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ISSN No: 2456
International
Research
Investigation of Structural and Thermal Properties o
Nanostructured P
B. Sathish Mohan1
, Y.
1
Dept. of Inorganic & Analytical Chemistry,
3
Dept. of Inorganic and Analytical Chemistry,
Andhra University, Visakhapatnam,
ABSTRACT
In this paper, we report a preparation of
(PANI) nanostructure by oxidative polymerisation in
presence of HCl as do pant. The structural,
morphological and thermal properties of as
PANI was investigated by X-ray diffraction (XRD),
Fourier transform infrared (FTIR), UV-Visible diffuse
reflectance spectrophotometer (DRS), Field emission
scanning electron microscopy (FESEM) and
gravimetric analysis (TGA).It is found that the
morphology of PANI is fibril like shape with band
gap of 2.74eV. Thermal conductivity of PANI
nanostructure was calculated as a function of
temperature.
Keywords: PANI, oxidative polymerisation and
thermal conductivity.
1. INTRODUCTION
Intrinsic conducting polymers (ICPs) have been
emerged as potential materials for many technological
applications such as sensors, EMI shielding,
chromic displays, batteries, energy storage, solar cells
and catalysis [1-3]. Among all ICPs such as,
polypyrrole, Poly (3,4-ethylenedioxythiophene),poly
aniline (PANI) and its derivatives have received great
attention due to their unique red ox chemistry and
electrical properties, high chemical and environmental
stability [4, 5].
The structure and properties of PANI are firmly
connected to their synthetic methods, there are
numerous methods like emulsion, micro
diffusion polymerization and interfaci
polymerization have been reported earlier [6
@ IJTSRD | Available Online @ www.ijtsrd.com | Volume – 2 | Issue – 5 | Jul-Aug 2018
ISSN No: 2456 - 6470 | www.ijtsrd.com | Volume
International Journal of Trend in Scientific
Research and Development (IJTSRD)
International Open Access Journal
Investigation of Structural and Thermal Properties o
Nanostructured PANI
Y. Pavan Kumar1
, D. Ramadevi2
, K. Basavaiah
1,2
Research Scholar, 3
Professor
of Inorganic & Analytical Chemistry, 2
AU College of Pharmaceutical Sciences,
of Inorganic and Analytical Chemistry,
Andhra University, Visakhapatnam, Andhra Pradesh, India
In this paper, we report a preparation of poly aniline
polymerisation in
. The structural,
morphological and thermal properties of as-prepared
ray diffraction (XRD),
Visible diffuse
Field emission
scanning electron microscopy (FESEM) and Thermo
analysis (TGA).It is found that the
shape with band
gap of 2.74eV. Thermal conductivity of PANI
nanostructure was calculated as a function of
PANI, oxidative polymerisation and
Intrinsic conducting polymers (ICPs) have been
emerged as potential materials for many technological
applications such as sensors, EMI shielding, electro
energy storage, solar cells
ICPs such as,
ethylenedioxythiophene),poly
aniline (PANI) and its derivatives have received great
ox chemistry and
electrical properties, high chemical and environmental
The structure and properties of PANI are firmly
connected to their synthetic methods, there are
micro-emulsion,
and interfacial
been reported earlier [6-8].
Generally, each of these methods has its own
advantages and limitations. To the best our
knowledge, these synthetic methods can be broadly
divided into two categories like chemical and
electrochemical [9]. Chemical polymerization can
result in various morphologies, like nanorods,
nanospheres, nanofibers, nanotubes, nanoflakes, and
nanoflowers [10,11].This paper addresses the
preparation of PANI nanofibrilsby chemical oxidative
polymerization of aniline in aqueous
APS as oxidant and studies its structural and thermal
properties.
