www.sciencemag.org/cgi/content/full/335/6065/199/DC1

Supporting Online Material for

Composites Reinforced in Three Dimensions by Using Low Magnetic Fields

Randall M. Erb, Rafael Libanori, Nuria Rothfuchs, André R. Studart*

*To whom correspondence should be addressed. E-mail: andre.studart@mat.ethz.ch

Published 13 January 2012, Science 335, 199 (2012)

DOI: 10.1126/science.1210822

This PDF file includes:

Materials and Methods SOM Text Figs. S1 to S11 Table S1 References (31–41)

Other Supporting Online Material for this manuscript includes the following: (available at www.sciencemag.org/cgi/content/full/335/6065/199/DC1)

Movie S1

 

Supporting Online Material

Composites Reinforced in Three Dimensions by Using Low Magnetic Fields

Randall M. Erb, Rafael Libanori, Nuria Rothfuchs André R. Studart

Complex Materials, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland

MATERIALS AND METHODS

1. Preparation of magnetically responsive alumina platelets

7.5 μm alumina platelets (Alusion®) were kindly supplied by Dr. John Robinson from

Antaria Limited, Australia. To enable magnetic control of these particles, 8 g of alumina platelets

were stirred in 200 mL of deionized water at pH=7 while 200 μL of EMG-705 ferrofluid (Ferrotec,

Germany) was added dropwise. The 12 nm iron oxide particles in the ferrofluid are coated with

anionic surfactant, which leads to electrostatic adsorption of the negatively charged magnetic

nanoparticles onto the positively charged platelets. At these concentrations, 1 hour incubation is

sufficient to coat the alumina platelets with all the iron oxide nanoparticles initially dispersed in

the suspension (Figure 1e in the main manuscript). The coated platelets were washed three

times with deionized water and then completely dried at 150°C for 24 hours. The platelets were

stored in a dry environment until use.

2. Preparation of magnetically responsive calcium sulfate rods

Calcium sulfate hemi-hydrate rods were prepared consistent with Wang et al. (31) 20

grams of calcium sulfate di-hydrate powder (Sigma-Aldrich) was added to an aqueous suspen-

sion containing 60 grams of deionized water and 40 grams of calcium chloride dihydrate (Sig-

ma-Aldrich). The mixture was boiled at 105°C for 30 minutes. The solution was then filtered us-

ing a Büchner funnel under vacuum. The filter cake was washed with boiling water and acetone.

Prepared rods were then stored dry until use. To make the rods magnetic, 20 milligrams of rods

and 10 μL of EMG-605 ferrofluid (Ferrotec, Germany) were added to 4 mL of saturated

Ca+2/SO4-2 solution at pH 10. The saturated solution was made by dissolving (under stirring)

calcium sulfate powder in deionized water until no further dissolution occurred (a powder precip-

itate collected at the bottom of the container). This was used to prevent the dissolution of the

rods in the aqueous media. After minutes, strong magnetization of the rods could be observed

with a handheld rare-earth magnet under a light microscope. Though there was excess iron ox-

ide in solution in this case, negative magnetophoretic alignment of the rods (as reported on pre-

viously (32)) was disproven since the rods migrated towards the magnet, proving that they have

a higher magnetic permeability than the surrounding fluid.

   

2

3. Preparation of homogenous polyurethane composite films

Homogenous polyurethane samples were prepared using thermoplastic polyurethane

(Elastollan® C64D, BASF, Germany), polyvinylpyrrolidone (PVP, Sigma-Aldrich, molecular

mass 360,000 g/mol), and the UHMR alumina platelets described above. In a typical composi-

tion, 2.4 grams of alumina platelets, 0.75 grams of PVP in powder form and 2.2 grams of polyu-

rethane pellets were suspended in 150 mL of dimethylformamide (DMF, Sigma-Aldrich) and

stirred at 60°C for 24 hours to fully dissolve the polyurethane. DMF was carefully removed in a

R-125 Rotavapor (Büchi, Switzerland) at 60°C and 10 mbar until the suspension was sufficiently

viscous for mold pouring (~500 mPa.s) and yet fluid enough to enable alignment of platelets

under a magnetic field. The polymer suspension was then poured onto a 1cm x 3cm x 9cm

polytetrafluoroethylene (PTFE) mold prepared in-house. For films with out-of-plane aligned

platelets, a magnetic field was applied using a custom 20 cm x 10 cm rectangular solenoid

(Magnetech Corporation, Michigan, USA) placed below the mold. Samples were heated with or

without a field at 60°C for 24 hours to remove the DMF and consolidate the polyurethane. The

films obtained after consolidation contained 20vol% alumina platelets, 20vol% PVP and 60vol%

polyurethane. An annealing step at 130°C for 3 hours was conducted to ensure good adhesion

between the alumina platelets and the polyurethane matrix. In addition to Figure 2f,g in the pa-

per, cross-sections of the composites were also obtained using a focused ion beam scanning

electron microscope (Zeiss NVision 40, EMEZ Facility at ETH-Zürich). These micrographs (Fig-

ure S1) clearly show distinct out-of-plane alignment of the alumina reinforcement particles when

a magnetic field is applied as opposed to the in-plane alignment achieved in the absence of the

field.

