Lamellar Morphology and Equilibrium Melting Temperatureof Syndiotactic Polystyrene in �-Crystalline Form

CHI WANG1, YONG-WEN CHENG1, YAO-CHUNG HSU1, TSANG-LANG LIN2

1Department of Chemical Engineering, National Cheng Kung University, Tainan 701-01, Taiwan, Republic of China

2Department of Engineering and System Science, National Tsing Hua University, Hsin-Chu 300,Taiwan, Republic of China

Received 28 November 2001; revised 16 April 2002; accepted 13 May 2002Published online 00 Month 2002 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/polb.10222

ABSTRACT: Lamellar morphology and thickness of syndiotactic polystyrene (sPS) sam-ples melt-crystallized at various temperatures were probed using transmission electronmicroscopy (TEM) and small-angle X-ray scattering (SAXS). In addition, the meltingtemperature and enthalpy of the crystallized samples were characterized with differ-ential scanning calorimetry. Under appropriate thermal treatments, all the samplesinvestigated in this study were crystallized into �� crystal modification, as revealed bywide-angle X-ray diffraction. From the SAXS intensity profiles, a scattering peak (orshoulder) associated with lamellar features as well as the presence of anomalousscattering at the zero-scattering vector were evidently observed. The peculiar zero-angle scattering was successfully described by the Debye–Bueche model, and subtrac-tion of its contribution from the raw intensity profiles was carried out to deduce theintensity profile merely associated with the lamellar feature. The lamellar thicknessobtained from Lorentz-corrected intensity profiles in this manner agrees with thatmeasured from the TEM images, provided that the two-phase model is applied. On thebasis of the Gibbs–Thomson equation, the modest estimations of equilibrium meltingtemperature and the surface free energy of the fold lamellar surface are 292.7 � 2.7 °Cand 20.2 � 2.6 erg/cm2, respectively, when lamellar thicknesses measured by TEM areapplied. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1626–1636, 2002Keywords: syndiotactic polystyrene; lamellar thickness; equilibrium melting tem-perature; SAXS; TEM

INTRODUCTION

Compared with the atatic and isotactic isomers,syndiotactic polystyrene (sPS) is a new materialwith many unique properties such as low dielec-tric constants, good chemical resistance, and highmelting points that make it very attractive for useas a high-quality engineering thermoplastic.Many efforts have been dedicated to the under-

standing of the crystallization and crystal struc-ture (lattice) of sPS and led to various conditionsunder which different types of crystal forms willbe developed. Careful determination of equilib-rium melting temperature (Tm

o ) of sPS is a ratherimportant task because the crystallization kinet-ics are strongly dependent on the amount of un-dercooling, �T (� Tm

o � Tc, where Tc is the crys-tallization temperature). Various conflicting val-ues of Tm

o have been reported in the literature.1–8

In general, two approaches exist that are widelyperformed to deduce Tm

o of polymers. One is basedon the Hoffman–Weeks (HW) equation, and theother is based on the Gibbs–Thomson (GT) equa-

Correspondence to: C. Wang (E-mail: chiwang@mail.ncku.edu.tw)Journal of Polymer Science: Part B: Polymer Physics, Vol. 40, 1626–1636 (2002)© 2002 Wiley Periodicals, Inc.

1626

tion. Because of its simplicity in measurementsand analyses, the HW plot is most frequentlyapplied in determining Tm

o of polymers. In thisapproach, the measured melting temperatures ofsamples crystallized at various Tc’s are plottedagainst Tc, and a linear extrapolation is con-ducted to the line Tm � Tc where the interceptgives Tm

o . In addition, a thickening coefficient isobtained from the reciprocal of the linear slope.On the basis of differential scanning calorimetry(DSC) measurements, the value of Tm

o for sPS in�-form crystals determined from the HW plot is285.5 °C.1 Similar experimental procedures havegiven 285 °C2 and 278.6 °C3 for samples crystal-lized for a longer period (ca. 4 h). Using a polar-ized light microscope, on the other hand, Cim-mino et al.4 obtained the Tm of an sPS samples atvarious Tc’s from the temperature where the bi-refringence patterns disappeared. On the basis ofthe HW plot, the derived Tm

o was 275 °C. A higherTm, 291.5 °C, was obtained by Gvozdic and Meier7

when an extremely careful annealing method wasperformed on sPS before melting. However, oneshould be aware that the major assumption onwhich the HW plot is based is the Tc indepen-dence of the thickening coefficient that may not bestrictly true as discussed in a previous article.8 Inaccordance HW theory, the experimentally mea-sured Tm should be determined at very low levelsof crystallinity where the thickening effect of la-mellae, if any, is greatly limited.9,10 If one usesthe Tm values at high levels of crystallinity for theHW plot, a lower extrapolated Tm

o is expected.Thus, Tm at zero crystallinity is preferred forconstructing the HW plot, and a more reliable Tm

o

is derived in this manner at 291 °C.8 However, amuch higher Tm

o is obtained at 320 °C8 when anonlinear extrapolation of the HW plot (developedrecently by Marand and coworkers10,11) is ap-plied.