2. Experimental section
2.1 Materials and method
Aniline (C6H7N), hydrochloric acid (HC
ammonium persulfate, APS ((NH
procured from Sigma Aldrich. The Milli Q water used
throughout the synthesis of PANI
2.2 Synthesis of PANI
In typical synthesis, 0.1 M of aniline was dissolved in
1 M HCl solution in a round bottom flask with
constant stirring at 0-5℃.Then an aqu
APS (0.1 M) was added drop
mixture under constant stirring for 4 h. The reaction
mixture is turned from pale blue colour to dark green
colour, which indicates the formation of PANI. The
reaction was further preceded fo
Then, the reaction mixture was allowed to attain room
temperature. As formed green precipitate was
centrifuged and washed periodically with water and
method to remove the oligomers, unreacted in
material. Then, finally dried under vacuum f
Aug 2018 Page: 1024
6470 | www.ijtsrd.com | Volume - 2 | Issue – 5
Scientific
(IJTSRD)
International Open Access Journal
Investigation of Structural and Thermal Properties of
K. Basavaiah3
Pharmaceutical Sciences,
Generally, each of these methods has its own
advantages and limitations. To the best our
knowledge, these synthetic methods can be broadly
divided into two categories like chemical and
9]. Chemical polymerization can
result in various morphologies, like nanorods,
nanospheres, nanofibers, nanotubes, nanoflakes, and
[10,11].This paper addresses the
nanofibrilsby chemical oxidative
n aqueous medium using
studies its structural and thermal
N), hydrochloric acid (HCl) and
ammonium persulfate, APS ((NH4)2S2O8) were
procured from Sigma Aldrich. The Milli Q water used
throughout the synthesis of PANI,
In typical synthesis, 0.1 M of aniline was dissolved in
l solution in a round bottom flask with
℃.Then an aqueous solution of
APS (0.1 M) was added drop wise to the reaction
mixture under constant stirring for 4 h. The reaction
mixture is turned from pale blue colour to dark green
colour, which indicates the formation of PANI. The
reaction was further preceded for 12 h at 0-5 ℃.
Then, the reaction mixture was allowed to attain room
temperature. As formed green precipitate was
centrifuged and washed periodically with water and
method to remove the oligomers, unreacted in
dried under vacuum for 12 h,
International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470
@ IJTSRD | Available Online @ www.ijtsrd.com | Volume – 2 | Issue – 5 | Jul-Aug 2018 Page: 1025
2.3 Characterisation
The crystalline and phase formation of PANI was
studied by X-ray diffraction (XRD, Bruker D8 Focus)
with a Cu k alpha radiation source with scan range of
2θ = 10–70° at a speed rate 0.02° per step. The
morphology of the PANI was characterized by
scanning electron microscope (FESEM, JEOL field
emission scanning electron microscope, JSM-6700F).
The band gap was calculated by UV-Visible diffuse
reflectance spectrophotometer (DRS, Shimadzu,
2700R) in the range from 200 to 800 nm. The
rmogravimetricanalysis of PANI was carried out by
TGA (TA instruments Q-500) in the temperature
range of 30 to 700 °C with an air flow rate of 60 m
L/min and a heating rate of 10 °C/min under Ar
atmosphere.
3. Results and Discussion
The XRD patterns of PANI were depicted in Figure
1(a). The characteristic diffraction peaks centred at
2θ= 14.5 ͦ, 20 ͦ, 25. 9 ͦ, 27.8 ͦ which corresponds to
parallel and perpendicular to phenyl rings of PANI,
The XRD of PANI is in well agreement with the
literature report [12].
The band gap energy of as-prepared PANI was
calculated using UV-Visible DRS and the UV DRS
spectrum was depicted in Figure1(b). The band gap of
PANI was calculated from diffuse reflectance spectra
by using equation 1.
E g= h ʋ = h c/λ = 1240/ λ Eq. (1)
Where E g is band gap energy, h is planks constant, ʋ
is wave frequency, c is light of speed and λ is the
wavelength. It can be found that the PANI has an
absorption edge around 457 nm corresponds to the
band gap of 2.74eV.
Figure 1: a) XRD patterns and b) UV DRS spectrum of PANI
FTIR spectrum of PANI is shown in Figure2. The characteristic peaks at 515 and 808 cm-1
were due to the
presence of C-H out-of planes bending vibrations and para-disubstituted benzene rings respectively [12]. The
peak at 1307 cm-1
is ascribed to C-N stretching vibrations. The three characteristic peaks at 1154, 1491 and
1589 cm-1
are corresponds to in-plane bending vibrations in C-H, C-N and C-C respectively. A broad peak at
3403 cm-1
is associated to the presence of N-H stretching of aromatic amines in PANI.