4. Preparation of locally reinforced polyurethane composite films

Locally reinforced heterogeneous composites were prepared using the polyurethane and

magnetized alumina platelets described above. 0.358 grams of alumina platelets in powder form

were added to 3.61 grams of polyurethane pellets so that a volume fraction of alumina platelets

of 3 vol% could be obtained in the final composite. These solids were suspended in 150 mL of

DMF and stirred at 60°C for 24 hours to fully dissolve the polyurethane. The resulting suspen-

sion was then poured into a 5cm circular flexible silicon mold. A magnetic field gradient was ap-

plied using the edge of a 5cm x 5cm x 2cm rare earth magnet (Supermagnete, Switzerland)

placed below the mold. The magnetized alumina platelets were attracted to the linear region of

magnetic field maximum nearest the edge of the magnet. The platelets were magnetically con-

centrated for 1 hour. Then the mold was placed in the oven at 80°C for 24 hours to remove the

DMF and consolidate the polyurethane. An annealing step at 130°C for 3 hours was conducted

to ensure good adhesion between the alumina platelets and the polyurethane matrix. The sam-

ple showed a clear gradient in the concentration of UHMR particles as shown in Figure S2a.

   

3

Dogbone samples for tensile testing were punched out of the reinforced and non-reinforced re-

gions of the film.

5. Tensile testing of homogeneous and locally reinforced polyurethane composites

Tensile strength samples were produced from: (a) the homogeneous alumina-PVP-

polyurethane composites (Table S1) and (b) the locally reinforced alumina-polyurethane com-

posites described above. Standard dog bone shapes were punched from the final material with

the tested region being 12 mm x 2 mm. Thicknesses varied but were generally around 0.1mm.

Tensile samples were tested with an Instron 4411 Universal Testing Machine. Samples were

pulled at constant rates of 10 mm/minute. Force and displacement data were collected and

converted into stress vs. strain plots. The slope of the stress vs. strain data in the linear elastic

regime was measured to be the Young’s modulus of the material. At least five samples were

tested in each case.

6. Dissolution of iron oxide with phosphoric acid

To remove the iron oxide particles from consolidated composites, samples of platelet-

reinforced polyurethane were subjected to incubation in 14M phosphoric acid solutions. After 1

hour incubation, the polyurethane samples lose their brownish color with the dissolution of the

iron oxide nanoparticles (insets of Figure S3a-b). The microstructures of the composites were

verified after this treatment to find the iron oxide nanoparticles dissolved, but the oriented plate-

lets and the matrix still intact (Figure S3a-b).

7. Hardness tests

Hardness tests were performed on acrylate-based composites reinforced with deliberately

aligned alumina platelets. The polymer matrix is composed of the two monomers bisphenol A

glycerolate dimethacrylate (Sigma-Aldrich) and triethylene glycol dimethacrylate (95%, Aldrich

Chemistry) at concentrations of 50 and 49 wt%, respectively, in the final polymeric phase. A

homogenous mixture of these monomers is obtained at 60°C through mechanical stirring with a

glass stir bar. 1 wt% of the photoinitiator campherchinone (97%, Sigma-Aldrich) with the co-

initiator ethyl 4-dimethylaminobenzoate (99+%, Sigma-Aldrich) in a 1:1 mole fraction was used.

In addition, 10 vol% alumina platelets that were coated with magnetic nanoparticles as de-

scribed above were added to the polymer solution. Instead of 25 µl ferrofluid / g platelets, a

concentration of 100µl / g was used.

Samples for the hardness test were prepared using a mold consisting of 0.5mm thick Tef-

lon film spacers sandwiched between a top and bottom glass cover. The viscous resin was

placed on a glass slide between two spacers and spread by pressing the other glass slide on

top. In one planar direction the resin was confined by the spacers, in the other planar direction

   

4

the resin was free to expand. The glass covers were kept together with tape and clamps. To

achieve vertical aligned platelets within the polymer, a magnetic field of 160 mT was applied for

10 minutes. The shear flow of the resin within the glass slides was exploited to obtain samples

with horizontally aligned platelets, which were afterwards kept in a horizontal position for 30

minutes. Polymerization was induced by irradiation with visible light through the top glass slide

using a VIVADENT Bluephase 20i LED lamp for 40 seconds in case of the pure resin and for 2

minutes in case of the vertically and horizontally aligned samples.

