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Study of cooperative relaxation modes in complex systems by thermally stimulated current spectroscopy
JOURNA L OF
ELSEVIER
Journal of Non-Crystalline Solids 172-174 (1994) 884-890
Study of cooperative relaxation modes in complex systems by thermally stimulated current spectroscopy Colette Lacabanne*, Alain Lamure, Gilbert Teyssedre, Alain Bernes, Magali Mourgues Solid State Physics Laboratory, Paul Sabatier University, 118 Route de Narbonne, 31062 Toulouse c~dex, France
Abstract
Cooperative relaxation modes associated with transitions of various systems have been experimentallyresolved into elementary processes characterized by activation enthalpies and entropies following a compensation law. Two transitions with no kinetic effect solid-solid transition and Curie transition have been studied. In both cases, the corresponding dielectric relaxations are characterized by a compensation phenomenon with transition temperature as the compensation temperature. Dielectric relaxations liberated at the glass transition, Tg, have also been studied. They are also associated with a compensation law but, in that case, the compensation temperature is T~ + 10/30°. This lag has been attributed to the kinetic character of Tg. Note that it is lower in amorphous polymers than in semicrystalline polymers. The distribution function of activation parameters is broader in amorphous polymers than in semicrystalline ones.
1. Introduction
The compensation law has been debated for many years. Evidence for it occurs in phenomena such as thermal killing of unicellular organisms [1], thermal denaturation of macromolecules [2], mixing and complexation reactions [-3-6], thermal dissolution of metallic monolayers [-7,8], physisorption [9,10], non-isothermal kinetics E11], conduction in semiconductors [12-19], and in insulators [20-22]. The experimental resolution of cooperative relaxation modes by using the technique of fractional polarizations has shown the
* Corresponding author. Tel: +33 61 55 66 11. Telefax: +33 61 55 62 33.
existence of compensation phenomena for activation enthalpies and entropies. Dielectric relaxation modes have been resolved by thermally stimulated currents (TSC) in crystals with apatitic structure [23-25], in amorphous homopolymers like polystyrene ( P S ) F26,27], polymethylmethacrylate (PMMA) [28,29], polyphenylene sulfide (PPS) [,30], polyethylene terephthalate (PET) [31], polycarbonate (PC) [32,33], in polymeric networks like polyepoxy [34,35], in semicrystalline polymers like polyvinylidene fluoride (PVDF) [36,37], polypropylene (PP) [,38,39], and polyamide PA66 [40,41] and in semicrystalline copolymers [-42,43]. Anelastic relaxation modes have been analyzed by thermally stimulated creep in amorphous polyolefins 1-44,45] in polyvinylchloride (PV,C) [46] in PMMA [47], in polyepoxy [48,49] in various
0022-3093/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved. SSD1 0 0 2 2 - 3 0 9 3 ( 9 4 ) 0 0 2 2 8 - F
885
C. Lacabanne et al. /Journal o / Non-Crystalline Solids 172-174 (1994) 884-890
semicrystalline polymers like polyurethanes [50], polyamides PA66 [51], PAll and PAl2 [52,53] and in polymeric blends [54,55]. Such compensation phenomena for anelastic relaxation have been confirmed by McCrum et al. [56] by double T jump experiments in polypropylene and by mechanical creep in HDPE [57]. It is also interesting to note that an ageing compensation effect has been observed in polymeric materials [58,59]• Thermodynamic considerations on the compensation law have been proposed by Crine [60]. Several authors have tempted to propose models for describing the compensation behavior [61-64]: from his model, Parez [65] reaches compensation temperatures in good agreement with experimental values for amorphous polymers like PMMA [66]. Based on Ngai's or Perez' models, Marchal [67] uses a different approach to interpret the compensation phenomenon. The aim of this paper is to present the relationships between the compensation phenomena observed for dielectric relaxation and the corresponding transitions.
2. Experimental The TSC spectroscopy has been used for exploring the distribution function of the dielectric relaxation time. The experiments were performed on a TSC/RMA spectrometer from Solomat; the heating rate was 7 K/min. The complex TSC spectra have been resolved into elementary peaks by using fractional polarizations with a window of 5 or 10 ° The applied voltages were ranging from 200 to 500 V with samples 20-100 gm thick. Data obtained on films of poly(vinylidene fluoride trifluoroethylene) P(VDF/TrFE) 75/25 copolymers, manufactured by Solvay, are reported first. A special attention will be paid to the dielectric relaxations associated with the ferroelectric to paraelectric transition observed on Differential Scanning Calorimetry thermograms. Phospho-calcic hydroxyapatite undergoes a solid-solid transition that can be observed by X-ray diffraction. Dielectric relaxations initiated at this transition were analyzed in compressed pow-
der pellets of synthetic phosphocalcic hydroxyapatite. Polyethylene terephthalate /PET has been chosen to explore the influence of molecular orientation on the dielectric relaxation associated with the glass transition. PET films were prepared by Rh6ne Poulenc: (i) the unoriented film has no trace of crystallinity; (ii) the biaxially oriented film is 40% crystalline. It is the Terphane R grade. The rigidity of the chain has a significant influence on the molecular mobility associated with the glass transition. In order to throw some light on this point, data on poly(ether-ether-ketone)/PEEK are reported. Films prepared by ICI designated as Stabar K200 were used in two forms: (i) as-received films with 12% of crystallinity; (ii) cold crystallized films with 31% of crystallinity.
