Experimental Study of Crystallization of Polyetheretherketone (PEEK) Over a Large Temperature Range Using a Nano-Calorimeter

Polymer Testing 36 (2014) 10–19

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Polymer Testing

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Material behaviour Experimental study of crystallization of PolyEtherEtherKetone (PEEK) over a large temperature range using a nano-calorimeter

Xavier Tardif a,*, Baptiste Pignon b, Nicolas Boyard b, Jürn W.P. Schmelzer c, Vincent Sobotka b, Didier Delaunay b, Christoph Schick c a IRT Jules Verne, Chemin du Chaffault, 44340 Bouguenais, France b LUNAM Université, Université de Nantes, CNRS, Laboratoire de Thermocinétique de Nantes, UMR 6607, La Chantrerie, rue Christian Pauc, BP 50609, 44306 Nantes cedex 3, France c University of Rostock, Institute of Physics, Wismarsche Str. 43-45, 18051 Rostock, Germany article info abstract

Article history: The recently developed fast scanning differential calorimetry is used for the first time to Received 30 January 2014 determine the crystallization kinetics of Poly(EtherEtherKetone) (PEEK). In our experi- Accepted 15 March 2014 ments, crystallization is studied in isothermal conditions over a large temperature range from 170 Cto310C. Two different measurement protocols were employed. Between Keywords: 200 C and 300 C the heat flow was directly measured during isothermal crystallization. PEEK Outside this temperature range we measured the heat of fusion on heating after inter- Flash DSC rupted isothermal crystallization. We show that data can be analyzed with the Avrami Crystallization kinetics Avrami approach incorporating a term describing secondary crystallization. The crystallization fi Secondary crystallization half-times are measured. The Avrami kinetic coef cient KAv associated with primary crystallization is evaluated from isothermal crystallization between 170 C and 310 C where data were not previously available. The kinetics of crystallization of PEEK has only one maximum located around 230 C and its Avrami exponent is close to 3, suggesting instantaneous nucleation with subsequent spherical growth. The whole isothermal crystallization process is modeled in terms of Hillier’s model since it takes secondary crystallization kinetics into account. Finally, it is shown that the double melting peak behavior observed after isothermal crystallization (below 260 C) is a consequence of the reorganization process during heating. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction since its maximum crystallinity is close to 40% [1]. The glass transition temperature of PEEK is 143 C [2], the fi N PolyEtherEtherKetone (PEEK) is a high performance in nite polymer melting temperature, Tm , is usually semi-crystalline thermoplastic that is nowadays the sub- considered to be about 390 C [3] and its pyrolysis tem- ject of a large number of studies because its mechanical perature is 550 C [4]. and chemical properties are very promising, especially for Composite part quality (residual stresses, shape dis- leading edge industries. It is a low crystalline polymer, tortion.) at the completion of the manufacturing process can be predicted from thermo-elastic simulations involving coupling between mechanical and thermal properties of * Corresponding author. the samples under consideration. However, the imple- E-mail addresses: [email protected], xav.tardif@gmail. com (X. Tardif). mentation of such an approach requires comprehensive http://dx.doi.org/10.1016/j.polymertesting.2014.03.013 0142-9418/Ó 2014 Elsevier Ltd. All rights reserved. X. Tardif et al. / Polymer Testing 36 (2014) 10–19 11 and accurate knowledge of the thermo-physical properties secondary crystallization on the overall crystallization to provide coherent results. In particular, in the case of kinetics. semi-crystalline polymers, the modeling of the samples So far, only morphology and crystallization kinetics of also requires detailed knowledge of the crystallization PEEK at high temperatures have been studied employing kinetics. different methods [2,3,21–23]. Crystallization kinetics is The phase change of an amorphous polymer into a commonly studied at high temperatures (between 280 C semi-crystalline solid material is commonly described by and 320 C for PEEK) in isothermal conditions from DSC overall crystallization kinetic theories [5]. Kinetic studies (Differential Scanning Calorimeter) experimental data generally start by considering experiments performed because of the low cooling rates in DSC and/or from optical under isothermal conditions. The ratio of the crystalline microscopy experiments by measuring the growth rate phase, a(t), with respect to time, t, can be described in such (nucleation step cannot be observed) of spherulites (acti- cases by the Avrami equation Eq (1) [6–8], vated nuclei) and their number. For example, Wei et al. [21] study experimentally the kinetics of crystallization of PEEK að Þ¼ ð , nÞ; t 1 exp KAv t (1) at high temperatures by an Avrami approach with temperature modulated DSC. Following the Avrami approach, which is characterized by the Avrami kinetic coefficient they observed that secondary crystallization is character- “KAv” and the Avrami exponent “n”. The Avrami kinetic ized by an Avrami exponent 0.52 < n < 1.37 if these pro- coefficient is a function of temperature and pressure, while cesses proceed above 290 C. However, it is difficult to the Avrami exponent depends on shape, growth mode of assign a physical meaning to these values based on the the crystallites and the nature of the nucleation process Avrami theory. Wang et al. [3] studied isothermal crystal- (sporadic: constant nucleation frequency or instantaneous: lization of PEEK with a