PROGRESS REPORT
Polymer Foams
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Hollow-Structured Materials for Thermal Insulation
Feng Hu, Siyu Wu, and Yugang Sun*
conversion, conservation, and storage.
The performance of a thermal insulation is characterized by the thermal conductivity of a material that is determined
by its physical structure and chemical
composition.
Materials with intrinsic low thermal
conductivities such as fiberglass, asbestos,
and rock wool are widely used to achieve
high thermal insulation performance.[2]
However, their performance are still below
the requirements in residential applications such as energy-efficient buildings
and in aeronautic and astronautic applications under extreme conditions. Tackling
this challenge requires an urgent development of new insulation (composite)
materials, in particular, with unique engineered structures. For instance, silica
aerogels with high porosities and low
mass densities have been recognized as
a class of excellent materials with superior thermal insulation even though solid
silica has a high thermal conductivity
(1.2–1.4 W m−1 K−1). The low thermal conductivities of aerogels mainly originate from the restricted heat transfer across
the gas phase confined in the voids, which are formed from
aggregated assembly of silica nanoparticles. The dependence of
high thermal insulation performance of aerogels on the existence of voids (or hollow structures) has stimulated great efforts
in developing new thermal-insulation materials by generating
hollow structures (e.g., voids and bubbles) in bulk materials
and composites. Although some review articles have summarized the progress in fabricating various thermal-insulation
materials including aerogels, polymer foams, and composite
films,[3] a review with a perspective on the general structure–
property relationship between the hollow structures and reduction of thermal conductivity in all insulation materials is still
absent. Herein, we present a comprehensive and timely overview on the present thermal-insulation materials containing
hollow structures with an emphasis on the structure–property
relationship.
A hollow structure is typically defined as a solid structure
with a void space inside a distinct shell.[4] The engineering
bulk materials, such as the thermal-insulation materials,
are considered as assemblies of many fused or aggregated
hollow structures. They appear as bulk materials containing
large amount (or high density) of individual voids, denoted as
“hollow-structured materials” or HSMs in this article. The voids
in HSMs could be produced from inheriting the hollow interiors of shells, bubbling of dissolved gases in these insulation
materials, and assembling solid materials into 3D networks
Heating and cooling represent a significant portion of overall energy
consumption of our society. Due to the diffusive nature of thermal energy,
thermal insulation is critical for energy management to reduce energy waste
and improve energy efficiency. Thermal insulation relies on the reduction
of thermal conductivity of appropriate materials that are engineerable in
compositions and structures. Hollow-structured materials (HSMs) show
a great promise in thermal insulation since the existence of high-density
gaseous voids breaks the continuity of heat-transport pathways in the HSMs
to lower their thermal conductivities efficiently. Herein, a timely overview of
the recent progress in developing HSMs for thermal insulation is presented,
with the focus on summarizing the strategies for creating gaseous voids in
solid materials and thus synthesizing various HSMs. Systematic analysis of
the documented results reveals the relationship of thermal conductivities of
the HSMs and the size and density of voids, i.e., reducing the void size below
≈350 nm is more favorable to decrease the thermal conductivity of the HSMs
because of the possible confinement effect originated from the nanometersized voids. The challenges and promises of the HSMs faced in future
research are also discussed.
1. Introduction
Energy consumption and environmental pollution have become
global concerns due to the rapid depletion of fossil fuel and the
surge of greenhouse gas emission. An agreement has been
reached to alleviate these challenges by exploring renewable
energy resources as well as improving the energy efficiency of
traditional supplies/technologies. Currently, renewable energy
resources, e.g., solar, wind, biomass energy, etc., support about
14% of the total world energy demand with a remarkable potential of continuous growth.[1] The related technologies such as
photovoltaics still suffer from the drawbacks of low-efficiency
energy conversion and high-cost storage. On the other hand,
research on energy management and minimization of energy
consumption becomes more vital than ever in recent years.
Thermal insulation, which reduces heat flow with thermal
resistant materials, plays a critical role on the improvement of
energy efficiency involved in essentially every process of energy
Dr. F. Hu, S. Wu, Prof. Y. Sun
Department of Chemistry
Temple University
1901 North 13th Street, Philadelphia, PA 19122, USA
E-mail: ygsun@temple.edu
The ORCID identification number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/adma.201801001.
DOI: 10.1002/adma.201801001
Adv. Mater. 2019, 31, 1801001
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with interconnected openings. These three strategies can be
described in details: i) hollow shells are synthesized with the
assistance of sacrificial templates followed by assembly of them
into HSMs, ii) turning the gases dissolved in the bulk materials into voids through a gas foaming process forms better
insulating materials called cellular foams, and iii) assembling
solid nanoparticles into or directly converting appropriate precursors to solid networks in the presence of solvent results in
HSMs after the solvent is removed to leave voids. A number
of HSMs include aerogels, polymer foams, and hollow spherebased composite films have been widely explored to serve as
the thermal-insulation materials with enhanced performance
compared to their solid counterparts without voids.
The existence of hollow voids in HSMs of various compositions significantly influences their thermal insulation property.
An HSM is summarized with the scheme of Figure 1 regardless of its type. An HSM comprises phase I of a continuous
matrix, phase II of void-confined gas, and the interfacial phase
III that bridges I and II. The compositions of individual phases
can be varied independently or simultaneously to form different
HSMs. For example, in a CO2-foamed cellular poly(methyl
methacrylate) (PMMA) film phases I and II are PMMA matrix
and CO2 gas, respectively, while interfacial phase III is considered as only a solid/gas (PMMA/CO2) interface without a
physical thickness. In a silica aerogel the interfacial phase III
is the solid silica network while both phases I and II are air.
The total volume of the voids (phase II), which is determined
by the average size and number of the voids, in an HSM with
a unit of volume is used to describe the porosity of the HSM.
These chemical and physical parameters are closely related
to the spatial distributions (or assembly) of individual phases
(i.e., I, II, and III), which influence the thermal conductivity
of the corresponding HSMs. Therefore, we summarize in this
report the HSMs with high thermal insulation performance,
discuss the correlation of thermal conductivity and the hollow
structures, and wrap up the report with the personal perspectives regarding the challenges and opportunities of developing
HSMs for high-performance thermal-insulation materials.
2. Heat Transfer in HSMs
Thermal transport in a thermal-insulation material follows
three major modes of heat transfer, i.e., convection, radiation,
and conduction. Convection is the macroscopic movement
of the fluid (e.g., liquid and gas), which mixes the cold part
and hot part of the fluid to enable heat transfer in the fluid.
In HSMs convection becomes possible in the gases confined
in voids only when the Grashof number is greater than 1000.
The Grashof number (Gr) describes the ratio of the buoyant
force driving convection to the viscous force opposing it with
an expression[5]
Gr =
g ⋅ α ⋅ ΔT ⋅ d 3 ⋅ ρ g
(1)
η3
where g is the gravitational acceleration constant (9.81 m s−2),
α is the volume expansion coefficient of the gas, ΔT is the temperature difference across individual voids, d is the diameter of
Adv. Mater. 2019, 31, 1801001
Feng Hu received his Ph.D.
degree in chemistry from
the University of Chinese
Academy of Sciences
(UCAS) in 2017. He is
currently a postdoctoral
fellow in Dr. Sun’s group in
Temple University. His main
research interests focus on
the developments of novel
composite nanomaterials for
efficient energy management,
with an emphasis on exploring high optically transparent
and insulating composite films.
Siyu Wu received his B.S.
degree from the University
of Science and Technology of
China (USTC) in 2017. He is
currently a Ph.D. student in
the Department of Chemistry
at Temple University. His
current research activities
include the synthesis and in
situ high-energy synchrotron
X-ray characterization of
efficient catalysts.
Yugang Sun received his
B.S. and Ph.D. degrees in
chemistry from the University
of Science and Technology
of China (USTC) in 1996
and 2001, respectively. He is
currently a professor at the
Department of Chemistry,
Temple University. His
current research interests
focus on design of quantumsized nanoparticles for energy
applications and understanding of nanoparticle growth
kinetics using in situ synchrotron X-ray techniques.
the voids (assuming spherical shape), and ρg and η represent
the density and dynamic viscosity of the gas, respectively. Convection of air with a pressure of 1 atmosphere (at Gr ≥ 1000)
requires the void diameter to be larger than 10 mm. Therefore, gas convection in typical HSMs with void sizes of several
micrometers or less is suppressed completely, making essentially no contribution to thermal conductivity.