The hardness tests were conducted in the Laboratory of Metal Physics and Technology of

Prof. Dr. Jörg F. Löffler at ETH Zürich. A Wolpert Microhardness Tester MXT-α was used to

measure Vickers hardness of the three samples: pure resin, composite with vertically and hori-

zontally aligned alumina platelets. For each sample ten measurements were carried out using

an HV0.5 indenter and a dwell time of 10 seconds. It was ensured that the indenter tip did not

directly hit a platelet. Based on the arithmetic average length of the indent diagonals the value

of the Vickers hardness was calculated. 8. Wear tests

Wear tests were performed in acrylate-based composites typically used as dental resins in

restorative dentistry. Bisphenol A glycerolate dimethacrylate (Sigma-Aldrich) and triethylene

glycol dimethacrylate (95%, Sigma-Aldrich) in a weight ratio of 50:49, respectively, were mixed

with alumina platelets coated with magnetic nanoparticles prepared as described above. A

commercial dental resin consisting of approximately 85wt% 5μm particles (Clearfil AP-X, Ku-

raray, Japan) was then added and mixed manually with a spatula. (33) The acrylate monomer

mixture, alumina platelets and the commercial dental resin were mixed in such a ratio to obtain

composites with final concentrations of 10.9, 1.1 and 87.9 vol%, respectively.

No additional photoinitiator was used. A 0.5mm thick Teflon film spacer with a quadratic

hole sandwiched between two glass slides served as mold. The mold was filled with the

pastelike resin, the two glass slides were pressed together and fix by tape and clamps. In case

of the vertical aligned platelets, a vertical field of 230 mT was applied for 10min. In case of the

horizontally aligned platelets a horizontal field of 150 mT was applied for 10min. The polymeri-

zation was induced by irradiation with visible light using a VIVADENT Bluephase 20i LED lamp

for 40 seconds. Typical samples are shown in Figure S4.

The wear tests were conducted in the laboratory of Prof. Dr. Paul Smith at ETH-Zürich us-

ing a similar setup to that developed by Tervoort et al (34). Samples described above were

glued to the wear testing substrate. A ball revolution of 500 rpm was used with a normal load of

1.98 N. Distilled water was dripped over the testing site to work as lubricating medium and to

rinse away wear debris. Each test lasted approximately 8 hours. Ball penetration depth was

measured with a laser. The raw data was noise-reduced by reporting averaged measurements

for every 100 consecutive data points (100 seconds).

   

5

9. Preparation and testing of bilayer 3D reinforced epoxy composites

Bilayer 3D reinforced epoxy compostites (Figure 3e, Figure S5a-d) were produced to study

the effect of specific orientations of reinforcing particles on the flexural modulus and out-of-

plane hardness of laminated rectangular bars. For composites with alumina platelets, 6.57 g of

alumina platelets were stirred using a mechanical mixer at 1000 rpm into 9.38 g of Araldit

GY250 and 8.44 g of Aradur 917 (Huntsman Co, USA) for 1 hour. The mixture was then con-

nected to a V-215 Büchi rotary evaporator and stirred at 15 rpm and 10 mBar for 30 minutes to

remove air bubbles. 0.14 g of AGY070 polymerization catalyst was added to the solution, which

was subsequently stirred again in the rotary evaporator for 15 minutes. The solution was then

cast into 1 cm x 5 cm x 6 cm Teflon molds and positioned under the 5cm x 5cm x 2cm rare

earth magnet that was connected to a small motor and was rotating vertically. The epoxy was

allowed to sit in the field for 12 hours. The sample was then transferred to an oven at 60°C

where it was placed for 4 hours within a vertically rotating field created by three temperature-

rated computer programmed solenoids. One solenoid was positioned vertically below the sam-

ple, while the other two solenoids were positioned horizontally on either side of the sample. The

current to the solenoids was driven using two 20-5M Bipolar Operational Power Supplies

(Kepco, USA) and regulated as two sinsoudal current waveforms offset by 90° using a LabView

program controlling a CYDAS 1602HDP A/D board (CyberResearch, USA). Afterwards, the

sample was removed from the rotating field and given a final heat treatment of 4 hours at 100°C.

