Metal nanoparticle has been a promising option for fillers in thermal interface materials due to its low cost and ease of fabrication. However, nanoparticle aggregation effect is not well understood because of its complexity. Theoretical models, like effective medium approximation model, barely cover aggregation effect. In this work, we have fabricated nickel–epoxy nanocomposites and observed higher thermal conductivity than effective medium theory predicts. Smaller particles are also found to show higher thermal conductivity, contrary to classical models indicate. A two-level effective medium approximation (EMA) model is developed to account for aggregation effect and to explain the size-dependent enhancement of thermal conductivity by introducing local concentration in aggregation structures.

References

References
1.
Ellis
,
B.
,
1993
,
Chemistry and Technology of Epoxy Resins
,
Blackie Academic & Professional
,
New York
.
2.
Hsu
,
S. H.
,
Chou
,
C. W.
, and
Tseng
,
S. M.
,
2004
, “
Enhanced Thermal and Mechanical Properties in Polyurethane/Au Nanocomposites
,”
Macromol. Mater. Eng.
,
289
(
12
), pp.
1096
1101
.
3.
Karthikeyan
,
N.
,
Philip
,
J.
, and
Raj
,
B.
,
2008
, “
Effect of Clustering on the Thermal Conductivity of Nanofluids
,”
Mater. Chem. Phys.
,
109
(
1
), pp.
50
55
.
4.
Pardiñas-Blanco
,
I.
,
Hoppe
,
C. E.
,
López-Quintela
,
M.
, and
Rivas
,
J.
,
2007
, “
Control on the Dispersion of Gold Nanoparticles in an Epoxy Network
,”
J. Non-Cryst. Solids
,
353
(
8–10
), pp.
826
828
.
5.
Philip
,
J.
,
Shima
,
P. D.
, and
Raj
,
B.
,
2008
, “
Evidence for Enhanced Thermal Conduction Through Percolating Structures in Nanofluids
,”
Nanotechnology
,
19
(
30
), p.
305706
.
6.
Philip
,
J.
,
Shima
,
P. D.
, and
Raj
,
B.
,
2008
, “
Nanofluid With Tunable Thermal Properties
,”
Appl. Phys. Lett.
,
92
(
4
), pp.
2
5
.
7.
Philip
,
J.
,
Shima
,
P. D.
, and
Raj
,
B.
,
2007
, “
Enhancement of Thermal Conductivity in Magnetite Based Nanofluid Due to Chainlike Structures
,”
Appl. Phys. Lett.
,
91
(
20
), pp.
2
5
.
8.
Reinecke
,
B. N.
,
Shan
,
J. W.
,
Suabedissen
,
K. K.
, and
Cherkasova
,
A. S.
,
2008
, “
On the Anisotropic Thermal Conductivity of Magnetorheological Suspensions
,”
J. Appl. Phys.
,
104
(
2
), p. 023507.
9.
Wu
,
S.
,
Ladani
,
R. B.
,
Zhang
,
J.
,
Kinloch
,
A. J.
,
Zhao
,
Z.
,
Ma
,
J.
,
Zhang
,
X.
,
Mouritz
,
A. P.
,
Ghorbani
,
K.
, and
Wang
,
C. H.
,
2015
, “
Epoxy Nanocomposites Containing Magnetite-Carbon Nanofibers Aligned Using a Weak Magnetic Field
,”
Polymer
,
68
, pp.
25
34
.
10.
Zhu
,
H.
,
Zhang
,
C.
,
Liu
,
S.
,
Tang
,
Y.
, and
Yin
,
Y.
,
2006
, “
Effects of Nanoparticle Clustering and Alignment on Thermal Conductivities of Fe3O4 Aqueous Nanofluids
,”
Appl. Phys. Lett.
,
89
(
2
), p. 023123.
11.
Lee
,
J.-H.
,
Lee
,
S.-H.
,
Choi
,
C. J.
,
Jang
,
S. P.
, and
Choi
,
S. U. S.
,
2011
, “
A Review of Thermal Conductivity Data, Mechanisms and Models for Nanofluids
,”
Int. J. Micro-Nano Scale Transp.
