Nanocomposites for thermoelectrics and thermal
engineering
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Liao, Bolin, and Gang Chen. “Nanocomposites for
Thermoelectrics and Thermal Engineering.” MRS Bulletin 40, no.
09 (September 2015): 746–752.
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http://dx.doi.org/10.1557/mrs.2015.197
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Cambridge University Press (Materials Research Society)
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Author's final manuscript
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Wed May 25 18:08:04 EDT 2016
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Nanocomposites for Thermoelectrics and Thermal Engineering
Bolin Liao and Gang Chen*
Abstract
The making of composites has served as a working principle of achieving material
properties beyond those of their homogeneous counterparts. The classical
effective medium theory, generally applicable to composites with domain sizes at
macroscale, models the constituent phases with local properties drawn from the
corresponding bulk values, and usually predicts the properties of a composite
being certain averages of its constituents. When the characteristic size of
individual domains in a composite shrinks to nanometer-scale, however, the
interactions between domains induced by interfacial and classical/quantum size
effects become important, or even dominant, and the classical effective medium
theories fall short of fully capturing these effects. These unique features of
nanocomposites have enabled engineering of novel thermoelectric materials with
synergistic effects among their constituents, and led to significant improvements
of the thermoelectric materials in recent years. For other applications requiring a
high thermal conductivity, however, interfacial and size effects on thermal
transport in nanocomposites are not favorable, although certain practical
applications often call for the composite approach. Therefore understanding
nanoscale transport in nanocomposites can help choose right strategies in
enhancing the thermal performance for different applications. We review the
emerging principles of heat and charge transport in nanocomposites and give
working examples from thermoelectrics as well as thermal engineering in general.
Keywords: nanocomposite; thermoelectrics; thermal engineering.
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Introduction
The possibility of converting thermal energy directly to electricity holds
promise of improving the efficiencies of current power systems as well as future
sustainable energy systems1. Solid-state thermoelectric (TE) materials2,3 hold this
promise via the celebrated Seebeck effect, where a temperature gradient drives the
thermal diffusion of charge carriers, giving rise to a counterbalancing electrical
voltage. The reverse (Peltier) effect, where a drift electrical current carries heat
along, can deliver cooling power without any moving parts or (potentially
hazardous) working fluids4. Attractive as it is, the application of TEs has long
been limited by their low efficiency. The efficiency of a TE device is proportional
(
)
to the nondimensional figure of merit zT º S 2s T k e + k p , where S is the
Seebeck coefficient defined as the ratio of the open circuit voltage to the applied
temperature difference ( S º - DV DT ), s is the electrical conductivity (the
combination S 2s is usually called the power factor), T is the absolute
temperature, and k e and k p are electron and phonon contributions to the
thermal conductivity, respectively. The low zT, and thus the low efficiency, stems
from the fact that these material properties are intertwined and usually show
opposite trends in a single material. For example, the Seebeck coefficient
measures the average entropy transported by charge carriers, and prefers
nonsymmetric transport properties of charge carriers above and below the Fermi
level (carriers above the Fermi level transport positive entropy, while carriers
below the Fermi level transport negative entropy). For this reason Seebeck
coefficient is usually high when the Fermi level is inside a band gap
(nondegenerate semiconductors), degrades when the Fermi level moves into a
band (degenerate semiconductors), and becomes negligibly small in a metal. On
the other hand, the electrical conductivity is proportional to the carrier
concentration and thus follows the opposite trend. This general correlation
between the Seebeck coefficient and the electrical conductivity is commonly
known as the Pisarenko relation5, which implies that increasing the carrier
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mobility is crucial for boosting the power factor. Moreover, the electronic thermal
conductivity usually grows with an increasing electrical conductivity, indicated by
the Wiedemann-Franz law ( k e = LT s , where L is a proportionality constant
called the “Lorenz number”6), due to the fact that heat and electricity is
transported by the same group of carriers in this case. Furthermore, although the
phonon thermal conductivity does not directly connect to the electronic properties,
the conventional methods of reducing the phonon thermal conductivity, such as
introducing defects and alloying, also increase the scattering of electrons, and
deteriorate the electrical conductivity. From the above discussion, it is clear that
an ideal TE material should possess a combination of properties of nondegenerate
semiconductors (a high Seebeck coefficient), metals (a high electrical
conductivity), insulators (a low electronic thermal conductivity) and amorphous
materials (a low phonon thermal conductivity). In this light, it is tempting to think
that creating mixtures of materials, i.e. composites, would be a promising route
towards better thermoelectrics.
The idea of making composites has long been exploited in materials
research for achieving balanced material properties. Classical modeling of
composites usually invokes the “effective medium theory”, which dates back to
the works of Lord Rayleigh7 and Maxwell8 on the effective electrical conductivity,
and of Maxwell-Garnett9 on the effective dielectric constant of a host material
containing minute particles of different materials, with the essential assumption
that the local material properties of a composite take on values of the
corresponding bulk constituent. This assumption is valid when sizes of individual
constituent domains are large so that the classical/quantum size effects10,11 can be
safely ignored as well as certain interfacial phenomena (such as the crossinterface static charge redistribution due to the mismatch of Fermi levels), the
local equilibrium distributions of carriers can be established and thus in general
applicable to macrocomposites, with domain sizes in the macro scale and much
larger than the carriers’ mean free path and/or coherence length. The effective
medium theory for macrocomposites has been applied to thermal transport, e.g. by
Nan et al.12, taking into account both the spatial distribution of the material
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properties and the Kapitza thermal interface resistance. It is worth mentioning that
even in the realm of macrocomposites and diffusive transport, the emerging
concept of “transformation thermodynamics”13 utilizing the form invariance of
the heat equation under coordinate transformations, in analogy to transformation
optics14, has enabled experimental designs15,16 of sophisticated thermal
functionalities, such as cloaks, concentrators and inverters. More surprisingly, the
diffusive nature of the heat equation renders it possible to realize exact thermal
cloaks with isotropic and homogeneous materials17–19, following the same
philosophy behind a successful design of static magnetic field cloaks20.
In the case of thermoelectrics, the analysis of a macrocomposite can be
traced back to Herring21 and was later extended by Bergman and Levy22 in an
elegant way, where they obtained effective thermoelectric properties of a twocomponent macrocomposite by decoupling the charge and heat transport via a
field transformation, and provided more general results for a multi-component
macrocomposite by a variational calculation. Their work indicated that zT of the
macrocomposite cannot exceed the largest zT of its components under most
practical conditions, although later studies pointed out possible exceptions23,24.
