Supporting Information Magnetic Elastomers for Stretchable Inductors
Supporting Information
Magnetic Elastomers for Stretchable Inductors Nathan Lazarus1*, Chris D. Meyer1, Sarah S. Bedair1, Geoffrey A. Slipher1, and Iain M. Kierzewski2 1
US Army Research Laboratory, 2800 Powder Mill Rd., Adelphi, MD 20783
2
General Technical Services, 2800 Powder Mill Rd., Adelphi, MD 20783
*Corresponding author: [email protected]
S1
Experimental Section Ferroelastomer preparation: Equal volumes of parts A and B of Ecoflex 00-30 silicone (Smooth-on) were mixed together for a minimum of a minute and a half, followed by degassing at -95 kPa vacuum. The appropriate mass of magnetic particles were then added and stirred for a minimum of 3 minutes by hand to reach a uniform appearance and viscosity, followed again by degassing completely at -95 kPa, first in a polyethylene beaker then again in the desired mold. The sample is then heated to 85˚C on a hotplate until fully cured. Characterization: Each inductor was measured using an Agilent 4294A precision impedance analyzer (40 Hz to 110 MHz) to obtain the reactance and resulting inductance over frequency. The inductance was then extracted by averaging the value at low frequencies, at least an order of magnitude below the resonant frequency of the inductor. Magnetic core inductor fabrication: The stretchable inductors tested in this work consist of three layers, a molded (ferroelastomer) layer with two unpatterned Ecoflex 00-30 sealing layers on the top and bottom. 3D printed molds, printed in either acrylonitrile butadiene styrene (ABS) or polycarbonate (PC), were used to define channels for the liquid metal. After mixing and degassing as above, the uncured liquid ferroelastomer was poured into the bottom mold (Figure S2(b)), where the sample is again degassed for approximately 1 minute at -95 kPa. The top mold (Figure S2(a)) is then pushed into the ferrolastomer, with holes in the mold used to allow excess liquid to be removed. The sample is then heated to 85˚C on a hotplate until fully cured. The molded part is then removed from the molds and a hollow syringe tip is used to verify that the via holes are completely clear of ferroelastomer. For sealing, a layer of liquid Ecoflex 00-30 precursors are poured into a blank mold and allowed to partially cure at room temperature for S2
one hour and ten minutes; the molded ferroelastomer part is then laid onto the partially cured silicone and a weight is applied. The silicone is then fully cured on a hotplate at 85˚C. The sealing process is done twice, to seal the top and bottom set of fluidic channels respectively. Inlet and outlet holes are cored out using a narrow gauge hollow syringe tip, followed by injection with liquid metal and sealing with drops of uncured Ecoflex 00-30. Particle spacing discussion: Stretching along either axis for the ferroelastomer results in a drop in permeability. This results from an increase in the average particle spacing within the elastomer. In an incompressible material, the volume upon stretching remains unchanged. Alternatively, this means that the strains along each Cartesian axis εx, εy, and εz must satisfy the expression: (1 x )(1 y )(1 z ) 1
(S.1)
With a uniaxial strain in x, and assuming equal deformations in y and z, this means that the strains are related according to: (1 y ) (1 z )
1 (1 x )
(S.2)
For two neighboring particles, the distance between them after an applied uniaxial strain in x is therefore:
d stretch (1 x ) 2 ( xinit ) 2
1 1 ( yinit ) 2 ( zinit ) 2 (1 x ) (1 x )
(S.3)
with xinit, yinit and zinit being the initial distance along each axis. Particles located along the x axis get farther apart, while along the y and z axes they get closer together. If the particles are randomly distributed, however, most particles get farther apart than closer together. Figure S3 S3
shows an example case, with particles oriented in the xy plane (meaning that zinit is zero), with the initial distance normalized to one. Since the projection onto the x axis increases linearly, but the projection onto y decreases only with a square root relation, more than 80% of particles increase in distance. The average particle spacing therefore increases, resulting in the drop in permeability for stretching in either direction.