Perkin-Elmer DSC 7. Above 280 C, all the nuclei are formed instantaneously). The Avrami they used the Avrami equation whereas below 170 C they approach supposes four assumptions: (i) The nuclei are studied the cold crystallization process. In the range in randomly dispersed in the bulk. (ii) The growth rate is only between those two temperatures the crystallization pro- dependent on temperature at a given pressure. (iii) The cess was too fast to be studied by DSC. Kuo et al. [22] also nucleation rate is also only dependent on temperature at a performed isothermal crystallization of PEEK from 260 C given pressure and (iv) disappearance of potential nuclei to 310 C by DSC analysis using a Perkin Elmer Diamond when activated or absorbed. However, polymer and com- DSC. Finally, the kinetic coefficient KAv and the Avrami posite processing involves much more complex thermal exponent n are computed from the experimental data. conditions, including non-isothermal crystallization. Its These methods are dedicated to small samples (wmg) appropriate theoretical treatment requires the develop- and cannot survey the whole area of conditions encoun- ment of appropriate models to describe the associated ki- tered in all the material forming processes: pressure up to netics. In particular, Ozawa [9] extended the Avrami theory 40 MPa, cooling rate up to 1000 K/s and shear rate of to the case of crystallization at a constant cooling rate. 400 s 1 (conditions for injection molding). Thus, the Introducing an additional isokinetic assumption into the Avrami function has to be extrapolated to lower tempera- Avrami model, Nakamura [10] proposed a new description tures [24]. of the overall crystallization kinetics valid whatever tem- Despite a large number of characterization devices, the perature course is followed. The Nakamura model is widely study of the kinetics at very low crystallization tempera- used in crystallization modeling and, particularly, in in- tures (e.g. T < 260C for PEEK, T < 80C for PP) remains a jection molding [11,12]. A differential form of this approach challenging task. It requires as a precondition to reach very has been advanced by Patel and Spruiell [13]. An alternative high cooling rates and, hence, to reduce the sample mass. to these models is the use of a system of differential “rate Thus, it requires greatly improved sensitivity of the calo- equations” [14–16]. rimetric sensor and to reduce the time constant of the However, at least some of the assumptions underlying apparatus. In this context, laboratory devices [25–28], and above mentioned theories are often not fulfilled over the especially the nano-DSC [29–31], have been developed to whole crystallization time. Deviations can be attributed, in reach cooling rates up to more than 103 K/s. These nano- particular, to higher complexity of the nucleation process DSC devices were developed for very small sample mass: and/or secondary crystallization. The latter phenomenon is from 10 nano grams to hundreds of nano grams. This new as a rule not taken into account in the previously cited apparatus supplies us with a novel opportunity to reach theories, but it is well known to occur in polyamide (PA), lower crystallization temperatures as compared to classical polyethylene (PE), polyoxymethylene (POM), polyethylene DSC and to determine the parameters of overall crystalli- oxide (PEO) and PEEK. It essentially consists of perfecting of zation kinetic models. the spherulites created during primary crystallization, and In the present work, a commercial nano calorimeter, occurs when they impinge each other. At this time, the Flash DSC 1, Mettler Toledo, has been used to follow the degree of crystallinity (crystalline volume divided by the isothermal crystallization of PEEK from 170Cto310C. The total volume of the polymer) of the spherulites themselves Flash DSC 1 allows one to reach heating rates up to is increasing by thickening of the crystals, growth of new 20,000 K/s and cooling rates up to 5,000 K/s. The analysis of lamellae within or between existing stack of lamellae, and the results is performed in the framework of the Avrami [6– then growth of new lamellae from the amorphous part of 8] approach which models accurately isothermal crystalli- the spherulites [17]. Few models (mainly for isothermal zation of polymers. Then, the secondary crystallization conditions [18–20]) are proposed to include the effect of impact is also evaluated. Isothermal crystallization is 12 X. Tardif et al. / Polymer Testing 36 (2014) 10–19 studied following two different methods of data treatment. material was added several times with the same procedure Both methods are described here in detail and the crys- to increase the mass of the sample. tallization half-time results are presented and compared The DSC flash sensor was calibrated with a piece of in- with classical DSC measurements and data available in the dium placed on the reference sensor of the chip. The sensor literature for PEEK with a similar molecular weight. These chip was then heated at various scanning rates and the data are very helpful to appraise the validity of the mea- onset of the melting peak measured. We thus determined surement. Finally, experimental KAv function data over a the evolution of DT (thermal lag), which represents the large temperature range are presented for the first time. difference between the theoretical melting temperature of These results can be employed to describe the overall indium and that experimentally measured DT ¼ Tm,theo crystallization kinetics of PEEK in polymer processing. Tm,xP versus the heating rate. In the following sections the data are presented after correction by DT corresponding to 2. Experimental their scanning rate [35].

