Charge Distribution and Crystalline Structure inPolyethylene Nucleated with Sorbitol

XIANG LI,1 YI CAO,1 QIANGGUO DU,1 YI YIN,2 DEMIN TU2

1 Department of Macromolecular Science and the Key Laboratory of Molecular Engineering of Polymer, Fudan University,Shanghai 200433, China

2 Department of Electrical Engineering, Xi’an Jiaotong University, Xi’an 710049, China

Received 30 August 2000; revised 8 January 2001; accepted 25 January 2001Published online 10 August 2001; DOI 10.1002/app.1889

ABSTRACT: The charge distribution in samples under direct current electrical field wasmeasured by the pulsed electro-acoustic method, which showed that the space chargeswere greatly decreased and field distribution tended to be uniform in low-densitypolyethylene (LDPE) by adding 0.3 wt % bis-(p-ethylbenzylidene)sorbitol. The crystal-line structures of LDPE and LDPE/sorbitol were studied. The non-isothermal crystal-lization kinetics were investigated by differential scanning calorimetry, which showedthat sorbitol increases crystallization temperature and crystallinity, but lowers theAvrami exponent of crystallization. The results of wide-angle X-ray diffraction (WAXD)and small-angle light scattering (SALS) experiments show that the crystal form doesnot change, whereas the perfection of spherulites degrades in the presence of sorbitol.In addition to the obvious difference in crystalline morphology, observed by scanningelectron microscopy, the spherulites in the LDPE/sorbitol sample are smaller in sizeand more in number than those of LDPE. It is well known that in semicrystallinepolymers, impurities are expelled from crystalline regions into amorphous regions orinterfaces of spherulites. The decrease of space charges can probably be attributed tothe uniform distribution of impurities in the whole material, with smaller and imper-fect spherulites. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 611–619, 2001

Key words: charge distribution; polyethylene; Sorbitol; nonisothermal crystalliza-tion; SALS

INTRODUCTION

Polymers and polymer blends are frequently usedas insulators in electric engineering. The insula-tion characteristic of polymers lies in many local-ized states in the energy band structure and ac-cumulation of space charge. It is therefore impor-tant to understand the mechanism of formationand accumulation of space charge in power cableand to discuss the possibility of elimination. Poly-

ethylene (PE) has been extensively used as aninsulating material for power cables and commu-nication cables because of its high resistivity andlow tand. Many papers have been published oncharge distribution and electrical conduction inthe PE system.1–4 It has been reported, for exam-ple, that the impulse breakdown strength of PEcan be improved by blending with the ionomer2

and ethylene-vinyl acetate copolymer (EVA).4

PE is a typical semicrystalline polymer. Itscrystalline structure must affect the distributionof space charge. A few research works have beendevoted to the relationship between charge distri-bution and crystalline morphology.5, 6 However,

Correspondence to: Q. Du (qgdu@fudan.edu.cn).Journal of Applied Polymer Science, Vol. 82, 611–619 (2001)© 2001 John Wiley & Sons, Inc.

611

we are still far away from a complete understand-ing because of the complexity of crystalline struc-ture, which includes crystallinity, the crystallineform, the size and perfection of spherulites, thethickness of crystalline lamellae, etc.

Sorbitol is a typical nucleating agent forpolypropylene to improve its transparence, butonly a few studies have been devoted to the low-density lipoprotein (LDPE)/sorbitol system. Inthis work 0.3 wt % of sorbitol was added to LDPE.The crystallization kinetics were compared withthe virgin LDPE under nonisothermal conditionsby the differential scanning calorimetry (DSC)method, and the relationship of the charge distri-bution and crystalline morphology was discussedwith the aid of the pulsed electro-acoustic (PEA),small-angle light scattering (SALS), wide-angleX-ray diffraction (WAXD), and scanning electronmicroscopy (SEM) methods.

EXPERIMENTAL

Materials

LDPE was cable grade product DJ200 of Shang-hai Petrochemical Company Ltd.. Bis-(p-ethyl-benzylidene)sorbitol was obtained from MitsuiToatsu Chemicals Inc., Japan, and was used asreceived.

