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Mechanical γ and β relaxations in polyethylene—I. Glass transitions of polyethylene
Eur. Polvm. J. Vol. 28, No. 8, pp. 935 948, 1992 Printed in Great Britain
0014-3057/92 $5.00 + 0.00 Pergamon Press Ltd
M E C H A N I C A L 7 A N D /~ R E L A X A T I O N S IN P O L Y E T H Y L E N E - - I . GLASS T R A N S I T I O N S OF P O L Y E T H Y L E N E N. ALBEROLA,~'2j. y . CAVAILLE2.3and J. PEREZ2 tLaboratoire Materiaux Composites, ESIGEC, Universit+ de Savoie, BP 1104, 73011 Chambery Cedex, France 2Laboratoire GEMPPM, INSA, Bat. 502, Av. A. Einstein, 69621 Villeurbanne, France 3CERMAV, BP 53X, 38041 Grenoble Cedex, France (Received 6 November 1991)
Abstract--The mechanical 7 relaxation of a linear polyethylene has been extensively analysed by means of high resolution mechanical spectrometry. This analysis was completed by quantitative measurements of the morphological parameters governing the characteristics of the 5, relaxation, such as the crystallinity index and the crystalline lamellar thickness distribution determined from differential scanning calorimetry. The 7 relaxation was found to have the characteristics of mechanical relaxation due to glass transition: there is a high apparent activation energy; linear polyethylene exhibits structural recovery induced by annealing at a temperature below the )' peak, whereas the 7 relaxation has a WLF temperature dependence. As for the i' relaxation, it was found that the/3 relaxation displayed by a branched polyethylene has the characteristics of a glass transition (high value of apparent activation energy; structural recovery during ageing at T < Tt~). Recalling definitions of the glass temperature, it was proposed that the lower glass transition (7 region) is characteristic of Van der Waals interactions between CH 2 groups while the upper glass transition ({/ region) is specific of Van der Waals interactions between CH 2 and CH 3 groups.
INTRODUCTION
Many investigations have been directed to characterization of the ~, relaxation of polyethylene by various methods including mechanical and dielectrical spectrometry, N M R and thermostimulated depolarization measurements. The origin (crystalline and/or amorphous phase) and the nature of the molecular motions involved in the 7 relaxation have been extensively discussed and remain controversial. The discussion is widened because of the possible presence of many processes contained in this relaxation and because of the localization of these possible processes. Moreover, work dealing with the mechanisms of the 7 relaxation is mainly based on dielectric measurements. As polyethylene is not dielectrically active, the characterization of this polymer requires attachment of dipoles (carbonyls or chlorines). Thus, the characteristics of the processes exhibited by this method cannot be strictly compared to the data from mechanical measurements because the analysed polymers are not chemically the same. According to some authors, the 7 relaxation consists of a well-defined peak called the 71 process and a peak as a shoulder located at lower temperature and referred to as the 72 process. All authors agree that the main component of the ~ relaxation has its origin in the amorphous phase [1, 2]. Thus, it was shown that amorphous polyethylene exhibits a mechanical relaxation in the same temperature range [3]. Illers [4], Willbourn [5] and Cooper and McCrum [6] suggested that the ~1 process could originate from local mobility of some monomer units in the amorphous phase. Then, the main component of the ? relaxation could be regarded as a subglass transition.
Boyd and Breitling [7] have considered that the 71 relaxation could not be induced by a crankshaft motion involving six or eight carbon atoms as suggested by the Schatzki models [8] because the volume involved in this motion is too large and requires too much energy. More recently, Audren and Ronarc'h [9] suggested, from thermostimulated depolarization measurements on doped low-density polyethylene, that the 7~ process is induced by the motion of chain segments having approximately between 10 and 20 carbon atoms. According to Stehling and Mandelkern [10], the main component of the 7 relaxation could be related to the glassrubber transition of polyethylene. As a matter of fact, in this temperature range, polyethylene exhibits characteristics of a glass transition i.e. an abrupt increase in the coefficient of thermal expansion and an increase in the specific heat. The 7., relaxation was first related to defect diffusion in the crystalline phase [11, 12]. Then, Stehling and Mandelkern considered that this process originates in the interfacial zone between crystalline and amorphous phase. Audren and Ronarc'h [9] showed that the 72 relaxation could be generated by the motion of chain segments having less than 10 carbon atoms. According to other authors [13-16], the 7 relaxation consists of three components called 71, )'2 and ~'3 in order of decreasing temperature and ascribed respectively to motions of polar groups in: (i) the amorphous phase; (it) defects in the crystalline phase; and (iii) the cilia attached to the chain-folded surfaces of crystallites in polyethylene. According to 935
936
N. ALBEROLAet al. another point of view, the 7 relaxation was regarded as a single process attributed to polar groups in the amorphous phase with a somewhat wide distribution of relaxation times [17-20].
This literature review shows that all authors agree that the 71 (~' relaxation regarded as a multiple process) or the 7 relaxation (7 relaxation considered as a single process) originate from the amorphous phase. According to some authors, the ~ (or 71) relaxation is related to the glass transition of polyethylene [10] and for others, the 7 (or ~,~) relaxation can be regarded as a subglass transition [4-6, 18, 19]. It is of interest therefore to consider the thermorheological characteristics of the 7 (or 71) relaxation. Thus, according to lllers [4], Sato [20] and Buerger and Boyd [21], the 7 relaxation shows an Arrhenius temperature dependence as for secondary transitions. Matsuoka and Alosio [22] consider however, that the 7 relaxation has a W L F temperature dependence as for the primary glass transition observed in amorphous polymers. According to Pechold et al. [23], the 7 relaxation has neither an Arrhenius nor a W L F temperature dependence. The reported values of the apparent activation energies of the 7 (or Yl) range from 20 to 80 kJ/mol [20, 24, 25]. Sato [20] has shown that an increase in crystallinity owing to decrease in branching leads to: (i) an increase in the apparent activation energy of the dielectric 7 (or 7i) relaxation; and (ii) a shift of the 7 relaxation towards higher temperature. Discussion about the location of the glass transition of polyethylene is increased because of the presence of another relaxation, the 13 relaxation, displayed by branched relaxation in the - 3 0 to - 10°C range which could also be attributed to glass transition of polyethylene (this relaxation is barely detected in linear polyethylene). Wunderlich and Baur [26] have shown a characteristic increase in the specific heat of amorphous polyethylene at about -36°C. Chang [27] has shown that quenched branched and linear polyethylenes under adiabatic conditions exhibit spontaneous temperature drifts in the 13 region at about -35°C. These spontaneous temperature drifts can always be observed in the glass transition zone and serve as an indicator of the rate at which the glass approaches an equilibrium state. Such phenomena are not observed in the ~ region. Moreover, from volume relaxation studies, Davies and Eby [28] have shown that polyethylene exhibits structural recovery during physical ageing in the fl temperature range as do vitreous systems annealed at a temperature below their glass temperature. In addition, the high values of apparent activation energy (200-300 kJ/mol) of the mechanical /3 relaxation reported by some authors [29] are in agreement with the assignment of the fl relaxation to the glass transition of polyethylene. Both ~ and fl relaxations therefore could be related to glass transitions of polyethylene. Boyer [30] has suggested that semicrystalline polyethylene could show two glass transitions, Tg(L) and Ts(U ) located at about - 8 0 and - 3 0 ° C respectively. These glass
transitions are ascribed to the existence of two types of amorphous regions. Ts(L ) might be related to "free" amorphous phase consisting of low molecular weight chains which have not crystallized and Ts(U ) to "tied" amorphous domains constrained by crystalline structures. The location of a lower glass transition at about - 8 0 ° C is supported by Lam and Geil [31] who observed the onset of crystallization of vitrified solutions of polyethylene at this temperature. The location of Tg(L) at about - 8 0 ° C is, however, not credible for two reasons: (i) no mechanical relaxation (frequency ~ 1 Hz) is detected about this temperature. This is not consistent with what is usually observed for other polymers; (ii) it is not really pertinent to associate the temperature of the beginning of the crystallization to the glass transitions for macromolecular systems. As a matter of fact, in these systems, it can be assumed that the crystalline organization needs greater thermal activation than for obtaining new degrees of freedom at the glass transition. Hence, the glass transition of polyethylene should be located at a temperature below -80°C. Consequently, according to Boyer's suggestion, it is more credible to associate the 7 relaxation to Tg(L) of polyethylene. The mechanisms of the 7 relaxation therefore remain unresolved and the location of the glass transition of polyethylene is still to be established, although there are some sound arguments to associate the fl relaxation with a glass-rubber transition. The short survey concerning the mechanical ~ and fl relaxations in polyethylene shows a lack of experimental data from frequency scans, under isothermal conditions, in these temperature ranges in order to establish precisely the temperature frequency dependence of these relaxations. The present work attempts to contribute to these different points. Thus, high resolution dynamic mechanical spectrometry has been carried out on linear and branched polyethylene by means of an original low-frequency torsion pendulum. We have focused the analysis on the 7 relaxation spectra vs temperature or frequency (isothermal conditions) displayed by samples showing different microstructures resulting from different thermal histories. The differences in sample microstructure obtained by annealing at various temperature were characterized mainly by means of a simple model giving lamellar size distribution from colorimetric data. EXPERIMENTAL PROCEDURES Materials
The materials used in this study were a high density linear polyethylene (system A) provided by the Hoechst Company and a commercial low density branched polyethylene (system B). Some of the characteristics of these materials are listed in Table 1.
