indicates the number of red and blue objects (normalized with respect to the maximum number of red and blue objects as seen in the zero field condition that is Fig. 2f), both of which show a sharp decrease followed by an increase from (f) to (g). (j) represents the number of particles per stack ($N_s$) which shows an increase followed by a decrease under an increasing number of fields, indicating that stacking produced by the B field is opposed by the E field, leading to the incomplete breakdown of larger stacks.
• Figure 3: Structural configurations formed under crossed E and B fields as a function of the magnetic field strength and peak-to-peak voltage of the electric field. (a) Optical micrographs at a constant E field frequency of 10 kHz show predominance of chain formation at higher magnetic fields and formation of non close-packed colloidal clusters at higher electric field values. In the intermediate regime, the electrical and magnetic forces reach a subtle balance, leading to a hierarchical arrangement where short chain segments constitute clustered 'domains' separated by large gaps. (b) Fast Fourier Transform (FFT) of the images bring out the appearance and disappearance of oriented configurations and structural order for particular values of E and B.
• Figure 4: Structural configurations formed under crossed E and B fields as a function of the frequency and peak-to-peak voltage (Vpp) of the electric field. (a) Optical micrographs at a constant magnetic field strength of 0.62 mT show predominance of chain formation at higher frequencies and formation of non close-packed colloidal clusters at high Vpp values. In the intermediate regime, the attractive and repulsive forces originating from dipolar and electrohydrodynamic forces reach a subtle balance. This leads to a hierarchical arrangement where short, separated chain segments constitute clustered 'domains' separated by large gaps. (b) Fast Fourier Transform (FFT) of the images indicate the appearance and disappearance of oriented configurations and structural order for particular values of E and B.
• Figure 5: Anisotropy in structural configurations quantified using Fast Fourier Transforms of the images. Angular intensity profiles were obtained from FFT images, where the intensity is summed along all points on a radius at a given angle for (a) the constant-frequency case (corresponding to Fig. 3) and (b) for the constant magnetic-field case (corresponding to Fig. 4). The anisotropy in both cases are clearly observed with case (b) showing overall a larger anisotropy than case (a). Tuning of the field parameters leads to a reduction of the anisotropy.