Thermal radiation in an HSM film is the heat transfer refers
to the transmission of electromagnetic waves emitted by objects
and surfaces with temperatures higher than 0 K. Heat transfer
in this way highly depends on the optical responses to electromagnetic waves mainly in the infrared region that corresponds
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in both solid and gas, which strongly depends on the hollow
structures of an HSM, makes major contribution to the overall
thermal conduction of the HSM, representing the focus of this
review.
2.1. Thermal Conduction of Gases in HSMs
The contribution of the gas in an HSM to thermal conductivity
originates from the collisions of gas molecules in the voids
(phase II in Figure 1) and the collisions between the gas molecules and the solid walls of the interfacial phase III. The collisions can be described with the kinetic theory model, giving the
thermal conductivity of a bulk gas by[8]
1
kg,0 = ⋅ C g,0 ⋅ ν g,0 ⋅ Λ g,0 ⋅ ε (3)
3
Figure 1. Illustrative diagram showing the morphology of a typical HSM
that is constructed with three immiscible phases. Phase I represents
the continuous component responsible for the heat transport pathways.
Phase II is the gas confined in voids. The interfacial phase III bridges
phase I and phase II, and it can be composed of a solid component but
this is not necessary.
to temperatures of hundreds of K. Typically, an HSM for
thermal insulation is optically thick compared to the mean free
path of infrared photons,[6] making the radiative heat transport
a local phenomenon mainly influenced by the scattering and
absorption in the HSM. In this case, the radiative conductivity
can be described by[7]
kr =
16 ni2 ⋅ σ ⋅ T 3
(2)
3 e (T ) ⋅ ρ
where σ is the Stefan–Boltzmann constant, ni is the mean
index of refraction of the specimen, T is the temperature, e(T)
is the specific Rossland mean extinction coefficient with a unit
of m2 kg−1, and ρ is the apparent density of the HSM. The
thermal radiation should not be overlooked since the e(T) of
HSM varies significantly from components to components. For
example, silica aerogels show small absorption in mid-infrared
region (3–5 µm) but organic aerogels made of polymers such as
resorcinol–formaldehydes (RF) are nearly opaque to this spectral band. Therefore, one can effectively decrease the thermal
radiation by doping the solid component of an HSM with
strong infrared opacifiers such as carbon black.[6] This strategy
depends more likely on the composition rather than the geometrical structure of the HSM, which is out of the scope of
this review focusing on overviewing the construction of hollow
structured materials and the structure–property relationship.
Thermal conduction relies on the motion of microscopic
energy carriers including molecules, atoms, as well as free
electrons and phonons. Thermal conduction in a solid mainly
depends on the lattice vibration of solid molecules around their
equilibrium positions, while thermal conduction in a gas originates from the collision of gas molecules. Thermal conduction
Adv. Mater. 2019, 31, 1801001
where Cg,0, vg,0, and Λg,0 represent the volumetric specific heat
of the gas, the root-mean-squared velocity of gas molecules,
and the mean free path of gas molecules, respectively. ε is the
correction factor describing the influence of viscosity on the
thermal conductivity determined with the kinetic theory model.
According to the kinetic theory, the mean free path of bulk gas
molecules is
Λ g,0 =
kB ⋅ T
(4)
2 ⋅ π ⋅P ⋅ l2
where l is the collision diameter of the gas molecules and P,
T, and kB represent the gas pressure, the temperature, and
the Boltzmann constant, respectively. In an ideal bulk gas,
thermal conductivity is independent of gas pressure since the
volumetric specific heat, Cv,0, is proportional to the pressure
(corresponding to the number density of gas molecules) and
the mean free path, Λg,0, is inversely proportional to the pressure. In contrast, the movement of gas molecules is limited
by the size of voids in an HSM, reducing their mean free path
due to the collisions of gas molecules with the solid matrix
when the average void size is smaller than Λg,0.[8a,9] The
reduced mean free path represents a typical spatial confinement effect, which requires the use of an apparent effective
mean free path, Λg,eff, to describe the corresponding lowered
thermal conductivity, i.e., effective thermal conductivity of gas
in a confined space
1
kg,eff = ⋅ C g,0 ⋅ v g,0 ⋅ Λ g,eff ⋅ ε (5)
3
The value of Λg,e is determined by following the Mattiesson
rule[8a]
1
1
1
=
+ (6)
Λ g,eff Λ g,0 d
where d represents the characteristic size of the void to
highlight the spatial confinement effect. Combining
Equations (1)–(6) derives the effective thermal conductivity
confined in voids with a characteristic dimension of d as
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kg,eff =
C g,0 ⋅ v g,0 ⋅ ε  2 ⋅π ⋅ P ⋅ l 2 1 
+ 
 k ⋅ T
d
3
B
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−1
or kg,eff =
kg,0
(7)
1 + Λ g,0 /d
where Λg,0/d represents a useful parameter to evaluate the
confinement effect on thermal conductivity of the gas in
the voids with sizes smaller than Λg,0. The ratio of Λg,0/d
is reported as the Knudsen number (Kn). According to
Equation (7), the effective thermal conductivity decreases as
the value of Kn increases. Therefore, increasing the mean
free path of the corresponding bulk gas molecules and/
or reducing the characteristic dimension of the voids in an
HSM, which can effectively increase the Knudsen number,
represents a feasible strategy to lower the thermal conductivity of gas confined in small voids. Many other models based
on the Knudsen number have also been proposed to empirically describe the influence of spatial confinement on the gas
thermal conductivity in small voids of HSMs.[3d,10] The “corrected” effective thermal conductivity of gases confined in
small voids allows us to more accurately describe the contribution of gases in an HSM to the overall thermal conductivity
of the HSM. For an HSM with a defined shape and volume,
the voids occupy only a fraction of volume of the HSM, which
is usually described as porosity, Π. In general, the small voids
uniformly distribute throughout the HSM, resulting in highfrequency collision between the gas molecules and the solid
walls because the characteristic dimension of the voids are
smaller than Λg,0. The collisions lead to an energy transfer
from the gas molecules of the void phase II to the solid
phase I (or interfacial phase III), which is described with a
parameter, β. Considering these two factors, i.e., Π and β, the
contribution of gas in the void phase II to the total thermal
conductivity of the HSM (or gas thermal conductivity) can be
predicted by the Kaganer’s model[7a,10c,11]
kg,HSM =
kg,0 ⋅ Π
(8)
1 + 2 ⋅ β ⋅ Kn
Increasing the mean free path of gas molecules can be realized by reducing the gas pressure in the voids of an HSM. For
example, Kistler first reported the reduced thermal conductivity
of silica aerogels under lower pressure.[12] The low thermal
conduction of 0.006 W m−1 K−1 was achieved in the resorcinol–
formaldehyde aerogel monoliths with a density of 80 kg m−3
when the monoliths were evacuated to 10 mbar.[11a] As a consequence, the thermal conductivity of the gas in an aerogel can be
obtained by subtracting the thermal conductivity of the aerogel
measured at vacuum from that measured at the ambient pressure of a specific gas. According to Equation (8), the Knudsen
number can be determined to estimate the average size and
size distribution of the voids in the aerogel with the consideration of the mean free path of the specific gas at the ambient
pressure.[7a,10d,13] Moreover, filling the voids of an HSM with a
gas that exhibits larger mean free path can also reduce the gas
thermal conductivity. Kistler exchanged the air in silica aerogels
with CO2 and CCl2F2 to lower the thermal conductivity of the
aerogels.[12]
Reducing the size of voids in an HSM is more promising
since we can avoid the use of expensive long-mean-freepath gases and the vacuum process that may cause materials
Adv. Mater. 2019, 31, 1801001
Figure 2. Effect of void size on thermal conductivity of gases in
open cell polymeric foams and resorcinol–formaldehyde aerogels
(symbols). The curve represents the calculation result according
to the Knudsen equation, showing the good agreement with the
experimental measurements. PMMA: poly(methyl methacrylate); MAM:
block copolymer poly(methyl methacrylate)-co-poly(butyl acrylate)co-poly(methyl methacrylate); PE: polyethylene. Reproduced with
permission.[15] Copyright 2014, Elsevier Ltd.
failure.[14] For instance, the thermal conductivity of polyetherimide (PEI) foams is reduced to as low as 0.015 W m−1 K−1,
a value even lower than that of air, when the size of the voids
is reduced to ≈100 nm.[14b] The small voids largely restrict
the motion and collision of the gas molecules, accounting for
the reduced thermal conductivity. The experimental observations are consistent with theoretical studies using the finite
and molecular dynamics models for a wide range of materials
including silica aerogels, polyolefin foams, PMMA foams,
and PEI foams. The reduction of thermal conduction of gases
confined in small spaces is recognized as the Knudsen effect
described by Equation (8). The Knudsen effect was, for the
first time, demonstrated by Notario et al. in PMMA foams.[15]
Figure 2 compares the thermal conductivities of gases in various aerogels, PE foams, and PMMA-based foams, highlighting
their dependence on the size of voids and independence of the
composition of solid phases.