Preparation of Samples

LDPE and 0.3 wt % sorbitol were mixed in themixer of a Brabender Plasticorder at a rotor speedof 40 rpm and a temperature of 230 °C for 5 min.As a control, the virgin LDPE was subjected tothe same processing. Films ;0.5 mm in thicknesswere prepared using a hot press at 170 °C for 5min. These films were used for the measurementof PEA, WAXD, DSC, and SEM experiments.

Space Charge Measurement

The space charge distribution in samples wasmeasured by the PEA method, as shown in Figure1 [direct current (dc) source, 0–20 kV; pulsewidth, 20 ns; pulse voltage, 0–1 kV]. The diame-ter of copper electrode was 25 mm. Aluminumwas deposited on two sides of plate samples as theelectrodes. Silicone oil was used as an acousticcoupling agent to make a good acoustic contactbetween the sample electrode and the measureelectrode. The principle of this method and details

of measurement were described in a previous pa-per.7

DSC Analysis

The crystallization kinetics of the samples wereinvestigated under nonisothermal conditions.8–11

A Perkin Elmer DSC-7 was used for the thermalanalysis and data gathering. The sample was firstrapidly heated up to 170 °C, ;60 °C higher thanthe melting point of LDPE, and maintained atthis temperature for 5 min to erase any previousmorphological history that the sample might becarrying. The sample then nonisothermally crys-tallized when it was cooled down to 0 °C at se-lected cooling rates of 2.5, 5, 10, and 20 °C/min.The entire process of crystallization was per-formed under nitrogen. The enthalpy of crystalli-zation of 100% crystalline LDPE was reported as68.2 cal/g,12 and the degree of the crystallinitywas calculated from the crystallization enthalpyof samples.

WAXD and SALS

WAXD measurements were carried out at roomtemperature on a diffractometer equipped with aCuKa tube and Ni filter over a range of diffractionangle 2u 5 5–40°. The HV light-scattering pat-terns were recorded on a SALS photometerequipped with a polarizer, an analyzer, and aHe-Ne laser source.

Crystalline Morphology

The morphology of the samples was analyzedwith a Hitachi S-520 scanning electronic micro-scope. The samples for morphology measurement

Figure 1 Schematic diagram of apparatus for mea-surement of sample space charge distribution.

612 LI ET AL.

were prepared by cryogenically fracturing thesamples in liquid nitrogen. The amorphous re-gions were selectively extracted from these sam-ples with toluene vapor.

RESULTS AND DISCUSSION

Charge distribution in LDPE and LDPE/sorbitolare shown in Figures 2 and 3. Figure 2 shows thecharge distribution obtained while the dc voltageswere being applied at the stresses of 10, 20, 30,and 40 kv/mm and Figure 3 shows the chargedistribution after short circuit (discharging) for10 s and 1, 10, 30, and 60 min. Under the dcvoltages, the data in Figure 2 show the hetero-charges in the samples of LDPE and LDPE/sorbi-tol. The peak of negative charges is much largerthan that of positive charges, although the het-erocharges appear in both samples, which is prob-ably due to the neutralization. The charges inboth samples increase to a different extent as thevoltage increases; however, the density of chargein LDPE/sorbitol during charging is extremelysmall compared with pure LDPE. In general, theheterocharges in PE generate from chain ends,short branch chains, and impurities including ini-tiator, peroxides, and metal irons generated inthe course of synthesis and process.3 As is shownin Figure 3, it is more interesting that almost nocharge remained in LDPE/sorbitol after discharg-ing as short as 10 s, whereas a few positivecharges remained in pure LDPE. In terms ofthese phenomena, we can presume that consider-able hopping sites or shallow traps must exist inLDPE/sorbitol, so that the charges formed duringthe charging step disappear easily to the elec-trodes on removal of the voltage. Because of the

many deep traps in the pure LDPE, the chargesonce formed in the sample may not disappeareasily after discharging.

