Journal of Polymer Research 9: 175–181, 2002.© 2002 Kluwer Academic Publishers. Printed in the Netherlands.

175

Bulk Crystallization Kinetics of Metallocene Polyethylenes with Well-controlledMolecular Weight and Short Chain Branch Content

Fang-Chyou Chiu1, Ya Peng2 and Qiang Fu2,∗1Department of Chemical and Materials Engineering, Chang Gung University, Taoyuan 333, Taiwan2Department of Polymer Science and Materials, Sichuan University, State Key Laboratory of Polymer MaterialsEngineering, Chengdu 610065, Sichuan, PROC ( ∗Author for correspondence; Tel.: +86-28-85460953;Fax: +86-28-85405402; E-mail: fuqiang1963@yahoo.com)

Received 19 March 2002; accepted in revised form 16 May 2002

Key words: crystallization, metallocene polyethylene, regime transition

Abstract

Collaborating with Phillips Petroleum Company, we obtained a series of metallocene polyethylenes (mPE) with narrowmolecular weight distribution and uniform short chain branching. The overall crystallization data of these mPEs and twoother linear PEs determined from differential scanning calorimetry (DSC) was analyzed and compared using the well-known Avrami equation. The crystallization temperature and the crystallization rate were found to depend on the molecularweight and short chain branch (SCB) content as well. However, the SCB content played a comparatively dominant role.The secondary-nucleation-theory-based regime transition concept was applied to analyze the kinetic data, too. The crystalgrowth regimes and the regime transition temperatures observed were discussed in terms of the effect of SCB on the relativerates of surface nucleation and lateral spreading.

Introduction

Conventionally, the crystallization kinetics of small mole-cules can be analyzed using the regime transition theory. Forpolymer crystallization, the regime transition concept wasnot applied until Lauritzen and Hoffman’s first report [1],with experimental evidence of regime I–regime II transi-tions observed for polyethylene (PE) fractions. Phillips [2]shortly thereafter predicted the existence of a third regime(regime III). The regimes are defined by the relative ratesof the nucleation of polymer stems onto the substrate sur-face and the lateral spreading of polymers across the sub-strate layer. Schematic diagrams of the three crystal growthregimes are shown in Figure 1 [3]. At higher crystallizationtemperatures, the lateral spreading rate proceeds rapidly af-ter surface nucleation is completed; and the chain moleculescover the entire substrate surface before another successivesurface nucleation, which is called regime I crystallization(Figure 1(a)). For regime II crystallization, the crystalliza-tion temperature is lowered; and the surface nucleation rateoccurs comparably to the lateral spreading rate, resulting ina process of multiple nucleations growing on a mono-crystallayer, as shown in Figure 1(b). When the crystallizationtemperature is further decreased, regime III crystallization isencountered. The number of surface nuclei per unit length ofsubstrate increases, as shown in Figure 1(c). Thus, multiplenucleations occur simultaneously on several crystal growthlayers.

Several papers have reported on various crystal growthregimes and regime transition temperatures for PEs. Usingpolarized light microscopy, Hoffman et al. [4] and Chiuet al. [5] measured the crystal growth rates of linear PEfractions and observed the regime transitions. Lambert andPhillips [6] measured the crystal growth rates of linear lowdensity PE (LLDPE) fractions with similar molecular weightbut different short chain branch (SCB) content. They con-cluded that the regime I–regime II transitions of LLDPEsshifted to slightly lower temperatures in comparison withthat of a linear PE fraction. The SCB indeed reduced therates of surface nucleation and lateral spreading, but to adifferent degree. Their result also showed that regime tran-sition temperatures estimated from the bulk kinetic dataagreed fairly with that determined directly from the growthrate data. Furthermore, the regime II–regime III transitionswere observed in the gel fractions of cross-linked linearPE fractions [7]. It was thus concluded that many factors,such as molecular architecture, molecular weight, molecularweight distribution (MWD), and impurity, would influencethe crystal growth mechanism of PEs.