International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470
@ IJTSRD | Available Online @ www.ijtsrd.com | Volume – 2 | Issue – 5 | Jul-Aug 2018 Page: 1026
Figure 2: FTIR spectrum of PAN
The representative FESEM images of as-prepared PANI by chemical oxidative polymerization method were
displayed in Fig. 3. The FESEM images clearly reveal the fibril like morphology.
Figure 3: FESEM images of PANI
The TGA curve for PANI is presented in Fig. 4 (a). The TGA curve shows three characteristic weight losses at
three different temperatures are 93, 455 and 550 ℃. Figure 4a shows the thermal decomposition of PANI by
weight loss percentage increases with the temperature. It shows a weight loss of 11.2 % up to 93 ℃, 19 % from
94-455 ℃ and 49.4 % from 455-550℃ respectively due to loss of water molecules and reduces the benzeneoid
rings [13-15].
International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470
@ IJTSRD | Available Online @ www.ijtsrd.com | Volume – 2 | Issue – 5 | Jul-Aug 2018 Page: 1027
Figure 4: a) TGA curve an db) Thermal conductivity of PANI
The thermal conductivity of prepared PANI was
measured using TA probe (Figure 4b). The
temperature increases, thermal conductivity increases
up to certain level and then decreases; this is due to
the thermal conductivity is mostly depends on the
motion of free electrons. As the temperature
increases, the molecular vibrations increase (in
turn decreasing the mean free path of molecules).
Hence, they block the flow of free electrons, thus
reducing the conductivity. The maximum thermal
conductivity was shown at the temperature of 80 ℃
was shown in Table 1.
Table 1: Thermal conductivity of PANI at
different temperatures
S.
No
Temp
(o
C)
Thermal conductivity
(W/m. K)
1 40 0.245
2 50 0.316
3 60 0.349
4 70 0.468
5 80 0.589
6 90 0.482
7 100 0.355
8 110 0.319
Conclusion
In summary, we have demonstrated a facile,
reproducible method for the preparation of PANI
nanofibrils via oxidative polymerization method using
APS as an oxidant. The prepared PANI was
characterized using XRD, FTIR, FESEM, UV-DRS
and TGA to study its structural and thermal
properties. The results clearly show that PANI has
high thermal conductivity and hence it has thermal
stability.
Conflicts of Interest
The authors clearly declared that there is no any
conflict of interest.
Acknowledgement
The author, B. Sathish Mohan honour to acknowledge
the University Grants Commission (UGC) for
sponsoring the Rajiv Gandhi National Fellowship
(RGNF-SC-AND-2016-17-9309).Also, I thankful to
UGC-DRS-SAP-1 and DST-FIST in the Department
of Inorganic and Analytical Chemistry, Andhra
University,
References
1. J. A. Conklin, S. C. Huang, S. M. Huang, T. Wan,
R. B. Kaner, Thermal properties of poly aniline
and poly(aniline-co-o-ethyl aniline),Macro mol.,
28 (1995), 6522-6527.
2. L. Ding, X. Wang, R. V. Gregory, Thermal
properties of chemically synthesized poly anilines
(EB) powder, Synth. Met., 104 (1999), 73-78.
3. S. H. Goh, H. S. O. Chan, C. H. Ong, Miscible
blends of conductive poly aniline with tertiary
amide polymers, J. Appl. Polym. Sci. 68 (1998),
1839-1844.
4. S. Bhadra, D. Khastgir, N.K. Singha, J.H. Lee,
Progress in preparation, processing and
applications of poly aniline, Prog, Polym.
Sci., 34 (2009), 783-810.
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@ IJTSRD | Available Online @ www.ijtsrd.com | Volume – 2 | Issue – 5 | Jul-Aug 2018 Page: 1028
5. C.H.Silva, N.A. Galiote, F. Huguenin, É. Teixeira
M.L. Temperini, Spectroscopic, morphological
and electro chromic characterization of layer-by-
layer hybrid films of poly aniline and
hexaniobatenanoscrolls, J. Mater. Chem.,
22 (2012), 14052-14060.
6. Li XG, Zhou HJ, Huang MR., Synthesis and
properties of a functional copolymer from N-ethyl
aniline and aniline by an emulsion polymerization,
Polymer. 46 (2005),1523–1533.