The complexity of the coupled charge and heat transport has prohibited a rigorous
treatment of two-phase macrocomposite thermoelectrics so far.
With the advent of nanotechnology in the past few decades, composites
with domain sizes down to nanoscale can now be routinely fabricated. With
domain sizes comparable to or smaller than the carriers’ mean free path and/or
coherence length, these nanocomposites can host a gamut of new properties due
to the ballistic/coherent transport of energy and charge carriers and interfacial
phenomena. While there exist modifications and extensions of the effective
medium theory to accommodate some of these effects25, a complete
understanding entails efficient modeling techniques through multiple length and
time scales, which are still under development. On the application side, these
added degrees of freedom in nanocomposites have broadened the available phase
space for the material optimization and enabled the synthesis of superior
nanocomposite TEs with enhanced zT much beyond unity26–30. Meanwhile, the
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possibility of coherent phonon transport in nanocomposites has opened up the
new research field of “phononics”, where the thermal transport can be potentially
controlled in extraordinary ways for diverse application opportunities.
Furthermore, thermal interface materials for many applications use composites to
improve the thermal transport of the base polymers, although “nano” may not be
the best approach due to the increased interface resistance. In this article we
review the unique features of transport properties emerging in nanocomposites
followed by examples in thermoelectrics and thermal engineering, including soft
nanocomposites, as summarized schematically in Fig. 1.
Interfacial Phenomena
One characteristic of nanocomposites is the high density of interfaces
between nano-sized domains, and thus various interactions between domains
across the interfaces play a significant role in the overall transport properties of
nanocomposites. One example is the static charge redistribution over the
interfaces, e.g. between nanodomains and the host matrix: charge carriers can
flow to the other side when there is a mismatch between the Fermi levels of the
nanodomain and the host. Since optimized thermoelectrics are usually heavilydoped semiconductors, conventional doping methods using uniformly distributed
atomic impurities can largely degrade the carrier mobility due to frequent ionizedimpurity scatterings. Doping with nanodomains bypasses this problem in that the
impurities are confined within the nanodomains, whereas conducting carriers
travel mostly in the host and thus are spatially separated from the scattering
centers. This concept of “modulation doping” has previously been applied to
microelectronics in planar structures to enhance the carrier mobility31,32. The
application of modulation doping to 3D bulk nanocomposites33,34 has been
demonstrated by mixing heavily-doped minority nanograins with undoped
majority nanograins and hot-pressing into a bulk nanocomposite, as depicted in
Fig. 2(a). With properly designed nanograin properties, it was shown in a Si/Ge
alloy34 that the power factor can be significantly enhanced above its uniformly
doped counterpart without increasing the thermal conductivity. The same concept
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has also been realized in other bulk nanocomposites35–37, Ge/Si core-shell
nanowires38, and similarly by the field-effect doping39.
Furthermore, the interfaces within a nanocomposite can be designed for
preferred carrier scattering characteristics. It has been known40 that the Seebeck
coefficient benefits from sharp changes of scattering rates with respect to the
carrier energy near the Fermi level. One prominent idea is to introduce impurity
states that resonant with the band continuum, leading to a peak in the carrier
scattering rate as well as the density of states41,42. Beyond atomic defects,
nanoscale domains (or nanoparticles, nanoprecipitates etc.) provide more degrees
of freedom in scattering engineering, such as the particle size, shape, composition
and spatial distribution. Unlike normal non-resonant atomic defects, whose
characteristic size is much smaller than the electron wavelength and thus invoke
Rayleigh-type scattering with monotonous dependence of scattering strength on
the electron energy43, nanoscale domains have comparable sizes to the electron
wavelength, and their scattering characteristics are analogous to Mie scattering of
electromagnetic waves44, where the interference effect is important and results in
much richer features in the scattering strength. In this regime, the partial wave
method45 can be used for exact calculations of the scattering cross section of
single nanodomains with regular shapes, and has been applied to designing
nanoparticles with desired scattering features46–48, including the electron
filtering49, where a cutoff energy is established below which carriers are much
more strongly scattered50–52.
The ideas of modulation doping and scattering engineering can be further
combined: although the modulation doping in bulk nanocomposites improves the
carrier mobility over the conventional uniform doping, the interfaces between
nanodomains and the host can still scatter or trap carriers33, compromising the
mobility enhancement. One solution is to design the geometry, composition and
structure of the nanodomains to minimize, or even vanish, their scattering cross
sections for carriers around the Fermi level. Furthermore, a sharp dip in the
spectrum of the scattering cross section can potentially improve the Seebeck
coefficient as well. Such a design was first put forward by Liao et al.53, as core-
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shell spherical nanoparticles with carefully designed geometry, band offsets and
effective masses to make the contributions from the first two partial waves to the
total scattering cross section vanish at the same time, as illustrated in Fig. 2(b)(c).
They were able to demonstrate a reduced scattering cross section smaller than
0.01% of the nanoparticle’s physical cross section. In a model calculation, they
showed the so-called “invisible doping” can improve the power factor of GaAs by
one order of magnitude at 50K54. Realistic designs using hollow nanoparticles55
and graphene56 were also proposed.
Mobility enhancements due to interactions between nanodomains across
the interfaces have also been recently observed in organic/inorganic hybrid
thermoelectrics. One example is the improved polymer chain alignment and
ordering of polyaniline (PANI) around single-walled carbon nanotubes (SWNT)
in a PANI/SWNT composite that significantly enhances the carrier mobility57,
induced by strengthened p - p interactions between polymer and nanotubes
across the interfaces, as schematically shown in Fig. 2(d).
Interfaces can have multiple effects on phonon transport as well. For
example, the reflection and transmission of phonons at an interface leads to the
thermal boundary resistance (or interfacial thermal resistance)11, which is already
present in macrocomposites. Such phonon reflection not only exists at interfaces
between different materials, but also at the grain boundaries within the same
material58–60. In nanocomposites, such interfacial thermal resistance becomes
dominant and can significantly reduce the thermal conductivity. It is generally
assumed that interfaces can randomize phonon phases and scatter phonons to
different states, giving rise to the classical size effect that will be reviewed in the
next section. There are also increasing recognition that interfaces are not effective
in randomizing the phases of long wavelength phonons, and it is possible to
observe coherent phonon transport.
