1. Temperature Dependence of the
Specific Absorption Rate of a
Frozen Ferrofluid
Presented by:
Nathaniel Mosher
Kettering University
Flint, Michigan
Other contributors:
R.J. Tackett, R.E. Kumon, C. Rablau, E. Perkins-Harbin,
L. Wang, J.S. Thakur, and P.P. Vaishnava

2. Motivation
Specific
AbsorptionRate
Temperature
?
Brownian Relaxation
Néel Relaxation

3. Specific Absorption Rate (SAR) of Ferrofluid
S𝐴𝑅 =
𝑀𝑠𝑎𝑚𝑝𝑙𝑒
𝑚 𝑁𝑃
𝐶𝑖𝑐𝑒
∆𝑇
∆𝑡
𝑆𝐴𝑅 =
𝑃
𝑚 𝑁𝑃
=
𝜇0 𝜋𝜒′′
𝑓𝐻0
2
𝑚 𝑁𝑃
First Law of Thermodynamics in the Adiabatic Limit
Cice(T) per Yen, et. al. CRREL-81-10 (1981).

4. Turning off Brownian Relaxation by Freezing
VS
Fluid
Dependent
Magnetic
Anisotropy
Dependent
Brownian Relaxation Néel Relaxation

5. Synthesis of Fe3O4 via coprecipitation
Iron oxide
nanoparticles
+
NaOH
Add Dextran (15-20 kDa)
Dextran coated
Fe3O4
Sonicate for
24 h
FeCl2.4H2O
+
HCl(aq)
Add
NH4OH
until pH 10
Iron oxide
nanoparticles
FeCl3.6H2O
+
HCl(aq)
Fe3O4
Nanoparticle
Dextran
Molecule
O2
protection

6. Sample is Fe3O4 with a 13.4 ±4.7 nm diameter
1.5 2.0 2.5 3.0
(442)
(531)
(440)
(333)
(422)
(331)
(400)
(222)
(311)
I(arb.units)
d (Å)
(220)
Space Group: Fm3m
a = 8.36 Å
20 nm
0 5 10 15 20 25 30 35
0
5
10
15
20
25
NumberofParticles
Nanoparticle diameter (nm)
𝐷 = 13.4 nm ± 4.7 nm

7. Experimental Setup for Hyperthermia
Copper
coil
Amplification
Circuit
Transformer
C1 C2
Induction Heating System
Sample
vial
Frozen
ferrofluid
Thermometer
Fiber optic
sensor
Computer
Thermal
insulation

8. Temperature curves were recorded with/without
alternate magnetic fields and then fitted
𝑆𝐴𝑅magnetic 𝑇 =
𝑀sample
𝑚np
𝐶ice 𝑇
∆𝑇magnetic
∆𝑡
𝑆𝐴𝑅ambient 𝑇 =
𝑀sample
𝑚np
𝐶ice 𝑇
∆𝑇ambient
∆𝑡
0 30 60 90 120 150 180 210 240 270
-110
-100
-90
-80
-70
-60
-50
-40
Ambient
T(°C)
t (s)
0 10 20 30 40 50 60 70 80
-110
-100
-90
-80
-70
-60
-50
-40
150kHz
232kHz
T(°C)
t (s)
Magnetic Field On Magnetic Field Off

9. SAR has significant ambient component that
was subtracted
𝑆𝐴𝑅corrected 𝑇 = 𝑆𝐴𝑅magnetic 𝑇 − 𝑆𝐴𝑅ambient 𝑇
-110 -100 -90 -80 -70 -60 -50 -40
45
50
55
60
65
70
75
80
Uncorrected
Corrected
SAR(W/g)
T (°C)
150 kHz
-110 -100 -90 -80 -70 -60 -50 -40
85
90
95
100
105
110
115
Uncorrected
Corrected
SAR(W/g)
T (°C)
232 kHz

10. SAR shows a temperature dependence
-110 -100 -90 -80 -70 -60 -50 -40
82
84
86
88
90
92
SAR(W/g) T (°C)
232 kHz
~10 % decrease in SAR
over the temperature interval
-110 -100 -90 -80 -70 -60 -50 -40
44
46
48
50
52
54
56
SAR(W/g)
T (°C)
150 kHz
~20 % decrease in SAR
over the temperature interval

11. 0 10 20 30 40 50 60 70 80
-110
-100
-90
-80
-70
-60
-50
-40
150kHz
232kHz
T(°C)
t (s)
-110 -100 -90 -80 -70 -60 -50 -40
45
50
55
60
65
70
75
80
Uncorrected
Corrected
SAR(W/g)
T (°C)
150 kHz
-110 -100 -90 -80 -70 -60 -50 -40
44
46
48
50
52
54
56
SAR(W/g)
T (°C)
150 kHz
~20 % decrease in SAR
over the temperature interval
Summary

12. Conclusions
-110 -100 -90 -80 -70 -60 -50 -40
44
46
48
50
52
54
56
SAR(W/g)
T (°C)
150 kHz
~20 % decrease in SAR
over the temperature interval
• SAR shows
temperature
dependence
in Néel regime
• Ambient needs
correcting for
accurate results
Future Work
• Extending results to liquid samples
• Quantify Brownian contribution

13. Acknowledgements
We thank Research Council and the Provost of Kettering
university Dr. James Zhang for the award of the Academic
Research Fellowship and the travel grant.
Also, we thank the Society of Physics Students for providing a
research grant as well as a travel grant
Questions?