,
1
(
4
), pp.
269
322
.
12.
Lee
,
S.
,
Cahill
,
D. G.
, and
Allen
,
T. H.
,
1995
, “
Thermal Conductivity of Sputtered Oxide Film
,”
Phys. Rev. B
,
52
(
1
), pp.
253
257
.
13.
Wang
,
M.
, and
Pan
,
N.
,
2008
, “
Predictions of Effective Physical Properties of Complex Multiphase Materials
,”
Mater. Sci. Eng., R
,
63
(
1
), pp.
1
30
.
14.
Maxwell
,
J.
,
1954
,
A Treatise on Electricity and Magnetism
,
Dover Publications
, Mineola, NY.
15.
Garnett
,
J. C. M.
,
1906
, “
Colours in Metal Glasses, in Metallic Films, and in Metallic Solutions. II
,”
Philos. Trans. R. Soc., A
,
205
(
387–401
), pp.
237
288
.
16.
Hamilton
,
R. L.
, and
Crosser
,
O. K.
,
1962
, “
Thermal Conductivity of Heterogeneous Two-Component Systems
,”
Ind. Eng. Chem. Fundam.
,
1
(
3
), pp.
187
191
.
17.
Minnich
,
A.
, and
Chen
,
G.
,
2007
, “
Modified Effective Medium Formulation for the Thermal Conductivity of Nanocomposites
,”
Appl. Phys. Lett.
,
91
(
7
), p.
073105
.
18.
Nan
,
C.-W.
,
Birringer
,
R.
,
Clarke
,
D. R.
, and
Gleiter
,
H.
,
1997
, “
Effective Thermal Conductivity of Particulate Composites With Interfacial Thermal Resistance
,”
J. Appl. Phys.
,
81
(
10
), pp.
6692
6699
.
19.
Eucken
,
A.
,
1932
, “
Thermal Conductivity of Ceramic Refractory Materials: Calculation From Thermal Conductivities of Constituents
,” Ceramic Abstracts, Vol. 11.
20.
Landauer
,
R.
,
1952
, “
The Electrical Resistance of Binary Metallic Mixtures
,”
J. Appl. Phys.
,
23
(
7
), pp.
779
784
.
21.
Zhang
,
G.
,
Xia
,
Y.
,
Wang
,
H.
,
Tao
,
Y.
,
Tao
,
G.
,
Tu
,
S.
, and
Wu
,
H.
,
2010
, “
A Percolation Model of Thermal Conductivity for Filled Polymer Composites
,”
J. Compos. Mater.
,
44
(
8
), pp.
963
970
.
22.
Nan
,
C.-W.
,
1993
, “
Physics of Inhomogeneous Inorganic Materials
,”
Prog. Mater. Sci.
,
37
(
1
), pp.
1
116
.
23.
Nan
,
C.-W.
,
Shen
,
Y.
, and
Ma
,
J.
,
2010
, “
Physical Properties of Composites Near Percolation
,”
Annu. Rev. Mater. Res.
,
40
(
1
), pp.
131
151
.
24.
Wang
,
B. X.
,
Zhou
,
L. P.
, and
Peng
,
X. F.
,
2003
, “
A Fractal Model for Predicting the Effective Thermal Conductivity of Liquid With Suspension of Nanoparticles
,”
Int. J. Heat Mass Transfer
,
46
(
14
), pp.
2665
2672
.
25.
Meakin
,
P.
,
Majid
,
I.
,
Havlin
,
S.
, and
Stanley
,
H. E.
,
1999
, “
Topological Properties of Diffusion Limited Aggregation and Cluster–Cluster Aggregation
,”
J. Phys. A: Math. Gen.
,
17
(
18
), pp.
L975
L981
.
26.
Meakin
,
P.
,
1987
, “
Fractal Aggregates
,”
Adv. Colloid Interface Sci.
,
28
, pp.
249
331
.
27.
Prasher
,
R.
,
Evans
,
W.
,
Meakin
,
P.
,
Fish
,
J.
,
Phelan
,
P.
, and
Keblinski
,
P.