2.1. Material 2.4. Procedure

The polyetheretherketone material studied is a semi- The isothermal crystallization of PEEK was studied with crystalline thermoplastic polymer provided by Victrex the temperature cycle shown in Fig. 2. First, the polymer whose commercial name is PEEK 150G. It has a molecular was kept for 0.1 s at 380 C to erase the thermal history of weight of 85 000 kg/mol. Crystallization of PEEK with a the sample, particularly, to melt all crystals. The applied similar molecular weight at high temperature has been scanning rate was 2000 K/s for both heating and cooling. studied in [3,22]. This scanning rate was chosen to prevent any crystallization during cooling or heating. 2.2. Fast scanning calorimetry Isothermal crystallization was studied by two methods. If the crystallization heat flow is high enough to be A Mettler Flash DSC 1 was employed [32–34]. This is a measured, the crystallization rate is directly evaluated chip based fast scanning device with power compensation. from the isothermal step (it is experimentally the case for “ The diameter of the active area of the chip sensor is 500 mm 200 C T 280 C). This method is called the continuous ” and the thickness of the membrane is ca. 2 mm, as depicted way in this paper. Outside of this temperature range the in Fig. 1. Employing this sensor, one can reach heating rates crystallization kinetics is very slow, so the associated heat fl of 20,000 K/s and cooling rates of 5,000 K/s [32,33] in the ow is released over a long time and below the detection temperature range of interest. limit of the device. Then, a second protocol was used. The temperature cycle presented in Fig. 2 was repeated with changing crystallization time, and the melting enthalpy 2.3. Sample preparation determined during the heating step as a measure of the crystallization enthalpy during the previous annealing The sample was prepared from granules of the polymer step. The second protocol is called “discrete way”. The under a microscope and placed in the center of the chip used isothermal crystallization times are reported in Table sensor. It was then melted at a low heating rate of 10 K/s to 1. establish good thermal contact with the membrane by In Fig. 3, the heat flow measured during the heating of wetting it. A larger sample is necessary to study the fully amorphous PEEK is presented. The PEEK has been fl isothermal crystallization because the heat ow is very heated up to 380 C and quenched at 2000 K/s. The small and to ensure bulk crystallization. Therefore, the

Fig. 1. PEEK sample (ca. 350 ng) on the chip sensor. Fig. 2. Temperature cycle applied to the polymer sample. X. Tardif et al. / Polymer Testing 36 (2014) 10–19 13

Table 1 Crystallization times at each temperature.

