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Contribution of chain alignment and crystallization in the evolution of cooperativity in drawn polymers
Polymer xxx (2014) 1e8
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Contribution of chain alignment and crystallization in the evolution of cooperativity in drawn polymers F. Hamonic a, D. Prevosto b, **, E. Dargent a, A. Saiter a, * a AMME-LECAP EA4528 International Laboratory, Institut des Matériaux de Rouen, Université et INSA de Rouen, BP12, 76801 Saint Etienne du Rouvray Cedex, France b Institute for Chemical and Physical Processes, CNR, Largo Pontecorvo 3, 56127 Pisa, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 January 2014 Received in revised form 13 April 2014 Accepted 15 April 2014 Available online xxx
The effects of Strain Induced Crystallization and chain orientation on the cooperativity evolution with temperature are studied on two polymers with similar molecular structure but different crystallization attitude. For this goal, we focus on poly(ethylene terephthalate) (PET) and the copolyester poly(ethylene glycol-co-cyclohexane-1,4-dimethanol terephthalate) (PETg), the last one having very low ability to crystallize. From Temperature Modulated Differential Scanning Calorimetry and Broadband Dielectric Spectroscopy investigations, we show that the crystalline phase appearance in PET implies a large reduction of the Cooperative Rearranging Region size, accompanied with a variation from fragile to strong behavior of the structural relaxation time temperature dependence. Such large variations are not observed in PETg at the same draw ratio. In the case of PETg, a small contribution of chain alignment to the CRR size evolution is evidenced. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Cooperativity Crystallinity Drawing
1. Introduction Understanding the influence that mechanical treatments have on polymer dynamics is of fundamental importance for a deeper comprehension of the polymer physics, in particular the relation of glass transition phenomenon to macromolecule organization. Mechanical treatments of polymers modify the macromolecule organization and their physical properties. As an example, drawing process can produce chain alignment in the draw direction and in some cases the appearance of a crystalline phase, this phenomenon being called Strain Induced Crystallization (SIC) [1e10]. Also, electrospinning technique used in the production of polymer nanofibers induces chain alignment along the fiber axis and in some polymers the growth of a crystalline phase [11e13]. Since the theory proposed by Adam and Gibbs [14], it is well accepted that the relaxation process related to the glass transition, called a relaxation process, is cooperative in nature: a structural unit can move only if a certain number of neighboring structural units also are moving. This concept implied the notion of
* Corresponding author. Tel.: þ33 (0) 2 32 95 50 86; fax: þ33 (0) 2 32 95 50 82. ** Corresponding author. E-mail addresses: [email protected] (D. Prevosto), allison.saiter@univ-rouen. fr (A. Saiter).
Cooperative Rearranging Region (CRR), which can be estimated according to different models and theories in terms of structural unit number belonging to that, or in terms of characteristic length scale [15e24]. In the recent years, the evolution of CRR size upon varying external parameters as well molecular characteristics has been experimentally studied to understand how cooperativity correlates with other relaxation parameters such as fragility, glass transition temperature, relaxation time. However the influence of drawing on CRR has not deeply investigated. According to Donth et al. [19], a CRR can be estimated from the von Laue approach describing a system with a fluctuating temperature. Each CRR represents a fluctuating region of molecular mobility (relaxation time) and it can be represented as a group of “sub-subsystems” called structural units, each one having its own glass transition temperature related to its own relaxation time. In a recent work [25] by assuming that temperature and polarization fluctuations have the same relaxation time distribution, we proposed to extend the Donth’s approach initially based on calorimetric measurements to dielectric measurements. In such a way it is possible investigating the cooperativity evolution with temperature, from the crossover temperature to the glass transition temperature. In semicrystalline polymers, the crystalline phase confines the amorphous one thus affecting the a relaxation dynamics. This effect depends on the crystallinity degree and on the crystal morphology
http://dx.doi.org/10.1016/j.polymer.2014.04.030 0032-3861/Ó 2014 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Hamonic F, et al., Contribution of chain alignment and crystallization in the evolution of cooperativity in drawn polymers, Polymer (2014), http://dx.doi.org/10.1016/j.polymer.2014.04.030
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[26e28]. In the case of amorphous phase confinement due to the presence of crystalline lamellae induced by thermal crystallization, several studies show that the greater the crystallinity degree, the smaller the cooperativity length [29e34]. The originality of this work is the study of cooperativity evolution in the case of SIC, this crystallization mode inducing crystallite formation not spherulites. Furthermore, in order to consider not only the effects of crystallization but also of chain orientation, this work is focused on poly(ethylene terephthalate) (PET) and the copolyester poly(ethylene glycol-co-cyclohexane-1,4-dimethanol terephthalate), PETg. In fact, PETg is molecularly similar to PET in structure with the adjunct of a few percent of ethylene glycols and of cyclohexane-1,4-dimethanol, CHDM [35]. Such small modification is sufficient to avoid almost completely the crystallization in PETg. With respect to previous reports on the cooperativity evolution during crystallization, the most original contributions of this paper are distinguishing the effects of chain orientation and crystallization on the evolution of the cooperativity. Moreover, the study of cooperativity evolution from the Donth’s approach over a broad temperature interval, from the glass transition up to the onset of cooperativity, is here proposed for the first time in the case of strain induced crystallization, this crystallization mode inducing crystallite formation not spherulites. By this way, we studied materials with a structural anisotropy, which is not the case in the majority of semicrystalline polymers studied in the literature. 2. Experiment 2.1. Materials PET samples are obtained from 500 mm thick films extruded by Carolex Co. The number-average molecular weight is Mn ¼ 31,000 g mol1 and the density is equal to r ¼ 1.336 g cm3. PETg plates (4 4 0.2 cm3) are obtained from pellets by injection molding. The PETg used (6763 from Tennessee Eastman Co.) is an amorphous copolymer, consisting of cyclohexanedimethanol, ethylene glycol and terephthalic acid with a molar ratio of approximately 1:2:3. The number-average molecular weight is Mn ¼ 26,000 g mol1 and the density is equal to r ¼ 1.27 g cm3. PET and PETg films are uniaxially drawn at a strain rate of 0.14 s1 at 100 C, the draw temperature being chosen just above the glass transition temperature to avoid cold crystallization. After drawing, samples are cold air-quenched down to room temperature in order to prevent chain relaxation. The draw ratio ranges studied in this work are 1 l 6.6 for PET and 1 l 7.6 for PETg. For more clarity, the samples studied will be noted PETl and PETgl where l indicates the draw ratio. 2.2. Temperature Modulated Differential Scanning Calorimetry Temperature Modulated Differential Scanning Calorimetry (TMDSC) experiments have been performed in a Thermal Analysis instrument (TA DSC 2920) equipped with a low-temperature cell (minimal temperature ¼ 203 K). Nitrogen was used as purge gas (70 mL/min). The TMDSC experiments have been performed in “Heat-Iso” mode (oscillation amplitude of 0.318 K, oscillation period of 60 s and heating rate of 2 K/min), which is advised for the study in semicrystalline polymers [36]. Calibration in temperature and energy was carried out using standard values of melting of indium and zinc. Calibration in specific heat capacity was carried out using sapphire as a reference. More details about calibration are given in reference [37]. From TMDSC, different signals can be obtained: the classical total heat flow and the apparent specific complex heat capacity Cp calculated as
Aq 1 * Cp ¼ Ab m
(1)
where Aq is the amplitude of the modulated heat flow, Ab the amplitude of the modulated heating rate and m the sample mass. Due to the phase lag 4 between the calorimeter response function (i.e. the total heat flow) and heating modulation, two apparent heat capacity components noted Cp0 (the in-phase component) and Cp00 (the out-of-phase component) are calculated according to the following equations:
C0p ¼ Cp cos4
(2)
C00p ¼ Cp sin4
(3)
The Cp0 versus temperature curve appears usually as an endothermic step at the glass transition temperature, and the Cp00 shows a peak in the glass transition region. 2.3. Dielectric spectroscopy Dielectric relaxation spectra were measured with an Alpha Analyser from Novocontrol (measurement frequency interval: 102e107 Hz), with a parallel plate capacitor cell, and the temperature was controlled through a heated flow of nitrogen gas, by means of a Quatro Cryosystem. Measurements have been performed in the temperature interval 320 K < T < 433 K, with the exception of undrawn PET sample that has been measured up to 378 K because of appearance of thermal crystallization. Samples have been dried in vacuum at a temperature of about 343 K before measuring, and during the whole period of the measurement were kept in a pure nitrogen atmosphere. 3. Results 3.1. TMDSC data Representative measurements of Cp00 are reported in Fig. 1 for undrawn samples (PET1.0 and PETg1.0) and for the maximal draw ratio (PET6.6 and PETg7.6). The curves corresponding to the classical endothermic step are published in another work [38]. For undrawn samples (black curves in Fig. 1), we observe a narrow peak with a maximum at the characteristic temperature Ta (Table 1). Due to the rather low frequency used, Ta from the reported TMDSC measurements is close to the glass transition temperature classically measured by DSC: Ta ¼ 348 K for PET1.0 and Ta ¼ 349 K for PETg1.0 (Table 1). For drawn samples (red curves (in web version) in Fig. 1), the behavior depends clearly on the sample studied: for PET6.6, we observe a broadening of the peak and a shift at high temperature (Ta ¼ 380 K). This shift of 30 K is very significant and can be correlated to the appearance of crystalline phase induced by drawing. Indeed, the crystallinity degree is equal to 37% for PET6.6 (see Table 1), producing a glass transition temperature increase due to the coupling effect [39,40]. This effect can be explained by the fact that the glass transition in the Mobile Amorphous Phase (MAP) is often crystallinity-dependent, and large variations of glass transition temperatures with the crystallinity degree could be observed for polyesters [41]. For PETg7.6, we also observe a broadening of the peak but less significant than for PET. As shown in Table 1, the crystallinity degree is equal to 5%, this low value explaining the absence of shift in the peak position. According to Donth’s approach mentioned in the introduction, the CRR average volume denoted as Va can be estimated according to the following equation [19,42]:
Please cite this article in press as: Hamonic F, et al., Contribution of chain alignment and crystallization in the evolution of cooperativity in drawn polymers, Polymer (2014), http://dx.doi.org/10.1016/j.polymer.2014.04.030
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C
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Fig. 1. Spectra of the imaginary part of complex heat capacity at 1.6$102 Hz of (a) PET1.0 (triangles), PET6.6 (stars) and (b) PETg1.0 (triangles), PETg7.6 (stars). Continuous lines are fit curves with a Gaussian function.
