Magnetic Particle Self-Assembly at Functionalized Interfaces

We study the assembly of magnetite nanoparticles in water-based ferrofluids in wetting layers close to silicon substrates with different functionalization without and with an out-of-plane magnetic field. For particles of nominal sizes 5, 15, and 25 nm, we extract density profiles from neutron reflectivity measurements. We show that self-assembly is only promoted by a magnetic field if a seed layer is formed at the silicon substrate. Such a layer can be formed by chemisorption of activated N-hydroxysuccinimide ester-coated nanoparticles at a (3-aminopropyl)triethoxysilane functionalized surface. Less dense packing is reported for physisorption of the same particles at a piranha-treated (strongly hydrophilic) silicon wafer, and no wetting layer is found for a self-assembled monolayer of octadecyltrichlorosilane (strongly hydrophobic) at the interface. We show that once the seed layer is formed and under an out-of-plane magnetic field further wetting layers assemble. These layers become denser with time, larger magnetic fields, higher particle concentrations, and larger moment of the nanoparticles.

S 2

Functionlisation of the magnetic nano-particles
The purchased NPs are functionalized by NHS (see figure S1). The NPs are each comprised of magnetic core (Fe 3 O 4 ), oleic acid group (R), and the N-Hydroxysuccinimide group (NHS). The NHS group is amphiphilic; therefore, its hydrophilic end protrudes out in water and its hydrophobic end interacts with the hydrophobic end of the oleic acid group which is -CH3. The particles are stabilized in water by steric interactions (hydrophobichydrophobic) between the oleic acid group and the NHS moiety. In addition, repulsion among the particles is achieved by the negative charge on the SO3 group, which is expected to be screened over the Debye length. As a consequence, on longer length scales the interactions among particles are dominated by the magnetic dipolar interaction.
These particles were dispersed in water and within the next few minutes injected into the previously mounted neutron reflectivity cell. The particles when dispersed in water were stable and did not agglomerate as concluded from DLS measurements after almost a month. Also, we did not see agglomeration in the SANS measurements, which took over several hours. Agglomeration on the time scales of our experiments can be neglected.
Since it is aqueous the temptation is to assume electrostatic, but this needs to be detailed in the manuscript Stabilization of magnetic particles can be achieved by playing on one or both of the two repulsive forces: electrostatic and steric repulsion. Controlling the strength of these forces is a key parameter to elaborate particles with good stability. The steric force is difficult to predict and quantify. However, theoretically for polymers. It depends mainly upon its molecular weight. The electrostatic repulsion can be followed through the knowledge of the diffusion potential that may be very close to the zeta potential.
The NHS stabilized particle is shown in the figure below. It comprises of magnetic core (Fe3O4), Oleic acid group (R), and the N-Hydroxysuccinimide group (NHS). The NHS group is amphiphilic; therefore, its hydrophilic end protrudes out in water and its hydrophobic end interacts with the hydrophobic end of the oleic acid group which is -CH3. So, unlike the reviewer my first impression is that the particles are stabilized by steric interactions (hydrophobic-hydrophobic) between the oleic acid group and the NHS moiety.

Characterisation of the magnetic nano-particles
A more detailed summary of the NP characterization is provided in Ref. [21], including electron microscopy and x-ray diffraction data. To provide experimental data on the key parameters we show the results of magnetization measurements (SQUID) and the SANS data, summarized in  S2 (right panel) shows SANS data together with fits, which assume a power exponent together with polydispersed core/shell spherical NPs for each sample. Including the power law is needed to describe the low-Q upturn frequently seen in magnetic nanoparticle colloids [S1, S2]. It likely originates from excess surfactant since the power-law scattering contrast is pronounced in the D2O (rather than the H2O) solvent, which has a pronounced contrast with the surfactant. In addition, only minimal evidence of a correlation peak associated with long-range inter-particle ordering is found. We note that low-Q scattering associated with excess surfactant has been described by others on related systems [S3]. The SLD values for the shell material are larger than that of bulk shell material (0.16 × 10 -4 nm -2 ) due to the presence of water in the shell, which can be estimated from the fitted SLDs for the shells (see Table 1) and those of the solvent (4.6 × 10 -4 nm -2 ) and bulk shell material. We find approximately 59 %, 50 % and 63 % of water in the shells for samples FF5, FF15 and FF25, respectively. For more details we refer to Ref. 21. n the grid and left for 2 min. Excess fluid was removed with a filir-dried at room temperature and examined. Representative TEM Fig. 1 (panels a). The average particle diameters are 4.1 ± 0.5 nm, nm. X-ray powder diffraction (XRD) patterns of the iron oxide rographs of iron-oxide NP samples, FF5, FF15, and FF25. Scale ray diffraction patterns of the NPs, FF5 (red), FF15 (blue), and g to a cubic structure. Panel c): Hysteresis loops for iron oxide lue) and FF25 (green) at 300 K.
were obtained using a Philips PW 1820 diffractometer 1 equipped e mean crystal sizes of the NPs are calculated using average values g reflections and applying the Scherrer equation. 54 The NP diam-0.7 nm, and 21.1 ± 1.3 nm, which are consistent with the results s that the NPs are single crystals.

