J. Phys. Chem. B 2007, 111, 7535-7540
7535
Electrical, Optical, Thermoelectric Power, and Dielectrical Properties of Organic Semiconductor Poly(1,12-bis(carbazolyl) Dodecane) Film F. Yakuphanoglu,*,† Houting Liu,‡ and Jingkun Xu‡ Department of Physics, Faculty of Arts and Sciences, Fırat UniVersity, Elazig 23119, Turkey, and Jiangxi Key Laboratory of Organic Chemistry, Jiangxi Science and Technology Normal UniVersity, Nanchang 330013, China ReceiVed: February 14, 2007; In Final Form: April 10, 2007
Electrical conductivity, optical, thermoelectric, and dielectrical properties of the poly(1,12-bis(carbazolyl) dodecane) film have been investigated. The activation energy for electrical conductivity and room-temperature electrical conductivity (at 25 °C) values were found to be 0.25 eV and 2.65 × 10-6 S/cm, respectively. The thermoelectric power results suggest that the conductivity is due to large polarons (i.e., the carriers in polymer move by hopping in the localized states at band gap edges). Electrical conductivity and thermoelectric power results confirm that the polymer is a p-type organic semiconductor. Optical absorption results suggest that the direct allowed transitions are dominant in the fundamental absorption edge in the polymer with optical band gap value of 2.72 eV. The refractive index dispersion of the polymer obeys the single oscillator model with oscillator energy (Eo ) 3.06 eV) and dispersion energy (Ed ) 17.82 eV) values. Alternating current conductivity results suggest that the hopping conductivity is dominant in the polymer. The dielectrical properties exhibit a non-Debye relaxation.
1. Introduction Electronic transport properties of organic semiconducting polymers have been extensively investigated.1-4 The conjugated polymers exhibit conducting or semiconducting behavior. Semiconductor polymers are now attracting considerable attention as promising materials for the development of optoelectronic devices such as light-emitting diodes, photovoltaic cells, and nonlinear optical systems.5 The pursuit of novel polymeric materials is still a very important topic in academic and industrial laboratories, especially the design and syntheses of smart materials combining the good mechanical properties of traditional materials together with interesting electrical, optical, or magnetic properties. During the past decades, conjugated polymers with different chemical structures emitting different colors in the whole visible range have been widely investigated. Among them, increasing interest has been paid to polycarbazole (PCz) and its derivatives because of their potential application in hole transporting and photoluminescence efficiency units.6-9 To study the charge transport mechanism occurring in organic semiconductors, analysis of both the thermoelectric power and temperature dependence on direct conductivity is required. The thermoelectric power performance will be one of such interesting properties specific for electroconductive polymers. The thermoelectric materials is one of the promising materials, effective for saving energy and for developing advanced materials.10 In this paper, the electrical conductivity, optical, thermoelectric power, and dielectrical properties of PCz film as a new semiconductor material were investigated in detail. 2. Experimental Methods 2.1. Synthesis of Poly(1,12-bis(carbazolyl)dodecane). 1,12-Dibromododecane (2.0 g, 6 mmol) and NaOH (13.75 g, 0.34 * Corresponding author. E-mail:
[email protected]. † Fırat University. ‡ Jiangxi Science and Technology Normal University.
mol) were added to a 250 mL three-necked flask containing carbazole (2.0 g, 12 mmol) in DMSO (30 mL). The mixture was stirred at room temperature for 4 h. Then, the reaction mixture was poured into water, extracted with CHCl3 (60 mL), washed with brine and deionizedwater, then dried over MgSO4. After filtration and evaporation of the solvent, the resulting white powder was dissolved in CHCl3 and was purified by flash column chromatography using hexane/CHCl3 ) 5:1 as the eluent. The chemical structure of the 1,12-bis(carbazolyl)dodecane is shown in Figure 1.11 The electrosyntheses of its polymer, poly(1,12-bis(carbazolyl)dodecane), were performed in a mixed electrolyte of boron trifluoride diethyl etherate and CHCl3, according to the method reported previously.11 2.2. Electrical and Optical Measurements of Poly(1,12bis(carbazolyl)dodecane) Film. For the electrical conductivity measurements, the polymer was prepared in the form of film with thickness of 145 µm. To measure electrical conductivity, electrical contacts were formed via gold wires by brushing silver paint. The bias applied for the direct current (dc) conductivity measurement is 1 V. Electrical conductivity was performed as a function of temperature by the alternating polarity method to eliminate electrical polarization, triboelectric, and piezoelectric effects using KEITHLEY 6517A electrometer. The currentvoltage (I-V) measurement of the polymer film was performed in ohmic region by KEITHLEY 2400 sourcemeter. For the thermoelectric power (TEP) measurements, gold electrodes were deposited onto the two ends of the polymer. A temperature gradient (∆T ∼ 5 K) was established within the polymer so that the majority charge carriers can diffuse from the hot to the cold end and thereby, an electrical potential difference across the polymer was established. In equilibrium, this potential difference is balanced by the thermal gradient.12 Temperature dependence on Seebeck coefficient called as ratio of the potential difference to the temperature difference was measured using a KEITHLEY 2182A nanovoltmeter. Alternating current conduc-
10.1021/jp071283l CCC: $37.00 © 2007 American Chemical Society Published on Web 06/09/2007
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Figure 1. The chemical structure of the monomer, 1,12-bis(carbazolyl)dodecane, and its polymer, poly (1,12-bis(carbazolyl)dodecane).
