解説

先進セラミックス研究センター年報（2016）. Vol. 5, 21‑36

Electrically Functional Silicone Composites and Their Applicationin Mechanical Sensors
Chen Guo, Dianming Sun, Chika Takai, Razavi Hadi, Takashi Shirai, Feng Wang, Masayoshi Fuji
Advanced Ceramics Research Center, Nagoya Institute of Technology
3-101-1, Honmachi, Tajimi, Gifu 507-0033, JapanAs a type of special elastomer, silicone elastomer possesses a lot of advantages such as an extreme flexibility, a very wide
temperature tolerance range, an excellent insulation and an unparalleled good biocompatibility, which can be utilized in industrial,
health care or daily lives. In order to widen the areas of use, overcome some drawbacks of the silicone elastomer, many kinds offunctional fillers could be integrated into the elastomer. Just to take advantage of its excellent insulation, inorganic fillers withhigh dielectric constants, such as BaTiO3 and TiO2, could be added into the silicone elastomer to fabricate a flexible composite
with a high dielectric constant, which can be utilized as an actuator, or be appropriate to be assembled to a tactile or vibration
sensor. On the other side, inorganic fillers with high electrical conductivities and large relative surface areas, such as MWCNT,
carbon short fiber or graphene, could be integrated into the elastomer to provide a low resistivity. This type of composite has an
obvious piezoresistive property, which is suitable for being used within a tactile sensor. Many previous outstanding works werediscussed in the article.
Keywords: silicone elastomer; electrical function; barium titanate; dielectric constant; MWCNT; piezoresistive property;

mechanical sensor

1. A brief introduction of silicone elastomers

Elastomer is a vague definition of a wide range ofpolymeric materials. Elastomers are amorphous
polymers with glass transition temperatures below room
temperature, which display elastomeric behaviors suchas viscoelasticity, very weak inter-molecular forces andgenerally low Youngʼs modulus accompanied with highfailure strain compared to other materials. “Rubber” and“elastomer” can be used interchangeably, the latter often
refers to synthetically produced elastomeric polymers.
An elastomer can be crosslinked or not. A crosslinked
elastomer has covalent bonds between the different
polymer chains, connecting all of them within a single
networked molecule, which prevents the plastic
deformation caused by the slippage of molecular chains.
An elastomer without chemical covalent bonds usually
has physically crosslinks such as hydrogen bonds andVan der Waals forces between their polymer chains,defined as thermoplastic elastomer (TPE) that can beproduced with a simple casting molding method and canbe recycled. The backbones of the polymer chains in acommon elastomer are usually made up of carboncarbon or carbon-oxygen bonds, the flexibility of theelastomer is related to the saturation levels of the
carbon-carbon bonds and the sizes or the cis/transstructures of the side chains.

Silicone, which has a scientific name of polysiloxane,
is a series of polymeric materials made up of repeating
units of a siloxane with a backbone of alternating silicon
atoms and oxygen atoms, frequently combined with side
chains of carbon and hydrogen. The chemical structuresof the silicone backbones are similar with the structuresof quarts, giving it a superb heat-resistant ability [1,2]. A
longer bond length and a larger bond angle of siliconoxygen-silicon bond in silicone lead to an easierconfiguration variation, which brings a highly flexible
behavior. Many benefits are brought from silicone
elastomers, such as an excellent environmental
resistance, a low compression set, a low level of
combustible components, and a high physiologicalinertness. All types of silicones are known to be good
insulation which can act as the substrates of dielectrics[3]. However, there are also some disadvantages ofsilicone elastomers, such as a poor abrasion, a poor
petroleum resistance, and relative low tear strength.
Many of them could be overcome by the composite
process.
2. Introduction of elastomer-based
functional composites

Composites that are made up of functional particles
and elastomer have both the functionality of the particles― 21 ―Electrically Functional Silicone Composites and Their Application in Mechanical Sensors

and the low elastic modules of the elastomer. A poly(dimethylsiloxane)-titania nanocomposites was preparedusing heat-treated titania as fillers by Suryakanta Nayak
et. al. [4], dielectric and mechanical properties of thecomposites were measured, it was found that both thedielectric constant and the loss factor of the composites
was increased dramatically with the addition of thetitanium dioxide filler, whereas resistivity wasdecreased. Both electrical and mechanical properties
were affected by heat treatment of titania particles. It
was known that heat treatment decreased the moisture
content and also affected the concentration of Ti3+ in
TiO2, which in turn affects electrical properties of thesystem. It was confirmed that presence of surfacehydroxyl groups enhances the dielectric constant of thecomposites. Federico carpiʼ group [5] firstly reported theembedding of highly dielectric ceramic inclusions in arubber medium as a method to improve theelectromechanical material for dielectric elastomer
actuation. In comparison with pure silicone, a decreased
elastic modulus, as well as an increased dielectric
constant was exhibited. The utilization of this composite
as an elastomeric dielectric for planar actuators enabled
a reduction of the driving electrical fields. Especially thestrain and stress were more than 8 and 4 times higher
than the corresponding values that generated with thepure silicone matrix for the analogous electrical stimuli.
In Zsolt Varga ʼ study, the magnetic elastomer was
prepared by dispersing carbonyl iron particles randomly
into dimethylpolysiloxane (PDMS) [6]. It was found thatthe elastic modulus of this magneto elastomer could be
increased by an external magnetic field which is called
as temporary reinforcement. Anisotropic samples wereprepared by varying the spatial distribution of themagnetic particles in the elastic matrix to enhance themagnetic reinforcement effect. It was found that muchlarger increase in modulus can be exhibited by theuniaxial field structures than the one with randomly
dispersed particles. The most significant temporary
reinforcement effect was found if the applied field, theparticle alignment, and the mechanical stress are allparallel with each other. A novel polymer composite wasdeveloped by Jiawen Xu et al. [7], using self-passivatedaluminum particles as the filler. The nanoscale insulatingoxide layer of which allows the composites to have ahigh dielectric constant as a percolation system, while
confines the electrons within the aluminum particle,
which helps to keep a low loss of the composites. A highdielectric constant with low dissipation factor was