In recent decades, the single-sited feature of metallo-cene-catalyzed PE (mPE) has led to a narrow MWD and auniform SCB distribution. Due to its superior mechanicaland thermal properties, mPE has received a lot of interestboth industrially and academically since its synthesis [8–15].Hitherto, mPE with better control of molecular architecturehas become a model polymer for studying the crystalliza-tion kinetics and crystalline morphology. In this article, we

176 Fang-Chyou Chiu et al.

Figure 1. Schematic diagrams of crystal growth regimes with decreasingcrystallization temperature: (a) regime I; (b) regime II and (c) regime III [3].

report the results of an investigation on the bulk crystalliza-tion kinetics of mPE fractions with well-controlled mole-cular weight and SCB content using differential scanningcalorimetry (DSC). The possible crystal growth regimes andthe regime transition temperatures observed are discussed interms of the effect of SCB on the surface nucleation rate andthe lateral spreading rate (reptation rate).

Experimental

Materials

The molecular characteristics of the mPE fractions inves-tigated are listed in Table 1. They were obtained using across-fractionation (CF) technique composed of a solventgradient fractionation (SGF) process followed by a tem-perature gradient fractionation (TGF) process [14]. These

materials possess narrow MWD along with uniform SCBdistribution. The original unfractionated whole mPE samplewas synthesized using a Zr-based homogeneous metallocenecatalyst, and it was ethyl group (1-butene comonomer)branched. Additionally, two linear PEs with different mole-cular weights were investigated for comparative purposes.Thus, the PE samples studied were classified into threegroups: (I) linear PEs with two different molecular weights;(II) low molecular weight mPEs with two SCB contents(branching effect can be studied) and (III) high molecularweight mPEs with two SCB contents (molecular weight ef-fect as well as branching effect can be studied, comparedwith group II samples). Compared with the LLDPE frac-tions (hexyl branched) studied by Lambert and Phillips [6],the mPEs used here show two main features: (1) they weresynthesized using a metallocene catalyst instead of a con-ventional catalyst; therefore, the molecular weight and SCBcontent are well defined and more homogeneous inter- andintramolecularly; (2) the molecular weight and SCB contentare relatively higher, hence the crystallization kinetics areexpected to be more complicated.

Instrument and Measurements

Since the SCB content of the mPEs was relatively high, noevident spherulite but only tiny crystallites or fringed mi-cellar crystals can be grown from the melt [16]. It is thusimpossible to study the crystallization kinetics through lightmicroscopy by recording the crystal growth rate. Neverthe-less, as evidenced by previous reports [6, 7, 17], the crystalgrowth regime(s) could still be identified irrespective of theexperimental method employed. That is, the overall crys-tallization rate data can also result in a reliable conclusion,presuming a heterogeneous nucleation process is involved.

The crystallization kinetics investigations were con-ducted on a Perkin-Elmer DSC Pyris 1 system. The spec-imens for measurements weighed in the range of 3–5 mg.During the measurements, dried N2 gas was purged at aconstant flow rate. The temperature reading and calorimetric

Table 1. Molecular characteristics of polyethylenes used in the study

Group/sample ID Sample Mw Mn Mw/Mn SCB type SCB

description (g/mol) (g/mol) (mole %)

I 9507-1 Low MW/linear 24.9k 23.0k 1.08 – –

(SGF)

9507-2 High MW/linear 201k 170k 1.18 – –

(SGF)

II 9507-3 Low MW/high B 29.9k 27.2k 1.10 Ethyl 7.34

(CF)

9507-4 Low MW/low B 28.5k 25.9k 1.10 Ethyl 5.95

(CF)

III 9507-5 High MW/high B 136k 119k 1.14 Ethyl 8.58

(CF)

9507-6 High MW/low B 103k 92k 1.12 Ethyl 5.51

(CF)

Abbreviations: SGF: Solvent Gradient Fractionated; CF: Cross Fractionated; SCB type: Short Chain Branch Type; Linear: linear polymer; High B: higherbranched; Low B: lower branched.

Crystallization Kinetics of Metallocene Polyethylenes 177

Table 2. Apparent DSC thermal properties

Sample Ta, c∗ ( ◦C) �Ha, c

∗ (J/g) Tm# ( ◦C) �Hf

# (J/g)

9507-1 117.5 213 134.2 213

9507-2 114.1 154 136.5 158

9507-3 70.5 63 90.3 52

9507-4 78.8 78 97.8 64

9507-5 59.6 45 78.4 44

9507-6 75.8 67 98.3 56

∗Samples cooled from the melt under the rate of 10 ◦C/min.#Samples heated under the rate of 10 ◦C/min.

measurements were calibrated with a standard material, in-dium. Upon the experiments, the specimens were first heatedto 160 ◦C for 5 min to remove the residual crystals. Then, thespecimens were cooled at a rate of 10 ◦C/min to room tem-perature for non-isothermal crystallization behavior study.For isothermal crystallization experiments, the specimenswere cooled rapidly from the melt to the predetermined crys-tallization temperature (Tc) at a rate of 100 ◦C/min, and heldat that Tc until the crystallization was completed. There-after, the specimens were heated again to obtain the DSCendotherms at a rate of 10 ◦C/min.

