real space and wave-number space studies of the phase structure and morphology of ipp/peoc blends...

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516

Real Space and Wave-Number Space Studiesof the Phase Structure and Morphology ofiPP/PEOc Blends Using Scanning ElectronMicroscopy

Lin Zhu, Na Song, Xinhua Xu*

The influence of blend composition on the phase structure and morphology of poly(propy-lene)/poly(ethylene-co-octene) blends was studied using SEM. A diameter dg was defined andcalculated in real space to discuss the phase structure andmorphology of iPP/PEOc blends. Thefigure-estimation method was introduced to determine the distribution width of dg. It wasshown that the distribution of dg obeys a log-normal distribution and the distribution width s

of dg was calculated. In wave-number (h) space,the correlation distance, ac, was defined by apply-ing light scattering theory to power spectrumimages obtained by 2D Fourier transformation.Moreover, a fractal dimension, Dc, was introducedto describe the uniformity of the spatial distri-bution.

Introduction

Polymer blending has received much attention both in

theoretical research and practical applications, since it has

been proven to be an excellent way of developing new

materials exhibiting combinations of properties that

cannot be obtained from any one polymer. There has been

an extraordinary growth in the field of polymer blends

during the last few decades compared to homopolymers

and copolymers.[1]

It is well established that the ultimate properties of

polymer blends are determined by the type of phase

morphology and the phase dimensions. Therefore, to

control the blend properties, the final morphology, which

depends largely on the morphological evolution during a

L. Zhu, N. Song, X. XuSchool of Materials Science and Engineering, Tianjin University,Tianjin 300072, ChinaFax: þ86 22 2740 6127; E-mail: [email protected]

Macromol. Mater. Eng. 2009, 294, 516–524

� 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

melt-blending process carried out with a twin-screw

extruder or a batch mixer, should be understood. The

microscopic phase structure and morphology of polymer

blends can be directly observed by some microscopy

methods, e.g., scanning electron microscopy (SEM), trans-

mission electron micrograph (TEM), and the microphoto-

graphs represent the dimensional distribution and the

orientation of dispersed phase. Furthermore, thanks to

improvements in the coupling of microelectronics and

computer science, automatic image treatment and analysis

systems can be designed. Digital image analysis (DIA) can

provide a quantitative approach to the microphotographs

based on mathematical concepts.[2–4] Using DIA, not only

various information, e.g., the dimension and the shape of

the dispersed phase, but also the power spectrum image

obtained by two-dimensional Fourier transformation

(2DFT) of an original image can be obtained. Since the power

spectrum image in the wave-number (h) space directly

corresponds to an image obtained by small-angle light

scattering (SALS).[4] Therefore, theeffectivewaytostudythe

DOI: 10.1002/mame.200900068

Real Space and Wave-Number Space Studies . . .

phase structure and morphology can be realized by the

analysis of the microphotographs using DIA. On the other

hand, after the scaling theorywas introduced into polymer

field, the understanding of the polymer systems has been

much extended.[5–7] In fact, the phase structure and

morphology may have some relations with the fractal

behavior.[8] However, the potential fractal behavior in the

phase structure and morphology of polymer blends has

been paid rare attention up to now.

Becauseof its easyprocessing, lowcost, andgoodthermal

and mechanical properties, isotactic poly(propylene) (iPP)

has been extensively used as a commodity polymer.

However, its application is somewhat limited due to its

highshrinkage rate, andrelativelypoor impact resistanceat

room or low temperatures. Therefore, how to improve the

impact toughness of PP resin has been extensively paid

attention. It is generally known that the toughness of

poly(propylene) (PP) can be improved by the addition of

elastomer such as the ethylene/propylene copolymer

(EPR)[9,10] and ethylene/propylene/diene terpolymer

(EPDM).[11,12] Among the elastomers used, poly(ethylene-

co-octene) (PEOc) being narrowmolecular weight distribu-

tion produced via metallocene technology has been

commercialized and have distinctive properties due to

long chain branching. So it has started displacing the

traditional impact modifiers, and many literatures have

reported about them in recent years.[13–17]

In this paper, the phase structure andmorphology of iPP/

PEOc blends were investigated both in the real space and

the wave-number (h) space based on the DIA of SEM

micrographs. The average sizes of dispersed phase particles

and their distribution width were calculated. Moreover,

the fractal dimension, Dc, was obtained to describe the

phase structure and morphology of iPP/PEOc blends using

the correlation function.

