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Physical aging of poly(vinyl acetate). A thermally stimulated depolarization current investigation
Journal of Non-Crystalline Solids 287 (2001) 237±241
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Physical aging of poly(vinyl acetate). A thermally stimulated depolarization current investigation L. Goitiandia *, A. Alegrõa Dpto. Fõsica de Materiales, Facultad de Quõmica y Centro Mixto CSIC±UPV/EHU, Apdo. 1072, 20080 San Sebasti an, Spain
Abstract The in¯uence of physical aging on the dielectric a-relaxation of poly(vinyl acetate) (PVAc) is investigated by means of the thermally stimulated depolarization currents (TSDCs) technique. The obtained TSDC data are analyzed in terms of the Kohlrausch±Williams±Watts (KWW) equation for an isothermal decay of a stored charge. Assuming that at temperatures less than the glass transition temperature the shape of the KWW function depends neither on the temperature nor on the thermal history, the generalized Bucci and Fieschi equation allows us to obtain the dependence of the KWW time. The results obtained are interpreted in the Adam and Gibbs theory framework. Ó 2001 Elsevier Science B.V. All rights reserved.
1. Introduction Glassy polymers, as well as every other glassy material, are not in equilibrium, not only with respect to the corresponding crystalline material, if it exists (for many polymeric systems it does not), but also with respect to the metastable equilibrium liquid-like or relaxed glassy state [1±4]. As a consequence, at temperatures less than the glass transition, Tg , glassy polymers relax towards a metastable equilibrium state. In polymer science, this phenomenon is commonly referred to as physical aging [5±8], although in the inorganic glass literature it is often termed structural relaxation. Physical aging is of practical importance because the properties of the material change
* Corresponding author. Tel.: +34-943 018 195; fax: +34-943 212 236. E-mail addresses: [email protected] (L. Goitiandia), [email protected] (A. Alegrõa).
during this process, the eects being more important when the working temperature is less than Tg by <10%. This is the case for the most widely used amorphous polymers, which have Tg s below 200°C. Moreover, physical aging also aects the polymer segmental dynamics [5±8]. This in¯uence leads to changes in several dynamically controlled phenomena [5]. Therefore, physical aging is a dynamic process, which at the same time aects the dynamics of the system [9]. This feature, together with the non-exponentiality of the glass-forming systems dynamics [10±12], makes the phenomenology of physical aging complex. The thermal stimulated depolarization current (TSDC) technique [13±16] has been used in this work. In the TSDC technique, a polarized sample is cooled to freeze-in sample polarization. By recording as a function of time the electric current produced by the depolarization process during a subsequent heating, a current peak is obtained when the poled species become mobile enough to randomize. In spite of the advantages of TSDC for
0022-3093/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 1 ) 0 0 5 7 8 - 6
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L. Goitiandia, A. Alegrõa / Journal of Non-Crystalline Solids 287 (2001) 237±241
investigating the relaxation processes of polymers, the interpretation of the TSDC spectra is still controversial [17,18]. This problem was already addressed by us in previous publications [19,20]. There we showed that the TSDC experiments on the a-relaxation of polymers can consistently be analyzed in the same framework often used for conventional dielectric experiments, i.e., in terms of the Kohlrausch±Williams±Watts (KWW) equation [21] for the isothermal decay of the stored charge, which is expressed as " # b t Q t Q0 exp ; 1 sa where Q0 is the initially stored charge, sa is the relaxation time and 0 < b < 1 is a parameter accounting for the non-Debye character of the a-relaxation, which for polymers around Tg , is typically in the range 0.4±0.5 [22]. On these grounds, the following equation is found [19]: 1 Q Q0 sa b ln I Q
