x-ray diffraction studies on reverse-annealed polyethylenes

$: X-ray diffraction studies on reverse-annealed polyethylenes$
X-Ray Diffraction Studies on Reverse-AnnealedPolyethylenes

F. CSER,1* J. L. HOPEWELL,1 R. A. SHANKS2

1 Cooperative Research Centre for Polymers, 32 Business Drive, Notting Hill, VIC 3168, Australia

2 Department of Applied Chemistry, RMIT University, Melbourne, VIC 3000, Australia

Received 20 December 1999; accepted 3 June 2000Published online 27 April 2001

ABSTRACT: Linear low and high density polyethylene sheets were compression moldedand crystallized at a 5–10°C/min cooling rate. Parts of the sheets were annealed atdifferent temperatures up to 2°C below the melting temperature. The small angle X-rayscattering (SAXS) and the wide angle X-ray scattering intensities of the annealedsamples were studied. SAXS intensities showed particle scattering with a bimodal sizedistribution. The estimated radii of gyration were 15–17 nm and 5–7 nm, respectively.The crystallinity and the radius of gyration increased slightly with increasing anneal-ing temperature for some samples; others did not show any change. No peaks charac-teristic of intercorrelated lamellar crystallinity in the SAXS intensities developedduring the annealing. The original broad peak of high density polyethylene disappearedfrom the SAXS recordings on annealing. The length of the perfect chain versus meltingtemperature was calculated by the Thomson-Gibbs formula and Flory’s concept ofmelting temperature depression where methyl groups and tertiary carbon atoms at thebranches were regarded as second components (solvent). Linear relationships werefound for both cases. Experimental data for a linear low density polyethylene obtainedfrom the literature were in between the two functions. A lamellar model of crystalli-zation corresponding to the data is proposed. © 2001 John Wiley & Sons, Inc. J Appl PolymSci 81: 340–349, 2001

Key words: polyethylene; annealing; X-ray diffraction; particle size; coupled system

INTRODUCTION

Several melting peaks can be produced in differ-ent grades of linear low density polyethylene(LLDPE) and low density polyethylene (LDPE) bystepwise isothermal crystallization.1–5 A thermalmemory effect was first used to explain the phe-nomenon.1,2 The thermal memory effect could be

eliminated by a strain of 300–400%1 or by a smallincrease in the temperature above the peak tem-perature of the individual melting endotherms(e.g., by 3 K). The change took place in the mate-rial in a time scale of 2–3 min.5

It was proposed by others6–9 that the multipleendotherm in the melting process was the resultof some kind of fractionation of the material. Thebases of this were the differences in the density ofthe branching along the polymeric chains. Thesmaller the unperturbed length of chain mole-cules between two branches, the lower the melt-ing peak temperature of the endotherm.

Defoor and coworkers7 prepared bimodalblends of polyethylene (PE) and investigated

* Present address: RMIT University, Dept. of Chemical andMetallurgical Engineering, P.O. Box 2746V, Melbourne, VIC3001, Australia.

Correspondence to: F. Cser.Journal of Applied Polymer Science, Vol. 81, 340–349 (2001)© 2001 John Wiley & Sons, Inc.

340

them both by differential scanning calorimetry(DSC) and small angle X-ray scattering (SAXS).Because their materials showed bimodal meltingbehavior, they expected double peaks in the SAXScurves, but only observed singular peaks. Thesepeaks were obtained only after applying a Lorentzcorrection to the SAXS intensities [i.e., multiply-ing by sin2(Q)]. There were no peaks in the orig-inal SAXS recordings.