.
Va ¼
D 1 Cp0 rðdTÞ
2
kB Ta2
(4)
where Ta is the peak temperature in isofrequency curve (either TMDSC or BDS), r the density at Ta, kB the Boltzmann constant, dT the average temperature fluctuation related to the dynamic glass transition of an average CRR. The cooperativity length can be then estimated with x ¼ (Va)1/3. The number of particles per CRR noted Na can be estimated by:
Na ¼
r NA Va M0
¼
NA D 1 C 0 p 2
M0 ðdTÞ
kB Ta2
(5)
where NA is the Avogadro number and M0 the molar mass of the relevant structural unit. The cooperativity length values obtained for PET and PETg as a function of draw ratio are reported in Table 1. It decreases from 2.9 nm to 1.1 nm in PET when l varies from 1 to 6.6, and it decreases from 2.9 nm to 2.2 nm for PETg when l varies from 1 to 7.6. 3.2. Dielectric relaxation Dielectric relaxation spectra of undrawn PET and PETg samples show the relaxation behavior commonly reported in literature [9,25,28,43,44], characterized by structural and secondary relaxations and a conductivity contribution. Measurements herein reported have been performed only in the supercooled liquid state and the analysis focuses on the structural peak only. For PET we observed the appearance of cold crystallization effects in our spectra at temperature higher than 378 K, which constitutes the higher limit of our investigation. Representative spectra of PET and PETg measured at 378 K and 383 K respectively are reported in Fig. 2: the peak is the structural one, and the rise of signal at low frequencies is due to conductivity. Dielectric spectra of PET show great changes when samples are drawn (see representative spectra in Fig. 2a). The structural peak decreases in amplitude, shifts towards lower frequencies and it broadens. Moreover the conductivity is disturbed by the appearance of a new peak. The observed scenario is characteristic of semicrystalline PET, and in fact a
microstructural analysis of the sample by calorimetry and x-ray diffraction reveal a significant amount of crystalline phase for l 2.4 [38]. The structural peak at 378 K in PET6.0 is hidden by the conductivity. However at higher temperatures the structural contribution emerges as a well separated peak. In supplemental information a plot (Fig. S1) with some spectra of PET6.0 at different temperatures are reported, together with the contribution of the relaxation processes estimated by the fitting procedure. Because of the superposition of conductivity and structural contributions in the spectra the parameters of PET6.0 at temperature below 388 K have larger error than those at higher temperature. Dielectric relaxation spectra measured on PETg are much less affected by the mechanical treatment (see representative spectra in Fig. 2b). Similarly to PET we observe a decrease in amplitude, shift towards lower frequencies and broadening of the structural peak, but quantitatively the effect is smaller. Microstructural analysis of PETg reveals the appearance of a crystalline phase only for l 4.4, and the percentage of crystalline phase is only few percents, much smaller than PET [38]. As mentioned before, the maximum crystallinity degree obtained with drawing is about 37% for PET and 5% for PETg (Table 1). Interestingly also the PETg spectra measured on totally amorphous sample but different draw ratio (PETg1.0 and PETg4.0) show a different intensity of the loss peak. Dielectric relaxation of PET1.0 and PETg1.0 were fitted with a superposition of a Havriliak Negami curve for the structural process and ColeeCole function, CC, for the secondary process:
εðuÞ ¼ εN þ
X h i
Dεi 1 þ ðiusi Þ1ai
ibi
(6)
where the i index varies over the different processes εN is the totally relaxed dielectric constant, Dεi is the dielectric strength, si is the characteristic time, bi and ai describe the asymmetry and the broadness of the i-process. Note that the CC function is a Havriliak Negami with the b parameter fixed to 1. Moreover a conductivity contribution has been added, as well as another CC function to improve the reproduction of spectra in the frequency region between the conductivity and the structural relaxation. The addition of this last contribution improved the interpolation of experimental
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Table 1 The table report: sample name, draw ratio (l), half width at half height (dT) and peak temperature (Ta) of the Cp00 peak, size of CRR (x), size of the mobile amorphous region (Lma), percentage of crystal (Xc) and amorphous rigid (Xra) phase, orientation function of the amorphous (fa) and crystal (fc) phases. Details of the microstructural analysis are reported in Ref. [34].
PET PET1.2 PET2 PET2.4 PET3.2 PET4 PET4.8 PET6.6 PETg PETg2.8 PETg4.0 PETg4.4 PETg5.4 PETg7.6
l
dT (K)
Ta (K)
x (nm) Xc (%) Xra (%) Lma (nm) fa
1 1.2 2.0 2.4 3.2 4.0 4.8 6.6 1 2.8 4.0 4.4 5.4 7.6
3.1 3.3 3.5 3.4 5.8 8.5 7.9 10.5 3.1 3.2 3.6 3.8 3.7 3.9
348 349 349 349 356 367 368 380 349 350 350 349 348 349
2.9 2.7 2.7 2.7 1.8 1.4 1.4 1.1 2.9 2.7 2.5 2.3 2.3 2.2
0 0 0 12 22 34 36 37 0 0 0 4 4 5
0 0 0 1 2 14 16 18 0 0 0 10 15 20
e e e 21 10 4 4 3 e e e 56 53 53
e e 0.10 0.12 0.12 0.17 0.19 0.17 e 0.10 0.10 0.12 0.12 0.11
fc e e e e 0.7 0.8 0.8 0.9 e e e 0.7 0.8 0.9
data with minimal variations of the shape parameters of the structural process. During the analysis the parameter a of the secondary process has been fixed to 0.5 for PET, which is in the range of values reported in literature. For PETg a about 0.4 was found more suitable for reproducing the data. In drawn samples the parameter b of the structural process in PET has been also fixed to 1, which agrees with previous finding for isotropic and drawn thermally crystallized sample [45,46], and the parameter (1-a) is found to be about 0.2, which also agree with stretched crystallized sample [46]. As parameter for the characteristic time scale of the a relaxation process we choose the relaxation time corresponding to loss maximum, s ¼ 1/(2pna,max). Values of s as a function of inverse temperature are reported in Fig. 3. The data for PET1.0, PETg1.0, PETg4.0 and PETg7.6 are well described by the VogeleFulchere Tammann (VFT) equation, s ¼ s0exp[DT0/(TT0)], which is characteristic for the a relaxation related to the glass transition. In PET4.4 a strong decrease of curvature is observed, but still a VFT function can be used to interpolate the data. Instead for PET6.0 an Arrhenius law must be used to fit the temperature dependence of s.