2.2. Thermal Conduction of Solids in HSMs
Heat transfer in solids mainly relies on the molecular vibrations in the materials. Different from the gas molecules that
can move freely, molecules in solid materials can only vibrate
around their equilibrium positions upon thermal excitation.
In quantum mechanics, the energies of molecular vibrations
are quantized and discrete. The vibrations with the minimum
energy correspond to phonons. A phonon is a quantum
mechanical description of an elementary vibrational motion
in which a lattice of atoms or molecules uniformly oscillates
at a single frequency. The property of phonon transport in a
solid determines the thermal conductivity of the material. The
thermal conductivity of a bulk solid can also be described with
the kinetic model (Equation (9))[16]
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2Λ
ks,HSM = (1 − Π) ⋅ ks,eff = (1 − Π) ⋅ ks,0 ⋅  1 + s,0 

d +δ 
Figure 3. Schematic illustration showing the influence of void size on
heat transport in a polymer foam. Phase I and phase II correspond to
the polymer matrix and void-confined gas, respectively. The characteristic
size (δ) of the polymer and the size (d) of the voids are defined in the left
frame. The heat conduction pathway in the solid phase I is illustrated with
the multiple arrows in the middle frame, highlighting the dependence on
the value of δ.
1
ks,0 = ⋅ Cs,0 ⋅ v ph,0 ⋅ Λ s,0 (9)
3
where Cs,0, vph,0, and Λs,0 represent the volumetric specific heat
of the solid, the root-mean-squared velocity of phonons in the
solid, and the mean free path of phonons in the solid, respectively. Phonon scattering takes account in the thermal conductivity when the mean free path of the phonons is comparable
to the characteristic dimension of the solid.[17] For example, the
characteristic dimension of the solid in an HSM is determined
by both the void size, d, and the dimensional parameter, δ,
which is the smallest thickness of the walls of phase I between
adjacent voids shown in Figure 3. Similar to the influence of
spatial confinement of gas molecules on thermal conductivity,
the size effect on thermal conductivity of the solid in the HSM
can also be described by using an effective mean free path of
phonons, Λs,eff [17a]
1
1
2
=
+
(10)
Λ s,eff Λ s,0 d + δ
Accordingly, the thermal conductivity of the porous solid
is[17,18]
 1
1
2 
ks,eff = ⋅ Cs,0 ⋅ v ph,0 ⋅ 
+
3
 Λ s,0 d + δ 
−1
−1
2Λ s,0 
or ks,eff = ks,0 ⋅  1 +


d + δ  (11)
Equation (11) clearly shows that the thermal transport
mechanism of a porous solid is consistent with the corresponding bulk solid when the dimensions of the voids are
much larger than the intrinsic mean free path of phonons in
the solid. Since the solid represents only a fraction of volume
of the HSM, the contribution of the solid material to the total
thermal conductivity of the HSM (or solid thermal conduction)
is expressed by
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−1
(12)
Therefore, simultaneously decreasing the size of the voids
and reducing the value of δ in an HSM can lower the contribution of the solid to the total thermal conductivity of the HSM
when the porosity of the HSM is constant.[14b,19] For instance,
when a foamed polymer contains spherical voids packed in
face-centered geometry with a porosity (Π) of 80%, the characteristic size (δ) exhibits a relationship of δ = 0.13d with the
3
π
d 
,
diameter (d) of the spherical voids according to Π = 

6  d +δ 
highlighting the promise in reducing δ through the generation
of small voids in an HSM. Moreover, the collision frequency
of gas molecules in the voids of an HSM decreases with the
decrease of the size of the voids because fewer gas molecules
are confined in individual voids. For example, collisions of gas
molecules are largely excluded in the voids with sizes on the
order of the mean free path of the gas molecules, e.g., ≈70 nm
for air under ambient conditions,[20] significantly reducing
the contribution of heat conduction by the gas in the voids
according to Equation (8).
The mean free path of (Λs,0) in amorphous solids (e.g., polymers, sol–gel silica, etc.) is usually at a sub-nanometer scale,
much less than both the void size (d) and dimensional parameter (δ) of HSMs that are often larger than 10 nm or even at
the micrometer scale.[21] Such significant difference in length
scale causes the term 2Λs,0/(d +δ) close to zero, indicating that
the possible interfacial phonon scattering is negligible in typical HSMs. Therefore, the contribution of the solid to the total
thermal conductivity of an HSM is mainly determined by the
porosity (Π) and the intrinsic thermal conductivity of the corresponding bulk solid (ks,0)
ks,HSM = (1 − Π)ks,0 (13)
The surfaces and edges of a porous HSM behave differently
from the solid material in contact with the voids inside the
HSM, in particular when the HSM is thin enough to expose
a significant fraction (fs) of solid to the surfaces and edges.
Such a difference leads to different contributions to thermal
conductivity for the solid material at different locations in the
HSM. Glicksman developed a model to take the difference into
account and describe the solid thermal conductivity in an HSM
containing cubic voids as[22]
2 f 
ks,HSM =  − s  (1 − Π)ks,0 (14)
3 3 
According to the minimum thermal conductivity model
(MTCM),[23] the value of ks,0 of an amorphous solid is proportional to its atomic density (ρ0) and the average sound velocity
(vsound,0). If a porous HSM exhibits an apparent density of ρ
and sound velocity of vsound, the contribution of the solid to the
total thermal conductivity can be described in an alternative
way[13a,24,25]
ks,HSM = ks,0 ⋅
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ρ ⋅ ν sound
(15)
ρ0 ⋅ ν sound,0
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Figure 4. A) Illustrative diagram showing a polymer foam consisting of the solid polymer (phase I) and the void-confined gas (phase II). B–D) Scanning
electron microscopy (SEM) images of nanocellular open cell foams constituted 50 wt% of PMMA and 50 wt% of MAM (B), microcellular open cell
foams constituted by 25 wt% of PMMA and 75 wt% of MAM (C), and nanocellular closed cell foams constituted by 95 wt% of PMMA and 5 wt% of
MAM (D). E) Relationship between the thermal conductivity divided by the relative density (ρrel) of the foamed samples and the pore size. The relative
density is the value of foam density divided by the density of the corresponding solids. F) Calculated thermal conductivity as a function of the relative
density for PMMA foams with cells of varying sizes. The calculations were processed by considering three contribution of gas conduction (Kaganer’s
model), solid conduction (Ashby’s model), and radiation (Williams and Aldao’s model). B–F) Adapted with permission.[15] Copyright 2014, Elsevier Ltd.
Although various models have been reported in literatures, all of them consistently indicate that maintaining high
porosity and small size (e.g., <100 nm) of voids in an HSM
can simultaneously reduce the thermal conductivities in both
the gas and solid phases. This property enables HSMs to be a
class of unique thermal-insulation materials with significantly
enhanced thermal insulation performance compared to the corresponding solid materials. Representative HSMs of various
compositions are discussed in the following sections to highlight their superior thermal insulation performance.