Balbontin and coworkers8 studied the distribu-tion of the 1-butene units in LLDPE by differentmethods. Stepwise crystallization was applied us-ing steps in the temperature of 10°C, and theunperturbed chain length was determined bothfrom 13C-NMR and DSC data. The authors com-pared the lamellar thickness of the crystalliteswith the average length of the chain moleculesbetween two branches in different fractions of thepolymer, obtained by temperature rising elutionfractionation. The lamellar thicknesses were cal-culated from the melting peak temperatures us-ing the Thomson-Gibbs formula 7,8:

Tm 5 Tm0 p S1 2

2se

DH p LD (1)

where Tm is the measured melting temperature,Tm

0 is the melting temperature of the crystalswith infinite thickness (414 K), DH is the meltingenthalpy of the crystals (279 J z cm23 for PE), L isthe thickness of the crystals, and se is the surfaceenergy of the crystals (8.7 mJ z cm22 for PE). Theconcept presumes that the melting is proceedingalong the chain direction (c), i.e., the change inthe crystallinity is proportional to the change inthe thickness of the lamellae, only (see Fig. 1).

The average distance between two branches(unperturbed chain length) was calculated fromthe composition of the given fraction presuming ahomogeneous distribution of the branches alongthe chains. One monomeric unit has a length of2.53 Å, so the unperturbed chain length is calcu-lated by multiplying the number of ethylene mo-nomeric units between two branching by 2.53 Å.They found a reasonable agreement between thecalculated distances and the lamellar thicknessusing two data sets.8

In our previous works,5,10 DSC and tempera-ture-modulated DSC (TMDSC) data were pre-sented that had been obtained on LDPE, LLDPE,high density polyethylene (HDPE), and isotacticpolypropylene on samples crystallized by step-wise cooling using 3-K steps. Each step was fol-

lowed by a 50-min isothermal period. The proce-dure is referred to as thermal fractionation (TF).

We found that the TF techniques producedmultiple endotherms in polymers when branch-ing or comonomers were present. HDPE and iso-tactic polypropylene did not show multiple peaksin the endotherm after TF. We also found a strongreversing heat flow during the melting processand this heat flow had multiple peaks also. Nev-ertheless, the reversibility of the melting de-creased after TF.5 LLDPE produced using a met-allocene catalyst also showed multiple peaks inthe melting after TF.

TF samples have also been reverse annealed ina TMDSC.10 Reverse annealing means a series ofheating/cooling cycles performed in TMDSC. Thetemperature of the samples was increased by a 2K/min rate to 1 K below the peak temperature ofthe melting endotherm; then it was kept constantfor 10 min. The sample was then cooled to 0°C ata 2 K/min cooling rate. This process was repeatedaccording the respective maxima found in themelting endotherm of the TF samples but theannealing temperature of the consecutive cycleswas increased just under the maximum temper-ature of the next peak.

The heat capacities decreased to lower valuesduring the annealing, which corresponded to thatof the cooling cycle of the crystallized materialwhen the annealing temperature was below thatof the crystallization. In the other case, the heatcapacities decreased to a value that was an ex-trapolation of the heat capacities of the crystal-lized material to higher temperatures. We found

Figure 1 Melting of semicrystalline polymers accord-ing to the Thomson-Gibbs concept.

X-RAY DIFFRACTION OF REVERSE-ANNEALED PE 341

that the heat capacities reached their minimumvalue within 1–3 min. The peak temperature ofthe next maximum in the endotherm increased by2 K with respect to the same peak measuredduring a simple melting cycle.10 The endothermpeak at the highest temperature was also shiftedby 2–3 K to higher values with respect to itsoriginal position in the TF sample. It is generallyaccepted that this shift is the result of an increaseof the lamellar thickness of the crystallites.11 Thischange should influence the SAXS intensities ofthe material. The aim of this work was to showthe effect of the annealing of the PEs on the SAXSintensities.

Semicrystalline polymers are generally re-garded as periodic systems where consecutive lay-ers of the lamellar crystallites and the amorphousphases form a periodic structural system. A dif-fraction peak is expected for these systems. Thedistance of periodicity (d) can be calculated fromthe peak of the maximum of the X-ray intensitiesusing the Bragg equation :

d 52 sin~u!

l(2)

where Q is the half of the diffraction angle of thepeak and l is the wavelength of the X-ray. Thisformula is generally applied to calculate thelength of periodic systems (Bragg periodicity).The structure is supposed to have crystalline la-mellas with a fairly homogeneous thickness andseparated by an amorphous phase with also afairly homogeneous layer thickness. The lamellarthickness of the crystals is generally calculatedfrom the Bragg periodicity modified by the degreeof crystallinity of the system. This latter was de-termined from wide angle X-ray diffraction(WAXS), DSC, or density measurements (see, e.g.,Dlugosz et al.12