S4
Cumulative Distribution (%)
Supplementary Figures: 100 80
60 40 20 0 0
20 Particle Size (μm)
40
Cumulative Distribution (%)
(a) 100 80 60 40 20
0 0
100 Particle Size (μm)
200
(b) Figure S1. Particle distributions for (a) molypermalloy powder and (b) Sendust platelets. The Sendust distribution was provided by the manufacturer datasheet, the molypermalloy powder size distribution was measured based on optical size estimation of 180 particles.
S5
Hole for excess silicone
Alignment ring (a)
Inlet
Alignment peg
Outlet (b)
Figure S2. (a) Top and (b) bottom 3D printed molds for fabricating stretchable solenoid oriented with strains parallel to inductor core direction
S6
1+εx
After stretching 1
dstretch
Before stretching 1
1 1 x (a)
Yinit
Unstrained
10% X Strain
50% X Strain
100% X Strain
dstretch (Normalized)
2.5
2
1.5
1
0.5 0
0.2
0.4 0.6 Yinit (Normalized)
0.8
1
(b) Figure S3. Calculation of particle spacing upon uniaxial strain in the x direction for arbitrarily positioned particles in the xy plane: (a) geometry definitions (εx is applied strain in x direction)
S7
and (b) calculated particle spacing after stretching. Particles with dstretch greater than 1 on the plot have increased in spacing compared with initial (normalized) distance
S8
Inductance (nH)
700 650 600 550 500 0
1
2
3
4
5
3
4
5
4
5
Cycle
(a)
Inductance (nH)
700
650
600
550 0
1
2 Cycle
(b) Sendust
MPP
Relative Permeability
3
2.9 2.8
2.7 2.6 2.5 0
1
2
3 Cycle
(c) Figure S4. Measured inductance for five cycle loading test to 40% maximum applied uniaxial strain for (a) 80% MPP and (b) 20% Sendust ferroelastomers and (c) plot of relative permeability S9
in each case. The stretchable inductors used were oriented with axis perpendicular to the direction of applied strain, and data points were taken every 10% increment of applied strain.
Table S1. Survey of silicone-based ferroelastomers particle size 100 nm 5 μm 5 μm 5 μm 5 μm 10 nm
Magnetic Elastomers for Stretchable Inductors Nathan Lazarus1*, Chris D. Meyer1, Sarah S. Bedair1, Geoffrey A. Slipher1, and Iain M. Kierzewski2 1
US Army Research Laboratory, 2800 Powder Mill Rd., Adelphi, MD 20783
2
General Technical Services, 2800 Powder Mill Rd., Adelphi, MD 20783
*Corresponding author: [email protected]
S1
Experimental Section Ferroelastomer preparation: Equal volumes of parts A and B of Ecoflex 00-30 silicone (Smooth-on) were mixed together for a minimum of a minute and a half, followed by degassing at -95 kPa vacuum. The appropriate mass of magnetic particles were then added and stirred for a minimum of 3 minutes by hand to reach a uniform appearance and viscosity, followed again by degassing completely at -95 kPa, first in a polyethylene beaker then again in the desired mold. The sample is then heated to 85˚C on a hotplate until fully cured. Characterization: Each inductor was measured using an Agilent 4294A precision impedance analyzer (40 Hz to 110 MHz) to obtain the reactance and resulting inductance over frequency. The inductance was then extracted by averaging the value at low frequencies, at least an order of magnitude below the resonant frequency of the inductor. Magnetic core inductor fabrication: The stretchable inductors tested in this work consist of three layers, a molded (ferroelastomer) layer with two unpatterned Ecoflex 00-30 sealing layers on the top and bottom. 3D printed molds, printed in either acrylonitrile butadiene styrene (ABS) or polycarbonate (PC), were used to define channels for the liquid metal. After mixing and degassing as above, the uncured liquid ferroelastomer was poured into the bottom mold (Figure S2(b)), where the sample is again degassed for approximately 1 minute at -95 kPa. The top mold (Figure S2(a)) is then pushed into the ferrolastomer, with holes in the mold used to allow excess liquid to be removed. The sample is then heated to 85˚C on a hotplate until fully cured. The molded part is then removed from the molds and a hollow syringe tip is used to verify that the via holes are completely clear of ferroelastomer. For sealing, a layer of liquid Ecoflex 00-30 precursors are poured into a blank mold and allowed to partially cure at room temperature for S2