1=b
;
2
where I dQ t=dt. This equation is a generalization of the Bucci and Fieschi equation [23] and with it sa T is calculated in the measured temperature range from a single global TSDC spectrum, provided that the parameter b is independently determined [19]. For b 1 (Debye process), Eq. (2) reduces to the Bucci and Fieschi expression. The value of b, which is used as an input in Eq. (2), has to be known. However, by means of a series of independent dielectric experiments performed isothermally at temperatures
2. Experimental The preparation and properties of the sample used in this work as well as the experimental set-up used for these measurements were described elsewhere [19]. The TSDC measurements were performed using 10 K/min heating and cooling rates. The voltage was applied at a temperature Tpon 322 K (Tg 315 K [19]), where the dipoles are able to orientate. The sample was then cooled at 10 K/min to the aging temperature Ta 303 K, and after a certain waiting time, tw , at this temperature, the sample was again cooled to the depolarization temperature, Tpoff 273 K. At this temperature, where dipoles are assumed to be frozen, the poling voltage was switched o and the current due to the sample depolarization was detected during the subsequent heating at 10 K/min. It is important to notice that the polarization conditions remained the same for all the experiments and the only dierence in the experimental conditions for the dierent spectra was tw . In the present work the following tw s were used: 100, 464, 1000, 2154, 4642, 10 000, 21 540, 46 420, 100 000 and 215 440 s. 3. Results Fig. 1 shows several of the global TSDC data obtained in PVAc with dierent tw s. From inspection of Fig. 1, the TSDC peaks obtained for long waiting times have smaller widths and appear at higher temperatures than those obtained for shorter aging times. Using the evaluation method given by Eq. (2), with b 0:45 (the b obtained by conventional dielectric relaxation techniques at Tg ) [19], we obtain sa T for PVAc in the measured temperature range (see Fig. 2). In this ®gure it is apparent that the sa T obtained in the non-aged sample at high temperatures agrees well with the Vogel Fulcher (VF), line corresponding to the extrapolation of sa T as determined on the same sample by means of isothermal dielectric measurements, both in frequency and time domain [24,25]. However, at the peak position, but mainly at lower temperatures, the relaxation time obtained from the TSDC measurements crosses over
L. Goitiandia, A. Alegrõa / Journal of Non-Crystalline Solids 287 (2001) 237±241
239
4. Discussion
Fig. 1. TSDC data of PVAc annealed at Ta 303 K during several waiting times tw : non-aged, 1000 s, } 4642 s, 21 440 s, and () 215 440 s. The solid lines are a guide for the eye.
Fig. 2. sa T obtained by means of Eq. (2) with b 0:45 from the TSDC spectra shown in Fig. 1. (The symbols have the same meaning as in Fig. 1). Solid thick line is the extrapolation of the VF ®t of the frequency domain data. The vertical dashed line shows the annealing temperature. The solid lines show the Arrhenius ®ts of sa T data.
from the VF dependence towards an Arrhenius dependence eventually attained at the lowest temperatures. From the data of Fig. 2, it is also apparent that near the glass transition temperature the experimental sa T s increase by more than one decade by physical aging of at least 1 103 s. It is also evident that the slope of the Arrhenius functions ®tting the data, i.e. the apparent activation energy at low temperatures, decreases when increasing the aging time.