Classical and Quantum Size Effect
The potential benefits of nanostructuring to thermoelectrics were first
recognized by Hicks and Dresselhaus in their seminal papers61,62 modeling
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thermoelectric thin films and nanowires. In those structures with certain
dimensions smaller than the electron coherence length, electrons are confined to a
physical space with lower dimensions, and the resulting density of states exhibit
sharp transitions with respect to energy and is desirable for a high Seebeck
coefficient. Although this “quantum confinement effect” was later observed in
various low-dimensional systems, such as quantum dots63, quantum wells64,
superlattices65,66, nanowires67 and a 2-dimensional electron gas confined in a
single-layer oxide68 (as illustrated in Fig. 3(a)), these structures are not easily
scalable and hence not suitable for practical applications in larger scales. In
addition to the dimensionality modification, the quantum confinement effect has
also been applied to adjusting the relative positions of electronic bands for better
thermoelectric performance, first proposed in a GaAs/AlAs superlattice
structure69. Since the Seebeck coefficient also benefits from sharp changes of
density of states with respect to the carrier energy near the Fermi level, aligning
the edges of multiple bands can lead to largely enhanced density of states and the
Seebeck coefficient without sacrificing the carrier mobility. This “band
convergence” idea has later been generalized and realized experimentally by
rational alloying of bulk materials with different band gaps27,70–74, as shown in Fig.
3(b). A noticeable alternative approach towards “band convergence” is to realize
highly symmetric (such as cubic) long-range order in solid solutions or mixtures
of low-symmetry constituents75,76, taking advantage of the direct relation between
the crystal symmetry and the band degeneracy.
In addition to the quantum confinement effect of electrons, the nanoscale
interfaces impose strong boundary scatterings on phonons and suppress the
thermal conductivity (the classical size effect, or Casimir effect). Reducing the
phonon thermal conductivity of TEs by engineering phonon scattering dates back
to the very early stages of TEs, when researchers used alloying to interrupt the
phonon propagation. The prominent example is the Si/Ge alloy, the best TE
material for high-temperature (> 900 K) applications for a long time, deployed by
NASA for radioisotope thermoelectric generators for space missions in the
1970s77. A related concept is to introduce “filler” impurity atoms into complex
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compounds with cage-like structures, such as skutterudites78–82, where the filler
atoms “rattle” inside the cage structure and disrupt the phonon propagation due to
the mismatch of natural frequencies. Both alloying and “filler-rattler” approaches
introduce atomic scale disorders that are effective in scattering shorterwavelength phonons, but less effective in scattering phonons with longer
wavelengths that are the major heat carriers in most TE materials. Starting from
1990s, the ultralow thermal conductivity in semiconductor superlattices (lower
than corresponding bulk alloys) with nanoscale periods was observed
experimentally83–86. It was later recognized87,88 that the non-Fourier behavior in
superlattices is largely due to the ballistic phonon transport in each layer and
phonon scatterings at the interfaces, recently quantified by first-principles
simulations89. This insight led to later development of bulk nanocomposites26
consisting of compact nanograins with a high density of grain boundaries acting
as effective filters for phonons with long wavelengths and mean free paths. The
manufacturing process usually includes ball milling and hot pressing (or spark
plasma sintering, SPS), and is cost-effective. This strategy has been successfully
applied to reduce the thermal conductivity of a wide range of TE materials,
including BiSbTe26,90, Si/Ge alloy91,92, lead chalcogenides93–96, half-Heuslers97–99,
skutterudites100, and low-temperature TEs101,102, and has been extensively
reviewed elsewhere103–107. A recent effort of introducing dislocation arrays into
the grain boundaries in BiSbTe via liquid-phase compaction has further boosted
the room temperature zT to ~1.86108. A similar approach is through bottom-up
assembly of nanocrystalline units109–114, first prepared by chemical methods, and
then compacted and sintered to form bulk nanocomposites. In parallel,
incorporating nanoscale precipitates in a host matrix through techniques of solidstate chemistry has proven to be another effective way of scattering phonons and
reducing the thermal conductivity. One well-studied example is the Ag1115–117
,
xPbmSbTem+2
or “LAST”, system, where a second phase richer in Ag and
Sb was observed to emerge in the host matrix and form nanoscale domains with a
long range order118. This strategy has also been realized in other material
systems119–122, and in particular, two well-known modes of phase segregation: the
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“spinodal decomposition” and “nucleation and growth” were explored in the
PbTe-PbS system123, and spontaneously forming nanostructures were identified as
being responsible for the low thermal conductivity of AgSbTe2124. Further
improvements were achieved by embedding nanocrystals endotaxially, i.e.
complete lattice matching to the host matrix, as demonstrated first in the PbTeSrTe system125, where the carrier mobility was preserved. It is worth mentioning
that the lattice thermal conductivity reduction due to phonon boundary scatterings
has also been observed in certain naturally forming superlattice structures, such as
the Ruddlesden-Popper phase of perovskite oxides126, as well as a recently
synthesized layered transition metal dichalcogenide TiS2 intercalated by organic
cations between TiS2 layers127.
The key assumption behind the success of the nanostructuring approach is
the length scale separation between the electron and phonon mean free paths:
electron mean free paths are much shorter than phonon mean free paths in most
TE materials, and thus electrons are less affected by the nanostructures. This idea
was recently quantified by first-principles simulations of both phonon128–134 and
electron transport135. The first-principles simulation also reveals the wide
distribution of phonon mean free paths in real materials (usually spanning nm to
μm range, see Fig. 3(c)), which necessitates nanostructures of disparate length
scales to fully block the phonon flow. Along this path, the nanostructuring
approach culminates in the synthesis of all-scale hierarchical micro/nanostructures
in a single material28, schematically illustrated in Fig. 3(d): atomic-scale lattice
disorders by alloy doping, nanoscale endotaxial precipitates and microscale grain
boundaries. These features combine to suppress the lattice thermal conductivity
and lead to a high reported zT~2.2 in a Na-doped PbTe-SrTe system28, and have
also been realized in other material systems136–139. Despite being conceptually
simple, this approach still has subtleties, for example on the interplay among
nanostructures with different length scales, that require further study and
clarification.
An open question is what is the minimal phonon thermal conductivity one
can achieve and whether nanocomposites can help reducing the phonon thermal
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conductivity to below the lower limit of the homogeneous parent material. For
bulk homogenous materials, one classical work is the minimum thermal
conductivity theory of Slack140, later extended by Cahill and Pohl141 based on the
kinetic theory, equating the phonon mean free path to half of its wavelength, the
minimal possible value from Einstein’s random walk model140,141. However,
experiments in various superlattice structures had shown that this is not truly the
minimum142,143. Based on the angular dependence of phonon reflection at
interfaces, Chen142 gave an argument that the thermal conductivity of superlattices
should have a lower limit than that proposed by Cahill and Pohl. In nanostructures,
another proposed lower bound of the thermal conductivity is the Casimir limit
(typically higher than the minimum of Cahill and Pohl), where the minimal
phonon mean free path is set by the characteristic size of the sample, for example,
the film thickness. These studies all imply that phonons lose their coherence
(phase information) at the interfaces, and are viewed as in the classical size effect
regime. The possibility of obtaining an even lower thermal conductivity in the
coherent transport regime will be discussed in the next section.