Table 1. Characteristics of analysed samples (P = Polydispersity;% B, numberofCH 3for 1000C System
A B
of the main chain; d, density) ~. h/,, P %B
6.105 4.106 3.105 3.104
6 l0
d
<2.5 0.939 >10 0.892
937
Mechanical 7 and fl relaxations in polyethylene-~l
Thermal treatments As received linear polyethylene sheets are heated at 170°C for 30 min in N 2 and then quenched in water at 15°C. Five samples were cut to the following dimensions: 80 x 40 x 1.3 mm. Four of these samples, the so-called annealed samples, were annealed for 24 hr at I00, 110, 120 and 130°C respectively in N 2 and then quenched in water at 15°C. One of these specimens, the so-called quenched sample, was kept at room temperature. For experimental work, all samples were cut to the following dimensions: 40 × 6 × 1.3mm for dynamic mechanical experiments and 2 × 2 × 1.3 mm 3 for calorimetric analysis. Branched polyethylene was studied as received and it was cut to the same dimensions as for linear polyethylene, but the thickness of branched polyethylene sheets was about 0.5 mm.
Dynamic mechanical spectrometry As explained in the introduction, obtaining new information about the mechanical 7 relaxation needs a dynamic Ld__~ M M
mechanical spectrometer with higher resolution than usual, So, dynamic mechanical measurements were performed with a set-up* well-suited to study low magnitude mechanical relaxation. This apparatus is an automated low frequency inverted torsion pendulum [32] which provides the real (G') and imaginary (G") parts of the shear modulus and the internal friction parameters tan dp(=G"/G') as a function of temperature (for one or several fixed frequencies) or frequency (under isothermal conditions). For temperature scans (isochronal conditions), runs were performed from - 1 7 0 to 20°C at 15°C/hr and at three frequencies 1,0.1 and 0.01 Hz. Frequency scans were carried out under isothermal conditions in the - 1 6 0 to 20°C range over a wide range of frequency (10-4-I Hz).
Differential scanning calorimetry Thermograms were recorded using a Perkin-Elmer DSC 1B apparatus over the range 20 to 150~C. The experiments were carried out for all samples at a heating rate of
(a)
1 dM
dL
(b)
M dL
I
l
400
400
L(,~)
M dL
I 400
L(A)
1
-~- d--M-M (d)
I 0
dM
;~C
dL
(e)
I
400 L(~,)
4O0 L(~,)
Fig. 1. Lamellar thickness distribution curves for the samples: (a) quenched from 170 to 20°C and annealed for 24hr at (b) 100°C, (c) I10°C, (d) 120°C and (e) 130°C. *Designed by the GEMPPM Laboratory and commercialized by Metravib (69132 Ecully, France).
938
N. ALBEROLA et al.
8°C/rain. The instrument was calibrated with an indium standard to give the onset of melting at 156.6°C. The crystallinity index (X¢) of each sample was determined through the relationship [33]:
[34] shows that the temperature of the melting curve is an increasing function of the crystallite thickness: it has been extended for any temperature of the melting thermogram. Then, it yields: T
xo = (Ha - H o ) / H =
where Ha and H c are the enthalpies in the melt and crystalline states respectively. Their difference is determined from the area of the melting endothermic peak. The enthalpy of melting (Hm) per mass unit is 288 J/g [33]. It is well-known that the melting temperature depends on crystallite size [34]. In a previous paper [35], we developed a simple model to give the crystallite thickness distribution curve from the thermogram. Thus, the Thomson equation
To(l
=
--
2a/Hm'l )
where T is the melting temperature (K) of lamellae of thickness l, TOis the equilibrium melting temperature of an infinite crystal ( T O= 414.5 K), .4 is the free surface energy per unit area of the basal face (cr = 70" 10 -3 J/m 2) and H m is taken [33] for 288 J/M 3. The crystallite thickness distribution with / is given by: 1 d M ( d E / d T ) ( T o - T) 2 M
dl
2(7.To.M
(a) 10
a
(D
i_.1
g,
.J
6
I -180
-140
I
I
-100
--60
I
I
-20
20
T (°C)
(b) o.1
/
-o-
0
I -180
-140
I
I
--100
--60
l --20
I 20
T(*C)
Fig. 2. Plots of log G' (a) and tan ~b (b) vs temperature for quenched sample: I I , 1 Hz; O, 0.I Hz; &, 0.01 Hz. Plots of log G' against temperature at the three frequencies are shifted along the log G ' scale of one decade one from another. The curve at 0.1 Hz is the reference.
Mechanical 7 and fl relaxations in polyethylene--I where M is the mass of the total crystalline phase, dM/M is the mass fraction of crystalline phase which melts between T and (T + dT) and dE/dT, given by the recorded DSC curve, is the energy required to melt the dM fraction. Some experiments were carried out in the - 150 to 20°C temperature range.
Table 2. Degree of crystallinity (Xc) from DSC and parameters of lamellar thickness distribution curves lmax(A) b System
RESULTS
0.1 and 0.01 Hz vs temperature are shown in Fig. 2.
~
t
T
l~.d(A) b
40 50 52 61 70
(50) (60) (60) 70 70
110 130 140 180 220
230 300 350 400 700
The well-defined y peak is located between - 1 1 8 and -127°C. The magnitude of the 7 relaxation estimated by the Gu/GR ratio (GR < Gu) is about 2.5. Moreover, it can be seen that the 7 peak is enlarged at lower temperature. In the - 8 0 to - 3 0 ° C range, isochronal run at 0.1 Hz shows a broad relaxation with low magnitude (0.02) which could correspond to the fl relaxation. Graphs of log G' and tan ~b against frequency for isothermal conditions are shown in Fig. 3. Annealed samples. Plots of log G' and tan ~b at 0.1 Hz vs temperature are displayed in Fig. 4. With increasing annealing temperature, the 7 peak is shifted towards higher temperature and its magnitude markedly decreases. The modulus drop associated with the tan q~ maximum decreases as the annealing temperature is increased. Beyond the 7 relaxation, the relaxed modulus (GR) increases as the annealing temperature. The characteristic parameters of the y relaxation are reported in Table 3. Moreover, the sample annealed at 130°C exhibits a weak peak as a shoulder called 72 located at about - 1 6 0 ' C on the rising side of the main peak.
Mechanical spectrometry Quenched sample. Plots of log G' and tan ~b at 1,
0.1
Xc(%)"
aThe estimated uncertainty in the crystalline level is about 10%; bthe estimated errors in the values of crystalline thickness is about 10% for the thicker lamellae (T) and about 20% for the thinner ones (t).
In the low temperature range from - 150 to 20°C, no changes in the baseline of heat capacity can be detected for any heating rate or for any sample. Figure 1 shows the lamellar thickness distribution curves for the linear polyethylene samples. All distribution curves shows two overlapping peaks which are more or less separated according to the thermal history. For example, the lamellar size distribution curve for the sample annealed at 130°C is centred around two typical thicknesses viz. 70 and 220A. With increasing annealing temperature, the most probable lamellar thickness of the thicker lamellae is increased while the most probable crystallite thickness of the thinner ones does not change significantly. The upper limit of the half-width of the distribution curve shifts towards greater sizes on increasing the annealing temperature. The crystalline content increases because the annealing temperature is raised as does the most probable thickness of the thicker lamellae. Table 2 gives characteristic values determined from the thermograms and from the thickness distribution curves.
.
A
Quenched +annea&d at: 100°C II0~C 120'C 130'C
DSC experiments
.
939
.
.
~_
-- _-- - -
~
9.0
"9-
g
F8.5
0 -4
I -3
I -2
I --1
0
Log EFIHz'I
Fig. 3. Quenched sample: graphs of log G' and tan q~ against frequency for various temperatures: @, 134°C; l l 130°C; A, 128°C; V, 126°C; V, 121°C; I-q, 118°C; O, 115°C; A, 108°C.
940
N. ALBEROLAet al.
o.1
8
6
0
I
-180
I
-140
-100
I
]
-60
-20
20
T (°C) Fig. 4. Plots of log G' and tan ~b at 0.l Hz vs temperature for samples annealed for 24 hr at I00°C (A), l l0°C (&) and 130°C (O) [quenched sample (m)].
The magnitude of the background loss in the - 8 0 to 30°C range, where the fl relaxation could be located, decreases with increasing annealing temperature. In order to obtain more informations about the presence of the 72 peak, isothermal scans are performed on the sample annealed at 130°C in the - 173 to - 1 5 5 ° C range over the 10-4-1 Hz frequency
Table 3. Characteristic values of the 7 relaxation: I R, magnitude of the ), relaxation (IR = Gu/GR) Gu GR (109Pa) (109Pa)
System A
Quenched+annealed at: 100°C 110°C 130°C
1.5 1.8 1.9 2.0
0.6 1.0 I.l 1.4
Ia
tan~bm~ x
2.5 1.9 1.7 1.4
0.08 0.06 0.05 0.04
0.02
"OI-
0 - 17'5
I
I
-165
}L
-155
T (°C)
Fig. 5. lsochronal spectra in the 72 region for the sample annealed for 24 hr at 130°C at: 0.000l Hz (O), 0.002 Hz (D); 0.01 Hz (&), 0.1 Hz ( O ) and 1 Hz ( I ) .
941
Mechanical ~, and # relaxations in polyethylene--I range, by steps of 2°C. Isochronal spectra corresponding to the five frequencies, i.e. 1, 0.1,0.01, 0.002 and 0.0001 Hz are reported in Fig. 5. With increasing frequency, the peak magnitude is decreased while its temperature location is slightly changed. But, because of the closeness of the 7 relaxation, these observations must be considered with caution. Anyhow, these measurements give evidence for the presence of a secondary 7 relaxation at about -160°C.