Experimental Part

Materials

The basicmaterials used in this studywere a commercial grade iPP

(1 300) with density of 0.90 g � cm�3 and melt flow index of

1.10 g � (10min)�1 (measured under 2.16 kg at 230 8C), supplied by

Beijing Yanshan Petrifaction Co. and a commercial grade PEOc

(Engage 8150), a metallocene catalyzed copolymer with 25wt.-%

of comonomer, provided by Dow Elastomers with density of

0.87 g � cm�3 and melt flow index of 0.5 g � (10min)�1 (measured

under 2.16 kg at 190 8C).

Blend Preparation

The blendswere prepared in an internalmixer (XXS-30mixerwith

rotordiameterof35mmandtotal volumeof50 cm3,China). Prior to

processing, allmaterialswere dried for 12hunder vacuumat 50 8C.



The virgin constituent polymers and blends with different

compositions [iPP/PEOc¼60:40, 70:30, 75:25, 80:20, 85:15, 90:10,

95:5 by volume concentration]were prepared. In order to study the

effects of the blend composition on structure and morphology of

the PEOc toughened PP, the blend experiments were performed in

the internal mixer for 10min at constant rotor speed of 40 rpm at

200 8C.The following equation was used to calculate the PEOc volume

concentration:

VPEOc %ð Þ ¼ WPEOc=rPEOcWPP=rPP þWPEOc=rPEOc

� 100% (1)

where V, W, and r are volume, weight, and density of

corresponding components in the subscripts, respectively.

Morphological Characterization

The phase structure and morphology of the blends were

investigated using the scanning electron microscope (Philips

XL-30 ESEM). Because it was difficult to extract the iPP phase

without affecting the PEOc phase using the solvent, all samples

werecryogenically fractured in liquidnitrogenforat least10min to

make sure that the fracture was sufficiently brittle and they were

etched in heptane at 60 8C for 10min to extract the elastomeric

PEOc phase. The samples were dried for a period of 72h and were

coated with gold prior to SEM examination. Considering that

the quality and resolution of SEM images are strongly affected by

the thickness of the plated gold, the sputter time was strictly

controlled to be identical for each sample. The microscope

operating at 25 kV was used to view the specimens, and several

SEM microphotographs were taken for each sample.

Image Analysis

The SEMmicrographswere binarizedusing our self-made software

EMPP, and the particles of the dispersed phase were chosen as our

studied object. The number of pixels embodied by every particle

was calculated using the software. Then the software created a

circle that enclosed the same number of pixels and defined the

diameter of the circle as that of each particle; thus, the equivalent

diameter, dg, of each particle can be obtained. Consequently, the

average size of the dispersed phase over all particles could be

calculated by averaging the dg using Equation (2),

dg ¼P1

i ni dg� �

iP1i ni

(2)

where ni is the number of particles. To obtain more reliable data,

about 100 particles were considered to calculate this structure

parameter for each sample.

In order to compare dg with other diameters, the number-

average diameters and volume average diameters were also

obtained using the following equations, respectively:

www.mme-journal.de 517

L. Zhu, N. Song, X. Xu

518

The number-average diameter is

Macrom

� 2009

Dn ¼P

NiDiPNi

(3)

The volume average diameter is

Dv ¼P

NiD4iP

NiD3i

(4)

where Di is the diameter of each droplet and Ni is the number of

droplet with a diameter Di.

