Analysis of crystallization kinetics of poly(ether ether ketone) by a nonisothermal method
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Analysis of Crystallization Kinetics of Poly(ether etherketone) by a Nonisothermal Method
MING CHEN, CHIA-TING CHUNG
Institute of Materials Science and Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan 80424,Republic of China
Received 12 January 1998; revised 13 March 1998; accepted 13 March 1998
ABSTRACT: During cooling at a rate of 10°C/min from the melt state of PEEK we havefollowed the growth of spherulites using an optical microscope equipped with a camera.The isothermal growth rates of crystallization in the temperature range of 266–308°Ccould be estimated by means of a differential equation. These continuous growth ratedata were used further for kinetic analysis, which indicated that PEEK exhibited anunmistakable regime II3 III transition at 296°C. The results compared favorably withthose obtained by the traditional isothermal method, which is time consuming. Due tochain folding, the Thomas–Staveley constant should be closer to 0.25 instead of 0.1 or0.3. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2393–2399, 1998Keywords: PEEK; nonisothermal; growth rate; crystallization; kinetics
The mechanical properties of semicrystallinepolymer and its fiber-reinforced composites havecrucial dependence on the crystallinity and mor-phology of the polymer. It is well known that apolymer having small spherulites typically dis-plays higher fracture toughness than a polymerhaving larger spherulites. Many polymeric ob-jects may contain considerable material with themolecular morphology characteristic of regimeIII. It is therefore essential to understand thecrystallization behavior in order to produce mate-rials with controlled and reproducible properties.The thermal stability experiments1 indicated thatpoly(ether ether ketone) (PEEK) was stable innitrogen up to the temperature of 400°C, holdingfor 15 min. This treatment was effective in reduc-ing nucleation density to the point of allowingspherulitic growth rate measurements and mor-phology control. After this treatment, the subse-
quent crystallization behavior (isothermal ornonisothermal) became independent of the priorthermal history. Therefore, a wider range of crys-tallization temperature could be obtained, whichis of primary importance for a reliable analysis ofgrowth-rate data in terms of the nucleation the-ory, which was developed mainly by Hoffman andco-workers.2–5 Detailed kinetic analysis of the iso-thermal growth-rate data6 indicated the exis-tence of an unmistakable regime II 3 III transi-tion at 296 6 1°C for PEEK specimens, withoutdegradation and crosslinking. Values of the lat-eral surface free energy (s) and the work of chainfolding (q) suggested that the energy barrier (U*)should be taken nearer to 1500 cal/mol in the caseof T` 5 Tg 2 30 K and 2000 cal/mol in the case ofT` 5 Tg 2 51.6 K. The relative differences ofgrowth rates between the solvent cast films andthe melt pressed films became larger at temper-atures above the regime transition.6
Another effect was observed in both short andcontinuous carbon fiber-reinforced PEEK compos-ites. The results of crystallinity measurement at aDSC (differential scanning calorimetry) heatingrate of 50°C/min indicated that the upper peaktemperature of double-melting peaks and the de-
Correspondence to: M. Chen (E-mail: [email protected])Journal of Polymer Science: Part B: Polymer Physics, Vol. 36, 2393–2399 (1998)© 1998 John Wiley & Sons, Inc. CCC 0887-6266/98/132393-07
gree of crystallinity were related to the regimetransition from II to III in both studies of isother-mally and nonisothermally crystallized speci-mens.7–9
The traditional method of measuring isother-mal growth rates is time consuming, especiallywhen the spherulitic growth rate is low at thehigher crystallization temperature. At the lowercrystallization temperature, both the nucleationdensity and the growth rate may be too high to bemeasured by the isothermal method. In thisstudy, a dynamic crystallization method via dif-ferential equations10 was used to measure theisothermal spherulitic growth rates of PEEK bymeans of polarized light microscopy (PLM). Theresults compared favorably with those obtainedby the traditional isothermal method. In thepresent work, we shall demonstrate that, in therange of crystallization temperature consideredin this work, an unmistakable regime II 3 IIItransition is exhibited at 296°C. This microscopicstudy also showed that there was no morpholog-ical change between regimes II and III. Finally,the a value in the modified Thomas–Staveleyequation11 will be discussed.