There is another concept of the origin of theSAXS intensities—the particle scattering princi-ple. The structural basis of this scattering is adispersion of one phase in the other one where thetwo phases have different electron densities.13

The scattering intensities are functions of the dif-ference in the electron densities between the ma-trix and the dispersed particles, the volume con-centration of the particles as well as their radii ofgyration. This scattering has a maximum at zeroangle with a Gaussian shape of the scatteringtoward greater angles. The log(I) versus square ofthe scattering vector s (s 5 2p/d) results in a slope

of the Gaussian scattering curve and this slopecan be used to determine the dimension (radius ofgyration) of the scattering particle [differentialform of the Guinier approximation; see eq. (3)].

d ln~I!ds2 5 3 p RG

2 (3)

where RG is the radius of gyration of the scatter-ing particle. From the radius of gyration, thethickness of a lamella with infinite lateral exten-sion can be obtained with a multiplication by 121/2

(3.464. . .).A multiplication factor has been used to modify

SAXS intensity data of semicrystalline polymers insome of the relevant literature12,15–17 since theearly seventies. This means that the intensities aregenerally multiplied by a factor of sin2(Q) (in prac-tical calculations by s2). This kind of correction iscalled the Lorentz correction. The Lorentz factor isused in the structure factor calculation of reciprocallattice systems14 (single crystals) and means a mul-tiplication by a factor proportional to sin(2Q).

The use of this factor for semicrystalline poly-mers may be severely criticized because the factorproduces an artificial peak in the intensities andmight be completely misleading in the interpre-tation of the data.12,18 It can, but should not, beused to correct the position of the peaks of thereciprocal lattice diffraction. If there are also par-ticles in the periodical system, particle scatteringwill be superimposed on the scattering caused byreciprocal lattice and a Lorentz correction willdestroy the shape of the curve, such that it cannotbe used for calculations. The sum of the intensi-ties originating from the particle scattering mightshift the position of the peak derived from thereciprocal lattice and its position will also be in-correct. Therefore, the two scattering types mustbe separated from each other and handled indi-vidually.

In our recent research, the SAXS curves of manyPEs, polypropylenes, and their blends, did not showany definite maximum indicating the dominance oreven the presence of a reciprocal lattice type ofscattering. Therefore, the Lorentz correction wasabandoned and the system was handled as if itconsisted of particles dispersed in a matrix.

EXPERIMENTAL

Materials

All of the materials are industrial products andwere prepared by the Zigler/Natta process. Their

342 CSER, HOPEWELL, AND SHANKS

main characteristics are given in Table I. C8-LLDPE1 has 1.25 m % of octene as comonomer.Mw 5 124,600, Mn 5 33,200, and the polydisper-sity is 3.75. The composition and the molecularweight for C8-LLDPE2 are not given, but theyshould be nearly the same as for C8-LLDPE1.C6-LLDPE has 2.3 m % hexane as comonomer. Itsmolecular weight is not given. Neither thecomonomer content, nor the molecular weightdata are given for C4-LLDPE. These latter poly-mers should have higher polydispersity than theC8-LLDPEs, as they showed sharper melting en-dothermic peak with a much broader secondarycrystallization.10

Sample Preparation

The pellets were compression molded at 150°Cusing 150-MPa pressure to from sheets of 2-mmthickness. The sheets were crystallized within thedie using water cooling. The approximate coolingrate at the crystallization was 5–10°C/min.

Smaller portions of the sheets were heated andannealed for 60 min at various temperatures inan oven with a well-regulated temperature con-trol. The program for LLDPEs started at 94°C,then with heating increments of 4°C. The maxi-mum annealing temperature was 122°C. This is3–4°C below the peak temperature of the materi-als determined by TMDSC using a 2 K/min heat-ing rate on samples cooled from the melt by a 2K/min cooling rate (standard state). The samplesannealed for 60 min were then cooled to roomtemperature at a slow cooling rate (!2 K/min) bywrapping the samples in heat isolating foam.HDPE was annealed at temperatures startedfrom 112 up to 132°C. The latter temperature wastoo high and the sample melted partially.

