Poly(p-phenylene sulfide) nonisothermal cold-crystallization

Poly(p-phenylene sulfide) NonisothermalCold-Crystallization

ANDREA MARTINELLI,1 LUCIO D’ILARIO,1 RUGGERO CAMINITI2

1Dipartimento di Chimica, Universita di Roma ‘‘La Sapienza’’, PO Box 34-ROMA 62, Rome, Italy

2Istituto Nazionale per la Fisica della Materia, Universita di Roma ‘‘La Sapienza’’, PO Box 34-ROMA 62, Rome, Italy

Received 22 February 2005; revised 7 June 2005; accepted 22 June 2005DOI: 10.1002/polb.20554Published online in Wiley InterScience (www.interscience.wiley.com).

ABSTRACT: The poly(p-phenylene sulfide) (PPS) nonisothermal cold-crystallizationbehavior was investigated in a wide heating rate range. The techniques employedwere the usual Differential Scanning Calorimetry (DSC), and the less conventionalFT-IR spectroscopy and Energy Dispersive X-ray Diffraction (EDXD). The low heatingrates (U) explored by EDXD (0.1 K min�1) and FT-IR (0.5–10 K min�1) are contiguousand complementary to the DSC ones (5–30 K min�1). The crystallization temperaturechanges from 95 8C at U ¼ 0.05 K min�1 to 130 8C at U ¼ 30 K min�1. In such a widetemperature range the Kissinger model failed. The model is based on an Arrheniustemperature dependence of the crystallization rate and is widely employed to evalu-ate the activation energy of the crystallization process. The experimental results weresatisfactorily fit by replacing in the Kissinger model the Arrhenius equation with theVogel–Fulcher–Tamann function and fixing U* ¼ 6.28 k J mol�1, the activationenergy needed for the chains movements, according to Hoffmann. The temperature atwhich the polymer chains are motionless (T? ¼ 42 8C) was found by fitting the exper-imental data. It appears to be reasonable in the light of our previously reported iso-thermal crystallization results, which indicated T? ¼ 48 8C. Moreover, at the lowerheating rate, mostly explored by FT-IR, a secondary stepwise crystallization processwas well evidenced. In first approximation, it contributes to about 17% of the crystal-linity reached by the sample. VVC 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys

43: 2725–2736, 2005

Keywords: poly(p-phenylene sulfide); crystallization; FT-IR; differential scanningcalorimetry (DSC); energy dispersive X-ray diffraction (EDXD)

INTRODUCTION

High Tg and Tc polymers are particularly suit-able for studying the cold-crystallization processthat can easily be followed above room tem-perature (the amorphous glassy state beingobtained by quenching). Among these polymersthe most studied ones are poly(ether ether ketone)(PEEK),1–3 poly(ethylene terephthalate) (PET),4,5

poly(ethylene naphthalate) (PEN),6 and poly(p-phenylene sulfide) (PPS).7,8

Although till now the cold-crystallization hasnot played an important role in the technologi-cal applications of polymers, the melt crystalli-zation being the principal process of industrialmanufacturing, a number of papers has beenpublished on this topic. They were mainly con-cerned with the kinetic aspects of the process1–9

and the way it is influenced by the molecularweight,10,11 chain orientation,12 aging below andabove Tg,

13–15 and by the exposure to theorganic solvents.16 In particular, in recent yearsthe very early stage of the cold-crystallization

Correspondence to: L. D’Ilario (E-mail: [email protected])

Journal of Polymer Science: Part B: Polymer Physics, Vol. 43, 2725–2736 (2005)VVC 2005 Wiley Periodicals, Inc.

2725

process has been investigated. The density fluc-tuations in glassy films of PET17,18 and PEN19

were measured during the annealing above Tg

by using the time-resolved small-angle X-rayscattering (SAXS) technique. In those experi-ments a spinodal decomposition type of phaseseparation was observed, whose characteristicwavelength is longer than that of the intercrys-talline correlation peak (long period peak). Sucha process was enlightened during the crystalli-zation induction period, that is, the period pre-ceding the appearance of either the wide-anglediffraction (WAXD) crystalline peak or that ofthe Differential Scanning Calorimetry (DSC)endothermic crystallization peak. It was noticedthat the maximum of the SAXS scattering inten-sity profile during the induction period shiftedtoward smaller q while the maximum intensityincreased.