obtained from an aluminum/epoxy composite. The
thickness of the alumina insulating layer is found tohave a negative relation with the particle size. It was
found that the polymer matrix can significantly change
the dielectric properties of the composites. Functional
composites consist of a dielectric active ceramics phaseincorporated with a polymer matrix have found use in avariety of applications for sensors and actuators. As thepioneer of this research area, R.E. Newnham has studied
a lot of piezoelectric smart composite materials for awide variety of engineering applications, firstly
established the notation for the connectivity of functional
composites [8,9]. This notation describes the number ofdimensions that each phase is physically in contact withitself. The first number in the notation denotes thephysical connectivity of the active phase and the second
number refers to that of the passive phase. Composites
with 0-3 connectivity consist of functional particles
randomly dispersed in a 3D polymer matrix. The
primary advantage of a composite with 0-3 connectivity
is that it is easy to fabricate, especially to make a thinmembrane from it, while remaining the functional
activity of the particles [10]. Their research groupstudied fired 0-3 piezoelectric composites for biomedical
ultrasonic imaging applications, consisting of pellets ofLead Zirconate Titanate (PZT) ceramic powders andbackfilled with a series of epoxy resins. It was foundthat composite made out of PZT-Spurr epoxy and fired
at 900 㱥 gave the best performance and the best
efficiency as an underwater sensor [11].
3. BT/elastomer composites and theirmechanical sensing study

BaTiO3 (which has an abbreviation of BT) is a kind ofsignificant dielectric material with ferroelectric
properties under its curie point, which is widely used for
ceramic capacitors [12]. The dielectric constant of BT
strongly depends on the grain sizes, coarse-grained
ceramics of 20~50μm BT show dielectric constant of
about 1500~2000 at room temperature, the roomtemperature dielectric constant has a maximum of about
3500~4000 when the dense, fine-grained BT has a sizeof about 1μm [13]. BT with diameters of 300nm and
500nm (BT300 and BT500) that are often utilized inindustry were used in the author ʼ s previous work.
Although having such a high dielectric constant, BT still
suffers from some problems such as low breakdown
strength, brittleness, and processing difficulties. On theother hand, despite low dielectric constant, organic― 22 ―

Chen Guo, Dianming Sun, Chika Takai, Razavi Hadi, Takashi Shirai, Feng Wang, Masayoshi Fuji

polymers have several advantages such as low dielectricloss, high electric breakdown strength, low elastic
modules and good processability [14,15]. The problems
could be overcome by integrated the BT particles into a
flexible elastomer to fabricate a dielectric elastomericcomposite, which would lead to a lot of potential novel
applications. For instance, a dielectric elastomer actuatorcan be made by sandwiching membrane of dielectriccomposites between two compliant electrodes, after
loading a voltage between the compliant electrodes,
compression in the thickness direction and stretching inarea direction of the elastomer membrane could occur
due to the Coulombic force [16-21]. On the contrary, amechanical sensor can be assembled by such a dielectric

elastomer and be used to detect the external tactile
pressure or mechanical impact by measuring thecapacity change.
Because of the poor compatibility between inorganic
dielectric particles and organic silicone elastomer,
agglomeration of particles is difficult to avoid, bringing
a high dielectric loss and a lot of pores that would reducethe dielectric constant of the composite [15].
Consequently, it is of great significance to improve thecompatibility between inorganic dielectric particles andelastomers. The reason of improvement of dielectric
constant due to the surface modification of the BT
particles by the silicone coupling agent is described as
below.

Figure 1 Theoretical models of BT/silicone composites membrane
a: the most serious agglomeration, absolutely divided into two parts
b: the middle status between a and cc: dispersed very well, absolutely becomes one partAs shown in Fig.1, dispersion status of the BT
particles in the silicone elastomer consists of 3 different
types. During the fabrication, BT particles are usuallydispersed into the uncured silicone elastomer andcontinually affected by gravity until being cured. The
silicone elastomer has a density of 0.93g/cm3 and the BT
particles have a density of about 6.02g/cm3 which is far
more greater than the former, therefore in the curing
procedure, the BT particles always tend to precipitate
and agglomerate. In Fig.1, part a exhibits an extreme
situation that all the BT particles precipitated to thebottom and aggregated, making the whole membrane
into two parts: the silicone elastomer part at the upperside and the BT particles part at the bottom. Part c shows
an extreme situation oppositely that every single BTparticle is separated apart and uniformly distributed in
the silicone substrate. Part b is a kind of natural status
between situations a and c. As an ideal status, all of theBT particles are distributed into a lot of separated unitsof agglomeration. Each unit contains several BT
particles and is uniformly distributed in the silicone
substrate. The size of each unit is not a constant andcould vary as the amount of BT particles.
Assume that the dielectric constant of a vacuum is ε0,
the area of membrane is S, the thickness of themembrane is d, and the volume fraction of the BT
particles in the composite is x. Every membrane issandwiched with a good contact by a pair of parallel
electrodes with areas of S. Assume that the dielectric
constant of the silicone elastomer, BT particles, and thecomposite is εe, εf and ε, respectively. The capacitance Cof the elastomeric composite can be calculated asfollows:(1)
For situation a in Fig.1, the capacitance of the silicone― 23 ―Electrically Functional Silicone Composites and Their Application in Mechanical Sensorsof the membrane because of its good dispersity. The
dielectric constant of the membrane can be calculatedas:(4)
From Eq. (4), we can get the dielectric constant:part and the BT part can be calculated, and capacitanceof the entire membrane is reversely proportional to thecapacitance of the silicone part and the BT part, so thecapacitance of the entire membrane can be calculated as:

(5)
(2)

BT particles of 300~500nm have a dielectric constantof about 3300 [23]. According to the previous result, thesilicone elastomer has a dielectric constant of about 8.
By substituting εe=8 and εf=3300 into Eq. (3) and Eq. (5),the theoretic dielectric constant of the membrane insituation a and c in Fig.1 can be calculated.

Comparing Eq. (2) with Eq. (1), we can get the dielectricof the membrane as:(3)
For situation c in Fig.1, the Lenchteneckerʼ logarithmic
law [22] can be used to calculate the dielectric constant

Table1 Theoretical dielectric constant of membrane in situation a and cvolume fraction

10%

20%

30%

40%

50%

ε in situation a

8.9

10.0

11.4

13.3

16.0

ε in situation c

14.6

26.7

48.7

88.9

162.6

As shown in Table1. It is confirmed from thecalculated results that within a wide volume fraction
range from 10% to 50%, the well dispersed BT/silicone
membrane has a higher dielectric constant than the
agglomerated one. BT/silicone membranes, in reality,
should have a dielectric constant value between situationa and situation c in Fig.1. The dielectric constant of thecomposite membrane can be raised by improving thedispersity status of the BT particles, making it close tosituation c in Fig.1.
Shu-Hui Xie, Bao-Ku Zhu and their coworkers [24]synthesized polyimide/BT composites through a
colloidal process, finding that the BT particles in the sizeof 100 nm were dispersed homogeneously in thepolyimide matrix without aggregation. Dang Zhi-Min
and his coworkers [25] found that dielectric constant in
the polyvinylidene difluoride (PVDF) matrix composites
with BT treated by 1.0wt% silane coupling agent KH550
was increased. Their group also found that [26] anappropriate silane coupling agent can be used to improve
the interaction between BT and epoxy resin to get a highrelative permittivity BT/epoxy resin composites. L.
Ramajo et al. [27] studied the influence of silane
coupling agents on the microstructure and dielectric
behavior of epoxy/BT composites, finding that theircomposites presented good dielectric properties and astrong dependence on the silane concentration.
In author ʼ previous work [28], to improve thedispersity of BT particles, silicone coupling agent wasused to modify their surface. The TG, FTIR results
showed that coupling agent was successfully coated on
the surface of BT particles. BT/silicone composites
membranes were fabricated using raw BT particles andBT particles modified by silicone coupling agent. The
particle size distribution measurement and SEM
observation showed that BT particles became much
more compatible with silicone substrate, the dispersity
was considerably improved by surface modification.
Dielectric properties were evaluated by LCR meter. The
dielectric constant of composites membranes wasincreased after the dispersion status of BT particles being
improved by surface modification with silicone coupling
agent. Theoretical calculation from extreme cases provesthat agglomeration of BT particles in the verticaldirection can seriously reduce the dielectric constant ofcomposites membranes, the dielectric constant can beraised by improving the dispersion of BT particles.
Although significantly lower than theoretic values, thepiezoelectric properties of BT/Silicone composites show
the expectation of being applied in mechanical sensors
due to its rapid response to instantaneous electric signals,
simple structures, and low costs.

― 24 ―

Chen Guo, Dianming Sun, Chika Takai, Razavi Hadi, Takashi Shirai, Feng Wang, Masayoshi Fuji
Figure 2 SEM images of cross section of BT/silicone composites
a. raw BT300/silicone composite b. surface modified BT300/silicone composite

Fig.2 shows the SEM images of BT/silicone
composites. The cross sections of sample membranes
were obtained by breaking them after soaking in liquid
nitrogen. Part a shows the SEM image of raw BT300/
silicone composites with a volume fraction of 20%. The
agglomerates of large amounts of BT300 particles can
be clearly observed. At the same time, some cavities canbe found in the visual field. To avoid the bubbles asmuch as possible, mixing of the samples was carried out
at vacuum environment. Nevertheless, due to the highviscosity of the BT/silicone mixture, it is almost
impossible to eliminating all of the bubbles.
Furthermore, due to the large contact angle between BT
particles and silicone monomer, it is also impossible tocoat the entire surface of the particles and occupy all the
space in the composites. BT particles without surface
modification are highly hydrophilic while silicone
elastomer is highly hydrophobic, during theagglomerating procedure, silicone molecules would be
repulsed from around the generated agglomerates andproducing many bubbles which would turn into pores
after curing. These agglomerates and pores may reducethe dielectric properties of the composites membranes.
There is no apparent sign showing silicone has beencoated onto the BT particles from the part a, this may
due to the poor compatibility between BT and silicone.
Part b in Fig.2 shows the SEM image of a sample of
8.57%wt modified BT300/silicone composites with avolume fraction of 20%. It is found that BT particles
were dispersed much better than in part a. Although
there are still agglomerates in the substrates, their sizes
become much smaller and were distributed to a wider
area. More importantly, it can be observed that the BT
particles are all coated with a layer of silicone elastomer,
which may be due to the improved compatibility
between BT and silicone after surface modification.
Observation of SEM images proves that surface
modification by silicone coupling agent can obviously
improve their dispersity in silicone elastomer.

