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The activation energy spectrum for the enthalpy relaxation of a glassy liquid crystalline polymer: memory effects
IOURNA
ELSEVIER
L OF
Journal of Non-CrystallineSolids 172-174 (1994) 644-646
The activation energy spectrum for the enthalpy relaxation of a glassy liquid crystalline polymer: memory effects V. L o r e n z o a'*, J . M . P e r e f i a b, E. P ~ r e z b, R. B e n a v e n t e b, A. Bello b "E.T.S. de Ingenieros Industriales, Josd Guti&rez Abascal, 2, 28006 Madrid, Spain b Instituto de Ciencia y Tecnologia de Pollmeros (CSIC), Juan de la Cierva, 3, 28006 Madrid, Spain
Abstract
Crossover experiments in poly(diethylene glycol p,p'-bibenzoate) have been carried out by differential scanning calorimetry. The experimental conditions have been discussed in terms of the activation energy spectrum model and the results have been compared with the theoretical predictions of the model.
1. Introduction
Glassy state is a metastable one, so when a glass forming substance is cooled below its glass transition temperature, Tg, its structure evolves toward equilibrium. During this evolution, changes in many physical properties are observed due to atomic or molecular rearrangements in the amorphous material. The kinetics of these changes, which are called structural relaxation or physical aging, display a very rich phenomenology that includes memory effects [1]. Some models for relaxation that explain all the features of kinetic behaviour of supercooled liquids have appeared, including the activation energy spectrum (AES) model [2], the coupling model [3] or the domains model [4]. Isothermal annealing of poly(diethylene glycol p,p'-bibenzoate) (PDEB) below its glass transition * Corresponding author. Tel: +34-1 336 3168. Telefax: +34-1 336 3007.
temperature, Tg, has been studied previously in terms of the AES model and the parameters that characterize the spectra have been experimentally determined [5]. One of these parameters have been used in this work in order to explain the results of crossover experiments in PDEB. 2. Experimental
PDEB, a polyester which exhibits liquid crystalline character, was synthesized by melt transesterification of diethyl ester of p,p'-bibenzoic acid (4,4'-biphenyldicarboxylic acid) and diethylene glycol, using isopropyl titanate as catalyst. The obtained polyester was purified by dissolving in chloroform and precipitating in methanol. Its intrinsic viscosity, measured at 25°C, was 1.02 dL g - 1 [6]. A Perkin-Elmer DSC7 calorimeter was used for experiments. The thermal histories imposed to the samples were as follows: starting from a temperature of 75°C, well above the Tg, the sample was
0022-3093/94/$07.00 © 1994 Elsevier Science B.V.All rights reserved SSDI 0022-3093(94)002 1 9-D
V. Lorenzo et al. / Journal of Non-Crystalline Solids 172-174 (1994) 644-646
quenched at a rate of 10°C min-1 to the initial annealing temperature, TA~. This temperature was maintained for the time tA~ and then the sample was heated to TA2. After a time elapsed tA2, the sample was uniformly heated through the glass transition. Values of 313 and 318 K were selected for TA~ and TAZ, respectively. The initial annealing times were 0, 7, 15 and 40 min. IftA1 = 0, the results of crossover experiments equal those of an isothermal annealing at TA2.
3. Results Fig. 1 shows the results of a crossover experiment and those of an isothermal annealing one at TA2. The relaxation function, ~b, has been calculated according to
~=
A Q ( T A I , 0 , TA2, OO) -- AQ(TAI, tA1 , TA2, tA2 )
AQ(TAb 0, TA2, oo), (1) where AQ(TA~, tax, TA2, tA2) is the heat absorption in a crossover experiment whose parameters are
0.9
(~ 0.8
//
\ x~x~x ~x
o
0.6
0.5
i
I
10
i
l
those given in the paranthesis. It has been suggested that the limiting value for the heat absorption in an isothermal annealing experiment, AQ(TAI, 0, T A 2 , ~ ) equals Acp(Tg - TA2) where Ac v is the specific heat increment between the liquid and the glassy state at the Tg [7]. The values that were obtained for the calorimetric Tg and Ac v are 325 K and 0.222 J g- ~ K - 1, respectively. In the crossover experiment, 4~ increases as tA2 increases, displays a maximum and then memory effects fade, i.e., 4~ approaches asymptotically to AQ(TA~, 0, TA2, tA2) for longer annealing times. This kind of behaviour parallels the results reported on volume recovery of poly(vinyl acetate) [8] and on the Curie temperature of some metallic glasses [9].