Figure 3. Cyclic voltametry of the polymer film recorded in CH3CN + 0.1 M Bu4NBF4 at potential scan rates of 100 mV s-1. The polymer film was synthesized electrochemically from 60% BF3Et2O + 40% CHCl3 at a constant applied potential of 0.8 V versus SCE.
Figure 2. UV-vis spectra of the polymer.
tivity (ac) and dielectrical properties of the polymer have been performed using a HIOKI 3532-50 LCR. The UV-vis spectra of the polymer film with thickness of 0.52 µm in solid state deposited on an indium-tin-oxide (ITO) were recorded of by a Perkin-Elmer Lambda 900 spectrophotometer. The cyclic voltametry measurements were performed by model 263 potentiostat-galvanostat (EG&G Princeton Applied Research) under computer control. 3. Results and Discussion 3.1. Optical Absorption Spectra of the Polymer Film. The UV-vis spectrum of the polymer is shown in Figure 2. The UV-vis spectra of the polymer film show the absorption peaks located at 396 and 600-1100 nm (Figure 2). The absorption peak at 396 nm is due to a valence band-conduction band (ππ*) transition.11 The broad band from 600 to 1100 nm is due to the characteristic of conductive species such as the existence of polaron. The peak at about 825 nm is related to the doping process that is responsible for the polymer conductivity. When the polymer is doped, polaron formation occurs.12 This polaron, which has spin g ) 1/2 and electronic charge (e, is partially delocalized on polymeric structure. 3.2. Electrochemistry of the Polymer Film. Cyclic voltammetry (CV) was used to investigate the redox behavior of the polymer and to assess the highest-occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy levels. In CV measurement, the working electrode and counter electrode were platinum wires and stainless steel wires placed 0.5 cm apart. All potentials have been recalibrated to saturated calomel electrode (SCE). In fact, the distances between the working and counter electrodes have little effect on the CVs during the electrochemical polymerization. The main effect of this distance in Figure 3 is that the Y axis would be bigger or smaller with smaller or larger distances, respectively. It has no effect on the potentials (X axis) during the experiment. However, in our experiment, the CV in Figure 3 was used to estimate the HOMO and LUMO levels, which were calculated by the oxidation potential onset of the polymer from X axis. Therefore,
the distance between the working and counter electrode has no effect on the HOMO and LUMO levels. Figure 3 shows the cyclic voltammetry of as-formed poly(1,12-bis(carbazolyl)dodecane) in CH3CN containing 0.1 mol L-1 Bu4NBF4 at a scanning rate of 100 mV s-1. The HOMO energy level versus vacuum level was calculated from the measured onset potential of oxidation (0.52 V versus FOC) by assuming the energy level of FOC is 4.8 eV below the vacuum level, and the LUMO energy level was calculated from the HOMO energy level and the absorption edge in the UV-vis spectra of the polymer. The HOMO and LUMO energy levels obtained from electrochemical and UV-vis spectrum are-5.32 eV and-2.6 eV, respectively.13-14 The HOMO energy is higher than the carbazole monomer, which agrees with the results of others.15 The electrochemical band gap of the polymer was calculated using HOMO and LUMO values and was found to be 2.72 eV. 3.3. The Optical and Refractive Index Dispersion Properties of the Polymer Film. The optical energy gap and optical transition type of the polymer film can be determined by the following relation16
Rhν ) A(hν - Eg)m
(1)
where A is an energy-independent constant and Eg is the optical band gap. m is a constant that determines the type of optical transitions. For indirect allowed transition, m ) 2, and for indirect forbidden transition, m ) 3; for direct allowed transition, m ) 1/2 and for direct forbidden transition, m ) 3/2. To determine the type of optical transition, eq 1 can be written as