The polydispersity (d) was characterized by means of the ratio:

d ¼ Dv

�Dn (5)

Results and Discussion

Studies in Real Space

The SEM micrographs of iPP/PEOc blends with different

compositions prepared at the rotor speed of 40 rpm for

10min at 200 8C are depicted in Figure 1(a–g). The light area

of the SEM represented the iPP phase and the black for the

PEOc phase which was etched off with black holes left. For

the whole sample studied, PEOc was distributed in the

matrix phase in the form of spherical particles, forming the

dispersed phase and iPP was the continuous phase, i.e., a

droplet dispersion type of morphology could be observed

and this type of morphology was observed for many other

blends. It also could be seen that, as the concentration of

the dispersed phase increased, the dispersed phase size

increased and the structure and shape of the particles

became more and more complex (Figure 1).

Although these micrographs showed a vivid phase

structure and morphology, it was hard to quantitatively

determine the variation of phase size just based on

these micrographs. For this reason, the SEM micrographs

were transformed by DIA software designed by our group.

These results, i.e., the binarymicrographs are obtained and

shown inFigure1(h–n).Using the software, thedomain size

was calculated in the form of dg to quantitatively describe

the phase size. In addition, the number-average diameters

and volume average diameters were also calculated and

obtained to compare them with dg. Actually, when the

samples were fractured, the section might go through or

around the particle, thus, a difference existed between our

statisticalvalueandtherealvalueofdiameter.But, sincewe

just wanted to find the changing rule of the diameter with

blend composition rather than their absolute value and the

methodwasbasedon the statistics. Sowherever the section

was, the influence on the result was negligible.

ol. Mater. Eng. 2009, 294, 516–524

WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

The variations of dg, Dn, and Dv as the function of

concentration of PEOc are shown in Figure 2. When the

concentration of the dispersed phase was low, the size of

dispersed particles was small. As the concentration of

dispersedphase increased, thesizeof thedispersedparticles

increased. However, this incrementwas not largewhen the

volume fraction of PEOc was lower than 30%. This

phenomenon indicated that the increase in PEOc concen-

trationfirst raised thenumber of domainsbutnot their size.

Only when the volume fraction of PEOc was higher than

30%, the number of domains approached to saturation and

the size of these domains increased greatly (Figure 2). A

similar result has also been found by others. Nair et al.

studied the relation between phase dimensions and

compositions of nylon/PS blends and found that when

the volume fraction of the dispersed phase was small, the

diameterof thedispersedphaseparticles increased linearly,

but when the concentration of the dispersed phase was

relatively high, the size of particles increased more rapidly

due to the coalescence of the particles and the fibrillation of

nylon.[18] Besides, thevariationofdgwas inaccordwith that

ofDn andDv,whichmeantdgwas an effective parameter to

study the sizes of the dispersed phase particles.

However, itwashardtodeterminethedistributionwidth

of sizes quantitatively based on these images only. In this

paper, the graph-estimation method was introduced to

study the distribution of dg in detail.[19]

Detailed calculations leading to the figure-estimation

theory were given in the Appendix. Based on the figure-

estimation theory, the cumulative distribution of particle

size of different iPP/PEOc blends as the function of

concentration of PEOc is calculated and shown in

Figure 3 (the corresponding curves were omitted for

clarity). Thedistributions ofdgwithdifferent concentration

of PEOc could be transformed into ascending lines,

indicating that the distribution of dg obeyed a log-normal

distribution and therefore, the corresponding parameter s

can be easily calculated to describe the size distribution

(Figure 3).

Figure 4 shows the variations of distributionwidth s and

the polydispersity d as the function of concentration of

PEOc.When the content of the dispersedphasewas low, the

distribution width of dg was narrow. As the content of the

dispersedphase increased, thesizeof thedispersedparticles

and the distribution width of dg increased, which could be

ascribed to increase in the number of domains. In this case,

the density of domains increased and these domains were

distributed rather than clustering together. So the distribu-

tion width of dg and the polydispersity d was small

(Figure 4). However, the number of domains was saturated

when the concentration of PEOc increased further. There-

fore, some neighboring domains would aggregate into a

large and irregular one, which destroyed the uniformity of

the distribution of the particles. So the distributionwidth s

DOI: 10.1002/mame.200900068


Figure 1. (a–g) SEM micrographs, (h–n) their corresponding binary micrographs, and (o–u) their corresponding 2DFT transformed patterns ofPP/PEOc blends with different compositions.

which had a similar variation with the polydispersity d

increased further.