Results and Discussion

Bulk Crystallization Behavior

The non-isothermal crystallization behavior of the sampleswas compared first. Table 2 lists the apparent non-isothermalcrystallization temperature (Ta, c), and the apparent heatof crystallization (�Ha, c) determined from the coolingprocesses. Included in the table are also the melting tem-perature Tm and the heat of fusion (�Hf) revealed fromthe subsequent heating scans. From the table, it is foundthat increasing the molecular weight or SCB content resultsin decreases of Ta, c, �Ha, c and �Hf values. Particularly,the SCB content exhibits a major influence. Regarding theTm values, the trend is not so obvious due to the complexmelting endotherms. But the effect of SCB content is alsonoticed.

Based on the non-isothermal crystallization data, theisothermal crystallization experiments were conducted. Thefollowing logarithmic Avrami equation [18–20] is frequentlyused to analyze the isothermal crystallization kinetics ofpolymers:

log[−ln(1 − Xt)] = log K + n log t, (1)

where K (composite rate constant) and n (mechanism con-stant) are the Avrami parameters which depend on the nu-cleation type, crystal growth geometry and the linear growthrate; Xt is the relative fractional crystallinity which can bedetermined from DSC exotherm at time t by the followingequation:

Xt =∫ t

0

dHt

dtdt

/ ∫ t0

0

dHt

dtdt, (2)

Figure 2. The typical DSC traces of 9507-2 crystallized at indicated tem-peratures: (a) Tc = 120 ◦C; (b) Tc = 121 ◦C; (c) Tc = 122 ◦C;(d) Tc = 123 ◦C and (e) Tc = 124 ◦C.

Figure 3. The typical DSC traces of 9507-4 crystallized at indicated tem-peratures: (a) Tc = 85 ◦C; (b) Tc = 86 ◦C; (c) Tc = 87 ◦C; (d) Tc = 90 ◦Cand (e) Tc = 91 ◦C.

where dHt is the enthalpy change and t0 is the time at theend of crystallization. It is expected from the non-isothermalcrystallization data that the time and temperature for crys-tallization exotherm to be observed are very much differentfor different specimens. Figures 2 and 3 depict the typ-ical DSC isothermal crystallization traces of 9507-2 and9507-4 as examples (other data not shown here for brevity).For linear 9507-2, the crystallization temperatures indi-cated are between 120∼124 ◦C, while for branched 9507-4,the crystallization temperatures are much lowered down to85∼91 ◦C. The typical Avrami plots of log[−ln(1 −Xt)] vs.log t for 9507-2 and 9507-4 are shown in Figures 4 and 5.Each curve shows at least an initial linear portion that isapproximately parallel to each other. The deviation fromlinearity at the late stage of crystallization is ascribed to thesecondary crystallization. The slopes and the intercepts (atlog t = 0) of these linear portions correspond to the Avramin and log K values, respectively. The representative n andK values are listed in Table 3. Consequently, the crystal-lization half-time (t1/2), the time at which 50% of relativecrystallinity was completed, could be obtained through thefollowing equation:

t1/2 = (ln 2/K)1/n. (3)

178 Fang-Chyou Chiu et al.

Figure 4. Typical plots of log[−ln(1 − Xt )] versus log t for 9507-2.

Figure 5. Typical plots of log[−ln(1 − Xt )] versus log t for 9507-4.