A different behavior was found in isothermalcold-crystallization experiments carried out inour laboratory on the glassy PPS.8 We observedthat the crystallization induction time was veryshort or absent when annealing at temperaturesvery near to the Tg. Such a behavior could bedue to a heterogeneous nucleation mechanism,eventually originated by the presence of a largenumber of crystalline nuclei in the amorphousmaterial, grown during the quenching of themelt polymer. Such nuclei should be character-ized by a very short and nonhomogeneous rangeorder, which is not able to produce Bragg reflec-tions during the X-ray diffraction experiment.This behavior could be troublesome in the cold-crystallization kinetic investigation carried outby the DSC technique. Indeed the lack of theinduction period and a very high crystallizationrate could induce a polymer nonisothermal crys-tallization during the thermal stabilization ofthe calorimeter or during the sample heating.On the other hand the attempt to slow down thecrystallization kinetic by choosing a temperaturevery near to Tg does not succeed because of theinsufficient apparatus sensibility in measuringthe low heat fluxes. All these problems oftenmake narrow the temperature range in whichthe DSC technique can collect reliable experi-mental data for verifying kinetic theories.

In the aforementioned paper8 we reported ourresults, obtained in a wide crystallization tem-perature range (90–112 8C), on the PPS isother-mal cold-crystallization kinetic. We were able tocarry out such an investigation by using threedifferent experimental techniques. The first one

was the usual DSC technique, by which weexplored the highest temperature range. Thesecond and the third ones were the less conven-tional FT-IR spectroscopy and the Energy Dis-persive X-ray Diffraction (EDXD), useful inexploring the lowest temperature range inwhich the crystallization process is particularlyslow.

The same three techniques were nowemployed to investigate the nonisothermal cold-crystallization of PPS, thus enlarging the usu-ally studied heating rate range. The low heatingrates U explored by EDXD (0.1 K min�1) andFT-IR (0.5–10 K min�1) are in fact contiguousand complementary to the DSC ones (5–30 Kmin�1). The FT-IR and EDXD spectra collectedduring the polymer crystallization at U � 10 Kmin�1 are indeed few and not profitable for acorrect description of the process. On the otherhand the heat flow associated with the transfor-mation may be correctly measured only whenthe transition is fast enough, that is at rela-tively high temperature. The DSC signal was infact properly recorded from U ¼ 5 K min�1. Theresults of such a work will be illustrated in thepresent paper.

EXPERIMENTAL

PPS Ryton V-I (hMwi ¼ 14,000; hMni ¼ 11,000)from Phillips Petroleum was purified by a pre-vious treatment with tetrahydrofuran in Soxhletcolumn to remove all the low molecular weightspecies. For all the experiments the sampleswere prepared by heating the polymer at 300 8Cfor 40 min and then by quenching it in liquidnitrogen. The over Tm temperature and the resi-dence time in the melt state were chosen toensure an optimal rearrangement of the polymerchains, allowing the best loss of the order char-acteristic of the original crystalline phase with-out significant changes of the chemical nature ofthe polymer (crosslinking, degradation etc.).

The DSC (Differential Scanning Colorimetry)measurements were carried out under N2 flowby means of the Mettler TA3000 instrument,equipped with a silver furnace. About 8 mg ofquenched sample were heated from 25 to 320 8Cat a heating rate ranging from 5 to 35 K min�1.

IR spectroscopical measurements were accom-plished by Mattson Galaxy 5020 FT-IR instru-ment working at 1 cm�1 resolution. Samples wereheated in the range of 23–140 8C at heating rate

2726 MARTINELLI, D’ILARIO, AND CAMINITI

(U) ranging from 0.005 to 10 K min�1 using aSpecac P/N 21525 variable temperature cell,driven by a Hellma P/N 830004 temperature con-troller. The number of the collected interfero-grams for each spectrum was varied according toU (i.e., 50 for U ¼ 0.005, 0.1, and 0.5 K min�1;25 forU ¼ 1Kmin�1; 5 forU ¼ 4, 7, and 10Kmin�1),so that the temperature at the beginning and at theend of each spectrum did not differ by more than 1 K.The calibration of the heating cell was carried outfor each U by standard organic compounds, asreported in a previous paper.20 All the experi-ments were accomplished by dispersing the poly-mer powder in KBr disks. The disks were firstheated at 300 8C for 40 min and then quenched inliquid N2.