PEEK powder, commercial-grade 150P, was ob-tained from ICI. All the samples were carefullydried at 120°C under vacuum before use. Jonas etal.12 measured the molecular weight of PEEK150P by gel permeation chromatography. Aver-age results gave Mn 5 10,300 g/mol, Mw 5 26,800g/mol, and Mz 5 52,200 g/mol.
Polarized Light Microscopy
A Nikon Optiphot-pol polarizing microscope wasused in conjunction with a Linkam THMS-600heating stage. The stage was equipped with aLinkam TMS-91 temperature control systemwhich enabled samples to be heated and cooled atan adjustable rate. The development of thespherulites was followed by photography at ap-propriate intervals with a Nikon camera attachedto the microscope. The magnification of eachrun was calibrated by photographing a stagemicrometer whose smallest division is 10 mm. Af-ter the film was developed, the spherulitic radiiwere measured from the photographs.
Growth rate measurements were always con-ducted on freshly made films. The specimens wereprepared by placing a small amount of the poly-mer (powder form) on a thin circular cover glassand placing another circular cover glass on top ofthe powders. The resulting sandwich was placedon a small hot block regulated at 395 6 1°C tomelt PEEK for 3 min under nitrogen. A thin filmwas obtained by applying a slight pressure on thetop cover glass. The material was then slid off themelting block onto the heating stage under nitro-gen atmosphere and heated at 100°C/min fromroom temperature to 400°C and kept at 400°C for15 min in order to melt the crystalline residues.The edge of the specimens was focused to monitorthe spherulitic growth. In the dynamic crystalli-zation experiment, the sample was quickly cooledto and remained at 310°C for 10 s in order to getsuitable size and amount of spherulites. Next ascan from 310°C to 250°C at a cooling rate of10°C/min was photographed. When performingisothermal crystallization experiments, the sam-ple was quickly (130°C/min) cooled to a chosencrystallization temperature, Tc, and held at thistemperature while recording the crystallizationas a function of time.
RESULTS AND DISCUSSION
Dynamic Growth Rates
Figure 1 shows three photographs of a series ofPLM micrographs to illustrate the spheruliticmorphology of PEEK crystals at 290°C, 273°Cand 268°C, on which the spherulitic sizes weremeasured. Each spherulite with size larger than10 mm can be used to evaluate the growth ratesbefore impingement. Typical patterns of the Mal-tese cross extinction were evident, but the bound-ary of spherulites was not clear because of thelong exposure time. If a CCD camera is available,the above problem could be solved and the coolingrate of the dynamic crystallization could be in-creased above 10°C/min. It is also observed inFigure 1 that the number of nuclei slightly in-creased with decreasing crystallization tempera-ture and the lowest temperature at which spheru-litic sizes could be measured was 266°C. Belowthis temperature both the nucleation density andthe growth rates were too high to be measured.The radius variation of one typical spherulite dur-ing the temperature ramp at a cooling rate of
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10°C/min is shown in Figure 2. One more point at330°C is added by assuming the radius was zero.A curve fitting method was used to fit the radii ofthe spherulite and was graphically plotted as asolid line in Figure 2. Polynomial fitting withorder greater than 3 gives a curve that decreasessmoothly in the temperature range of 310–330°C.To simplify the calculation of growth rates for thistypical spherulite, we choose a fourth-order equa-tion which can be written in the form
R 5 f~T! 5 2.3831 3 104 2 2.8884 3 102*T
1 1.3099*T2 2 2.6319 3 1023*T3
1 1.9749 3 1026*T4
where R is the radius of spherulite as function oftemperature in unit mm and T is the temperaturein unit °C. The radius–temperature relation canbe obtained by differentiating the above equationwith respect to T.