3. Polymer Foams
Polymer foams represent the widely used thermal-insulation
materials because of their good thermal insulation performance,
Adv. Mater. 2019, 31, 1801001
mechanical flexibility, durability, and low manufacturing cost.
A polymer foam is a stable solid polymer monolith or film with
trapped pockets of a desirable gas. The polymer and gas correspond
to phase I and phase II, respectively. The interfacial phase III is the
interface between phase I and phase II without a physical thickness in a polymer foam (Figure 4A). The solid phase I typically consists of one polymer or potentially of a polymer mixture containing
multiple miscible components. Low-concentration additives are
sometimes added to polymers to facilitate the foaming process
or tune mechanical properties of the polymers. The trapped gas
(phase II) can be confined as individual bubbles (closed-cell
foams, Figure 4B,C) or interconnected channels (open-cell foams,
Figure 4D). Forming polymer foams with inert gases such as CO2
and nitrogen has been intensively studied due to the environmentfriendly manufacturing process. An appropriate gas is first dissolved in a polymer at high pressures, usually at the supercritical
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conditions of the gas. Removing the supercritical conditions (e.g.,
decreasing pressure) triggers a solid–gas phase separation between
the polymer and the gas, leading to the nucleation and growth of
gas bubbles in the polymer matrix. The key to form polymer foams
with low thermal conductivities is to boost the nucleation of gases,
which potentially increases the density of voids and thus reduces
the size of individual voids. According to the classical nucleation
theory, increasing the supersaturation of a gas in a polymer that
can be achieved by dissolving the gas at higher pressure for a
longer time benefits the fast homogeneous nucleation. The nucleation of the gas can also be promoted through heterogeneous nucleation process by mixing high concentration of small nanoparticles,
which serves as nucleation sites, in the polymer. The density, size,
and morphology of the gas bubbles (or voids) in the polymer foam
strongly depends on the process condition including pressure,
temperature, saturation time, and depressurization rate, as well as
the type of polymer and the density of nanoparticle fillers.[3a–c,26]
In general, heterogeneous nucleation with a high concentration of
nanoparticle fillers in polymers can efficiently reduce the void size
and increase the void density compared with that from homogeneous nucleation.
The porosity of polymer foams is usually higher than 50%,
while the size of voids in polymer foams varies in a wide range
from thousands of micrometers to tens of nanometers. The
values of both parameters influence the thermal conductivity of
polymer foams, based on the above theoretical discussion. The
formation of small gas voids in a polymer reduces the contribution of the polymer to the thermal conductivity of the corresponding HSM due to the increased porosity, meanwhile the
small void size enables the Knudsen effect to lower the contribution of the gas to the thermal conductivity of the HSM. A
number of polymer foams have been synthesized and studied
for thermal insulation, such as PS foams,[27] PU foams,[27e,28]
PE foams,[14a,29] polyetherimide foams,[14b] PMMA foams,[15,30]
polyether block amide (PEBA) foams,[31] and poly(vinylidene
fluoride) (PVDF) foams.[32] Table 1 summarizes the sizes
and densities of voids in the polymer foams and their corresponding thermal conductivities. The void fraction has a key
effect on the effective thermal conductivity of a polymer foam.
For example, PMMA foam with a porosity of 51.7% has a
thermal conductivity of 0.107 W m−1 K−1, which can be largely
reduced to ≈0.035 W m−1 K−1 by increasing the porosity of
PMMA foam to 95.2%.[15,30] Park and co-workers have recently
achieved extremely low thermal conductivities of 0.030 W
m−1 K−1 for PEBA foam and 0.027 W m−1 K−1 for PVDF foam
which have the porosities of 83.3% and 96.4%, respectively.[31,32]
These values are close to the thermal conductivity of air (i.e.,
≈0.026 W m−1 K−1), highlighting the great promise of polymer
foams in thermal insulation.
Thermal conductivity of the polymer foams with a constant porosity indeed decreases with the decrease in the size
of the voids, in particular when the diameter of the voids is
on the sub-micrometer scale. Thermal conductivity of the polymer foams with voids larger than 100 µm is dependent on
the porosity and almost independent of the size of the voids.
For example, polyurethane (PU) foams with void sizes from
147 to 341 µm and similar porosities (95.7–97.1%) exhibit
similar thermal conductivities varying in a very narrow range
(0.0334–0.0342 W m−1 K−1).[28b] Significant reduction of thermal
Adv. Mater. 2019, 31, 1801001
Table 1. Thermal conductivities and void parameters of polymer foams
formed from homogeneous nucleation processes.a)
Polymer matrix
(phase I)
Thermal conductivity Year[Ref.]
[W m−1 K−1]
Void size
[µm]
Porosity
[%]
PS foam
≈200
97.2
0.0331
PU foam
≈200
96.9
0.0267
PU foam
300
96.3
0.0342
214
96.2
0.0339
147
95.8
0.0334
194
98.2
0.037
880
97.6
0.043
PE foam
EVA/PE foamb)
PEI foam
PMMA/MAM
foam
528
96.6
0.044
3294 ± 185
97.5
0.0460
1053 ± 87
96.9
0.0387
630 ± 52
97.1
0.0376
0.26
74
0.019
0.24
77
0.016
0.086
80
0.015
0.290
60.1
0.0884
0.235
56.8
0.0925
0.150
48.3
0.0948
0.0782
8.07
72.0
PMMA foam
0.82
51.7
0.1072
PMMA foam
445.9
95.24
0.0373
202.0
94.76
0.0363
208.5
95.55
0.0347
108.2
94.64
0.0353
2015[27e]
1998[28a]
2001[14a]
2008[29b]
2013[14b]
2015[15]
2017[30]
127.8
95.22
0.0343
PEBA
≈32
83.33
≈0.030
2018[31]
PVDF
≈150
96.4
0.027
2018[32]
a)
Phase II was air in voids; b)EVA: ethylene–vinyl acetate copolymer.
conductivity of polymer foams requires the size of voids to be
comparable to the mean free path of gas molecules in the voids,
which is usually on the order of tens of nanometer. Therefore,
recent research focuses on the synthesis of polymer foams with
voids smaller than 200 nm, which are generally called nanocellular foams, to achieve high insulation performance.[3b,c,e] In
nanocellular foams collisions of gas molecules are largely limited in the small voids, leading to the significant suppression
of the gas thermal conductivity due to the Knudsen effect.[15]
Notario et al. demonstrated the strong relationship between the
void size and thermal conductivity in PMMA foams, as shown
in Figure 4E. The ratio of thermal conductivity (k) and relative
density (ρrel = ρfoam/ρsolid) generally shows a decrease trend
with the void size from 1 µm to 100 nm, which can be attributed to the Knudsen effect. Simulation results show the PMMA
foam with a void size of 10 nm has the lowest thermal conductivity compared with PMMA foams with a larger void size
in the range of the relative density from 0.05 to 0.6 (Figure 4F).
A theoretical study recently points out the good insulating
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property with a nanocellular polymer foam requests the void
size less than 200 nm and a porosity in the range of 90–95%.[19]
The synergistic effects of nanometer-sized voids on heat
transport in both gases and polymers enable the synthesis of
polymer insulation materials with very low thermal conductivities. For instance, Sundarram and Li successfully reduced
thermal conductivity of the PEI foam to 0.015 W m−1 K−1 by
forming CO2 voids of 86 nm in diameter with a porosity of
80%.[14b]
Despite the successful tuning ability of foaming process on
the size of voids in the homogeneous nucleation synthesis, it is
still extremely challenging to reduce the void size down to the
ideal values while maintaining a high porosity. The difficulty
originates from the low nucleation efficiency, i.e., low density of
nuclei formed from the spontaneous homogeneous nucleation.
This challenge has been tackled by blending polymers with nanoparticles of different compositions that exhibit stronger affinity
toward gases than that of polymer. The nanoparticle fillers can
serve as nucleation sites of gas to promote the nucleation efficiency. When the concentration of the nanoparticle fillers is
high enough, the density of gas voids can be increased to the
appropriate values. At a specific porosity (i.e., the total volume of
voids remaining constant), the size of individual voids decreases
accordingly, benefiting the reduction of thermal conductivity of
the resulting polymer foams. Various nanoparticles have been
evaluated as fillers to improve thermal insulation performance
of polymer foams. Typical nanoparticles fillers include clay
nanoparticles,[33] TiN nanoparticles,[34] silica nanoparticles,[35]
carbon fibers or nanotubes,[36] organic domains,[37] and so forth.