A reason for the observed in¯uence of physical aging on the dielectric a-relaxation can be found in the framework of the theories which relate the relaxation time to structural parameters, for instance, the con®gurational entropy [26,27]. A series of recent papers has shown that this approach, whose formalism is known as the Adam and Gibbs (AG) theory, is appropriate to describe the eects of the annealing and prior history on the enthalpy relaxation of glassy polymers [6,7,28,29]. Moreover, we found [24] that the AG theory also accounts for the temperature dependence of relaxation time, sa , through the Tg range. The AG theory relates the reorientation time of a given unit to the molar con®gurational entropy of the sample, Sc , in the following way: NA sC Dl s s0 exp ; 3 kB TSC where NA is Avogadro's number, sC is the entropy per unit of the minimum number of particles which rearrange cooperatively, Dl is the molar elementary activation energy and s0 is the reciprocal of an attempt frequency. The s0 and Dl deduced for PVAc from previous dielectric measurements above Tg were [30]: 10 12 s and 8.3 kcal/mol, respectively. Although Eq. (3) gives a qualitative account for the Arrhenius dependence in the glassy state, if Sc is temperature independent, our results show that increasing the aging time (reducing Sc ) the apparent activation energy decreases. This change is shown in Fig. 3 where we depict the apparent activation energy, Ea , of sa T , which was calculated in the range 300±280 K as follows: Ea
kB
dln sa T : d 1=T
4
When applying Eq. (4) to the Adam and Gibbs relaxation time, Eq. (3), we found NA sC Dl 1 dSC Ea 1 : 5 SC TSC d 1=T It is evident that the Ea expected from the AG theory depends not only on the SC but also on
240
L. Goitiandia, A. Alegrõa / Journal of Non-Crystalline Solids 287 (2001) 237±241
this temperature dependence is suppressed on annealed samples. For these samples, the apparent activation energy of the a-relaxation time in the glassy state obtained experimentally corresponds to that expected for an isocon®gurational glassy state. Acknowledgements
Fig. 3. Apparent activation energy Ea of the sa T Arrheniuslike dependence obtained in the range 280±300 K using Eq. (3) (see Fig. 2). The dashed area shows the value of Ea corresponding to the equilibrium value of Sc at the aging temperature (303 K).
dSC =d 1=T . When Eq. (5) is evaluated for a constant Sc , close to Sc Tg , an Ea close to 26 kcal/mol is obtained (see the shadowed area in Fig. 3). This Ea is nearly half of that found experimentally for the non-aged sample. Therefore, based on our data we suggest that in the non-aged sample there is a change of Sc with temperature, even at a temperature of 30 K < Tg 30 K. This change in Sc would be related to a residual segmental mobility of the polymer in the glassy state at temperatures
5. Conclusions We have found that the AG formalism properly accounts for the in¯uence of physical aging of PVAc as observed by the TSDC technique. Based on our results we conclude that the con®gurational entropy changes from Tg 50 K to Tg . However,
This work has been supported by the Spanish Ministry of Education (MEC) (project PB970638), the Government of the Basque Country (projects GV-PI98/20 and EX-1999-11), and the University of the Basque Country (projects 206.215-G20/98). The authors thank Iberdrola S.A. for the partial ®nancial support.
References [1] R.N. Haward (Ed.), The Physics of Glassy Polymer, Materials Science Series, Applied Science, London, 1973. [2] J.D. Ferry, Viscoelastic Properties of Solid Polymers, Wiley, New York, 1979. [3] N.M. March, A.S. Robert, M. Tosi (Eds.), Amorphous Solids and the Liquid State, Plenum, London, 1985. [4] I. Gutzow, J. Schmelzer, The Vitreous State, Springer, Berlin, 1995. [5] L.C.E. Struik, Physical Aging in Amorphous Polymers and Others Materials, Elsevier, Amsterdam, 1978. [6] I.M. Hodge, Macromolecules 20 (1987) 2897. [7] I.M. Hodge, J. Non-Cryst. Solids 169 (1994) 211. [8] J.M. Hutchinson, Prog. Polym. Sci. 20 (1995) 703. [9] A.J. Kovacsm, Fortschr. Hochpolym. Forschung 3 (1963) 394. [10] N.G. McCrum, B.E. Read, G. Williams, Anelastic and Dielectric Eects in Polymeric Solids, Wiley, London, 1967. [11] J. Colmenero, A. Alegrõa (Eds.), Basic Features of the Glassy State, World Scienti®c, Singapore, 1990. [12] K.L. Ngai, G.R. Wright (Eds.), Relaxation in Complex Systems, North Holland, Amsterdam, 1991. [13] P. Bra unlich (Ed.), Thermally Stimulated Relaxations in Solids, Topics in Applied Physics, vol. 37, Springer, New York, 1979. [14] J. van Turnhout, in: G.M. Sessler (Ed.), Electrets, Topics in Applied Physics, vol. 33, Springer, New York, 1980, pp. 81±201. [15] N.T. Correia, J.M. Ramos, J. Polym. Sci. B 37 (1999) 227. [16] M.J. Sanchis, R. Diaz-Calleja, Macromolecules 32 (1999) 3457. [17] V. Halpern, J. Phys. D: Appl. Phys. 82 (1994) 2628.