3. Results Fig. 1 shows the elementary spectra isolated by fractional polarizations in the temperature range - 100 to + 100°C. The variation of the depolarization current, I, as a function of temperature, T, shows the existence of two relaxation modes, respectively, situated at - 3 6 (low temperature (LT) mode) and 100°C (high-temperature (HT) mode).
4.0
ea
~-. 2.0
o.o
-1od
. . . -.5 0. . . . . o. . . .
£o . . . .
Ibo'
T (*6")
Fig. 1. Elementary peaks isolated by the technique of fractional polarizations in P(VDF/TrFE).
886
C. Lacabanne et al. / Journal o f Non-Crystalline Solids 172-174 (1994) 884-890
Each elementary spectrum is well described by the hypothesis of a single relaxation time, z ( T ) . The corresponding temperature dependences z(T) of the various processes have been plotted on an Arrhenius diagram shown in Fig. 2. The experimental points are situated between l02 and l03 s. They have been described by an Arrhenius-Eyring equation, r = (h/kT) exp(AG/kT),
I 0 -'°"
Q
d 10
¢
(1) 10
-50
where h is the Planck constant, k is the Boltzmann constant and AG is the free enthalpy of activation. Since the temperature variation of the preexponential factor is negligible compared to that of the exponential factor, Eq. (1) is analogous to z = Zo exp(AH/kT),
(2)
where AH is the activation enthalpy, and
_
_
7"[ 1),
(4)
where z~ is the compensation time and Tc is the compensation temperature; Tc and z¢ are the coordinates of the converging point.
i
-so i
o I
I
I
50 I
[
,oo I I
I
~oo I I
T(C)
10 ~ 10" 5
10
~.
1
,,~ \~
10 -a
10
-s
5.'0
i
2.'0
3.'0
(eV) Fig. 3. % as a function of AH for PVDF/TrFE.
(3)
where AS is the activation entropy. By extrapolating the experimental variation of z(T) for the LT and HT peaks (dashed lines on Fig. 2) a converging point is defined. The corresponding relaxation times obey a compensation law 1
i
1.0
By comparing Eqs. (2) and (4), we deduce that
Zo ~- (h/kT) exp - (AS~k),
z(T) = zc exp(AH/k) (T-
®
4.'0
3/0
2.0
10S. T -' (K-')
Fig. 2. Arrhenius diagram of dielectric relaxation times of P(VDF/TrFE).
Zo = zc exp - (AH/kTc), The variation of In Zo as a function of AH is represented in Fig. 3. On this so-called compensation diagram the experimental points corresponding to the LT and HT modes are aligned: the bottom line is for the LT mode; the top line is for the HT mode.
4. Discussion
4.1. Ferroelectric-paraelectric relaxation/ transition Because of the fl conformation of the PVDF chains, the P(VDF/TrFE) copolymer is ferroelectric. The ferroelectric to paraelectric transition can be observed by Differential Scanning Calorimetry at 130°C. The HT mode observed by TSC corresponds to the dielectric manifestation of the ferroelectric to paraelectric transition (also designated as Curie transition). It is important to note here that a series of P(VDF/TrFE) copolymers with different chemical compositions has been investigated. In all cases, Tc corresponds to the Curie transition temperature. These data of course ascertain the previous hypothesis.
887
C. Lacabanne et al. / Journal qf Non-C~vstalline Solids 172 174 (1994) 884-890
4.2. Solid-solid relaxation/transition Phosphocalcic hydroxyapatite undergoes a solid solid transition that can be observed by X-ray diffraction at Tt = 212°C. It originates from the randomization of hydroxyldipoles inside the apatitic channel so that a monoclinic to hexagonal transition is exhibited. We have reported in Fig. 4 the results of the analysis to TSC spectra deduced from fractional polarizations. In that case, the compensation process involves 18 peaks so that the compensation point is very well defined: Tc = 211.5°C. On the compensation diagram of Fig. 5, the compensation phenomenon appears as a straight line, confirming that the various relax-
-;~o
-~,oo
q
,
r(c)
, coo
]
~10
ation times obey Eq. (4). The relaxation mode has been assigned to the dielectric manifestation of the monoclinic-hexagonal transition of hydroxyapatite. This hypothesis has been confirmed by further studies of a series of crystals of different chemical composition, i.e. with different transition temperatures since the relationship Tt,-~Tc remains verified.