4. Discussion The AES model predicts that the maximum abscissa, tA*2,can be estimated by means of the expression t*2 >~ Vo-1 exp{[TA1/TAz] ln(V0tAt)},
(2)
where Vo is a frequency factor that equals 1.3 × 10 -13 min -1 for PDEB [5]. The position of the maximum is calculated to be greater or equal to 4.2, 9 and 23 for initial annealing times of 7, 15 and 40 rain, respectively. Experimentally it is observed that t~2 is lower than 5 min for tA1 = 7 min and ranges between 5 and 12 min for tA1 = 15 and between 12 and 20 min for tA1 = 40 min. The agreement between experiments and theoretical predictions is good except for the longest first annealing time. In this case, a reasonable value has been found. At this point, it is interesting to analyze the way for choosing the parameters of the crossover experiments. It has been reported in [8,9] that TA1, tA1 and TA2 should fulfil the condition
1.0
0.7
645
~
20
I
30
'
I
AQ(TA~, tA~, TA2, 0) = AQ(TA1, 0,TA2, O0)
(3)
40
t~(min) Fig. 1 Relaxation functions, @,calculated according to Eq. (1) for isothermal annealing of PDEB at 318 K ( , O) and for a crossover experiment whose thermal history was: quenching from 348 to 313 K for 15 min followedby rapid heatingto 318 K ( -- , A). tA2 is the annealing time and t~2 has been calculated according to Eq. (2).
and, consequently, a careful first annealing is required. It is easy to prove in the frame of the AES model that memory effects will also be observed in any other case provided that TA1 < TA2. Effectively, after the initial annealing, all the processes with activation energy E < Eo(TA1, tA1 ) = k T A 1 ln(VotA1) have contributed to the relaxation. When
646.
1I. Lorenzo et al. / Journal o f Non-Crystalline Solids 172-174 (1994) 644-646
the temperature is raised to TA2 , Q(E) is greater than qs (E) for E < Eo and, then, all these processes contribute to a sharp ~ increase. Only when q(E) contribution overcomes that of the processes with E < Eo, ~b decreases. According to this, the maximum is reached when Eo(TA2, tA2) /> Eo(TA1, tA1) expression that leads to Eq. (2). 5. Conclusions
It has been proved that memory effects can be observed for any TA2 > TA1, irrespective of the tA1 value, and that Eq. (2) predicts correctly the q~ maximum position, even when condition (3) is not fulfilled. The financial support of the CICYT (Project No. MAT91-0380) is gratefully acknowledged.
References [1] G.B. Mackenna in: Comprehensive Polymer Science, Vol. 2, Polymer Properties, ed. C. Booth and C. Price, (Pergamon, Oxford, 1990)p. 311. I-2] M.R. Gibbs, J.E. Evetts and J.A. Leake, J. Mater. Sci. 18 (1983) 278. [3] K.L. Ngai, R.W. Rendell, A.K. Rajagopal and S. Teitler, Ann. NY Acad. Sci. 484 (1986) 150. 1-4] S. Matsuoka, Relaxation Phenomena in Polymers (Hansher, Munich, 1992). [5] V. Lorenzo, J.M. Perefia, E. P~rez, R. Benavente and A. Bello. [6] E. P6rez, R. Benavente, M.M. Marug~in, A. Bello and J.M. Perefia, Polym. Bull. 25 (1991) 413. [7] S.E.B. Petrie, J. Polym. Sci. A2 10 (1972) 1255. [8] A.J. Kovacs, Fortschr. Hochpolym.-Forsch. 3 (1964) 394. [9] A.L. Greer and F. Spaepen, Ann. NY Acad. Sci. 371 (1981) 218.
