THERMAL CHARACTERIZATION OF…
PHYSICAL REVIEW B 69, 235201 (2004)
camphor sulphonic acid can be classified as an inhomog-
enously disordered metal comprising of “metallic islands”
separated by insulating barriers (metallic island model).17
However, doping of polyaniline with CSA at this high level
͑50%͒ results in interchain coupling and consequently an
enhanced ordering between crystalline regions (metallic re-
gions) as well as on the chains bridging the metallic regions.
Such an ordering results in the increase of localization length
of electronic wave function and hence allows the coherent
transport of both heat and electricity. Transport models for
three-dimensional amorphous semiconductors have often
been used to account for the charge delocalization phenom-
ena in conducting polymers, despite fundamental
differences.18 In conducting polymers the dopant ions are
positioned interstitially between chains, whereas in conven-
tional semiconductors they are usually substituted directly
into the host lattice.18 Further, covalent bonding along poly-
mer chains and weak bonding between them result in a
quasi-one-dimensional morphology which has an important
role in the charge delocalization of these systems.19 In a rela-
tively ordered crystalline material, as in the present case,
protonation of polyaniline with sulphonic acid results in a
decrease in hopping distance and consequently enhances the
hopping mechanism (phonon-assisted tunneling between
electronic localized states centered at different positions).20 It
is difficult to distinguish between different conduction
mechanisms such as quasi-1D variable range hopping
tivity as well as thermal diffusivity of its constituents.26 The
thermal properties of all the composites are discontinuous
functions of the location and consequently neither Fourier’s
law nor heat conduction equation can be applied.26 However,
the effective thermal parameters, i.e., the properties of
equivalent homogeneous material that produces the same
physical effects of the specimen under investigation, is of
great significance and has wide applications in device fabri-
cation. Eventhough the effective heat capacity follows the
mixture rule, it has already been reported that the effective
thermal diffusivity of composites depend on the thermal dif-
fusivity of constituents as well as on their relative volume
fraction.26 In the present case also, the composites of CSA
doped PANI and CoPc exhibit a thermal diffusivity value,
which is intermediate to that of CSA doped PANI and CoPc.
This can be ascribed to the existence of interfacial thermal
contact resistance between the different constituent phases in
a composite as well as on their thermal expansion
mismatch.27 The existence of such thermal barriers results in
a lowering of the effective thermal diffusivity of the compos-
ite. It is evident from our observations that introduction of
10% CoPc results in large inhomogeneties in the sample,
which consequently lowered its thermal diffusivity in a sub-
stantial manner. However, further increase in volume fraction
of CoPc does not cause considerable variation in their al-
ready inhomogeneous distribution and is evident in their
thermal diffusivity values. The present analysis shows that
the combination of a good thermal diffuser with a bad dif-
fuser can result in composites of intermediate thermal diffu-
sivity value. The measured thermal diffusivity value of CoPc
falls in the typical range of the thermal diffusivity of
phthalocyanines.28
In order to ensure the effective charge transport mecha-
nism in these materials, both dc and ac electrical conductiv-
ity measurements were carried out by employing the two
probe technique on the specimen placed in a conductivity
cell under high vacuum, ͑10−5 Torr͒ using Keithley Voltage
source. The results obtained are tabulated in Table II. It is
seen from the table that the variation in electrical conductiv-
ity of the samples also follows the thermal diffusivity mea-
surements. However, the order of variation is small in the
case of thermal diffusivity as compared to electrical
conductivity.29 This is due to the fact that thermal energy
transport mechanism in conducting polymers is dominated
by phonon assisted mechanism, whereas electrical conduc-
tion is dominated by the variable range hopping process and
metallic diffusion of electrons.30
mechanism,21
3D
hopping
with
electron-electron
interaction,22 tunneling between mesoscopic metallic islands
23
or correlated hopping between polaronic clusters in
polyaniline.24 Nevertheless, experimental investigations
show that results can be explained very well in terms of the
metallic content as well as in terms of dominant hopping/
tunneling mechanism. In addition to that, previous x-ray
analysis shows that there is a significant degree of crystallin-
ity in PANI:CSA.25 In these crystalline regions of the poly-
mer, a precise phase order exists between adjacent polymer
chains and this is expected to allow coherent carrier transport
along and between individual chains. This means that carrier
delocalization can occur in more than one dimension, on a
scale larger than the average interchain separation.4 There-
fore, the mean-free-path is limited not by scattering at inter-
chain transfer events but by phonon scattering due to thermal
motion of the crystal lattice, or by molecular vibrational
modes and it become apparent in bulk conductivity of the
specimen at room temperature.4 Therefore, 50% CSA doped
polyaniline can be considered as a heterogeneous conductor
in which two transport mechanisms such as metallic diffu-
sion within the crystalline regions and temperature activated
transport in the disordered region contribute to the conduc-
tion mechanism. Hence the increase in mobility of charge
carriers with protonation of polyaniline with sulphonic acid
results in strong interaction between electrons and phonons
due to lattice vibration, especially at room temperature,
which in turn results in coherent transport of thermal energy
via electron-phonon interaction (polarons). As a result, 50%
CSA doped PANI, exhibits highest value for thermal diffu-
sivity.
The effective thermal parameters of composites depend
on the thermal properties of its constituents as well as on the
microstructural parameters such as volume fraction of each
phase, shape, size, and distribution of the particles. Hence a
study on the correlation between thermal diffusivity and
hardness of the material was carried out, wherein, the surface
hardness of all the specimens under investigation were mea-
sured using the indentation technique (Shore D hardness
technique). The values obtained for the hardness of the
samples under investigation are given in Table II. It is seen
from the Tables I and II that there exists an inverse relation
between thermal diffusivity and hardness of the specimen, as
observed by other researchers.31 The increase in relative vol-
The effective thermal diffusivity value of composite ma-
terials has been reported to depend on the thermal conduc-
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