4.3. Glass relaxation~transition The low-temperature relaxation mode of P(VDF/TrFE) 75/25 copolymer previously shown in Figs. 1-3 is characterized by a compensation temperature Tc = Tg + 26 °. The same phenomenological behavior is observed for a series of semicrystalline polymers like PVDF [36,37], polypropylene 1-38,39], polyamides [40,41,49,50% polyurethanes [48] and poly(ether-etherketone) (PEEK) as we shall see later on. Fig. 6 shows the Tc-Tg lag
z
d
AMORPHOUS
F-
SEMICRYSTALLINE
10 -* Tc-21t
5"C ~ ~ ' ~
,
,
,
,
,
,
10
,
,
,
,
11
200
10 -" ,
5
~03. T -' (A"-')
Fig. 4. Arrhenius diagram of dielectric relaxation times of phosphocalcic hydroxyapatite.
I
POLYEPOXY
PEEK
IPMMA 100
;L
4 PS PPS pET
I 0 -s PAll
d
PAl2
POLYAMIDES
~OLYOLEFINS
1 0 -,o
o.o
o.'e
o.'4
(ev)
0:6
Fig. 5. Compensation diagram of phosphocalcic hydroxyapatite.
Fig. 6 Tc Tg lag for amorphous and semicrystalline polymers. @,Tg; &,To.
888
C. Lacabanne et al. / Journal o f Non-Crystalline Solids 172-174 (1994) 884-890
(triangles indicate To, dots are for Tg) for those semicrystalline polymers, on the right part of the diagram and for reference amorphous polymers, on the left part of the diagram. A study of the influence of various physicochemical parameters on this lag has been undertaken. Data reported here concern chain stiffness and molecular orientation. Unoriented PET films and biaxially oriented PET films have been compared for exploring the influence of molecular orientation. Data from the TSC study of both films are reported in Fig. 7: on this compensation diagram, the crosses correspond to the unoriented amorphous PET and the dots to the biaxially oriented semicrystalline PET. The slope is practically the same for both films: in other words, molecular orientation does not modify the compensation temperature in a significant way. Contrarily, the width of the distribution function is considerably decreased. According to the model proposed by Hoffman et al. [68], for describing dielectric relaxation in paraffins, the activation enthalpy and entropy are varying like the size of the mobile sequence. In semicrystalline PET, the mobile sequences are of course limited by the presence of crystallites but the variation shows an unexpected magnitude. In order to throw some light on this point, data obtained on poly (ether-ether-ketone) (PEEK) are
1 0-21
reported. Fig. 8 shows the compensation diagram obtained for as-received films, 12% crystalline (dots) and for cold crystallized films, 31% crystalline (triangles). The slope of the compensation line is practically independent of the crystallinity: Tc ~ T~ + 12 °. As shown in Fig. 6, this lag is comparable with the ones observed for other semicrystalline polymers. We also note that the crystallinity increase is accompanied by a decrease of the width of the distribution function. The comparison of PET and PEEK data is relevant since both polymers have analogous crystallization kinetics. It is important to emphasize that the increase of chain stiffness is associated with an increase of the activation enthalpy and entropy on the side of maximum values. It is interesting to note that the restriction of the molecular mobility reflected by the decreasing of the magnitude of the compensation law, associated with Tg in PET, is in good agreement with the assumptions of Illers and Breuer [69] from low angle X-ray data. On the other hand, according to Coburn and Boyd [70], a loosening of constraints by crystals is observed upon annealing. Our observations show that this vanishing is due to the establishing of local order in the so-called 'constrained amorphous phase' [71]. This phase developed at the periphery of crystallites cannot propagate cooperative movements. It is coherent
\
I 0-20
A&
-t.~5 ~q
o F-
10
\
-4(
I 0 •40
o
~" 10-6° \
10-6 o7
~" " ",+ ~'o
2'o
' ~'o
(ev)
4o
",+ ' 5o
Fig. 7. Compensation diagram of unoriented amorphous PET ( + ), and biaxially oriented semicrystalline PET ((3).
I O-a°. 1.0
3.'0
5.'0
7.0
~-Z (eV) Fig. 8. Compensation diagram of 12% crystalline PEEK (©) and 31% crystalline PEEK (&).
C. Lacabanne et al. / Journal o f Non-Crystalline Solids 17~174 (19943 884-890
with hypothesis of 'rigid' amorphous phase widely developed by Wunderlich [72].