7. Huang K, Meng XH, Wan MX., Poly aniline hol-
low microspheres constructed with their own self-
assembled nanofibers, J ApplPolym Sci. 100
(2006), 3050–3054.
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MS., Synthesis and electro rheology of multi
walled carbon nanotube /poly aniline
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9. D.W. Hatchett, M. Josowicz, J. Janata,
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Nan flakes to nanorods and nanospheres transition
of selenious acid doped poly aniline,
Polymer, 49 (2008), 432-437.
11. H.D. Tran, J.M. D'Arcy, Y. Wang, P.J. Beltramo,
V.A. Strong, R.B. Kaner,The oxidation of aniline
to produce poly aniline: a process yielding many
different nanoscale structures, J. Mater.
Chem., 21 (2011), 3534-3550.
12. Palaniappan S and Amarnath C A, A novel poly
aniline–maleic acid–dodecyl hydro gensulfate salt:
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Synth Met, 82(1996), 207.
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Investigation of Structural and Thermal Properties of Nanostructured PANI

  • 1. @ IJTSRD | Available Online @ www.ijtsrd.com ISSN No: 2456 International Research Investigation of Structural and Thermal Properties o Nanostructured P B. Sathish Mohan1 , Y. 1 Dept. of Inorganic & Analytical Chemistry, 3 Dept. of Inorganic and Analytical Chemistry, Andhra University, Visakhapatnam, ABSTRACT In this paper, we report a preparation of (PANI) nanostructure by oxidative polymerisation in presence of HCl as do pant. The structural, morphological and thermal properties of as PANI was investigated by X-ray diffraction (XRD), Fourier transform infrared (FTIR), UV-Visible diffuse reflectance spectrophotometer (DRS), Field emission scanning electron microscopy (FESEM) and gravimetric analysis (TGA).It is found that the morphology of PANI is fibril like shape with band gap of 2.74eV. Thermal conductivity of PANI nanostructure was calculated as a function of temperature. Keywords: PANI, oxidative polymerisation and thermal conductivity. 1. INTRODUCTION Intrinsic conducting polymers (ICPs) have been emerged as potential materials for many technological applications such as sensors, EMI shielding, chromic displays, batteries, energy storage, solar cells and catalysis [1-3]. Among all ICPs such as, polypyrrole, Poly (3,4-ethylenedioxythiophene),poly aniline (PANI) and its derivatives have received great attention due to their unique red ox chemistry and electrical properties, high chemical and environmental stability [4, 5]. The structure and properties of PANI are firmly connected to their synthetic methods, there are numerous methods like emulsion, micro diffusion polymerization and interfaci polymerization have been reported earlier [6 @ IJTSRD | Available Online @ www.ijtsrd.com | Volume – 2 | Issue – 5 | Jul-Aug 2018 ISSN No: 2456 - 6470 | www.ijtsrd.com | Volume International Journal of Trend in Scientific Research and Development (IJTSRD) International Open Access Journal Investigation of Structural and Thermal Properties o Nanostructured PANI Y. Pavan Kumar1 , D. Ramadevi2 , K. Basavaiah 1,2 Research Scholar, 3 Professor of Inorganic & Analytical Chemistry, 2 AU College of Pharmaceutical Sciences, of Inorganic and Analytical Chemistry, Andhra University, Visakhapatnam, Andhra Pradesh, India In this paper, we report a preparation of poly aniline polymerisation in . The structural, morphological and thermal properties of as-prepared ray diffraction (XRD), Visible diffuse Field emission scanning electron microscopy (FESEM) and Thermo analysis (TGA).It is found that the shape with band gap of 2.74eV. Thermal conductivity of PANI nanostructure was calculated as a function of PANI, oxidative polymerisation and Intrinsic conducting polymers (ICPs) have been emerged as potential materials for many technological applications such as sensors, EMI shielding, electro energy storage, solar cells ICPs such as, ethylenedioxythiophene),poly aniline (PANI) and its derivatives have received great ox chemistry and electrical properties, high chemical and environmental The structure and properties of PANI are firmly connected to their synthetic methods, there are micro-emulsion, and interfacial been reported earlier [6-8]. Generally, each of these methods has its own advantages and limitations. To the best our knowledge, these synthetic methods can be broadly divided into two categories like chemical and electrochemical [9]. Chemical polymerization can result in various morphologies, like nanorods, nanospheres, nanofibers, nanotubes, nanoflakes, and nanoflowers [10,11].This paper addresses the preparation of PANI nanofibrilsby chemical oxidative polymerization of aniline in aqueous APS as oxidant and studies its structural and thermal properties. 