X-Ray Diffractometry

A Rigaku Geigerflex generator was used with awide angle and a Kratki type small angle goniom-

eter. A 30-kV accelerating voltage and a 30-mAcurrent was applied for producing Ni-filteredCu-Ka radiation.

Wide angle X-ray intensities were collected from2Q 5 3 to 50° with steps of 0.05° using transmissiontechniques on the compression molded sampleswith 2-mm thickness. Data were collected and pro-cessed using separate graphics software.

Small angle X-ray intensities were collectedfrom 2Q 5 21 to 1° in steps of 0.002° using thesame samples as for wide angle X-ray. Back-ground intensities were collected for each type ofsample (thickness, absorption) from a mastersample positioned just in front of the counter.Data were collected and processed using a com-puter program for removing the background andcalculating the average of the data from the twosides of the primary beam. The maximum resolu-tion of the SAXS camera was 120 nm as the in-tensities could generally be collected up to 2Q5 0.06°. Slit correction was applied using smoothderivation of the raw data (five data points, sec-ond order approach) and a numerical integration.As the SAXS intensities showed particle type ofscattering,13 Lorentz correction14 was not ap-plied.

The peak melting temperature of the sampleswas determined from the total heat flow curvesobtained by a TMDSC, using a TA Instruments2920 MDSC.19 An intercooler device was used toproduce the cooling power. Helium was used asthe purge gas with a flow rate of 25 mL/min.Heating and cooling rates of 2 K/min were appliedwith a 0.6-K modulation amplitude and 40-s mod-ulation period. This is a medium type of modula-tion (cooling during the heating).20 The caloricdata are collected in Table II.

RESULTS

Figures 2 and 3 show the WAXS intensities ver-sus scattering angle for C6-LLDPE and HDPE,

Table I The Type, Density, and the Melt Flow Index of the Materials Used

MaterialMedium of thePolymerization Comonomer Density (kg z m23) MFI (g/10 min)

C8-LLDPE1 Solution Octene 923 0.94C8-LLDPE2 Solution Octene 923 1.10C6-LLDPE Gas phase Hexane 922 0.78C4-LLDPE Gas phase Butene 918 1.00HDPE Gas Phase — NA 0.20


respectively. There are very small changes in theWAXS intensities, if they are there at all, as thedifferences approach the reproducibility of theWAXS measurements.

There is no remarkable change in the crystal-linity of the samples during the annealing. Thissupports our previous result obtained byTMDSC.10 Nevertheless, there are some changesin the heat flow curves of the samples caused bythe annealing, but this does not influence eitherthe overall crystallinity or the particle size of thecrystals at all. The greatest change can be seenfor samples that have been annealed at a temper-ature just below the melting temperature. Thereis one broad melting peak below the annealingtemperature and a sharp, strong one correspond-ing to the melting. The ratio of the sharp secondmelting peak with respect to the broad one isapproximately 1:3.10

According to the concept of folded chain lamel-lar crystallization, the extension of the crystalline

lamellae with respect to their thickness is great.Particle size of the crystals along the direction of[110] and [200] can be calculated from the halfwidth of the diffraction peak using the Scherrerformula21 [see eq. (4)]:

L 5K p l

d p B p cos~Q!(4)

where L is the particle size expressed in the scaleof l, d is the Bragg periodicity corresponding tothe peak, B is the half width of the peak expressedin radians, and K is a constant with a value of1.07. The particle size calculated from the linewidth of the diffraction peaks shown in Figures 2and 3 [(110) and (200)] is 6.5 nm. This means thatthe unperturbed lateral dimension of the lamellaeis small. Kavesh and Schultz22 suggested thatthis smaller particle size of the lamellae is the

Figure 3 WAXS intensities of the HDPE after an-nealing at different temperatures.