The parameters of the VFT analysis are reported in Table 2. Drawing induces an increase of the dielectric Tg value (calculated as s(Tg) ¼ 100 s) in each sample, and for PET also a decrease of fragility. For PETg the fragility changes in the range m ¼ 140 15, which is probably within the error interval of the analysis. In order to estimate the parameters Ta and dT, needed for the calculation of CRR dimension, the dielectric data have been represented in isofrequency curves as a function of temperature, considering only the structural relaxation contribution as estimated by the above described analysis. Representative curves at the frequency of 1 kHz are shown in Fig. 4. A Gaussian curve has been fitted to the dielectric curves, thus obtaining the values of Ta and dT to be used in Eqs. (4) and (5) to calculate the CRR size. The analysis in terms of Gauss function is satisfactory at least in the region of the peak, thus providing a reliable estimation of its full width at half height. We observed a good correspondence for the values of dT as estimated from TMDSC (Table 1) and dielectric data these last being dT ¼ 3.0 and 15 for PET1.0 and PET6.6 at 1 Hz respectively, dT ¼ 3.4 and 4 for PETg1.0 and PETg7.6 respectively (also at 1 Hz). The theoretical background justifying this equivalence has been discussed in a previous publication [25]. Finally, it is possible to observe that the shift of the peak temperature in dielectric spectra at 1 kHz is larger than that of TMDSC data (Fig. 1), the latter being measured at much lower frequency. The difference in the frequency of measurements is the reason of the larger shift observed in dielectric data as can be deduced from the Arrhenius plot (Fig. 3).
4. Discussion Drawing polymeric materials produces changes in their microstructures, as for example chain alignment and increase of density [47], or it can induce crystallization, which also modify density [2,3,4,5,6], or it is sometimes supposed to change the number of entanglements [48]. All of these structural modifications alter intermolecular interactions and consequently polymer dynamics and glass transition temperature, which can be studied in terms of CRR size and its temperature evolution. At small values of drawing (l < 3) we observe only a slight decrease of the number of relaxing units in a CRR, Na, in both PET
Fig. 2. Dielectric spectra at (a) 378 K for PET1.0 (triangles), PET4.4 (squares), PET6.0 (stars) and (b) at 383 for PETg1.0 (triangles), PETg4.0 (squares), PETg7.6 (stars). Lines are fitting to the spectra according to the procedure reported in the text.
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Fig. 3. Arrhenius map for (a) PET1.0 (upwarded triangles) PET4.4 (squares) PET6.0 (stars); (b) PETg1.0 (upwarded triangles), PETg4.0 (squares), PETg7.6 (stars). The lines represent the fit to VFT for each sample with the exception of PET6.6 where an Arrhenius law has been used.
and PETg. The decrease of Na is rather small (10%) also in PET2.4 in which 12% of crystallinity is measured. The investigation in this interval of draw ratio refers only to TMDSC measures and we can observe that Ta is almost unaffected (Table 1). A common event to PET and PETg samples is the appearance of a progressively anisotropic macromolecular chain organization, with alignment in the draw direction also when the crystalline phase is not yet developed (for more details see to Refs. [38,49]). The oriented amorphous fraction has an orientation function close to 0.45 while the global amorphous phase orientation function fa is close to 0.1 (Table 1) as can be deduced by WAXS measurements. Chain orientation can be at the origin of a slight decrease of Na. However, the observed variation in PET and PETg is about 10e20% and definitive conclusion would need more precise estimation of Na. In agreement with the expected reduction of Na, in literature it is reported that chain alignment produces a mobility increase in absence of crystal formation, as for example in drawn polycarbonate and polystyrene, where faster volume relaxation was observed in the glassy state respect to the undrawn materials [47]. On the other hand drawn amorphous crosslinked elastomers do not present any variation of structural dynamics with chain orientation [50]. In this respect, it is important noticing that the chain orientation in crosslinked elastomer slightly alters the molecular packing, thus producing only small variation in intermolecular interaction. At larger drawing (l > 3) the percentage of crystalline phase significantly increases in PET up to a maximum
Table 2 Parameters of the VFT fit of relaxation time data. The value of Tg is calculated by s(Tg) ¼ 100 s. For PET6.0 the VFT fit is not applicable and Tg is estimated by the extrapolation of relaxation time curve to 100 s. The fragility is calculated according to the definition m ¼ (vlogs/v Tg/T)T¼Tg.
s0 (s) PET1.0 PET4.4 PET6.0 PETg1.0 PETg4.0 PETg7.6
2 1 e 6 3 2
1012 1014 1013 1012 1013
D
TK (K)
Tg (K)
m
2.7 7.4 e 3.6 3.1 4.4
320 301 e 310 316 308
347 361 366 344 347 348
177 97 55 143 149 127
of about 37% whereas in PETg the maximum value is only 5% (Table 1). The Xc increase occurs quite in a step way close to a critical value of drawing comprised between 4.0 and 4.4 for PETg and close to 2.4 in PET. In this draw ratio interval we have BDS and TMDSC measurements, both showing a significant decrease of Na for both samples (Figs. 5 and 6), which is larger for PET respect to PETg. The decrease of Na or CRR region size can be explained in terms of two phenomena. The first and more prominent is the geometrical confinement of the amorphous phase in regions constrained among the crystalline phase. As a prove we can compare the CRR size at Tg and the size of mobile amorphous region, Lma (Table 1), calculated in the glassy state. This last can be estimated by assuming that the linear fraction of crystal phase is equal to the volumetric one (Xc), and then calculating Lma ¼ Lc(1Xc)/XcLra nm, where Lra is the size of the rigid amorphous fraction (RAF) [51]. The RAF region size is not well known for drawn polymer, and we estimated its dimension according to the ratio of RAF volume over that of crystalline phase. In PETg the presence of a small fraction of crystal does not produce confinement (Lma is several tens of nm) at any value of l. On the other hand the large decrease of x in PET is accompanied by a large decrease of Lma (which is of the order of nm in the range l > 3) thus confirming the geometrical restriction induced effect (Table 1). This result is in agreement with several others reported in literature [51,52]. The second aspect contributing to a CRR size decrease is a consequence of the sample structural heterogeneity, which originates from the presence of a crystalline, a RAF and a MAP each having different chain conformation. Such structural heterogeneity leads also to a dynamic heterogeneity, which simply reflects the fact that the sample is not homogeneous from the point of view of chain conformation. The consequence is a broadening of the structural relaxation peak as measured by dielectric spectroscopy and a larger value of dT as obtained by the fit, as for example observed with fluctuation concentration in the case of mixtures or in the case of hybrid networks as shown by V.A. Bershtein et al. [53,54]. The larger value of dT in Eq. (4) leads to a smaller value of Va and equivalently x, which however is not really giving information on the glass formation phenomenon. We think this effect, together
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Fig. 4. Isofrequency dielectric loss spectra (1 kHz) for (a) PET1.0 (upwarded triangles) PET4.4 (squares) PET6.0 (triangle). The data of PET1.0 have been divided by a factor 2 to adjust the y-scale; (b) PETg1.0 (upwarded triangles), PETg4.0 (squares), PETg7.6 (stars). Lines represent fitting curve with a Gaussian function.
with chain alignment, is at the origin of the observed decrease of x (or equivalently Na) in PETg, where geometrical confinement cannot occur (Lma > 10 x). It is possible to note that such effect corresponds to a reduction of x of about 20% which is much smaller than the 60% decrease observed in PET where a high degree of crystallinity is developed. If a reduction of CRR size or equivalently Na seems to be contrasting with the observed increase of Tg or Ta from isofrequency plot (Tables 1 and 2), it is to be noted that this increase can be related to the presence of immobile polymer chains in the material. Such immobile chains are in the crystalline region and influence the mobility of the rest of the sample through the coupling effect [39,40,41]. The picture we want to propose is that the system is
composed by a crystalline phase, almost totally immobile, by a RAF, which is also almost completely immobile, and finally a MAP. Polymer chains in the MAP interact with those in the RAF and crystal that are immobile. Moreover, some chains can reside in part in the MAP and in part in the RAF. It can be understood that because of the interactions and the presence of chains in different phases the overall dynamics can be slowed down, even if a smaller number of relaxing units belong to a CRR. This can be viewed as an increase of the energy barrier for the rotation of relaxing units. The idea of an increase of energy barrier is also at the basis of the model recently developed by M. Pieruccini and co-workers for confined dynamics in semicrystalline polymers [46]. In fact, they suggested that when crystals grow and confine the MAP an increase of energy
Fig. 5. Number of structural units in a CRR as a function of the mobile amorphous fraction Xma in materials: PET (squares), PETg (open circles).