Studies in Wave-Number (h) Space

The size and distribution of dispersed phase in polymer

blends cannot only be defined in the real space, but also in



the wave-number (h) space. The images in the h space can

be gained by applying 2DFT to the image in the real space.

Furthermore, there existed a corresponding relationship

between the 2DFT images and SALS images as mentioned

by Tanaka.[4]

The observed intensity of an image by a scanning

electron microscope I(r) (r is the position vector), is



Figure 2. The variation of dg as the function of PEOc concen-tration.

Figure 4. The variation of distribution width s as the function ofPEOc concentration.

520

proportional to the difference of the refractive index dn(r) to

good approximation, i.e.,

Figdiff

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I hð Þ / dn rð Þ (6)

The power spectrum of 2DFT of an original image P(h) is

expressed as

P hð Þ ¼ F hð Þj j2¼ FF� (7)

where F(h) is the Fourier transform of I(r) expressed by

F hð Þ ¼ZV

I rð Þ exp �jhrð Þdr with j ¼ffiffiffiffiffiffiffi�1

p(8)

ure 3. The cumulative distribution of dg of PP/PEOc blends witherent composition.

ol. Mater. Eng. 2009, 294, 516–524


From the convolution theorem,

FF� ¼ZV

I rð ÞI 0ð Þh i exp �jhrð Þdr (9)

Therefore, P(h) is generally given by

P hð Þ ¼ZV

I rð ÞI 0ð Þh i exp �jhrð Þdr

/ZV

n rð Þn 0ð Þh i exp �jhrð Þdr (10)

On the other hand, the scattering intensity S(h) obtained

by a light scattering experiment is given by

S hð Þ /ZV

n rð Þn 0ð Þh i exp �jhrð Þdr (11)

By comparing Equation (10) with Equation (11), it was

found that thepower spectrumof2DFTof anoriginal image

is equivalent to the scattering intensity S(h). Therefore,

the phase structure and morphology of polymer blends

couldbedescribed in termsof light scattering theory,which

was introduced in the Appendix section.

The corresponding power spectrum micrographs are

shown in Figure 1(o–u). It could be seen that the facula on

thepower spectrummicrographs became smaller, brighter,

andbasically roundas the concentration of dispersedphase

increased.When the concentration of dispersed phaseswas

higher, especially at 60/40 vol.-%, the facula was elliptical,

because of the distortion of particles. Besides, the direction

of the longer axis of the ellipsewas perpendicular to that of

DOI: 10.1002/mame.200900068


Figure 5. The variation of ac1 and ac2 as the function of PEOcconcentration.

tropismof particles (Figure 1). The resultwas in accordwith

that of Izumitani and Hashimoto.[20]

Bymeansof theSALS theory, the correlationdistancesac1and ac2 could be calculated as functions of the PEOc

concentrations (shown in Figure 5). It could be shown that

the value of ac2 increased, while the value of ac1 decreased

as the concentration of PEOc increased. Furthermore, the

value of ac2 had a similar variation with dg, Dn, and Dv

(Figure 2), which indicated that it was valid to apply

corresponding light scattering theory to 2DFTmicrographs

to study the phase structure and morphology.

Besides the sizes of dispersed phase particles and their

distribution, the uniformity of the spatial distribution of

particles was another aspect which should be paid more

attention. In this paper, the fractal dimension, Dc, was

introduced todescribe thisuniformityusing the correlation

function.[21] The correlation function was a fundamental

statistical quantity, thus the fractal dimension can be

obtained using it.

Let r�(x) be the density at a position x of a set of points,

which are randomly distributed through space. Then the

correlation function c(r) is defined as

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c rð Þ �< r� xð Þr� xþ rð Þ > (12)

Figure 6. The plot of lg [I(h)] versus lg h for PP/PEOc (80:20) blend.