,
2006
, “
Effect of Aggregation on Thermal Conduction in Colloidal Nanofluids
,”
Appl. Phys. Lett.
,
89
(
14
), pp.
1
4
.
28.
Evans
,
W.
,
Prasher
,
R.
,
Fish
,
J.
,
Meakin
,
P.
,
Phelan
,
P.
, and
Keblinski
,
P.
,
2008
, “
Effect of Aggregation and Interfacial Thermal Resistance on Thermal Conductivity of Nanocomposites and Colloidal Nanofluids
,”
Int. J. Heat Mass Transfer
,
51
(
5–6
), pp.
1431
1438
.
29.
Chen
,
G.
,
1998
, “
Thermal Conductivity and Ballistic-Phonon Transport in the Cross-Plane Direction of Superlattices
,”
Phys. Rev. B
,
57
(
23
), pp.
14958
14973
.
30.
Chen
,
C.
, and
Curliss
,
D.
,
2003
, “
Preparation, Characterization, and Nanostructural Evolution of Epoxy Nanocomposites
,”
Appl. Polym. Sci.
,
90
(
8
), pp. 2276–2287.
31.
Cahill
,
D. G.
,
1990
, “
Thermal Conductivity Measurement From 30 to 750 K: The 3ω Method
,”
Rev. Sci. Instrum.
,
61
(
2
), pp.
802
808
.
32.
Cahill
,
D. G.
,
1989
, “
Thermal Conductivity of Thin Films: Measurements and Understanding
,”
J. Vac. Sci. Technol., A
,
7
(
3
), pp.
1259
1266
.
33.
Bodenschatz
,
N.
,
Liemert
,
A.
,
Schnurr
,
S.
,
Wiedwald
,
U.
, and
Ziemann
,
P.
,
2013
, “
Extending the 3ω Method: Thermal Conductivity Characterization of Thin Films
,”
Rev. Sci. Instrum.
,
84
(
8
), p. 084904.
34.
Borca-Tasciuc
,
T.
,
Kumar
,
A. R.
, and
Chen
,
G.
,
2001
, “
Data Reduction in 3ω Method for Thin-Film Thermal Conductivity Determination
,”
Rev. Sci. Instrum.
,
72
(
4
), pp.
2139
2147
.
35.
Hashin
,
Z.
, and
Shtrikman
,
S.
,
1962
, “
A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials
,”
J. Appl. Phys.
,
33
(
10
), pp.
3125
3131
.
36.
Pashayi
,
K.
,
Fard
,
H. R.
,
Lai
,
F.
,
Iruvanti
,
S.
,
Plawsky
,
J.
, and
Borca-Tasciuc
,
T.
,
2012
, “
High Thermal Conductivity Epoxy-Silver Composites Based on Self-Constructed Nanostructured Metallic Networks
,”
J. Appl. Phys.
,
111
(
10
), p.
104310
.
37.
Toprak
,
M.
,
Stiewe
,
C.
,
Platzek
,
D.
,
Williams
,
S.
,
Bertini
,
L.
,
Muller
,
E.
,
Gatti
,
C.
,
Zhang
,
Y.
,
Rowe
,
M.
, and
Muhammed
,
M.
,
2004
, “
The Impact of Nanostructuring on the Thermal Conductivity of Thermoelectric CoSb3
,”
Adv. Funct. Mater.
,
14
(
12
), pp.
1189
1196
.
38.
Ong
,
W.-L.
,
Majumdar
,
S.
,
Malen
,
J. A.
, and
McGaughey
,
A. J. H.
,
2014
, “
Coupling of Organic and Inorganic Vibrational States and Their Thermal Transport in Nanocrystal Arrays
,”
J. Phys. Chem. C
,
118
(
14
), pp.
7288
7295
.
39.
Wang
,
Y.
,
Ruan
,
X.
, and
Roy
,
A. K.
,
2012
, “
Two-Temperature Nonequilibrium Molecular Dynamics Simulation of Thermal Transport Across Metal-Nonmetal Interfaces
,”
Phys. Rev. B
,
85
(
20
), p.
205311
.
You do not currently have access to this content.