The value of t1/2 can be used to qualitatively represent thecrystallization rate. The lower the t1/2 value the faster therate of crystallization. Figure 6 shows the plots of t1/2 vs.Tc for all of the samples. The molecular weight effect onthe crystallization rate can be evidenced from the data ofthe two linear PE samples (9507-1 and 9507-2). The t1/2 of9507-2 is approximately 6 times larger than that of 9507-1at the same Tc, whereas the molecular weight of the for-mer is about 8 times higher than that of the later. Regardingthe branch content effect, a large shift of Tc to lower tem-peratures for branched mPEs is observed. It is also worthynoting that only a few degrees of Tc difference exist be-tween the two linear PEs with noticeable molecular weightdifference. However, at a similar molecular weight, the Tcdifference between the linear PE and the branched mPE ismore than 30 ◦C for the same t1/2. It is indicative that theSCB plays a key role in controlling the crystallization ratesof branched mPEs. Comparing the data from 9507-4 withthat from 9507-6, only a ca. 3 ◦C difference in Tc exists forthe same t1/2. This is ascribed to the fact that these twosamples have almost identical SCB content although a ca.3.5 times difference in molecular weight exists.

It is also informative to compare the kinetics of 9507-3with that of 9507-6. The 9507-3 has a lower molecularweight but a higher SCB content than that of 9507-6. Thet1/2 of the 9507-3 is much larger than that of 9507-6 at thesame Tc. This result further suggests that the SCB effect onthe crystallization rate is more evident than that of the mole-cular weight effect. For 9507-5, possessing both the highestmolecular weight and the highest SCB content, the Tcs arethe lowest among all the samples to reach the same t1/2. In

Table 3. Representative Avrami exponent n and rate constant K

Sample Tc (◦C) n K Sample Tc (◦C) n K

9507-1 123 2.3 6.2 9507-2 120 2.9 6.2

124 2.6 0.53 121 2.9 3.1

125 2.8 0.066 122 3.0 0.73

126 3.1 0.0069 123 3.0 0.082

127 3.0 4.3E-4 124 3.3 0.0026

9507-3 80 2.3 0.19 9507-4 85 2.5 6.4

81 2.5 0.068 86 2.8 3.5

82 2.5 0.016 87 2.7 1.2

83 2.7 0.0051 90 2.5 0.023

84 2.5 0.0022 91 2.7 0.0040

85 2.4 3.7E-4 93 2.9 3.4E-4

9507-5 67 2.6 1.6 9507-6 85 2.4 0.45

68 2.5 0.40 86 2.6 0.067

69 2.7 0.067 87 2.8 0.021

70 2.9 0.014 88 2.5 0.0084

71 2.4 0.0041 89 2.4 0.0012

72 2.1 0.0017 90 3.1 5.4E-4

Figure 6. Crystallization half time as a function of crystallization tempera-ture for all the samples.

this case, the molecular weight and SCB content express acombined effect on the crystallization rate, while the SCBcontent plays a major role.

Regime Transition Analysis

It is recognized that making a detailed interpretation of theDSC bulk crystallization data is not easy. Since the datacontains the individual contribution of the nucleation rate,primary crystal growth rate and secondary crystallizationrate. However, as mentioned in the Experimental section,it is possible to estimate the crystal growth regimes and theregime transition temperatures over the Tc range studied byusing the bulk crystallization rate data.

The crystal growth regime can be analyzed using thefollowing Lauritzen–Hoffman equation [4]:

G = G0 exp{−U∗/[R(Tc − T∞)]} exp{−Kg/[Tc(�T )f ]},(4)

where G0 is a pre-exponential factor that includes all termsthat are taken as effectively independent of the temperature,

Crystallization Kinetics of Metallocene Polyethylenes 179

G is the linear crystal growth rate, U∗ is the activation en-ergy for the chain motion (1500 cal/mol [4–7, 23]), R isthe gas constant, T∞ is the temperature below which chainmotion ceases (T∞ = Tg − 30 ◦C), Tc is the crystallizationtemperature, �T is the degree of supercooling, f is a correc-tion factor, f = 2Tc/(T

0m + Tc), to account for the variation

in �H 0f (the bulk enthalpy of fusion per unit volume for fully

crystalline polymer) with temperature, Kg is the nucleationconstant containing contributions from the surface free en-ergies, and it can be expressed using either of the followingtwo equations:

Kg = 4b0σσeT0m/k(�H 0

f ) (for regime I and III), (5)

Kg = 2b0σσeT0m/k(�H 0

f ) (for regime II), (6)

where σ and σe is the lateral and fold surface free energy,respectively; b0 is the layer thickness of the growth front(4.15 × 10−8 cm); k is the Boltzmann constant.