Here c rð Þ �< � >denotes an average. If the distribution is

uniformand isotropic, the correlation function is a function

only of the distance, r, between the two points.

In theoretical models, we often assume that the

exponential function exp r=r0ð Þ or the Gaussian

exp �r2�r20

� �is the correlation function. But these functions

do not possess the fractal property because both of them

have a r0. Any pair of pointswhose distance is less than r0 is

strongly related to each other, but the correlation decays

rapidly for r� r0.

ol. Mater. Eng. 2009, 294, 516–524


On the other hand, when the distribution is fractal, the

correlation function followsapower law. Then there isno r0and the rate of decrease in the correlation is always at the

same rate. For instance, if the correlation is something like

c rð Þ / r�a (13)

then the correlation becomes 2�a times smaller as the

distance of the two points becomes 2 times longer. The

relation between the exponent a and the fractal dimension

Dc is simply

Dc ¼ d� a (14)

where d denotes the dimension of the space.

If the correlation function c(r) scales as in Equation (13),

its Fourier-transform I(h), which is called the power

spectrum, also follows a power law. Indeed, when

0<d – Dc< 1,

I hð Þ ¼ 4

Z 1

0dr cos 2phrð Þ c rð Þ / hd�Dc�1 (15)

Using this relation, the fractal dimension fromthepower

spectrum can be estimated. Here, we should note the

meaning of Dc. Dc means the dimension of a spatial

distribution, i.e., if the points cluster together, they have an

intimate relation andDc is larger, the scattering uniformity

is imperfect.

The range of the dimensionless region can be confirmed

by the linear part of the curve shown inFigure 6. The chosen

component of theblendwas randomly selected fromall the

iPP/PEOc blends systems. Figure 7 shows the variation ofDc

as the function of PEOc concentration. As the concentration

of the dispersed phase increased, the value of Dc increased,



Figure 7. The variation of Dc as the function of PEOc concen-tration.

522

which indicated that the uniformity of the spatial

distribution became more imperfect (Figure 7). Further-

more, the value of Dc had a similar variation with

distribution width s and the polydispersity d, which also

indicated that it was valid to apply corresponding light

scattering theory to 2DFT micrographs to study the phase

structure and morphology.

Conclusion

The influence of blend composition on the phase structure

andmorphology of iPP/PEOcblendswas studiedusing SEM.

The results showed that the diameter (dg, Dn, and Dv)

increased with the increase in the volume fraction of the

dispersed phase. In addition, the distribution of dg obeys a

log-normal distribution, and the distribution width of dgand the polydispersity d increased as the content of the

dispersed phase increased. Besides, the phase structure and

morphology of iPP/PEOc blends were also studied in the

wave-number (h) space applying light-scattering theory to

2DFT images, and the results were in accord with those in

the real space. Furthermore, a fractal dimension, Dc, was

introduced to describe the uniformity of the spatial

distribution. The result showed that Dc was an effective

parameter to study the distribution of particles of the

dispersed phase.

Appendix

Figure Estimation Theory of the Log-NormalDistribution

In the present work, the figure-estimation theory was

introduced to judge whether the distribution of a variable

was the log-normal distribution.[19]



Supposing t is a positive random variable, then if ln

t¼N(m, s2), t obeys a log-normal distribution and can be

markedas t¼ ln(m,s2).Here,m is theexpectationands is the

standard variance. The s reflects the distribution range of t,

the larger s, thewider the distribution range.We introduce

the graph-estimation method to judge whether the

distribution of dg obeys the log-normal distribution.