To study the crystallization behavior undernonisothermal conditions, the Ozawa equation9

was used to analyze the data. Ozawa assumesthat crystallization occurs at a constant coolingrate and that crystallization originates from nu-clei and grows as a spherulite with constant ra-dial growth rate at a given temperature. Theweight fraction of the crystallized material downto the temperature T is defined by eqs.1 or 2:

1 2 XT 5 exp$2K~T!/Dn% (1)

or

log$2ln~1 2 XT!% 5 log K~T! 2 n log D (2)

where XT is the fraction of material crystallizeddown to the temperature T; D is the cooling rate;K(T) is the cooling function that is related tonucleation form, nucleation rate, growth rate, andso on; and n is the Avrami exponent obtainedfrom the slope in the plot of log{2ln(1 2 XT)versus log D at a given temperature.

In this study, nonisothermal crystallizationwas conducted according to the method describedin the Experimental section. Figure 4 shows thecorresponding DSC thermograms for samples ob-tained at the cooling rate of 10 °C/min. Figures 5and 6 show the DSC thermograms of LDPE andLDPE/sorbitol at several cooling rates, respec-tively. It is shown that crystallization of LDPE/sorbitol occurs at a higher temperature than that

Figure 3 Charge distribution after short circuit of (a)LDPE and (b) LDPE/sorbitol.

Figure 2 Charge distribution at various voltages of(a) LDPE and (b) LDPE/sorbitol.

CRYSTALLIZATION KINETICS OF POLYETHYLENE NUCLEATED WITH SORBITOL 613

of pure LDPE. The starting temperature of crys-tallization gradually lowers with increasing cool-ing rate for both samples. When cooling slowly,there is sufficient time to nucleate; therefore, thesample can crystallize at higher temperature. Onthe contrary, at faster cooling rate, the activationof nuclei occurs at lower temperature. In addition,the width of half-peak in DSC curve inverselyrelates to the perfection of crystal.13 Because the

sample of LDPE/sorbitol shows wider peaks thanLDPE at any cooling rate, the sample in the crys-talline region must contain many more defectsstemming typically from kinking, jogging, back-folding, and displacement of chains, from chainends and from voids in space. When the coolingrate is low, the nonisothermal crystallization issimilar to the isothermal crystallization at highertemperature. Crystallization proceeds at a slowerrate, resulting in more perfect and stable crystals.As the cooling rate increases, supercooling be-comes greater and more defective crystals areobtained. From the DSC curves, it is evident thatsecondary crystallization occurs at ;55 °C, espe-cially at a high scanning rate. The secondary crys-tallization gives rise to more imperfect crystalsaround spherule surfaces because some segmentsof macromolecular chain in the amorphous re-gions can crystallize under low temperature.

The Avrami exponent n can also be determinedfrom Ozawa plots and the slope of the plot oflog{2ln(1 2 XT )} versus log D by the least squaremethod. In determination of the exponent, thecrystalline weight fraction should be ,0.5 be-cause the effects of impingement, truncation ofspherulites, and secondary crystallization kinet-ics might become very important at higher crys-talline fractions, which may change the crystalli-zation mechanism.8, 14 The Avrami exponents so

Figure 4 DSC thermograms of nonisothermal crys-tallization for LDPE and LDPE/sorbitol at the coolingrate of 10 °C/min.

Figure 5 DSC thermograms of nonisothermal crys-tallization for LDPE for different cooling rates.

Figure 6 DSC thermograms of nonisothermal crys-tallization for LDPE/sorbitol for different cooling rates.

614 LI ET AL.

obtained are plotted in Figure 7 and given inTable I. The value for LDPE/sorbitol is apprecia-bly lower than that measured for neat LDPE. Themeasured Avrami exponent of LDPE agrees wellwith the literature data (n 5 1.72).15 These re-sults confirm that the dispersed Sorbitol particlesplay a role of nucleating agent for the crystalliza-tion of LDPE and decrease supercooling temper-ature of the crystallization.