Given the existing mechanisms for electron and phonon engineering in
nanocomposites, lots of efforts has been made to realize these mechanisms
simultaneously in a same material system in a synergistic way. This so-called
“panoscopic” approach144,145 has led to successful examples30,72,146,147, while more
work needs to be done (for example, combining nanoprecipitates and modulation
doping) to promote the thermoelectric performance to the next level. We should
recognize that current modeling and simulation tools are not able to deal with
such complicated mesoscale systems, and as a consequence, most effective
approaches and optimization strategies are yet to be developed.
Coherence Effect
An interesting question is whether one can explore the wave effects of
phonons to achieve an even lower thermal conductivity than the minimum value
predicted in the classical size effect regime (the Casimir limit), for example, by
exploring the bandgaps formed in periodic structures60,148–151. This will require the
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phonons maintain their phases when traversing through the structure. This field of
“phononics”152,153 includes both acoustic waves with macroscopic wavelengths
and thermal phonons with a wide span of wavelengths down to nanometers,
entailing nanocomposites for wave effects to occur. The emergence of bandgaps
has been reported for acoustic waves in mesoscopic periodic structures154–156.
Although there have been experimental observations60,148–150 of reduced thermal
conductivity in nanoscale periodic structures possibly due to coherent effects
(such as the group velocity modification149), there is no decisive evidence of the
effect of phonon band gaps on the thermal conductivity. Recently, the
experimental evidence of coherent phonon transport was seen in the dependence
of the low-temperature thermal conductivity of a GaAs/AlAs superlattice on the
number of superlattice periods157, as illustrated in Fig. 4(a)(b). If the transport is
incoherent, the interfaces in the superlattice completely randomize the phonon
phases, and each layer of the superlattice acts as an independent thermal resistor,
connected in series to form the total thermal resistance of the superlattice. In this
case the thermal resistance scales linearly with the number of periods, while the
thermal resistivity, and thus conductivity, remains constant. In contrast, if
phonons travel coherently through the whole superlattice, the total thermal
conductance will not depend on the number of periods, and correspondingly the
thermal conductivity scales linearly with the number of periods. The direct
experimental measurement of this linear scaling of the thermal conductivity
established the presence of coherent phonon transport, corroborated with firstprinciples simulations157,158. From this experiment and past simulations159,160, the
coherent transport in such superlattice structures actually is not desirable if one’s
goal is to reduce the thermal conductivity. In fact, to reduce the thermal
conductivity, one should target to destroy the phonon coherence. Thus, whether
one can design phononic crystals to reduce the thermal conductivity below the
Casimir limit is an open question. It is also interesting to ask whether one can
explore other wave effects, e.g. localization161, to further reduce the thermal
conductivity. The observation of the coherent phonon transport in superlattices
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raises hope that one can explore phonon wave effects to manipulate the thermal
conductivity in composite structures.
Soft Matter as Nanocomposites
The reduced thermal conductivity of nanocomposites, although desirable
and effective for thermoelectric materials, is not preferable when one’s goal is to
improve the thermal transport. One example is the composite approach to improve
the thermal conductivity of polymers, which typically have a low intrinsic thermal
conductivity less than ~0.2-0.5 W/mK. Adding fillers with a high thermal
conductivity into polymers has been widely used as a means to improve the
thermal conductivity of polymers162–164. Applying the existing effective medium
models to such polymers, however, will quickly show that the key thermal
resistance comes from the polymer phase, even for micron-sized high thermal
conductivity phases. If nano-sized inclusions are used, interfacial resistances
between polymer and the inclusions become important and size effects further
limit the improvement of the thermal conductivity. For example, adding carbon
nanotubes to polymers so far has been able to improve the thermal conductivity
only up to a few W/mK164. In applications such as thermal interface materials or
underfills for microelectronics packaging165, nano-sized inclusions may be
favorable to fill uneven surfaces, suggesting that one may need to incorporate
inclusions of multiple size regions. On the other hand, if one can improve the
thermal conductivity of the base polymers, the composite approach will be more
effective.
Simulations166,167 and experiments168,169 have shown that stretched
polymer fibers can possess a much higher thermal conductivity due to the
improved chain alignment and crystallinity with an origin in the anomalous heat
conduction in lower-dimensional materials170,171 (see Fig. 5(a)(b) as an example),
and it is also shown that the polymer thermal conductivity even in the amorphous
phase
can
be
improved
by
using
nanoscale
templates
through
electropolymerization172 or properly chosen blend of polymers and linker
structure173.
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Another regime of thermal transport in composites is when one phase
begins to percolate. Although the electrical conductivity percolation in a
composite is a well-know phenomenon174 accompanied by a power-law increase
of the electrical conductivity above the percolation threshold, the same behavior
has not been observed for thermal transport, because it is not just limited to the
percolating phase. Recently, however, an interesting percolation behavior has
been observed in nanofluids - liquids with suspended nanoparticles175,176. These
solid-liquid nanocomposites have shown anomalously enhanced thermal
conductivity beyond the prediction of the classical effective medium theory in
certain cases, while the enhancement was not observed in other cases175. The large
variation of the experimental findings is now understood to be related to the
complex structures formed by the nanoparticles within the fluid that can be
sensitive to the external conditions and preparation procedures175. Gao et al.
observed the clustering of nanoparticles in a freezing experiment of a nanofluid
containing alumina nanoparticles, and in particular, when the base fluid
crystalizes, the nanoparticles are pushed to the grain boundaries and form a
percolation network177. Further experiments on graphite-flake suspensions (as
illustrated in Fig. 5(c)(d)) showed that the thermal conductivity increases faster
with the volume fraction of graphite below the percolation threshold than above,
contrary to that of the electrical conductivity176. This behavior was explained as a
result of the graphite clusters minimizing the interfacial energy below the
percolation threshold, leading to better contacts between the flakes and smaller
contact resistances176. The underlying mechanism exemplifies the significance of
the structure-property relations manifested especially in soft matters, where the
internal structures can vary greatly178, and there are still many open questions on
how the variations of the internal structures, such as the percolation effect, affect
the thermal and thermoelectric properties of soft matters.