The application of the Energy Dispersive X-ray Diffraction (EDXD) technique to the studyof phase transitions has been recently pro-posed21 for the dynamic investigation of thestructural transformations of inorganic and poly-meric materials. Unlike DSC, the EDXD techni-que may reveal transitions involving a modestheat flux as the slow ones or those betweenstructural states characterized by a comparableentropic content.

The samples for the EDXD experiments wereprepared according to the aforementioned proce-dure by using about 200 mg of polymer. The sam-ple thickness was about 2 mm. The variable tem-perature cell of IR experiments was employed,keeping the samples under dynamic vacuum. Thesample temperature was recorded with a K-typethermocouple hold in physical contact with thepolymer. The temperature range explored was25–140 8C at a heating rate of 0.1 K min�1. Thediffraction experiments were carried out in trans-mission geometry by using an energy-dispersiveX-ray diffractometer assembled in our labora-tory22 on a Seifert and Rich high-voltage powersupply, whose stability is better than 0.1%. A dif-fraction angle of 58 was used, corresponding to1 < q < 4 A�1 and allowing the observation of themain diffraction peaks. Each spectrum was meas-ured for 200 s. The detailed description of theexperimental apparatus and measurement proce-dure was reported elsewhere.20

RESULTS AND DISCUSSION

EDXD Analysis

In Figure 1 the PPS EDXD profiles are reported.They were recorded at different temperatures

during the heating process carried out at 0.1 Kmin�1. The sharp peaks at q below 1.1 A�1 aredue to the fluorescence of the X-ray source.

The most evident variations are due to thesharpening of the peak centered at q ¼ 1.36A�1, which drastically increases during crystalli-zation and shifts to 1.42 A�1 (assigned to thenot resolved (110), (111), and (200) crystalplanes reflections) and to the transformation ofthe amorphous sample shoulder, observed atq ¼ 1.85 A�1, into a well-defined peak (not resolved(112) and (211) reflection). Moreover the appear-ance of four new shoulders at 2.1, 2.5, 2.7, and3.1 A�1 may be clearly distinguished in the spec-trum recorded at 105 8C (assigned to (020),(311), (114), and (223) reflection, respectively).

After the spectral analysis we decided toinvestigate the total radiation intensity changesmeasured in the q regions 1.30–1.53 A�1 and2.26–2.82 A�1, that is, where the largest modifi-cations are localized. Such a procedure, set up

Figure 1. Poly(p-phenylene sulfide) EDXD profilesrecorded at different temperatures during the heatingprocess carried out at 0.1 K min�1.

POLY(P-PHENYLENE SULFIDE) NONISOTHERMAL COLD-CRYSTALLIZATION 2727

in the PPS glass transition study,20 was chosento evaluate the actual scattering vector set var-iations, avoiding the possible compensationeffects that could arise on the contrary in theanalysis of the integral change. This indeedcould hide the complexity of the transformation.In Figure 2 the results of such an analysis arereported.

As for the glass transition case,20 the diffractedX-ray intensity strongly depends on the scatter-ing vector range analyzed when the polymer isheated up to the crystallization temperature.

The main effects evidenced by Figure 2 maybe summarized as follows:

1. All the figures show a marked intensity dropat 87 8C. Such a temperature may be consid-ered as the glass transition process onset,which was discussed in a previous paper.20

2. The q regions 1.30–1.53 A�1 and 2.26–2.82A�1 evidence at 97 8C, the onset of the cold-crystallization, leading to the sudden dif-fracted intensity increase, followed (in bothcases) by a slower increase that may be attrib-uted to a secondary crystallization process.