Table 2 summarizes the detailed information of the composition and structure of the composite foams as well as their corresponding thermal conductivities. For example, the presence
of clay nanoparticles with a mass concentration of around 2%
(≈2 wt%) in PU could reduce the size of voids in the PU foams
from 514 to 360 µm under the same foaming conditions.[33b]
High dispersion of nanoparticle fillers in polymers is essential to
fully benefit the heterogeneous nucleation in which the density
of gas voids is improved compared to the homogeneous nucleation in polymers without nanoparticle fillers.[35a,36a] Surface
modification of inorganic nanoparticle fillers with appropriate
organic molecules that are compatible with the polymers represents a practical strategy to increase the dispersity of nanoparticles. Typical examples include the modification of clay
nanoparticles with polymeric 4,4ʹ-diphenylmethane diisocyanate (PMDI) and the modification of silica nanoparticles with
3-(trimethoxysilyl)-propyl methacrylate (MSMA). The modified
silica nanoparticles expose vinyl groups to the surroundings and
are labeled as vinyl-modified silica nanoparticles or VMS nanoparticles. Using the modified nanoparticles decreases the size
of voids and improves the uniformity of the voids in polymer
foams. For instance, Yeh et al. dispersed the VMS nanoparticles
in PMMA through a polymerization reaction of methyl methacrylate (MMA) in the presence of VMS nanoparticles.[35a] The
well-dispersed VMS nanoparticles significantly increased the
heterogeneous nucleation efficiency, resulting in an increase
of density of voids and a decrease of void size compared with
the foams with unmodified silica nanoparticles. In the presence
of 2 wt% VMS nano­particles the resulting PMMA foam exhibited a void density 2.69 × 1012 cm−3 and a void size of 10.90 µm,
which were 116.9% higher and 34.2% smaller, respectively,
compared with the foam formed in the presence of 2 wt%
unmodified silica nanoparticles that exhibited a void density
of 1.24 × 1012 cm−3 and a void size of 16.57 µm. In contrast,
the pure PMMA foam formed under the same condition exhibited a much smaller void density of only 5.48 × 1011 cm−3 and a
larger void size of 22.43 µm. The comparison again highlights
that adding monodisperse nanoparticle fillers to polymers can
reduce the size of voids in the polymer foams, favoring the
Table 2. Thermal conductivities and void parameters of polymer foams formed from homogeneous nucleation processes in the presence of
nanoparticles.
Composite matrix (phase I)
PU/clay foam
Gas (phase II)
d)
HFC-365mfc
PU foam
Filler mass concentration [wt%]
Void size [µm]
3
360
Porosity [%]
Thermal conductivity [W m−1 K−1]
Year[Ref.]
0.0185
2007[33b]
0
514
PU/clay foam
Air
5
163
94.0
0.0166
2008[33c]
PU/clay foam
Air
5
390
95.1
0.0332
2016[33d]
PU/CNF foama)
Air
0.5
86
0.0157
2010[36a]
PMMA foam
Air
0
22.43
61.6
0.0944
2009[35a]
PMMA/VMS foam
1
12.71
50.3
0.0860
2
10.90
47.0
0.0801
PMMA/RS
2
16.57
57.4
0.0904
PS/CNT foamb)
Air
1
5.8
Phenolic/TiN foam
Air
1
102.1 ± 4
PMMA/PU foam
Air
1
PP/PTFE foam
BPP/PTFE
a)
foamc)
0.0194
0.0328
2015[36b]
0.0312
2016[34]
0.205
0.0248
2017[37a]
0.930
0.0369
97.6
Air
5
22.5
0.0365
2017[37b]
Air
1
45
0.0324
2018[37c]
CNF: carbon nanofiber; b)CNT: carbon nanotube; c)BPP: branched polypropylene; d)1,1,1,3,3-pentafluorobutane.
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Figure 5. A) Illustrative diagram of an HSM made of blended polymer and hollow silica particles. Phases I, II, and III correspond to the polymer, air,
and silica, respectively. Cross-sectional B) SEM and C) TEM images of organosilicate hybrid films containing 10 wt% of hollow silica nanoparticles
with an average diameter of 50 nm and a shell thickness of 8–10 nm. B,C) Adapted with permission.[40] Copyright 2013, Springer Nature. D) Optical
photograph of the transparent polyethersulfone composite film containing 2.5 wt% of hollow silica spheres with 200 nm in diameter and 6.2 nm in
shell thickness. The film had a thickness of 35 µm, which is highlighted inside the rectangle outlined with dotted lines. D) Adapted with permission.[38d]
Copyright 2016, American Chemical Society.
reduction of their thermal conductivities. The PMMA foams
containing 1 and 2 wt% VMS nanoparticle fillers exhibited
low thermal conductivities of 0.0860 and 0.0801 W m−1 K−1,
respectively, which were 8.9% and 15.1% lower than that of the
PMMA foam. Besides inorganic nanoparticles, immiscible polymers are also possibly used as fillers to promote heterogeneous
nucleation of gas. In a synthesis of PMMA foams with CO2 gas,
PU that could form nanosized domains in PMMA matrix was
added as filler to promote nucleation of CO2 voids,[37a] forming
PMMA/PU composite foams with a void size of 205 nm and
porosity larger than 85%. The nanosized voids and high porosity
reduce the thermal conductivity of the PMMA/PU foams down
to 0.0248 W m−1 K−1.
4. Blends of Polymers and Hollow Silica Particles
Voids in a polymer matrix can be achieved by directly adding
hollow particles (or shells), which are synthesized independently,
to a solution or melt of the polymer followed by solidifying the
polymer. Such a direct mixing process does not require the supercritical conditions (e.g., high pressure and high temperature) of
Adv. Mater. 2019, 31, 1801001
gases used in the synthesis of polymer foams. In a blend of a
polymer and hollow particles of an inorganic material (e.g., silica),
the polymer and the empty interiors of the hollow particles represent the solid phase I and gas phase II, respectively, of an HSM
(Figure 5A). The inorganic walls of the hollow particles represent
the interfacial phase III of the HSM. According to the discussions
in Section 2, the gas thermal conductivity in the void phase II can
be reduced by using small hollow particles. The presence of the
interfacial phase III makes a positive contribution to thermal conductivity because the inorganic solids are usually more thermally
conductive than polymers. This undesired contribution can be
alleviated by reducing the wall thickness of the hollow particles.
Therefore, availability of small hollow particles with thin walls
becomes important to synthesize composite polymer insulation
materials with low thermal conductivities.
Several types of blended polymers containing hollow inorganic
shells are summarized in Table 3 with detailed information (e.g.,
component, filler size and concentration, porosity, etc.) and their
corresponding thermal conductivities. Hollow silica (or glass)
particles represent a class of widely explored materials to bring
voids into composite polymer insulation materials because of the
low cost of silica particles and their optical transparency.[38] For
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Table 3. Thermal conductivities and other parameters of blended polymers and hollow inorganic shells (glass, ceramic, and TiO2).
Polymer matrix (phase I) Interfacial phase III
Porosityc) [%]
Filler
Thermal conductivity [W m−1 K−1]
Year[Ref.]