Fig. S2:
The panel to the left shows hysteresis loops for iron oxide nanocrystals FF5 (red), FF15 (blue) and FF25 (green) at 300 K as extracted from SQUID measurements of the dried powder. The panel to the right shows SANS data for samples FF5 (red symbols), FF15 (blue symbols) and FF25 (green sym-bols) and fits to the data (solid lines). Data for FF5 and FF15 are scaled by a factor of four and two for better visibility, respectively. Figure  S 4

Summary of packing and compositions
Sketches of the packing densities and concentrations of the constituents as calculated from the fits to the neutron reflectivity data and calculations assuming a hexagonal dense packing are shown in Fig.  S3.

Sample cell for neutron reflectometry
For the NR experiments, a solid-liquid cell with a loading capacity of 2.5 ml was designed. Fig. S4 shows a sketch of the solid-liquid cell. The wet cell comprises of a 2 mm thick polytetrafluoroethylene (PTFE) gasket (with injection and outlet ports) used for containing and sealing the liquid sample between the silicon crystal (50×50×10 mm) and the polycarbonate base. The crystal and the base plate were clamped together with an aluminum frame.
The cell was further supported on a frame for mounting on the neutron instrument, see Fig. S5(a).
For applying an out-of-plane magnetic field, a neodymium magnet (40×40×15) mm was placed behind the silicon substrate (10 mm distance from the sample), Fig. S5(b). The total thickness of the liquid sample was less than 1 mm and the field at the sample position was measured using a Hall probe. Given the small thickness of the sample field gradients are samll, if present at all. During the neutron experiments the maximum beam footprint of the silicon wafer was 45 mm and decreasing with increasing incident beam angle to minimize edge effects. R experiments, a solid-liquid cell with a loading capacity of 2.5 ml was designed Fig. 1 sketch of the solid-liquid cell. The wet cell comprises of a 2 mm thick fluoroethylene (PTFE) gasket (with injection and outlet ports) used for containing and e liquid sample between the silicon crystal (50×50×10 mm) and the polycarbonate base. al and the base plate were clamped together with an aluminum frame. The cell was further on a frame for mounting on the neutron instrument, see Fig. 2(a). ing out-of-plane magnetic field, neodymium magnet (40×40×15) mm was placed e silicon substrate, Fig. 2(b). The field at the sample position was measured using a e.
etch of the solid-liquid cell with cutaway view of the holder for the substrate, liquid et. The scattering geometry is shown on the left-hand side.
Solid-liquid cell (front face-silicon) mounted on instrument MARIA. (b) Cell with a t magnet attached behind the silicon crystal.
For the NR experiments, a solid-liquid cell with a loading capacity of 2.5 ml was designed Fig. 1 shows a sketch of the solid-liquid cell. The wet cell comprises of a 2 mm thick polytetrafluoroethylene (PTFE) gasket (with injection and outlet ports) used for containing and sealing the liquid sample between the silicon crystal (50×50×10 mm) and the polycarbonate base. The crystal and the base plate were clamped together with an aluminum frame. The cell was further supported on a frame for mounting on the neutron instrument, see Fig. 2(a). For applying out-of-plane magnetic field, neodymium magnet (40×40×15) mm was placed behind the silicon substrate, Fig. 2(b). The field at the sample position was measured using a Hall probe.    Figure S6 shows neutron reflectivity curves plotted versus Qz and normalized to Q -4 for a more dilute (0.5 vol%) solution of FF5 in contact to a APTES coated substrates for applied out-of-plane magnetic fields of up to 250 mT. The corresponding SLD profiles are shown in the figure as well. It turns out that only when a field of 250 mT is applied the first wetting layer becomes close packed. The layer structures and compositions are sketched in Figure S7 and S8. Fig. S6. NR data for FF5 (0.5 vol. %) taken without (red symbols) and with a magnetic field of 100 mT perpendicular to the Si (100) for 2 hrs (blue symbols) and after 12 hrs (teal symbols). Data for the sample under a field of 250 mT applied for 2 hrs (black symbols) is shown as well. (left) Plot of R. ! " as function of ! . The solid lines represent fits to the data. (right) Profile of nuclear SLD plotted as function of distance from the Si (100) surface. Also included are the SLD values for the magnetite core, water and shell material (gray dashed lines), as well as for the close-packed particle ordering within the slabs (orange dashed lines).