Summary
In this article, the progress made in applying the concept of
nanocomposites to the field of thermoelectrics and thermal engineering is
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reviewed at a high level, with an emphasis on the emerging principles of heat and
charge
transport
in
nanocomposites
that
are
distinct
from
those
in
macrocomposites. Looking forward, we believe a synergistic fusion of these new
features and principles will lead to better material performances, which can be
accelerated through advances in both the multiscale transport modeling
techniques and the material synthesis and processing capabilities.
Acknowledgments
This article is supported by S3TEC, an Energy Frontier Research Center
funded by the U.S. Department of Energy, Office of Basic Energy Sciences, under
Award No. DE-FG02-09ER46577 (for research on thermoelectric power
generation), the Air Force Office of Scientific Research Multidisciplinary
Research Program of the University Research Initiative (AFOSR MURI) via Ohio
State University, Contract FA9550-10-1-0533 (for research on thermoelectric
cooling), and by the U.S. Department of Energy/Office of Energy Efficiency &
Renewable Energy/Advanced Manufacturing Program (DOE/EEREAMO) under
award number DE-EE0005756 (for developing polymers with high thermal
conductivity).
REFERENCES
1. S. Chu, A. Majumdar, Nature. 488, 294–303 (2012).
2. T. M. Tritt, M. A. Subramanian, MRS Bull. 31, 188–198 (2006).
3. T. M. Tritt, H. Böttner, L. Chen, MRS Bull. 33, 366–368 (2008).
4. L. E. Bell, Science. 321, 1457–1461 (2008).
5. A. F. Ioffe, Physics of Semiconductors (Academic Press, New York, 1960).
6. N. W. Ashcroft, N. D. Mermin, Solid State Physics (Harcourt College
Publishers, Fort Worth, 1976).
7. Lord Rayleigh, Philos. Mag. 34, 481–502 (1892).
8. J. C. Maxwell, A Treatise on Electricity and Magnetism (Clarendon, Oxford,
UK, 1904), vol. 1.
15
MRS Bulletin
Article Template
Author Name/Issue Date
9. J. C. M. Garnett, Philos. Trans. R. Soc. Lond. Math. Phys. Eng. Sci. 203, 385–
420 (1904).
10.
S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge
University Press, Cambridge, 1997).
11.
G. Chen, Nanoscale Energy Transport and Conversion: a Parallel
Treatment of Electrons, Molecules, Phonons, and Photons (Oxford
University Press, Oxford; New York, 2005).
12.
C.-W. Nan, R. Birringer, D. R. Clarke, H. Gleiter, J. Appl. Phys. 81, 6692–
6699 (1997).
13.
S. Guenneau, C. Amra, D. Veynante, Opt. Express. 20, 8207–8218 (2012).
14.
J. B. Pendry, D. Schurig, D. R. Smith, Science. 312, 1780–1782 (2006).
15.
S. Narayana, Y. Sato, Phys. Rev. Lett. 108, 214303 (2012).
16.
R. Schittny, M. Kadic, S. Guenneau, M. Wegener, Phys. Rev. Lett. 110,
195901 (2013).
17.
T. Han, T. Yuan, B. Li, C.-W. Qiu, Sci. Rep. 3, 1593 (2013).
18.
H. Xu, X. Shi, F. Gao, H. Sun, B. Zhang, Phys. Rev. Lett. 112, 054301
(2014).
19.
T. Han et al., Phys. Rev. Lett. 112, 054302 (2014).
20.
F. Gömöry et al., Science. 335, 1466–1468 (2012).
21.
C. Herring, J. Appl. Phys. 31, 1939–1953 (1960).
22.
D. J. Bergman, O. Levy, J. Appl. Phys. 70, 6821–6833 (1991).
23.
D. Fu, A. X. Levander, R. Zhang, J. W. Ager, J. Wu, Phys. Rev. B. 84,
045205 (2011).
24.
Y. Yang, S. H. Xie, F. Y. Ma, J. Y. Li, J. Appl. Phys. 111, 013510 (2012).
25.
A. Minnich, G. Chen, Appl. Phys. Lett. 91, 073105 (2007).
26.
B. Poudel et al., Science. 320, 634–638 (2008).
27.
Y. Pei et al., Nature. 473, 66–69 (2011).
28.
K. Biswas et al., Nature. 489, 414–418 (2012).
16
MRS Bulletin
Article Template
Author Name/Issue Date
29.
J. P. Heremans, M. S. Dresselhaus, L. E. Bell, D. T. Morelli, Nat.
Nanotechnol. 8, 471–473 (2013).
30.
H. J. Wu et al., Nat. Commun. 5, 5515 (2014).
31.
R. Dingle, H. L. Störmer, A. C. Gossard, W. Wiegmann, Appl. Phys. Lett.
33, 665–667 (1978).
32.
H. Daembkes, Ed., Modulation-Doped Field-Effect Transistors: Principles,
Design and Technology (IEEE, New York, 1990).
33.
M. Zebarjadi et al., Nano Lett. 11, 2225–2230 (2011).
34.
B. Yu et al., Nano Lett. 12, 2077–2082 (2012).
35.
M. Koirala et al., Appl. Phys. Lett. 102, 213111–213111–5 (2013).
36.
Y.-L. Pei, H. Wu, D. Wu, F. Zheng, J. He, J. Am. Chem. Soc. 136, 13902–
13908 (2014).
37.
D. Wu et al., Adv. Funct. Mater. 24, 7763–7771 (2014).
38.
J. Moon, J.-H. Kim, Z. C. Y. Chen, J. Xiang, R. Chen, Nano Lett. 13,
1196–1202 (2013).
39.
B. M. Curtin, E. A. Codecido, S. Krämer, J. E. Bowers, Nano Lett. 13,
5503–5508 (2013).
40.
G. D. Mahan, J. O. Sofo, Proc. Natl. Acad. Sci. 93, 7436–7439 (1996).
41.
J. P. Heremans et al., Science. 321, 554–557 (2008).
42.
J. P. Heremans, B. Wiendlocha, A. M. Chamoire, Energy Environ. Sci. 5,
5510–5530 (2012).
43.
M. Lundstrom, Fundamentals of Carrier Transport (Cambridge University
Press, New York, 2009).
44.
C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small
Particles (Wiley-VCH, New York, 1998).
45.
L. I. Schiff, Quantum Mechanics (Mcgraw-Hill College, New York, 1968).
46.