Temperature [C] 170 180 200 210 220 230 240 250 260 270 280 300 310 Discrete way maximum time [s] 800 1000 400 x 100 100 100 100 100 x 100 800 800 Continuous way crystallization time [s] x x 10 10 10 10 10 10 10 10 x x x

measured heat flow follows Eq. (2) where m is the sample 250 C. At these temperatures, the first melting peak tem- mass, cp its specific heat and fxP is the measured heat flow. perature increases versus the crystallization temperature, whereas the temperature of the higher one does not f ¼ dT change. This behavior indicates complete melting recrys- XP mcp (2) dt tallization for these samples at the heating rate of 2000 K/s, The sample mass was evaluated to be 355 ng thanks to as discussed in Section 4.1. the specific heat taken in the ATHAS database (Table 2). In The total melting enthalpy versus the isothermal crystallization temperature is summarised in Table 3. this paper, the sample mass is not required to analyze the results and is provided here merely for information. Note Above a crystallization temperature of 250 C, only one that the mass is, in our case, higher as compared to results melting peak is observed. The present sample is too given in other papers dealing with nano-DSC studies massive to evaluate the impact of the heating rate on the (generally around 50 ng). The goal is to ensure that bulk melting curves. To address this issue, a low mass sample crystallization is the main phenomenon during the cooling was prepared and the heating rate impact was evaluated of the sample. after isothermal crystallization at a given temperature. The Fig. 3 also provides the glass transition temperature of a results are presented in Tables 4 and 5. Tables 4 and 5 show, how the heating rate modifies the fully amorphous sample. In this case, the glass transition occurs at 154 C which is 10 K above the glass transition onset temperature T of both melting peaks and the ratio D D temperature from cooling at 10 K/min [1,2], but is consis- ( H1/ H2) of their areas. On the one hand, increasing the tent with the Bartenev-Ritland equation [36,37] regarding heating rate decreases the area of the second peak; it also the high scanning rate. decreases its onset temperature. On the other hand, increasing the heating rate increases the area of the first peak and its onset temperature. Thus, the partitioning of 3. Results the melting enthalpy between both peaks depends on the scanning rate, as detailed in Section 4.1. 3.1. Melting behavior

Fig. 4 presents the heating curves of the polymer after 3.2. Crystallization kinetics from isothermal measurements keeping it at various crystallization temperatures until completion of crystallization. The polymer exhibits a dou- In this sub-section, the procedure is applied for ble melting peak for crystallization temperatures below isothermal crystallization between 200 C and 280 C. The crystallization heat ﬂow is thus directly measured from the isothermal step. Fig. 5 presents the evolution of the heat ﬂow during isothermal crystallization at 240 C. The chosen baseline is

Fig. 3. Heating curve of a fully amorphous sample at 2 000K/s.

Table 2 Speciﬁc heat from ATHAS database for PEEK. Fig. 4. Heating curves of the PEEK at 2 000 K/s after complete isothermal Dcp (Tg) ¼ 0.254 [J/gK] crystallization at different temperatures in the range in between 170 C and cp (T > Tg) ¼ 1720 þ T * 1.54 [J/gK] 310 C. 14 X. Tardif et al. / Polymer Testing 36 (2014) 10–19

Table 3 Total melting enthalpy versus isothermal crystallization temperature.

Crystallization temperature (C) 170 180 200 210 220 230 240 250 260 270 280 300 310

DHm (mJ) 11.38 10.25 11.34 11.11 11.27 13.5 13.8 14.5 14.9 14.8 15.6 15.7 15.3

Table 4 Impact of heating rate on the melting curves after isothermal crystallization at 170 C.

Heating rate 500 K/s 1 000 K/s 2 000 K/s 5 000 K/s 10 000 K/s Isothermal crystallization at 170 C Onset T of 1st peak 197 C 199 C 202 C 203 C 200 C Onset T of 2nd peak 290 C 284 C 279 C 271 C 258 C

DH1/DH2 29.3% 32.3% 38.9% 47.9% 65.7%

Table 5 Impact of heating rate on the melting curves after isothermal crystallization at 200 C.