The conversion degree of the crystallizationprocess may be evaluated by the equation

XðTÞ ¼ ðIt � IinÞ=ðIfin � IinÞ ð1Þwhere Iin and Ifin are the intensity scatteredby the sample before (T ¼ 97 8C) and after

(T ¼ 108 8C) the transition. For all the scatter-ing vectors studied the vmax was reached at99 8C. Even if it was difficult to detect the tran-sition end, the total time from the onset to theend of the crystallization process was found tobe independent of the spectral range chosen.The following table shows the values of the max-imum rate of transformation [dX(T)/dt]max rela-tive to the different EDXD regions (q) analyzed.

FT-IR Analysis

The temperature change effect on the infraredspectra may generally be rather complex,depending on the temperature range as well ason the physical state of the sample, and mayinvolve peak intensity, shape, and frequency.Such spectral modifications may arise from tem-perature-induced structural changes and tem-perature-induced spectroscopic changes.23 Infact, starting from the Beer’s law, the tempera-ture dependence of the band intensity associatedwith a sample component of concentration Xmay be expressed as

dIk=dt ¼ ek dX=dT þ X dek=dT ð2Þ

where ek is the extinction coefficient at thewavelength k, which is usually assumed to belinearly dependent on the temperature.

When the absorptions are associated with thedifferent structural components of a sample,that is the crystalline or amorphous fraction of asemicrystalline polymer, the infrared spectros-copy can be helpfully employed to follow thethermal transitions. Concurrently a slopechange of the band intensity as function of tem-perature may be observed.

Such a phenomenon was employed by us todetermine the glass transition temperature ofthe amorphous PPS in experiments carried outin the wide heating rate range of 0.05–7 Kmin�1.20 Although only a few absorptions ana-lyzed as function of T show a discontinuity incorrespondence of the glass transition, the over-all infrared spectrum changes when the crystal-lization process takes place. Figure 3 shows the

Figure 2. EDXD total radiation intensity changesmeasured in the q regions (A) 1.30–1.53 A�1 and (B)2.26–2.82 A�1.

q (A�1) [dX(T)/dt]max(10�4 s�1)

1.30–1.53 3.72.26–2.82 2.6


intensity variations of the peaks at 819, 1072,1091, and 1570 cm�1 (U ¼ 0.05 K min�1).In Table 1 the assignments after Zimmermanet al.24 are reported. The absorbance values areshifted for sake of clarity.

At T � 84 8C the abrupt absorbance increasereveals the cold-crystallization process, whichproceeds in two steps, the primary and secon-dary crystallization. This feature confirms theanalogous effect found by us in isothermal

experiments, in which a stepwise crystallinityincrease, described by the Avrami law, wasdetected after the primary process.8

As it may be seen the bands at 819, 1091,and 1570 cm�1 are those that better reveal thesecondary crystallization process, the primaryone being well evidenced also at 1072 cm�1.

The 819 cm�1 band, due to the C��H out-of-plain bending and sensitive to the packing ofnearby chains,24 is characterized by a low valueof dek/dT over all the temperature range studied.The intensity variation of the aforementionedband will therefore be employed for the kineticanalysis of the PPS nonisothermal crystalliza-tion described elsewhere.

The crystallization onset temperature Tonsetc ,

measured at the beginning of the transforma-tion, increases with U, as it is shown in Figure 4,and does not vary in the different spectralregions. To compare the spectral evolution of thedifferent experiments the absorbance ratio (R) ofthe bands at 1091 and 1072 cm�1, which is ameasure of the relative polymer crystallin-ity,24,25 was followed as a function of the heatingrate. Figure 5 shows such a variation in corre-spondence to the apparent end of the primaryand secondary crystallization, that is by exclud-ing overlapping processes.

As it may be seen, greater crystalline conver-sion is reached at higher U, that is in the trans-formation processes taking place at highertemperature. Such a finding, which was alsoobserved in our isothermal cold-crystallizationstudy,8 may be better interpreted in the light ofthe higher diffusional capacity of the polymerchains at the highest temperature. Indeed the

Figure 3. Absorbance variation of the peaks at1570, 1091, 1072, and 819 cm�1 as a function of tem-perature (U ¼ 0.05 K min�1). The absorbance valuesare shifted for sickness of clarity.