The sample was then cut into the appropriate slabs and assembled to produce the laminate

structures schematically shown in Figure 3e. In all cases, the top and bottom layers were cut to

be 1 mm and 2 mm thick, respectively, with a width of 5 mm and a length of 50 mm. The top

and bottom layers were glued together using the same epoxy/alumina composition and pressed

together using binder clips. The laminated structure was subjected to the same heat treatment

to cure the epoxy. Resulting microstructures are shown in Figure S5a-d showing successful ori-

entation of the alumina platelets in the epoxy composites.

Samples were then tested in a 3-point bending apparatus hooked up to an Instron 4411

Universal Testing Machine (Figure S5e). In all cases, the span of the test was 3 cm and the dis-

placement rate was 5 mm/min. Force and displacement data were collected and converted into

flexural modulus. At least three samples were tested in each case and found to have high re-

producibility. Hardness tests, described above, were carried out in the out-of-plane direction of

the top layer of the laminate structures.

10. Preparation of PVA structures with holes that are locally reinforced

Polyvinyl alcohol (PVA, molecular mass = 13,000-23,000 g/mol, Sigma-Aldrich) was fully

dissolved in deionized water by 24 hour stirring at 60°C to form a 25wt% PVA aqueous solution.

0.60 grams of magnetized alumina platelets were added into 14.48 grams of the viscous PVA

   

6

solution and stirred until complete homogenous. This amount of magnetized alumina platelets

leads to a volume fraction of particles of 5 vol% in the final composite. The suspension was cast

in a 7.5x1.5cm PTFE mold with a 6 mm cylinder directly in the middle that housed a small cylin-

drical permanent magnet (4 mm in diameter and 10 mm in height). The permanent magnet at-

tracted the UHMR platelets around the hole and simultaneously oriented them in the out-of-

plane direction (Figure 4e in the paper).

11. Preparation of laminated polyurethane structures combining in- and out-plane rein-forcement

Laminated polyurethane structures were made by first synthesizing two homogenous films

with in-plane and out-of-plane platelet orientation via the methods described above. However,

no annealing was conducted in these samples. Two equally sized substrates of each sample

were cut from the materials. A thin layer of DMF was applied with a cotton swab to the top of the

in-plane reinforced surface. The out-of-plane reinforced sample was then firmly pressed, by

hand, against the wet substrate. The sample was then put in the oven for 3 hours at 130°C to

remove the excess DMF. The sample was finally cut, dipped into liquid nitrogren, and freeze

fractured. The fractured cross-section was imaged using a scanning electron microscope, which

revealed a good bonding between the two laminated layers (Figure 2h in the paper). 12. Preparation of composites under a rotating magnetic field

A rotating field setup was employed identical to that described in an earlier study (35). Two

orthogonal solenoids were placed in the oven, one aligned along the x axis (horizontal) and one

along the z axis (vertical). Low frequency (1 Hz) sinusoidal current waveforms were run through

the two solenoids with a 90° offset between them. This produced a circular rotating magnetic

field. The current was adjusted until the point centered between the solenoids achieved a mag-

netic field of 10 mT as measured with a 410 Handheld Gaussmeter (Lakeshore, OH, USA). Vis-

cous suspensions consisting of polyurethane and magnetized alumina platelets in DMF were

prepared as detailed above and poured into a PTFE mold placed above one solenoid such that

the substrate was in the x-y plane. The sample was then heated at 60°C under a continuously

rotating magnetic field for 24 hours. The sample was removed and annealed at 130°C for 3

hours. Part of the sample was cut, dipped into liquid nitrogen, and freeze fractured to reveal the

cross-section. The cross-section and the top surface of the sample were imaged using a scan-

ning electron microscope (Figure 2j in the paper).

13. Preparation of polyurethane structures with spatially graded reinforcement

Spatial gradient polyurethane structures were produced by first preparing the DMF-based

alumina-PVP-polyurethane suspensions described above. For this experiment, an amount of

   

7

platelets leading to a particle volume fraction of 5 vol% in the final composite was used. The

solution was poured into the PTFE mold at very low viscosities (~ 50 mPa.s). Due to the low

viscosity, the magnetized platelets could readily migrate towards the solenoid. Platelets were

thus spatially concentrated at the bottom surface of the mold in an aligned fashion due to the

magnetic field and gradient. The film was then consolidated under 60°C for 24 hours. The con-

solidated sample was annealed for 3 hours at 130°C. The sample was finally cut, dipped into

liquid nitrogren, and freeze fractured to reveal the cross-section. The cross-section was imaged

using a scanning electron microscope (Figure 4g in the paper). 14. Preparation of swellable PVA structures

Polyvinyl alcohol (PVA, molecular mass = 13,000-23,000 g/mol, Sigma-Aldrich) was fully

dissolved in deionized water by 24 hour stirring at 60°C to form a 25wt% PVA aqueous solution.