Heating rate 500 K/s 1 000 K/s 2 000 K/s 5 000 K/s 10 000 K/s Isothermal crystallization at 200 C Onset T of 1st peak 221C 225C 227C 227C 222C Onset T of 2nd peak 291C 288C 284CX X

DH1/DH2 35.6% 55.8% 61.1% X X

of a sigmoidal shape in order to take into account the evaluated between t1 and t2, which are the limits of the variation of the heat losses from the sample due to changes heat flow integration: of the material properties during crystallization. The de- R t gree of crystallinity of the sample is calculated from the 2 dh aðÞ¼ t1 equation: t (4) DHXP DH The relative crystallinity versus time (see Fig. 6) exhibits c ¼ XP (3) C mDH the typical “s” shape of the Avrami function [6–8] (Eq. 1). Based on our experimental data, the Avrami exponent DH is the heat of fusion of fully crystalline PEEK at TN m and kinetic coefficient were identified. They were esti- (130 J/g [38])andm is the mass of the sample. The mated by plotting the degree of crystallinity a with respect measured total enthalpy is 8.6 mJ, which corresponds to to time in the form ln(ln(1 a)) ¼ ln K þ n ln t. The slope 24.2 J/g and a degree of crystallinity of 19%, not taking of the curve gives then the n value and the offset gives the into account the temperature dependence of the heat of KAv value. Fig. 6 presents the evolution of the relative fusion. The same experiment was performed for fl crystallinity evaluated from the heat ow and the Avrami isothermal crystallization between 200 C and 280 C fit for isothermal crystallization at 240 C. The same pro- and the related crystallization enthalpies are summar- cedure was applied to isothermal crystallization data be- ised in Table 6. tween 200 C and 280 C (see Table 6). Thanks to the crystallization heat flow, the isothermal The Avrami exponent varies around an integer value relative crystallinity (also called degree of crystallization) is close to 3, while the Avrami coefficient passes through a maximum in a temperature range from 230C and 240C before decreasing as the temperature increases. Such behavior could be interpreted as the result of athermal nucleation accompanied by independent growth in three spatial directions. In such interpretation, the maximum in

Table 6 Crystallization half-time and ﬁt values for the Avrami parameters.

Temperature Crystallization DHC Avrami Avrami coefﬁcient n ( C) half-time (s) (mJ) exponent n KAv (s ) 200 1.36 7.2 2.80 0.272 210 1.1 5.8 2.71 0.850 220 0.51 8.6 2.74 4.15 230 0.48 9.2 2.97 5.05 240 0.5 8.6 3.13 5.02 250 0.62 9.1 3.3 3.04 260 0.78 8.1 2.60 1.61 270 1.4 8.1 2.96 0.60 280 2.32 6.8 2.80 0.0514 Fig. 5. Heat ﬂow during isothermal crystallization of PEEK at 240 C. X. Tardif et al. / Polymer Testing 36 (2014) 10–19 15

Fig. 8. Crystallization enthalpy versus the time for 240 C isothermal Fig. 6. Relative crystallized fraction evolution during isothermal crystalli- crystallization. zation at 240 C.