M. Zebarjadi et al., Appl. Phys. Lett. 94, 202105 (2009).
47.
J.-H. Bahk et al., Appl. Phys. Lett. 99, 072118 (2011).
48.
J.-H. Bahk, P. Santhanam, Z. Bian, R. Ram, A. Shakouri, Appl. Phys. Lett.
100, 012102 (2012).
17
MRS Bulletin
Article Template
Author Name/Issue Date
49.
J.-H. Bahk, Z. Bian, A. Shakouri, Phys. Rev. B. 87, 075204 (2013).
50.
G. D. Mahan, J. Appl. Phys. 76, 4362–4366 (1994).
51.
A. Shakouri, J. E. Bowers, Appl. Phys. Lett. 71, 1234–1236 (1997).
52.
P. Puneet et al., Sci. Rep. 3, 3212 (2013).
53.
B. Liao, M. Zebarjadi, K. Esfarjani, G. Chen, Phys. Rev. Lett. 109, 126806
(2012).
54.
M. Zebarjadi, B. Liao, K. Esfarjani, M. Dresselhaus, G. Chen, Adv. Mater.
25, 1577–1582 (2013).
55.
W. Shen, T. Tian, B. Liao, M. Zebarjadi, Phys. Rev. B. 90, 075301 (2014).
56.
B. Liao, M. Zebarjadi, K. Esfarjani, G. Chen, Phys. Rev. B. 88, 155432
(2013).
57.
Q. Yao, Q. Wang, L. Wang, L. Chen, Energy Environ. Sci. 7, 3801–3807
(2014).
58.
A. McConnell, S. Uma, K. E. Goodson, J. Microelectromechanical Syst.
10, 360–369 (2001).
59.
Q. G. Zhang, B. Y. Cao, X. Zhang, M. Fujii, K. Takahashi, Phys. Rev. B.
74, 134109 (2006).
60.
J. Ma et al., Nano Lett. 13, 618–624 (2013).
61.
L. D. Hicks, M. S. Dresselhaus, Phys. Rev. B. 47, 12727–12731 (1993).
62.
L. D. Hicks, M. S. Dresselhaus, Phys. Rev. B. 47, 16631–16634 (1993).
63.
T. C. Harman, P. J. Taylor, M. P. Walsh, B. E. LaForge, Science. 297,
2229–2232 (2002).
64.
L. D. Hicks, T. C. Harman, X. Sun, M. S. Dresselhaus, Phys. Rev. B. 53,
R10493–R10496 (1996).
65.
R. Venkatasubramanian, E. Siivola, T. Colpitts, B. O’Quinn, Nature. 413,
597–602 (2001).
66.
I. Chowdhury et al., Nat. Nanotechnol. 4, 235–238 (2009).
67.
A. I. Boukai et al., Nature. 451, 168–171 (2008).
68.
H. Ohta et al., Nat. Mater. 6, 129–134 (2007).
18
MRS Bulletin
Article Template
Author Name/Issue Date
69.
T. Koga, X. Sun, S. B. Cronin, M. S. Dresselhaus, Appl. Phys. Lett. 73,
2950–2952 (1998).
70.
Y. Pei et al., Adv. Mater. 23, 5674–5678 (2011).
71.
W. Liu et al., Phys. Rev. Lett. 108, 166601 (2012).
72.
L. D. Zhao et al., Energy Environ. Sci. 6, 3346–3355 (2013).
73.
H. Wang, Z. M. Gibbs, Y. Takagiwa, G. J. Snyder, Energy Environ. Sci. 7,
804–811 (2014).
74.
A. Banik, U. S. Shenoy, S. Anand, U. V. Waghmare, K. Biswas, Chem.
Mater. 27, 581–587 (2015).
75.
J. Zhang et al., Adv. Mater. 26, 3848–3853 (2014).
76.
W. G. Zeier et al., J. Mater. Chem. C. 2, 10189–10194 (2014).
77.
D. M. Rowe, CRC Handbook of Thermoelectrics (CRC-Press, Boca Raton,
FL, 1995).
78.
B. C. Sales, D. Mandrus, R. K. Williams, Science. 272, 1325–1328 (1996).
79.
W. Zhao et al., J. Am. Chem. Soc. 131, 3713–3720 (2009).
80.
X. Shi et al., J. Am. Chem. Soc. 133, 7837–7846 (2011).
81.
T. Dahal, Q. Jie, Y. Lan, C. Guo, Z. Ren, Phys. Chem. Chem. Phys. 16,
18170–18175 (2014).
82.
W. Zhao et al., Nat. Commun. 6, 7197 (2015).
83.
G. Chen, C. L. Tien, X. Wu, J. S. Smith, J. Heat Transf. 116, 325–331
(1994).
84.
S.-M. Lee, D. G. Cahill, R. Venkatasubramanian, Appl. Phys. Lett. 70,
2957–2959 (1997).
85.
T. Borca-Tasciuc et al., Superlattices Microstruct. 28, 199–206 (2000).
86.
W. S. Capinski et al., Phys. Rev. B. 59, 8105–8113 (1999).
87.
G. Chen, J. Heat Transf. 119, 220–229 (1997).
88.
G. Chen, Phys. Rev. B. 57, 14958–14973 (1998).
89.
J. Garg, G. Chen, Phys. Rev. B. 87, 140302 (2013).
19
MRS Bulletin
Article Template
Author Name/Issue Date
90.
W.-S. Liu et al., Adv. Energy Mater. 1, 577–587 (2011).
91.
G. Joshi et al., Nano Lett. 8, 4670–4674 (2008).
92.
G. H. Zhu et al., Phys. Rev. Lett. 102, 196803 (2009).
93.
Q. Zhang et al., J. Am. Chem. Soc. 134, 17731–17738 (2012).
94.
Q. Zhang et al., J. Am. Chem. Soc. 134, 10031–10038 (2012).
95.
Q. Zhang et al., Nano Lett. 12, 2324–2330 (2012).
96.
H. Wang et al., Proc. Natl. Acad. Sci. 111, 10949–10954 (2014).
97.
X. Yan et al., Nano Lett. 11, 556–560 (2011).
98.
G. Joshi et al., Adv. Energy Mater. 1, 643–647 (2011).
99.
S. Chen et al., Adv. Energy Mater. 3, 1210–1214 (2013).
100. Q. Jie et al., Phys. Chem. Chem. Phys. 15, 6809–6816 (2013).
101. H. Zhao et al., Nanotechnology. 23, 505402 (2012).
102. M. Koirala et al., Nano Lett. 14, 5016–5020 (2014).
103. A. J. Minnich, M. S. Dresselhaus, Z. F. Ren, G. Chen, Energy Environ. Sci.
2, 466–479 (2009).