The value of Avrami exponent may be com-prised of two parts: the contribution of the nucle-ation and the contribution of growth. The ob-served difference of the Avrami exponent may beessentially attributed to the nucleation of sorbi-tol. The Avrami exponent is close to 1 for LDPE/sorbitol and 2 for LDPE. The integral value ofLDPE/sorbitol implies that it primarily formsone-dimensional crystallites from heterogeneousnucleation. Taking the considerable short-branching chains in LDPE into account, it is notdifficult to understand that the value is lower

compared with the number of dimensions of per-fect spherulites. The short-branching chains areexpected to be expelled from the crystal latticeand would effectively hinder crystal growth, giv-ing rise to defects. As a result, the material wouldexhibit lower crystallinity.

The WAXD curves for the LDPE and LDPE/sorbitol samples are shown in Figure 8. Both sam-ples have three principal crystalline reflectionpeaks at 2u of 21.4, 23.7, and 36.1°, correspondingto the 110, 200, and 020 lattice planes of theorthorhombic crystalline form of PE, respectively.The amorphous scattering centered at 2uof 19.8°.Reflections of a monoclinic or triclinic form arenot seen on the X-ray diffractogram. These re-sults show that sorbitol does not change crystalform. Interplanar distances shown in Table II arecalculated by the Brag equation. Only a littledifference was found for the two samples. Thewidth of crystal peaks in WAXD crystallograms isinversely related to crystallite breadth perpendic-ular to the crystal plane.16 Because the sample ofLDPE/sorbitol shows wider peaks than LDPE,especially 200 (see Figure 8), the effect of sorbitolis not only a decrease in the average size of thecrystallites, but also a decrease in the order oforiented macromolecular. These changes in thecrystal structure are in good agreement with theresults observed by the SEM and SALS (vide in-fra).

A light scattering method was used to investi-gate the crystalline superstructure occurring inthe polymer film. The HV scattering gives thefamiliar four-leaf-clover-type pattern, with itsmaximum intensity at the position angle (m) of45° and at a particular scattering angle (u), whichis inversely related to the size of spherulite.17 Theperfection of the spherulite decreases as the de-gree of diffusion of the four-leaf-clover-type struc-

Figure 7 Plot of log[2ln(1 2 XC)] versus log D forLDPE and LDPE/sorbitol at 85 °C.

Table I The Half-Peak Width, Avrami Exponent, and Crystallinity from DSC Thermograms at theCooling Rate of 10°C min21

Parameter

LDPE LDPE/Sorbitol

2.5°Cmin21

5°Cmin21

10°Cmin21

20°Cmin21

2.5°Cmin21

5°Cmin21

10°Cmin21

20°Cmin21

Half-peak width ofDSC peak (°C) 3.5 5.2 7.5 14.7 6.2 8.5 11.5 21.0

Avrami exponent — — 1.79 — — — 1.35 —Crystallinity from

DSC (%) — — 42.0 — — — 37.8 —

CRYSTALLIZATION KINETICS OF POLYETHYLENE NUCLEATED WITH SORBITOL 615

ture increases. The theories of spherulitic scatter-ing have been developed based on a model18 of ahomogeneous anisotropic sphere embedded in theisotropic medium, and the HV scattering intensityof spherulite can be written as shown in eq. 3.This approach has successfully described theprincipal feature of most experimental patternsfrom spherulitic systems.

IHV 5 AVS2S 3

U3D 2F ~at 2 ar!cos2u

2 sin m cos

3 m~4 sin U 2 U cos U 2 3SiU!G2

(3)

where HV is scattering with vertical polarizer andhorizontal polarization analyzer, ar is the radialpolarizablity, at is tangent polarizablity, u is the

scattering angle, m is the position angle, VS is thevolume of the spherulite, and U is the shape fac-tor and has the form

U 54pRS

lsin

u

2 (4)

SiU 5 E0

U sin xx dx (5)

where RS is the radius of the spherulite.The dependence of scattering intensity on the

position angle stems from the dependence of3/U3(4 sin U 2 U cos U 2 3SiU on the value of U.There is a maximum of scattering intensity in thescattering profile when U has the value of ;4.0,

Figure 8 WAXD diffractograms of (a) LPDE/sorbitol and (b) LDPE.