is the melting enthalpy. The glass transition is observed on the Avrami kinetic coefficient reflects the temperature the heating curves. The temperature range of the glass dependence of the growth rate, which is also characterized transition where the transition occurs depends on the de- by a maximum determined by the decrease of viscosity and gree of crystallinity. The amplitude of the DCp-step due to the decrease of thermodynamic driving force with increase the glass transition also decreases with the crystallinity of temperature (e.g. [39]). level. The evolution of the crystallization enthalpy measured 3.3. Isothermal crystallization kinetics from the melting from the continuous way and the discrete one are pre- curves sented in Fig. 8. The “discrete points” are estimated by integrating the melting heat flow of each curve. The At low crystallization rates, the related heat flow is not maximum enthalpy is more important for the discrete way high enough to be recorded accurately during an and its evolution does not exhibit the same s-shape of the isothermal step. For this reason, the discrete protocol has isothermal crystallization. From t ¼ 2 s, the melting been employed for the whole temperature range: from enthalpy evolves linearly. The crystallization half-time is 170 Cto310 C. The melting enthalpy was evaluated by defined as the time at which a(t1/2) ¼ 0.5. For the discrete integration of the heat flow (see Section 2.4). protocol, this parameter has been determined in the time Fig. 7 shows the melting curves of the PEEK sample after ranging from 0 up to the moment from which the relative isothermal crystallization at 240 C at different times (be- crystallinity further evolves linearly with time. tween 0.001 s and 100 s). The crystallization half-time from the discrete protocol The polymer was crystallized at 240 C for a specific and the continuous one are very similar. The same proce- time; it was then heated at a rate 2000 K/s up to 380 C. As dure was applied for temperatures below 200 C and above expected, the longer the crystallization time is, the greater 280 C and the results for the crystallization half-time are plotted in Fig. 9. The curve has a parabolic shape and the

Fig. 7. Heating curves of PEEK at 2 000 K/s after isothermal crystallization at 240 C. Fig. 9. Evolution of the crystallization half-time versus temperature. 16 X. Tardif et al. / Polymer Testing 36 (2014) 10–19 lowest crystallization half-time is reached for a tempera- peaks as originating from the melting of two populations ture between 230 C and 240 C. grown during the isothermal crystallization. In order to The Avrami coefficients below 200 C and above 280 C substantiate this conclusion, they performed isothermal are calculated from the crystallization half-time (Eq. 5) and crystallization at 310 C with various annealing times (from assuming n ¼ 3 (an instantaneous nucleation and a 1 min to 22 h) and compared the heating curves. However, spherical shape of the crystals or growth in three inde- they did not evaluate the impact of the heating rate. Ko pendent spatial directions). For those temperatures, the et al. [41] present the same conclusion. These authors crystallization curve is only measured by the discrete pro- identify thermal conditions for the existence of the double tocol. This protocol is very accurate but the number of melting peak behavior: a low cooling rate (lower than 5 K/ points is not sufficient to apply the classical method of min) or a constant temperature with annealing times estimation of KAv and n. Then, it has been shown in Table 3 varying between one to several minutes, depending on the that n is very close to 3 selected temperature. Tan et al. [42] also claim that the first sffiffiffiffiffiffiffiffiffi melting peak (at the lowest temperature) is due to the melting of the crystals formed by secondary crystallization, ¼ n ln 2 KAv (5) whereas the higher melting peak is caused by the melting t1=2 of the primary crystals. However, they did not evaluate the The values of KAv and n are re-presented in Fig. 10 for the scanning rate impact on the heating curves. whole temperature range. Fig. 4 presents the melting curves of the sample after isothermal crystallization between 170 C and 310 C. For 4. Discussion the crystallization temperature below 260 C, one observes two melting peaks. The second peak is located at the same 4.1. Melting behavior temperature, whereas the onset temperature of the first one increases versus the crystallization temperature. As far The double melting behavior of PEEK at high tempera- as more than one peak exists on the DSC curve, it is not tures (higher than 280 C) has been noted by many authors possible to assign these peaks to a given phenomenon, as for years. The double melting peaks are obviously the discussed above. To interpret this observation, scanning at consequence of the melting of two crystal populations. Two different heating rates after isothermal crystallization different processes can be the cause of this effect: (i) The (Tables 4 and 5) is a powerful method for removing the growth of two different crystal populations during indetermination. The results show that the high tempera- isothermal crystallization, (ii) a reorganization phenome- ture melting peak (n 2) tends to lower temperatures with non during the heating step. increasing heating rate. The other peak (n 1) moves to On the one hand, Cheng et al. [40] were among the first higher temperatures and the ratio of enthalpies DH1/DH2 is to observe the double melting peak. They showed that increasing. At a heating rate of more than 10,000 K/s, only increasing the heating rate increases the ratio of “low- to one melting peak remains. Thus, only one population of high-melting enthalpy” and suggested a reorganization crystals melts. At a given heating rate, as soon as some process as the origin. They also observed that the high- crystals are molten, the still oriented polymer melt re- melting peak does not change whereas the lower one in- crystallizes to form thicker (and thus stable) lamellae. This creases versus the isothermal crystallization temperature. continuous process proceeds until no further recrystalli- More recently, Wei et al. [21], through modulated DSC, also zation is possible and the final crystals melt (it depends on highlight the reorganization process after isothermal time determined by the heating rate). Final melting moves, crystallization from 280 C. therefore, to lower temperatures at higher heating rates. All On the other hand, from microscopic observations and these observations are evidence that the double melting DSC analysis, Basset et al. [38] explained the two melting peak is due to the melting-recrystallization process on heating. For a crystallization temperature higher than 260 C, a single melting peak is observed (Fig. 4) and is associated to the melting of crystals formed during the isothermal step. As the melting temperature increases, the recrystallization kinetics becomes too slow, avoiding a second melting peak of more perfect crystals [43].