d[ln(Rhν)] m ) hν - Eg d[hν]
(2)
The curve of ln(Rhν) versus ln(hν - Eg) was plotted and the m value was found to be about one half of the slope of the curve plotted. This suggests that the direct-allowed transitions are dominant in the fundamental absorption edge of the polymer. Figure 4 shows a plot of (Rhν)2 versus hν for the polymer. The optical band gap was determined by extrapolating the linear portion of the plot to (Rhν)2 ) 0 (Figure 4) and was found to be 2.72 eV. The optical band gap value of the polymer is in good agreement with the electrochemical band gap. The refractive index dispersion properties of the polymer can be analyzed by the following transmittance T, absorption coefficient R, and reflectance R relations:14-15
Properties of Poly(1,12-bis(carbazolyl) Dodecane) Film
T(λ) )
(1 - R(λ))2 e-Rd 1 - R(λ)2 e-2Rd
J. Phys. Chem. B, Vol. 111, No. 26, 2007 7537
(3)
where d is the film thickness, R is the absorption coefficient, and R is the reflectance which is described as17-18
R(λ) )
(n(λ) - 1)2 + k(λ)2 (n(λ) + 1)2 + k(λ)2
(4)
If one solves eq 4, this equation gives
n(λ) )
(1 + R(λ)) + x4R(λ) - (1 - R(λ))2k(λ)2 1 - R(λ)
(5) Figure 5. Refractive index spectrum of the polymer.
where k is the extinction coefficient given by18
k)
Rλ 4π
(6)
The refractive index and extinction coefficient can be calculated by means of these equations. The complex optical refractive index for the polymer film is given by
nˆ ) n(λ) + ik(λ)
(7)
where n is the real part and k is the imaginary part of complex refractive index. The refractive index of the film was calculated using eq 5. The spectral dependence of the refractive index is shown in Figure 5. The refractive index curve indicates a normal dispersion behavior between 400 and 580 nm. For the photon energies less than the energy gap, the refractive index is expressed as19
n2 - 1 )
EoEd Eo - (hc/λ)2 2
Figure 6. Plot of (n2 - 1)-1 versus (hν)2 of the polymer.
polymer film. The wavelength dependence of refractive index can be expressed by the following dispersion relation20
(8)
where Eo is the single oscillator energy and Ed is the dispersion energy, which is a measure of the intensity of interband optical transitions. The (n2 - 1)-1 versus (hν)2 plot is shown in Figure 6. Eo and Ed values were determined from the slope, (EoEd)-1 and intercept (Eo/Ed), on the vertical axis and were found to be 3.06 and 17.82 eV, respectively. Eo relates energy difference between the valence and conduction band (i.e., it is the average gap of the polymer film). This average gap band gives quantitative information on the overall band structure of the
n2 - 1 )
Soλo2 1 - (λo/λ)2
(9)
where λ is the wavelength of incident light. So is the average oscillator strength. A plot of (n2 - 1)-1 versus λ-2 gives a straight line. The So value was obtained from intercept of (n2 - 1)-1 versus λ-2 curve plotted and was found to be 3.55 × 1013 (m-2). Eq 9 also can be written as
n∞2 - 1 n -1 2
)1-
() λo λ
2
(10)
where n∞ is the high-frequency refractive index constant and λo is an average oscillator wavelength. n∞ and λo values were obtained from the linear parts of 1/(n2 - 1) versus λ-2 and were found to be 2.61 and 404.56 nm, respectively. 3.4. Direct Current Electrical Conductivity Properties of the Polymer. Figure 7a,b show plots of current-voltage and conductivity-temperature of the polymer. As seen in Figure 7a, the current-voltage characteristic of the polymer indicates a linear behavior (i.e., ohmic behavior). The electrical conductivity of organic semiconductors is analyzed by the well-known relation
σ ) σo exp(-E/kT)
Figure 4. Plot of (Rhν)2 versus energy of the polymer.