Table 1. Infrared Band Assignments of PPS According to Zimmerman24

Peak Position(cm�1) Band Assignment Note

819 C��H o.p.deformation

Crystalline band, sensitive to thepacking of nearby chains

1072 Sym. ring��Sstretching

Active in the IR because of the breakdownof the selection rules in theamorphous phase. Decreases with thechain symmetry

1091 Anti. ring��Sstretching

Increases with the chain symmetry

1570 Sym. C��C ringstretching

Active in the IR because of the breakdownof the selection rules in theamorphous phase. Decreases with thechain symmetry


faster the crystallization rate, the larger thedegree of order achieved. Moreover, Figure 5shows that the stepwise secondary crystalliza-tion represents about the 17% of the total proc-ess, independent of the heating rate.

DSC Analysis

The DSC technique may be convenientlyemployed to record the heat flow involved in thetransition at the highest heating rates. The DSCthermogram of quenched PPS carried out atU ¼ 10 K min�1 is shown in Figure 6.

The presence of the glass transition is wellevidenced in the thermogram and its onset isindicated by the arrow (Tonset

g ). Such a transitionis followed by the exothermic crystallizationprocess (the arrow indicates the beginning ofthe transition Tonset

c ) and then by the endother-mic melting peak (Tm). As it may be seen thecrystallization peak shows a shoulder at highertemperature. Such a phenomenon was alsoobserved by Menczel and Collins26 who found adouble endothermic crystallization peak in theirDSC experiment performed at U ¼ 10 K min�1

on quenched PPS.The effect of the heating rate on the PPS

cold-crystallization thermograms is shown inFigure 7. As U increases the first exothermicpeak shifts at higher temperature becoming

broader and convoluting the higher temperatureshoulder clearly visible at U ¼ 5 K min�1.

A difference of 15 K on the Tonsetc is observed

between the lowest and the highest heating rateexperiments, as it is shown in Figure 8A wherethe crystallization temperature is reported as afunction of U. In this temperature range thecrystallinity reached by the sample during theprimary (XI

c ) and secondary (XIIc ) crystallization

process does not vary. In fact, as shown inFigure 8B, the crystallization enthalpy DHc,evaluated by the total peak integrals of Figure7, remains nearly constant as a function of theheating rate. A crystalline phase fraction of XI

c

þ XIc ¼ (24 6 1)% was evaluated by using the

formula DHc/DH0m � 100, where DH0

m ¼ 112 Jg�1 is the heat of fusion for 100% crystallinePPS.7

At this point we can make use of our FT-IRresults. It is worth to remind that FT-IR wasunable to give the value of the absolute crystal-linity of our samples, but just the relativeweight of the primary and secondary process,which were found to be 83 and 17%, respec-tively. Then, to know which is the absolute pri-mary and secondary process crystallinity onehas to multiply these value for the 24% given byDSC technique for XI

c þ XIIc , thus obtaining XI

c

¼ 20% and XIIc ¼ 4%.

Figure 4. Dependence of crystallization onset tem-perature Tc

onset measured by FT-IR as a function ofthe heating rate U.

Figure 5. Absorbance ratio (R ¼ Abs1092/Abs1072)variation in correspondence to the end of the primaryand secondary crystallization, as a function of theheating rate.


As far as the amorphous fraction in semicrys-talline PPS samples is concerned, it must bestressed that, as widely reported in the litera-ture,27,28 it is considered to be composed of twodistinct phases: mobile amorphous phase andrigid amorphous phase (RAP). The formerbecomes liquid-like above the Tg, undergoing awell-defined Cp change, but the latter does not.The rigid amorphous fraction, whose evaluationwas not possible in the experiments we carriedout in this research, is assumed to be an inter-mediate component that resides between thecrystal lamellae and the mobile amorphousregion. As it will be better explained later, webelieve that the RAP, which does not show anyseparated Tg, is not involved in the well-definedstepwise secondary crystallization.

On heating at higher temperature, the poly-mer is subjected to a reorganization process ofthe amorphous phase or of the less ordered crys-talline fraction. Such a phenomenon, which ismore intense when the heating rate is lower,is evidenced by an increase of the Tm and ofthe melting enthalpy variation (DHm) as Udecreases, as it is shown in Figure 8.