4.2. Crystallization half-time

The crystallization half-time has been evaluated over the whole temperature range from the crystallization evolution curves (see Figs. 5 and 7). Its evolution versus temperature is shown in Fig. 9. Above and below the interval of 200–280 C, the crystallization half-time increases very quickly since crystalli- Fig. 10. Dependence of the Avrami kinetic coefficient and the Avrami zation is increasingly controlled either by diffusion at low exponent on temperature. temperatures or by nucleation at high temperatures. The X. Tardif et al. / Polymer Testing 36 (2014) 10–19 17 consistency of the data is confirmed by the results of Wang and coworkers ([3], red filled circles), since they show the same trend, and by isothermal crystallization measurements at high temperature (300 C < T < 320 C) with a DSC TA Q200 (black filled squares). However, our data and those of Kuo [22] do not agree. This deviation could be explained by chemical aging (crosslinking is known to occur in the melted state [44]) of the polymer, which is expected to slow down the crystallization kinetics.

4.3. Crystallization of PEEK

The crystallization curves shown in Fig. 8 both present results of isothermal crystallization at 240 C. As evident, they are slightly different. From the discrete protocol, the maximum crystallization enthalpy is found to be equal to 13.8 mJ, whereas the crystallization enthalpy measured Fig. 11. Comparison between discrete and continuous heat flows for from the continuous protocol is 8.6 mJ. At the initial states of isothermal crystallization at 240 C. the process (for times shorter than one second), the shapes of the two curves are very similar. However, they separate heat flow related to isothermal crystallization from the from each other after one second. While the enthalpy discrete data is calculated from the melting enthalpies (red determined via the continuous method tends rapidly to a squares). It is compared with the heat flux measured for constant value, evaluating it via the discrete method results isothermal crystallization (grey line). in a continuation of a linear increase of enthalpy over a The agreement between the discrete heat flow and the much larger time interval. In this latter case, the final part continuous heat flow is good at the beginning of crystalli- of the curve exhibits the typical secondary crystallization zation, but the crystallization rate determined from shape, which is a classical phenomenon for PEEK. The dif- continuous data decreases faster than that obtained from ference between the results is mainly due to the sensitivity the discrete method. The difference is due to secondary of the sensor. The heat flow associated with secondary crystallization, as discussed previously. In order to crystallization during an isothermal step is too low and comprehensively model the crystallization process, sec- released over a too long time to be measured, and is thus ondary crystallization is taken into account here through not contained in the continuous method data. the Hillier model [18], which considers the convolution of both crystallization processes. It is described by the set of 4.3.1. Primary crystallization kinetics Equations 6a–c: In this section, we propose to quantify the kinetics of Z t a ðÞ crystallization in the whole temperature range following aðÞ¼a ðÞþ 1 t a ðÞ s t 1 t a d 2 t (6a) the Avrami approach (secondary crystallization cannot be 0 1;m thus considered). The Avrami kinetic coefficient KAv and the exponent n are shown in Fig. 10. In the temperature range 200 C–280 C, both parameters are determined directly n1 a1ðtÞ¼a1;mð1 expðKAv;1,t ÞÞ (6b) from the continuous protocol curves. Outside this temperature range, KAv is computed from Eq. 5 in which n is sup- posed to be equal to 3 (deduced from experimental results ÀÁÀÁ n2 a2ðÞ¼t s a2;m 1 exp KAv;2ðÞt s (6c) in the 200 C–280 C temperature range). The KAv curve versus temperature has a bell-shape in agreement with where a(t) is the relative crystallinity. KAv,1 and n1 are the theory, and mirrors the crystallization half-time evolution. parameters of the Avrami model for primary crystallization. It has one maximum located at about 230C. The data Secondary crystallization is considered through n2 and points determined from flash DSC are the black unfilled KAv,2. am1 represents the quantity of crystalline part due to squares, and data points determined from classical DSC are Avrami crystallization and am2 is the quantity due to the black filled ones. According to the Avrami theory, values of secondary crystallization Then, a1(t) and a2(t) model the n (close to 3) tend to demonstrate that crystallization oc- primary and the secondary crystallization. They are defined curs following instantaneous nucleation and a three- and computed by the relations a1,m ¼ DHC/DHtot and dimensional growth of spherical entities. a2,m ¼ 1 a1,m $ DHtot and DHC are, respectively, the total