Figure 6 shows the frequency dependence of the storage modulus and tan 4~ at various temperatures in the 7 region determined for the samples annealed at 100°C [Fig. 6(a)] and 130°C [Fig. 6(b)]. For the quenched sample, the ? relaxation exhibited by the annealed samples seems to obey, to a first approximation, the time-temperature superposition principle. Master curves of the analysed samples are reported in Fig. 7. Graphs of loga T against 1000/T
(a) ~
0.1
9.0
o n (.9 i._1 o~
-eg I-
d 8.5
0 -4
I
I --2
--3
I -1
Log[F/Hz]
(b) 0.1
-
~
~
~
~ ~
9.5
F7 (3_
A--~--
"ec:
9.0
-4
I
-3
I
-2 Log[F/Hz]
I
-I
2"(..9,
0
Fig. 6. (a) Variation of log G" and tan q~ with frequency for annealed sample for 24 hr at 100°C as a function of temperature: 0 , 133°C; II, 131°C; O, 128°C; V , 124°C; A , 120°C; A , I17°C; V , 114°C; [], 11 I°C. (b) Variation of log G' and tan q~ with frequency for annealed sample for 24 hr at 130°C as a function of temperature: 0 , 133°C; O, 128°C; ~ , 121°C; A , 119°C; z~, 115°C; IS], 112°C.
N. ALBEROLAet al.
942
Table 4. Values o f the constants C~ and C 2 o f the W L F equation calculated for
are shown in Fig. 8. Apparent activation energies of the main relaxation determined from d l n a r / d ( 1 / T ) at -120°C are about 140, 150 and 170 kJ/mol for the quenched specimen and the annealed samples at 100 and 130°C respectively.
r~, = r, = -118°C System A
Quenched + annealed at: 100°C 130:'C
C,
C2(K)
15.0 15.4 16.3
50.5 50 48
DISCUSSION
Origin o f the g a m m a relaxation
With increasing annealing temperature, i.e. with increasing crystallinity index, the magnitude of the 7 relaxation decreases. Thus, it is concluded that the gamma relaxation can be due to molecular mobility in the amorphous phase. Furthermore, the apparent activation energy of the y relaxation is high (140, 150 and 170kJ/mol at -120°C), depending on the thermal treatment, and it is of the same order of magnitude as for apparent activation energies of mechanical relaxations due to glass transitions for amorphous [36] or semicrystalline [37] polymers. The values of apparent activation energies of the mechanical 7 relaxation are higher than those determined from dielectrical measurements [20, 24, 25]. But samples analysed by these two methods are not chemically identical i.e. samples analysed by dielectric measurements are modified with dipoles. The activation energy of subglass transitions are usually ten times lower. Moreover, the 7 relaxation shows, to a first approximation, a W L F temperature dependence as the primary transition observed in completely amorphous polymers [36]. Graphs of log az vs 1000/T have a W L F pattern (Fig. 8). According to the W L F equation: Log(aT) = - C I ( T -
Tref)/(C2 q- T -
Tref) [38],
the values of the constants C1 and C2 are calculated. The values reported in Table 4 are close to those of "universal constants" (C1=17.44, C 2 = 5 1 . 6 K )
for T r e r = - l l 8 ° C .
These data suggest that the 7 relaxation could be related to the glass transition of polyethylene. To demonstrate it, physical ageing is carried out on the quenched sample at a temperature below the temperature of the 7 peak in order to give evidence of a structural recovery of the vitreous phase of polyethylene as is usually observed for amorphous polymers annealed at temperatures close (but below) their glass temperature. This characteristic phenomenon is observed for the following experimental conditions: a first isochronal run was recorded on decreasing temperature from - 7 0 to -170°C at 15°C/hr. Then, the sample was rapidly heated to - 143°C and kept for 12 hr at this temperature. Next, it was cooled to -170°C and a second run was recorded on increasing the temperature (15°C/hr) to -90°C. Lastly, a third spectrum was recorded while decreasing the temperature (15°C/hr) from - 9 0 to - 1 7 0 ° C (Fig. 9). The comparison between spectra obtained in the first decreasing and while increasing the temperature shows that the ageing leads to shift of the rising side of the y peak. Thus, annealing at - 143°C induces a change in the configurational state
(a) 0.1
-
8
9.5
r-~ o ta
o~
_J
-4
I
I
l
I
I
-2
0
2
4
6
Log [ O T / H Z ]
Fig. 7--continued opposite.
I
8.5
Mechanical 7 and fl relaxations in polyethylene
I
943
(b) 0.1
--
9.5
r-~ o
n -O.c I.--
.J
T
I
-6
-4
I
I
I
I
-2
0
2
4
8.5
Log [ar/Hz]
Cc) 0 . 1 --
9.5
'7 n "O-
g
9.0
I.-
1 -6
I
I
I
I
I
-4
-2
0
2
4
Log
o~ J
8.5
EOT/Hz]
Fig. 7. Master curves of: (a) quenched (Tr~r = -128C); (b) + annealed at 100°C (Tr~f = - 121°C); (c) + annealed at 130~C (Tr~f = - 119C).
of the system. The decrease in the peak magnitude observed after ageing is consistent with the assumption of a decrease of molecular mobility related to the change in the configurational state. After ageing, heating the specimen at a temperature above the 7 temperature range thus would lead the system towards an equilibrium state as shown by the super-
position of the two spectra recorded for decreasing temperature: the configurational state of the system is then only governed by the cooling rate (15°C/hr). Beyond T = - ! 18°C, the superposition of the three spectra recorded at increasing and decreasing temperature appears to imply that, from this temperature, the amorphous phase is in a metastable
944
N. ALBEROLAe t
thermodynamic equilibrium state. These data appear to contrast with the conclusion reported by Chang [27] but the difference could be due to the high sensitivity of the measurements here described. Hence, this temperature could be designated as the glass temperature of polyethylene. Consequently, the ~2 relaxation located below the V relaxation could be a subglass transition as usually observed for amorphous polymers [36]. This subglass relaxation should be due to local motions of the main chain which initiated the mobility of the chains over a longer distance, characterizing the appearance of the vitreous transition. The crosslinking of the amorphous phase by the crystailites, acting as physical ties, induces a decrease in the magnitude of the V relaxation as usually observed for relaxations related to glass-rubber transitions in other semicrystalline polymers [38, 39]. In order to obtain evidence for the influence of such a microstructural parameter on the characteristics of the 7 relaxation, mechanical spectra of two samples quenched from 170 and 200°C respectively and exhibiting similar crystallinity index (40%) are compared. The lamellar size distribution curves of these two samples are shown in Fig. 10(a). Thus, the magnitude of the gamma relaxation exhibited by the sample quenched from 200°C, characterized by a sharper lamellar distribution curve shifted towards the lower values, is less than that of the sample quenched from 170°C [Fig. 10(b)]: for a fixed crystallinity index, the magnitude of the V relaxation decreases with decreasing thickness of the crystallites. Then, with increasing annealing temperature, the decrease in the ), relaxation magnitude could be due on the one hand to an increase in the crystallinity index and on the other hand to an increase in the
4t
al.
0.1
-0i
I
180
-140
- 100
I
-60
T(*C)
Fig. 9. Physical ageing of the quenched sample: , tan ~b spectrum recorded on increasing the temperature (15°C/hr) after 12hr at -143°C, (O) tan~b spectra recorded on decreasing the temperature (15°C/hr) on the first and second runs respectively (see text). relative amount of thin crystallites. Furthermore, the sample quenched from 200°C exhibits a higher storage modulus at T > T7 than the sample quenched from 170°C. Hence, at constant crystallinity content, the rubber modulus (T > TT) increases with decreasing thickness of the crystallites: crystalline lamellae are like physical ties crosslinking the amorphous phase. Moreover, physical crosslinking of the amorphous phase by crystallites leads not only to a decrease in the 7 relaxation magnitude but also to a broadening of the 7 relaxation as observed for other semicrystalline polymers. To a first approximation, the widening of the 7 relaxation can be evaluated from the ratio: height of the tan ~b peak (tan ~bmax) peak half-width (related to the drop in modulus)' The broadening in the 7 relaxation could lead to an apparent distribution of relaxation times of the amorphous chains induced by the crystalline phase. For a relaxation characterized by a single relaxation time (ideal linear solid and Zener relaxation), the peak height is related to the drop in modulus by the relationship:
"r" 0
.J
tan --4
~Zener 1/2 x/Gu/G R (G R and Gu, ~---
relaxed and unrelaxed modulus respectively). Then, the width of the relaxation can be evaluated by the ratio R: 3
7 1 0 3 / T ( K -1)
Fig. 8. Graphs of log aT (log aT: translational factor) against 1000/T). O, Quenched from 170°C to 20°C; I1, annealed for 24 hr at 100°C; &, annealed for 24 hr at 130°C.
R = tanSma,/tan~b .... . The R values are reported in Table 5. These features are also consistent with the characteristics of a mechanical relaxation related to the glass transition of polyethylene.
Mechanical ~, and ~ relaxations in polyethylene--I Table 5. Evaluation o f the width o f the "f relaxation System A
relaxations. Consequently, we have analysed the microstructure and the mechanical behaviour of a commercial branched polyethylene (system B).