Size [µm]
Wall thickness [µm]
Concentration
PU
Silica
0.375
0.040
0.25 wt%
0.14
0.05
2012[38b]
PU
Silica
0.1
0.010
10 wt%
6.11
0.029
2015[38c]
PES
Silica
0.181
0.006
12 vol%
9.77
0.030
2016[38d]
Epoxy resin (E51)
Glass
40
1.05
0
0
0.226
2015[38e]
10 vol%
8.51
0.211
20 vol%
17.01
0.196
30 vol%
25.52
0.174
40 vol%
34.02
0.163
50 vol%
42.53
0.156
Polyacrylate
TiO2
0.394
0.043
0.1825
2017[41b]
PVDFa)
Glass
72.5 ± 42.5
1.0 ± 0.5
0.047
2017[38f ]
Ceramic
91.6 ± 60
10 vol%
0.1815
Silica
27 ± 16
20 vol%
0.1493
Glass
52 ± 29
30 vol%
0.1362
b)
EPON 862
Silicone rubber
0.110
2017[42]
a)
PVDF: poly(vinylidene fluoride); b)EPON 862: epoxy resin; c)The porosity was calculated from dividing the volume of voids in fillers by the total volume of blended composites using the parameters including the wall thickness, concentration, and densities of fillers as well as densities of polymers.
example, Fuji and co-workers synthesized composite films by
dispersing 10 wt% hollow silica nanoshells (with a diameter of
around 100 nm and a wall thickness of ≈10 nm) in PU, achieving
a thermal conductivity of 0.029 W m−1 K−1, which is less than
one tenth of that of the pristine PU film (0.30 W m−1 K−1).[38c]
Similar to the polymer foams, a higher number density of hollow
silica nanoshells in a polymer reduces the characteristic size (δ)
of the polymer network when the geometrical parameters of the
silica nanoshells are constant, leading to a lower thermal conductivity of the polymer/silica composite material.[38a,39] Hollow
silica nanoshells have also been dispersed in varying polymers
to synthesize insulating materials with low thermal conductivities. Figure 5B,C shows the organosilicate (OS) composite films
containing well-dispersed hollow silica nanoparticles due to the
strong affinity between silica and OS matrix leading to a reduced
thermal conductivity.[40] Ernawati et al. prepared composite polyethersulfone (PES) films containing 2.5 wt% of well-dispersed
silica nanoshells (with a diameter of 181 nm and a shell thickness of 6.2 nm). The film with a thickness of ≈35 µm exhibited a
thermal conductivity of 0.03 W m−1 K−1, much lower than that of
the pure PES film (0.09 W m−1 K−1).[38d] Owing to the small size
of hollow silica nanoshells and the intrinsic optical transparency
of silica, the PES/silica composite film exhibited a high optical
transmittance of ≈90% in the visible region of 400–800 nm
(Figure 5D). The type of inorganic hollow nanoshells can also
be independently tuned to synthesize composite polymer insulation materials. For example, hollow TiO2 particles were dispersed
in polyacrylate to lower thermal conductivity of the polyacrylate
film.[41] Zhao et al. dispersed three types of commercial hollow
microparticles made of ceramic, silica, and glass in silicone
rubber.[42] Thermal conductivities of all the resulting composites
were lower than the pristine silicone rubber.
Adv. Mater. 2019, 31, 1801001
It is worthy of pointing out that high dispersity of inorganic hollow particles in polymers is critical to efficiently
lower thermal conductivity of the polymers especially when
the loading of hollow particles is high. A high concentration
of hollow particles in a polymer matrix can easily aggregate to
form continuous chains that provide additional heat transport
pathways with much higher thermal conductivity than that of
polymer.[43] This effect could erase the benefit brought by the
high-density voids towards reduction of thermal conductivity
of the composite thermal-insulation materials. Ruckdeschel
et al. have investigated the thermal transport in a binary colloidal mixture of hollow silica particles and P(MMA-co-nBA)
polymer particles with varying ratios.[44] The assembled monoliths of hollow silica (441 nm in diameter) and polymer particles
(423 nm in diameter) exhibit thermal conductivities of 0.013 and
0.057 W m−1 K−1 in vacuum, respectively. The thermal conductivities of the monoliths of binary colloidal mixtures increase
monotonically from 0.013 to 0.057 W m−1 K−1 as the ratio of polymer particles increases from 0% to 100%. Melting the polymer
particles at a temperature above the glass transition temperature
fuses the polymer particles into a continuous network, creating
additional percolation pathways for thermal transport and thus
increasing thermal conductivity accordingly. Moreover, the structural integrity of hollow shells is also important to achieve high
concentration of voids and thus low thermal conductivity of the
corresponding polymer composites.[45] This issue becomes more
challenging when using hollow shells with large sizes and thin
walls that are easily broken. Once the hollow shells are broken,
the voids will disappear and the resulting inorganic fragments
will increase the possibility to form inorganic heat transport
pathways, both of which prevent the reduction of thermal conductivity of the polymer–hollow-shell composites.[45]
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5. Assembly of Hollow Silica Particles
Inorganic hollow particles can be directly assembled into selfsupported macroscopic thermal-insulation materials. In an HSM
made from assembled hollow particles both the quasi-continuous
phase I and isolated void phase II are composed of gas, while the
particle shells form the interfacial phase III (Figure 6A). The adjacent particles in a closely packed assembly are in tight contacts,
which break the spatial continuity of the phase I to individual gas
pockets with much smaller volumes. Therefore, the contribution
of phase I to thermal conductivity of the HSM becomes minimum
and similar to that of the void phase II. In contrast, the tight contacts of the hollow particles create a high density of inorganic heat
transport pathways along the particle shells, which dominates the
thermal conductivity of the corresponding HSM. The accuracy in
controlling the size and shell thickness of hollow particles as well
as their assembly behavior is beneficial for correlating thermal
conductivities of the corresponding HSMs to the properties of
the hollow particles.[46] The relationship is useful to guide the synthesis of appropriate hollow particles for making HSMs with superior thermal insulation performance. The HSMs formed from
assembly of inorganic hollow particles can be operated at high
temperatures due to the absence of easy-burning polymers.
Gao et al. demonstrated the assembly of hollow silica particles
with 150 nm in void diameter and 10–15 nm in shell thickness
to form an HSM with a thermal conductivity of ≈0.02 W m−1 K−1
(Figure 6B).[46d] The significantly lowered thermal conductivity compared to that of bulk silica (1.2–1.4 W m−1 K−1)[47]
was attributed to the small contact areas of adjacent particles
that narrows the heat transport pathways. Puckdeschel and
co-workers designed experiments to systematically study the
dependence of thermal conductivity of the silica-particle HSMs
on the interfacial contacts of hollow silica particles.[46e] Beside
the contact interfaces, the defects (e.g., mesopores, organic
residuals retained from synthesis, nonuniform mass distribution, surface roughness, etc.) in individual silica shells also
influenced the thermal conductivity of the HSMs due to their
ability of scattering phonons. To differentiate the contributions
of the interfacial contacts between silica shells and the structural defects in individual silica shells, two groups of HSMs
made of the carefully synthesized silica nanoshells were fabricated and evaluated in thermal conductivities. The monodisperse silica nanoshells with a diameter of 316 nm and a shell
thickness of 44 nm were initially deposited on uniform polystyrene (PS) beads via a sol–gel reaction, forming PS@silica
core–shell particles. Calcination of the PS@silica core–shell
particles at elevated temperatures (≥500 °C) burned away the
templating PS beads encapsulated in the silica nanoshells,
leaving empty interiors in the silica nanoshells (i.e., hollow
silica nanoshells, Figure 6B,C). Calcination of the silica
nanoshells at elevated temperatures in air can reduce the density of structural defects in individual nanoshells and a higher
Figure 6. A) Illustrative diagram of an HSM formed from the assembly of hollow silica nanoshells. Both phase I and phase II are gas while the
interfacial phase III is silica. B) Transmission electron microscopy (TEM) image of assembled hollow silica nanoshells with a diameter of 150 nm and
a wall thickness of 10–15 nm. B) Adapted with permission.[46d] Copyright 2013, American Chemical Society. C) SEM image of assembled hollow silica
nanoshells. D) Thermal conductivities of the HSMs of assembled hollow silica nanoshells as a function of their Brunauer–Emmett–Teller (BET) surface
areas and annealing temperature (inset). The thermal conductivities were measured at 25 °C. E) Schematic illustration highlighting the difference in
the density of structural defects in the wall of individual nanoshells and the interfacial bonding (or interfacial contact) between adjacent nanoshells.
C–E) Adapted with permission.[46e] Copyright 2015, The Royal Society of Chemistry.