(11)
where k is the Boltzmann constant, T is the temperature, σo is the pre-exponential factor. The plot of conductivity indicates one straight line and the electrical conductivity increases with
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Yakuphanoglu et al.
Figure 8. Temperature dependence on thermoelectric power of the polymer.
where ∆T is the temperature difference between cold and hot surfaces of the polymer and ∆V is the Seebeck voltage. The Seebeck coefficient of the polymer decreases with increasing temperature. Temperature difference applied causes transport of carriers from hot to cold end, thus giving rise to thermovoltage across the ends. A transition from positive conductivity to negative conductivity at 64.05 °C takes place. If electrical conductivity is hopping, the temperature dependent on Seebeck coefficient is expressed as24 Figure 7. Current-voltage and conductivity-temperature plots of the polymer.
increase in temperature. The activation energy for electrical conductivity was determined from the slope of Figure 7b and found to be 0.25 eV. The room-temperature electrical conductivity (at 25 °C) was found to be 2.65 × 10-6 S/cm. The exponential character of the temperature dependence and electronic parameters calculated implies that the polymer is an organic semiconductor. The charge transport of the polymer most likely operates through the hopping of polarons,21 which are not delocalized over the chain. The consisted polaron can easily move away from its initial site and will diffuse along the polymer chain by supporting voltage. The conduction mechanism of the polymer is also analyzed by means of the pre-exponential factor, σo. Mott and Davis suggest that the preexponential factor σo for conduction in the extended states is of the order of 104 (S/cm), whereas a smaller value or so indicates conduction by hopping in the localized states. The obtained σo (5.07 × 10-2 S/cm) value is much smaller than 104 (S/cm) value,22 suggesting that the conduction mechanism is taking place by localized states. It should be noted here that the electrical conductivity of this polymer was performed about 1 month after its electrodeposition. The room-temperature electrical conductivity of this as-formed sample was found to be 1.36 S/cm11; after about 1 month, conductivity (σ ) 2.65 × 10-6 S/cm) decreased significantly. This suggests that the film undergoes bulk and molecular changes over time. 3.5. Thermoelectric Power Properties of the Polymer Film. Figure 8 shows temperature dependence on thermoelectric power for the polymer. The thermoelectric power indicates that the polymer at room temperature is a p-type semiconductor behavior and the holes contribute to TEP. The Seebeck coefficient S is described as23
S)
∆V ∆T
(12)
S)(
(
k Etp +C e kT
)
(13)
where + and - signs correspond to hole and electron type of conductivity, Etp is the activation energy of the thermoelectric power, C < 1 suggests the conductivity is small polaron hopping whereas C > 2 suggests conductivity is due to large polarons, and k is the Boltzmann constant. The thermoelectric power activation energy value Etp for the polymer was found to be 73.5 meV. The obtained C value is 2.53, suggesting that conductivity is due to large polarons. If thermoelectric activation energy is equal to conductivity activation energy, the transport takes place in the extended states. But, if the conductivity activation energy is higher than the thermoelectric power activation energy, the carriers move by the hopping in the localized states at the band gap edge.25 The obtained activation energy of 73.5 meV suggests that the carriers in polymer move by hopping in the localized states at band gap edges. This result is in agreement with electrical conductivity results of the polymer. The difference between electrical activation energy and thermoelectric power energy is defined as polaronic hopping energy WH ) Eσ - Es.26 Thus, the polaronic formation energy, Ep ) 2WH is determined, and the polaronic formation energy for the polymer was found to be 0.36 eV. It is evaluated that the polaron hopping for the polymer studied can be dominant mechanism.21 3.6. Alternating Current Conductivity and Dielectrical Properties of the Polymer Film. Figure 9 shows that the ac conductivity of the polymer depends on frequency at different temperatures. The ac conductivity plots indicate different conductivity regions (I, II, and III), which depend on frequency and increase with temperature. The alternating current conductivity of the polymer can be analyzed by the following relation
σ ∼ ωs
(14)
where f is the angular frequency, and s is an exponent. The conductivity regions are characterized by s1 and s2 frequency
Properties of Poly(1,12-bis(carbazolyl) Dodecane) Film
J. Phys. Chem. B, Vol. 111, No. 26, 2007 7539
Figure 9. Variation of ac conductivity with frequency at different temperatures.