The Tm depression due to the presence of thinlamellae is generally described by the GT equa-tion given by

Tm � Tm0 �1 � 2�e/��Hf

0lc)] (1)

where Tm is the measured melting temperaturefor lamellar crystals with a thickness of lc, �Hf

o isthe enthalpy of fusion per unit volume, and �e isthe fold-surface free energy. Thus, the determina-tion of Tm

o is carried out by evaluation of theintercept of the Tm versus 1/lc plot. Transmissionelectron microscopy (TEM) and small-angle X-ray

scattering (SAXS) are frequently conducted to de-termine the lamellar thickness of semicrystallinepolymers. A thin (or small amount of) sample ispreferred for isothermal crystallization to excludelarge morphological variation within samples af-ter crystallization, giving a wide distribution oflamellar thickness. To measure a true Tm of theas-prepared samples, the heating rate should besufficiently high enough to inhibit the extensivethickening, thus avoiding reorganization during aDSC heating scan. On the other hand, too high ofa heating rate may lead to the superheating ef-fect, giving an overestimated Tm. To the authors’best knowledge, only one article6 in the literaturereports sPS’s Tm

o value of 278.5 °C on the basis ofthe GT equation. In their SAXS measurements,6

Fourier transformation of the SAXS intensitieswere conducted to derive the correlation lengths.Without the complements of TEM observation,however, difficulties have been encountered inprecise assignments of the derived correlationlengths to lamellar thickness. Although numer-ous studies have been conducted on the crystalli-zation and polymorphic characters of sPS, littleinformation is available as far as the lamellarmorphology is concerned. On investigating thelamellar morphologies of injection-molded sPS,Lopez et al.12 and Barnes et al.13 have performedthe TEM and SAXS measurements, respectively.However, a mixture of �- and �-form crystals wasdeveloped in their molded samples because of thesevere flow and thermal conditions that couldhave complicated further analyses. The objectiveof this study is to investigate the lamellar mor-phology and thickness, probed by both SAXS andTEM for more appropriate determination of la-mellar thickness, for �-form sPS’s crystallized atvarious Tc’s. Supplemented by the DSC measure-ments for Tm, the Tm

o value is derived on the basisof the GT equation as well as the important ther-modynamic parameter, �e.

EXPERIMENTAL

Sample Preparation

The sPS pellets with a weight-average molecularweight (Mw) of 200 kg/mol were obtained fromDow Chemical Co. To prepare sPS in �-crystalform,8 the pellets were melt-pressed in a disk-shaped mold with a diameter of 17 mm and thick-ness of 1.2 mm at 290 °C and 0.6 MPa for 10 min,followed by ambient cooling at atmospheric pres-

SYNDIOTACTIC POLYSTYRENE 1627

sure. The as-prepared sPS crystals were in ��(orthorhombic) crystals as revealed by wide-angleX-ray scattering (WAXD). The sPS disk wasplaced in a glass mold and thermally equilibratedat 300 °C in a Mettler hot stage (FP-82) for 10min. Then the sample was quickly shifted to an-other well-controlled hot stage for isothermalcrystallization to proceed further. The crystalliza-tion conditions were set at 240 (0.5), 250 (1), and265 °C (8.5 h). Crystallization was ceased byquenching the samples to liquid nitrogen.

To control the uniformity of lamellar morphol-ogy within each sample for accurate Tm

o determi-nation, DSC pans instead of the glass mold wereused to hold a small amount of sPS (ca. 8 mgobtained by slicing the melt-pressed sPS disk) forisothermal crystallization. A well-controlled hotstage (Mettler, FP-82) was used to heat the sam-ple to 300 °C for 10 min and then quickly cooled tothe desired Tc (Tc � 235, 240, 245, 250, 255, and260 °C). After crystallization at each Tc for 6 h,the samples were quenched in liquid nitrogen.sPS samples were taken out of the DSC pans foradditional measurements.