0.6 grams of magnetized alumina platelets and 36.2 milligrams of citric acid (Brenntag

Schweizerhall AG) relative to the mass of PVA were added into 14.48 grams of the viscous PVA

solution and stirred until complete homogenous. The amount of magnetized alumina platelets

led to a volume fraction of particles of ~5 vol% in the final composite. The suspension was cast

in a PTFE mold (15 mm x 15mm x 5mm) and placed on a standard, commercial refrigerator

magnet. The refrigerator has linear magnetic domains of 5 mm in width (see Figure 4c in the

paper). The magnetized platelets sedimented to the bottom of the suspension and aligned ac-

cording to the local field direction from the refrigerator magnet. The samples were allowed to

fully dry in air for 24 hours. The sample was then heat treated for 1 hour at 140°C to promote

cross-linking of the PVA with the citric acid. (36) The specimen was finally placed in a water

bath for 1 hour and the shape change resulting from swelling was captured using a digital cam-

era.

SUPPORTING TEXT

1. Calculation of magnetic and gravitational potential energies of platelets

The magnetic and gravitational potential energies Um and Ug used in Eq. 1 (main manu-

script) depend on the orientation of the platelets with respect to the respective external fields

and were calculated as described below.

The gravitational energy, Ug, of a platelet of diameter 2b and thickness 2a as it is rotated

vertically is solved as:

Ug Platelet( ) =Vp ρp − ρf( )gbsinθ (S1)

   

8

where Vp is the volume of the platelet, g is the gravitational constant, ρp and ρf are the respec-

tive densities of the particle and the surrounding fluid, and θ is the angle between the disc long

axis and the horizontal plane (Figure S6). The gravitational energy has a minimum of 0 at θ=0°

and a maximum at θ=90°.

Instead, the magnetic energy of a platelet cannot be attained with simple analytic expres-

sions, and thus a common oblate ellipsoidal geometry is assumed. To reflect that the magnetic

content of the platelets is all on the surface, an ellipsoidal shell model is used. The magnetic

energy, Um, of an ellipsoidal shell of material can be solved as (37, 38):

Um Platelet( ) = 23π a + Δ( ) b + Δ( )2

− ab2⎡⎣⎢

⎤⎦⎥

μf μp − μf( )2Ga −Gb( )Ho

2 sin2ψ

μf − μf − μp( )Ga⎡⎣

⎤⎦ μf − μf − μp( )Gb⎡⎣

⎤⎦ (S2)

where 2a is the thickness of the platelet, μf and μp are the magnetic permeabilities of the fluid

and the particle, respectively, Ga and Gb are the geometrical demagnetizing coefficients, Ho is

the external field, Δ is the thickness of the iron oxide nanoparticle coating and ψ is the angle

between the applied magnetic field and the long axis of the ellipsoidal shell (Figure S6). Δ is

taken as the diameter of the magnetic nanoparticles, whereas the geometrical demagnetizing

coefficients are as follows:

Ga =ab2

2ds

s +a2( )3/2s +b2( )0

∞

∫

Gb =ab2

2ds

s +a2( )1/2s +b2( )2

0

∞

∫. (S3)

With sufficient platelet anisotropy (b/a>10), the geometrical coefficients can be estimated

with numerical values. For the case of our platelets, Ga ≈ 1 and Gb ≈ 0. Taking the permeability

of the fluid to be that of free space, μf = μo = 4π ⋅10−7m ⋅kg / s2A2 , the magnetic energy for the

platelet can be described as:

Um(Platelet) = 23π a + Δ( ) b + Δ( )2

− ab2⎡⎣⎢

⎤⎦⎥μp − μo( )2

μp

Ho2 sin2ψ

. (S4)

Um can be put in terms of the particle susceptibility, χp, where μp = μo χp +1( ) to yield:

   

9

Um(Platelet) = 23π a + Δ( ) b + Δ( )2

− ab2⎡⎣⎢

⎤⎦⎥μo

χp2

χp +1Ho

2 sin2ψ. (S5)

Here, the magnetic energy for the platelets has a maximum at ψ = 90° and a minimum at ψ = 0°.