L. Goitiandia, A. Alegrõa / Journal of Non-Crystalline Solids 287 (2001) 237±241 [18] E. Dargent, M. Kattan, C. Cabot, P. Lebaudy, J. Ledru, J. Grenet, J. Appl. Polym. Sci. 74 (1999) 2716. [19] A. Alegrõa, L. Goitiandia, J. Colmenero, Polymer 37 (1996) 2915. [20] A. Alegrõa, L. Goitiandia, J. Colmenero, J. Polym. Sci. B Phys. 38 (2000) 2105. [21] G. Williams, D.C. Watts, Trans. Faraday Soc. 66 (1970) 80. [22] A. Alegrõa, J. Colmenero, P.O. Mari, I.A. Campbell, Phys. Rev. E 59 (1999) 6888. [23] C. Bucci, R. Fieschi, Phys. Rev. Lett. 12 (1964) 16.
241
[24] A. Alegrõa, E. Guerrica-Echevarria, L. Goitiandia, I. Tellerõa, J. Colmenero, Macromolecules 28 (1995) 1516. [25] A. Alegrõa, L. Goitiandia, I. Tellerõa, J. Colmenero, Macromolecules 30 (1997) 3881. [26] G. Adam, J.H. Gibbs, J. Chem. Phys. 43 (1958) 139. [27] E.A. Di Marzio, F. Dowell, J. Appl. Phys. 50 (1979) 6061. [28] I.M. Hodge, Macromolecules 19 (1986) 936. [29] G.W. Scherer, J. Am. Ceram. Soc. 67 (1984) 504. [30] A. Alegrõa, L. Goitiandia, I. Tellerõa, J. Colmenero, Recent Res. Dev. Macromol. Res. 3 (1998) 49.
www.elsevier.com/locate/jnoncrysol
Physical aging of poly(vinyl acetate). A thermally stimulated depolarization current investigation L. Goitiandia *, A. Alegrõa Dpto. Fõsica de Materiales, Facultad de Quõmica y Centro Mixto CSIC±UPV/EHU, Apdo. 1072, 20080 San Sebasti an, Spain
Abstract The in¯uence of physical aging on the dielectric a-relaxation of poly(vinyl acetate) (PVAc) is investigated by means of the thermally stimulated depolarization currents (TSDCs) technique. The obtained TSDC data are analyzed in terms of the Kohlrausch±Williams±Watts (KWW) equation for an isothermal decay of a stored charge. Assuming that at temperatures less than the glass transition temperature the shape of the KWW function depends neither on the temperature nor on the thermal history, the generalized Bucci and Fieschi equation allows us to obtain the dependence of the KWW time. The results obtained are interpreted in the Adam and Gibbs theory framework. Ó 2001 Elsevier Science B.V. All rights reserved.
1. Introduction Glassy polymers, as well as every other glassy material, are not in equilibrium, not only with respect to the corresponding crystalline material, if it exists (for many polymeric systems it does not), but also with respect to the metastable equilibrium liquid-like or relaxed glassy state [1±4]. As a consequence, at temperatures less than the glass transition, Tg , glassy polymers relax towards a metastable equilibrium state. In polymer science, this phenomenon is commonly referred to as physical aging [5±8], although in the inorganic glass literature it is often termed structural relaxation. Physical aging is of practical importance because the properties of the material change
* Corresponding author. Tel.: +34-943 018 195; fax: +34-943 212 236. E-mail addresses: [email protected] (L. Goitiandia), [email protected] (A. Alegrõa).