R
Quenchedfrom: 170"C 200'C to 15'C
Quenchedfrom annealed at :
Branched polyethylene: origin of the ~ relaxation
0.10 0.09 170C
to 15r C +
100>C 110"C 13OC
945
0.08 0.03 0.02
Nevertheless, according to the literature [25-30], the fl relaxation displayed by branched polyethylene could also be related to the glass transition. There is a need for further examination of both ), and fl
Graphs of log G' and tan ~b vs temperature at 1, 0.1 and 0.01 Hz are shown in Fig. 11. The peak located about - 120°C corresponds to the ), relaxation as for linear polyethylene. In the - 7 0 to + 60°C range, the tan ~b spectra display a broad peak; it results from two maxima which overlap. According to the literature [25, 29], the lower temperature component of the broad peak could correspond to the B relaxation. The upper temperature component may be related to the ~ relaxation. The presence of a single ~t relaxation in such a polyethylene is due to the existence of only a single crystalline lamellae population [35] as shown
(a) I dM M
dL
I 400
0
L(~,)
(b) 0.1
10
- -
n
.d
0
I - 180
-140
I - 100
I
I
-60
-20
6 20
T I*CI
Fig. 10. (a) Lamellar thickness distribution curves for sample quenched from 170°C (O) and from 200°C ( ). (b) Isochronal spectra for sample quenched from 170°C (Q) and 200°C ( I ) to room temperature.
946
N . ALBEROLA el al.
O.2
-9.5
~4
"0-
0
'1
I
- 20
60
I
-q80
-I00 T
ft. 2"-
,o,
_J
5.5
(*C)
Fig. 11. Plots of log G' and tan ~ vs temperature for branched polyethylene (system B): A, 1 Hz; I , 0.1 Hz; II, 0.01 Hz. in Fig. 12. Frequency scans performed under isothermal conditions do not permit separation of the two relaxations. In order to define the fl relaxation, the two relaxations composing the broad peak are separated according to the following assumptions: (i) in agreement with literature data [24, 29] and with results obtained for linear polyethylene, the main component of the broad maximum in such a semicrystalline polyethylene is supposed to the c¢ relaxation, "i
dM
M
dL
(ii) to a first approximation, the ~ relaxation is assumed to be symmetric with respect to a vertical axis through its maximum. The result of this treatment is shown in Fig. 13: the magnitude of the ~ peak is about 0.1. The apparent activation energy of the ~ relaxation determined from the "so-calculated" isochronal spectra is about 200 kJ/mol. The high value of the apparent activation energy of the fl relaxation is of the same order of magnitude as that of mechanical relaxation due to glass transition. Moreover, physical ageing of the branched polyethylene for 24 hr at a temperature ( - 7 0 ° C ) below the temperature of the ~ peak leads to structural recovery as is well-known for vitreous systems annealed at temperatures below their temperatures of glass transition. Figure 14 shows the three runs at 15°C/hr recorded under the following conditions: (i) decreasing the temperature from room temperature to -80°C; (ii) increasing the temperature from - 100 to 20°C after the sample was kept for 24 hr at - 70°C; (iii) decreasing the temperature from 20 to 100°C. -
0
0
i 80
o
L(A)
Fig. 12. Lamellar thickness distribution curve of branched polyethylene.
The ageing for 24 hr at - 70°C induces changes in the configurational state as previously described for linear polyethylene annealed at a temperature below the 7 peak temperature. Beyond a temperature of about -33°C, the decreasing sides of the three spectra merged. It is assumed that the c¢relaxation is unaffected by physical ageing at - 70°C because the system has been first "annealed" for many hours at room temperature. According to the previous analysis performed for the ? relaxation, it can be concluded that - 3 3 ° C could be regarded also as the glass transition of polyethylene. It can be noted that this value is very
Mechanical 7 and fl relaxations in polyethylene--I 0.2
-
/
/
Pm ,* ' Am
•~ • A
"
-O=
947
a
o
[]
1~
~
0.1
• A' •~
• -' •
°, ~
4
As
• ~"
A
.." i
I
-140
n
-100
z~
--60
" %
\
• ,m
o
"'.
°
•
2o°O A
-180
o•
2 0o~ °
J'~"
0,.0 i ~
.m,'[ . m"
0
oo
A
•
4
~ • O,mm Ao%a
,
~
•
,
oOE] 8"
,
O o
QO
m
a
u
--20
20
60
T (OC)
Fig. 13. Separation of the • and ,8 relaxations displayed by the branched polyethyleneat three frequencies: 0.01Hz(A, fl:,~,~t),0.1Hz (O,/~: ©,~t) and lHz ( m ,8; U], ct). close to those reported by Wunderlich [26], Chang [27] and Davies and Eby [28]. In short, the /~ relaxation shows some characteristics of a glass transition. Polyethylene should therefore exhibit two glass transitions as suggested by Boyer [30] basing his assumption on topological considerations. The presence of different types of amorphous phase more or less constrained by the crystalline phase as assumed by Boyer [30] should 0.2--
result in a widening of the region of the glass transition rather than in the existence of two well defined glass temperatures. The presence of two glass temperatures in branched polyethylene can be reasonably explained by the existence of two types of intermolecular Van der Waals interactions with different energies. Thus, the glass transition at low temperature in the 7 region should be characteristic of Van der Waals interactions between CH2 groups of the main chains. The glass transition located at high temperature and associated with the /~ relaxation should be specific of Van der Waals interactions between CH 3 groups of side chains and the CH 2 groups. It is worthwhile to recall that the true concentration of CH 3 groups in the amorphous region is greater than the whole index determined from i.r. spectroscopy because side chains are not included in the crystalline lamellae; they are rejected and accumulate in the surrounding amorphous phase.
-O-
g
CONCLUSIONS
I---
0
I - 180
I
-- 6 0
-- 2 0
I 20
T (°C)
Fig. 14. Physical ageing of the branched polyethylene sample: (O), tan ~b spectrum recorded on increasing the temperature (15°C/hr) after keeping the sample for 24 hr at -70°C; - - . , superimposed tan ~ spectra recorded on decreasing the temperature (15°C/hr) on the first and second runs respectively(see text).
Mechanical spectrometry and differential scanning calorimetry measurements were carried out on linear and branched polyethylene in order to characterize the mechanical ), relaxation and the mechanical relaxation and to identify their molecular origins. Thus, the 7 relaxation displayed by a linear polyethylene and extensively analysed in this work shows the characteristics of a mechanical relaxation related to the glass transition of polyethylene: --high apparent activation energy of the mechanical y relaxation; --polyethylene shows structural recovery resulting from physical ageing at a temperature below the 7 peak', --the 7 relaxation has a WLF-temperature dependence as usually observed for primary transition of amorphous polymer;
N. ALBEROLAet al.
948
- - t h e magnitude of the 7 relaxation depends on the morphology of the system; - - t h e presence of a secondary relaxation 72 located at lower temperature (subglass transition). The fl relaxation displayed by branched polyethylene and located at higher temperature has also the characteristics of a mechanical relaxation due to glass transition: - - h i g h apparent activation energy (200 kJ/mol), - - b r a n c h e d polyethylene exhibits structural recovery induced by annealing at a temperature below the/3 maximum. Therefore, according to the definition of the glass transition temperature, the presence of two glass transitions in branched polyethylene could be due to the existence of Van der Waals interactions with different energies: the lower glass transition located in the gamma region might be characteristic of intermolecular Van der Waals interactions between CH2 groups and the upper glass transition located in the /3 region might concern intermolecular Van der Waals interactions involving C H 3 groups of the side chains and more or less segregated.
REFERENCES 1. I. M. Ward. Mechanical Properties of Solid Polymers, 2nd Edn. Wiley, New York (1983). 2. N. G. McCrum, B. E. Read and G. Williams.
Anelastic and Dielectric Effects in Polymeric Solids. Wiley, New York (1967). 3. D. E. Kline, J. A. Sauer and A. E. Woodward. J. Polym. Sci. XXIII, 455 (1956). 4. K. H. Illers. Kolloid-Z.Z. Polym. 252, 1 (1974). 5. A. H. Willbourn. Trans. Faraday Soc. 54, 717 (1958). 6. J. W. Cooper and N. G. McCrum. J. Mater. Sci. 7, 1221 (1972). 7. R. H. Boyd and S. M. Breitling. Macromolecules 7, 855 (1974). 8. T. Schatzki. J. Polym. Sci. 57, 496 (1962). 9. P. Audren and D. Ronarch. J. appl. Phys. 60, 946 (1986). 10. F. G. Stehling and L. Mandelkern. Macromolecules 3, 242 (1970). 11. K. M. Sinnot. J. appl. Phys. 37, 3385 (1966). 12. J. D. Hoffmann, G. Williams and E. Passaglia. J. Polym. Sci; Part C14 173 (1966).