The values for magnetic and gravitational energies are plotted against θ in Figure S7 for

the experimental system of platelets used in this work (i.e. θ +ψ = 90°, a = 100 nm, b = 3.75 μm,

ρp - ρf = 3.98 g/cm3-1 g/cm3). The susceptibility can be determined by χp = Cffχff, where Cff is the

surface coverage of iron oxide in the shell layer (0 to 1) and χff is the susceptibility of the bulk

iron oxide. The concentration of iron oxide is estimated to be Cff =0.13 (0.5 vol%) from electron

micrographs of surface coatings of the reinforcement particles, while the bulk susceptibility is

taken consistent with previous work as χff =21. (39) It is worth noting that the gravitational and

magnetic energies are orders of magnitude larger than kBT for the geometries and field

strengths considered here. This difference is due to the experimental platelets being 3 µm larger

in diameter than the ideal UHMR platelet size. Instead, using the ideal size of 4 µm in diameter

(see Figure 1 in main manuscript) would put the thermal and gravitational energies at the same

order of magnitude.

2. Calculation of the probability of alignment of platelets with thermal fluctuations

Thermal fluctuations play an important role in the randomization of the alignment of

UHMR particles in suspension. To better understand this role, we employ Boltzmann statistics

to calculate the theoretical variability in the alignment of our platelets taking into account both

magnetic fields and gravity. For each angle of possible alignment, (0° < θ < 90° due to sym-

metry), the Boltzmann factor for the energy of that state can be calculated as

e −Um Hmin,ψ( )−Ug θ( )⎡⎣

⎤⎦ kBT

. (S6)

The probability of a platelet inhabiting a given range of orientational states from θ1 to θ2 can be

determined as follows:

Pθ1 to θ2= e −Um Hmin,ψ( )−Ug θ( )⎡

⎣⎤⎦ kBT dθ

θ1

θ2

∫ Z

Z = e −Um Hmin,ψ( )−Ug θ( )⎡⎣

⎤⎦ kBT dθ

0°

90°

∫ (S7)

Here, Z is the partition function, which is the sum of the Boltzmann factor of all possible states

of orientation. To estimate the magnetic fields required to overcome gravity and to avoid disrupt-

ing alignment by thermal energy, we plot the probability for the experimental platelets, described

in the previous sections, to be aligned at various orientations under various fields in Figure S8a.

To aide visualization, we have binned the probabilities with a resolution of 1°. For example, the

   

10

probability that a platelet will be oriented from 89°-90° at 2.5 mT is shown in Figure S8a to be

0.45. Another way of visualizing this effect is by plotting the complementary cumulative distribu-

tion function, (CCDF), shown in Figure S8b. Here, we show the probability that a platelet will

display an orientation angle equal to or greater than θ. This facilitates determination of the mag-

netic field required to achieve different degrees of alignment.

3. Calculation of magnetic and gravitational potential energies of rods

Similarly to the case of platelets, the magnetic and gravitational potential energies of rods

dependent upon the orientation.

The gravitational energy, Ug, of a rod of length 2a and diameter 2b as it is rotated vertically

is solved as:

Ug rod( ) =Vp ρp − ρf( )gasinθ (S8)

where, similarly, Vp is the volume of the rod, g is the gravitational field and θ is the angle be-

tween the long axis of the rod and the horizontal plane (Figure S9). The gravitational energy has

a minimum of 0 at θ=0° and a maximum at θ=90°.

The magnetic energy of a rod also cannot be attained with simple analytic expressions,

and thus we use the following expression for a prolate ellipsoid:

Um rod( ) = 23π a + Δ( ) b + Δ( )2

− ab2⎡⎣⎢

⎤⎦⎥

μf μp − μf( )2Gb −Ga( )Ho

2 sin2ψ

μf − μf − μp( )Ga⎡⎣

⎤⎦ μf − μf − μp( )Gb⎡⎣

⎤⎦ (S9)

where the variables are the same as those in Eq. S2.

With sufficient rod anisotropy (a/b>10), the geometrical demagnetizing coefficients can be

estimated with numerical values as Ga ≈ 0 and Gb ≈ 0.5 . Thus, the magnetic energy for the rod

equals:

Um(rod) = 23π a + Δ( ) b + Δ( )2

− ab2⎡⎣⎢

⎤⎦⎥μp − μo( )2

μo + μp( ) Ho2 sin2ψ

. (S10)

Um can be put in terms of the particle susceptibility, χp, to yield:

   

11

Um(rod) = 23π a + Δ( ) b + Δ( )2

− ab2⎡⎣⎢

⎤⎦⎥μo

χp2

χp + 2( )Ho2 sin2ψ

. (S11)

The magnetic energy for the rods has a maximum at ψ = 90° and is zero at ψ = 0°.