ELSEVIER
L OF
Journal of Non-CrystallineSolids 172-174 (1994) 644-646
The activation energy spectrum for the enthalpy relaxation of a glassy liquid crystalline polymer: memory effects V. L o r e n z o a'*, J . M . P e r e f i a b, E. P ~ r e z b, R. B e n a v e n t e b, A. Bello b "E.T.S. de Ingenieros Industriales, Josd Guti&rez Abascal, 2, 28006 Madrid, Spain b Instituto de Ciencia y Tecnologia de Pollmeros (CSIC), Juan de la Cierva, 3, 28006 Madrid, Spain
Abstract
Crossover experiments in poly(diethylene glycol p,p'-bibenzoate) have been carried out by differential scanning calorimetry. The experimental conditions have been discussed in terms of the activation energy spectrum model and the results have been compared with the theoretical predictions of the model.
1. Introduction
Glassy state is a metastable one, so when a glass forming substance is cooled below its glass transition temperature, Tg, its structure evolves toward equilibrium. During this evolution, changes in many physical properties are observed due to atomic or molecular rearrangements in the amorphous material. The kinetics of these changes, which are called structural relaxation or physical aging, display a very rich phenomenology that includes memory effects [1]. Some models for relaxation that explain all the features of kinetic behaviour of supercooled liquids have appeared, including the activation energy spectrum (AES) model [2], the coupling model [3] or the domains model [4]. Isothermal annealing of poly(diethylene glycol p,p'-bibenzoate) (PDEB) below its glass transition * Corresponding author. Tel: +34-1 336 3168. Telefax: +34-1 336 3007.
temperature, Tg, has been studied previously in terms of the AES model and the parameters that characterize the spectra have been experimentally determined [5]. One of these parameters have been used in this work in order to explain the results of crossover experiments in PDEB. 2. Experimental
PDEB, a polyester which exhibits liquid crystalline character, was synthesized by melt transesterification of diethyl ester of p,p'-bibenzoic acid (4,4'-biphenyldicarboxylic acid) and diethylene glycol, using isopropyl titanate as catalyst. The obtained polyester was purified by dissolving in chloroform and precipitating in methanol. Its intrinsic viscosity, measured at 25°C, was 1.02 dL g - 1 [6]. A Perkin-Elmer DSC7 calorimeter was used for experiments. The thermal histories imposed to the samples were as follows: starting from a temperature of 75°C, well above the Tg, the sample was
0022-3093/94/$07.00 © 1994 Elsevier Science B.V.All rights reserved SSDI 0022-3093(94)002 1 9-D
V. Lorenzo et al. / Journal of Non-Crystalline Solids 172-174 (1994) 644-646
quenched at a rate of 10°C min-1 to the initial annealing temperature, TA~. This temperature was maintained for the time tA~ and then the sample was heated to TA2. After a time elapsed tA2, the sample was uniformly heated through the glass transition. Values of 313 and 318 K were selected for TA~ and TAZ, respectively. The initial annealing times were 0, 7, 15 and 40 min. IftA1 = 0, the results of crossover experiments equal those of an isothermal annealing at TA2.
3. Results Fig. 1 shows the results of a crossover experiment and those of an isothermal annealing one at TA2. The relaxation function, ~b, has been calculated according to
~=
A Q ( T A I , 0 , TA2, OO) -- AQ(TAI, tA1 , TA2, tA2 )
AQ(TAb 0, TA2, oo), (1) where AQ(TA~, tax, TA2, tA2) is the heat absorption in a crossover experiment whose parameters are
0.9
(~ 0.8
//
\ x~x~x ~x
o
0.6
0.5
i
I
10
i
l
those given in the paranthesis. It has been suggested that the limiting value for the heat absorption in an isothermal annealing experiment, AQ(TAI, 0, T A 2 , ~ ) equals Acp(Tg - TA2) where Ac v is the specific heat increment between the liquid and the glassy state at the Tg [7]. The values that were obtained for the calorimetric Tg and Ac v are 325 K and 0.222 J g- ~ K - 1, respectively. In the crossover experiment, 4~ increases as tA2 increases, displays a maximum and then memory effects fade, i.e., 4~ approaches asymptotically to AQ(TA~, 0, TA2, tA2) for longer annealing times. This kind of behaviour parallels the results reported on volume recovery of poly(vinyl acetate) [8] and on the Curie temperature of some metallic glasses [9].