during this process, the eects being more important when the working temperature is less than Tg by <10%. This is the case for the most widely used amorphous polymers, which have Tg s below 200°C. Moreover, physical aging also aects the polymer segmental dynamics [5±8]. This in¯uence leads to changes in several dynamically controlled phenomena [5]. Therefore, physical aging is a dynamic process, which at the same time aects the dynamics of the system [9]. This feature, together with the non-exponentiality of the glass-forming systems dynamics [10±12], makes the phenomenology of physical aging complex. The thermal stimulated depolarization current (TSDC) technique [13±16] has been used in this work. In the TSDC technique, a polarized sample is cooled to freeze-in sample polarization. By recording as a function of time the electric current produced by the depolarization process during a subsequent heating, a current peak is obtained when the poled species become mobile enough to randomize. In spite of the advantages of TSDC for
0022-3093/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 1 ) 0 0 5 7 8 - 6
238
L. Goitiandia, A. Alegrõa / Journal of Non-Crystalline Solids 287 (2001) 237±241
investigating the relaxation processes of polymers, the interpretation of the TSDC spectra is still controversial [17,18]. This problem was already addressed by us in previous publications [19,20]. There we showed that the TSDC experiments on the a-relaxation of polymers can consistently be analyzed in the same framework often used for conventional dielectric experiments, i.e., in terms of the Kohlrausch±Williams±Watts (KWW) equation [21] for the isothermal decay of the stored charge, which is expressed as " # b t Q t Q0 exp ; 1 sa where Q0 is the initially stored charge, sa is the relaxation time and 0 < b < 1 is a parameter accounting for the non-Debye character of the a-relaxation, which for polymers around Tg , is typically in the range 0.4±0.5 [22]. On these grounds, the following equation is found [19]: 1 Q Q0 sa b ln I Q
1=b
;
2
where I dQ t=dt. This equation is a generalization of the Bucci and Fieschi equation [23] and with it sa T is calculated in the measured temperature range from a single global TSDC spectrum, provided that the parameter b is independently determined [19]. For b 1 (Debye process), Eq. (2) reduces to the Bucci and Fieschi expression. The value of b, which is used as an input in Eq. (2), has to be known. However, by means of a series of independent dielectric experiments performed isothermally at temperatures
2. Experimental The preparation and properties of the sample used in this work as well as the experimental set-up used for these measurements were described elsewhere [19]. The TSDC measurements were performed using 10 K/min heating and cooling rates. The voltage was applied at a temperature Tpon 322 K (Tg 315 K [19]), where the dipoles are able to orientate. The sample was then cooled at 10 K/min to the aging temperature Ta 303 K, and after a certain waiting time, tw , at this temperature, the sample was again cooled to the depolarization temperature, Tpoff 273 K. At this temperature, where dipoles are assumed to be frozen, the poling voltage was switched o and the current due to the sample depolarization was detected during the subsequent heating at 10 K/min. It is important to notice that the polarization conditions remained the same for all the experiments and the only dierence in the experimental conditions for the dierent spectra was tw . In the present work the following tw s were used: 100, 464, 1000, 2154, 4642, 10 000, 21 540, 46 420, 100 000 and 215 440 s. 3. Results Fig. 1 shows several of the global TSDC data obtained in PVAc with dierent tw s. From inspection of Fig. 1, the TSDC peaks obtained for long waiting times have smaller widths and appear at higher temperatures than those obtained for shorter aging times. Using the evaluation method given by Eq. (2), with b 0:45 (the b obtained by conventional dielectric relaxation techniques at Tg ) [19], we obtain sa T for PVAc in the measured temperature range (see Fig. 2). In this ®gure it is apparent that the sa T obtained in the non-aged sample at high temperatures agrees well with the Vogel Fulcher (VF), line corresponding to the extrapolation of sa T as determined on the same sample by means of isothermal dielectric measurements, both in frequency and time domain [24,25]. However, at the peak position, but mainly at lower temperatures, the relaxation time obtained from the TSDC measurements crosses over
L. Goitiandia, A. Alegrõa / Journal of Non-Crystalline Solids 287 (2001) 237±241
239
4. Discussion
Fig. 1. TSDC data of PVAc annealed at Ta 303 K during several waiting times tw : non-aged, 1000 s, } 4642 s, 21 440 s, and () 215 440 s. The solid lines are a guide for the eye.