SAXS and WAXD Measurements

SAXS profiles of these samples were obtained atroom temperature with an 18-kW rotating anodeX-ray generator (Cu target, Rigaku) operated at40 kV and 200 mA. A set of three pinhole collima-tors was used. A two-dimensional position-sensi-tive detector (ORDELA model 2201X, Oak RidgeDetector Laboratory Inc.) with 256 � 256 chan-nels was used, and the sample-to-detector dis-tance was set at 4000 mm. The area scatteringintensities were averaged radially to obtain theone-dimensional intensity profile for further anal-yses. The scattering vector q (� 4�sin�/�, where2� is the scattering angle, and � is the wavelengthof X ray) ranged from 0.11 to 3.0 nm�1. The de-tails of the SAXS setup are described elsewhere.14

For materials with diffuse phase boundaries, Po-rod’s law predicts the scattered intensity at largeangles as follows15,16

limq3

[Kp � �Iraw � Ifl)q4 exp��2q2� � 0 (2)

where Iraw is the raw intensity, Ifl is the intensityarising from thermal-density fluctuations, Kp is thePorod constant, and � is the interfacial thicknessbetween the crystalline and amorphous regions. Anumerical simulation was carried out to obtain the

optimal parameters (Ifl, Kp, and �). Then cor-rected intensities, Icor � (Iraw-Ifl)exp(�2q2), wereused for additional analyses.

The WAXD data were obtained on a Philipsdiffractometer (PW1710) operated at 40 kV and100 mA with a scanning rate of 4°/min.

TEM Observations

The ultrathin films (ca. 50-nm thick) to be ob-served by TEM were prepared by sectioning thesamples at room temperature with an UltracutUCT (Leica) microtome. Staining of the ultrathinfilms was subsequently carried out with ruthe-nium tetraoxide (RuO4) vapors at room tempera-ture. The TEM micrographs shown in this workwere done with a JEM-2000FX (JEOL) micro-scope operated at 200 kV.

DSC Measurements

The melting enthalpy and temperature of the sPSsamples were measured with a PerkinElmerDSC7 from 23 to 300 °C with a heating rate of 10°C/min under nitrogen atmosphere to diminishoxidation. Indium and zinc standards were usedto calibrate the enthalpies of fusion and Tm’s priorto the heating scans. The Tm is reported at thepeak of the melting endotherm, and the area ofendotherm gives the melting enthalpy.

RESULTS AND DISCUSSION

For a preliminary study on the crystal morphol-ogy, thick samples crystallized in the glass moldat 240 (0.5), 250 (1), and 265 °C (8.5 h), respec-tively, were investigated first. The WAXD pat-terns are shown in Figure 1. For samples crystal-lized at 240 and 250 °C, diffracted peaks are evi-dently observed at 2� � 6.15, 10.4, 12.3, 13.5,18.6, 20.1, and 21.4°. These positions of the dif-fracted peaks are characteristics of sPS crystalsin �� form (orthorhombic unit cell with disorderedmodification17) corresponding to the diffractionplanes of (020), (110), (040), (130), (060), (111),and (041), respectively. A relatively small peak isalso found at 2� � 6.7° for samples crystallized at240 °C as indicated in Figure 1, suggesting theplausible presence of a small amount of � crystals(hexagonal unit cell).17 However, because noother characteristic diffraction peak for � crystalswas detected (especially the peak location at 2�� 11.6°),17 we may conclude that the majority of

1628 WANG ET AL.

the crystals are in the �� form. Samples crystal-lized at 265 °C, on the other hand, show under-developed crystalline structure with a broad dif-fracted intensity peak only centered at �20°. Ap-parently 8.5 h is not sufficiently long enough forcrystallization to be completed at 265 °C. Theamorphous halo obtained from the diffraction byatactic polystyrene (aPS, Mw � 50 kg/mol) is alsodepicted in Figure 1 to represent essentially thecontribution from the amorphous phase in sPS.As expected, the glassy PS shows a broad amor-phous halo centered at 2� � 19.0°, which isslightly lower than the strongest scattering peaksassociated with (111) and (041) planes of �-formsPS at 2� � 20.1 and 21.4°, respectively. It issuperimposed upon the patterns of sPS by fittingthe diffractogram by scaling the intensities of the2� regions at 8, 15, 22.5, and 28°. Thus, the dif-fracted peaks associated with the crystallinephase were obtained by subtracting the amor-phous halo from the total diffraction pattern.18

For samples crystallized at 265 °C, the broaddiffracted intensities for 2� � 19–22.5° and 8–15°are mainly attributed to the presence of smalland/or imperfect crystallites. The mass fractions