104. Y. Lan, A. J. Minnich, G. Chen, Z. Ren, Adv. Funct. Mater. 20, 357–376
(2010).
105. C. J. Vineis, A. Shakouri, A. Majumdar, M. G. Kanatzidis, Adv. Mater. 22,
3970–3980 (2010).
106. M. Zebarjadi, K. Esfarjani, M. S. Dresselhaus, Z. F. Ren, G. Chen, Energy
Environ. Sci. 5, 5147–5162 (2012).
107. W. Liu, X. Yan, G. Chen, Z. Ren, Nano Energy. 1, 42–56 (2012).
108. S. I. Kim et al., Science. 348, 109–114 (2015).
109. R. J. Mehta et al., Nat. Mater. 11, 233–240 (2012).
110. R. J. Mehta et al., Nano Lett. 12, 4523–4529 (2012).
111. A. Soni et al., Nano Lett. 12, 4305–4310 (2012).
112. Y. Zhang et al., Appl. Phys. Lett. 100, 193113 (2012).
20
MRS Bulletin
Article Template
Author Name/Issue Date
113. J. S. Son et al., Nano Lett. 12, 640–647 (2012).
114. M. Ibáñez et al., ACS Nano. 7, 2573–2586 (2013).
115. K. F. Hsu et al., Science. 303, 818–821 (2004).
116. M. Zhou, J.-F. Li, T. Kita, J. Am. Chem. Soc. 130, 4527–4532 (2008).
117. Z.-Y. Li, J.-F. Li, Adv. Energy Mater. 4, 1300937 (2014).
118. E. Quarez et al., J. Am. Chem. Soc. 127, 9177–9190 (2005).
119. J. Androulakis et al., Adv. Mater. 18, 1170–1173 (2006).
120. C. S. Birkel et al., Phys. Chem. Chem. Phys. 15, 6990–6997 (2013).
121. X. Chen et al., Adv. Energy Mater. 4, 1400452 (2014).
122. A. Yusufu et al., Nanoscale. 6, 13921–13927 (2014).
123. J. Androulakis et al., J. Am. Chem. Soc. 129, 9780–9788 (2007).
124. J. Ma et al., Nat. Nanotechnol. 8, 445–451 (2013).
125. K. Biswas et al., Nat. Chem. 3, 160–166 (2011).
126. Y. Wang, K. H. Lee, H. Ohta, K. Koumoto, J. Appl. Phys. 105, 103701
(2009).
127. C. Wan et al., Nat. Mater. (2015), doi:10.1038/nmat4251.
128. D. A. Broido, M. Malorny, G. Birner, N. Mingo, D. A. Stewart, Appl. Phys.
Lett. 91, 231922 (2007).
129. K. Esfarjani, G. Chen, H. T. Stokes, Phys. Rev. B. 84, 085204 (2011).
130. Z. Tian et al., Phys. Rev. B. 85, 184303 (2012).
131. T. Luo, J. Garg, J. Shiomi, K. Esfarjani, G. Chen, Europhys. Lett. 101,
16001 (2013).
132. B. Liao, S. Lee, K. Esfarjani, G. Chen, Phys. Rev. B. 89, 035108 (2014).
133. S. Lee, K. Esfarjani, J. Mendoza, M. S. Dresselhaus, G. Chen, Phys. Rev. B.
89, 085206 (2014).
134. Z. Tian, S. Lee, G. Chen, J. Heat Transf. 135, 061605–061605 (2013).
135. B. Qiu et al., Europhys. Lett. 109, 57006 (2015).
21
MRS Bulletin
Article Template
Author Name/Issue Date
136. Y. Lee et al., J. Am. Chem. Soc. 135, 5152–5160 (2013).
137. K. Ahn et al., Energy Environ. Sci. 6, 1529–1537 (2013).
138. G. Tan, Y. Zheng, X. Tang, Appl. Phys. Lett. 103, 183904 (2013).
139. H. Lu, C.-A. Wang, Y. Huang, H. Xie, Sci. Rep. 4, 6823 (2014).
140. G. A. Slack, in Solid State Physics, H. Ehrenreich, F. Seitz, D. Turnbull,
Eds. (Academic Press, 1979), vol. 34, pp. 1–71.
141. D. G. Cahill, R. O. Pohl, Annu. Rev. Phys. Chem. 39, 93–121 (1988).
142. G. Chen, in Semiconductors and Semimetals, T. M. Tritt, Ed. (Elsevier,
2001), vol. 71 of Recent Trends in Thermoelectric Materials Research III,
pp. 203–259.
143. C. Chiritescu et al., Science. 315, 351–353 (2007).
144. J. He, M. G. Kanatzidis, V. P. Dravid, Mater. Today. 16, 166–176 (2013).
145. L.-D. Zhao, V. P. Dravid, M. G. Kanatzidis, Energy Environ. Sci. 7, 251–
268 (2013).
146. G. Tan et al., Energy Environ. Sci. 8, 267–277 (2014).
147. G. Tan et al., J. Am. Chem. Soc. 136, 7006–7017 (2014).
148. N. Zen, T. A. Puurtinen, T. J. Isotalo, S. Chaudhuri, I. J. Maasilta, Nat.
Commun. 5, 4435 (2014).
149. J.-K. Yu, S. Mitrovic, D. Tham, J. Varghese, J. R. Heath, Nat.
Nanotechnol. 5, 718–721 (2010).
150. P. E. Hopkins et al., Nano Lett. 11, 107–112 (2011).
151. L. Yang, N. Yang, B. Li, Nano Lett. 14, 1734–1738 (2014).
152. N. Li et al., Rev. Mod. Phys. 84, 1045–1066 (2012).
153. M. Maldovan, Nature. 503, 209–217 (2013).
154. T. Gorishnyy, C. K. Ullal, M. Maldovan, G. Fytas, E. L. Thomas, Phys.
Rev. Lett. 94, 115501 (2005).
155. W. Cheng, J. Wang, U. Jonas, G. Fytas, N. Stefanou, Nat. Mater. 5, 830–
836 (2006).
156. G. Zhu et al., Phys. Rev. B. 88, 144307 (2013).
22
MRS Bulletin
Article Template
Author Name/Issue Date
157. M. N. Luckyanova et al., Science. 338, 936–939 (2012).
158. Z. Tian, K. Esfarjani, G. Chen, Phys. Rev. B. 89, 235307 (2014).
159. C. Dames, G. Chen, J. Appl. Phys. 95, 682–693 (2004).
160. Y. Chalopin, K. Esfarjani, A. Henry, S. Volz, G. Chen, Phys. Rev. B. 85,
195302 (2012).