5. Conclusions Dielectric spectroscopy is well suited to the analysis of relaxation phenomena associated with transitions since the distribution function of activation enthalpy and entropy can be characterized. Relaxation modes due to cooperative movements have relaxation times following a compensation law. (i) First transitions with no kinetic effects (ferroelectric-paraelectric transition, solid-solid transition) have been considered. In this case, the compensation temperature corresponds to the transition temperature; (ii) Second, glass transitions characterized by their kinetic effects have been investigated. Then a lag exists between the compensation temperature and the glass transition temperature. This lag increases with the stiffness of the polymeric chain and it can reach some 30 ~. In semicrystalline polymers with stiff chains, the relaxation/transition concerns only the 'mobile' amorphous phase, while the 'rigid' amorphous phase does not propagate cooperative movements.
References [1] G. Kemeny and B. Rosenberg, Nature 243 (1973) 400. [2] G. Kemeny and S.D. Mahanti, Proc. Nat. Acad. Sci. 72 (1975) 999. [3] S. Takagi, T. Kimura and M. Maeda, Thermochim. Acta 88 (19853 247. [4] D. Patterson and H. Barbe. J. Phys. Chem. 80 (1976) 2435. [5] G. Michaux and J. Reisse, J. Am. Chem. Soc. 104 (19823 6895. [6] Y. lnoue and T. Hakushi, J. Chem. Soc. Perkin Trans. II (1985) 935. [7] R. Vanselow, J. Phys. 45 C9 (19843 53. [8] S.B. Kanungo, Indian J. Chem. 13 11975) 180. [9] E. Sommer and H.J. Kreuzer, Phys. Rev. Lett. 49 (1982) 61. [10] E. Sommer and H.J. Kreuzer, Surf. Sci 119 (19821 L331. [11] Z. Adonyi and G. Korosi, Thermochim. Aeta 60 (19833 23. [12] G.G. Roberts, J. Phys. C4 (1971) 3167. [13] D.D. Eley, J. Polym. Sci. C17 (1967) 73. [14] B. Rosenberg, B.B. Bhowmik, H.C. Harder and E. Postow, J. Chem. Phys. 49 (19683 4108.
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[15] B. Mallik, A. Ghosh and T.N. Misra, Jpn. J. Appl. Phys. 18 (19793 677. [16] B. Mallik, A. Ghosh and T.N. Misra, Jpn. J. Appl. Phys. 19 ( 19801 207. [17] B. Mallik, A. Ghosh and T.N. Misra, Phys. Status Solidi 62 t19803 267. [18] A. Sircar, B. Mallik and T.N. Misra, Proc. Indian Acad. Sci. 93 (19843 99. [19] G.F. Myachina, T.G. Ermakova and V.A. Lopyrev, Phys. Status Solidi 81 (19843 377. [20] T. Dosdale and R.J. Brook, J. Mater. Sci. 13 (1978) 167. [21] G. Sawa, K. Kitagawa and M. leda, Jpn. J. Appl. Phys. 11 (1972) 416. [22] R. Dewberry, J. Phys. D9 (19763 265. [23] N. Hitmi, D. Chatain, C. Lacabanne, J. Dugas, J.C. Trombe, C. Rey and G. Montel, Phys. Status Solidi 18 (19803 277. [24] N. Hitmi, C. Lacabanne and R.A. Young, J. Phys. Chem. 44 (1984) 701. [25] N. Hitmi, th6se d'etat, University of Toulouse (19813. [26] A. Bern+s, R.F. Boyer, D. Chatain, C. Lacabanne and J. P. Ibar, in: Order in the Amorphous State of Polymers, ed. S.E. Keinath, R.L. Miller and J.K. Rick (Plenum, New York, 1986) p. 305. [27] A. Bern6s, th6se d'universit6, University of Toulouse (19933. [28] A. Chafai, D. Chatain, J. Dugas, C. Lacabanne and E. Vayssi6, J. Macromol. Sci. Phys. Ed. B22 (1983) 633. [29] A. Gourari, M. Bendaoud, C. Lacabanne and R.F. Boyer, J. Polym Sci. Polym. Phys. 23 (1985) 889. [30] M. Mourgues-Martin, A. Bern6s, C. Lacabanne O. Nouvel and G. Seytre, IEEE Trans. Elec. Insul. 27 (1992) 795. [31] A. Bern+s, D. Chatain and C. Lacabanne, Thermochim. Acta 204 (1992) 69. [32] A. Bern6s, D. Chatain and C. Lacabanne, Polymer 32 (1992) 4882. [33] A. Bettacchioli, th6se d'universit6, University of Toulouse (1987). [34] C. Lavergne, A. Dufresne, D. Chatain and C. Lacabanne, J. Therm. Anal. 40 (1993) 705. [35] C. Lavergne, th+se d'universit+, University of Toulouse (19923. [36] C. Lacabanne, D. Chatain, T. El Sayed, D. Broussoux and F. Micheron, Ferroelectrics 30 (1980) 307. [37] T. E1 Sayed, th+se d'universit6, University of Toulouse (19833. [38] M. Jarrigeon, B. Chabert, D. Chatain, C. Lacabanne and G. Nemoz, J. Macromol. Sci. Phys. Rev. BI7 (1980) 1. [39] D. Ronarc'h, P. Audren and J.L. Moura, J. Appl. Phys. 58 (19853 474. [40] D. Chatain, P.G. Gautier and C. Lacabanne, J. Polym. Sci. Phys. Ed. 11 (19733 1631. [41] D. Chatain, thSse d'etat, University of Toulouse (19743. [42] H.S. Faruque and C. Lacabanne, Polymer 27 (19863 527. [43] H.S. Faruque, th~se docteur-ingSnieur, University of Toulouse (1984).