13. S. Fukui and T. Hideshima. Jap. J. appl. Phys. 16, 159 (1976). 14. S. Fukui and T. Hideshima. Jap. J. appl. Phys. 16, 497 (1976). 15. Y. Yamada, M. Kakizaki and T. Hideshima. Jap. J. appl. Phys. 21, 352 (1981). 16. T. Kakudate, M. Kakizaki and T. Hideshima. J. Polym. Sci.; Polym. Phys. Edn 23, 787 (1985). 17. C. R. Ashcraft and R. H. Boyd. 3". Polym. Sci. 14, 2153 (1976). 18. R. H. Boyd. Polymer 26, 323 (1985). 19. R. H. Boyd. Polymer 26, 1123 (1985). 20. Y. Sato. J. appl. Polym. Sci. 26, 27 (1981). 21. D. E. Buerger and R. H. Boyd. Macromolecules 22, 2694 (1989). 22. S. Matsuoka and C. J. Aloisio. Polym. Prepr. 5, 416 (1964). 23. W. Pechold, V. Eisele and G. Knauss. Kolloid Z.-Z. Polym. 196, 27 (1964). 24. M. Kakizaki and T. Hideshima. J. Macromolec. Sci. Phys. 138, 367 (1983). 25. J. M. Perena and J. M. G. Fatou. Anales de Fisica 70, 348 (1974). 26. B. Wunderlich and H. Bauer. Adv. Polym. Sci. 7, 151 (1970). 27. S. S. Chang. J. Polym. Sci.: Symp. 43, 43 (1973). 28. G. T. Davies and R. K. Eby. Macromolecules 44, 4274 (1973). 29. Y. T. Jang, D. Parikh and P. H. Philipps. J. Polym. Sci. 23, 2483 (1985). 30. R. F. Boyer. Macromolecule. 6, 288 (1972). 31. R. Lam and P. H. Geil. Polym. Bull. 1, 127 (1978). 32. S. Etienne, J. Y. Cavaille, J. Perez, R. Point. and M. Salvia. Rev. Sci. lnstrum. 53, 1261 (1982). 33. B. Wunderlich. Macromolecular Physics, Vol. 1. Academic Press, New York (1980). 34. J. D. Hoffman, J. I. Lauritzen, E. Passaglia, G. S. Ross, L. J. Frolen and J. J. Weeks. Kolloid-Z.Z. Polym. 231, 564 (1968). 35. N. Alberola, J. Y. Cavaille and J. Perez. J. Polym. Sci.; B; Polym. Phys. 28, 569 (1989). 36. J. Y. Cavaille, J. Perez and G. P. Johari. Phys. Rev. 1139, 2411 (1989). 37. C. Jourdan, J. Y. Cavaille and J. Perez. J. Polym. Sci. B: Polym. Phys. 27, 2361 (1989). 38. J. D. Ferry. Viscoelastic Properties of Polymer. Wiley, New York (1970). 39. M. Takayanagi. Molecular motions in crystalline polymers. In "'Molecular Basis of Transitions and Relaxations", Midland Macromolecular Monographs, No. 4, Gordon and Breach Science, New York (1978).
0014-3057/92 $5.00 + 0.00 Pergamon Press Ltd
M E C H A N I C A L 7 A N D /~ R E L A X A T I O N S IN P O L Y E T H Y L E N E - - I . GLASS T R A N S I T I O N S OF P O L Y E T H Y L E N E N. ALBEROLA,~'2j. y . CAVAILLE2.3and J. PEREZ2 tLaboratoire Materiaux Composites, ESIGEC, Universit+ de Savoie, BP 1104, 73011 Chambery Cedex, France 2Laboratoire GEMPPM, INSA, Bat. 502, Av. A. Einstein, 69621 Villeurbanne, France 3CERMAV, BP 53X, 38041 Grenoble Cedex, France (Received 6 November 1991)
Abstract--The mechanical 7 relaxation of a linear polyethylene has been extensively analysed by means of high resolution mechanical spectrometry. This analysis was completed by quantitative measurements of the morphological parameters governing the characteristics of the 5, relaxation, such as the crystallinity index and the crystalline lamellar thickness distribution determined from differential scanning calorimetry. The 7 relaxation was found to have the characteristics of mechanical relaxation due to glass transition: there is a high apparent activation energy; linear polyethylene exhibits structural recovery induced by annealing at a temperature below the )' peak, whereas the 7 relaxation has a WLF temperature dependence. As for the i' relaxation, it was found that the/3 relaxation displayed by a branched polyethylene has the characteristics of a glass transition (high value of apparent activation energy; structural recovery during ageing at T < Tt~). Recalling definitions of the glass temperature, it was proposed that the lower glass transition (7 region) is characteristic of Van der Waals interactions between CH 2 groups while the upper glass transition ({/ region) is specific of Van der Waals interactions between CH 2 and CH 3 groups.
INTRODUCTION
Many investigations have been directed to characterization of the ~, relaxation of polyethylene by various methods including mechanical and dielectrical spectrometry, N M R and thermostimulated depolarization measurements. The origin (crystalline and/or amorphous phase) and the nature of the molecular motions involved in the 7 relaxation have been extensively discussed and remain controversial. The discussion is widened because of the possible presence of many processes contained in this relaxation and because of the localization of these possible processes. Moreover, work dealing with the mechanisms of the 7 relaxation is mainly based on dielectric measurements. As polyethylene is not dielectrically active, the characterization of this polymer requires attachment of dipoles (carbonyls or chlorines). Thus, the characteristics of the processes exhibited by this method cannot be strictly compared to the data from mechanical measurements because the analysed polymers are not chemically the same. According to some authors, the 7 relaxation consists of a well-defined peak called the 71 process and a peak as a shoulder located at lower temperature and referred to as the 72 process. All authors agree that the main component of the ~ relaxation has its origin in the amorphous phase [1, 2]. Thus, it was shown that amorphous polyethylene exhibits a mechanical relaxation in the same temperature range [3]. Illers [4], Willbourn [5] and Cooper and McCrum [6] suggested that the ~1 process could originate from local mobility of some monomer units in the amorphous phase. Then, the main component of the ? relaxation could be regarded as a subglass transition.
Boyd and Breitling [7] have considered that the 71 relaxation could not be induced by a crankshaft motion involving six or eight carbon atoms as suggested by the Schatzki models [8] because the volume involved in this motion is too large and requires too much energy. More recently, Audren and Ronarc'h [9] suggested, from thermostimulated depolarization measurements on doped low-density polyethylene, that the 7~ process is induced by the motion of chain segments having approximately between 10 and 20 carbon atoms. According to Stehling and Mandelkern [10], the main component of the 7 relaxation could be related to the glassrubber transition of polyethylene. As a matter of fact, in this temperature range, polyethylene exhibits characteristics of a glass transition i.e. an abrupt increase in the coefficient of thermal expansion and an increase in the specific heat. The 7., relaxation was first related to defect diffusion in the crystalline phase [11, 12]. Then, Stehling and Mandelkern considered that this process originates in the interfacial zone between crystalline and amorphous phase. Audren and Ronarc'h [9] showed that the 72 relaxation could be generated by the motion of chain segments having less than 10 carbon atoms. According to other authors [13-16], the 7 relaxation consists of three components called 71, )'2 and ~'3 in order of decreasing temperature and ascribed respectively to motions of polar groups in: (i) the amorphous phase; (it) defects in the crystalline phase; and (iii) the cilia attached to the chain-folded surfaces of crystallites in polyethylene. According to 935
936
N. ALBEROLAet al. another point of view, the 7 relaxation was regarded as a single process attributed to polar groups in the amorphous phase with a somewhat wide distribution of relaxation times [17-20].
This literature review shows that all authors agree that the 71 (~' relaxation regarded as a multiple process) or the 7 relaxation (7 relaxation considered as a single process) originate from the amorphous phase. According to some authors, the ~ (or 71) relaxation is related to the glass transition of polyethylene [10] and for others, the 7 (or ~,~) relaxation can be regarded as a subglass transition [4-6, 18, 19]. It is of interest therefore to consider the thermorheological characteristics of the 7 (or 71) relaxation. Thus, according to lllers [4], Sato [20] and Buerger and Boyd [21], the 7 relaxation shows an Arrhenius temperature dependence as for secondary transitions. Matsuoka and Alosio [22] consider however, that the 7 relaxation has a W L F temperature dependence as for the primary glass transition observed in amorphous polymers. According to Pechold et al. [23], the 7 relaxation has neither an Arrhenius nor a W L F temperature dependence. The reported values of the apparent activation energies of the 7 (or Yl) range from 20 to 80 kJ/mol [20, 24, 25]. Sato [20] has shown that an increase in crystallinity owing to decrease in branching leads to: (i) an increase in the apparent activation energy of the dielectric 7 (or 7i) relaxation; and (ii) a shift of the 7 relaxation towards higher temperature. Discussion about the location of the glass transition of polyethylene is increased because of the presence of another relaxation, the 13 relaxation, displayed by branched relaxation in the - 3 0 to - 10°C range which could also be attributed to glass transition of polyethylene (this relaxation is barely detected in linear polyethylene). Wunderlich and Baur [26] have shown a characteristic increase in the specific heat of amorphous polyethylene at about -36°C. Chang [27] has shown that quenched branched and linear polyethylenes under adiabatic conditions exhibit spontaneous temperature drifts in the 13 region at about -35°C. These spontaneous temperature drifts can always be observed in the glass transition zone and serve as an indicator of the rate at which the glass approaches an equilibrium state. Such phenomena are not observed in the ~ region. Moreover, from volume relaxation studies, Davies and Eby [28] have shown that polyethylene exhibits structural recovery during physical ageing in the fl temperature range as do vitreous systems annealed at a temperature below their glass temperature. In addition, the high values of apparent activation energy (200-300 kJ/mol) of the mechanical /3 relaxation reported by some authors [29] are in agreement with the assignment of the fl relaxation to the glass transition of polyethylene. Both ~ and fl relaxations therefore could be related to glass transitions of polyethylene. Boyer [30] has suggested that semicrystalline polyethylene could show two glass transitions, Tg(L) and Ts(U ) located at about - 8 0 and - 3 0 ° C respectively. These glass
transitions are ascribed to the existence of two types of amorphous regions. Ts(L ) might be related to "free" amorphous phase consisting of low molecular weight chains which have not crystallized and Ts(U ) to "tied" amorphous domains constrained by crystalline structures. The location of a lower glass transition at about - 8 0 ° C is supported by Lam and Geil [31] who observed the onset of crystallization of vitrified solutions of polyethylene at this temperature. The location of Tg(L) at about - 8 0 ° C is, however, not credible for two reasons: (i) no mechanical relaxation (frequency ~ 1 Hz) is detected about this temperature. This is not consistent with what is usually observed for other polymers; (ii) it is not really pertinent to associate the temperature of the beginning of the crystallization to the glass transitions for macromolecular systems. As a matter of fact, in these systems, it can be assumed that the crystalline organization needs greater thermal activation than for obtaining new degrees of freedom at the glass transition. Hence, the glass transition of polyethylene should be located at a temperature below -80°C. Consequently, according to Boyer's suggestion, it is more credible to associate the 7 relaxation to Tg(L) of polyethylene. The mechanisms of the 7 relaxation therefore remain unresolved and the location of the glass transition of polyethylene is still to be established, although there are some sound arguments to associate the fl relaxation with a glass-rubber transition. The short survey concerning the mechanical ~ and fl relaxations in polyethylene shows a lack of experimental data from frequency scans, under isothermal conditions, in these temperature ranges in order to establish precisely the temperature frequency dependence of these relaxations. The present work attempts to contribute to these different points. Thus, high resolution dynamic mechanical spectrometry has been carried out on linear and branched polyethylene by means of an original low-frequency torsion pendulum. We have focused the analysis on the 7 relaxation spectra vs temperature or frequency (isothermal conditions) displayed by samples showing different microstructures resulting from different thermal histories. The differences in sample microstructure obtained by annealing at various temperature were characterized mainly by means of a simple model giving lamellar size distribution from colorimetric data. EXPERIMENTAL PROCEDURES Materials
The materials used in this study were a high density linear polyethylene (system A) provided by the Hoechst Company and a commercial low density branched polyethylene (system B). Some of the characteristics of these materials are listed in Table 1.