dRdT 5 f9~T! 5 22.8884 3 102 1 2.6198*T
2 7.8957 3 1023*T2 1 7.8996 3 1026*T3 (1)
Similar differential equations can be obtained forthe other spherulites before impingement.10 Usu-ally R is a function of T and time (t). In thisdynamic study, two variables, T and t, are relatedby a constant cooling rate of 10°C/min. There isonly one independent variable for R. Therefore
dRdT 5 f9~T! 5
The value of dR/dT at a chosen temperature canbe evaluated from eq. (1). The isothermal growthrate (dR/dt, in unit mm/sec) at that chosen tem-perature can be estimated by substituting thevalue of dT/dt (21/6°C/sec, i.e., 210°C/min) intoeq. (2). The fitted growth rates versus crystalliza-tion temperature are plotted as a dash line inFigure 3. A third-order equation, eq. (1), can beused to fit these growth rate data without theupturn phenomenon below 310°C. As expected,this confirms the decrease of the growth rate withtemperature increase from 266°C to 310°C. Thedata from the dynamic crystallization experimentwere a continuous curve which can be used fur-ther for kinetic analysis.
Figure 2. Variation of spherulitic radius with tem-perature during the temperature ramp at a cooling rateof 10°C/min from 310°C.
Figure 1. Polarized light micrographs showing thespherulitic growth at (a) 290°C, (b) 273°C, and (c)268°C from the dynamic crystallization experiment at acooling rate of 10°C/min. The scale bar corresponds to50 mm.
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Isothermal Growth Rates
By measuring the spherulitic radii from PLM mi-crographs taken at successive intervals duringthe isothermal crystallization, the growth ratewas determined by a linear least-squares fit of theinitial linear portion of the growth rate curvesbefore impingement. The average growth ratesover numerous spherulites were 42 6 2, 45 6 2,52 6 3, 76 6 4 and 95 6 5 3 1023 mm/sec at 298,297, 295, 290, and 287°C, respectively. Dynamicgrowth rates were compared with the data fromthe isothermal crystallization experiments whichare plotted as open diamonds in Figure 3, show-ing good agreement between these experiments.Thus, we have demonstrated that the tediousmeasurement of isothermal spherulitic growthrate may be replaced by a single dynamic exper-iment which yields results identical to those fromthe traditional method, but in a wider tempera-ture range. Comparing the growth rates at thesame temperature, the values in this study wereless than those obtained in a previous study,6
because the edge of the specimen was thinnerthan the central part of itself. The lower nucle-ation density at the edge of the specimen alsoallowed the growth rates to be measured at lowertemperatures.
Existence of Regime II 3 III Transition
Let us follow the regime analyses of the Laurit-zen–Hoffman (LH) model,2 to treat our fittedgrowth rate data shown in Figure 3. The growth
rate of polymers during crystallization is de-scribed in a given regime by eq. (3).
G 5 G0 exp@2U*/R~Tc 2 T`!#
3 exp@2Kg/Tc~DT!f# (3)
where U* and T` are the WLF (Williams-Landel-Ferry) energy term and WLF temperature, re-spectively, Tc is the crystallization temperature,DT [ (Tm
o 2 Tc) is the undercooling, Tmo is the
equilibrium melting temperature, and f is a cor-rection term of the order of unity, usually repre-sented by
f 5 2Tc /~Tmo 1 Tc! (4)
Kg 5 nb0sseTmo /rkDhf (5)
where n 5 4 for regimes I and III and n 5 2 forregime II. The layer thickness is b0, s is thelateral surface free energy, se is the fold surfacefree energy, r is the density, k is the Boltzmannconstant, and Dhf is the heat of fusion per unitweight of crystal at the equilibrium melting tem-perature Tm
o . The preexponential factor G0 hasonly a weak dependence on temperature.