Fig. 2. sa T obtained by means of Eq. (2) with b 0:45 from the TSDC spectra shown in Fig. 1. (The symbols have the same meaning as in Fig. 1). Solid thick line is the extrapolation of the VF ®t of the frequency domain data. The vertical dashed line shows the annealing temperature. The solid lines show the Arrhenius ®ts of sa T data.
from the VF dependence towards an Arrhenius dependence eventually attained at the lowest temperatures. From the data of Fig. 2, it is also apparent that near the glass transition temperature the experimental sa T s increase by more than one decade by physical aging of at least 1 103 s. It is also evident that the slope of the Arrhenius functions ®tting the data, i.e. the apparent activation energy at low temperatures, decreases when increasing the aging time.
A reason for the observed in¯uence of physical aging on the dielectric a-relaxation can be found in the framework of the theories which relate the relaxation time to structural parameters, for instance, the con®gurational entropy [26,27]. A series of recent papers has shown that this approach, whose formalism is known as the Adam and Gibbs (AG) theory, is appropriate to describe the eects of the annealing and prior history on the enthalpy relaxation of glassy polymers [6,7,28,29]. Moreover, we found [24] that the AG theory also accounts for the temperature dependence of relaxation time, sa , through the Tg range. The AG theory relates the reorientation time of a given unit to the molar con®gurational entropy of the sample, Sc , in the following way: NA sC Dl s s0 exp ; 3 kB TSC where NA is Avogadro's number, sC is the entropy per unit of the minimum number of particles which rearrange cooperatively, Dl is the molar elementary activation energy and s0 is the reciprocal of an attempt frequency. The s0 and Dl deduced for PVAc from previous dielectric measurements above Tg were [30]: 10 12 s and 8.3 kcal/mol, respectively. Although Eq. (3) gives a qualitative account for the Arrhenius dependence in the glassy state, if Sc is temperature independent, our results show that increasing the aging time (reducing Sc ) the apparent activation energy decreases. This change is shown in Fig. 3 where we depict the apparent activation energy, Ea , of sa T , which was calculated in the range 300±280 K as follows: Ea
kB
dln sa T : d 1=T
4
When applying Eq. (4) to the Adam and Gibbs relaxation time, Eq. (3), we found NA sC Dl 1 dSC Ea 1 : 5 SC TSC d 1=T It is evident that the Ea expected from the AG theory depends not only on the SC but also on
240
L. Goitiandia, A. Alegrõa / Journal of Non-Crystalline Solids 287 (2001) 237±241
this temperature dependence is suppressed on annealed samples. For these samples, the apparent activation energy of the a-relaxation time in the glassy state obtained experimentally corresponds to that expected for an isocon®gurational glassy state. Acknowledgements
Fig. 3. Apparent activation energy Ea of the sa T Arrheniuslike dependence obtained in the range 280±300 K using Eq. (3) (see Fig. 2). The dashed area shows the value of Ea corresponding to the equilibrium value of Sc at the aging temperature (303 K).
dSC =d 1=T . When Eq. (5) is evaluated for a constant Sc , close to Sc Tg , an Ea close to 26 kcal/mol is obtained (see the shadowed area in Fig. 3). This Ea is nearly half of that found experimentally for the non-aged sample. Therefore, based on our data we suggest that in the non-aged sample there is a change of Sc with temperature, even at a temperature of 30 K < Tg 30 K. This change in Sc would be related to a residual segmental mobility of the polymer in the glassy state at temperatures
5. Conclusions We have found that the AG formalism properly accounts for the in¯uence of physical aging of PVAc as observed by the TSDC technique. Based on our results we conclude that the con®gurational entropy changes from Tg 50 K to Tg . However,
This work has been supported by the Spanish Ministry of Education (MEC) (project PB970638), the Government of the Basque Country (projects GV-PI98/20 and EX-1999-11), and the University of the Basque Country (projects 206.215-G20/98). The authors thank Iberdrola S.A. for the partial ®nancial support.