Fig. 6. Temperature evolution of the number of structural units in a CRR: PET1.0 (triangles), PET4.4 (squares), PET6.0 (circles) PETg1.0 (open triangles), PETg4.0 (open squares), PETg7.6 (open circles).
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fluctuation needed for the relaxation occurs (DF in Ref. [46]). Such prediction has been confirmed analyzing data of thermally crystallized PET samples. A priori, it is surprising noticing the presence of a large amount of RAF in PETg that is comparable to that observed in PET even if the crystalline phase is only 5%. In fact, the RAF is expected to appear at the interface with the crystals. Since the crystalline phase amount is minor in PETg respect to PET and the size of the crystal is similar in the two materials [38], we would expect lower volume fraction of RAF in PETg with respect to PET. The presence of such large amount of RAF is originated from the disordered nature of the PETg: the presence of 1,4-cyclohexanedimethanol group hinders the formation of a well ordered crystalline phase of PETg chains, which however still organize in an oriented and constrained structure where chains packing constrain their conformations [38]. We can note that the existence of RAF in absence of crystalline phase has been already observed by Q. Ma et al. in the case of electrospun nanocomposites [55]. This fraction of material is not as the common RAF, but it produces the same modification of calorimetric signal, i.e. decrease of DCp. For this reason the same naming is maintained. In our samples, PETg7.6 and PET4.4 have very similar volume fraction of RAF but very different variation of Tg or Ta as measured at low frequency evidencing the importance of the crystalline phase in slowing down the dynamics. However, the variation with temperature of the CRR size can be estimated by combining BDS and TMDSC measurements [25,56]. The CRR size or analogously the value of Na is expected to increase on approaching Tg, and such increase has been also related to the VFT behavior of the s(T) curve. For the first time we report herein the evolution of Na on approaching the glass transition for a polymer presenting an Arrhenius temperature dependence of relaxation time. In fact, in the case of PET6.0 the Arrhenius equation gives the best fitting of the experimental data, even though with a huge value of activation energy, 380 kJ/mol. This value is much higher than those characteristic for secondary process, thus reflecting the non-local nature of the process. From the analysis in terms of Arrhenius equation we obtain also a very small value of relaxation time in the limit of infinitely high temperature, i.e. log s0 ¼ 53. Unphysical and very small values of the pre-factors in the Arrhenius equation are associated to a large value of the activation entropy of the relaxation process that is signature of its cooperative nature. In secondary processes the cooperativity is of intramolecular nature in structural process is on intermolecular nature [57]. Following Ref. [58] we can estimate that the activation entropy DSb is about 93 R for the relaxation process in PET6.0, being much larger than what expected for secondary processes [57,58,59]. It is difficult to understand a so high value of activation entropy originating from intramolecular cooperativity and in fact we associated the observed process to the glass transition, as supported by the good correspondence between the values of Tg estimated by dielectric relaxation and calorimetry [8,27,35,49]. In correspondence with the Arrhenius dependence of relaxation time of PET6.0 we note that not only the value of Na at Tg is very small, but also we have only a slight (or any) variation of Na with temperature. It is important to note that the absolute value of Na in PET6.0 should be taken with care; in fact the analysis of dielectric spectra in this sample is affected by a large uncertainty especially at low temperature. However, we repute the indication of a negligible temperature evolution of Na correct outside any experimental error. The behavior of PET6.0 is not in agreement with the finding of a significant increase of number of units in a heterogeneity region or the increase in size of CRR size on approaching the glass transition as calculated with the Donth’s Model in strong glass formers GeO2, B2O3 and SiO2 [60,61]. The understanding of such discrepancy is not possible with the present knowledge.
7
5. Conclusions We report the investigation of the effects of chain alignment and strain induced crystallization in PET and PETg dynamics, as performed through the temperature evolution study of relaxation time and number of structural units in a cooperative region. Drawing PET produces a large amount of crystal, which on the contrary is not observed in PETg. The appearance of crystal phase seems to be at the origin of the main modification on polymer dynamic properties during drawing. In fact, in PET we observed a large reduction of structural unit number in Cooperative Rearranging Regions, Na, that is accompanied with the variation from fragile to strong behavior of the structural relaxation time temperature dependence, and a large variation of Tg. Such large variations are not observed in PETg at the same draw ratio, where the crystallization almost does not occur. However, we evidenced variations of Tg and Na of about 10% in PETg that are due to chain alignment. Finally, in PET at the maximum draw ratio we observed an Arrhenius temperature dependence of structural relaxation time, which is associated to an almost constant value of Na. Acknowledgments Dr D. Prevosto acknowledges University of Rouen for support during his visit in 2012. The authors thank the Region Haute Normandie for the financial support of the PhD fellowship of F. Hamonic. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.polymer.2014.04.030. References [1] Delpouve N, Stoclet G, Saiter A, Dargent E, Marais S. J Phys Chem B 2012;116: 4615. [2] Stoclet G, Seguela R, Vanmansart C, Rochas C, Lefebvre JM. Polymer 2012;53: 519. [3] Chaaria F, Chaouchea M, Doucet J. Polymer 2003;44:473. [4] Gorlier E, Haudin JM, Billon N. Polymer 2001;42:9541. [5] Stoclet G, Seguela R, Lefebvre JM, Elkoun SB, Vanmansart CA. Macromolecules 2010;43:1488. [6] Delpouve N, Lixon C, Saiter A, Dargent E, Grenet J. J Therm Anal Cal 2009;97: 541. [7] Lixon C, Delpouve N, Saiter A, Dargent E. Eur Polym J 2008;44:3377. [8] Kattan M, Dargent E, Grenet J. Polymer 2002;43:1399. [9] Dargent E, Bureau E, Delbreilh L, Zumailan A, Saiter JM. Polymer 2005;46: 3090. [10] Hamonic F, Saiter A, Prevosto D, Dargent E, Saiter JM. AIP Conf Proc 2012;1459:211. [11] Chun Liao C, Chien Wang C, Chen Shih K, Yung Chen C. Eur Pol J 2011;47:911. [12] Stachewicz U, Bailey RJ, Wang W, Barber AH. Polymer 2012;53:5132. [13] Bayley GM, Mallon PE. Polymer 2012;53:5523. [14] Adam G, Gibbs JH. J Chem Phys 1965;43:139. [15] Solunov CA. Eur Polym J 1999;35:1543. [16] Miller AA. J Chem Phys 1968;49:1393. [17] Miller AA. Macromolecules 1978;11:859. [18] Berthier L, Biroli G, Bouchaud JP, Cipelletti L, El Masri EL, L’Hote D, et al. Science 2005;310:1797. [19] Donth E, Hempel E, Schick C. J Phys Condens Matter 2000;12:L281. [20] Saiter A, Bureau E, Zapolsky H, Marais S, Saiter JM. J Non-Cryst Solids 2004;345:556. [21] Zapolsky H, Saiter A, Solunov H. J Optoelectron Adv Mater 2007;9:141. [22] Furushima Y, Ishikiriyama K, Higashioji T. Polymer 2013;54:4078. [23] Saiter A, Couderc H, Grenet J. J Therm Anal Calor 2007;88:483. [24] Arabeche K, Delbreilh L, Saiter JM, Michler GH, Adhikari R, Baer E. Polymer 2014;55:1546. [25] Saiter A, Delbreilh L, Couderc H, Arabeche K, Schonhals A, Saiter JM. J Phys Rev E 2010;81:041805. [26] Bras A, Viciosa MT, Dionosio M, Mano JF. J Therm Anal Calor 2007;88:425. [27] Saiter JM, Dargent E, Kattan M, Cabot C, Grenet J. Polymer 2003;44:3995. [28] Saiter A, Dargent E, Saiter JM, Grenet J. J Non-Cryst Solids 2008;354:345. [29] Schick C. Eur Phys J Spec Top 2010;189:3.