Table II Peak Melting Temperature and Melting Enthalpy Obtained from the Total Heat FlowCurves, Crystallinity from Melting Enthalpy after Annealing and Crystallinity from Densityof the PE Samples

C4-LLDPE C6-LLDPE C8-LLDPE1 C8-LLDPE2 HDPE

Annealing at (°C) 122 122 122 122 128Tm (°C) 127.46 127.69 127.07 127.38 132.29DHm [J/g] 114.75 139.4 136.7 140.6 202.4Crystallinity (DSC) (%) 39.6 48.1 47.1 48.5 69.8Crystallinity (dens.) (%) 43.9 46.5 47.1 47.1 NAL1 (X-ray) (nm) 52 41 52 56 50L2 (X-ray) (nm) 19 21 20 17 17L (caloric) (nm) 18 18 18 18 29

Figure 2 WAXS intensities of the C4-LLDPE afterannealing at different temperatures.


result of distortions within a physically much big-ger lamella.

The lamellar thickness is supposed to be ob-tained from the SAXS intensities. Figures 4–8show the SAXS intensities of the different PEs asthe function of their annealing temperature in aGuinier representation. Because the changes arevery small, most of the Figures show only theSAXS intensities of the samples annealed at thehighest temperature in comparison with those ofthe reference samples.

C4-LLDPE and C6-LLDPE do not have anypeaks in SAXS intensities, as can be seen in Figures4 and 5. They show two intercepting straight lines,the slope of which change slightly (C4-LLDPE) ornot at all (C6-LLDPE) after annealing. The radii of

gyration for the particle sizes corresponding to thestraight lines of C4-LLDPE are 15.0 nm and 5.6 nm(52 and 19 nm); those for C6-LLDPE are 11.8 nmand 6.1 nm (41 and 21 nm). The figures in paren-theses are the corresponding lamellar thicknesses.

C8-LLDPEs show initially a broad peak super-imposed on a straight line as it is shown in Fig-ures 6 and 7. The intensities at higher anglesthan that of the peak decrease with increasingannealing temperature; those with smaller anglesincreasing with decreasing angles and form astraight line at the highest annealing tempera-tures. The change is particularly great for C8-LLDPE1. The radii of gyration for C8-LLDPE1are 14.8, 5.03 (52 and 20 nm); those for C8-

Figure 4 Guinier representation of the SAXS inten-sities of the C4-LLDPE annealed at 122°C for 1 h andof its reference.

Figure 5 Guinier representation of the SAXS inten-sities of the C6-LLDPE annealed at 122°C for 1 h andof its reference.

Figure 6 Guinier representation of the SAXS inten-sities of the C8-LLDPE1 annealed at 122°C for 1 h andof its reference.

Figure 7 Guinier representation of the SAXS inten-sities of the C8-LLDPE2 annealed at 122°C for 1 h andof its reference.


LLDPE2 are 16.2 and 5.05 nm (56 and 17 nm),respectively.

Because all of these LLDPEs have a meltingpeak temperature after annealing at 127°C, theirmaximal lamellar thickness calculated by theThomson-Gibbs formula is 18 nm. This value cor-responds to the second, i.e., to the smallest value,which can be obtained from the Guinier interpre-tation of the SAXS intensities (see Table II).

HDPE has a definite peak in the SAXS inten-sities of the reference sample, which is evident inthe I versus s representation in Figure 8. Here,we show the SAXS intensities of all of the an-nealed samples. Using the Lorentz correction, twobroad peaks formed with maxima correspondingto periodicities of 26 nm and 13 nm, respective-ly.18 These maximums can be accepted as first-and second-order Bragg reflections of a reciprocallattice. From the “line width,” however, the par-ticle sizes of the periodicity are 75 and 46 nm. Thecorresponding numbers of lamellas in the crystal-line particles are 2.9 and 3.5. These are verysmall numbers. They mean there is no true recip-rocal lattice and consequently no intercorrelatedlamellar structure in the system. Therefore, thepeaks formed after the Lorentz correction in theSAXS intensities are artefacts.18

Samples with increasing annealing tempera-ture show increasing scattering intensities atlower angles (below the peak) and decreasingones at higher angles (above the peak). The sam-ple annealed at 128°C, just below the meltingtemperature, definitively shows a particle type ofscattering with bimodal particle size distributionand it shows practically no peak (Fig. 9).The

straight line at lower angles corresponds to aradius of gyration of 14.4 nm; that at the greaterangles to 4.9 nm. These values represent lamellarthicknesses of 50 and 17 nm. Figure 9 also showsthe SAXS intensities of the reference sample forcomparison. This sample shows particles with aradius of gyration of 5.0 nm, corresponding to alamellar thickness of 17.3 nm.