of crystallinity, determined from the area ratio ofthe crystalline peaks to the total scattering, were0.36, 0.38, and 0.17, respectively, for sPS crystal-lized at 240, 250, and 265 °C. DSC heating scanswere carried out at a rate of 10 °C/min to detectthe Tm’s and enthalpies for these samples. Twomelting peaks located at 263.8 and 271.0 °C wereobserved for sPS crystallized at 240 °C with amelting enthalpy of 30.5 J/g. On the other hand, asample crystallized at 250 °C exhibited only onemelting peak located at 269.9 °C and a meltingenthalpy of 32.1 J/g. For sPS crystallized at 265°C for 8.5 h, a small crystallization exotherm cen-tered at 200 °C was detected that indicated theoccurrence of cold crystallization during the heat-ing scan. It also suggests the incomplete crystal-lization of sPS prior to DSC heating traces, inaccordance with the WAXD pattern in Figure 1.On the basis of the DSC measurements, the massfractions of crystallinity, determined from the ra-tio of the melting enthalpy to the heat of fusion forpure crystal (82.4 J/g),19 were 0.37 and 0.39 forsPS crystallized at 240 and 250 °C, respectively.Essentially the mass-fractional crystallinity ob-tained from WAXD and DSC measurements issimilar. Provided that the two-phase model isvalid, the following relation is applied to convertthe mass-fractional crystallinity (c,w) to the vol-ume-fractional crystallinity (c,v)20

c,v � c,w(a/c)/�1 � �1 � a/c)c,w] (3)

where c and a are the densities for the crystal-line and amorphous phases, respectively. Thedensity for the orthorhombic crystal lattice21 is1.067 g/cm3, whereas the density of the amor-phous phase20 is 1.052 g/cm3. Therefore, the vol-ume-fractional crystallinity is 0.36 and 0.38 forsamples crystallized at 240 and 250 °C, respec-tively.

Lamellar Morphology

TEM micrographs of sPS samples crystallized at240, 250, and 265 °C are illustrated in Figure 2.The dark lines correspond to the amorphousphase of sPS, and the bright lines are associatedwith crystalline lamellae with which the lamellarthickness is given by the line width. The bulksamples are completely filled with lamellar stackswhen crystallized at 240 and 250 °C as deter-mined in Figures 2(a,b), whereas only isolatedlamellar stacks (sheaflike spherulitic precursors)

Figure 1. WAXD profiles for sPS samples crystal-lized isothermally at 240, 250, and 265 °C (the dottedlines are WAXD profiles of aPS superimposed on that ofsPS by scaling the intensities at 2� � 8, 15, 22.5, and28°).

SYNDIOTACTIC POLYSTYRENE 1629

are frequently observed within the samples crys-tallized at 265 °C. Figure 2(c) indicates the un-derdeveloped spherulitic structure of which thecharacteristics of two “eyes” are marked by theletter “E”.12 According to Norton and Keller’s22

classification, the growth mechanism of sPSspherulites can be classified to category 2 wheresheaflike unidirectional growth leads to thespherical symmetry. Initially, unidirectionalgrowth of a single lamellar crystal is observed,followed by deposition of other lamellar nuclei onits lateral surfaces to form lamellar stacks (orbundles) gradually. To occupy the available spacefor crystal growth, not only the dimension in-crease in the lateral surface of lamellar stackstakes place but also the occurrence of branchingand fanning of the lamellar stacks, preserving thesheaflike features with a characteristic of twoeyes, as shown in Figure 2(c). From all the TEMmicrographs, the lamellar thickness was mea-sured, and the histogram of the lamellar thick-ness distribution is depicted in Figure 3 from anaccumulation of about 1500 lamellae for each Tc.It is evident that the lamellar thickness rangesfrom about 4 to 12 nm, and the most-probablelamellar thickness is 7.2 nm for samples crystal-lized at 240 and 250 °C. However, the populationof thick lamellae (9–10 nm) increases at Tc � 250°C as compared with that for Tc � 240 °C. Thenumber-average lamellar thicknesses is 6.8 and7.0 nm for samples crystallized at 240 and 250 °C,respectively. Thus, slightly thicker lamellae aredeveloped at lower undercooling (higher Tc), asexpected from the theoretical consideration.

Plots of the Lorentz-corrected SAXS intensitiesversus scattering vector, q, of samples crystal-lized isothermally at 240, 250, and 265 °C areillustrated in Figure 4. For clarity, a vertical shiftof the curves is performed. A scattering peak isevident for samples crystallized at 240 and 250°C. For samples crystallized at 265 °C, on theother hand, only a gradual decrease in Icorq

2 isdetected, giving no scattering Icorq

2 peak. Thepresence of the scattering Icorq

2 peak gives a gen-eral indication of the existence of a periodic la-mellar/amorphous-layer structure within thesamples. The usual practice to determine the pe-riodicity is to apply Bragg’s law in calculating thelong period L from the location of the peak max-imum qm, given by L � 2�/qm. The movement ofthe scattering peak toward smaller angles athigher Tc confirms the general expectation that Lincreases with decreasing undercooling. In addi-tion to the scattering peak, strong scattering at a

Figure 2. TEM micrographs of sPS crystallized iso-thermally at (a) 240 °C, (b) 250 °C, and (c) 265 °C, allat the same magnification indicated by the scale barin (a).