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Polymer journal homepage: www.elsevier.com/locate/polymer
Contribution of chain alignment and crystallization in the evolution of cooperativity in drawn polymers F. Hamonic a, D. Prevosto b, **, E. Dargent a, A. Saiter a, * a AMME-LECAP EA4528 International Laboratory, Institut des Matériaux de Rouen, Université et INSA de Rouen, BP12, 76801 Saint Etienne du Rouvray Cedex, France b Institute for Chemical and Physical Processes, CNR, Largo Pontecorvo 3, 56127 Pisa, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 January 2014 Received in revised form 13 April 2014 Accepted 15 April 2014 Available online xxx
The effects of Strain Induced Crystallization and chain orientation on the cooperativity evolution with temperature are studied on two polymers with similar molecular structure but different crystallization attitude. For this goal, we focus on poly(ethylene terephthalate) (PET) and the copolyester poly(ethylene glycol-co-cyclohexane-1,4-dimethanol terephthalate) (PETg), the last one having very low ability to crystallize. From Temperature Modulated Differential Scanning Calorimetry and Broadband Dielectric Spectroscopy investigations, we show that the crystalline phase appearance in PET implies a large reduction of the Cooperative Rearranging Region size, accompanied with a variation from fragile to strong behavior of the structural relaxation time temperature dependence. Such large variations are not observed in PETg at the same draw ratio. In the case of PETg, a small contribution of chain alignment to the CRR size evolution is evidenced. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Cooperativity Crystallinity Drawing
1. Introduction Understanding the influence that mechanical treatments have on polymer dynamics is of fundamental importance for a deeper comprehension of the polymer physics, in particular the relation of glass transition phenomenon to macromolecule organization. Mechanical treatments of polymers modify the macromolecule organization and their physical properties. As an example, drawing process can produce chain alignment in the draw direction and in some cases the appearance of a crystalline phase, this phenomenon being called Strain Induced Crystallization (SIC) [1e10]. Also, electrospinning technique used in the production of polymer nanofibers induces chain alignment along the fiber axis and in some polymers the growth of a crystalline phase [11e13]. Since the theory proposed by Adam and Gibbs [14], it is well accepted that the relaxation process related to the glass transition, called a relaxation process, is cooperative in nature: a structural unit can move only if a certain number of neighboring structural units also are moving. This concept implied the notion of
* Corresponding author. Tel.: þ33 (0) 2 32 95 50 86; fax: þ33 (0) 2 32 95 50 82. ** Corresponding author. E-mail addresses: [email protected] (D. Prevosto), allison.saiter@univ-rouen. fr (A. Saiter).
Cooperative Rearranging Region (CRR), which can be estimated according to different models and theories in terms of structural unit number belonging to that, or in terms of characteristic length scale [15e24]. In the recent years, the evolution of CRR size upon varying external parameters as well molecular characteristics has been experimentally studied to understand how cooperativity correlates with other relaxation parameters such as fragility, glass transition temperature, relaxation time. However the influence of drawing on CRR has not deeply investigated. According to Donth et al. [19], a CRR can be estimated from the von Laue approach describing a system with a fluctuating temperature. Each CRR represents a fluctuating region of molecular mobility (relaxation time) and it can be represented as a group of “sub-subsystems” called structural units, each one having its own glass transition temperature related to its own relaxation time. In a recent work [25] by assuming that temperature and polarization fluctuations have the same relaxation time distribution, we proposed to extend the Donth’s approach initially based on calorimetric measurements to dielectric measurements. In such a way it is possible investigating the cooperativity evolution with temperature, from the crossover temperature to the glass transition temperature. In semicrystalline polymers, the crystalline phase confines the amorphous one thus affecting the a relaxation dynamics. This effect depends on the crystallinity degree and on the crystal morphology
http://dx.doi.org/10.1016/j.polymer.2014.04.030 0032-3861/Ó 2014 Elsevier Ltd. All rights reserved.
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[26e28]. In the case of amorphous phase confinement due to the presence of crystalline lamellae induced by thermal crystallization, several studies show that the greater the crystallinity degree, the smaller the cooperativity length [29e34]. The originality of this work is the study of cooperativity evolution in the case of SIC, this crystallization mode inducing crystallite formation not spherulites. Furthermore, in order to consider not only the effects of crystallization but also of chain orientation, this work is focused on poly(ethylene terephthalate) (PET) and the copolyester poly(ethylene glycol-co-cyclohexane-1,4-dimethanol terephthalate), PETg. In fact, PETg is molecularly similar to PET in structure with the adjunct of a few percent of ethylene glycols and of cyclohexane-1,4-dimethanol, CHDM [35]. Such small modification is sufficient to avoid almost completely the crystallization in PETg. With respect to previous reports on the cooperativity evolution during crystallization, the most original contributions of this paper are distinguishing the effects of chain orientation and crystallization on the evolution of the cooperativity. Moreover, the study of cooperativity evolution from the Donth’s approach over a broad temperature interval, from the glass transition up to the onset of cooperativity, is here proposed for the first time in the case of strain induced crystallization, this crystallization mode inducing crystallite formation not spherulites. By this way, we studied materials with a structural anisotropy, which is not the case in the majority of semicrystalline polymers studied in the literature. 2. Experiment 2.1. Materials PET samples are obtained from 500 mm thick films extruded by Carolex Co. The number-average molecular weight is Mn ¼ 31,000 g mol1 and the density is equal to r ¼ 1.336 g cm3. PETg plates (4 4 0.2 cm3) are obtained from pellets by injection molding. The PETg used (6763 from Tennessee Eastman Co.) is an amorphous copolymer, consisting of cyclohexanedimethanol, ethylene glycol and terephthalic acid with a molar ratio of approximately 1:2:3. The number-average molecular weight is Mn ¼ 26,000 g mol1 and the density is equal to r ¼ 1.27 g cm3. PET and PETg films are uniaxially drawn at a strain rate of 0.14 s1 at 100 C, the draw temperature being chosen just above the glass transition temperature to avoid cold crystallization. After drawing, samples are cold air-quenched down to room temperature in order to prevent chain relaxation. The draw ratio ranges studied in this work are 1 l 6.6 for PET and 1 l 7.6 for PETg. For more clarity, the samples studied will be noted PETl and PETgl where l indicates the draw ratio. 2.2. Temperature Modulated Differential Scanning Calorimetry Temperature Modulated Differential Scanning Calorimetry (TMDSC) experiments have been performed in a Thermal Analysis instrument (TA DSC 2920) equipped with a low-temperature cell (minimal temperature ¼ 203 K). Nitrogen was used as purge gas (70 mL/min). The TMDSC experiments have been performed in “Heat-Iso” mode (oscillation amplitude of 0.318 K, oscillation period of 60 s and heating rate of 2 K/min), which is advised for the study in semicrystalline polymers [36]. Calibration in temperature and energy was carried out using standard values of melting of indium and zinc. Calibration in specific heat capacity was carried out using sapphire as a reference. More details about calibration are given in reference [37]. From TMDSC, different signals can be obtained: the classical total heat flow and the apparent specific complex heat capacity Cp calculated as
Aq 1 * Cp ¼ Ab m
(1)
where Aq is the amplitude of the modulated heat flow, Ab the amplitude of the modulated heating rate and m the sample mass. Due to the phase lag 4 between the calorimeter response function (i.e. the total heat flow) and heating modulation, two apparent heat capacity components noted Cp0 (the in-phase component) and Cp00 (the out-of-phase component) are calculated according to the following equations:
C0p ¼ Cp cos4
(2)
C00p ¼ Cp sin4
(3)
The Cp0 versus temperature curve appears usually as an endothermic step at the glass transition temperature, and the Cp00 shows a peak in the glass transition region. 2.3. Dielectric spectroscopy Dielectric relaxation spectra were measured with an Alpha Analyser from Novocontrol (measurement frequency interval: 102e107 Hz), with a parallel plate capacitor cell, and the temperature was controlled through a heated flow of nitrogen gas, by means of a Quatro Cryosystem. Measurements have been performed in the temperature interval 320 K < T < 433 K, with the exception of undrawn PET sample that has been measured up to 378 K because of appearance of thermal crystallization. Samples have been dried in vacuum at a temperature of about 343 K before measuring, and during the whole period of the measurement were kept in a pure nitrogen atmosphere. 3. Results 3.1. TMDSC data Representative measurements of Cp00 are reported in Fig. 1 for undrawn samples (PET1.0 and PETg1.0) and for the maximal draw ratio (PET6.6 and PETg7.6). The curves corresponding to the classical endothermic step are published in another work [38]. For undrawn samples (black curves in Fig. 1), we observe a narrow peak with a maximum at the characteristic temperature Ta (Table 1). Due to the rather low frequency used, Ta from the reported TMDSC measurements is close to the glass transition temperature classically measured by DSC: Ta ¼ 348 K for PET1.0 and Ta ¼ 349 K for PETg1.0 (Table 1). For drawn samples (red curves (in web version) in Fig. 1), the behavior depends clearly on the sample studied: for PET6.6, we observe a broadening of the peak and a shift at high temperature (Ta ¼ 380 K). This shift of 30 K is very significant and can be correlated to the appearance of crystalline phase induced by drawing. Indeed, the crystallinity degree is equal to 37% for PET6.6 (see Table 1), producing a glass transition temperature increase due to the coupling effect [39,40]. This effect can be explained by the fact that the glass transition in the Mobile Amorphous Phase (MAP) is often crystallinity-dependent, and large variations of glass transition temperatures with the crystallinity degree could be observed for polyesters [41]. For PETg7.6, we also observe a broadening of the peak but less significant than for PET. As shown in Table 1, the crystallinity degree is equal to 5%, this low value explaining the absence of shift in the peak position. According to Donth’s approach mentioned in the introduction, the CRR average volume denoted as Va can be estimated according to the following equation [19,42]:
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C
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Fig. 1. Spectra of the imaginary part of complex heat capacity at 1.6$102 Hz of (a) PET1.0 (triangles), PET6.6 (stars) and (b) PETg1.0 (triangles), PETg7.6 (stars). Continuous lines are fit curves with a Gaussian function.