TABLE 1: The Electronic Parameters of the Polymer T (K)
s1
s2
b
303 313 323 333 343 353
0.473 0.484 0.482 0.450 0.403 0.371
1.29 1.26 1.02 0.98 0.88 0.87
0.414 0.409 0.414 0.455 0.503 0.529
exponents, respectively. The values of s1 and s2 for regions I and III were determined and are given in Table 1. The s1 values below 0.5 suggest a non-Debye conductivity. The s1 and s2 values decrease with temperature. When the frequency is increased, the mean displacement of the charge carriers is reduced and thus, the ac conductivity of the polymer follows the law, σ ∼ ωs. The frequency dependence of conductivity suggests the hopping conductivity.27
Figure 10. Plots of 1 and 2 vs ln f at different temperatures.
The complex dielectric constant of the polymer is defined as27
* ) ′ + i′′
(15)
where ′ and ′′ are the real and imaginary part of the dielectric constant, respectively. Figure 10a,b show plots of ′ and ′′ versus ln f at different temperatures. An increase in temperature causes the increase of the dielectric constant of the polymer. When the temperature is increased, the orientation of electric dipoles is facilitated, and this causes an increase in the orientational polarization and in turn, ′ increases. The large value of ′′ is also due to the motion of the free carrier within the polymer. No peak was observed in plot of ′′ versus ln f at different temperatures, and ′′ obeys a power law dispersion. The values of ′ are very high at low frequencies. These high values may be due to the interfacials and electrode effects. Interfacial polarization arises from the presence of polar and conductive regions in the polymer. This phenomenon obstructs the relaxation process analysis. Therefore, we prefer to describe the dielectric relaxation process using the electric modulus formalism.27 The complex electric modulus is defined as28
M* )
′ ′′ 1 ) +i 2 * ′2 + ′′2 ′ + ′′2
(16)
Figure 11a shows M′ plots at different temperatures. M′ values decrease with increasing temperature. At lower frequencies, the
Figure 11. Plots of M′ and M′ of the polymer at different temperatures.
values of M′ tends almost to zero. This confirms removal of the electrode polarization. M′′ plots of the polymer at different temperatures are shown in Figure 11b. The plots of M′′ indicate an asymmetric peak and the position of the peak shifts to higher frequencies with temperature. This suggests a temperature-
7540 J. Phys. Chem. B, Vol. 111, No. 26, 2007
Yakuphanoglu et al. suggest that the hopping conductivity is dominant in the polymer. The complex electrical modulus results indicate the existence of a non-Debye relaxation in the polymer. Acknowledgment. This work was supported by the Turkish Scientific and Technological Research Council of TURKEY (TUBITAK) (Project Number:105T137) and NSFC (50663001). The authors wish to thank The Scientific and Technological Research Council of Turkey. References and Notes (1) Kuzmani, M., Mehring, M., Roth, S., Eds. Electronic Properties of Polymers and Related Compounds; Springer-Verlag: Berlin, 1995. (2) Bredas, J. L., Chance, R. R., Eds. Conjugated Polymer Materials: Opportunities in Electronics, Optoelectronics, and Molecular Electronics; Kluwer Academic Press: Dordrecht, The Netherlands, 1990.
Figure 12. Plot of ln τ versus 1000/T for the polymer.
dependent relaxation. The peak height does not significantly change with temperature. The peak of electric modulus can be analyzed by exponential decay function of the electric field29
φ(t) ) exp(-t/τ)β
(17)
where β ) 1.14/w is the stretching exponent and here w is the full-width at half-maximum. φ(t) describes the relaxation of electric filed in the material. The complex electrical modulus is described as27-28
M*(ω) ) M∞[1 -
∫0
∞
(3) Mort, J.; Pai, D. M. Electronic Properties of Polymers; WileyInterscience Publication: New York, 1982. (4) Katon, D. E.; Organic Semiconducting Polymers; Marcel Dekker: New York, 1968. (5) Morin, J. F.; Leclerc, M.; Ades, D.; Siove, A. Macromol. Rapid Commun. 2005, 26, 761. (6) Zhang, Z.; Fujiki, M.; Tang, H.; Motonaga, M.; Torimitsu, K. Macromolecules 2002, 35, 1988. (7) Huang, J.; Niu, Y.; Yang, W.; Mo, Y.; Yuan, M.; Cao, Y. Macromolecules 2002, 35, 6080. (8) Liu, B.; Yu, W.; Lai, Y.; Huang, W. Chem. Mater. 2001, 13, 1984. (9) Misra, S. C. K.; Chandra, S. Indian J. Chem. 1994, 33A, 583.