Following the results of a previous study,6 1500cal/mol and Tg 2 30 K were chosen for the val-ues of U* and T`, respectively. The values Tm
5 395°C 5 668 K and Tg 5 418 K were employedfor PEEK.13 Figure 4 shows a plot of log G 1 U*/
Figure 4. Kinetic analysis of the dynamic growthrate data. In this case, U* 5 1500 cal/mol, T` 5 Tg 2 30K, and the growth rate data from 268°C to 296°C areused to fit a linear line in the higher undercoolingregion.
Figure 3. Comparison of the calculated isothermalgrowth rates with the data points from the isothermalcrystallization experiments.
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2.303R(Tc 2 Tg 1 30) versus 1/Tc(DT)f, which canthus provide the value of Kg (slope 3 2.303) andlog G0 (intercept) for each regime. In this case, thegrowth rate data from 266°C to 296°C were usedto fit a linear line in the higher undercoolingregion. The excellent fit with two lines is reflectedin the correlation coefficients (.0.988). The breakin the curve occurs at Tc 5 296°C, and the ratio ofthe slopes is 1.806. The values of the kinetic pa-rameters are tabulated in row 4 of Table I. Thelast data point for the fitted linear line in thehigher undercooling region (see the second col-umn of Table I) was then varied separately tomaximize the correlation coefficients in columns 3and 7. Table I shows the results of these calcula-tions. Any correlation coefficient above 0.988 rep-resents an extremely good fit of the data and thebest is marked in bold font. It is immediately seenthat an attempt to put one straight line throughall the data would lead to an inadmissible fit. Thepresence of two distinctly linear regions is there-fore unmistakable.
Day et al.14 reported that only one sample (Mw5 32,000) showed a regime II 3 III transition atabout 298°C, which was based on the overallgrowth rate data, the assumption that theAvrami exponent was normalized to n 5 2, and aset of T` 5 Tg 2 55 K and U* ' 4500 cal/mol.Kinetic analyses for the other two sets of U*, T`,with values of (2000 cal/mol, Tg 2 51.6 K) and(4500 cal/mol, Tg 2 55 K) are also tabulated inTable I. The results indicate that the data rangefrom 266°C to 296°C used to fit a linear line in thehigher undercooling region maximizes the corre-lation coefficient in both cases; they are marked inbold font. Thus, we have shown that PEEK exhib-its an unmistakable regime II3 III transition at296°C (see last column of Table I). This constanttransition temperature fits very well with the pre-diction of 296 6 1°C proposed in the previousstudy.6
Determination of s and q
Once the regimes have been established, thegrowth rate data can be used to obtain sse byusing eq. (5). With the values b0 5 0.468 nm,15 Tm
5 395°C, Dhf 5 130 J/g as determined by Blundellet al.,13 and the corresponding values of Kg listedin the fourth and eighth columns of Table I, ssecan be obtained for both regimes. Hay et al.16
measured the amorphous density of quenchedPEEK as 1.2642 6 0.001 g/cm3 by displacement inwater at 20°C and gave the crystalline density as Tab
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1.378 6 0.005 g/cm3 by wide-angle X-ray scatter-ing. The density of PEEK is estimated to be 1.30g/cm3 by assuming 32% crystallinity. If one as-sumes that the folding surface free energy of thelamellae is unlikely to change significantly withrespect to temperature and that changes in theproduct can be assigned solely to s, it is possibleto estimate s as sse/se. The value se 5 49 ergcm22 was determined by Blundell et al.13 andused in this work.
The lateral surface free energy (s) is listed inthe columns 5 and 9 of Table I. Judged in com-parison with the undesirable feature that s $ se(49 erg cm22) and the Kg’s ratio exceeds 2, theresults indicate that the set of T` 5 Tg 2 55 K andU* ' 4500 cal/mol is not acceptable for PEEK150P. In the other two sets of U*, T` with valuesof (1500 cal/mol, Tg 2 30 K) and (2000 cal/mol, Tg2 51.6 K), we find that the s(II) of the best fit wasaround 36 erg cm22, which was close to Blundell’sestimation of 37 erg cm22. The ratio of Kg (see thetenth column) is about 1.80 for best fits. The Kg’sratio exceeds 2 is marked in parenthesis. Table Ialso illustrates changes in G0(III)/G0(II), the ratioof pre-exponential factors, which is given in theeleventh column. The ratio of G0(III)/G0(II) for thebest fits is about 1.4 3 103.