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temperature leads to a more significant result. When the silica
nanoshells are in contact and well packed, thermal annealing
can also increase the interfacial bonding between the adjacent
nanoshells, resulting in possible enlargement of the interfacial
contact area and enhancement of phonon exchange between
the adjacent nanoshells. Both effects indicate that thermal
conductivity of the assembled monoliths of silica nanoshells
increases with the annealing temperature. To differentiate
the influence of structural defects and interfacial bonding on
thermal conductivity of the silica nanoshell monoliths, two
groups of samples were compared comprehensively. The first
group of HSMs were made from assembly of the PS@silica
core–shell particles following by calcination at different temperatures resulting in both changes of interfacial bonding
and structural defects between/in the silica nanoshells. High
calcination temperature increases the interfacial bonding but
reduces the density of structural defects, which leads to the
increase of thermal conductivity (solid symbols, Figure 6D)
corresponding to a structural transition from (1) to (3)
(Figure 6E). Compared to the HSM formed from the assembly
of the PS@silica nanoshells following by calcination at 500 °C,
thermal conductivity of the HSM with the calcination of 950 °C
increased by about 100%, i.e., from 0.071 to 0.140 W m−1 K−1
(solid symbols, inset of Figure 6D). The increase of thermal
conductivity is caused by both the reduced density of structural defects in individual nanoshells and the enlarged interfacial bonding between nanoshells (structural 3 vs structure 1,
Figure 6E). The second group of HSMs were fabricated from
the assembly of hollow silica nanoshells synthesized at 950 °C,
followed by thermal annealing at different temperatures. Since
the hollow silica nanoshells were synthesized at 950 °C which
significantly reduced the structural defects, the assembly of
silica nanoshells followed by different annealing temperatures
only brought the changes of interfacial bonding. Thermal conductivity of the HSM annealed at 950 °C increased by 64%,
i.e., from 0.094 to 0.154 W m−1 K−1, compared to the HSM
annealed at 450 °C (closed symbols, inset of Figure 6D). The
increase in thermal conductivity of the second group samples
was mainly contributed by the enlarged interfacial bonding
between nanoshells at higher temperatures, corresponding to
a structural transition from (2) to (3) (Figure 6E). Assuming
thermal annealing of the assembled PS@silica core–shell
particles and the assembled silica hollow nanoshells (formed
from calcination of the PS@silica core–shell particles) at
the same temperature produces similar interfacial bonding
between the silica nanoshells, the variation of internal density
structural defects in individual silica nanoshells is responsible
for the difference of thermal conductivity between these two
groups of samples shown in the inset of Figure 6D. Lowering
the density of structural defects in individual silica nanoshells
corresponds to the increase of thermal conductivity from
0.071 to 0.094 W m−1 K−1, which is reflected as the structural transition of (1) → (2) shown in Figure 6D,E. This difference is equivalent to 32%, which is on the similar scale to
the difference caused by increasing interfacial bonding in the
(2) → (3) transition even though the absolute value is smaller
(32% vs 64%). The comparisons indicate that both reducing
the interfacial bonding between adjacent silica nanoshells
(i.e., narrowing the heat transport pathways) and increasing
the density of structural defects in individual silica nanoshells
can lower thermal conductivity of an HSM assembled from
the silica nanoshells despite the former is more effective. The
same author in another work proposed to reduce the thermal
conductivity by reducing the interparticle contact points
from 12 to 6 by changing the assembly order from ordered
packing to random packing.[46f ] The geometry of the hollow
silica particles (i.e., size and shell thickness) also plays significant roles on the thermal conductivity of the ensemble.[46f ]
Two different series of hollow silica particles with different
diameters (267, 387, and 469 nm) or shell thicknesses (14,
27, and 40 nm) are used to systematically identify the correlation between the geometry parameter with the thermal
conductivity of the corresponding ensembles (Figure 7A,B).
Thermal conductivity measurements in Figure 7C show that
the thermal conductivity decreased as the walls of the silica
nanoshells became thinner. Increasing the diameter of silica
nanoshells with a similar shell thickness further lowered
the thermal conductivity. A low value of 0.027 W m−1 K−1
was achieved in vacuum for the assembly of hollow silica
nanoshells with 469 nm in diameter and 17 nm in shell thickness (HS-469/17), which increased up to 0.082 W m−1 K−1 for
that of HS-266/40 (smaller nanoshells with thicker walls).
Figure 7. A) TEM images of hollow silica nanoparticles with various diameters and wall thicknesses. B) SEM images of the monolithic HSMs assembled
from the corresponding hollow silica nanoparticles shown in (A). C) Thermal conductivities of the HSMs of B) measured in helium and air at 1000 mbar
as well as vacuum (i.e., in the presence of 0.05 mbar of air). Adapted with permission.[46f ] Copyright 2017, Wiley-VCH.
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The self-support macroscopic films of hollow silica structures
can also be synthesized from a one-step process, in which formation of hollow silica nanoshells and their self-assembly simultaneous occur at a two-phase interface (e.g., gas/water or oil/
water interface).[48] For example, Mille and Corkery synthesized
films of assembled hollow silica shells by using a microemulsion
method that involved the formation of silica shells at an oil/water
interface.[48b] The walls of the silica shells were mesoporous, and
the existence of a high density of nanometer-sized pores lowered
the mass density of the silica shells to only 0.58 g cm−3. The
thermal conductivity of the film was 0.041 W m−1 K−1, which
represents only 3% of the thermal conductivity of bulk silica.
6. Aerogels
The 3D structure of HSMs made from assembly of hollow silica
shells discussed in Section 5 can be mimicked by forming aerogels of silica nanoparticles. In a silica aerogel, the solid network
composed by silica nanoparticles is the interfacial phase III
highlighted by the dotted line in Figure 8A. The phase I and
phase II of aerogels are composed of gas. The characteristic
size, δ, could be below zero due to the high void fraction and
quasi-continuous solid network, indicating the interconnection
of voids. The rendered 3D model of a typical silica aerogel is
schematically shown in Figure 8B, highlighting the interlaced
network of assembled chains of silica nanoparticles. In an silica
aerogel HSM shown in Figure 8C, the voids and gas pockets
are usually less than 100 nm in size, i.e., on the order of several
nanometers to ten of nanometers, which significantly reduces
the contribution of trapped gas to the thermal conductivity of
the HSM.[49] The solid heat transport pathways are formed from
the intricate network of silica nanoparticle chains. The small
size (i.e., 2–5 nm) of the silica nanoparticles defines the characteristic size of the heat transport pathways that is very small and
can lower the thermal conductivity. The high density of internanoparticle interfaces favors the strong phonon scattering
and thus reduce the thermal conductivity. Therefore, highquality silica aerogels can have very high porosities (>97%) and
low thermal conductivities around 0.03 W m−1 K−1 at ambient
atmospheric condition. The thermal conductivity can be further
reduced by vacuuming the aerogels to a value that is even lower
than the thermal conductivity of still air (0.026 W m−1 K−1).
Silica aerogels were invented by Kistler in 1931[50] and have
attracted great attention due to their unique properties including
extremely low mass density, high surface area, and low thermal
conductivity.[51] Successful synthesis of high-quality silica aerogels
is challenging. The critical step is the removal of entrapped solvents from the wet gels without breaking the integrity of the 3D
networks of silica nanoparticles. Direct drying of a wet silica gel
under ambient conditions leads to shrink its volume due to collapse of the voids. Such a mechanical failure originates from the
poor mechanical properties of the fractal silica network and the
strong capillary forces exerting on the solid network during solvent
evaporation.[52] Kistler and Caldwell used supercritical organic solvents (e.g., dichlorodifluoromethane) to wet a silica gel followed by
drying the wet gel at the critical point of the solvent, at which the
conversion from liquid to gas was imperceptible without involvement of capillary compressive forces.[53] Complete removal of
organic solvent left the intact skeleton of silica nanoparticles that
maintained almost the same apparent volume as that of the wet
gel. An alternative way to prevent the mechanical failure is to
eliminate the surface tension force by switching the surface property of the silica nanoparticles from hydrophilic to hydrophobic.