.
Va ¼
D 1 Cp0 rðdTÞ
2
kB Ta2
(4)
where Ta is the peak temperature in isofrequency curve (either TMDSC or BDS), r the density at Ta, kB the Boltzmann constant, dT the average temperature fluctuation related to the dynamic glass transition of an average CRR. The cooperativity length can be then estimated with x ¼ (Va)1/3. The number of particles per CRR noted Na can be estimated by:
Na ¼
r NA Va M0
¼
NA D 1 C 0 p 2
M0 ðdTÞ
kB Ta2
(5)
where NA is the Avogadro number and M0 the molar mass of the relevant structural unit. The cooperativity length values obtained for PET and PETg as a function of draw ratio are reported in Table 1. It decreases from 2.9 nm to 1.1 nm in PET when l varies from 1 to 6.6, and it decreases from 2.9 nm to 2.2 nm for PETg when l varies from 1 to 7.6. 3.2. Dielectric relaxation Dielectric relaxation spectra of undrawn PET and PETg samples show the relaxation behavior commonly reported in literature [9,25,28,43,44], characterized by structural and secondary relaxations and a conductivity contribution. Measurements herein reported have been performed only in the supercooled liquid state and the analysis focuses on the structural peak only. For PET we observed the appearance of cold crystallization effects in our spectra at temperature higher than 378 K, which constitutes the higher limit of our investigation. Representative spectra of PET and PETg measured at 378 K and 383 K respectively are reported in Fig. 2: the peak is the structural one, and the rise of signal at low frequencies is due to conductivity. Dielectric spectra of PET show great changes when samples are drawn (see representative spectra in Fig. 2a). The structural peak decreases in amplitude, shifts towards lower frequencies and it broadens. Moreover the conductivity is disturbed by the appearance of a new peak. The observed scenario is characteristic of semicrystalline PET, and in fact a
microstructural analysis of the sample by calorimetry and x-ray diffraction reveal a significant amount of crystalline phase for l 2.4 [38]. The structural peak at 378 K in PET6.0 is hidden by the conductivity. However at higher temperatures the structural contribution emerges as a well separated peak. In supplemental information a plot (Fig. S1) with some spectra of PET6.0 at different temperatures are reported, together with the contribution of the relaxation processes estimated by the fitting procedure. Because of the superposition of conductivity and structural contributions in the spectra the parameters of PET6.0 at temperature below 388 K have larger error than those at higher temperature. Dielectric relaxation spectra measured on PETg are much less affected by the mechanical treatment (see representative spectra in Fig. 2b). Similarly to PET we observe a decrease in amplitude, shift towards lower frequencies and broadening of the structural peak, but quantitatively the effect is smaller. Microstructural analysis of PETg reveals the appearance of a crystalline phase only for l 4.4, and the percentage of crystalline phase is only few percents, much smaller than PET [38]. As mentioned before, the maximum crystallinity degree obtained with drawing is about 37% for PET and 5% for PETg (Table 1). Interestingly also the PETg spectra measured on totally amorphous sample but different draw ratio (PETg1.0 and PETg4.0) show a different intensity of the loss peak. Dielectric relaxation of PET1.0 and PETg1.0 were fitted with a superposition of a Havriliak Negami curve for the structural process and ColeeCole function, CC, for the secondary process:
εðuÞ ¼ εN þ
X h i
Dεi 1 þ ðiusi Þ1ai
ibi
(6)
where the i index varies over the different processes εN is the totally relaxed dielectric constant, Dεi is the dielectric strength, si is the characteristic time, bi and ai describe the asymmetry and the broadness of the i-process. Note that the CC function is a Havriliak Negami with the b parameter fixed to 1. Moreover a conductivity contribution has been added, as well as another CC function to improve the reproduction of spectra in the frequency region between the conductivity and the structural relaxation. The addition of this last contribution improved the interpolation of experimental
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Table 1 The table report: sample name, draw ratio (l), half width at half height (dT) and peak temperature (Ta) of the Cp00 peak, size of CRR (x), size of the mobile amorphous region (Lma), percentage of crystal (Xc) and amorphous rigid (Xra) phase, orientation function of the amorphous (fa) and crystal (fc) phases. Details of the microstructural analysis are reported in Ref. [34].
PET PET1.2 PET2 PET2.4 PET3.2 PET4 PET4.8 PET6.6 PETg PETg2.8 PETg4.0 PETg4.4 PETg5.4 PETg7.6
l
dT (K)
Ta (K)
x (nm) Xc (%) Xra (%) Lma (nm) fa
1 1.2 2.0 2.4 3.2 4.0 4.8 6.6 1 2.8 4.0 4.4 5.4 7.6
3.1 3.3 3.5 3.4 5.8 8.5 7.9 10.5 3.1 3.2 3.6 3.8 3.7 3.9
348 349 349 349 356 367 368 380 349 350 350 349 348 349
2.9 2.7 2.7 2.7 1.8 1.4 1.4 1.1 2.9 2.7 2.5 2.3 2.3 2.2
0 0 0 12 22 34 36 37 0 0 0 4 4 5
0 0 0 1 2 14 16 18 0 0 0 10 15 20
e e e 21 10 4 4 3 e e e 56 53 53
e e 0.10 0.12 0.12 0.17 0.19 0.17 e 0.10 0.10 0.12 0.12 0.11
fc e e e e 0.7 0.8 0.8 0.9 e e e 0.7 0.8 0.9
data with minimal variations of the shape parameters of the structural process. During the analysis the parameter a of the secondary process has been fixed to 0.5 for PET, which is in the range of values reported in literature. For PETg a about 0.4 was found more suitable for reproducing the data. In drawn samples the parameter b of the structural process in PET has been also fixed to 1, which agrees with previous finding for isotropic and drawn thermally crystallized sample [45,46], and the parameter (1-a) is found to be about 0.2, which also agree with stretched crystallized sample [46]. As parameter for the characteristic time scale of the a relaxation process we choose the relaxation time corresponding to loss maximum, s ¼ 1/(2pna,max). Values of s as a function of inverse temperature are reported in Fig. 3. The data for PET1.0, PETg1.0, PETg4.0 and PETg7.6 are well described by the VogeleFulchere Tammann (VFT) equation, s ¼ s0exp[DT0/(TT0)], which is characteristic for the a relaxation related to the glass transition. In PET4.4 a strong decrease of curvature is observed, but still a VFT function can be used to interpolate the data. Instead for PET6.0 an Arrhenius law must be used to fit the temperature dependence of s.