From the peak melting temperature, a 29-nmlamellar thickness could be calculated using theThomson-Gibbs formula. This value correspondsto the larger lamellar size obtained from theGuinier representation of the SAXS intensities(see Table II).

The change of the SAXS intensities towardthose without peaks is completely unexpected. Ifwe would have some lamellar structure, particu-larly with a degree of crystallinity higher than50% as is the case for HDPE, where it is 70%, theannealing should improve its packing. As a con-sequence, a structure with stronger periodicity isexpected that should result in a sharper, andconsequently, in a greater peak based on SAXSintensities. This is not the case. The diffraction“peak” that was originally present in the diffrac-togram actually strongly reduced during the heattreatment.

Naturally, a peak can be produced by the ap-plication of a Lorentz correction as is the case inmany articles.15–17 The intensity curve of HDPEwas analyzed previously,18 and three componentswere fitted to the curve. Two of them were func-tions of the particle scattering and one was recip-rocal lattice scattering. The integral valuesshowed that the reciprocal lattice component

Figure 8 Guinier representation of the SAXS inten-sities of HDPE during annealing at different tempera-tures.

Figure 9 Guinier representation of the SAXS inten-sities of the HDPE annealed at 128°C and of its refer-ence.


might not exceed 10% in its volume. The mode ofscattering was predominantly particle scattering.It can be seen that the reciprocal lattice scatter-ing is decreased and has nearly been vanished byincreasing the temperature of the annealing.

DISCUSSION

The original expectations of the study were to getdefinite periodicity with increased length by anincreased temperature of annealing. Instead ofour expectations, we have received either nochanges in a purely particle type of scattering(C6-LLDPE) or an even smaller extent of period-icity (HDPE) than without annealing. The parti-cle type of the scattering was enhanced; neverthe-less, it was expected to be reduced.

Table II contains the peak melting tempera-tures of the polymers annealed just below themelting temperature and the correspondingthickness of the crystalline lamellae as estimatedby the Thomson-Gibbs formula . According to eq.(2) we can construct a graph representing thelamellar thickness as a function of the peak melt-ing temperature (Fig. 10).

It has been shown18 that the lamellar thick-ness calculated from the X-ray data, and thosecalculated by this formula are not comparable.This is also the case in this research. LLDPEshowed a very similar melting peak temperatureand similar SAXS intensities before and after an-nealing. In contrast, HDPE had a much highermelting peak temperature after annealing, but itsSAXS intensities after annealing did not differmarkedly from those of the LLDPEs. This is nat-

urally a contradiction. Balbotin et al.8 also con-cluded that the X-ray lamellar thickness does notcorrelate with the values obtained from the melt-ing peak temperature.

There is another way to calculate the meltingtemperature of semicrystalline polymers contain-ing comonomers, proposed by Flory.23 LDPE andLLDPE are copolymers. If we regard the branch-ing points as well as the end groups of the poly-meric chains as if they were another chemicalcomponent with respect to the elements of themain chain, we have a two-component thermody-namic system. One of the components is formedfrom the monomeric units of the main chain,which is called in our case polymethylene. Theother one is formed from all of the atomic groups,which are different from the elements of the per-fect segments. The peak melting temperature canbe regarded as the end temperature of the solu-tion of the perfect crystalline elements in theother component, as solvent. Equation (5) de-scribes the change of the peak melting tempera-ture as a function of the concentration of thesolvent (with indices 1):