Figure 3 Dielectric constants of BT300/silicone and BT500/silicone membranes at different frequencies

Dielectric properties of BT/silicone membranes were
measured by a LCR meter. Dielectric constants of
BT300/silicone and BT500/silicone composite
membranes with different volume fractions at afrequency from 400Hz to 100kHz are shown in the left

side and right side of Fig.3, respectively. It can be
known that for every membrane with the same volume
fraction but different modification ratios, there is no
obvious variation observed from the dielectric constantfrequency curves from low frequency to high frequency.

― 25 ―Electrically Functional Silicone Composites and Their Application in Mechanical Sensors

This is because the whole dielectric properties were
measured at a low-frequency area. Obviously, dielectric
constant considerably grows as increasing of the volume
fraction of BT particles. At a frequency of 10 kHz, thedielectric constant of pure silicone membrane is about 8,
and it can be raised to about 35 for raw BT300/silicone
membrane with volume fraction of 40%. It is found thatthe dielectric constant was raised up slightly after
surface modification by silicone coupling agent. For
example, at a frequency of 10 kHz, for BT300/silicone
membrane with a volume fraction of 20%, the dielectric
constant changes from 15, 18, 18.5 to 17.5, as
modification mass ratio increasing from 0, 2.86%,
8.57% to 14.29%, respectively. And for BT-300/silicone
membrane with a volume fraction of 40%, dielectric
constants are 34, 34, 35.5 to 35, for membranes withmodification mass ratios of 0, 2.86%, 8.57% and14.29%, respectively. BT-500/silicone membranes show
the similar variation and have almost the same dielectric
values with the BT-300/silicone membranes. For surface
modified BT500/silicone membrane with a volume
fraction of 40%, the dielectric constant reaches about 33.
There are obvious dielectric loss for the BT/silicone
composite due to a lot of factors [14] as follows: Direct
current conduct (DC conduct); space charge migration(interfacial polarization contribution); dipole loss causedby movement of molecular dipoles. It is believed thatthe dielectric loss may decrease after surface
modification with silicone coupling agent, because if the
majority of BT particles are coated by coupling agent
layers with an excellent insulation property, conductivity
through BT particles could be significantly reduced,
accumulation and migration of electric charge within thecomposites could be restricted at the same time.

Figure 4 Periodic variation of stress and current of measuring circuit containing BT/silicone membranes

In order to measure the piezoelectricity of the BT/
silicone composites, the measuring circuit including apair of copper electrodes and the composite membranes
sandwiched between them was prepared to act as asimple parallel plate capacitor. A multimeter was
mounted into the circuit to detect the instantaneous
current, a constant voltage of 5V was loaded by a DC
power. The membrane accompanied with electrodes wasset on a metal plate, a periodical stress was loaded on
the membrane by a metal press. Firstly, the press
descended with a constant speed of 1000 mm/min,compressing the membrane until its thickness becoming
the half; then the press rose up immediately with thesame speed until returning to the original position. This
procedure was repeated periodically. During the

movement, capacitance varies as the changing ofthickness, creating a charge-discharge recycle, a weak
periodic current could be detected by the multimeter. In
the experiment [28], BT300/silicone membrane with athickness of 3.01mm was used. Fig.4 shows the periodic
variation of current occurs in measuring circuit with
about 3 cycles. The varying period of current and stressare about 250ms for measuring circuit containing
BT300/silicone membrane membrane. For a circuit
containing BT300/silicone membrane, stress increases
from 0 to about 900kPa and returns to 0 with a sharp
peak. It can be found that from cycle 1 to cycle 3, themax stress becomes much smaller, which is due to thestress relaxation of silicone elastomer. At first half
period, currents increases from 0 to about 0.9nA― 26 ―

Chen Guo, Dianming Sun, Chika Takai, Razavi Hadi, Takashi Shirai, Feng Wang, Masayoshi Fuji

immediately and soon decreases to 0; at the second half
period, the currents changes to the opposite direction,
like the first half period, then increases from 0 to about
0.8nA immediately and soon decreases to 0. The
variation of currents does not show the linear trend
mainly because of the nonlinear variation of thickness.
The measuring circuit is expected to be appropriate toapplications as a mechanical sensor, benefiting from its
rapid response to instantaneous electric signals, simple
structures, and a low cost.
4. Multi-walled carbon nanotubes/silicone
conductive foams and their piezoresistive
behaviors

Carbon nanotube (CNT) is a type of cylindrical-likecarbon nanomaterial with many unusual properties suchas extraordinary thermal conductivity, mechanical andelectrical properties which are valuable in many
structural and functional applications [29-33]. Especiallythe multi-walled carbon nanotube (MWCNT) has arelatively low cost and many special behaviors [34-36].
The carbon nanotube has metallic conductivity or
semiconducting behavior along its tubular axis. In
theory, an armchair type carbon nanotube can carry anelectric current density about 1000 times greater thanthat of copper [37]. Thus CNTs are famous for being
investigated as the conductivity enhancing fillers inpolymeric composites. J. O. Aguilar et al. studied theinfluence of CNT clustering on the electrical propertiesof polymer composite films by comparing thecomposites with CNTs uniformly dispersed and withthose agglomerated in clusters at micro-scale. They
found that films with micrometer-size agglomerations
have a slightly lower percolation threshold and a higher
conductivity than those with uniformly dispersed CNTs,
which can be explained that the increased density of
CNT-to-CNT junctions favors the formation of the
conductive networks [38].
The demand for diverse types of sensors with smart
property and low cost is growing rapidly as the recent
development of novel technologies, especially artificial
intelligence (AI), virtual reality (VR), bionics andbiotechnology. Many previous works have been
conducted for the implementation of carbon nanotubes
in advanced sensor applications [39-45]. M. L. Yola etal. developed a novel imprinted electrochemical
biosensor based on Fe@AuNPs and f-MWCNs for direct
determination of cefixime (CEF) in human plasma,
which showed high sensitivity and selectivity towards