Ordinarily, the logarithm in a log-normal distribution is a

common logarithm, and the function of a log-normal

distribution is given by

F tð Þ ¼ log effiffiffiffiffiffi2p

pst

Z t

0exp � 1

2

log t � m

s

� �2" #

dt

for t 2 0;þ1ð Þ(A1)

This function is a continuously increasing curvebutnot a

straight line. It can be described by the standard normal

distribution function as follows:

F tð Þ ¼Z log t�mð Þ=s

0

1ffiffiffiffiffiffi2p

p e�x2=2dx

¼ Flog t � m

s

� �for t 2 0;þ1ð Þ (A2)

Since the standard normal distribution function is a

monotonously increasing function, its inverse function

exists. The inverse function can be defined as

F�1 F tð Þ½ � ¼ log t � m

s(A3)

If we mark F�1[F(t)] as Y and log t as X, then the inverse

function can be changed to be

Y ¼ 1

sX � m

s(A4)

This equation corresponds to a straight line in the X-Y

reference frame whose slope is 1/s and intercept is �m/s.

Thus, the relation between a log-normal distribution

functionandan increasing straight line in theX-Y reference

frame is found, which is described as the graph-estimation

method. Basedon thismethod, it canbe judgedwhether the

distribution of the value dg of obeys the log-normal

distribution and determine the distribution width of dg.

Light Scattering Theory

To obtain further information on the phase structure and

morphology of polymer blends, the light scattering theory

is introduced in this section. Several parameters, suchas the

diameter and chord length, could be used to describe the

DOI: 10.1002/mame.200900068


particle sizes of dispersed phase. In this paper, the light

scattering theory is introduced to compute the correlation

distance, ac1 and ac2, which is used to describe the particles

sizes of dispersed phase.

It is well known that the dispersed phase scatters in the

matrix in the form of particles. Therefore, the size of

particles can be computed using a correlation function. For

this purpose, the modification of Debye and Bueche,[22]

whichdescribes the scattering fromrandomheterogeneous

media, is used; it is given by

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Ih ¼ 4pKVhh2Z 1

0g rð Þ sin hrð Þ

hrr2 dr (B1)

Figure A1. The sketch map of ac on curves of I(h)�1/2 versus h2.

where K is a proportionality constant and h¼ (4p/l) �sin(u/2). h2 is the mean square fluctuation and h is the

fluctuation in scattering power of the system, which for

SALS is equal to the deviation in polarization from itsmean

value at position r. g(r) is the correlation function

corresponding to fluctuation of medium.

General for systems not having a apparently defined

structure, g(r) often decreases monotonically with r and

may be represented by an empirical equation such as

g rð Þ ¼ exp �g=acð Þ (B2)

where the parameter ac is known as correlation distance

and can be used to describe the size of the heterogeneity.

For discrete particles in dilute solution, ac is related to the

particle size. For more concentrated systems, ac is not

simply related to the size of the structural unit but depends

upon both interparticle and intraparticle distances. It may

be considered as an average wavelength of the h(r)

fluctuations whereas h2 is a mean-square fluctuation.

If the second equation is substituted into the first

equation, one can obtain

Figure A2. The physical signification of the correlation distancesac1 and ac2.
I hð Þ ¼ K00h2a3
c 1þ h2a2c

� ��2(B3)

Upon rearrangement, it gives

I hð Þ½ ��1=2

¼ K 00h2a3c

� ��1=21þ h2a2

c

� �(B4)

Consequently, aplot of I(h)�1/2 againsth2 should lead toa

straight line having a ratio of slope to intercept of ac. But a

plot of I(h)�1/2 against h2 can lead to two straight lines (see

FigureA1) for SALSwhere u is small, the correspondingac1 is

due to scattering from large particles. As for SALS, when

u!1, the corresponding ac2 is due to scattering fromsmall

particles. Crugnola and Deanin[23] suggested the dimen-

sions of the ac1 and ac2 parameters, measured by the light

scattering, have the physical significance shown in

Figure A2.

ol. Mater. Eng. 2009, 294, 516–524


Acknowledgements: The authors gratefully acknowledge thefinancial support of the National Natural Science Foundation ofChina (no. 20490220).

Received: March 3, 2009; Revised: May 18, 2009; Accepted: May19, 2009; DOI: 10.1002/mame.200900068

Keywords: microstructure; morphology; polymer blends; scan-ning electron microscopy (SEM)

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DOI: 10.1002/mame.200900068

real space and wave-number space studies of the phase structure and morphology of ipp/peoc blends...

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