The values for magnetic and gravitational energy are plotted against θ in Figure S10 for the

experimental system of rods used in this work, (i.e. θ +ψ = 90°, a = 500 nm, b = 5 µm, ρp - ρf =

2.50 g/cm3-1 g/cm3). Again, the concentration of iron oxide is estimated to be Cff =0.13 (0.5

vol%).

4. Calculation of the probability of alignment of rods with thermal fluctuations

As in the case of platelets, thermal fluctuations play an important role in the randomiza-

tion of the alignment of UHMR rods in suspension. Thus, we again employ Boltzmann statistics

to understand this role and to calculate the theoretical magnetic fields required for alignment of

our rods. The Boltzmann factor for the energy of one particular state can be calculated accord-

ing to Eq. S7. The probability for the experimental rods to be at a given angle is plotted for vari-

ous fields in Figure S11a. Again, we have binned the probabilities with a resolution of 1°. The

corresponding complementary cumulative distribution function is provided in Figure S11b.

5. Alignment of platelets and rods due to increase in packing entropy

As first pointed out by Onsager, (26) anisometric particles dispersed in a fluid can undergo

ordering and phase separation above a critical number density of particles, n, due to an in-

crease in packing entropy. This phase transition is typically described by the dimensionless pa-

rameter nD3, with D being the diameter of the platelet (7.5 μm in our experiments). Assuming

that coexisting isotropic and nematic phases are formed for nD3 values between 6.8 and 7.7,

(40) we estimate that ordering of platelets due to the packing entropic effect starts to occur only

for volume fractions φ higher than 0.142 (14.2 vol%). n = 4φ πD2L( ) was assumed in this calcu-

lation, with L being the platelet thickness.

6. Importance of accumulation of nanoparticles on the shell

To determine the importance of having the magnetic nanoparticles adsorbed only in the

shell of the UHMR particles, the scenario where an equal amount of magnetic nanoparticles is

distributed throughout the volume of particles was considered. The volume fraction of iron oxide

with respect to the total volume of solids can be approximated as follows:

   

12

φff ≈Cff

a+ Δ( ) b+ Δ( )2

ab2−1

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥ . (S12)

For alumina platelets of 7.5 μm diameter and 200 nm thickness and surface coverage of

12 nm iron oxide nanoparticles of 13% (consistent with typical experimental conditions), we ob-

tain a volume fraction φff of 1.65 vol%. The alignment field in this case is 1.04 mT.

On the other hand, if the nanoparticles are distributed throughout the platelet volume then

the particle susceptibility will have to be recalculated according to:

χ p = χ ffφff . (S13)

The magnetic energy is thus put in terms of the whole platelet with this susceptibility and

not just a shell layer. We obtain an alignment field for this case of 1.76 mT, which is 69% larger

than that for the magnetic shells, showing that confinement of the iron oxide nanoparticles to the

surface is very beneficial.

7. Verification of energy model by varying surface coverage

To confirm the energy model, alumina platelets with different surface coverage of iron ox-

ide nanoparticles were aligned in magnetic fields. The response was characterized by deter-

mining the field at which 50% of the alumina platelets were aligned and 50% were dominated by

gravity and were pinned to the substrate. Alumina platelets of different magnetic susceptibilities

were made as described above but with changing the amount of ferrofluid added in the initial

suspension relative to the mass of the platelets.

The surface coverage of iron oxide on the platelets was taken from photoanalysis of scan-

ning electron micrographs to depend linearly on the amount of ferrofluid added to the initial sus-

pension as 3.4 μL/g per percent coverage.

For this analysis, the following iron oxide coatings were produced: 1, 10, 37.5 and 100 μL

of ferrofluid per gram of alumina platelets. The ferrofluid contains 3.6 vol% iron oxide particles

with respect to the total volume of particles, water and surfactants.

The theory developed in the previous section could then be verified for these different sus-

ceptibilities. The susceptibility of the 12 nm shell of iron oxide particles encasing the platelets

was calculated according to: χp = χff φff, where χff = 21 is the bulk susceptibility of the iron oxide

nanoparticles consistent with earlier investigations. (39) Very good agreement is found between

the experimental and the theoretically estimated alignment field, Hmin, as shown in Figure 1f

(main manuscript). The experimental magnetic fields reported throughout this study were

measured with a 410 Handheld Gaussmeter (Lakeshore, OH, USA).

