Triggered self-assembly of magnetic nanoparticles

Colloidal magnetic nanoparticles are candidates for application in biology, medicine and nanomanufac-turing. Understanding how these particles interact collectively in fluids, especially how they assemble and aggregate under external magnetic fields, is critical for high quality, safe, and reliable deployment of these particles. Here, by applying magnetic forces that vary strongly over the same length scale as the colloidal stabilizing force and then varying this colloidal repulsion, we can trigger self-assembly of these nanoparticles into parallel line patterns on the surface of a disk drive medium. Localized within nanometers of the medium surface, this effect is strongly dependent on the ionic properties of the colloidal fluid but at a level too small to cause bulk colloidal aggregation. We use real-time optical diffraction to monitor the dynamics of self-assembly, detecting local colloidal changes with greatly enhanced sensitivity compared with conventional light scattering. Simulations predict the triggering but not the dynamics, especially at short measurement times. Beyond using spatially-varying magnetic forces to balance interactions and drive assembly in magnetic nanoparticles, future measurements leveraging the sensitivity of this approach could identify novel colloidal effects that impact real-world applications of these nanoparticles.

1 All-nanoparticle diffraction grating a, A TEM image of EMG707 nanoparticles. b, Size distribution of EMG707 nanoparticles (d av and sd represent the average particle size and standard deviation of size distribution respectively).
c, A SEM image of an all-nanoparticle diffraction grating assembled on the disk drive surface.
was immersed into the DI water for 3 s to remove any nanoparticles (NPs) that remain between transitions. Note this procedure is identical to how the assembly is performed in the fluid cell, except for the real-time measurements, the NPs are pumped into the cell with a syringe pump and then rinsed with DI water using a second syringe pump. We have conducted SEM analysis on assembled gratings as a function of IS using the procedure discussed above. The SEM images do not demonstrate the dramatic effects seen in the diffraction data. However we do observe 200 -1000 nm aggregates that are randomly distributed on the medium for > 0.1 M IS. It is very difficult to reproduce the precise procedure used in the fluid cell and generate coated media suitable for SEM imaging, so the SEM images we have taken are really not directly comparable with the diffraction measurements.
2 Magnetic fields and gradients above transitions on longitudinal disk drive media The magnetic field above transitions on longitudinal disk drive media can be decomposed into components as (S1) The field component alongŷ (H y ) is zero because the transition is assumed to be very wide compared with the relevant x-and z-dimensions. Figure S2a (S2b) shows representative field components H x (H z ) as a function of x (z) above a transition in the south-south configuration on longi- tudinal disk drive media (inset to Figure S2b). In Figure S2 the coordinate origin is located at the transition and at the center of the medium, with the z axis perpendicular to the medium surface.
The field components H x and H z are calculated using the standard equations for a longitudinally recorded transition 1 , where the medium thickness δ = 30 nm 1 , transition parameter a = 10 nm 1 , and remanent magneti-

Real-time diffraction and scattering measurements
The total laser signal reaching the diffraction detector (DD in Figure 1b) includes the scattered signal from the fluid/surface (> 80% of the scattering is from the fluid for the longest measurement time as determined by horizontally translating the grating), and the diffracted intensity from an assembled grating. The DE from the assembling grating is obtained by subtracting the scattered signal from the total DD signal. The right magnitude to subtract is found by calibrating the relative difference in scattered signal between the DD and the scattering detector (SD in Figure 1b). To perform this calibration, a 0.2 mm thick silicon wafer is placed on top of the medium template in the fluid cell, i.e. to avoid any diffraction due to an assembling grating. Thus the DD signal comes entirely from scattered laser light. After pumping a series of ferrofluids with varying concentrations and particle sizes into the cell, the scattered light from the fluid is recorded simultaneously on both DD and SD, and the intensities at 15 minutes are plotted for each ferrofluid as shown in Figure   S3. The data from the two detectors are linearly related, and a linear fit yields a conversion factor = 4.24. Therefore, to obtain the correct scattering value to subtract from the DD, the SD signal is scaled by 4.24 and then subtracted from the DD signal, in order to yield the correct diffracted intensity during real-time assembly.

Diffraction and scattering efficiencies for nanoparticle suspensions with large ionic strengths
The solid and dashed curves in Figure S4 show  6 Impact of the suspension ionic strength on nanoparticle stability and self-assembly Colloidally suspended particles undergo Brownian motion and aggregate in liquid due to van der Waals interactions 4-7 . To achieve a stable suspension, the EMG707 particles are coated with anionic surfactants on the particle surface that generate interparticle Coulomb repulsions to prevent particles from aggregation (see Materials in Methods). This repulsion arises from the interaction between electrical double layers 8 around the particle surfaces, where charged surfaces interact with electrolyte ions (e.g., added salt ions) in the suspension. The interaction energy (ψ) between particles i and j is numerically calculated as 9, 10 where 0 is the permittivity of free space, is the dielectric constant of water, ψ 0 is the surface potential that is approximately equal to the particle zeta potential ζ, H is the surface-to-surface distance between particles, e is the electrical charge, k b is the Boltzmann constant, T is the temperature, and Y is the dimensionless effective surface potential [10][11][12] . In Eq. (S4), 1/κ is a characteristic decay length, known as the Debye length, which is defined to be 8 where N A is the Avogadro number.