A silylation process can graft methylsilane reagents such as
methyltriethoxysilane (MTES), trimethylethoxysilane (TMES), and
Figure 8. A) Schematic illustration of the microscopic geometry of a silica aerogel slice. Both phase I and phase II are gas, and phase III is a network
of the chains of assembled silica nanoparticles. B) Rendered 3D illustration of a silica aerogel. C) TEM and SEM (inset) images of a slice of typical
silica aerogel. C) Adapted with permission.[54b] Copyright 2008, Springer Nature. D) SEM and TEM (inset) images of an aerogel made from singlewalled carbon nanotubes. E) Comparison of thermal conductivity of the SWCNT aerogels and conventional carbon aerogels with various densities.
D,E) Adapted with permission.[58] Copyright 2013, Wiley-VCH.
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trimethylchlorosilane (TMCS), to the silica nanoparticles, resulting
in hydrophobic surfaces.[54] For example, Wei et al. modified the
silica nanoparticle surfaces with TMCS and the corresponding
silica wet gel was dried essentially without suffering of volume
shrinkage (<1%) even under ambient conditions.[55] Avoiding
the significant volume shrinkage retained the high porosity of
the dry silica aerogel, enabling a low thermal conductivity of
0.036 W m−1 K−1, much lower than that formed from the unmodified silica nanoparticles (0.417 W m−1 K−1). These successes shed
light on the commercialization of silica aerogels to the market.
The silica aerogels with high porosities are mechanically
fragile, limiting their applications. Their poor mechanical
strength can be improved by forming composite aerogels with
other materials (e.g., PMMA, fabrics and xonotlite) that exhibit
good thermal insulation and excellent mechanical flexibility.[56]
Moreover, nonfragile aerogels made of different materials such
as 1D carbon nanotubes and mechanically flexible organics
are receiving equivalent attention.[8a,57] Zhang et al. fabricated
aerogels from single-walled carbon nanotubes (SWCNTs),[58]
showing an ultralow mass density of ≈6.6 kg cm−3 that was
much lower than the conventional carbon aerogels.[59] The
atomic-level continuity and excellent mechanical strength/
flexibility of the SWCNTs makes the 3D entangled network to
be more rigid (Figure 8D), facilitating the accommodation of
more gas to exhibit a lower average density. As a result, the
thermal conductivity of the SWCNT aerogel was measured to
0.056 W m−1 K−1[58] although the thermal conductivity of individual SWCNTs is high (Figure 8E).[60] An organic RF aerogel
exhibited a thermal conductivity of only 0.012 W m−1 K−1 under
ambient condition.[11a] Luo et al. synthesized the crosslinked
glycidyl methacrylate (GMA)–divinylbenzene (DVB) copolymer
monoliths (aerogels) containing voids with tunable sizes.[61]
Decreasing the void size from 889 to 190 nm led to a decrease
of thermal conductivity from 0.038 to 0.022 W m−1 K−1.
7. Conclusion and Outlook
Hollow-structured materials are a class of macroscopic monoliths containing numerous microscopic voids filled with gases,
in which the spatial distributions of the immiscible gaseous and
solid phases are controlled to deliver new properties that are difficult or even impossible to achieve using the corresponding solid
materials only. For example, the existence of high-density small
gaseous voids in a polymer foam breaks the continuity of the
polymer as well as the transport behavior in the polymer. Heat
transfer in a polymer foam can be dramatically interrupted since
the thermal conduction mechanisms in a gas and a solid polymer
are different, i.e., molecular collision in the gas versus molecular
vibration in the polymer. Simultaneously decreasing the size of the
gaseous voids and increasing the density of the voids enhances the
discontinuity of thermal transport pathways, favoring a significant
reduction of thermal conductivity in the foamed polymer compared with the solid ones. In particular, thermal transport behavior
may fall in a confinement region to further lower the thermal conductivity of a foamed polymer when the voids are small enough,
e.g., on the scale of less than 100 nm. Such a discontinuity of
thermal transport in HSMs makes the HSMs a class of promising
materials for superior thermal insulation (e.g., comparable or even
lower than the thermal conductivity of ambient air).
The recent intensive efforts on various types of HSMs are
well acknowledged to develop thermal-insulation materials with
extremely low thermal conductivity for high-end applications.
Figure 9 summarizes thermal conductivities of different HSMs
Figure 9. Dependence of the normalized thermal conductivities of various HSMs on the void size. The normalization was calculated from dividing
the recorded thermal conductivities (kHSM) by both the volume fraction and the intrinsic thermal conductivity of the solid components in the HSMs,
i.e., kHSM/[(1 − Π)ks,0]. The colors differentiate the type of HSMs, i.e., black, red, green, and blue correspond to the polymer foams formed through
(black full-filled symbols) homogeneous nucleation and (black half-filled symbols) heterogeneous nucleation (samples in Section 3), blend of
polymer and hollow silica nanoparticles (samples in Section 4), assembled hollow silica nanoshells (samples in Section 5), and aerogels (samples in
Section 6), respectively. The clustered distribution of the normalized thermal conductivities highlights the importance of the void size in influencing the
thermal conductivity of HSMs. The voids smaller than ≈350 nm bring a positive effect to reduce the thermal conductivity of an HSM in addition to the effect
of lowered mass density. In contrast, the HSMs with larger voids cannot completely benefit the lowered mass density to reduce their thermal conductivity.
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with varying porosities and void sizes. The recorded thermal
conductivities (kHSM = ks,HSM + kg,HSM) of the HSMs are normalized against the volume fractions of the solid components (1 − Π)
and the intrinsic thermal conductivities (ks,0) of the solid components in the HSMs by following kHSM/[(1 − Π)ks,0]. When the
thermal conductivities of the HSMs are dominated by the solid
heat transport pathways, the normalized thermal conductivities
would be close to 1 if the heat transport behavior is independent
of the voids. The broad distribution of thermal conductivities of
HSMs summarized in Figure 9 indicates that the void size represents an important parameter to influence the heat transport
properties in the HSMs. As the voids are smaller than ≈350 nm,
the HSMs exhibit normalized thermal conductivities lower than
1 regardless of the types of the HSMs (e.g., those discussed in Sections 3, 4, 5, 6). It indicates that reducing the void size may induce
size-dependent phenomena (e.g., confinement effects) to further
lower the thermal conductivity of an HSM in addition to the
contribution made by the lowered mass density. In contrast, the
normalized thermal conductivities of the HSMs with voids larger
than ≈350 nm are usually larger than 1. The summary of Figure 9
highlights the importance of reducing the void size on fabricating
high-quality insulation materials when the same porosity can be
achieved in the HSMs.
Besides low thermal conductivities, additional functions and
fabrication cost should also be well considered to bring an HSM
as a thermal-insulation material for practical applications. For
instance, silica aerogels possess extremely low thermal conductivities and are stable at extreme temperatures, but their mechanical
fragility and costly manufacturing process hinder their wide applications.[62] While we benefit from the low thermal conductivity
originated from the breakage of continuity of thermal transport
pathways in HSMs, the existence of gaseous voids also breaks the
continuity of light transport pathways due to scattering, leading
to optical opacity of HSMs. The light scattering caused by the
gaseous voids can be eliminated by reducing the void size below
100 nm to form optically transparent HSMs, which are useful for
thermal insulation requiring transparency, such as laminating
films of single pane windows.[63] The function of blocking UV
irradiation in the transparent insulation films can be added by
introducing TiO2, which is transparent in the visible region but
strongly absorbs UV light, to composite HSMs. For instance, an
organosilicate film containing dispersed silica/TiO2 hybrid hollow
nanoshells (with a size of 50 nm) exhibits a thermal conductivity
20% lower than the film without nanoshells.[40] The film is highly
transparent in the visible region and is efficient in blocking the
UV light. Doping HSMs with components that strongly absorb
infrared irradiations (e.g., carbon fibers) is useful to reduce the
radiative thermal conductivity of the HSMs.[64]
Acknowledgements
This work was completed with Government support under Award No.
DE-AR0000739, awarded by the Advanced Research Projects Agency–
Energy (ARPA-E), U.S. Department of Energy, through a subcontract
from the University of Chicago.
Conflict of Interest
The authors declare no conflict of interest.
Adv. Mater. 2019, 31, 1801001
Keywords
aerogels, hollow-structured materials, polymer foams, silica nanoshells,
thermal-insulation materials
Received: February 11, 2018
Revised: July 31, 2018
Published online: October 31, 2018
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