The parameters of the VFT analysis are reported in Table 2. Drawing induces an increase of the dielectric Tg value (calculated as s(Tg) ¼ 100 s) in each sample, and for PET also a decrease of fragility. For PETg the fragility changes in the range m ¼ 140 15, which is probably within the error interval of the analysis. In order to estimate the parameters Ta and dT, needed for the calculation of CRR dimension, the dielectric data have been represented in isofrequency curves as a function of temperature, considering only the structural relaxation contribution as estimated by the above described analysis. Representative curves at the frequency of 1 kHz are shown in Fig. 4. A Gaussian curve has been fitted to the dielectric curves, thus obtaining the values of Ta and dT to be used in Eqs. (4) and (5) to calculate the CRR size. The analysis in terms of Gauss function is satisfactory at least in the region of the peak, thus providing a reliable estimation of its full width at half height. We observed a good correspondence for the values of dT as estimated from TMDSC (Table 1) and dielectric data these last being dT ¼ 3.0 and 15 for PET1.0 and PET6.6 at 1 Hz respectively, dT ¼ 3.4 and 4 for PETg1.0 and PETg7.6 respectively (also at 1 Hz). The theoretical background justifying this equivalence has been discussed in a previous publication [25]. Finally, it is possible to observe that the shift of the peak temperature in dielectric spectra at 1 kHz is larger than that of TMDSC data (Fig. 1), the latter being measured at much lower frequency. The difference in the frequency of measurements is the reason of the larger shift observed in dielectric data as can be deduced from the Arrhenius plot (Fig. 3).
4. Discussion Drawing polymeric materials produces changes in their microstructures, as for example chain alignment and increase of density [47], or it can induce crystallization, which also modify density [2,3,4,5,6], or it is sometimes supposed to change the number of entanglements [48]. All of these structural modifications alter intermolecular interactions and consequently polymer dynamics and glass transition temperature, which can be studied in terms of CRR size and its temperature evolution. At small values of drawing (l < 3) we observe only a slight decrease of the number of relaxing units in a CRR, Na, in both PET
Fig. 2. Dielectric spectra at (a) 378 K for PET1.0 (triangles), PET4.4 (squares), PET6.0 (stars) and (b) at 383 for PETg1.0 (triangles), PETg4.0 (squares), PETg7.6 (stars). Lines are fitting to the spectra according to the procedure reported in the text.
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5
Fig. 3. Arrhenius map for (a) PET1.0 (upwarded triangles) PET4.4 (squares) PET6.0 (stars); (b) PETg1.0 (upwarded triangles), PETg4.0 (squares), PETg7.6 (stars). The lines represent the fit to VFT for each sample with the exception of PET6.6 where an Arrhenius law has been used.
and PETg. The decrease of Na is rather small (10%) also in PET2.4 in which 12% of crystallinity is measured. The investigation in this interval of draw ratio refers only to TMDSC measures and we can observe that Ta is almost unaffected (Table 1). A common event to PET and PETg samples is the appearance of a progressively anisotropic macromolecular chain organization, with alignment in the draw direction also when the crystalline phase is not yet developed (for more details see to Refs. [38,49]). The oriented amorphous fraction has an orientation function close to 0.45 while the global amorphous phase orientation function fa is close to 0.1 (Table 1) as can be deduced by WAXS measurements. Chain orientation can be at the origin of a slight decrease of Na. However, the observed variation in PET and PETg is about 10e20% and definitive conclusion would need more precise estimation of Na. In agreement with the expected reduction of Na, in literature it is reported that chain alignment produces a mobility increase in absence of crystal formation, as for example in drawn polycarbonate and polystyrene, where faster volume relaxation was observed in the glassy state respect to the undrawn materials [47]. On the other hand drawn amorphous crosslinked elastomers do not present any variation of structural dynamics with chain orientation [50]. In this respect, it is important noticing that the chain orientation in crosslinked elastomer slightly alters the molecular packing, thus producing only small variation in intermolecular interaction. At larger drawing (l > 3) the percentage of crystalline phase significantly increases in PET up to a maximum
Table 2 Parameters of the VFT fit of relaxation time data. The value of Tg is calculated by s(Tg) ¼ 100 s. For PET6.0 the VFT fit is not applicable and Tg is estimated by the extrapolation of relaxation time curve to 100 s. The fragility is calculated according to the definition m ¼ (vlogs/v Tg/T)T¼Tg.
s0 (s) PET1.0 PET4.4 PET6.0 PETg1.0 PETg4.0 PETg7.6
2 1 e 6 3 2
1012 1014 1013 1012 1013
D
TK (K)
Tg (K)
m
2.7 7.4 e 3.6 3.1 4.4
320 301 e 310 316 308
347 361 366 344 347 348
177 97 55 143 149 127
of about 37% whereas in PETg the maximum value is only 5% (Table 1). The Xc increase occurs quite in a step way close to a critical value of drawing comprised between 4.0 and 4.4 for PETg and close to 2.4 in PET. In this draw ratio interval we have BDS and TMDSC measurements, both showing a significant decrease of Na for both samples (Figs. 5 and 6), which is larger for PET respect to PETg. The decrease of Na or CRR region size can be explained in terms of two phenomena. The first and more prominent is the geometrical confinement of the amorphous phase in regions constrained among the crystalline phase. As a prove we can compare the CRR size at Tg and the size of mobile amorphous region, Lma (Table 1), calculated in the glassy state. This last can be estimated by assuming that the linear fraction of crystal phase is equal to the volumetric one (Xc), and then calculating Lma ¼ Lc(1Xc)/XcLra nm, where Lra is the size of the rigid amorphous fraction (RAF) [51]. The RAF region size is not well known for drawn polymer, and we estimated its dimension according to the ratio of RAF volume over that of crystalline phase. In PETg the presence of a small fraction of crystal does not produce confinement (Lma is several tens of nm) at any value of l. On the other hand the large decrease of x in PET is accompanied by a large decrease of Lma (which is of the order of nm in the range l > 3) thus confirming the geometrical restriction induced effect (Table 1). This result is in agreement with several others reported in literature [51,52]. The second aspect contributing to a CRR size decrease is a consequence of the sample structural heterogeneity, which originates from the presence of a crystalline, a RAF and a MAP each having different chain conformation. Such structural heterogeneity leads also to a dynamic heterogeneity, which simply reflects the fact that the sample is not homogeneous from the point of view of chain conformation. The consequence is a broadening of the structural relaxation peak as measured by dielectric spectroscopy and a larger value of dT as obtained by the fit, as for example observed with fluctuation concentration in the case of mixtures or in the case of hybrid networks as shown by V.A. Bershtein et al. [53,54]. The larger value of dT in Eq. (4) leads to a smaller value of Va and equivalently x, which however is not really giving information on the glass formation phenomenon. We think this effect, together
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Fig. 4. Isofrequency dielectric loss spectra (1 kHz) for (a) PET1.0 (upwarded triangles) PET4.4 (squares) PET6.0 (triangle). The data of PET1.0 have been divided by a factor 2 to adjust the y-scale; (b) PETg1.0 (upwarded triangles), PETg4.0 (squares), PETg7.6 (stars). Lines represent fitting curve with a Gaussian function.
with chain alignment, is at the origin of the observed decrease of x (or equivalently Na) in PETg, where geometrical confinement cannot occur (Lma > 10 x). It is possible to note that such effect corresponds to a reduction of x of about 20% which is much smaller than the 60% decrease observed in PET where a high degree of crystallinity is developed. If a reduction of CRR size or equivalently Na seems to be contrasting with the observed increase of Tg or Ta from isofrequency plot (Tables 1 and 2), it is to be noted that this increase can be related to the presence of immobile polymer chains in the material. Such immobile chains are in the crystalline region and influence the mobility of the rest of the sample through the coupling effect [39,40,41]. The picture we want to propose is that the system is
composed by a crystalline phase, almost totally immobile, by a RAF, which is also almost completely immobile, and finally a MAP. Polymer chains in the MAP interact with those in the RAF and crystal that are immobile. Moreover, some chains can reside in part in the MAP and in part in the RAF. It can be understood that because of the interactions and the presence of chains in different phases the overall dynamics can be slowed down, even if a smaller number of relaxing units belong to a CRR. This can be viewed as an increase of the energy barrier for the rotation of relaxing units. The idea of an increase of energy barrier is also at the basis of the model recently developed by M. Pieruccini and co-workers for confined dynamics in semicrystalline polymers [46]. In fact, they suggested that when crystals grow and confine the MAP an increase of energy
Fig. 5. Number of structural units in a CRR as a function of the mobile amorphous fraction Xma in materials: PET (squares), PETg (open circles).