1630 WANG ET AL.

lower angle is evident and gives rise to an asym-metric character of the intensity profiles, indi-cated by the significant rise of scattering intensity

at low q regions. The presence of anomalous scat-tering at zero angles suggests that a differentscattering mechanism, besides the lamellar scat-tering, has to be considered. Strong zero-anglescattering has been detected in some polymer-blend systems14,23 as well as the neat poly-mer.24,25 Several proposals have been offered,such as the existence of microvoids,13 grain-boundary phase,13 single lamella24 or isolatedamorphous zones,24 and foreign particles.25 Be-cause the sPS material used in this study pos-sesses a high stereoregularity (more than 99%),the tacticity (or impurity) effect to induce thiszero-angle scattering is excluded. Now, the mech-anism to cause the zero-angle scattering is notcertain. It may be associated with the small do-mains arising from the presence of microvoids13

or the defect structure (stacking faults) within thelamellar crystals as observed by Tosaka et al.26

via the electron diffraction technique. Neverthe-less, one thing for certain is the existence of athird phase besides the lamellar/amorphous lay-ers.

To account for the strong zero-angle scatteringIo as a function of the scattering vector, the De-bye–Bueche model27 is applied tentatively andgiven as follows

Figure 4. Lorentz-corrected intensity profiles of sPScrystallized isothermally at 240, 250, and 265 °C.

Figure 3. Histograms of lamellar thickness derivedfrom TEM micrographs of sPS crystallized isother-mally at (a) 240 °C and (b) 250 °C.

SYNDIOTACTIC POLYSTYRENE 1631

Io � A/�1 � ac2q2)2 (4)

where A is a constant, and ac is a correlationlength associated with the heterogeneity withinthe sample. The Debye–Bueche model has beensuccessfully applied to describe the intensity pro-files for randomly distributed heterogeneous do-mains in the polymer blends.14,23 According to eq4, a plot of I cor

�0.5 versus q2 will give a straight lineat low q regions, as shown in Figure 5. It isevident that a similar intensity profile was ob-tained in the q2 range from 0.01 to 0.03 nm�2.Apparently, the Debye–Bueche model is appropri-ate here and fits the scattering intensity ratherwell at low q. The deviation of measured intensi-ties from the straight line at relatively high q (q2

0.03 nm�2) is due to the lamellar scattering.The correlation length ac is obtained from thesquare root of the slope/intercept ratio. From theDebye–Bueche plot, the calculated ac values are6.9, 7.0, and 7.0 nm for samples crystallized at240, 250, and 265 °C, respectively. The correla-tion length ac is smaller than the long period butclose to the lamellar thickness (as discussed sub-sequently), possibly suggesting the zero-anglescattering is relevant to the presence of certainelectron contrast within the lamellae (or amor-phous layers). After subtracting the zero-anglescattering intensity from the observed scatteringintensity, the Lorentz-corrected plots of (Icor� Io)q

2 versus q are given in Figure 6 where amore appropriate determination of the long pe-riod can be made. The long periods determined

from the peak positions are 17.8 and 19.0 nm forsamples crystallized at 240 and 250 °C, respec-tively. A SAXS intensity profile for samples crys-tallized at 265 °C for 8.5 h, however, did notprovide clear presence of a scattering peak, sug-gesting incomplete crystallization of crystalliz-able sPS chains. It is consistent with the TEMobservations, Figure 2(c), giving sporadic under-developed spherulites isolated with one another.Because the sample is completely filled with la-mellar stacks as determined in Figures 2(a,b), thelamellar thickness (lc) can be estimated by lc� L � c,v, where c,v is the volume-fractionalcrystallinity determined from eq 3 with WAXD (orDSC) results. The lamellar thicknesses deter-mined in this manner are 6.4 and 7.2 nm forsamples crystallized at 240 and 250 °C, respec-tively. These values agree with those obtained bythe TEM results.

A brief summary regarding the SAXS measure-ments is given as follows. Two aspects have to beconsidered in determining the morphological pa-rameters of sPS measured at room temperature.First, subtraction of the zero-angle scatteringfrom the observed intensity profiles is required to

Figure 5. Debye–Bueche plots of raw data to deter-mine the correlation length ac to account for the strongzero-angle scattering.

Figure 6. Lorentz-corrected intensity profiles of sPSafter subtraction of the contribution from zero-anglescattering.