CEF and offers the advantages of simplicity andefficiency in target detection from biological samples[39]; their groups also reported the synthesis andapplication of NiO-multiwall carbon nanotube
nanocomposite (NiO/MWCNTs) and 1-butyl-3methylimidazolium tetrafluoroborate ([Bmim]BF4) inthe carbon paste matrix as high sensitive sensors forvoltammetric determination of vitamin C in the presenceof vitamin B9 in food and drug samples [40]; a robust
micro-vibration sensor for biomimetic fingertips was
designed by J. A. Fishel et al., which can readily detect
the high-frequency vibrations by recording the fluid
conducted vibration signals when such a fingertip slides
across a ridged surface [41].
MWCNT/polymer conductive nanocomposites have
many unique electrical and mechanical properties, suchas piezoresistivity, electromagnetic interference (EMI)shielding effect and highly flexibility, which areappropriate for applications as smart functional
materials. MWCNT/polymeric conductive
nanocomposites provide obvious piezoresistive
behaviors, having applications in many special fields
due to their high flexibility, which can be easily
produced with large sizes and very low costs. The straindependent electrical resistance characteristics of
MWCNT/polyethylene oxide (PEO) were investigatedin the research of Park, M. et al. Unique and repeatable
relationships in resistance versus strain were obtained,
the overall pattern of which was found consists of linear
and nonlinear regions. This type of material was
expected to be used as tunable strain sensors such as
sensors embedded into systems [46]. Al-Saleh et al.
analyzed the EMI shielding mechanisms of MWCNT/
polypropylene composite plates experimentally andtheoretically, found that the absorption is the major
shielding mechanism and the reflection is the secondary
shielding mechanism. A negative influence on theoverall EMI shielding effectiveness brought by multiplereflection was shown by the theoretical analysis. They
believed that a multi-surface shield such as conductive
polymer composites might drastically enhance theoverall EMI shielding effectiveness if multiple-reflection
can be minimized [47].
Elastomer, such as a silicone elastomer, is a type ofmaterial with high flexibility, which acts as an excellent
matrix for tactile sensors or actuators [48]. However, italso has some disadvantages, like low tear strength, a
relatively high density, and an obvious viscoelasticity.
Foaming is a method to overcome this disadvantage [49-

― 27 ―Electrically Functional Silicone Composites and Their Application in Mechanical Sensors

53]. The flexibility can be significantly improved by thefoaming procedure. The viscoelasticity can be reduced
drastically as a shift of the deforming configuration. K.
A. Klicker et al. explored the effect of porosity on thehydrostatic piezoelectric sensitivity of 3-1 connectivity
in a foamed polyurethane matrix [52]. They found thatthe piezoelectric coefficient under hydrostatic loading
sharply increases when porosity is incorporated to 40%.
As an important method to enhance the sensitivity of thepiezoresistive property, foaming process has been widelyused to the conductive nanocomposites in industry. The
piezoresistive properties of MWCNT/polymer unfoamed
composites have been reported by many previous works.
H o w e v e r, t h e r e i s a l m o s t n o r e p o r t a b o u t t h epiezoresistive properties of foamed MWCNT/polymer
composites from other research groups. In authorʼs study[54], a series of novel MWCNT/silicone conductive
foamed nanocomposites were fabricated. The diverse
porous structures, the distribution-orientation status of
the MWCNTs in the silicone matrix were observed by alaser microscope and SEM with or without acompressive load. The influences of the porous structure
and porosity on the foam density, elastic modulus,
resistivity as well as piezoresistive property werestudied. A piezoresistive model for the foamed
conductive fillers reinforced elastomeric composites wasdeveloped, the calculated results of the resistive
variations were used to compare to the measured values.
Various theoretical electrically conductive models andpiezoresistive models have been developed in many
previous works [55-57]. In M. Tayaʼ work, an analyticalmodeling was developed to study the piezoresistive
behavior of a conductive short fiber reinforced elastomer
composite, the reorientation distributions of the
conductive short fibers due to stretching strain werecomputed by using a fiber reorientation model. It was
found that the threshold fiber volume fraction increases
as the applied strain increases [58]. An analytical modelof the effective electrical conductivity of carbon
nanotube composites was developed by Fei Deng et al.,which takes account of not only the CNT concentrationand percolation, but also CNT conductivity anisotropy,
aspect ratio and non-straightness [59].
In the works of Xiang-wu Zhang [60,61], the total
resistance in conductive composites is considered to bea function of both the resistance through eachconducting particle and the polymer matrix. The
resistivity of the matrix is assumed to be constanteverywhere, the resistance of the conductive paths

perpendicular to the current flow was neglected. Thenthe number of the conductive particles between
electrodes, the number of the conducting paths and theaverage distance between the adjacent particles become
the main factors, the resistance for the conductive
composites can be described as
(6)
where
(7)
s is the average minimum distance between two adjacentconductive particles, A is the effective cross-sectional
area of one electrically conducting path, h is Plank ʼconstant, e and m are the electron charge and electron
mass, φ is the tunneling potential barrier height, N is thenumber of conducting paths in the composite and M is
the number of conductive particles forming one
conducting path. If the initial average minimum distance
between two adjacent conductive particles and the initialresistance is assumed as s 0 and R 0, respectively, therelative resistance of the conductive composites when astress is applied can be described as(8)Figure 5 An image of an electrically conductive path in a cubic
space of the conductive foamed composite