Fig. 6. Temperature evolution of the number of structural units in a CRR: PET1.0 (triangles), PET4.4 (squares), PET6.0 (circles) PETg1.0 (open triangles), PETg4.0 (open squares), PETg7.6 (open circles).
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fluctuation needed for the relaxation occurs (DF in Ref. [46]). Such prediction has been confirmed analyzing data of thermally crystallized PET samples. A priori, it is surprising noticing the presence of a large amount of RAF in PETg that is comparable to that observed in PET even if the crystalline phase is only 5%. In fact, the RAF is expected to appear at the interface with the crystals. Since the crystalline phase amount is minor in PETg respect to PET and the size of the crystal is similar in the two materials [38], we would expect lower volume fraction of RAF in PETg with respect to PET. The presence of such large amount of RAF is originated from the disordered nature of the PETg: the presence of 1,4-cyclohexanedimethanol group hinders the formation of a well ordered crystalline phase of PETg chains, which however still organize in an oriented and constrained structure where chains packing constrain their conformations [38]. We can note that the existence of RAF in absence of crystalline phase has been already observed by Q. Ma et al. in the case of electrospun nanocomposites [55]. This fraction of material is not as the common RAF, but it produces the same modification of calorimetric signal, i.e. decrease of DCp. For this reason the same naming is maintained. In our samples, PETg7.6 and PET4.4 have very similar volume fraction of RAF but very different variation of Tg or Ta as measured at low frequency evidencing the importance of the crystalline phase in slowing down the dynamics. However, the variation with temperature of the CRR size can be estimated by combining BDS and TMDSC measurements [25,56]. The CRR size or analogously the value of Na is expected to increase on approaching Tg, and such increase has been also related to the VFT behavior of the s(T) curve. For the first time we report herein the evolution of Na on approaching the glass transition for a polymer presenting an Arrhenius temperature dependence of relaxation time. In fact, in the case of PET6.0 the Arrhenius equation gives the best fitting of the experimental data, even though with a huge value of activation energy, 380 kJ/mol. This value is much higher than those characteristic for secondary process, thus reflecting the non-local nature of the process. From the analysis in terms of Arrhenius equation we obtain also a very small value of relaxation time in the limit of infinitely high temperature, i.e. log s0 ¼ 53. Unphysical and very small values of the pre-factors in the Arrhenius equation are associated to a large value of the activation entropy of the relaxation process that is signature of its cooperative nature. In secondary processes the cooperativity is of intramolecular nature in structural process is on intermolecular nature [57]. Following Ref. [58] we can estimate that the activation entropy DSb is about 93 R for the relaxation process in PET6.0, being much larger than what expected for secondary processes [57,58,59]. It is difficult to understand a so high value of activation entropy originating from intramolecular cooperativity and in fact we associated the observed process to the glass transition, as supported by the good correspondence between the values of Tg estimated by dielectric relaxation and calorimetry [8,27,35,49]. In correspondence with the Arrhenius dependence of relaxation time of PET6.0 we note that not only the value of Na at Tg is very small, but also we have only a slight (or any) variation of Na with temperature. It is important to note that the absolute value of Na in PET6.0 should be taken with care; in fact the analysis of dielectric spectra in this sample is affected by a large uncertainty especially at low temperature. However, we repute the indication of a negligible temperature evolution of Na correct outside any experimental error. The behavior of PET6.0 is not in agreement with the finding of a significant increase of number of units in a heterogeneity region or the increase in size of CRR size on approaching the glass transition as calculated with the Donth’s Model in strong glass formers GeO2, B2O3 and SiO2 [60,61]. The understanding of such discrepancy is not possible with the present knowledge.
7
5. Conclusions We report the investigation of the effects of chain alignment and strain induced crystallization in PET and PETg dynamics, as performed through the temperature evolution study of relaxation time and number of structural units in a cooperative region. Drawing PET produces a large amount of crystal, which on the contrary is not observed in PETg. The appearance of crystal phase seems to be at the origin of the main modification on polymer dynamic properties during drawing. In fact, in PET we observed a large reduction of structural unit number in Cooperative Rearranging Regions, Na, that is accompanied with the variation from fragile to strong behavior of the structural relaxation time temperature dependence, and a large variation of Tg. Such large variations are not observed in PETg at the same draw ratio, where the crystallization almost does not occur. However, we evidenced variations of Tg and Na of about 10% in PETg that are due to chain alignment. Finally, in PET at the maximum draw ratio we observed an Arrhenius temperature dependence of structural relaxation time, which is associated to an almost constant value of Na. Acknowledgments Dr D. Prevosto acknowledges University of Rouen for support during his visit in 2012. The authors thank the Region Haute Normandie for the financial support of the PhD fellowship of F. Hamonic. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.polymer.2014.04.030. References [1] Delpouve N, Stoclet G, Saiter A, Dargent E, Marais S. J Phys Chem B 2012;116: 4615. [2] Stoclet G, Seguela R, Vanmansart C, Rochas C, Lefebvre JM. Polymer 2012;53: 519. [3] Chaaria F, Chaouchea M, Doucet J. Polymer 2003;44:473. [4] Gorlier E, Haudin JM, Billon N. Polymer 2001;42:9541. [5] Stoclet G, Seguela R, Lefebvre JM, Elkoun SB, Vanmansart CA. Macromolecules 2010;43:1488. [6] Delpouve N, Lixon C, Saiter A, Dargent E, Grenet J. J Therm Anal Cal 2009;97: 541. [7] Lixon C, Delpouve N, Saiter A, Dargent E. Eur Polym J 2008;44:3377. [8] Kattan M, Dargent E, Grenet J. Polymer 2002;43:1399. [9] Dargent E, Bureau E, Delbreilh L, Zumailan A, Saiter JM. Polymer 2005;46: 3090. [10] Hamonic F, Saiter A, Prevosto D, Dargent E, Saiter JM. AIP Conf Proc 2012;1459:211. [11] Chun Liao C, Chien Wang C, Chen Shih K, Yung Chen C. Eur Pol J 2011;47:911. [12] Stachewicz U, Bailey RJ, Wang W, Barber AH. Polymer 2012;53:5132. [13] Bayley GM, Mallon PE. Polymer 2012;53:5523. [14] Adam G, Gibbs JH. J Chem Phys 1965;43:139. [15] Solunov CA. Eur Polym J 1999;35:1543. [16] Miller AA. J Chem Phys 1968;49:1393. [17] Miller AA. Macromolecules 1978;11:859. [18] Berthier L, Biroli G, Bouchaud JP, Cipelletti L, El Masri EL, L’Hote D, et al. Science 2005;310:1797. [19] Donth E, Hempel E, Schick C. J Phys Condens Matter 2000;12:L281. [20] Saiter A, Bureau E, Zapolsky H, Marais S, Saiter JM. J Non-Cryst Solids 2004;345:556. [21] Zapolsky H, Saiter A, Solunov H. J Optoelectron Adv Mater 2007;9:141. [22] Furushima Y, Ishikiriyama K, Higashioji T. Polymer 2013;54:4078. [23] Saiter A, Couderc H, Grenet J. J Therm Anal Calor 2007;88:483. [24] Arabeche K, Delbreilh L, Saiter JM, Michler GH, Adhikari R, Baer E. Polymer 2014;55:1546. [25] Saiter A, Delbreilh L, Couderc H, Arabeche K, Schonhals A, Saiter JM. J Phys Rev E 2010;81:041805. [26] Bras A, Viciosa MT, Dionosio M, Mano JF. J Therm Anal Calor 2007;88:425. [27] Saiter JM, Dargent E, Kattan M, Cabot C, Grenet J. Polymer 2003;44:3995. [28] Saiter A, Dargent E, Saiter JM, Grenet J. J Non-Cryst Solids 2008;354:345. [29] Schick C. Eur Phys J Spec Top 2010;189:3.
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Please cite this article in press as: Hamonic F, et al., Contribution of chain alignment and crystallization in the evolution of cooperativity in drawn polymers, Polymer (2014), http://dx.doi.org/10.1016/j.polymer.2014.04.030