Table 1. Characteristics of analysed samples (P = Polydispersity;% B, numberofCH 3for 1000C System
A B
of the main chain; d, density) ~. h/,, P %B
6.105 4.106 3.105 3.104
6 l0
d
<2.5 0.939 >10 0.892
937
Mechanical 7 and fl relaxations in polyethylene-~l
Thermal treatments As received linear polyethylene sheets are heated at 170°C for 30 min in N 2 and then quenched in water at 15°C. Five samples were cut to the following dimensions: 80 x 40 x 1.3 mm. Four of these samples, the so-called annealed samples, were annealed for 24 hr at I00, 110, 120 and 130°C respectively in N 2 and then quenched in water at 15°C. One of these specimens, the so-called quenched sample, was kept at room temperature. For experimental work, all samples were cut to the following dimensions: 40 × 6 × 1.3mm for dynamic mechanical experiments and 2 × 2 × 1.3 mm 3 for calorimetric analysis. Branched polyethylene was studied as received and it was cut to the same dimensions as for linear polyethylene, but the thickness of branched polyethylene sheets was about 0.5 mm.
Dynamic mechanical spectrometry As explained in the introduction, obtaining new information about the mechanical 7 relaxation needs a dynamic Ld__~ M M
mechanical spectrometer with higher resolution than usual, So, dynamic mechanical measurements were performed with a set-up* well-suited to study low magnitude mechanical relaxation. This apparatus is an automated low frequency inverted torsion pendulum [32] which provides the real (G') and imaginary (G") parts of the shear modulus and the internal friction parameters tan dp(=G"/G') as a function of temperature (for one or several fixed frequencies) or frequency (under isothermal conditions). For temperature scans (isochronal conditions), runs were performed from - 1 7 0 to 20°C at 15°C/hr and at three frequencies 1,0.1 and 0.01 Hz. Frequency scans were carried out under isothermal conditions in the - 1 6 0 to 20°C range over a wide range of frequency (10-4-I Hz).
Differential scanning calorimetry Thermograms were recorded using a Perkin-Elmer DSC 1B apparatus over the range 20 to 150~C. The experiments were carried out for all samples at a heating rate of
(a)
1 dM
dL
(b)
M dL
I
l
400
400
L(,~)
M dL
I 400
L(A)
1
-~- d--M-M (d)
I 0
dM
;~C
dL
(e)
I
400 L(~,)
4O0 L(~,)
Fig. 1. Lamellar thickness distribution curves for the samples: (a) quenched from 170 to 20°C and annealed for 24hr at (b) 100°C, (c) I10°C, (d) 120°C and (e) 130°C. *Designed by the GEMPPM Laboratory and commercialized by Metravib (69132 Ecully, France).
938
N. ALBEROLA et al.
8°C/rain. The instrument was calibrated with an indium standard to give the onset of melting at 156.6°C. The crystallinity index (X¢) of each sample was determined through the relationship [33]:
[34] shows that the temperature of the melting curve is an increasing function of the crystallite thickness: it has been extended for any temperature of the melting thermogram. Then, it yields: T
xo = (Ha - H o ) / H =
where Ha and H c are the enthalpies in the melt and crystalline states respectively. Their difference is determined from the area of the melting endothermic peak. The enthalpy of melting (Hm) per mass unit is 288 J/g [33]. It is well-known that the melting temperature depends on crystallite size [34]. In a previous paper [35], we developed a simple model to give the crystallite thickness distribution curve from the thermogram. Thus, the Thomson equation
To(l
=
--
2a/Hm'l )
where T is the melting temperature (K) of lamellae of thickness l, TOis the equilibrium melting temperature of an infinite crystal ( T O= 414.5 K), .4 is the free surface energy per unit area of the basal face (cr = 70" 10 -3 J/m 2) and H m is taken [33] for 288 J/M 3. The crystallite thickness distribution with / is given by: 1 d M ( d E / d T ) ( T o - T) 2 M
dl
2(7.To.M
(a) 10
a
(D
i_.1
g,
.J
6
I -180
-140
I
I
-100
--60
I
I
-20
20
T (°C)
(b) o.1
/
-o-
0
I -180
-140
I
I
--100
--60
l --20
I 20
T(*C)
Fig. 2. Plots of log G' (a) and tan ~b (b) vs temperature for quenched sample: I I , 1 Hz; O, 0.I Hz; &, 0.01 Hz. Plots of log G' against temperature at the three frequencies are shifted along the log G ' scale of one decade one from another. The curve at 0.1 Hz is the reference.
Mechanical 7 and fl relaxations in polyethylene--I where M is the mass of the total crystalline phase, dM/M is the mass fraction of crystalline phase which melts between T and (T + dT) and dE/dT, given by the recorded DSC curve, is the energy required to melt the dM fraction. Some experiments were carried out in the - 150 to 20°C temperature range.
Table 2. Degree of crystallinity (Xc) from DSC and parameters of lamellar thickness distribution curves lmax(A) b System
RESULTS
0.1 and 0.01 Hz vs temperature are shown in Fig. 2.
~
t
T
l~.d(A) b
40 50 52 61 70
(50) (60) (60) 70 70
110 130 140 180 220
230 300 350 400 700
The well-defined y peak is located between - 1 1 8 and -127°C. The magnitude of the 7 relaxation estimated by the Gu/GR ratio (GR < Gu) is about 2.5. Moreover, it can be seen that the 7 peak is enlarged at lower temperature. In the - 8 0 to - 3 0 ° C range, isochronal run at 0.1 Hz shows a broad relaxation with low magnitude (0.02) which could correspond to the fl relaxation. Graphs of log G' and tan ~b against frequency for isothermal conditions are shown in Fig. 3. Annealed samples. Plots of log G' and tan ~b at 0.1 Hz vs temperature are displayed in Fig. 4. With increasing annealing temperature, the 7 peak is shifted towards higher temperature and its magnitude markedly decreases. The modulus drop associated with the tan q~ maximum decreases as the annealing temperature is increased. Beyond the 7 relaxation, the relaxed modulus (GR) increases as the annealing temperature. The characteristic parameters of the y relaxation are reported in Table 3. Moreover, the sample annealed at 130°C exhibits a weak peak as a shoulder called 72 located at about - 1 6 0 ' C on the rising side of the main peak.
Mechanical spectrometry Quenched sample. Plots of log G' and tan ~b at 1,
0.1
Xc(%)"
aThe estimated uncertainty in the crystalline level is about 10%; bthe estimated errors in the values of crystalline thickness is about 10% for the thicker lamellae (T) and about 20% for the thinner ones (t).
In the low temperature range from - 150 to 20°C, no changes in the baseline of heat capacity can be detected for any heating rate or for any sample. Figure 1 shows the lamellar thickness distribution curves for the linear polyethylene samples. All distribution curves shows two overlapping peaks which are more or less separated according to the thermal history. For example, the lamellar size distribution curve for the sample annealed at 130°C is centred around two typical thicknesses viz. 70 and 220A. With increasing annealing temperature, the most probable lamellar thickness of the thicker lamellae is increased while the most probable crystallite thickness of the thinner ones does not change significantly. The upper limit of the half-width of the distribution curve shifts towards greater sizes on increasing the annealing temperature. The crystalline content increases because the annealing temperature is raised as does the most probable thickness of the thicker lamellae. Table 2 gives characteristic values determined from the thermograms and from the thickness distribution curves.
.
A
Quenched +annea&d at: 100°C II0~C 120'C 130'C
DSC experiments
.
939
.
.
~_
-- _-- - -
~
9.0
"9-
g
F8.5
0 -4
I -3
I -2
I --1
0
Log EFIHz'I
Fig. 3. Quenched sample: graphs of log G' and tan q~ against frequency for various temperatures: @, 134°C; l l 130°C; A, 128°C; V, 126°C; V, 121°C; I-q, 118°C; O, 115°C; A, 108°C.
940
N. ALBEROLAet al.
o.1
8
6
0
I
-180
I
-140
-100
I
]
-60
-20
20
T (°C) Fig. 4. Plots of log G' and tan ~b at 0.l Hz vs temperature for samples annealed for 24 hr at I00°C (A), l l0°C (&) and 130°C (O) [quenched sample (m)].