1632 WANG ET AL.

deduce the scattering exclusively because of thelamellar scattering, giving a more reliable long-period value. Second, because the density differ-ence between the crystal and amorphous phases(c � a) is relatively small for sPS samples, itleads to a low scattering contrast for SAXS mea-surements, and long X-ray exposure time is usu-ally required. Owing to the poor scattering con-trast at room temperature, the scattering associ-ated with the lamellar morphology might beobscured because of the presence of strong zero-angle scattering. In the most severe condition, nodetectable scattering peak (or shoulder) relevantto the lamellar features is observed.13,23 To en-hance the scattering contrast and obtain a preciselong period, SAXS measurements at high temper-atures are suggested by Barnes et al.13

Tmo

To determine Tmo of sPS on the basis of the GT

equation, one has to measure the Tm of crystallamellae of which its thickness is given. Becausethe thermal conductivity of polymers is suffi-ciently low, it is not an easy task to prepare eachsample with uniform morphology after crystalli-zation. To reduce significant thermal variationwithin bulk samples during crystallization, thinand a small amount of samples are preferred for abetter control of the morphological uniformity.DSC pans are quite suitable to hold a smallamount of sPS (ca. 8 mg) for precise morphologi-cal control. Subsequent measurements of Tm andlc performed by DSC heating traces and TEM(and SAXS), respectively, give consistent results,leading a more reliable determination of Tm

o . Fig-ure 7 portrays the DSC heating scans for samplescrystallized isothermally at various tempera-tures. Two melting peaks are evidently observedfor samples crystallized at Tc � 235 and 240 °C.The low Tm increases with Tc, whereas the highTm remains unchanged. When crystallized attemperatures higher than 245 °C, only one appar-ent melting peak is detected. The presence ofdouble melting behavior suggests the coexistenceof two lamellar populations with different thick-nesses (or perfection) and/or possible occurrenceof reorganization/recrystallization phenomenaduring the heating scan, which is beyond thescope of this study. However, it is generally rec-ognized that when double melting behavior takesplace, the low Tm is more representative for thevirgin lamellae crystallized prior to DSC heating

traces. The high Tm, on the other hand, could beattributed to the melting of thickened lamellae,resulting from melting of the virgin lamellae andsubsequent reorganization. Another plausible ex-planation for the high melting peak is due to thepresence of thicker lamellae that are developedright after crystallization, leading to a bimodaldistribution of lamellar thickness. From our his-tograms of the lamellar thickness distributionprobed by TEM, however, it is difficult to distin-guish the type of distribution because of the lim-ited resolution of TEM images. Therefore, thedouble melting behavior of sPS may be associatedwith two different perfections of lamellar crystals,probably resulting from stacking faults as re-vealed by Tosaka and coworkers.26,28 According toFigure 7, the measured Tm increases with in-creasing Tc, suggesting thicker lamellae devel-oped at lower undercooling. The melting enthalpyincreases slightly from 29.0 J/g at Tc � 235 °C to32.0 J/g at 260 °C, as indicated in Figure 8.

From the SAXS results, the anomalous scatter-ing at zero angle is always found in all samples.To elucidate the correct long period, the observedintensity has been corrected for the zero-angle

Figure 7. DSC heating scans of samples crystallizedat various Tc’s (heating rate: 10 °C/min).

SYNDIOTACTIC POLYSTYRENE 1633

scattering by subtracting the intensity contribu-tion predicted by the Debye–Bueche model, asdescribed previously. Also shown in Figure 8 isthe derived correlation length associated with theinhomogeneity. It seems that ac remains constantat 6.0 nm despite the large range of Tc (� 235–260°C) investigated. After subtracting the zero-angleintensity from the observed SAXS intensity pro-files, the long period is estimated from theLorentz-corrected intensity plots with Bragg’s re-lation. The long period increases gradually from17.5 nm at Tc � 235 °C to 21.0 nm at Tc � 260 °C,as displayed in Figure 9. Also shown in Figure 9 isthe lamellar thickness determined from the mul-tiplication of the long period with volume-frac-tional crystallinity measured from DSC (Fig. 8)along with eq 3. The average lamellar thicknesses

measured from the TEM micrographs are alsoprovided in Figure 9. Thicker lamellae are devel-oped at higher Tc, and both SAXS and TEM giveconsistent lc values, provided that the two-phasemodel assumption is applied.

In accordance with eq 1, a plot of Tm against1/lc should be linear with a slope of �2�e/�Hf

o, andthe intercept gives the Tm

o . Figure 10 shows thevariation of the Tm’s with the reciprocal of thelamellar thickness, probed by TEM, for samplesmelt-crystallized at various Tc’s. Results of sam-ples crystallized at 235 and 240 °C (filled squares)that show double melting peaks are tentativelyincluded for comparison, and the low Tm’s areused. If one excludes the results for 235 and 240°C for simplicity, Tm

o is estimated from the inter-cept of the linear regression dotted line as 290.0°C, which agrees with that, 291 °C, obtained fromthe linear HW plot8 when the Tm at zero crystal-linity is plotted against Tc. Moreover, the derived�e/�Hf

o is about 0.197 nm, which is consistentwith the reported value, 0.20 nm, obtained fromthe single-lamellae measurements.26 For a com-parison purpose, also shown in Figure 10 is thelinear regression solid line of all symbols, giving

Figure 8. Variation of correlation length ac obtainedfrom the Debye–Bueche plot and melting enthalpy de-termined from DSC heating scans with Tc.