2. Experimental section 2.1 Materials and method Aniline (C6H7N), hydrochloric acid (HC ammonium persulfate, APS ((NH procured from Sigma Aldrich. The Milli Q water used throughout the synthesis of PANI 2.2 Synthesis of PANI In typical synthesis, 0.1 M of aniline was dissolved in 1 M HCl solution in a round bottom flask with constant stirring at 0-5℃.Then an aqu APS (0.1 M) was added drop mixture under constant stirring for 4 h. The reaction mixture is turned from pale blue colour to dark green colour, which indicates the formation of PANI. The reaction was further preceded fo Then, the reaction mixture was allowed to attain room temperature. As formed green precipitate was centrifuged and washed periodically with water and method to remove the oligomers, unreacted in material. Then, finally dried under vacuum f Aug 2018 Page: 1024 6470 | www.ijtsrd.com | Volume - 2 | Issue – 5 Scientific (IJTSRD) International Open Access Journal Investigation of Structural and Thermal Properties of K. Basavaiah3 Pharmaceutical Sciences, Generally, each of these methods has its own advantages and limitations. To the best our knowledge, these synthetic methods can be broadly divided into two categories like chemical and 9]. Chemical polymerization can result in various morphologies, like nanorods, nanospheres, nanofibers, nanotubes, nanoflakes, and [10,11].This paper addresses the nanofibrilsby chemical oxidative n aqueous medium using studies its structural and thermal N), hydrochloric acid (HCl) and ammonium persulfate, APS ((NH4)2S2O8) were procured from Sigma Aldrich. The Milli Q water used throughout the synthesis of PANI, In typical synthesis, 0.1 M of aniline was dissolved in l solution in a round bottom flask with ℃.Then an aqueous solution of APS (0.1 M) was added drop wise to the reaction mixture under constant stirring for 4 h. The reaction mixture is turned from pale blue colour to dark green colour, which indicates the formation of PANI. The reaction was further preceded for 12 h at 0-5 ℃. Then, the reaction mixture was allowed to attain room temperature. As formed green precipitate was centrifuged and washed periodically with water and method to remove the oligomers, unreacted in dried under vacuum for 12 h,
  • 2. International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470 @ IJTSRD | Available Online @ www.ijtsrd.com | Volume – 2 | Issue – 5 | Jul-Aug 2018 Page: 1025 2.3 Characterisation The crystalline and phase formation of PANI was studied by X-ray diffraction (XRD, Bruker D8 Focus) with a Cu k alpha radiation source with scan range of 2θ = 10–70° at a speed rate 0.02° per step. The morphology of the PANI was characterized by scanning electron microscope (FESEM, JEOL field emission scanning electron microscope, JSM-6700F). The band gap was calculated by UV-Visible diffuse reflectance spectrophotometer (DRS, Shimadzu, 2700R) in the range from 200 to 800 nm. The rmogravimetricanalysis of PANI was carried out by TGA (TA instruments Q-500) in the temperature range of 30 to 700 °C with an air flow rate of 60 m L/min and a heating rate of 10 °C/min under Ar atmosphere. 3. Results and Discussion The XRD patterns of PANI were depicted in Figure 1(a). The characteristic diffraction peaks centred at 2θ= 14.5 ͦ, 20 ͦ, 25. 9 ͦ, 27.8 ͦ which corresponds to parallel and perpendicular to phenyl rings of PANI, The XRD of PANI is in well agreement with the literature report [12]. The band gap energy of as-prepared PANI was calculated using UV-Visible DRS and the UV DRS spectrum was depicted in Figure1(b). The band gap of PANI was calculated from diffuse reflectance spectra by using equation 1. E g= h ʋ = h c/λ = 1240/ λ Eq. (1) Where E g is band gap energy, h is planks constant, ʋ is wave frequency, c is light of speed and λ is the wavelength. It can be found that the PANI has an absorption edge around 457 nm corresponds to the band gap of 2.74eV. Figure 1: a) XRD patterns and b) UV DRS spectrum of PANI FTIR spectrum of PANI is shown in Figure2. The characteristic peaks at 515 and 808 cm-1 were due to the presence of C-H out-of planes bending vibrations and para-disubstituted benzene rings respectively [12]. The peak at 1307 cm-1 is ascribed to C-N stretching vibrations. The three characteristic peaks at 1154, 1491 and 1589 cm-1 are corresponds to in-plane bending vibrations in C-H, C-N and C-C respectively. A broad peak at 3403 cm-1 is associated to the presence of N-H stretching of aromatic amines in PANI.