161. P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic
Phenomena (Academic Press, San Diego, 1995).
162. C. P. Wong, R. S. Bollampally, J. Appl. Polym. Sci. 74, 3396–3403 (1999).
163. Y. P. Mamunya, V. V. Davydenko, P. Pissis, E. V. Lebedev, Eur. Polym. J.
38, 1887–1897 (2002).
164. Z. Han, A. Fina, Prog. Polym. Sci. 36, 914–944 (2011).
165. R. Prasher, Proc. IEEE. 94, 1571–1586 (2006).
166. A. Henry, G. Chen, Phys. Rev. Lett. 101, 235502 (2008).
167. J. Liu, R. Yang, Phys. Rev. B. 81, 174122 (2010).
168. S. Shen, A. Henry, J. Tong, R. Zheng, G. Chen, Nat. Nanotechnol. 5, 251–
255 (2010).
169. X. Huang, G. Liu, X. Wang, Adv. Mater. 24, 1482–1486 (2012).
170. A. Dhar, Adv. Phys. 57, 457–537 (2008).
171. S. Liu, P. Hänggi, N. Li, J. Ren, B. Li, Phys. Rev. Lett. 112, 040601 (2014).
172. V. Singh et al., Nat. Nanotechnol. 9, 384–390 (2014).
173. G.-H. Kim et al., Nat. Mater. 14, 295–300 (2015).
174. S. Kirkpatrick, Rev. Mod. Phys. 45, 574–588 (1973).
175. J. J. Wang, R. T. Zheng, J. W. Gao, G. Chen, Nano Today. 7, 124–136
(2012).
176. R. Zheng et al., Nano Lett. 12, 188–192 (2012).
177. J. W. Gao, R. T. Zheng, H. Ohtani, D. S. Zhu, G. Chen, Nano Lett. 9,
4128–4132 (2009).
178. P. J. Lu et al., Nature. 453, 499–503 (2008).
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Figure Captions
Figure 1. Schematics showing distinct transport phenomena in (a)
macrocomposites and (b) nanocomposites. Blue lines represent interfaces between
different material domains.
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Article Template
Author Name/Issue Date
Figure 2. (a) Right: schematic of the concept of 3D bulk modulation doping; left:
the power factor enhancement of a Si/Ge alloy via modulation doping compared
with conventional uniform doping and state-of-the-art bulk samples. Reproduced
from reference 34. (b) A streamline plot of the probability flux of an electron
passing through a design of “electron cloak”, with the background color depicting
the phase of the wavefunction. (c) A sharp dip in the scattering cross section with
respect to the carrier energy created by an “electron cloak” via suppressing the
first two partial waves (l=0 and l=1) simultaneously. (b) and (c) reproduced from
reference 53.(d) A schematic showing the enhanced alignment of PANI molecules
around a single-walled carbon nanotube. Reproduced from reference 57 with
permission of the Royal Society of Chemistry.
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Author Name/Issue Date
Figure 3. (a) The enhancement of Seebeck coefficient in a 2D electron gas
confined in a single atomic layer of SrTi0.8Nb0.2O3 sandwiched by insulating
SrTiO3 layers. Reproduced from reference 68 with permission from Nature
Publishing Group. (b) A schematic showing the convergence of multiple band
edges via temperature tuning in a PbTe1-xSex alloy. Reproduced from reference 27
with permission from Nature Publishing Group. (c) The accumulated contribution
to the total phonon thermal conductivity versus the phonon mean free path
distributions in several thermoelectric materials from first-principles simulations.
Reproduced from reference 134. (d) A schematic showing a hierarchical design of
nanostructures covering different length scales for blocking phonons with
different mean free paths. Reproduced from reference 28 with permission from
Nature Publishing Group.
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Author Name/Issue Date
Figure 4. (a) A TEM image (and HRTEM image in the inset) of the GaAs/AlAs
superlattice; (b) the measured thermal conductivity dependence on the number of
superlattice periods. Reproduced from reference 157.
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Article Template
Author Name/Issue Date
Figure 5. (a) A TEM image of a drawn polyethylene nanofibre and (b) the
measured thermal conductivity of the nanofibre with respect to the draw ratio. (a)
and (b) are reproduced from reference 168. (c) and (d) are optical microscopic
images of stable graphite suspension with ethylene glycol as the base fluid. In (c)
the graphite volume fraction is 0.03%, below the percolation threshold, and the
clustering of graphite flakes can be observed, while in (d) the graphite volume
fraction is 0.1%, and the formation of a percolation network can be observed. (c)
and (d) are reproduced from reference 176.
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Author biographies
Bolin Liao
77 Massachusetts Avenue, 7-034
Cambridge, MA, 02139,
USA
Phone: 617-324-2068
Email: bolin@mit.edu
Bolin Liao is currently a PhD candidate in the Department of Mechanical
Engineering at MIT, under the supervision of Prof. Gang Chen. Bolin graduated
from Tsinghua University, Beijing, in 2010 with a Bachelor of Engineering
degree in Microelectronics, and obtained his Master of Science degree in
Mechanical Engineering from MIT in 2012. His main research interest is focused
on nanoscale transport phenonema of electrons, phonons and magnons, and their
applications in solid-state energy systems. Bolin has published his results in
Physical Review Letters, Advanced Materials, Proceedings of National Academy
of Sciences etc., and has served as a referee for journals including Physical
Review Letters, Energy and Environmental Sciences, Physical Review B etc.
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Article Template
Author Name/Issue Date
Prof. Gang Chen
77 Massachusetts Avenue, 3-174
Cambridge, MA, 02139
USA
Phone: 617-253-3523
Email: gchen2@mit.edu
Gang Chen is currently the Head of the Department of Mechanical
Engineering and Carl Richard Soderberg Professor of Power Engineering at
Massachusetts Institute of Technology (MIT), and is the director of the "SolidState Solar-Thermal Energy Conversion Center (S3TEC Center)" - an Energy
Frontier Research Center funded by the US Department of Energy. He received
an NSF Young Investigator Award, an R&D 100 award, a Heat Transfer
Memorial Award, and a Nukiyama Memorial Award. He is a fellow of AAAS,
APS, ASME, and the Guggenheim Foundation. He is an academician of
Academia Sinica and a member of the US National Academy of Engineering.
30