   

13

8. Theoretical estimate for the elastic modulus of the locally reinforced composites

Stress versus strain curves for the reinforced and non-reinforced regions of locally rein-

forced composites were obtained as described above. The Young’s modulus, E, was found to

be 310 MPa for the reinforced region compared with 250 MPa for the pure polyurethane. SEM

analysis showed that the reinforced region exhibits a clear bilayer structure (Figure S2b). Bi-

layer composite theory is thus employed to estimate the stiffness of the thin reinforced layer

responsible for the increase in the Young’s modulus. The Young’s modulus of the bilayer, Enet,

can be determined with a rule of mixtures as:

Enet = φaEa + 1−φa( )Eb , (S14)

where φ is volume fraction, a refers to the thin reinforced layer containing the UHMR particles,

and b refers to the pure polymer layer. To accurately determine the volume fraction of the thin

reinforced region, scanning electron micrographs similar to that shown in Figure S2b were ana-

lyzed. It was found that φa = 0.3. Assuming an elastic modulus, Eb, equal to 250 MPa for the

non-reinforced polyurethane layer, we obtain a Young’s modulus, Ea, of 450 MPa for the thin

reinforced layer.

   

14

FIGURES

Figure S1 – Focused-Ion Beam Scanning Electron Micrographs of alumina-polyurethane com-

posites showing clear orientational preference of UHMR particles: a) with no field and b) under

an external magnetic field.

Figure S2 – a) Photograph of the locally reinforced alumina-polyurethane composite synthe-

sized through concentrating the UHMR particles into a thin region of the film (dark brown). b)

Scanning electron micrograph of cross-section of same film depicting clear bi-layer structure in

these samples.

   

15

Figure S3 – Scanning electron micrographs of the surface of out-of-plane reinforced alumina-

polyurethane composites a) before and b) after 1 hour incubation in 14M phosphoric acid solu-

tion. Iron oxide nanoparticles (small white dots in (a)) are dissolved during this treatment.

Figure S4 – Dental resin composites containing 1 vol% of UHMR alumina platelets in a) in-

plane and b) out-of-plane configurations.

   

16

Figure S5 – a-d) Epoxy composite laminates containing 10 vol% of UHMR alumina platelets in

the different configurations schematically shown in Figure 3e. e) Picture of the three-point bend-

ing apparatus used to test the flexural properties of these samples.

Figure S6 – Schematic of platelet angle orientation.

   

17

Figure S7 – Magnetic and gravitational energies of UHMR platelets versus angle relative to

substrate (Figure S1) for 7.5 μm alumina platelets coated with 0.5 vol % magnetic nanoparticles

for different magnetic fields. As field increases, the energy landscape becomes dominated by

the magnetic energy indicating out-of-plane alignment.

Figure S8 – a) Probability of UHMR platelets to be in different orientational states for 7.5 μm

alumina platelets coated with 0.5 vol % magnetic nanoparticles under different magnetic fields.

b) The corresponding complementary cumulative distribution function. The probability for align-

ment makes a sharp transition around 1 mT, (as verified experimentally), when magnetic energy

outweighs gravitational energy. The spread in the curves is due to thermal randomization.

   

18

Figure S9 – Schematic of rod angle orientation

Figure S10 – Magnetic and gravitational energies of UHMR rods versus angle relative to sub-

strate (Figure S1) for 10 μm calcium sulfate rods coated with 0.5 vol % magnetic nanoparticles

for different magnetic fields. As field increases, the energy landscape becomes dominated by

the magnetic energy indicating out-of-plane alignment.

   

19

Figure S11 – a) Probability of UHMR rods to be in different orientational states for 10 μm calci-

um sulfate rods coated with 0.5 vol % magnetic nanoparticles for different magnetic fields. b)

The corresponding complementary cumulative distribution function. The probability for align-

ment makes a transition at 1.5 mT, (as verified experimentally), when magnetic energy out-

weighs gravitational energy. The spread in the curves is due to thermal randomization.

   

20

TABLE

Table S1. Tensile testing results for the homogeneous polyurethane composites described

above.

Sample Young’s Modulus Tensile Strength Strain at Rupture

Polyurethane + 20%

PVP

523 ± 148 MPa 28.64 ± 4.59 MPa 246.6 ± 74.4%

Polyurethane + 20%

PVP+ 20%Al2O3

(Parallel)

1471 ± 104 MPa 46.82 ± 2.30 MPa 4.83 ± 0.75%

Polyurethane + 20%

PVP+ 20%Al2O3

(Perpendicular)

1313 ± 200 MPa 25.21 ± 1.58 MPa 2.68 ± 0.38%

MOVIE

Movie S1 shows the real-time response of magnetized alumina platelets suspended in water in

the presence of an out-of-plane magnetic field in the order of 10 milliTesla. The movie depicts

the top view of a suspension of platelets deposited on a microscope slide while the magnetic

field is switched on and off.

   

21

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