exp(iωt)(-dφ(t)/dt)dt]
(18)
where M∞ is the limiting high-frequency real part of the modulus, and φ(t) is the relaxation function. The β values at different temperatures were calculated from Figure 11b and are given in Table 1. The β values change with temperature. It is evaluated that the broadening in the distribution of relaxation times indicates the same trend with temperature. The obtained β values suggest a non-Debye relaxation dominated in the polymer. The temperature dependence of relaxation time for the polymer is expressed as27
(10) Gutman, F.; Lyons, L. E. Organic Semiconductors; Wiley: New York, 1967. (11) Xu, J.; Wei, Z.; Du, Y.; Pu, S. Mater. Lett. 2007, 61 (11-12), 2486. (12) Yakuphanoglu, F.; Senkal, B. F. J. Phys. Chem. C 2007, 111 (4), 1840. (13) Kim, J. H.; Lee, H. Chem. Mater. 2002, 14, 2270. (14) Xu, J. K.; Liu, H. T.; Pu, S. Z.; Li, F. Y.; Luo, M. B. Macromolecules 2006, 39, 5611. (15) Brunner, K.; van Dijken, A.; Bo¨rner, H.; Bastiaansen, J. J. A. M.; Kiggen, N. M. M.; Langeveld, B. M. W. J. Am. Chem. Soc. 2004, 126, 6035. (16) Davis, E. A.; Mott, N. F. Philos. Mag. 1970, 22, 903.
τ ) τo exp(ER/kT)
(19)
(17) Moss, T. S. Semiconductor Optoelectronics; Butterworths: London, 1973.
where ER is activation energy of the relaxation process, τo is relaxation time at infinite temperature, k is the Boltzmann constant, and T is the temperature. Figure 12 shows plot of ln τ versus 1000/T. The ER and τo values were found to be 0.19 eV and 1.38 × 10-10 s. The relaxation time is decreased with increasing temperature as the dissipated thermal energy assists the formed dipoles to follow the motion of the alternating field.27-30
(18) Abeles, F., Ed. Optical Properties of Solids; North-Holland. Publishing Company: London, U.K., 1972. (19) DiDomenico, M.; Wemple, S. H. J. Appl. Phys. 1969, 40, 720. (20) Wemple, S. H.; DiDomenico, M. Phys. ReV. B 1971, 3, 1338. (21) Ameen, S.; Ali, V.; Zulfequar, M.; Mazharul Haq, M.; Husain, M. Curr. Appl. Phys. 2007, 7, 215. (22) Mott, N. F., Davis, E. A. Electronic Processes in Non-Crystalline Materials; Clarendon Press: Oxford, 1971. (23) Wolf, H. P. Semiconductors; Wiley: London, 1971.
4. Conclusions Electrical conductivity, optical, and thermoelectric power properties of poly(1,12-bis(carbazolyl) dodecane) film have been investigated. Electrical conductivity and thermoelectric power results confirm that the polymer is a p-type organic semiconductor with calculated electronic parameters (E ) 0.25 eV and σ25 ) 2.65 × 10-6 S/cm). The direct optical band gap value of the polymer was found to be 2.72 eV. The refractive index dispersion of the polymer obeys the single oscillator model with oscillator energy (Eo ) 3.06 eV) and dispersion energy (Ed ) 17.82 eV) values. Alternating current conductivity results
(24) Nagels, P. In Amorphous Semiconductors, Brodsky, M. H., Ed.; Springer: Berlin, 1985. (25) Sulitanu, N. Mater. Sci. Eng., B 2001, 83, 84. (26) Jaime, M.; Salamon, M. B. In Physics of Manganites; Kaplan, T. A., Mahanti, S. D., Eds.; Kluwer Academic/Plenum Publishers: New York, 1999. (27) Yakuphanoglu, F. Physica B 2007, 393, 139. (28) Moynihan, C. T.; Boesch, L. B.; Laberge, N. L. Phys. Chem. Glasses 1973, 14, 122. (29) Dixon, R. K. Phys. ReV. B 1990, 42, 8179. (30) Psarras, G. C.; Manolakaki, E.; Tsangaris, G. M. Composites, Part A 2003, 34, 1187.