The crystalline phase that undergoes themelting process, defined as DHm/DH0

m � 100spans from 46% at U ¼ 5 K min�1 to 40% atU ¼ 35 K min�1, was in good agreement withthe data recorded by Chung and Cebe in PPSisothermal cold-crystallization experiment.7

The literature reports that the quenching pro-cedure, as it was proposed in previous worksdealing with the isothermal crystallization pro-cess,8 produces a large number of crystallinenuclei. These nuclei are characterized only by ashort range order, which are not able to giveBragg reflections in the X-ray diffraction experi-ment. However, by comparing the experimental(U ¼ 5 K min�1) specific heat variation (DCp

¼ 0.27 J K�1 g�1) at the glass transition withthat of the theoretical one27 (DC0

p ¼ 0.277 J K�1

g�1), we found that our quenched samples werenearly wholly amorphous, the nuclei weightfraction being about (46 3)%. This figureallowed us to infer the crystalline phase evolu-tion of the sample during the heating process,which can be defined as third crystallizationprocess that is added to the aforementioned pri-mary and secondary ones. This may be due tothe polymer order perfection and to the furthermobile or rigid amorphous conversion takingplace during the sample heating between the

Figure 7. Effect of the heating rate on the DSCthermograms of the PPS cold-crystallization.

Figure 6. DSC thermogram of quenched PPS car-ried out at U ¼ 10 K min�1.


end of the exothermic crystallization peak andthe start of the melting one. The determinationof this crystalline fraction (XIII

c ) was based onthe following calculation

XIIIc ¼½ð�Hm��HcÞ=�H0

m��Cp=�C0p��100 ð3Þ

In our experiments we found a crystalline fraction(XIII

c ) variation ranging between 19% at U ¼ 5 Kmin�1 and 12% at U ¼ 35 K min�1. Such anamount is not negligible and must be taken intoaccount when the polymer crystallinity fraction isevaluated from the enthalpy of fusion data.

GENERAL OVERVIEW

As it was previously noticed the heating ratesused in the EDXD and FT-IR experiments arecontiguous and complementary to the DSC ones.In fact at U > 10 K min�1 the FT-IR spectrawere not able to satisfactorily describe the ther-mal transformation process discussed in thispaper; Moreover the heat flow associated withthem is easily measured only when the transi-tion is fast enough, that is when it occurs at rel-atively high temperature. The DSC signal wasindeed recorded starting from U ¼ 5 K min�1.As expected the crystallization temperatureincreases with increase in the heating rate.

Usually, the analysis of the Tc dependence onheating rate allows the evaluation of the appa-rent activation energy (Ec) for the transport ofthe macromolecular segments to the growingcrystalline surface, according to the equationproposed by Kissinger29:

d½lnðT2p=�Þ�=dð1=TpÞ ¼ �Ec=R ð4Þ

where Tp is the maximum crystallization ratetemperature, U the heating rate and R the gasconstant.

Such a model, which was widely used todescribe inorganic and polymeric material cold-crystallization processes,30–32 holds for an arrhe-nian temperature dependence of the crystalliza-tion rate and for a negligible nucleation rate

Figure 8. Dependence of (A) crystallization onsettemperature (Tc

onset), (B) crystallization enthalpy(DHc), (C) melting temperature (Tm), and (D) enthalpyof fusion (DHm) measured by DSC as a function of theheating rate U.


over the temperature range at which the meas-urements are carried out.

Although in the original model formulationthe approximation of a first order kinetics wasimposed, it was successively demonstrated thateq 4 holds for a wide class of kinetic models,including the heterogeneous transformations inisothermal condition that are described by theAvrami equation.33

The ln[Tp2/U] plot versus 1/Tp generally gives

a linear trend in the usually employed narrowheating or cooling rate range.30–32 In our casethe experimental data deviate from the linearity,as shown in Figure 9, and are distributed ontwo straight line whose slopes yield the valuesEc ¼ 365 k J mol�1 for U � 1 K min�1 andEc ¼ 170 k J mol�1 for U � 1 K min�1.