Table II d-Spacing of Crystal Planes from WAXD Analysis of LDPE andLDPE/Sorbitol

Sample

Crystal Plane

110 200 020 210 011

LDPE 4.1487 3.7511 2.4833 2.9898 2.2619LDPE/Sorbitol 4.1526 3.7604 2.4847 2.9917 2.2554

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and the corresponding scattering angle is um. Theradius of the spherulite can be obtained witheq. 6:

4pSRS

l Dsinum

2 5 4.0 (6)

The scattering vector has the following form:

q 54p

lsin

u

2 (7)

Then, the relation between the scattering vectorand spherulite size can be written as eq. 8, and

the size of spherulite can be roughly calculatedwith the measured value of qm:

qmRS 5 4.0 (8)

The SALS profiles are obtained from the scatter-ing of intensity (I) of spherulite versus the scat-tering vector (q) at a certain position angle m 5 45°C. The SALS patterns and profiles are shown inFigures 9 and 10, respectively. The crystals ap-pear as spherulite and the size of the LDPE islarger than that of the LDPE/sorbitol. Anotherfundamental difference between the crystals isthat the scattered intensity in Figures 9(a) and10(a) passes through a maximum, whereas thatin Figures 9(b) and 10(b) decreases continuouslywith the increase of scattering angle u. The re-sults show that the imperfection of the spheru-lites becomes more obvious in LDPE/sorbitol andthat spherulite exhibits some perfection in theLDPE sample for the existence of a peak. In gen-eral there is one way to interpret these phenom-ena.17 The interpretation is based on the possibil-ity that the structure is uniformly composed of asingle entity (i.e., spherulites). The average con-tour of the spherulite is considered to scatter lightat small angles, whereas internal heterogeneities

Figure 9 SALS patterns of (a) LDPE and (b) LDPE/sorbitol.

Figure 10 SAXS profiles of LDPE and LDPE/sorbitol. Intensity was plotted againstthe scattering vector q.

CRYSTALLIZATION KINETICS OF POLYETHYLENE NUCLEATED WITH SORBITOL 617

of the spherulites are considered to scatter lightat high angles. The heterogeneities are believedto arise from the existence of the crystallinefibrils, which are not parallel to the radical direc-tion of the spherulites but randomly assembledinside the spherulites. In Figure11, The SEM mi-crographs show the crystalline regions (white sec-tions) that are left after the amorphous regions(gray sections) were etched by toluene vapor (thetotal length of the bar equals 3 mm). It should benoted that the amorphous regions were over-etched by toluene vapor and the deeper-layerspherulites have partially appeared. The morpho-logic difference between samples can be deter-mined directly: Spherulites of LDPE/sorbitol aresmaller in size and much more in number thanthose of LDPE, and the average crystallite sizesare ;0.2 and ;0.3 mm, respectively. These resultsprovide direct evidence that sorbitol particles actas a nucleating agent and decrease the imperfec-tion of the spherulites.

The semicrystalline polymers, like PE, gener-ally have a biphasic structure: crystalline andamorphous phases. The defects in the crystallinephase have similar characteristics to those of theamorphous phase. When polymer is applied to ahigh electrical field, an electron has to traverseamorphous and crystalline regions that behavedifferently with respect to the transport mecha-nism. Crystalline regions have a resistivity tocharges because the molecular chains array in acompact and orderly manner. In contrast, amor-phous regions have a strong affinity for chargesnot only because chains array in a loose and dis-orderly manner, but also all the impurities (in-

cluding free radical residuals, peroxides, ions,and double bonds) almost disperse in amorphousphase, especially in the defects and interfaces ofspherulites. Meanwhile, amorphous regions con-stitute the continuous phase in which the randomchain can pass the charges on to the neighborchain by changing its configuration. Hence, thecharge distribution may depend strongly on themicrostructure of the polymeric morphology.