4. Discussion The AES model predicts that the maximum abscissa, tA*2,can be estimated by means of the expression t*2 >~ Vo-1 exp{[TA1/TAz] ln(V0tAt)},
(2)
where Vo is a frequency factor that equals 1.3 × 10 -13 min -1 for PDEB [5]. The position of the maximum is calculated to be greater or equal to 4.2, 9 and 23 for initial annealing times of 7, 15 and 40 rain, respectively. Experimentally it is observed that t~2 is lower than 5 min for tA1 = 7 min and ranges between 5 and 12 min for tA1 = 15 and between 12 and 20 min for tA1 = 40 min. The agreement between experiments and theoretical predictions is good except for the longest first annealing time. In this case, a reasonable value has been found. At this point, it is interesting to analyze the way for choosing the parameters of the crossover experiments. It has been reported in [8,9] that TA1, tA1 and TA2 should fulfil the condition
1.0
0.7
645
~
20
I
30
'
I
AQ(TA~, tA~, TA2, 0) = AQ(TA1, 0,TA2, O0)
(3)
40
t~(min) Fig. 1 Relaxation functions, @,calculated according to Eq. (1) for isothermal annealing of PDEB at 318 K ( , O) and for a crossover experiment whose thermal history was: quenching from 348 to 313 K for 15 min followedby rapid heatingto 318 K ( -- , A). tA2 is the annealing time and t~2 has been calculated according to Eq. (2).
and, consequently, a careful first annealing is required. It is easy to prove in the frame of the AES model that memory effects will also be observed in any other case provided that TA1 < TA2. Effectively, after the initial annealing, all the processes with activation energy E < Eo(TA1, tA1 ) = k T A 1 ln(VotA1) have contributed to the relaxation. When
646.
1I. Lorenzo et al. / Journal o f Non-Crystalline Solids 172-174 (1994) 644-646
the temperature is raised to TA2 , Q(E) is greater than qs (E) for E < Eo and, then, all these processes contribute to a sharp ~ increase. Only when q(E) contribution overcomes that of the processes with E < Eo, ~b decreases. According to this, the maximum is reached when Eo(TA2, tA2) /> Eo(TA1, tA1) expression that leads to Eq. (2). 5. Conclusions
It has been proved that memory effects can be observed for any TA2 > TA1, irrespective of the tA1 value, and that Eq. (2) predicts correctly the q~ maximum position, even when condition (3) is not fulfilled. The financial support of the CICYT (Project No. MAT91-0380) is gratefully acknowledged.
References [1] G.B. Mackenna in: Comprehensive Polymer Science, Vol. 2, Polymer Properties, ed. C. Booth and C. Price, (Pergamon, Oxford, 1990)p. 311. I-2] M.R. Gibbs, J.E. Evetts and J.A. Leake, J. Mater. Sci. 18 (1983) 278. [3] K.L. Ngai, R.W. Rendell, A.K. Rajagopal and S. Teitler, Ann. NY Acad. Sci. 484 (1986) 150. 1-4] S. Matsuoka, Relaxation Phenomena in Polymers (Hansher, Munich, 1992). [5] V. Lorenzo, J.M. Perefia, E. P~rez, R. Benavente and A. Bello. [6] E. P6rez, R. Benavente, M.M. Marug~in, A. Bello and J.M. Perefia, Polym. Bull. 25 (1991) 413. [7] S.E.B. Petrie, J. Polym. Sci. A2 10 (1972) 1255. [8] A.J. Kovacs, Fortschr. Hochpolym.-Forsch. 3 (1964) 394. [9] A.L. Greer and F. Spaepen, Ann. NY Acad. Sci. 371 (1981) 218.