SUPPORTING INFORMATION
High Thermal Conductivity Epoxy-Silver Composites Based on SelfConstructed Nanostructured Metallic Networks
Kamyar Pashayi§, Hafez Raeisi Fard§, Fengyuan Lai#
Sushumna Iruvanti‡, Joel Plawsky†, and Theodorian Borca-Tasciuc§,a)
§
Department of Mechanical, Aerospace and Nuclear Engineering, #Department of Materials
Science and Engineering, †Department of Chemical and Biological Engineering
Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA
‡
I.
IBM Systems & Technology Group, Hopewell Junction, NY 12533, USA
Microscopy images of particles
Figure S1 shows SEM and TEM images of silver microparticle and nanocomposite
respectively. These images prove particle sizes are the same as specified by manufacturer.
FIG. S1. a) SEM of silver microparticles after dispersion on a substrate and b) TEM of dispersed
silver nanoparticles in epoxy matrix at low volume fraction (< 1 vol%).
a)
Author to whom all correspondence should be addressed; electronic mail: borcat@rpi.edu
1
II.
Sample fabrication
Figure S2 shows schematically the fabrication steps for the composites, as described in the
methods section.
FIG. S2. Schematic of the fabrication process of the silver/epoxy composite: (a) high speed
sheer mixing of resin and hardener, (b) sonication of silver particles with epoxy for 1 h, (c)
molding the slurry in a silicone mold, (d) gas removal at room temperature for 2 hours, (e)
composite curing in Argon gas atmosphere at 150 ºC, (f) polishing of cured composite
III.
SEM of 20nm particle powders after sintering
Figure S3 shows an SEM image of 20nm silver particles after annealing at 150 ºC for 1 h in
Argon gas atmosphere. The particle-particle contact through necking characteristic to sintering is
evident in this image.
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FIG. S3. SEM of 20 nm silver nanoparticle powders after annealing at 150 ºC.
IV.
DSC for pure epoxy and PVP
The DSC curves in Figure S4a and Figure S4b show a phase transition around 165 ºC and
150 ºC for pure epoxy and PVP, respectively. These peaks represent curing and melting
temperature of pure epoxy and PVP respectively.
1.00
-0.10
-0.20
Heat Flow (W/g)
Heat Flow (W/g)
0.00
-1.00
-2.00
-3.00
-4.00
-5.00
50
-0.40
-0.50
a
0
-0.30
-0.60
0
100 150 200 250 300 350
Temperature (°C)
b
50
100 150 200 250 300
Temperature (°C)
350
FIG. S4. Differential scanning calorimetry of pure epoxy (a) and pure PVP (b) reveals curing of
the epoxy and melting of PVP at ~165 °C and 150 °C respectively.
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V.
Experimental thermal resistance measurements and data reduction
Figure S5 shows the schematic of the setup used for thermal conductivity measurement of the
composite samples. This setup consists of an electrical heater, a heat sink, and two
thermocouples to measure the thermal gradient. Thermocouples were embedded into soft indium
layers to allowthermal contact with the sample surface. Pressure is applied using a screw
mechanism that is thermally insulated from the sample by a thick Lexan block. A temperature
gradient is generated across the sample by applying heat in the top section of the upper indium
layer and dissipating the heat through the sample and the lower section of indium to the attached
aluminum sink. The temperature difference vs. power is recorded using LabVIEW.
Figure S6 shows examples of the measured temperature difference vs. power for 1mm
thickness samples (pure epoxy, microcomposite with 35 vol.%, 4.2µm silver, and nanocomposite
with 35 vol.% 20nm).Temperature range in these experiments was between 25 ºC and 45 ºC. The
slope of the curves is used to determine the experimental thermal resistance. Nanocomposites
exhibit a much smaller thermal resistance than the microcomposites and the pure epoxy samples.