Considering the situation of the conductive foamed
composite, the compression would become much more
complex because of the influence of the porous structureon the elastic modulus. A cubic space in the conductive
foam with a length of L was illustrated in the Fig.5. Bothvoids and conductive particles were assumed asspherical shapes and to be distributed in the polymer
matrix with absolute homogeneities. The voltage was
loaded to the composite, making the current flow

― 28 ―

Chen Guo, Dianming Sun, Chika Takai, Razavi Hadi, Takashi Shirai, Feng Wang, Masayoshi Fuji

through the vertical direction. The current was thought
homogeneously distributed in the space without being
blocked by the voids through the vertical direction. Oneof the conducting paths was shown in the Fig.5, which
was thought to keep being perpendicular to thehorizontal plane. If a uniaxial pressure is loaded on the
conductive foam through the vertical direction, the cubic

space will be compressed, the average distance between
the conductive particles will be shortened and theresistance of the conductive foam through the verticaldirection will be reduced. However, the influence of thevoids on the compressing procedure is extremelyc o m p l e x , m a k i n g i t d i ff i c u l t t o c a l c u l a t e t h epiezoresistive property of the conductive foam.

Figure 6 The flow chart of simplification of the piezoresistance analysis of a cubic space in the conductive foamed composite

In order to simplify the calculation procedures, several
assumptions were made for the voids: The sphericalvoids with an average diameter D were treated as cubic
shapes with an average length of l and could maintain aconstant average volume. As shown in the Fig.6, thevertical plane from the Fig.6 was illustrated. One
electrically conductive path through the verticaldirection was shown in the Fig.6. Therefore
(9)

D

(10)

the effect of the pressure of confined gas in the voids
and the atmospheric pressure on the compressing
procedure was neglected; the number of conductive
particles within one conductive path in the cubic space
was expressed as n. These cubic-like voids in this cubic
space were assumed to be combined together as a big
cubic-like void, which has a length of nl. This big void
was thought to be able to move freely within the cubic
space without affecting the calculation of thepiezoresistive property due to its cubic shape. Assume
that it was moved to the top of the cubic space, dividing
the space into a “hollow” part at the top and a “solid” part
inferior. The length of the big cubic-like void is(11)
Thus the ratio of the length of the big cubic void versus
the length of the entire cubic space can be calculated as(12)Here ρr is the relative density of the conductive foam (thedensity of the conductive foam divided by the density of
the unfoamed conductive composites with the same
volume fraction of conductive particles). l is the lengthof a single void before combination, L is the length of
the big void after combination, respectively.
When an external force was loaded on the cubic space
though the vertical direction, the compressive strain of
the upper “hollow” part εh and the compressive strain of
the inferior “solid” part εs were different because of thedifferent force areas. Considering this difference andneglecting the compression of the conductive particles,
the average inter-particle distance s in the conductive
foam can be calculated as(13)
In which σ is the applied uniaxial stress, E is the elastic
modulus of the unfoamed conductive composites withthe same volume fraction of conductive particles. The
average inter-particle distance can be calculated as(14)
In which d is the average particle diameter, f is thevolume fraction of the conductive particle in the
conductive foam, f/ρr is thought as the “real” volume
fraction in the polymer matrix. Then substitute the Eq.
(13) and Eq. (14) into the Eq. (8), the relative resistance― 29 ―Electrically Functional Silicone Composites and Their Application in Mechanical Sensorsof the conductive foam when a stress is applied can becalculated as

exp
(15)
The piezoresistive property can be simply estimatedwith the Eq. (15). This piezoresistive model can be used
to predict the effect of the porosity of the conductive
foam on its piezoresistance effectively. However there
are some drawbacks in this model which would reduce
the accuracy of the prediction: Pores in the conductive
foam were considered as cubic shapes, which have a
different compression mode with the spherical one.
Furthermore, the average pore diameter was neglected
due to the combination of the pores; the competition
between the pressures of the gas confined in the poresand the atmospheric pressure was neglected, which infact brings some effect on the compressing procedures;the electrically conductive particles were assumed to be
spherical. In fact, many fiber-like or sheet-like
conductive particles were found to have lower
percolation thresholds and be much more effective in
conductivity enhancing compared to the sphericalparticles.
In authorʼ previous work [62], piezoresistive models
for fiber-like conductive fillers/polymeric solid
composites and for fiber-like fillers/polymeric foam
were both developed. Those models were designed toreflect the effects of both the displacement andorientation of the fiber-like fillers precisely, althoughleading to some extremely complex calculation andthereby reduce the practicability. The Eq. (15)accompanied with Eq. (12) and Eq. (14) was used to
calculate the piezoresistive variations of the MWCNT/
silicone conductive foams and the results were used tocompare to the measured values.