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C. Lacabanne et al. / Journal o f Non-Crystalline Solids 172-174 (1994) 884-890
[44] C. Lacabanne, D. Chatain, J.C. Monpagens, A. Hiltner and E. Baer, Solid State Commun. 27 (1978) 1055. [45] J.C. Monpagens, th6se d'etat, University of Toulouse (1977). [46] J.J. del Val, A. Algeria, J. Colmenero and C. Lacabanne, J. Appl. Phys. 59 (1986) 3829. [47] M. Diffalah, th6se d'universit6, University of Toulouse (1993). [48] J. Boye, J.J. Martinez, C. Lacabanne, P. Perret and B. Chabert, Polymer 33 (1992) 323. [49] J. Boye, th6se, d'universit6, University of Toulouse (1990). [50] T. El Sayed, D. Chatain and C. Lacabanne, in: Rheology, Vol 3, ed. G. Astarita, G. Marucci and L. Nicholais, (Plenum, New York, 1980) p. 171. [51] M. Stefenel, th6se d'universit6, University of Toulouse (1984). [52] A. Cazzitti, P. Demont, L. Fourmand, D. Chatain, C. Lacabanne, M. Glotin and P. Bluet, in Proc. Symp. on Polymeric Materials, San Sebastian, Spain, 1987, p. 154. [53] A. Cazzitti. th6se d'universit6, University of Toulouse (1988). [54] P. Demont, L. Fourmaud, D. Chatain and C. Lacabanne, Advances in Chemistry Series 227 (1990) 191. [55] L. Fourmand, th6se d'universit6, University of Toulouse (1988). [56] N.G. McCrum, M. Pizzoli, C.K. Chai, I. Treurnicht and J. M. Hutchinson, Polymer 23 (1982) 473.
[57] A.A. Warnas, Polym. Commun. 32 (1991) 83. [58] P.K. David, Trans. Elec. Ins. E1 22 (1987) 229. [59] G.C. Montanari and A. Motoriz, J. Phys. D24 (1991) 1172. [60] J.P. Crine, J. Macromol. Sci. B23 (1984) 201. [61] A.K. Lawson, J. Phys. Chem. Solidi 3 (1957) 250. [62] E. Peacock-Lopez and H. Suhl, Phys. Rev. B26 (1982) 3774. [63] V.P. Zdanov, Surf. Sci. Lett. 159 (1985) L416. [64] H.K. Kang, T.A. Jachimowski and W.H. Weinburg, J. Chem. Phys. 93 (1980) 1418. [65] J. Perez, Physique et M6canique des Polym6res Amorphes (Technique et Documentation Lavoisier, Paris, 1992). [66] B.B. Sauer and P. Avakian, Polymer 33 (1992) 5128. [67] E. Marchal, Makromol. Chem. Rapid Commun. 14 (1993) 597. [68] J.D. Hoffman, G. Williams and E. Passaglia, J. Polym. Sci. C14 (1966) 173. [69] K.H. lllers and H.J. Breuer, J. Colloid Sci. 18 (1963) 1. [70] J.C. Coburn and R.H. Boyd, Macromolecules 19 (1986) 2238. [71] R.F. Boyer, Transitions and Relaxations in Amorphous and Semicrystalline Organic Polymers and Copolymers, Encyclop. Pol. Sci. and Tech. II (1977) 745. [72] S.Z.T. Cheng, R. Pan and B. Wunderlich, Makromol. Chem. 189 (1988) 244.