References [1] R.N. Haward (Ed.), The Physics of Glassy Polymer, Materials Science Series, Applied Science, London, 1973. [2] J.D. Ferry, Viscoelastic Properties of Solid Polymers, Wiley, New York, 1979. [3] N.M. March, A.S. Robert, M. Tosi (Eds.), Amorphous Solids and the Liquid State, Plenum, London, 1985. [4] I. Gutzow, J. Schmelzer, The Vitreous State, Springer, Berlin, 1995. [5] L.C.E. Struik, Physical Aging in Amorphous Polymers and Others Materials, Elsevier, Amsterdam, 1978. [6] I.M. Hodge, Macromolecules 20 (1987) 2897. [7] I.M. Hodge, J. Non-Cryst. Solids 169 (1994) 211. [8] J.M. Hutchinson, Prog. Polym. Sci. 20 (1995) 703. [9] A.J. Kovacsm, Fortschr. Hochpolym. Forschung 3 (1963) 394. [10] N.G. McCrum, B.E. Read, G. Williams, Anelastic and Dielectric Eects in Polymeric Solids, Wiley, London, 1967. [11] J. Colmenero, A. Alegrõa (Eds.), Basic Features of the Glassy State, World Scienti®c, Singapore, 1990. [12] K.L. Ngai, G.R. Wright (Eds.), Relaxation in Complex Systems, North Holland, Amsterdam, 1991. [13] P. Bra unlich (Ed.), Thermally Stimulated Relaxations in Solids, Topics in Applied Physics, vol. 37, Springer, New York, 1979. [14] J. van Turnhout, in: G.M. Sessler (Ed.), Electrets, Topics in Applied Physics, vol. 33, Springer, New York, 1980, pp. 81±201. [15] N.T. Correia, J.M. Ramos, J. Polym. Sci. B 37 (1999) 227. [16] M.J. Sanchis, R. Diaz-Calleja, Macromolecules 32 (1999) 3457. [17] V. Halpern, J. Phys. D: Appl. Phys. 82 (1994) 2628.
L. Goitiandia, A. Alegrõa / Journal of Non-Crystalline Solids 287 (2001) 237±241 [18] E. Dargent, M. Kattan, C. Cabot, P. Lebaudy, J. Ledru, J. Grenet, J. Appl. Polym. Sci. 74 (1999) 2716. [19] A. Alegrõa, L. Goitiandia, J. Colmenero, Polymer 37 (1996) 2915. [20] A. Alegrõa, L. Goitiandia, J. Colmenero, J. Polym. Sci. B Phys. 38 (2000) 2105. [21] G. Williams, D.C. Watts, Trans. Faraday Soc. 66 (1970) 80. [22] A. Alegrõa, J. Colmenero, P.O. Mari, I.A. Campbell, Phys. Rev. E 59 (1999) 6888. [23] C. Bucci, R. Fieschi, Phys. Rev. Lett. 12 (1964) 16.
241
[24] A. Alegrõa, E. Guerrica-Echevarria, L. Goitiandia, I. Tellerõa, J. Colmenero, Macromolecules 28 (1995) 1516. [25] A. Alegrõa, L. Goitiandia, I. Tellerõa, J. Colmenero, Macromolecules 30 (1997) 3881. [26] G. Adam, J.H. Gibbs, J. Chem. Phys. 43 (1958) 139. [27] E.A. Di Marzio, F. Dowell, J. Appl. Phys. 50 (1979) 6061. [28] I.M. Hodge, Macromolecules 19 (1986) 936. [29] G.W. Scherer, J. Am. Ceram. Soc. 67 (1984) 504. [30] A. Alegrõa, L. Goitiandia, I. Tellerõa, J. Colmenero, Recent Res. Dev. Macromol. Res. 3 (1998) 49.