4.3.2. Secondary crystallization kinetics

Fig. 8 shows that secondary crystallization cannot be Table 7 ignored in the description of the overall crystallization ki- Parameters for Hillier’s model applied to model the isothermal crystalli- netics of PEEK, and it has also a very strong impact on the zation at 240 C.

ﬁnal level of crystallinity. The derivatives of both crystalli- n1 n2 K1 (s )n1 am1 DHC (mJ) K2 (s )n2 am2 DHtot (mJ) zation curves describing crystallization at isothermal con- 5.15 3 0.45 8.6 2.43 2 0.55 13.6 ditions are plotted in Fig. 11 for a temperature of 240C. The 18 X. Tardif et al. / Polymer Testing 36 (2014) 10–19

Table 8 Parameters of secondary crystallization.

Temperature (C) 200 220 230 240 250 260 280 300 310

am1 0.41 0.48 0.46 0.45 0.43 0.42 0.53 0.85 0.7 n 4 4 KAv,2 (s ) 0.23 1.73 2.42 2.43 1.71 0.80 0.282 9.10 1.04*10 n2 2222221 1 1

enthalpy of crystallization and the enthalpy of primary crystallization half-times between 0.5 and 2000 s. It has also crystallization available in Table 7. Then, a1(t) and a2(t) been demonstrated that the double melting peak behavior is model the primary and the secondary crystallization. due to the reorganization during the heating step. If secondary crystallization occurs through the growth The crystallization kinetics of PEEK has, therefore, been of new lamellae, the value of n2 can be considered to be studied for the first time over a very large temperature equal to 2, the K2 value is searched to get the best fitting of range by the Mettler Toledo Flash DSC 1 and compared to the data (see Table 7). In spite of the small number of data literature data. The Avrami kinetic coefficient has been points for the measured heat flow, Hillier’s approach is evaluated from isothermal crystallization in the range be- obviously capable of modelling secondary crystallization. tween 160 C and 310 C, whereas previous data were not This model fully fits the initial part of the continuous data available on this scale. The kinetics of crystallization of set, in particular the maximum heat flow because second- PEEK has only one maximum located around 230 C and its ary crystallization occurs at the end of primary crystalli- Avrami exponent is close to 3, thus suggesting instanta- zation. Then, the end of crystallization is in agreement with neous nucleation with subsequent spherical growth. the discrete data set. The same procedure is also applied for In addition to primary crystallization, a secondary crys- the other isothermal crystallization curves and the identi- tallization process has been observed based on data from the fied parameters are reported in Table 8. melting enthalpy evolution. A first evaluation of the sec- One observes that KAv,2 has its maximum at the same ondary crystallization kinetics parameters at a given tem- temperature as that of primary crystallization. The values of perature has been performed employing Hillier’s model. This KAv,2 have always the same order of magnitude as compared approach is shown to be capable to describe secondary to KAv,1. However, KAv,2 has smaller values than KAv,1 below crystallization for PEEK. In future, this phenomenon will have 260 C and higher values above 260 C. 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