1Tm

21

Tm0 5

RDHu

Vu

V1~F1 2 xF1

2! (5)

where Tm is the peak melting temperature, Tm0 is

414 K for PE, R is the universal gas constant, DHuis the melting enthalpy of the solute, V1 and Vuare the molecular volume of the solvent and thesolute, x is the interaction parameter, and F1 isthe volume fraction of the solvent. This meansthat the polymeric system is handled as would bea two-component thermodynamic system. Thecomponents, however, are coupled by chemicalbonds. This kind of description was previouslyproposed to describe the transition and meltingtemperatures of liquid crystalline materials as afunction of the mol fraction of the soft segmentswith respect to the hard segments.24

The change of the melting temperature can beexpressed now with the mol fraction of the unper-turbed chain length (xu) in the following form 23:

DTTm

0 < Tm

RDHu

ln xu (6)

Equation 1 can also be transformed to a similarform :

DTTm

0 52sc

DHu

1L (7)

Figure 10 Lamellar thickness versus melting tem-perature calculated by the Thomson-Gibbs relation.


The two equations have identical form. Onedescribes the effect of the lamellar thickness onthe melting temperature; the other describes thatof the solvent that is actually coupled to the crys-talline solute. It is utilized in this transformation,that when xu ' 1, then ln(xu) ' xu.

The lamellar thickness can be related to thenumber of the carbon atoms in the perfect crys-talline chains as the periodicity along the chainaxes is 2.53 Å and so xu 5 2.35/L. The concentra-tion of the perfect chain elements can also berelated to the number of perfect chain elementsand through this to lamellar thickness. Both func-tions are shown in Figure 11 as a function of thepeak melting temperature. The two functionsform two straight lines with similar but differentslopes. Figure 11 also shows the peak meltingtemperature versus the length of the unperturbedmolecular segments data expressed as a mol frac-tion by Balbotin et al.8 obtained on C4-LLDPE.These data equally fit both functions because theyare mainly distributed in between.

Peticolas et al.25 and Dlugosz et al.12 were deal-ing with the correlation of the fold length deter-mined by low-frequency Raman spectra and bySAXS. Both found smaller length by Raman thanby SAXS. The lamellar thickness was evensmaller when a Lorentz correction was applied.Dlugosz et al.12 also showed a transmission elec-tron micrograph pattern of chlorosulfonic acid-treated PE with smaller periodicity than hadbeen expected from Raman measurements. Theauthors tried to explain their result by the tiltingof the polymeric chains. The problem is that theirobserved periodicity does not mean lamellarthickness of the crystals; it also contains the

thickness of the amorphous phase. This meansthat the correlation between the lamellar thick-ness measured by different methods is wrong.They found better correlation when they used amat of single crystals grown from dilute solution.Really, in this case there are also higher orderdiffraction peaks in the SAXS intensity curve[(002), (003), etc.] as has also been shown byWang and Harrison.26 We believe that the root ofthe problem is in the difference in the mode of thecrystallization. Crystals grown from dilute solu-tion show intercorrelated periodic systems, butcrystals grown from the bulk show particle-typesystems. A possible representation of this modelis shown in Figure 12.

The main characteristic of the bulk-crystal-lized samples is that the crystals do not have adefinite, plane-parallel shape. In other words, theparallel-arranged chain elements do not end at adefinite plane. The chains of the crystals continueinto the amorphous phase and through the amor-phous phase they pass into the next crystallite orreturn to the same lamella in an irregular way.Naturally, the branching segments and the chainends are in the amorphous phase, as the branch-ing cannot be incorporated into the crystals. (Thechain ends can be incorporated, but they wouldcause sever distortions; therefore, their incorpo-ration is energetically unfavorable.) The crystal-line lamellae are not arranged parallel becausethey do not correlate with each other. A planeparallel (epipedon) shape of crystallites would beforced to be arranged parallel and to form periodicstructures. This is not the case.

Figure 11 Comonomer content versus melting tem-perature of PEs.

Figure 12 The proposed structural model of semic-rystalline polymers. The amorphous phase is coupled tothe crystalline phase by chemical bond at the end of themolecular chains forming the crystals.


Because the amorphous phase is chemicallybound to the crystalline phase, the two thermo-dynamic systems are not isolated; they are cou-pled. The consequence is that in the heating cycleof the annealing, the thickness of the crystallineregion decreases with increasing temperaturewithout material transport through a surface. Atthe annealing temperature, the heat capacitiesare reduced to a lower value in a rapid processindicating changes in the liquid (amorphous)phase.