Figure 7 A brief image of the compressing procedure of unfoamed MWCNT/silicone elastomers by external pressure

Many types of fiber-like carbon fillers such as carbon
nanofiber (CNT) are found useful to confer conductivity
and piezoresistivity [63-66]. There are more
opportunities for the formation of the conductive pathsin the fiber-like particles filled composites. The
distributions and orientations of the fiber-like fillers
always change with the deformation of the substrates,
leading to a unique alteration of conductivity. Many
previous works focused on the piezoresistivity broughtby fiber-like particles [67-70].
According to the Eq. (8), if a pressure is loaded on thecomposite, the average minimum distance between

adjacent MWCNTs will be changed from s0 to s1, theresistance will become from R0 to

exp

(16)

As shown in Fig.7, the MWCNTs dispersed in thesubstrates are described as ideal cylinders with the samelength and the same radius of l and r. The continuous
substrate is described as divided cube-like rooms which
all have a same edge length of L , so the averageminimum distance between adjacent MWCNTs s ranges
randomly from 0 to L. The MWCNTs are thought to be
distributed in the substrate absolutely homogeneously,― 30 ―

Chen Guo, Dianming Sun, Chika Takai, Razavi Hadi, Takashi Shirai, Feng Wang, Masayoshi Fuji

whose centers absolutely coincide with the centers of the
cubes. When the composite deforms under the uniaxialpressure from the vertical direction, the edge length L is
assumed to vary with the deformation. θ is the angle
between the shortest connecting line of two adjacentfibers and the uniaxial pressure direction, which ranges
from 0 to π randomly. ε is the compressing strain of thecomposite, so(17)
Substitute it into the Eq. (8), the resistance of thecomposite under a pressure can be randomly calculated
as

cos

exp
Figure 8 A brief image of the piezoresistive mechanism for
microbeads cells filled conductive composites

exp
(18)
If the relationship between θ and s is neglected, theaverage resistance of composite under a pressure can becalculated by(19)
The effective volume fraction of MWCNTs can bethought as(20)
Therefore the average resistance of composite underpressure can be described as(21)
In authorʼs previous work [62], novel highly sensitive
piezoresistive foams with excellent elasticity were
fabricated by adding a new type of thermally expandable
microbeads, which leads to a cell-filled flexible
structure. Effects of MWCNT and the foaming agent on
the piezoresistivity were investigated. The deformationof the cross section caused by a uniaxial pressure wasobserved originally and its effect on the piezoresistivity
was discussed in detail.

The mechanism for the microbeads loaded MWCNT/
silicone elastomeric composite was also discussed. As it
shows in the Fig.8, the electric conductive paths are
confined in the matrix area between the insulated cells.
According to the SEM observation result, the cells wereslightly being compressed when the foams were under auniaxial pressure. In order to simplify the piezoresistivemodel, some assumptions are made: The cells always
keep perfect sphere-like shapes when under a pressure;the current passes through the foam matrix along theedges of these cells; the Poissonʼs deformation of thesubstrate area with cells only in its horizontal direction,such as the point L in the Fig.8, would be absolutely
blocked by the adjacent cells; the Poissonʼs deformation
would not be affected in the substrate area with cells
only in its vertical direction, like the point M; thePoissonʼs deformation of the other areas, such like thepoint N, would be partially affected. Based on theseassumptions, the Eq. (6) and Eq. (8) can be used todescribe the piezoresistive phenomenon of the cell
introduced foams, in which the conductive paths become
to longer semicircle. As in the Fig.8, for the point P in
the conductive path from A to B, if the angle between
the conductive direction and the horizontal direction isset as α , the ratio of the average minimum distance
between adjacent MWCNTs in the foam before and after
compression will be

cos
(22)
Substitute it into the Eq. (8), use the same method in Eq.

― 31 ―Electrically Functional Silicone Composites and Their Application in Mechanical Sensors(17) ~ Eq. (21), the average resistance of the foam undera pressure can be easily calculated as

The theoretical values calculated by Eq. (21) and Eq.
(23) were used to compare with the experimental results,
relatively well-fit results were obtained.

(23)

Figure 9 SEM images of the MWCNT/silicone conductive composite foamed by ADCA under and without a uniaxial load

In authorʼ previous work [54], the MWCNT/silicone
elastomeric composites were fabricated and foamed by 3
different types of foaming agents. The backscatteredelectron images of the dispersed MWCNT particles weretaken at a high magnification while normal SEM imagesof the voids structures were taken with a low
magnification. The images of the MWCNT/silicone
conductive elastomeric composite foamed byazodicarbonamide (ADCA) without a compression
strain were shown at the left hand of Fig.9. Largeamounts of MWCNT particles were found to be
distributed homogeneously in the silicone matrix. The
majority of which were found being covered tightly withsilicone elastomer except for several half-naked particles
distributed in the cross-section surface. These covered
MWCNT particles contacted, overlapped each other andformed cluster-liked conductive networks. It is believedthat the coated silicone layers interrupted the directcontact between the MWCNT fibers, making theresistivity of the conductive foams become much morechangeable. It can be found that all the MWCNT fibers
were distributed in the silicone matrix with randomorientations before compression. The images of the
MWCNT/silicone elastomeric composite foamed by
ADCA under a compression strain of 75% were shownat the right hand of Fig.9, the majority of the MWCNT
fibers were found to orient to the direction perpendicular
to the compressive strain, the contact and overlapping
were found dramatically enhanced by the externalpressures. This is considered to be the mainenhancement factor of the piezoresistive phenomenon of
the MWCNT/silicone elastomeric composites.