ELSEVIER
Journal of Non-Crystalline Solids 172-174 (1994) 884-890
Study of cooperative relaxation modes in complex systems by thermally stimulated current spectroscopy Colette Lacabanne*, Alain Lamure, Gilbert Teyssedre, Alain Bernes, Magali Mourgues Solid State Physics Laboratory, Paul Sabatier University, 118 Route de Narbonne, 31062 Toulouse c~dex, France
Abstract
Cooperative relaxation modes associated with transitions of various systems have been experimentallyresolved into elementary processes characterized by activation enthalpies and entropies following a compensation law. Two transitions with no kinetic effect solid-solid transition and Curie transition have been studied. In both cases, the corresponding dielectric relaxations are characterized by a compensation phenomenon with transition temperature as the compensation temperature. Dielectric relaxations liberated at the glass transition, Tg, have also been studied. They are also associated with a compensation law but, in that case, the compensation temperature is T~ + 10/30°. This lag has been attributed to the kinetic character of Tg. Note that it is lower in amorphous polymers than in semicrystalline polymers. The distribution function of activation parameters is broader in amorphous polymers than in semicrystalline ones.
1. Introduction
The compensation law has been debated for many years. Evidence for it occurs in phenomena such as thermal killing of unicellular organisms [1], thermal denaturation of macromolecules [2], mixing and complexation reactions [-3-6], thermal dissolution of metallic monolayers [-7,8], physisorption [9,10], non-isothermal kinetics E11], conduction in semiconductors [12-19], and in insulators [20-22]. The experimental resolution of cooperative relaxation modes by using the technique of fractional polarizations has shown the
* Corresponding author. Tel: +33 61 55 66 11. Telefax: +33 61 55 62 33.
existence of compensation phenomena for activation enthalpies and entropies. Dielectric relaxation modes have been resolved by thermally stimulated currents (TSC) in crystals with apatitic structure [23-25], in amorphous homopolymers like polystyrene ( P S ) F26,27], polymethylmethacrylate (PMMA) [28,29], polyphenylene sulfide (PPS) [,30], polyethylene terephthalate (PET) [31], polycarbonate (PC) [32,33], in polymeric networks like polyepoxy [34,35], in semicrystalline polymers like polyvinylidene fluoride (PVDF) [36,37], polypropylene (PP) [,38,39], and polyamide PA66 [40,41] and in semicrystalline copolymers [-42,43]. Anelastic relaxation modes have been analyzed by thermally stimulated creep in amorphous polyolefins 1-44,45] in polyvinylchloride (PV,C) [46] in PMMA [47], in polyepoxy [48,49] in various
0022-3093/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved. SSD1 0 0 2 2 - 3 0 9 3 ( 9 4 ) 0 0 2 2 8 - F
885
C. Lacabanne et al. /Journal o / Non-Crystalline Solids 172-174 (1994) 884-890
semicrystalline polymers like polyurethanes [50], polyamides PA66 [51], PAll and PAl2 [52,53] and in polymeric blends [54,55]. Such compensation phenomena for anelastic relaxation have been confirmed by McCrum et al. [56] by double T jump experiments in polypropylene and by mechanical creep in HDPE [57]. It is also interesting to note that an ageing compensation effect has been observed in polymeric materials [58,59]• Thermodynamic considerations on the compensation law have been proposed by Crine [60]. Several authors have tempted to propose models for describing the compensation behavior [61-64]: from his model, Parez [65] reaches compensation temperatures in good agreement with experimental values for amorphous polymers like PMMA [66]. Based on Ngai's or Perez' models, Marchal [67] uses a different approach to interpret the compensation phenomenon. The aim of this paper is to present the relationships between the compensation phenomena observed for dielectric relaxation and the corresponding transitions.
2. Experimental The TSC spectroscopy has been used for exploring the distribution function of the dielectric relaxation time. The experiments were performed on a TSC/RMA spectrometer from Solomat; the heating rate was 7 K/min. The complex TSC spectra have been resolved into elementary peaks by using fractional polarizations with a window of 5 or 10 ° The applied voltages were ranging from 200 to 500 V with samples 20-100 gm thick. Data obtained on films of poly(vinylidene fluoride trifluoroethylene) P(VDF/TrFE) 75/25 copolymers, manufactured by Solvay, are reported first. A special attention will be paid to the dielectric relaxations associated with the ferroelectric to paraelectric transition observed on Differential Scanning Calorimetry thermograms. Phospho-calcic hydroxyapatite undergoes a solid-solid transition that can be observed by X-ray diffraction. Dielectric relaxations initiated at this transition were analyzed in compressed pow-
der pellets of synthetic phosphocalcic hydroxyapatite. Polyethylene terephthalate /PET has been chosen to explore the influence of molecular orientation on the dielectric relaxation associated with the glass transition. PET films were prepared by Rh6ne Poulenc: (i) the unoriented film has no trace of crystallinity; (ii) the biaxially oriented film is 40% crystalline. It is the Terphane R grade. The rigidity of the chain has a significant influence on the molecular mobility associated with the glass transition. In order to throw some light on this point, data on poly(ether-ether-ketone)/PEEK are reported. Films prepared by ICI designated as Stabar K200 were used in two forms: (i) as-received films with 12% of crystallinity; (ii) cold crystallized films with 31% of crystallinity.