  • 3. International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470 @ IJTSRD | Available Online @ www.ijtsrd.com | Volume – 2 | Issue – 5 | Jul-Aug 2018 Page: 1026 Figure 2: FTIR spectrum of PAN The representative FESEM images of as-prepared PANI by chemical oxidative polymerization method were displayed in Fig. 3. The FESEM images clearly reveal the fibril like morphology. Figure 3: FESEM images of PANI The TGA curve for PANI is presented in Fig. 4 (a). The TGA curve shows three characteristic weight losses at three different temperatures are 93, 455 and 550 ℃. Figure 4a shows the thermal decomposition of PANI by weight loss percentage increases with the temperature. It shows a weight loss of 11.2 % up to 93 ℃, 19 % from 94-455 ℃ and 49.4 % from 455-550℃ respectively due to loss of water molecules and reduces the benzeneoid rings [13-15].
  • 4. International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470 @ IJTSRD | Available Online @ www.ijtsrd.com | Volume – 2 | Issue – 5 | Jul-Aug 2018 Page: 1027 Figure 4: a) TGA curve an db) Thermal conductivity of PANI The thermal conductivity of prepared PANI was measured using TA probe (Figure 4b). The temperature increases, thermal conductivity increases up to certain level and then decreases; this is due to the thermal conductivity is mostly depends on the motion of free electrons. As the temperature increases, the molecular vibrations increase (in turn decreasing the mean free path of molecules). Hence, they block the flow of free electrons, thus reducing the conductivity. The maximum thermal conductivity was shown at the temperature of 80 ℃ was shown in Table 1. Table 1: Thermal conductivity of PANI at different temperatures S. No Temp (o C) Thermal conductivity (W/m. K) 1 40 0.245 2 50 0.316 3 60 0.349 4 70 0.468 5 80 0.589 6 90 0.482 7 100 0.355 8 110 0.319 Conclusion In summary, we have demonstrated a facile, reproducible method for the preparation of PANI nanofibrils via oxidative polymerization method using APS as an oxidant. The prepared PANI was characterized using XRD, FTIR, FESEM, UV-DRS and TGA to study its structural and thermal properties. The results clearly show that PANI has high thermal conductivity and hence it has thermal stability. Conflicts of Interest The authors clearly declared that there is no any conflict of interest. Acknowledgement The author, B. Sathish Mohan honour to acknowledge the University Grants Commission (UGC) for sponsoring the Rajiv Gandhi National Fellowship (RGNF-SC-AND-2016-17-9309).Also, I thankful to UGC-DRS-SAP-1 and DST-FIST in the Department of Inorganic and Analytical Chemistry, Andhra University, References 1. J. A. Conklin, S. C. Huang, S. M. Huang, T. Wan, R. B. Kaner, Thermal properties of poly aniline and poly(aniline-co-o-ethyl aniline),Macro mol., 28 (1995), 6522-6527. 2. L. Ding, X. Wang, R. V. Gregory, Thermal properties of chemically synthesized poly anilines (EB) powder, Synth. Met., 104 (1999), 73-78. 3. S. H. Goh, H. S. O. Chan, C. H. Ong, Miscible blends of conductive poly aniline with tertiary amide polymers, J. Appl. Polym. Sci. 68 (1998), 1839-1844. 4. S. Bhadra, D. Khastgir, N.K. Singha, J.H. Lee, Progress in preparation, processing and applications of poly aniline, Prog, Polym. Sci., 34 (2009), 783-810.
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