― 32 ―

Chen Guo, Dianming Sun, Chika Takai, Razavi Hadi, Takashi Shirai, Feng Wang, Masayoshi Fuji

Figure 10 Piezoresistive properties of the MWCNT/silicone conductive foams

The piezoresistive properties of the MWCNT/silicone
elastomeric conductive composites with all types of
foaming agents, including p,pʼ-oxybis(benzenesulfonylh
ydrazide) (OBSH), azodicarbonamide (ADCA) andsodium hydro carbonate foaming agents (NaHCO 3),
were shown in Fig.10, illustrating the resistance-stressconnections. The resistance decrease can be found fromall samples as the increase of the stress, almost all of theresistance-stress curves were found to be nonlinear, due
to their complex foam compression modes. Obvious
decreases can only be found from the OBSH foamed
samples, especially from the one with a higher foaming
ratio. This demonstrates that a lower elastic modulus
brought by a foaming agent with a high foaming
efficiency leads to a higher piezoresistive sensitivity,
which can be enhanced simply by increasing the loadingof the foaming agent. The resistances of the OBSH

foamed samples dropped obviously when loaded with auniaxial stress of about 110kPa. It is believed that thevoids in the foams occupied much space of the silicone
matrix, enlarged the distances between the MWCNT
particles. Therefore the resistivity was improved
significantly. The resistance changes are precise andrapid enough to be utilized within a piezoresistive tactile
sensor. Oppositely, only slight resistance decreases wereobtained from ACDA and the NaHCO3 samples due tothe relative lower foaming efficiencies of the ACDA andthe NaHCO3 foaming agents. It is also noteworthy thatthe resistances maintained in higher ranges for OBSH
foamed samples and in lower ranges for other samples.
An obvious increase of the whole resistance range wasbrought to the silicone matrix by the OBSH foaming
agent.

Figure 11 Piezoresistivity of the MWCNT/silicone composite foamed by H750D microbeads under periodic pressures― 33 ―Electrically Functional Silicone Composites and Their Application in Mechanical Sensors

In authorʼ another work [62], the MWCNT/silicone
elastomeric conductive composites foamed by thermal
expand microbeads were fabricated. The piezoresistivityof the MWCNT/silicone composite foamed by H750D
microbeads under periodic pressures are shown in theFig.11. The measurements for the composite with an
MWCNT content of 15phr and with a H750D
microbeads content of 10phr are shown in Fig.11.
C o m p a r e d t o t h e u n f o a m e d e l a s t o m e r, t h epiezoresistivity curve of the composite shows a much
shorter period. The peaks of the curve are synchronous
well with the peaks in the stress curve. An obvious andrapid recovering of the resistances can be clearlyobserved because the introduction of the foaming agentschanged the compression mode of the composites.
H750D foaming agent is microbeads which can keep
their stiffness in some degree even after expanding. The
existence of the microbeads cells drastically reduces theviscous flow of the silicone molecule chains. It isconvinced that addition of the microbeads foaming
agents can effectively improve the sensitiveness andrepeatability of the MWCNT/silicone composites.
5. Conclusion

Silicone elastomer has a lot of advantages being usedas the substrate of the electrically functional elastomericcomposite. Taking advantage of excellent insulation ofsilicone elastomer, inorganic fillers with high dielectric
constants, such as BT and TiO2, could be added into thesilicone elastomer to fabricate a flexible composite witha high dielectric constant, which can be utilized as an
actuator or be assembled to a mechanical sensor. In
authorʼ study, BT/silicone membranes were fabricatedusing raw BT particles and BT particles modified bynovel silicone coupling agent. It was found that thedispersity of BT particles in silicone substrate wasconsiderably improved after surface modification.
Dielectric properties were evaluated by an LCR meter,
the results showed that dielectric constants of composites
membranes were increased after improving thedispersion status of BT particles. Theoretical calculationfrom extreme cases proves that agglomeration of BT
particles in vertical direction could seriously reduce thedielectric constants of composites membranes, thedielectric constant could be raised by improving thedispersion of BT particles. The current generated byvariation of BT/silicone membrane was detected, whichis expected to be applied to mechanical sensors
applications due to its rapid response to instantaneouselectric signals, simple structures, and low costs.
On the other side, electrically conductive particles
with large relative surface areas such as MWCNT,
carbon short fiber or graphene, could be integrated into
the elastomer to provide a low resistivity. This type ofcomposite has an obvious piezoresistive property, which
is suitable for application in a mechanical sensor. In
author ʼ previous works, novel MWCNT/silicone
conductive foamed nanocomposites were fabricated withan OBSH, an ADCA and a NaHCO 3 type foaming
agents. The porous structures of the foamed composites,
the distribution-orientation status of the MWCNTs in thesilicone matrix were both observed with a laser
microscope and a SEM. It was found that the majority ofthe voids in the matrix was being crashed by the externalpressure, which leads to a reduced modulus andimproves the piezoresistive property of the composites.
The contact and overlapping of the MWCNT particles
were found dramatically enhanced by the pressurecaused reorientation, which is considered to be the mainenhancing factor of the piezoresistive phenomenon of
the MWCNT/silicone conductive composites. The
densest and finest porous structures were obtained byusing the OBSH foaming agent which has the best
affinity with the silicone elastomer and a highest
foaming efficiency. The most sensitive piezoresistive
property was obtained by the OBSH foamed MWCNT/
silicone conductive nanocomposite. Another type ofnovel highly sensitive piezoresistive composites was
fabricated using MWCNT, silicone elastomer, andthermal expanding microbeads foaming agent. It isfound that the confinement of MWCNT particles by
microbeads cells improves the piezoresistive
sensitiveness and repeatability. Well fit were foundbetween the theoretical calculations and theexperimental piezoresistivity measurements of these
MWCNT/silicone elastomeric composites. In the future
work, mechanical sensors will be assembled with theBT/silicone elastomeric composites or MWCNT/silicone
elastomeric composites to detect static pressures andimpacts.
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