one hour and ten minutes; the molded ferroelastomer part is then laid onto the partially cured silicone and a weight is applied. The silicone is then fully cured on a hotplate at 85˚C. The sealing process is done twice, to seal the top and bottom set of fluidic channels respectively. Inlet and outlet holes are cored out using a narrow gauge hollow syringe tip, followed by injection with liquid metal and sealing with drops of uncured Ecoflex 00-30. Particle spacing discussion: Stretching along either axis for the ferroelastomer results in a drop in permeability. This results from an increase in the average particle spacing within the elastomer. In an incompressible material, the volume upon stretching remains unchanged. Alternatively, this means that the strains along each Cartesian axis εx, εy, and εz must satisfy the expression: (1 x )(1 y )(1 z ) 1
(S.1)
With a uniaxial strain in x, and assuming equal deformations in y and z, this means that the strains are related according to: (1 y ) (1 z )
1 (1 x )
(S.2)
For two neighboring particles, the distance between them after an applied uniaxial strain in x is therefore:
d stretch (1 x ) 2 ( xinit ) 2
1 1 ( yinit ) 2 ( zinit ) 2 (1 x ) (1 x )
(S.3)
with xinit, yinit and zinit being the initial distance along each axis. Particles located along the x axis get farther apart, while along the y and z axes they get closer together. If the particles are randomly distributed, however, most particles get farther apart than closer together. Figure S3 S3
shows an example case, with particles oriented in the xy plane (meaning that zinit is zero), with the initial distance normalized to one. Since the projection onto the x axis increases linearly, but the projection onto y decreases only with a square root relation, more than 80% of particles increase in distance. The average particle spacing therefore increases, resulting in the drop in permeability for stretching in either direction.
S4
Cumulative Distribution (%)
Supplementary Figures: 100 80
60 40 20 0 0
20 Particle Size (μm)
40
Cumulative Distribution (%)
(a) 100 80 60 40 20
0 0
100 Particle Size (μm)
200
(b) Figure S1. Particle distributions for (a) molypermalloy powder and (b) Sendust platelets. The Sendust distribution was provided by the manufacturer datasheet, the molypermalloy powder size distribution was measured based on optical size estimation of 180 particles.
S5
Hole for excess silicone
Alignment ring (a)
Inlet
Alignment peg
Outlet (b)
Figure S2. (a) Top and (b) bottom 3D printed molds for fabricating stretchable solenoid oriented with strains parallel to inductor core direction
S6
1+εx
After stretching 1
dstretch
Before stretching 1
1 1 x (a)
Yinit
Unstrained
10% X Strain
50% X Strain
100% X Strain
dstretch (Normalized)
2.5
2
1.5
1
0.5 0
0.2
0.4 0.6 Yinit (Normalized)
0.8
1
(b) Figure S3. Calculation of particle spacing upon uniaxial strain in the x direction for arbitrarily positioned particles in the xy plane: (a) geometry definitions (εx is applied strain in x direction)
S7
and (b) calculated particle spacing after stretching. Particles with dstretch greater than 1 on the plot have increased in spacing compared with initial (normalized) distance
S8
Inductance (nH)
700 650 600 550 500 0
1
2
3
4
5
3
4
5
4
5
Cycle
(a)
Inductance (nH)
700
650
600
550 0
1
2 Cycle
(b) Sendust
MPP
Relative Permeability
3
2.9 2.8
2.7 2.6 2.5 0
1
2
3 Cycle
(c) Figure S4. Measured inductance for five cycle loading test to 40% maximum applied uniaxial strain for (a) 80% MPP and (b) 20% Sendust ferroelastomers and (c) plot of relative permeability S9
in each case. The stretchable inductors used were oriented with axis perpendicular to the direction of applied strain, and data points were taken every 10% increment of applied strain.
Table S1. Survey of silicone-based ferroelastomers particle size 100 nm 5 μm 5 μm 5 μm 5 μm 10 nm