The magnitude of the background loss in the - 8 0 to 30°C range, where the fl relaxation could be located, decreases with increasing annealing temperature. In order to obtain more informations about the presence of the 72 peak, isothermal scans are performed on the sample annealed at 130°C in the - 173 to - 1 5 5 ° C range over the 10-4-1 Hz frequency
Table 3. Characteristic values of the 7 relaxation: I R, magnitude of the ), relaxation (IR = Gu/GR) Gu GR (109Pa) (109Pa)
System A
Quenched+annealed at: 100°C 110°C 130°C
1.5 1.8 1.9 2.0
0.6 1.0 I.l 1.4
Ia
tan~bm~ x
2.5 1.9 1.7 1.4
0.08 0.06 0.05 0.04
0.02
"OI-
0 - 17'5
I
I
-165
}L
-155
T (°C)
Fig. 5. lsochronal spectra in the 72 region for the sample annealed for 24 hr at 130°C at: 0.000l Hz (O), 0.002 Hz (D); 0.01 Hz (&), 0.1 Hz ( O ) and 1 Hz ( I ) .
941
Mechanical ~, and # relaxations in polyethylene--I range, by steps of 2°C. Isochronal spectra corresponding to the five frequencies, i.e. 1, 0.1,0.01, 0.002 and 0.0001 Hz are reported in Fig. 5. With increasing frequency, the peak magnitude is decreased while its temperature location is slightly changed. But, because of the closeness of the 7 relaxation, these observations must be considered with caution. Anyhow, these measurements give evidence for the presence of a secondary 7 relaxation at about -160°C.
Figure 6 shows the frequency dependence of the storage modulus and tan 4~ at various temperatures in the 7 region determined for the samples annealed at 100°C [Fig. 6(a)] and 130°C [Fig. 6(b)]. For the quenched sample, the ? relaxation exhibited by the annealed samples seems to obey, to a first approximation, the time-temperature superposition principle. Master curves of the analysed samples are reported in Fig. 7. Graphs of loga T against 1000/T
(a) ~
0.1
9.0
o n (.9 i._1 o~
-eg I-
d 8.5
0 -4
I
I --2
--3
I -1
Log[F/Hz]
(b) 0.1
-
~
~
~
~ ~
9.5
F7 (3_
A--~--
"ec:
9.0
-4
I
-3
I
-2 Log[F/Hz]
I
-I
2"(..9,
0
Fig. 6. (a) Variation of log G" and tan q~ with frequency for annealed sample for 24 hr at 100°C as a function of temperature: 0 , 133°C; II, 131°C; O, 128°C; V , 124°C; A , 120°C; A , I17°C; V , 114°C; [], 11 I°C. (b) Variation of log G' and tan q~ with frequency for annealed sample for 24 hr at 130°C as a function of temperature: 0 , 133°C; O, 128°C; ~ , 121°C; A , 119°C; z~, 115°C; IS], 112°C.
N. ALBEROLAet al.
942
Table 4. Values o f the constants C~ and C 2 o f the W L F equation calculated for
are shown in Fig. 8. Apparent activation energies of the main relaxation determined from d l n a r / d ( 1 / T ) at -120°C are about 140, 150 and 170 kJ/mol for the quenched specimen and the annealed samples at 100 and 130°C respectively.
r~, = r, = -118°C System A
Quenched + annealed at: 100°C 130:'C
C,
C2(K)
15.0 15.4 16.3
50.5 50 48
DISCUSSION
Origin o f the g a m m a relaxation
With increasing annealing temperature, i.e. with increasing crystallinity index, the magnitude of the 7 relaxation decreases. Thus, it is concluded that the gamma relaxation can be due to molecular mobility in the amorphous phase. Furthermore, the apparent activation energy of the y relaxation is high (140, 150 and 170kJ/mol at -120°C), depending on the thermal treatment, and it is of the same order of magnitude as for apparent activation energies of mechanical relaxations due to glass transitions for amorphous [36] or semicrystalline [37] polymers. The values of apparent activation energies of the mechanical 7 relaxation are higher than those determined from dielectrical measurements [20, 24, 25]. But samples analysed by these two methods are not chemically identical i.e. samples analysed by dielectric measurements are modified with dipoles. The activation energy of subglass transitions are usually ten times lower. Moreover, the 7 relaxation shows, to a first approximation, a W L F temperature dependence as the primary transition observed in completely amorphous polymers [36]. Graphs of log az vs 1000/T have a W L F pattern (Fig. 8). According to the W L F equation: Log(aT) = - C I ( T -
Tref)/(C2 q- T -
Tref) [38],
the values of the constants C1 and C2 are calculated. The values reported in Table 4 are close to those of "universal constants" (C1=17.44, C 2 = 5 1 . 6 K )
for T r e r = - l l 8 ° C .
These data suggest that the 7 relaxation could be related to the glass transition of polyethylene. To demonstrate it, physical ageing is carried out on the quenched sample at a temperature below the temperature of the 7 peak in order to give evidence of a structural recovery of the vitreous phase of polyethylene as is usually observed for amorphous polymers annealed at temperatures close (but below) their glass temperature. This characteristic phenomenon is observed for the following experimental conditions: a first isochronal run was recorded on decreasing temperature from - 7 0 to -170°C at 15°C/hr. Then, the sample was rapidly heated to - 143°C and kept for 12 hr at this temperature. Next, it was cooled to -170°C and a second run was recorded on increasing the temperature (15°C/hr) to -90°C. Lastly, a third spectrum was recorded while decreasing the temperature (15°C/hr) from - 9 0 to - 1 7 0 ° C (Fig. 9). The comparison between spectra obtained in the first decreasing and while increasing the temperature shows that the ageing leads to shift of the rising side of the y peak. Thus, annealing at - 143°C induces a change in the configurational state
(a) 0.1
-
8
9.5
r-~ o ta
o~
_J
-4
I
I
l
I
I
-2
0
2
4
6
Log [ O T / H Z ]
Fig. 7--continued opposite.
I
8.5
Mechanical 7 and fl relaxations in polyethylene
I
943
(b) 0.1
--
9.5
r-~ o
n -O.c I.--
.J
T
I
-6
-4
I
I
I
I
-2
0
2
4
8.5
Log [ar/Hz]
Cc) 0 . 1 --
9.5
'7 n "O-
g
9.0
I.-
1 -6
I
I
I
I
I
-4
-2
0
2
4
Log
o~ J
8.5
EOT/Hz]
Fig. 7. Master curves of: (a) quenched (Tr~r = -128C); (b) + annealed at 100°C (Tr~f = - 121°C); (c) + annealed at 130~C (Tr~f = - 119C).
of the system. The decrease in the peak magnitude observed after ageing is consistent with the assumption of a decrease of molecular mobility related to the change in the configurational state. After ageing, heating the specimen at a temperature above the 7 temperature range thus would lead the system towards an equilibrium state as shown by the super-
position of the two spectra recorded for decreasing temperature: the configurational state of the system is then only governed by the cooling rate (15°C/hr). Beyond T = - ! 18°C, the superposition of the three spectra recorded at increasing and decreasing temperature appears to imply that, from this temperature, the amorphous phase is in a metastable
944
N. ALBEROLAe t
thermodynamic equilibrium state. These data appear to contrast with the conclusion reported by Chang [27] but the difference could be due to the high sensitivity of the measurements here described. Hence, this temperature could be designated as the glass temperature of polyethylene. Consequently, the ~2 relaxation located below the V relaxation could be a subglass transition as usually observed for amorphous polymers [36]. This subglass relaxation should be due to local motions of the main chain which initiated the mobility of the chains over a longer distance, characterizing the appearance of the vitreous transition. The crosslinking of the amorphous phase by the crystailites, acting as physical ties, induces a decrease in the magnitude of the V relaxation as usually observed for relaxations related to glass-rubber transitions in other semicrystalline polymers [38, 39]. In order to obtain evidence for the influence of such a microstructural parameter on the characteristics of the 7 relaxation, mechanical spectra of two samples quenched from 170 and 200°C respectively and exhibiting similar crystallinity index (40%) are compared. The lamellar size distribution curves of these two samples are shown in Fig. 10(a). Thus, the magnitude of the gamma relaxation exhibited by the sample quenched from 200°C, characterized by a sharper lamellar distribution curve shifted towards the lower values, is less than that of the sample quenched from 170°C [Fig. 10(b)]: for a fixed crystallinity index, the magnitude of the V relaxation decreases with decreasing thickness of the crystallites. Then, with increasing annealing temperature, the decrease in the ), relaxation magnitude could be due on the one hand to an increase in the crystallinity index and on the other hand to an increase in the
4t
al.
0.1
-0i
I
180
-140
- 100
I
-60
T(*C)
Fig. 9. Physical ageing of the quenched sample: , tan ~b spectrum recorded on increasing the temperature (15°C/hr) after 12hr at -143°C, (O) tan~b spectra recorded on decreasing the temperature (15°C/hr) on the first and second runs respectively (see text). relative amount of thin crystallites. Furthermore, the sample quenched from 200°C exhibits a higher storage modulus at T > T7 than the sample quenched from 170°C. Hence, at constant crystallinity content, the rubber modulus (T > TT) increases with decreasing thickness of the crystallites: crystalline lamellae are like physical ties crosslinking the amorphous phase. Moreover, physical crosslinking of the amorphous phase by crystallites leads not only to a decrease in the 7 relaxation magnitude but also to a broadening of the 7 relaxation as observed for other semicrystalline polymers. To a first approximation, the widening of the 7 relaxation can be evaluated from the ratio: height of the tan ~b peak (tan ~bmax) peak half-width (related to the drop in modulus)' The broadening in the 7 relaxation could lead to an apparent distribution of relaxation times of the amorphous chains induced by the crystalline phase. For a relaxation characterized by a single relaxation time (ideal linear solid and Zener relaxation), the peak height is related to the drop in modulus by the relationship:
"r" 0
.J
tan --4
~Zener 1/2 x/Gu/G R (G R and Gu, ~---
relaxed and unrelaxed modulus respectively). Then, the width of the relaxation can be evaluated by the ratio R: 3
7 1 0 3 / T ( K -1)
Fig. 8. Graphs of log aT (log aT: translational factor) against 1000/T). O, Quenched from 170°C to 20°C; I1, annealed for 24 hr at 100°C; &, annealed for 24 hr at 130°C.