3. Results Fig. 1 shows the elementary spectra isolated by fractional polarizations in the temperature range - 100 to + 100°C. The variation of the depolarization current, I, as a function of temperature, T, shows the existence of two relaxation modes, respectively, situated at - 3 6 (low temperature (LT) mode) and 100°C (high-temperature (HT) mode).
4.0
ea
~-. 2.0
o.o
-1od
. . . -.5 0. . . . . o. . . .
£o . . . .
Ibo'
T (*6")
Fig. 1. Elementary peaks isolated by the technique of fractional polarizations in P(VDF/TrFE).
886
C. Lacabanne et al. / Journal o f Non-Crystalline Solids 172-174 (1994) 884-890
Each elementary spectrum is well described by the hypothesis of a single relaxation time, z ( T ) . The corresponding temperature dependences z(T) of the various processes have been plotted on an Arrhenius diagram shown in Fig. 2. The experimental points are situated between l02 and l03 s. They have been described by an Arrhenius-Eyring equation, r = (h/kT) exp(AG/kT),
I 0 -'°"
Q
d 10
¢
(1) 10
-50
where h is the Planck constant, k is the Boltzmann constant and AG is the free enthalpy of activation. Since the temperature variation of the preexponential factor is negligible compared to that of the exponential factor, Eq. (1) is analogous to z = Zo exp(AH/kT),
(2)
where AH is the activation enthalpy, and
_
_
7"[ 1),
(4)
where z~ is the compensation time and Tc is the compensation temperature; Tc and z¢ are the coordinates of the converging point.
i
-so i
o I
I
I
50 I
[
,oo I I
I
~oo I I
T(C)
10 ~ 10" 5
10
~.
1
,,~ \~
10 -a
10
-s
5.'0
i
2.'0
3.'0
(eV) Fig. 3. % as a function of AH for PVDF/TrFE.
(3)
where AS is the activation entropy. By extrapolating the experimental variation of z(T) for the LT and HT peaks (dashed lines on Fig. 2) a converging point is defined. The corresponding relaxation times obey a compensation law 1
i
1.0
By comparing Eqs. (2) and (4), we deduce that
Zo ~- (h/kT) exp - (AS~k),
z(T) = zc exp(AH/k) (T-
®
4.'0
3/0
2.0
10S. T -' (K-')
Fig. 2. Arrhenius diagram of dielectric relaxation times of P(VDF/TrFE).
Zo = zc exp - (AH/kTc), The variation of In Zo as a function of AH is represented in Fig. 3. On this so-called compensation diagram the experimental points corresponding to the LT and HT modes are aligned: the bottom line is for the LT mode; the top line is for the HT mode.
4. Discussion
4.1. Ferroelectric-paraelectric relaxation/ transition Because of the fl conformation of the PVDF chains, the P(VDF/TrFE) copolymer is ferroelectric. The ferroelectric to paraelectric transition can be observed by Differential Scanning Calorimetry at 130°C. The HT mode observed by TSC corresponds to the dielectric manifestation of the ferroelectric to paraelectric transition (also designated as Curie transition). It is important to note here that a series of P(VDF/TrFE) copolymers with different chemical compositions has been investigated. In all cases, Tc corresponds to the Curie transition temperature. These data of course ascertain the previous hypothesis.
887
C. Lacabanne et al. / Journal qf Non-C~vstalline Solids 172 174 (1994) 884-890
4.2. Solid-solid relaxation/transition Phosphocalcic hydroxyapatite undergoes a solid solid transition that can be observed by X-ray diffraction at Tt = 212°C. It originates from the randomization of hydroxyldipoles inside the apatitic channel so that a monoclinic to hexagonal transition is exhibited. We have reported in Fig. 4 the results of the analysis to TSC spectra deduced from fractional polarizations. In that case, the compensation process involves 18 peaks so that the compensation point is very well defined: Tc = 211.5°C. On the compensation diagram of Fig. 5, the compensation phenomenon appears as a straight line, confirming that the various relax-
-;~o
-~,oo
q
,
r(c)
, coo
]
~10
ation times obey Eq. (4). The relaxation mode has been assigned to the dielectric manifestation of the monoclinic-hexagonal transition of hydroxyapatite. This hypothesis has been confirmed by further studies of a series of crystals of different chemical composition, i.e. with different transition temperatures since the relationship Tt,-~Tc remains verified.