Figure 9. Variation of long period L and lamellarthickness lc with Tc.

Figure 10. Plot of melting temperature versus thereciprocal of lamellar thickness to determine the equi-librium melting temperature according to the Gibbs–Thomson equation (filled squares are the results for Tc

� 235 and 240 °C; linear regression for all symbols isshown by the solid line, giving Tm

o � 295.3 °C and�e/�Hf

o � 0.262 nm, whereas the dotted line is thelinear regression for open squares only, giving Tm

o

� 290.0 °C and �e/�Hfo � 0.197 nm).

1634 WANG ET AL.

plausibly the highest Tmo value. Slightly larger

values of Tmo (� 295.3 °C) and �e/�Hf

o (� 0.262nm) are obtained when results for Tc � 235 and240 °C are included. Apparently, the previouslyderived Tm

o value (320 °C) based on the nonlinearHW extrapolation8 is overestimated, whereas bet-ter agreement is reached if the linear HW plot isconducted. On the basis of the aforementionedconsiderations, the best and modest estimationsfor Tm

o and �e/�Hfo from the GT plot as shown in

Figure 10 are 292.7 � 2.7 °C and 0.23 � 0.03 nm,respectively.

On substituting the fusion enthalpy per unitvolume for lamellar crystals (87.9 J/cm3), the sur-face free energy of the fold lamellar surface is 20.2� 2.6 erg/cm2. After obtaining the fold-surfacefree energy, the work for chain folding can beestimated from the following simple relation:�2�eaobo, where ao is the molecular stem width,and bo is the growing-layer thickness. On thebasis of single lamellar crystals observed by TEM,the plausible growth front is the (040) plane.28,29

The lattice constants for �-form crystals with anorthorhombic unit cell are a �0.88, b � 2.88 andc � 0.51 nm. Assuming a (040) plane growth, thestem width and layer thickness are 0.88 and 0.72nm, respectively. The work of chain folding isthen calculated as 3.7 � 0.5 kcal/mol, which issmaller than the isotactic counterpart (iPS),30 7.1kcal/mol. The lower energy required to form achain fold suggests kinetically an easier processto develop a critical nucleus at the growth front,leading to a faster crystal growth if other factorsremain equal. On the measurements of spheru-litic growth rates, indeed Cimmino et al.31 havedemonstrated that sPS is a fast crystallizing poly-mer, as compared with iPS, at the same under-cooling. Moreover, Clark and Hoffman32 sug-gested that the work of chain folding is larger forpolymers with higher Tm

o because of the main-chain stiffness that is valid for isotactic polypro-pylene (iPP) and syndiotactic polypropylene (sPP)isomers. However, these results show that al-though sPS possesses a higher Tm

o as comparedwith iPS (Tm

o � 242 °C), the energy required forsPS chains to form a fold is smaller. It seems thatthe work for chain folding is associated with thenumber of twisted bonds for a fold and the differ-ence in potential energy for various conforma-tions (trans and gauche). On the other hand, Tm

o isexclusively related to the interaction of the chainspacked in the crystal lattice (enthalpy and en-tropy effects).

CONCLUSIONS

The widespread interest in sPS, as a result of itsstereoregular arrangement of styrene pendantalong the polymeric chains, has led to many stud-ies. This article is a contribution to the morpho-logical studies of sPS investigated by SAXS andTEM as well as Tm

o determination in accordancewith the GT relation. In addition to the scatteringpeak associated with the lamellar/amorphous lay-ers, strong and anomalous scattering at lowerscattering vectors is evidently observed fromSAXS intensity profiles. The presence of this scat-tering suggests that another mechanism, besidesconventional lamellar scattering, has to be con-sidered. To deduce the long period from SAXSdata, the scattering profiles of this anomalous lowq scattering are theoretically fitted on the basis ofthe Debye–Bueche model and subtracted from theobserved SAXS intensities. In this manner, thelamellar thicknesses obtained from SAXS agreewith those measured from TEM micrographs ifthe two-phase model is applied. On the basis ofthe GT relation, the derived Tm

o and �e values are292.7 � 2.7 °C and 20.2 � 2.6 erg/cm2, respec-tively. The faster crystal-growth rate of sPS ascompared with its isomeric counterpart iPS maybe attributed to a lower energy required to de-velop a chain fold.

