Supplementary Information for. Colloidal Ribbons and Rings from Janus Magnetic Rods

Transcription

1 Supplementary Information for Colloidal Ribbons and Rings from Janus Magnetic Rods Jing Yan, Kundan Chaudhary, Sung Chul Bae, Jennifer A. Lewis, and Steve Granick,,, and Department of Materials Science and Engineering and the Frederick Seitz Materials Research Laboratory, Department of Physics, Department of Chemistry, University of Illinois, Urbana, IL, 61801, USA.

2 Supplementary Figure S1: SEM image of bare silica rods. Representative SEM image of the silica rods before nickel coating. The scale bar is 1 µm.

3 Supplementary Figure S2: SEM images of the magnetic Janus rods. SEM images of the silica rods coated on one hemicylinder with Ni. To improve contrast, no outermost SiO 2 layer is deposited, and the Ni film is slightly thicker (16.5 nm) than the sample used for dipolar assembly. Due to low conductivity of silica particles, significant electrical charging occurs during the image capturing process. The brighter (more conductive side) is nickel. (a) A dense region of Janus rods. (b) A nearly standing-up Janus rod. (c) A rod lying on the substrate with the Janus interface roughly perpendicular to the substrate, illustrating hemicylindrical coating. (d) Typically the hydrophilic SiO 2 side faces the substrate and the Janus interface is barely seen. The scale bars are 0.5 µm.

4 Supplementary Figure S3: Ribbons in a static field. Image of straight ribbons after applying a field of 50 G overnight. Rods align side by side to form extended ribbons, which preferably lie flat on the substrate due to gravity. Some ribbons also stand up such that their zig-zag pattern can be seen. Due to their small size, the energy difference between standing-up and lying-down is about 2 kbt per rod easily overcome by other factors (excluded volume, magnetic field). The image also includes some overlapping multilayers of ribbons. The scale bar is 5 µm.

5 Supplementary Figure S4: Images of the experimental apparatus. Images of the experimental apparatus. (a) Overview. (b) Side view. The detector of the monitoring Gaussmeter is indicated by the red arrow, directly in touch with one of the iron cores. (c) Top view of the stage for the chamber, through the Helmholtz coil in the z direction. The long working distance air objective can be seen. An aluminum strip on the right is used to adjust tilt of the sample.

6 Supplementary Figure S5: Schematics for energy calculation. (a) Projected shape of a rod in two dimensions. (b) Schematic representation of side view of rods in trans (left) and cis (right) configurations. Yellow dots represent the location of the shifted dipole. Here, γ defines the zigzag angle. R trans and R cis are the dipole-dipole separation for trans and cis configurations, respectively. See Supplementary Discussion 1.

7 Supplementary Figure S6: Another example of ring rupture dynamics. Snapshots of rupture dynamics for a ring with two cis bonds at several magnetic fields, B ext. (a) B ext = 0.2 G. (b,c) B ext = 1.7 G. (d,e) B ext = 3.1 G. (f) A 20 Hz, 10 G alternating field is applied in the direction perpendicular to the image to force the ribbon to stand up. From (a) to (d), the dynamics is similar to what is described in Fig. 4 in the main text. When the twist releases, it preferentially occurs at the cis bond with higher energy, hence converting a cis bond to trans bond. Therefore, as shown in (f), in the final state the ribbons have exclusively trans bonds. The scale bar is 2 µm.

8 Supplementary Figure S7: Handcuff assembly by rings and ribbons. Handcuff structure formed by two standing-up rings connected by a short strand of ribbon (inset shows a schematic representation). The preferential location of the short ribbon on one side of the ring means that the ring s dipole is concentrated on the side indicated by the red arrows. Most likely, that is the location where tilting of rod is greatest, hence the projection of its dipole moment onto the field axis is largest. Larger tilting naturally leads to larger strain, making this the place most prone to rupture. This is consistent with our observation that ring breakage initiates from the side without exception. Here the field strength is 1.5 G, vertical in the image. The scale bar is 2 µm.

9 Supplementary Note 1: Estimation on the energy difference between cis and trans configuration To start, we need to know the remnant magnetization of a rod. The remnant magnetization of a magnetic thin film depends on various factors such as substrate materials, geometry, and deposition conditions. As technical difficulties precluded our direct measurement of this quantity for the rods, we assume a value of A/m from a closest match to the current system 55. Next, we calculated the volume of nickel deposited by our methods onto a rod. Though the film contour of unidirectional deposition onto a curved surface is complicated, the total volume of nickel on a rod equals to that of a film deposited on a flat substrate with area equal to that of the projection of the rod in two dimensions (2D), multiplied by the nominal coating thickness (9.8 nm). The 2D projection of the rod can be easily modeled as a rectangle with two semicircular caps (Supplementary Fig. 5a). Thus we arrive at a nickel volume of m 3 for a single rod. This translates into a dipole moment of A m 2 per particle. The center-to-center distances between two rods in the cis and trans configurations are the same; however, as the dipole moment is offset from the geometric center, the distances between the dipole moments differ. The offset can be estimated from the zigzag angle γ (see Supplementary Fig. 5b), which we measured to be 76 ± 4. For simplicity we assume close surface-surface contact, which leads to a dipole-dipole separation of m following R trans = dsin(γ/2) for the trans

10 configuration (d is the cylinder diameter) and m for the cis configuration. The energy difference between the two configurations is therefore: µ m E = 2 ( ) = J k T 2 water Ni 3 3 4π Rtrans Rcis B in which µ water is permeability of the aqueous suspension, m Ni the remnant magnetic moment per particle, and R trans and R cis are the dipole-dipole separation for trans and cis configurations, respectively. The factor of 2 comes from the orientation dependence of dipolar interaction. This analysis should be viewed as just an order-of-magnitude estimate, as it relies on many simplifications. Nevertheless, it gives the scale of magnetic interaction in this system, which is much larger than thermal energy and gravitational energy. Supplementary Note 2: Discussion on ring deformations Alim 51 et al. show that, due to the circular constraint, distortion on a circle formed by a ribbon must simultaneously excite all three deformation modes, bend, splay, and twist. We followed their Euler coordinate system and decomposed the continuous ribbon into discrete rods with their centers lying along the contour, and their long axis lying parallel to the width of the ribbon. With this procedure, images similar to experimental observation can be produced, such as that shown in Fig. 3d. For that case, there is a sinusoidal change in the Euler angle ψ (or equivalently the

11 angle θ) with a wavenumber of 2 and coefficient of 0.6. We also observed deformation corresponding to other wave numbers. There are several potential limitations of this description. First, deformations might not be homogeneous throughout the ribbon, but might be concentrated at certain locations that later become rupture points. Also, the Janus feature plays no part in this view. Detailed simulations are needed to fully resolve the distortion modes of these rings and how they depend on external field.