CONCLUSIONS

The reversed annealing experiments togetherwith the result in reversible melting studiesshowed that the structural relationships in semi-crystalline polymers should be reconsidered. Thegenerally accepted folded chain lamellar modeldescribes the properties of the polymeric singlecrystals formed from diluted solutions. Thismodel does not describe satisfactorily the struc-ture of bulk-crystallized polymers. The coupledtwo-phase thermodynamic system might be usedto characterize the caloric behavior of the bulk-crystallized semicrystalline polymers. Furthertheoretical work should be performed to have aproper thermodynamic description of this kind ofsystem.

The authors are indebted to Ms. K. Tajne for her par-ticipation in the experimental work.

REFERENCES

1. Varga, J.; Menczel, J.; Solti, A. J Therm Anal 1979,17, 333.

2. Varga, J.; Toth, E. Makromol Chem MacromolSymp 1986, 5, 213.

3. Addison, E.; Ribeiro, M.; Fontanille, M. Polymer1992, 33, 4337.

4. Wolf, B.; Kenig, S.; Klopstock, J.; Miltz, J. J ApplPolym Sci 1996, 62, 1339.

5. Cser, F.; Hopewell, J. L.; Shanks, R. A. J ThermAnal 1998, 54, 707.

6. Wild, L.; Chang, S.; Shankernarayanan, M. J.Polym Prepr 1990, 31, 270.

7. Defoor, F.; Groeninckx, G.; Raynaers, H.; Schouter-den, P.; Van Der Heiden, B. J Appl Polym Sci 1993,47, 1839.

8. Balbontin, G.; Camurati, I.; Dall Occo, T.; Finotti,A.; Franzese, R.; Vecellio, G. Angew MakromolChem 1994, 219, 139.

9. Zhou, H.; Wilkes, G. L. Polymer 1997, 38, 5735.10. Cser, F.; Hopewell, J. L.; Tajne, K.; Shanks, R. A. J

Therm Anal, to appear.11. Wunderlich, B. Macromolecular Physics; Academic

Press: New York, 1976; Vol. 2.12. Dlugosz, J.; Fraser, G. V.; Grubb, D.; Keller, A.;

Odell, J. A.; Goggin, L. Polymer 1976, B17, 471.13. Glatter, O.; Kratky, O. Small Angle X-ray Scatter-

ing; Academic Press: London, 1982.14. Bunn, C. W. Chemical Crystallography, 2nd ed.;

Clarendon Press: Oxford, 1961.15. Russel, T. P.; Koberstein, J. T. J Polym Sci Polym

Phys Ed 1985, 23, 1109.16. Butler, M. F.; Donald, A. M.; Ryan, A. J. Polymer

1997, 38, 5521.17. Ryan, A. J.; Brass, W.; Mant, G. R.; Derbyshire,

G. E. Polymer 1994, 35, 4537.18. Cser, F. J Appl Polym Sci, to appear.19. Reading, M.; Elliott, D.; Hill, V. L. J Therm Anal

1993, 40, 949.20. Cser, F.; Rasoul, F.; Kosior, E. J Therm Anal 1997,

50, 727.21. Lipson, H.; Steeppe, H. Introduction to X-Ray Pow-

der Diffraction Patterns; McMillan: London, 1970;p. 246.

22. Kavesh, S.; Schultz, J. M. J Polym Sci Part A 1970,8, 243.

23. Flory, P. J. Principles of Polymer Chemistry; Cor-nell University Press: Ithaca, NY, 1953; p. 569.

24. Cser, F. Mater Forum 1990, 14, 81.25. Peticolas, W. L.; Hibler, G. W.; Lippert, J. L.; Pe-

terlin, A.; Olf, H. Appl Phys Lett 1971, 18, 87.26. Wang, J.-I.; Harrison, I. R. J Appl Crystallogr 1978,

11, 525.


x-ray diffraction studies on reverse-annealed polyethylenes

Documents