Prior to applying the Lauritzen–Hoffman equation to an-alyze the crystallization kinetics, consideration should begiven to the controversial value of T 0

m. In fact, T 0m is com-

monly taken as 144.5 ◦C for a linear PE having an infinitemolecular weight [6, 7, 23]. Regarding the branched PEs, thecorrection for T 0

m can be made via Flory’s equation [21]. Forsimplicity, the value of T 0

m = 144.5 ◦C along with the valueof �H 0

f = 293 J/g [22] were adopted for all the data analy-sis here. This treatment will cause no difference in regimeobservations but a slight difference in the supercooling cal-culation as indicated in previous reports [4, 6]. The plots of[log(1/t1/2) + U∗/[2.303R(Tc − T∞)] vs. 1/(Tc�Tf ) forthe six samples are shown in Figure 7. The reciprocal valueof t1/2 is substituted for crystal growth rate G that includedin Eq. (4).

From Figure 7, depending on the Tc, either regime I orregime II crystallization is observed for the two linear PEs(9507-1 and 9507-2). The existence of these two regimesis expected, and is confirmed by the change in the slope ofthe data-fitted straight lines. The regime transition tempera-tures and the slope ratios are listed in Table 4. The transitiontemperature for 9507-1 and 9507-2 is around 125.5 ◦C and122.3 ◦C, respectively, and agree fairly with the data in thementioned literature.

It is also observed that introducing a high content of ethylbranch into the linear PE alters the crystal growth regimedrastically. For example, the regime I–regime II transitionof branched 9507-6 (high molecular weight) takes place ataround 88 ◦C, which is about 34 ◦C lower than that of linear9507-2 (high molecular weight). As reported by Lambertand Phillips [6], the regime I–regime II transition shiftedjust to 123.1 ◦C even for the highest branched LLDPE frac-tion (21.75 branches/1000 CH2). More interestingly, withan increase in the supercooling, the regime III crystalliza-tion of 9507-6 may occur as indicated by a clear turningpoint at about 86 ◦C. It is calculated that the slope ratio ofthe presumed regime III region to regime II region is about1.88, which is close to the theoretical value of 2. However,the regime III crystallization was not observed in Lambert’ssamples. The different result observed here is mainly due tothe differences in the samples’ microstructure. In fact, the

(a)

(b)Figure 7. Crystallization kinetics of the samples analyzed with regimetransition theory: (a) linear PEs; (b) branched mPEs.

traditional LLDPE can be considered as a blend of mole-cules with different ethylene segment sequence lengths. Thenon-uniformly distributed branches reduce more of the sur-face nucleation rate than the lateral spreading rate, so resultin an increase in supercoolings over which regime I exists.However, for the mPEs with uniform SCB distribution, thebranches may hamper both the surface nucleation rate andthe lateral spreading rate seriously, especially at high branchcontent. If a major reduction in the lateral spreading rate oc-curs, the surface nucleation rate will be relatively faster; thusthe regime III crystal growth may be observed. The effectof the high SCB content on the lateral spreading rate canalso be confirmed by the appearance of possible regime II–regime III transition in 9507-4, which possesses a slightlyhigher branch content but a lower molecular weight thanthose of 9507-6. No regime I crystal growth is observed inthis sample, and the presumed regime II–regime III transi-tion occurs at around 91.3 ◦C. Compared with that of 9507-6,the higher regime II–regime III transition temperature ofthis sample is due to the lower molecular weight. The ab-sence of regime I is reminiscent of the cross-linked PEs inPhillips’ et al. work [7]. The high SCB content exhibits asimilar function as those of cross-links which reduce the lat-eral spreading rate to a higher degree causing the relativelyfaster surface nucleation rate.

For the other two mPEs with even higher SCB content,9507-3 and 9507-5, a linear line without an obvious turningpoint is observed, indicating no regime transition possibly

180 Fang-Chyou Chiu et al.

Table 4. Regime transition data determined from bulk kinetics analysis

Sample Transition Slope ratio T 0m ( ◦C)∗ Supercooling

temperature ( ◦C) ( ◦C)

9507-1 125.5 (I–II) 1.53 (I/II) 144.5 19.0

9507-2 122.3 (I–II) 2.43 (I/II) 144.5 22.2

9507-3 – – 131.9 –

9507-4 91.3 (II–III) 1.85 (III/II) 134.3 43.0

9507-5 – – 129.9 –

9507-6 88.1 (I–II) 1.94 (I/II) 135.0 46.9

86.2 (II–III) 1.88 (III/II) 48.8

∗Calculated based on Flory’s [21] equation using T 0m = 144.5 ◦C for the

linear fractions.