R = tanSma,/tan~b .... . The R values are reported in Table 5. These features are also consistent with the characteristics of a mechanical relaxation related to the glass transition of polyethylene.
Mechanical ~, and ~ relaxations in polyethylene--I Table 5. Evaluation o f the width o f the "f relaxation System A
relaxations. Consequently, we have analysed the microstructure and the mechanical behaviour of a commercial branched polyethylene (system B).
R
Quenchedfrom: 170"C 200'C to 15'C
Quenchedfrom annealed at :
Branched polyethylene: origin of the ~ relaxation
0.10 0.09 170C
to 15r C +
100>C 110"C 13OC
945
0.08 0.03 0.02
Nevertheless, according to the literature [25-30], the fl relaxation displayed by branched polyethylene could also be related to the glass transition. There is a need for further examination of both ), and fl
Graphs of log G' and tan ~b vs temperature at 1, 0.1 and 0.01 Hz are shown in Fig. 11. The peak located about - 120°C corresponds to the ), relaxation as for linear polyethylene. In the - 7 0 to + 60°C range, the tan ~b spectra display a broad peak; it results from two maxima which overlap. According to the literature [25, 29], the lower temperature component of the broad peak could correspond to the B relaxation. The upper temperature component may be related to the ~ relaxation. The presence of a single ~t relaxation in such a polyethylene is due to the existence of only a single crystalline lamellae population [35] as shown
(a) I dM M
dL
I 400
0
L(~,)
(b) 0.1
10
- -
n
.d
0
I - 180
-140
I - 100
I
I
-60
-20
6 20
T I*CI
Fig. 10. (a) Lamellar thickness distribution curves for sample quenched from 170°C (O) and from 200°C ( ). (b) Isochronal spectra for sample quenched from 170°C (Q) and 200°C ( I ) to room temperature.
946
N . ALBEROLA el al.
O.2
-9.5
~4
"0-
0
'1
I
- 20
60
I
-q80
-I00 T
ft. 2"-
,o,
_J
5.5
(*C)
Fig. 11. Plots of log G' and tan ~ vs temperature for branched polyethylene (system B): A, 1 Hz; I , 0.1 Hz; II, 0.01 Hz. in Fig. 12. Frequency scans performed under isothermal conditions do not permit separation of the two relaxations. In order to define the fl relaxation, the two relaxations composing the broad peak are separated according to the following assumptions: (i) in agreement with literature data [24, 29] and with results obtained for linear polyethylene, the main component of the broad maximum in such a semicrystalline polyethylene is supposed to the c¢ relaxation, "i
dM
M
dL
(ii) to a first approximation, the ~ relaxation is assumed to be symmetric with respect to a vertical axis through its maximum. The result of this treatment is shown in Fig. 13: the magnitude of the ~ peak is about 0.1. The apparent activation energy of the ~ relaxation determined from the "so-calculated" isochronal spectra is about 200 kJ/mol. The high value of the apparent activation energy of the fl relaxation is of the same order of magnitude as that of mechanical relaxation due to glass transition. Moreover, physical ageing of the branched polyethylene for 24 hr at a temperature ( - 7 0 ° C ) below the temperature of the ~ peak leads to structural recovery as is well-known for vitreous systems annealed at temperatures below their temperatures of glass transition. Figure 14 shows the three runs at 15°C/hr recorded under the following conditions: (i) decreasing the temperature from room temperature to -80°C; (ii) increasing the temperature from - 100 to 20°C after the sample was kept for 24 hr at - 70°C; (iii) decreasing the temperature from 20 to 100°C. -
0
0
i 80
o
L(A)
Fig. 12. Lamellar thickness distribution curve of branched polyethylene.
The ageing for 24 hr at - 70°C induces changes in the configurational state as previously described for linear polyethylene annealed at a temperature below the 7 peak temperature. Beyond a temperature of about -33°C, the decreasing sides of the three spectra merged. It is assumed that the c¢relaxation is unaffected by physical ageing at - 70°C because the system has been first "annealed" for many hours at room temperature. According to the previous analysis performed for the ? relaxation, it can be concluded that - 3 3 ° C could be regarded also as the glass transition of polyethylene. It can be noted that this value is very
Mechanical 7 and fl relaxations in polyethylene--I 0.2
-
/
/
Pm ,* ' Am
•~ • A
"
-O=
947
a
o
[]
1~
~
0.1
• A' •~
• -' •
°, ~
4
As
• ~"
A
.." i
I
-140
n
-100
z~
--60
" %
\
• ,m
o
"'.
°
•
2o°O A
-180
o•
2 0o~ °
J'~"
0,.0 i ~
.m,'[ . m"
0
oo
A
•
4
~ • O,mm Ao%a
,
~
•
,
oOE] 8"
,
O o
QO
m
a
u
--20
20
60
T (OC)
Fig. 13. Separation of the • and ,8 relaxations displayed by the branched polyethyleneat three frequencies: 0.01Hz(A, fl:,~,~t),0.1Hz (O,/~: ©,~t) and lHz ( m ,8; U], ct). close to those reported by Wunderlich [26], Chang [27] and Davies and Eby [28]. In short, the /~ relaxation shows some characteristics of a glass transition. Polyethylene should therefore exhibit two glass transitions as suggested by Boyer [30] basing his assumption on topological considerations. The presence of different types of amorphous phase more or less constrained by the crystalline phase as assumed by Boyer [30] should 0.2--
result in a widening of the region of the glass transition rather than in the existence of two well defined glass temperatures. The presence of two glass temperatures in branched polyethylene can be reasonably explained by the existence of two types of intermolecular Van der Waals interactions with different energies. Thus, the glass transition at low temperature in the 7 region should be characteristic of Van der Waals interactions between CH2 groups of the main chains. The glass transition located at high temperature and associated with the /~ relaxation should be specific of Van der Waals interactions between CH 3 groups of side chains and the CH 2 groups. It is worthwhile to recall that the true concentration of CH 3 groups in the amorphous region is greater than the whole index determined from i.r. spectroscopy because side chains are not included in the crystalline lamellae; they are rejected and accumulate in the surrounding amorphous phase.
-O-
g
CONCLUSIONS
I---
0
I - 180
I
-- 6 0
-- 2 0
I 20
T (°C)
Fig. 14. Physical ageing of the branched polyethylene sample: (O), tan ~b spectrum recorded on increasing the temperature (15°C/hr) after keeping the sample for 24 hr at -70°C; - - . , superimposed tan ~ spectra recorded on decreasing the temperature (15°C/hr) on the first and second runs respectively(see text).
Mechanical spectrometry and differential scanning calorimetry measurements were carried out on linear and branched polyethylene in order to characterize the mechanical ), relaxation and the mechanical relaxation and to identify their molecular origins. Thus, the 7 relaxation displayed by a linear polyethylene and extensively analysed in this work shows the characteristics of a mechanical relaxation related to the glass transition of polyethylene: --high apparent activation energy of the mechanical y relaxation; --polyethylene shows structural recovery resulting from physical ageing at a temperature below the 7 peak', --the 7 relaxation has a WLF-temperature dependence as usually observed for primary transition of amorphous polymer;
N. ALBEROLAet al.
948
- - t h e magnitude of the 7 relaxation depends on the morphology of the system; - - t h e presence of a secondary relaxation 72 located at lower temperature (subglass transition). The fl relaxation displayed by branched polyethylene and located at higher temperature has also the characteristics of a mechanical relaxation due to glass transition: - - h i g h apparent activation energy (200 kJ/mol), - - b r a n c h e d polyethylene exhibits structural recovery induced by annealing at a temperature below the/3 maximum. Therefore, according to the definition of the glass transition temperature, the presence of two glass transitions in branched polyethylene could be due to the existence of Van der Waals interactions with different energies: the lower glass transition located in the gamma region might be characteristic of intermolecular Van der Waals interactions between CH2 groups and the upper glass transition located in the /3 region might concern intermolecular Van der Waals interactions involving C H 3 groups of the side chains and more or less segregated.
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Anelastic and Dielectric Effects in Polymeric Solids. Wiley, New York (1967). 3. D. E. Kline, J. A. Sauer and A. E. Woodward. J. Polym. Sci. XXIII, 455 (1956). 4. K. H. Illers. Kolloid-Z.Z. Polym. 252, 1 (1974). 5. A. H. Willbourn. Trans. Faraday Soc. 54, 717 (1958). 6. J. W. Cooper and N. G. McCrum. J. Mater. Sci. 7, 1221 (1972). 7. R. H. Boyd and S. M. Breitling. Macromolecules 7, 855 (1974). 8. T. Schatzki. J. Polym. Sci. 57, 496 (1962). 9. P. Audren and D. Ronarch. J. appl. Phys. 60, 946 (1986). 10. F. G. Stehling and L. Mandelkern. Macromolecules 3, 242 (1970). 11. K. M. Sinnot. J. appl. Phys. 37, 3385 (1966). 12. J. D. Hoffmann, G. Williams and E. Passaglia. J. Polym. Sci; Part C14 173 (1966).
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