4.3. Glass relaxation~transition The low-temperature relaxation mode of P(VDF/TrFE) 75/25 copolymer previously shown in Figs. 1-3 is characterized by a compensation temperature Tc = Tg + 26 °. The same phenomenological behavior is observed for a series of semicrystalline polymers like PVDF [36,37], polypropylene 1-38,39], polyamides [40,41,49,50% polyurethanes [48] and poly(ether-etherketone) (PEEK) as we shall see later on. Fig. 6 shows the Tc-Tg lag
z
d
AMORPHOUS
F-
SEMICRYSTALLINE
10 -* Tc-21t
5"C ~ ~ ' ~
,
,
,
,
,
,
10
,
,
,
,
11
200
10 -" ,
5
~03. T -' (A"-')
Fig. 4. Arrhenius diagram of dielectric relaxation times of phosphocalcic hydroxyapatite.
I
POLYEPOXY
PEEK
IPMMA 100
;L
4 PS PPS pET
I 0 -s PAll
d
PAl2
POLYAMIDES
~OLYOLEFINS
1 0 -,o
o.o
o.'e
o.'4
(ev)
0:6
Fig. 5. Compensation diagram of phosphocalcic hydroxyapatite.
Fig. 6 Tc Tg lag for amorphous and semicrystalline polymers. @,Tg; &,To.
888
C. Lacabanne et al. / Journal o f Non-Crystalline Solids 172-174 (1994) 884-890
(triangles indicate To, dots are for Tg) for those semicrystalline polymers, on the right part of the diagram and for reference amorphous polymers, on the left part of the diagram. A study of the influence of various physicochemical parameters on this lag has been undertaken. Data reported here concern chain stiffness and molecular orientation. Unoriented PET films and biaxially oriented PET films have been compared for exploring the influence of molecular orientation. Data from the TSC study of both films are reported in Fig. 7: on this compensation diagram, the crosses correspond to the unoriented amorphous PET and the dots to the biaxially oriented semicrystalline PET. The slope is practically the same for both films: in other words, molecular orientation does not modify the compensation temperature in a significant way. Contrarily, the width of the distribution function is considerably decreased. According to the model proposed by Hoffman et al. [68], for describing dielectric relaxation in paraffins, the activation enthalpy and entropy are varying like the size of the mobile sequence. In semicrystalline PET, the mobile sequences are of course limited by the presence of crystallites but the variation shows an unexpected magnitude. In order to throw some light on this point, data obtained on poly (ether-ether-ketone) (PEEK) are
1 0-21
reported. Fig. 8 shows the compensation diagram obtained for as-received films, 12% crystalline (dots) and for cold crystallized films, 31% crystalline (triangles). The slope of the compensation line is practically independent of the crystallinity: Tc ~ T~ + 12 °. As shown in Fig. 6, this lag is comparable with the ones observed for other semicrystalline polymers. We also note that the crystallinity increase is accompanied by a decrease of the width of the distribution function. The comparison of PET and PEEK data is relevant since both polymers have analogous crystallization kinetics. It is important to emphasize that the increase of chain stiffness is associated with an increase of the activation enthalpy and entropy on the side of maximum values. It is interesting to note that the restriction of the molecular mobility reflected by the decreasing of the magnitude of the compensation law, associated with Tg in PET, is in good agreement with the assumptions of Illers and Breuer [69] from low angle X-ray data. On the other hand, according to Coburn and Boyd [70], a loosening of constraints by crystals is observed upon annealing. Our observations show that this vanishing is due to the establishing of local order in the so-called 'constrained amorphous phase' [71]. This phase developed at the periphery of crystallites cannot propagate cooperative movements. It is coherent
\
I 0-20
A&
-t.~5 ~q
o F-
10
\
-4(
I 0 •40
o
~" 10-6° \
10-6 o7
~" " ",+ ~'o
2'o
' ~'o
(ev)
4o
",+ ' 5o
Fig. 7. Compensation diagram of unoriented amorphous PET ( + ), and biaxially oriented semicrystalline PET ((3).
I O-a°. 1.0
3.'0
5.'0
7.0
~-Z (eV) Fig. 8. Compensation diagram of 12% crystalline PEEK (©) and 31% crystalline PEEK (&).
C. Lacabanne et al. / Journal o f Non-Crystalline Solids 17~174 (19943 884-890
with hypothesis of 'rigid' amorphous phase widely developed by Wunderlich [72].
5. Conclusions Dielectric spectroscopy is well suited to the analysis of relaxation phenomena associated with transitions since the distribution function of activation enthalpy and entropy can be characterized. Relaxation modes due to cooperative movements have relaxation times following a compensation law. (i) First transitions with no kinetic effects (ferroelectric-paraelectric transition, solid-solid transition) have been considered. In this case, the compensation temperature corresponds to the transition temperature; (ii) Second, glass transitions characterized by their kinetic effects have been investigated. Then a lag exists between the compensation temperature and the glass transition temperature. This lag increases with the stiffness of the polymeric chain and it can reach some 30 ~. In semicrystalline polymers with stiff chains, the relaxation/transition concerns only the 'mobile' amorphous phase, while the 'rigid' amorphous phase does not propagate cooperative movements.
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