Although both values are lower than thosefound in the literature, derived from the isother-mal DSC crystallization experiments of Kon-neke2 (Ec ¼ 520 k J mol�1) and Maffezzuoliet al.34 (Ec ¼ 545.5 k J mol�1), the figure calcu-lated for U � 1 K min�1 is in good agreementwith those found by us8 (Ec ¼ 340 k J mol�1) forthe same PPS (Ryton V-I) in the same kind ofexperiments and in a very wide temperaturerange (90 < Tc < 112 8C) explored by means ofthe three techniques used in the present work.

Indeed the hypothesis of an arrheniandependence of the rate constant may be justified

by the small temperature range that is usuallyexplored in the crystallization experiments.Moreover, it is worth noticing that such a rangevaries in the cases of isothermal or nonisother-mal crystallization condition. This fact is oftenresponsible for the difference between the Ec

data obtained for the cold crystallization experi-ment studied by the Kissinger method and thoseobtained in isothermal condition.32,35

When a large temperature range is explored,the rate constant is better described by the empir-ical Vogel, Tamann, and Fulcher (VTF) relation.Such a law gives a better fit of the data obtainedat temperature near Tg, that is, far from T rangeat which the maximum rate is achieved. Here-after the VTF equation is reported as follows:

KðTÞ ¼ K0 exp � U�

RðTp � T1Þ� �

ð5Þ

where U* and T? are the activation energy neededfor the movements of chains and the temperatureat which they are motionless, respectively.

By replacing in the Kissinger model theArrhenius equation with the VTF function, oneobtains

dTðtÞdt

¼ U ¼ RK0ðTp � T1Þ2U� exp � U�

R0ðTp � T1Þ� �

ð6Þ

Figure 10. Dependence of U versus Tp. Experimen-tal data and model result by using eq 6.

Figure 9. Dependence of ln[(Tp)2/U] versus 1/Tp

according to the Kissinger model, as measured bymeans of EDXD, FT-IR, and DSC.


Such an equation correlates the crystallizationpeak temperature to the heating rate.

Figure 10 shows the U versus Tp plot andthe non linear best-fit curves obtained by usingeq 6, where U* ¼ 6.28 k J mol�1 was employedaccording to Hoffmann et al.36 The adjustableparameter are then K0 and T?. Eq 6 describeswell the Tp trend as function of U within theentire T range explored. The adjustable para-meter values obtained by the best fit procedureare K0 ¼ 330 6 40 8C and T? ¼ 42 6 1 8C.

The value T? ¼ 42 8C appears to be reason-able in the light of the isothermal crystallizationresults, which indicate T? ¼ 48 8C.8 Letting T?

¼ Tg � 30 8C,36 one obtains Tg ¼ 72 8C. Sucha Tg value was observed by us20 in a FT-IRand EDXD study of PPS glass transition usinglower heating rates (0.05�1 K min�1). It isworth noticing that it is lower than that usuallyfound in DSC experiments done at the typicalheating rate of 10 or 20 K min�1, which gives aTg value in the range 84–86 8C.

As far as the secondary crystallization is con-cerned, we were not able to correctly describe theprocess employing the aforementioned method.Although the transformation is clearly observableby the FT-IR technique at the lowest heatingrate, at the higher U such a transition overlapsthe primary one. Moreover, the polymer fractioninvolved in the secondary process was found to bequite low, being about 4% as already shown in theDSC Analysis section. This fact makes difficult torecognize the maximum transformation rate tem-perature, which approximately increases from107 to 143 8C in the heating rate range 0.05–7 Kmin�1. It must also be stressed that, as widelyreported in the literature,27,28 a RAP, that is, adisordered phase adjacent to the crystalline onethat does not become liquid-like above Tg, devel-ops during the crystalline phase growth. The lit-erature indicates that the RAP fraction, notmeasured in the present work, increases as thecrystallization temperature decreases and wasevaluated by Huo and Cebe28 to be about 40–30%in the 150–210 8C Tc range.