Financial support from the National Science Councilthrough NSC89-2216-E-006-050 is gratefully acknowl-edged. Valuable suggestions by Prof. S.-L. Chen atNTHU regarding the SAXS measurements are highlyappreciated. Helpful suggestions provided by the re-viewers on the deduction of thermodynamic parame-ters from Figure 10 are also acknowledged.

REFERENCES AND NOTES

1. Arnauts, J.; Berghmans, H. Polym Commun 1990,31, 343.

2. Woo, E. M.; Wu, F. S. Macromol Chem Phys 1998,199, 2041.

3. Ho, R. M.; Lin, C. P.; Tsai, H. Y.; Woo, E. M.Macromolecules 2000, 33, 6517.

4. Cimmino, S.; Pace, E. D.; Martuscelli, E.; Silvestre,C. Polymer 1991, 32, 1080.

5. Lin, R. H.; Woo, E. M. Polymer 2000, 41, 121.6. Yang, H.; Hsiao, B.; Landes, B.; Bubeck, R.; Huang,

Y.-B. Polym Mater Sci Eng 1999, 81, 285.7. Gvozdic, N. V.; Meier, D. J. Polym Commun 1991,

32, 493.

SYNDIOTACTIC POLYSTYRENE 1635

8. Wang, C.; Hsu, Y. C.; Lo, C. F. Polymer 2001, 42,8447.

9. Alamo, R. G.; Chan, E. K. M.; Mandelkern, L.;Voigt-Martin, I. G. Macromolecules 1992, 25, 6381.

10. Xu, J.; Sriniva, S.; Marand, H.; Agarwal, P. Mac-romolecules 1998, 31, 8230.

11. Marand, H.; Xu, J.; Srinivas, S. Macromolecules1998, 31, 8219.

12. Lopez, L. C.; Cieslinski, R. C.; Putzig, C. L.; Wes-son, R. D. Polymer 1995, 36, 2331.

13. Barnes, J. D.; McKenna, G. B.; Landers, B. G.;Bubeck, R. A.; Bank, D. Polym Eng Sci 1997, 37,1480.

14. Cheng, H. L.; Hsiao, M. S. Macromolecules 1998,31, 6579.

15. Andjelic, S.; Jamiolkowski, D.; McDvitt, J.; Fischer,J.; Zhou, J.; Wang, Z. G.; Hsiao, B. S. J Polym SciPart B: Polym Phys 2001, 39, 153.

16. Inomata, K.; Liu, L.-Z.; Nose, T.; Chu, B. Macro-molecules 1999, 32, 1554.

17. Guerra, G.; Vitagliano, V. M.; Rosa, C. D.; Petrac-cone, V.; Corradini, P. Macromolecules 1990, 23,1539.

18. Balta-Calleja, F. J.; Vonk, C. G. In X-ray Scatteringof Synthetic Polymers; Elsevier: New York, 1989; p191.

19. Gianotti, G.; Valvassori, A. Polymer 1990, 31, 473.20. Wunderlich, B. In Macromolecular Physics; Aca-

demic: New York, 1973; Vol. 1, pp 385–388.21. Sun, Z.; Morgan, R. J.; Lewis, D. N. Polymer 1992,

33, 660.22. Norton, D. R.; Keller, A. Polymer 1985, 26, 704.23. Hong, S. M.; Choi, S. H.; Lee, C. H.; Hwang, S. S.;

Kim, K. U.; Cho, I. Polym J 2000, 32, 187.24. Schultz, J. M. J Polym Sci Polym Phys Ed 1976, 14,

2291.25. Miyamoto, Y.; Fukao, K.; Miyaji, H. Colloid Polym

Sci 1995, 273, 66.26. Tosaka, M.; Hamada, N.; Tsuji, M.; Kohjiya, S.

Macromolecules 1997, 30, 6592.27. Debye, D.; Bueche, A. M. J Appl Phys 1949, 20, 518.28. Tosaka, M.; Hamada, N.; Tsuji, M.; Kohjiya, S.;

Ogawa, T.; Isoda, S.; Kobayashi, T. Macromole-cules 1997, 30, 4132.

29. Ho, R. M.; Lin, C. P.; Hseih, P. Y.; Chung, T. M.;Tsai, H. Y. Macromolecules 2001, 34, 6727.

30. Lauritzen, J. I.; Hoffman, J. D. J Appl Phys 1973,44, 4340.

31. Cimmino, S.; Di Pace, E.; Martuscelli, E.; Silvestre,C. Polymer 1991, 32, 1080.

32. Clark, E. J.; Hoffman, J. D. Macromolecules 1984,17, 878.

1636 WANG ET AL.