The slope of an experimental signal in Figure S6 is the total thermal resistance Rt, and is
the resultant thermal resistance of the parallel thermal resistance network containing the thermal
resistance for parasitic heat losses, Rhl and Rs+int (the sum of thermal resistance of the sample, Rs,
and the thermal resistance of the interfaces between the sample and the indium layers, Rint):
1
Rt
 1
Rhl
 1
Rs  int
 1
Rhl
 1
( Rs  Rint )
(1)
The heat losses are calibrated by testing samples of known  and high thermal resistance
such as glass slides of known thicknesses. The parasitic heat loss was found to be 250 K/W.
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FIG. S5. Schematic of the one-dimensional steady state thermal conductivity measurement
setup. The thermocouples were embedded in the center of the indium foil.
20
Pure Epoxy
Microcomposite
Nanocomposite
2
y = -0.93 + 85.78x R = 0.99
2
y = 0.19 + 39.50x R = 0.99
2
y = 0.28 + 2.08x R = 0.99
10
1
2
T -T (K)
15
5
0
0.0
0.5
1.0 1.5 2.0 2.5
HeaterPower(W)
3.0
3.5
FIG. S6. Measured temperature difference vs. power for 1 mm thickness samples of pure epoxy,
microcomposite with 20 vol%, 4.2 µm silver, and nanocomposite with 20 vol%, 20 nm silver.
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To account for the thermal resistance due to the two sample-indium interfaces, samples with
different thicknesses were tested as described below. In addition, to account for slight variations
in the cross-sectional area, A, from sample to sample, for each test the product A× (Rs+int) was
calculated, which yields the total resistivity of the sample plus the interfaces.
Two methods can be used to determine : the averaging method and the slope method. A
comparison of the two methods is shown in Table S1. The two methods yield similar results.
The uncertainty in the temperature measurement between the center of indium layers to
the edge is ±0.1 K. Uncertainty in measured voltages is ±0.01 Volt. The uncertainty in sample
thickness and sample area are ±0.01 mm and ±0.4 mm, respectively. The major contribution to
uncertainty in  measurements is due to sample thickness. The error bars in Figure 6 reflect the
actual uncertainties calculated for each sample.
Values for interface thermal resistivity (Table S1) are different between different
samples. In this work we used sand papers with ISO/FEPA grit designation between P30-P150.
Figure S7 shows a qualitative comparison between polished surfaces of microcomposites and
nanocomposites with 35 vol% fraction silver loading. The microcomposites present more defects
like pits, nicks, lines and scratches after polishing. These defects cause higher average interface
thermal resistivity in  measurements. This fact is verified by a comparison of the average
interface thermal resistance of microcomposites (109.1 mm2K/W) and nanocomposites (51.88
mm2W/K).
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Table S1. Interface and sample thermal properties. Propagation of uncertainty analysis is used to
estimate the uncertainties in each thermal conductivity experiment.
Silver
Interface
Thermal conductivity Thermal conductivity
Particle
concentration resistivity
size
from
averaging from the slope
(vol%)
(mm2K/W)
method (W/mK)
(W/mK)
15
77.60
0.20±0.01
0.20
25
9.60
0.31±0.00
0.31
35
149.79
0.44±0.02
0.38
45
91.06
0.58±0.03
0.59
15
141.20
0.22±0.01
0.22
25
162.16
0.32±0.02
0.32
35
213.61
0.56±0.06
0.57
45
27.85
0.57±0.03
0.58
15
55.41
4.10±0.06
4.22
25
24.38
10.82±0.14
11.07
35
3.86
17.72±0.24
19.77
45
30.69
27.19±0.61
27.12
15
20.70
3.55±0.67
3.62
25
5.95
6.97±0.19
7.14
35
218.09
15.94±0.38
15.85
45
56.12
23.97±0.68
24.30
1.8 µm
4.2 µm
20 nm
80 nm
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FIG. S7. SEM micrographs of polished surfaces of (a) microcomposites and (b) nanocomposites
with 35 vol% fraction silver loading.
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