exists in the Tc range studied. It is speculated for the presentthat the crystal growth regime existing is regime III, since thelateral spreading rate should be further hampered relativelyto the surface nucleation rate in the low Tc region. However,to support this statement more evidence is needed. Further-more, it was reported [8], depending on the SCB content,that the morphology of branched mPE could be classifiedinto four types. Type IV exhibits a lamellar morphologywith a well-developed spherulitic superstructure. Type IIIshows thinner lamellae and smaller spherulites. Type II hasa mixed morphology of small lamellae and bundled crys-tals. Very small spherulites can also be detected. Type Ishows neither lamellae nor spherulites. The fringed micellaror bundled crystals are inferred from the low crystallinityalong with the low melting temperatures. We have concludedthat 9507-4 and 9507-6 formed type II morphology; and9507-3 and 9507-5 exhibited type I morphology [16]. Therepresentative DSC heating traces of group I∼III samples(i.e., 9507-2, 9507-4 and 9507-5), isothermally crystallizedat various temperatures without prior cooling to room tem-perature, are shown in Figures 8–10, respectively. Only onemelting endotherm is found for linear 9507-2 regardless ofthe Tc. Two or three partially overlapped melting endothermsare found for branched 9507-4 and 9507-5, indicating a morecomplicated morphology exists. In this aspect, the relation-ship between the crystal morphology and the crystal growthregime may need to be verified.

Some Remarks Concerning the Regime Transition Theory

Over the years various crystallization models of polymershave been proposed and worked out. Meanwhile, the regimetransition theory is still widely and successfully used in mostof the data evaluation. One of the basic features of the regimetransition for traditional PEs is that regime I–regime II tran-sition always takes place around a supercooling of 17 ◦C[4, 5]. However, for the branched mPEs studied here, thetransitions occur at unexpectedly high supercoolings (seeTable 4). Questions thus arise. Does the regime transitiontheory, which is based on the concept of secondary nucle-ation, still hold true for our branched samples? If so, cana copolymer crystallize faster than or comparable to a ho-mopolymer? In fact, it was found [23], in the investigation ofa series of mPEs (ethylene-octene copolymers), at the low-est crystallization temperatures (i.e., well inside regime III

Figure 8. The DSC heating traces of 9507-2 crystallized at selected tem-peratures: (a) Tc = 124 ◦C; (b) Tc = 123 ◦C; (c) Tc = 121 ◦C and(d) Tc = 120 ◦C.

Figure 9. The DSC heating traces of 9507-4 crystallized at selected tem-peratures: (a) Tc = 85 ◦C; (b) Tc = 90 ◦C; (c) Tc = 91 ◦C and(d) Tc = 93 ◦C.

Figure 10. The DSC heating traces of 9507-5 crystallized at selected tem-peratures: (a) Tc = 67 ◦C; (b) Tc = 69 ◦C; (c) Tc = 71 ◦C; (d) Tc = 72 ◦Cand (e) Tc = 73 ◦C.

Crystallization Kinetics of Metallocene Polyethylenes 181

crystallization for all samples), the spherulite growth ratesof the samples merged with the growth curve of a linear PEand were virtually indistinguishable. These results seemed toindicate a major breakdown in the current theories of poly-mer crystallization, and suggested the possibility of someother process preceding the actual crystallization event it-self. Actually, recent novel experimental results have ledto a renewed interest in the topic of polymer crystallization[24–29]. The new results demand profound revisions of theexisting theoretical models including the regime transitiontheory. For example, the model put forth by Strobl [30] sug-gests that the formation/growth of lamellar crystallites is amulti-step process passing over intermediate states. To ourviewpoint, the branched mPEs with narrow MWD and uni-form SCB distribution may well serve as ideal compoundsto explore a new model for polymer crystallization.

Conclusion

Compared with linear PEs, dramatic decreases in the crystal-lization temperature and crystallization rate were observedfor branched mPEs. The crystallization temperature andcrystallization rate were highly branch-content dependent,and the effect of molecular weight was less important (inthe molecular weight range studied). The SCB caused theregime I–regime II transition of mPE shifting toward a lowertemperature if the transition still existed. Moreover, theregime II–regime III transitions were observed for certainmPEs. For mPEs with relatively higher SCB content, onlyregime III crystallization possibly existed. To elucidate thecrystallization kinetics in depth, the relationship betweencrystal morphology and crystallization mechanism shouldbe recognized. Furthermore, the effect of SCB content onthe rates of surface nucleation and lateral spreading shouldbe verified quantitatively.