Dielectric relaxation experiments28 showedthat the RAP gradually relaxes with a broadrelaxation time distribution while increasing thetemperature above the Tg. Moreover, Chenget al.27 found that at least over the 20–30 8Cabove the end of the glass transition of semi-crystalline PPS samples there is no indication ofa change in RAP. They quoted the ‘‘possible’’ but

undetectable glass transition temperature of theRAP above 147 8C, where a premelting peakmay hide the transition. Such a temperature ishigher than those of our secondary crystalliza-tion process. These facts let us exclude a directinvolvement of the RAP in the stepwise secon-dary crystallization we observed in our isother-mal and nonisothermal experiments. In the lightof such observation and as for other semirigidpara-linked aromatic polymers, characterized bya strong interaction between amorphous andcrystalline regions,3,37,38 it is our feeling thatthe PPS behavior in the secondary crystalliza-tion may be due to the evolution of a more con-strained mobile amorphous fraction that residesin proximity of the rigid phase (rigid amorphousand crystalline domains), grown in the course ofthe primary process. Because of the low mobilityof such a component, it relaxes and becomesliquid-like at higher temperature or after longertime, if the crystallization is carried out in iso-thermal conditions.

The hypothesis proposed here is supported bythe dynamic mechanical analysis resultsobtained on PPS samples characterized by dif-ferent crystalline phase content, which will bedescribed in a forthcoming paper.

CONCLUSIONS

In this paper the nonisothermal cold-crystalliza-tion behavior of glassy PPS was followed in awide heating rate range (0.05–35 K min�1). Wewere able to carry out such an investigation byusing three different experimental techniques.The low heating rates U were explored by EDXD(0.1 K min�1) and FT-IR (0.5–10 K min�1) andwere in fact contiguous and complementary tothe DSC (5–30 K min�1).

As far as the EDXD analysis is concerned,although the diffracted X-ray intensity stronglydepends on the scattering vector range ana-lyzed, the onset of the crystallization throughthe movement of chain segments of differ-ent length appears at the temperature of 97 8C.Moreover, a transient region between 110and 140 8C, that is after the primary crystal-lization, could be attributed to a secondaryprocess.

The FT-IR analysis showed that the transi-tion kinetics is independent from the peak fre-quency chosen to follow the process. The pres-ence of a secondary crystallization, also observed


in the EDXD analysis, confirms the analogouseffect found by us in isothermal experiments,8

in which a stepwise crystallinity increase,described by the Avrami law, was detected atthe end of the primary process.

The DSC thermograms show, beside the glasstransition, a double exothermic crystallization.As U increases the first exothermic peak shiftsat higher temperature and becomes broaderwhile the intensity of the second one decreases,making it hardly detectable at U ¼ 20 K min�1.The crystalline phase evolution due to the poly-mer order perfection and to the further amor-phous conversion taking place during the sam-ple heating between the end of the exothermiccrystallization process and the start of themelting one was found to vary between 19% atU ¼ 5 K min�1 and 12% at U ¼ 35 K min�1.

The experimental data obtained by the threetechniques have been all together analyzed. Thecrystallization temperature changes from 95 8Cat U ¼ 0.05 K min�1 to 130 8C at U ¼ 30 K min�1.In such a wide temperature range the Kissingermodel, based on an arrhenian temperaturedependence of the crystallization rate and widelyemployed to evaluate the activation energy of thecrystallization process, fails. The experimentalresults were satisfactorily described if in the Kis-singer model the Arrhenius equation wasreplaced by a Vogel–Fulcher–Tamann function,fixing the activation energy needed for thechains movements U* ¼ 6.28 k J mol�1, accord-ing to the value proposed by Hoffmann. Theparameter T? ¼ 42 8C, at which the polymerchains are motionless, found by fitting theexperimental data appears to be reasonablein the light of the previously reported isother-mal crystallization results, which indicateT? ¼ 48 8C.

Moreover, at the lower heating rate, mostlyfollowed by FT-IR, a stepwise secondary crystal-lization process was well evidenced. In firstapproximation, it involves about 17% of the totalcrystallinity reached by the sample.

We acknowledge MURST (Ricerche di Ateneo) forfinancial support.

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Poly(p-phenylene sulfide) nonisothermal cold-crystallization