The results of the PEA method indicate thatcharge distribution in LDPE/sorbitol is uniformduring charging and no charge remains in thebulk after discharging. These results can be in-terpreted as indicating that LDPE/sorbitol con-tains many hopping sites and shallow traps. Thehopping sites extend the mean free path ofcharges to enable subsequent charges to travelthe entire material freely and reduce the chargeaccumulation in a partial locality. Combined withthe analysis of crystalline morphology, we can usethese results to conclude that the generation ofconsiderable hopping sites relates directly to thepresence of considerable defects in crystallinestructure. So, the improvement of charge distri-bution in LDPE/sorbitol is attributed to two ef-fects: decreasing the size of spherulite as well asslightly increasing the crystallinity causes theaugmentation of the interfacial area betweencrystalline and amorphous regions and results inthe improvement of the impurity distribution.The direct result is that, in a partial locality, thedensities of the impurity and charge trap de-crease. Second, considerable impurities andcharges also can disperse in the crystalline re-gions because of the existence of defects. Consid-

Figure 11 SEM patterns of (a) LDPE and (b) LDPE/sorbitol.

618 LI ET AL.

erable defects and impurities, acting as hoppingsites in the process of charge recombination, con-tribute to disappearance of the injected charges.

CONCLUSIONS

In the present report we measured the chargedistribution of LDPE and LDPE/sorbitol andstudied the crystallization process under noniso-thermal conditions and crystalline morphology.We also investigated the microstructure ofspherulites and interpreted the distinction be-tween the two samples in terms of light scatteringtheories. From the results, the following conclu-sions can be made:

1. The charge distribution of LDPE can beobviously improved in the presence of sor-bitol.

2. Sorbitol, acting as a nucleating agent forLDPE, changes the crystallization mecha-nism and decreases the perfection of thecrystalline region as well as the inside ofspherulites. The defects may cause the uni-form distribution of impurities in the wholematerials, with smaller and imperfectspherulites, and cause the decrease ofspace charge. However, there is no changein the crystalline form between LDPE andLDPE/sorbitol.

3. The improvement of the charge distribu-tion in LDPE/sorbitol may be attributed tothe existence of defects in the crystallineregion as well as the inside of spherulitesmay cause

The work was supported by the Key Laboratory ofMolecular Engineering of Polymer, Ministry of Educa-tion in China. Professor Tu wishes to thank NaturalScience Fund Committee.

REFERENCES

1. Kitagawa, K.; Sawa, G.; Ieda, M. Jpn J Appl Phys1980, 19, 389.

2. Suh, K.S.; Hwang, S.J.; Lee, C.R. IEEE Trans Di-elec Elec Insul 1997, 4, 58.

3. Suh, K.S.; Koo, J.H.; Lee, S.H.; Park, J.K. Takada,T. IEEE Trans Dielec Elec Insul 1996, 3, 153.

4. Suh, K.S.; Kim, J.Y.; Lee, C.R.; Takada, T. IEEETrans Dielec Elec Insul 1996, 3, 201.

5. Fan, Z.H.; Yoshimura, N. IEEE Trans Dielec ElecInsul 1996, 3, 849.

6. Kolesov, S.N. IEEE Trans Dielec Elec Insul 1980,15, 382.

7. Li, Y.; Yasuda, M.; Takada, T. IEEE Trans DielecElec Insul 1994, 1, 188.

8. Lopez, L.C.; Wilkes, G.L. Polymer 19989, 29, 106.9. Ozawa, T. Polymer 1971, 12, 150.

10. Kozlowski, W. J Polym Sci, Part C 1970,38, 47.11. Eder, M.; Wlochowicz, A. Colloid Polym Sci 1983,

261, 621.12. Wunderlich, B.; Cormier, C.M. J Polym Sci, Part

A-2 1967, 5, 987.13. Gupta, A.K.; Purwar, S.N. J Appl Polym Sci 1984,

29, 1595.14. Eder, M.; Wlochowicz, A. Polymer 1983, 24, 1593.15. Gupta, A.K.; Rana, S.K.; Deopura, B.L. J Appl

Polym Sci 1994, 51, 231.16. Yoda, O.; Odajima, A. Jpn J Appl Phys 1980, 19,

1241.17. Hashimoto, T.; Murakmi,Y.; Okamori, Y.; Kawai,

H. Polym J 1974, 6, 554.18. Stein, R.S.; Rhodes, M.B. J Appl Phys 1960, 31,

1873.

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