Acknowledgments

F. C. Chiu appreciates the financial support from NationalScience Council of Taiwan under grant NSC90-2216-E-182-003. Q. Fu, would like to express his great thanks tothe China National Distinguished Young Investigator Fund

and the National Natural Science Foundation of China forthe financial support. All of the authors thank Dr. EricT. Hsieh (Phillips Petroleum Company, Bartlesville, Okla-homa, USA) for kindly supplying the studied samples.

References

1. J. I. Lauritzen and J. D. Hoffman, J. Appl. Phys., 44, 4340 (1973).2. P. J. Phillips, Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.), 20,

438 (1979).3. S. J. Organ and A. Keller, J. Mater. Sci., 20, 1571 (1985).4. J. D. Hoffman, L. J. Frolen, G. S. Ross and J. I. Lauritzen, J. Res. Nat.

Bur. Stand. Sect. A, 79, 671 (1975).5. F. C. Chiu, Q. Fu and E. T. Hsieh, J. Polym. Res., 6, 219 (1999).6. W. S. Lambert and P. J. Phillips, Macromolecules, 27, 3537 (1994).7. P. J. Phillips and W. S. Lambert, Macromolecules, 23, 2075 (1990).8. S. Bensason, J. Minick, A. Moet, S. Chum, A. Hiltner and E. Baer,

J. Polym. Sci., Polym. Phys. Ed., 34, 1301 (1996).9. A. Marigo, R. Zannetti and F. Milani, Eur. Polym. J., 33, 595 (1997).

10. F. C. Chiu, Q. Wang, Q. Fu, S. Z. D. Cheng, B. S. Hsiao, F. Yeh,M. K. Keating, E. T. Hsieh and C. C. Tso, J. Macromol. Sci. Phys. B,39(3), 317 (2000).

11. C. Wang, M. C. Chu, T. L. Lin, S. M. Lai, H. H. Shih and J. C. Yang,Polymer, 42, 1733 (2001).

12. Q. Fu, F. C. Chiu, T. He, J. Liu and E. T. Hsieh, Macromol. Chem.Phys., 202, 927 (2001).

13. F. C. Chiu, Q. Fu, Y. Peng and H. H. Shih, J. Polym. Sci., Polym.Phys. Ed., 40, 325 (2002).

14. E. T. Hsieh, C. C. Tso, J. D. Byers, T. W. Johnson, Q. Fu andS. Z. D. Cheng, J. Macromol. Sci. Phys. B, 36(5), 615 (1997).

15. M. H. Kim, P. J. Phillips and J. S. Lin, J. Polym. Sci., Polym. Phys. Ed.,38, 154 (2000).

16. Y. Peng, Q. Fu and F. C. Chiu, Polym. Int., in press.17. R. C. Allen and L. Mandelkern, Polym. Bull., 17, 473 (1987).18. M. Avrami, J. Chem. Phys., 7, 1103 (1939).19. M. Avrami, J. Chem. Phys., 8, 212 (1940).20. M. Avrami, J. Chem. Phys., 9, 177 (1941).21. P. J. Flory, J. Chem. Phys., 17, 223 (1949).22. B. Wunderlich, Thermal Analysis, Academic Press, New York, 1990.23. J. Wagner and P. J. Phillips, Polymer, 42, 8999 (2001).24. K. Tashiro, S. Sasaki, N. Gose and M. Kobayashi, Polymer J., 30, 485

(1998).25. N. V. Pogodina, S. K. Siddiquee, J. W. van Egmond and H. H. Winter,

Macromolecules, 32, 1167 (1999).26. G. Matsuba, K. Kaji, K. Nishida, T. Kanaya and M. Imai, Polymer J.,

31, 722 (1999).27. N. J. Terrill, P. A. Fairclough, E. Towns-Andrews, B. U. Komanschek,

R. J. Young and A. J. Ryan, Polymer Commun., 39, 2381 (1998).28. K. Fukao and Y. Miyamoto, Phys. Rev. Lett., 79, 4613 (1997).29. A. Keller and S. Z. D. Cheng, Polymer, 39, 4461 (1998).30. G. Strobl, Eur. Phys. J., E3, 165 (2000).