In the past, most assessments of the surfacefree energies, s, have relied on the use of themodified Thomas–Staveley equation,11 where thevalue a 5 0.1 was assumed to be universal. Thisexpression is
s 5 arDhfo~a0b0!
where r Dhfo and a0b0 are, respectively, the en-
thalpy of fusion per unit volume and the cross-sectional area of a chain in the crystal. The re-sults of the Roitman et al.17 study demonstratedthat the Thomas–Staveley constant is not at alluniversal and strongly depends on the chemicalnature of the polymer of interest. They proved thea value for poly(pivalolactone) is 0.25. This vari-ation of a with the chemical nature of the polymeris not yet understood, but may be related to en-tropic difference at the crystal/melt interface.
The work of chain folding q can be calculatedfrom
q 5 2a0b0se (7)
Combining eqs. (6) and (7), we get
q 5 2se~s/arDhfo!2 (8)
If one assumes se > 49 erg cm22 for the foldingsurface free energy, eq. (8) becomes q 5 4.943 1024 (s/a)2 kcal/mol, where the lateral surfacefree energy s is in the unit of erg cm22. From thevalues of s given in Table I, we can find that thework should be 51.1 kcal/mol in regime III, 63.1kcal/mol in regime II if a 5 0.1, and should be 8.2kcal/mol in regime III, 10.1 kcal/mol in regime IIif a 5 0.25. The work of chain folding appearsunreasonably high for a 5 0.1. Therefore for thecase of PEEK, a is close to 0.25 instead of 0.1.
As the melting temperature rises, the work ofchain folding increases because the stiffer chain isharder to bend to make the fold. Observe that it isq, and not se, that scales smoothly upward as Tm
increases. Thus one would expect q to increase asTm
o increases. Lovinger et al.18 estimated thework of chain folding for the medium molecularweight poly(p-phenylene sulphide) to be 8.9 kcal/mol by the selection of a 5 0.3. Consequently,high values should be expected from the quitestiff molecules of PEEK. The choice of a 5 0.3gives a work of 5.67 kcal/mol in regime III and7.02 kcal/mol in regime II. s and q values appearunreasonably low for a 5 0.3.
In one simple, dynamic experiment, at a coolingrate of 10°C/min, we have estimated the isother-mal growth rates of crystallization of PEEK in thetemperature range of 266–308°C. The data fromthe dynamic crystallization experiment was acontinuous curve which can be extended to alower temperature than the data points from theisothermal crystallization experiments. Thesecontinuous growth rate data can be used furtherfor kinetic analysis. They indicate that PEEK ex-hibited an unmistakable regime II 3 III transi-tion at 296°C. This constant transition tempera-ture fits very well with the prediction of 296 6 1°Cproposed in the previous study of isothermal crys-tallization experiments.
Values of s and q suggested that the set of T`
5 Tg 2 55 K and U* ' 4500 cal/mol was unac-ceptable. In the other two sets of U*, T` withvalues of (1500 cal/mol, Tg 2 30 K) and (2000cal/mol, Tg 2 51.6 K), we can find that s(II) of thebest fit was around 36 erg cm22, which was closeto Blundell’s estimation of 37 erg cm22. The ratio
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of preexponential factors, G0(III)/G0(II) was de-termined to be 103. The Kg(III)/Kg(II) ratio (1.80)was close to the predicted value of 2 as was Hoff-man’s ratio. The work of chain folding appearedunreasonably high for Thomas–Staveley constanta 5 0.1 and low for a 5 0.3. Therefore a is close to0.25 instead of 0.1 or 0.3 for the case of PEEK.
This work is financially supported by the National Sci-ence Council, ROC, under contract number NSC 80-0405-E110-01.
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