Stanisław Rabiej,
Włodzimierz Biniaś,
Dorota Biniaś
Akademia Techniczno Humanistyczna
ul. Willowa, 243-309 Bielsko-Biała
The Transition Phase in Polyethylenes
– WAXS and Raman Investigations
Abstract
The existence of the third, transition component, apart from the crystalline and amorphous
phases, in polyethylenes has already been proved in several papers. In this work, the WAXS
patterns of polyethylenes with various branch contents were analysed, aiming at the best
method of accounting for the third phase in the procedure of decomposition of the patterns
into crystalline peaks and amorphous scattering. It appeared that the best result was obtained when we assumed that the intermediate phase is represented by two peaks located
close to the crystalline reflections (110) and (200), on the left sides of these reflections.
The calculations performed have shown that both the density and the mass fraction of this
intermediate third phase decrease continuously with increasing 1-octene content. A comparison of the mass fractions of the three phases has shown that the total mass fractions
of the crystalline and transition phases determined with the WAXS and Raman methods
coincide very well; however, the values obtained for each individual phase do not agree
with one another.
Key words: WAXS, Raman spectroscopy, transition phase, crystallinity, polyethylene.
Introduction
The analysis of Wide Angle X-ray Scattering (WAXS) curves for various polyethylenes (this name covers polyethylene and
ethylene-1-alkene copolymers of different
degrees of branching) leads to the conclusion that the proper description of their
structure needs the introduction of a transition phase – an intermediate component in
addition to the crystalline and amorphous
phases. Such a conclusion has already
been presented in several papers [1-4]. It
was shown [4], that for a polyethylene in
a solid state, both the angular position 2θ
of the amorphous halo as well as its width
at half height are considerably higher than
the values expected from the extrapolation of the respective data for this polymer
in a molten state. This fact suggests that
the amorphous halo of a polyethylene in
a solid state is a sum of scattering from a
completely amorphous, liquid-like phase
and from the intermediate, better-ordered
regions that originate during crystallization. So, in analysing the WAXS profiles,
we have to determine how to account for
this third component in the deconvolution
of the diffractogram.
In this work, a series of ethylene-1-octene homogeneous copolymers with a
1-octene content ranging from 0.8 to
11.27 mol% and a linear polyethylene
standard were investigated. In contrast to other similar investigations, the
WAXS patterns were analysed in a broad
2θ range: 4°–60°, covering not only the
highest (200) and (110) peaks but all
the peaks characteristic of the crystalline phase, located at higher 2θ angles.
The mass fractions of all three phases
were calculated with the WAXS method
and compared with those obtained from
the analysis of the Raman spectra of the
investigated polymers, which was performed using the method developed by
Strobl and Hagedorn [5].
Experimental
Material
The measurements were carried out for
8 homogeneous ethylene-1-octene copolymers synthesized at DSM Research
(the Netherlands) using a metalocene catalyst system. The number of CH3 groups
per 1000 carbon atoms in the main chain
(CH3/1000 – degree of branching) and
mole % of 1-octene provided by the producer are given in Table 1. The melting
temperatures were determined by independent DSC measurements. Additionally,
the samples of linear polyethylene (LPE)
and a commercial high-density polyethylene (HDPE) were investigated as the reference samples. Before the measurements,
all the samples were melted at a temperature higher than their respective melting
temperatures to erase their thermal history
and cooled at the same rate of 10 °C/min
to room temperature. The crystallinity
of the samples was determined using the
wide-angle X-ray diffraction (WAXS) and
Raman spectroscopic methods.
WAXS method
Diffraction patterns were recorded in
a symmetrical reflection mode using a
URD-6 Seifert diffractometer and a copper target X-ray tube (λ = 1.54 Å) operated at 40 kV and 30 mA. Cu Kα radiation was monochromized with a graphite
monochromizer. WAXS curves were
recorded in the 2θ range 4°-60°, with a
step of 0.1°. The samples had the shape
of circular plates with a radius of 1 cm
and a thickness of 1 mm.
Raman spectroscopic method
The Raman spectra of the investigated
samples were recorded in the range of
3700-100 cm-1 with a resolution of 4 cm-1,
using the MICROSTAGE adapter of the
Raman module of the Magna–IR 860
FTIR spectrometer (Nicolet) equipped
with a YAG laser. The wavelength was
1064 nm, the diameter of the beam was
50 μm and its power 0.6 W. Each spectrum was obtained as the average of 2000
scans.
Results and discussion
The analysis and decomposition of the
WAXS curves into component peaks
and all the calculations were performed
using WAXSFIT [6], a new version of
Table1. Samples characteristics. CH3/1000 is a number of CH3 groups per 1000 atoms in
the main chain of a copolymer.
Sample
LPE
EO1
EO2
EO3
EO4
EO5
EO6
EO7
EO8
CH3/1000
0
3.9
8.4
19.2
23.3
23.6
27.7
35.9
42.1
Mole % of
1-octene
0
0.8
1.77
4.34
5.42
5.5
6.64
9.15
11.27
Melting
Temperature [oC]
132
130
119
101
96.3
94.1
92.3
69.5
60.5
Rabiej S., Biniaś W., Biniaś D.; The Transition Phase in Polyethylenes – WAXS and Raman Investigations.
FIBRES & TEXTILES in Eastern Europe January / December / B 2008, Vol. 16, No. 6 (71) pp. 57-62.
57
the Optifit [7] computer program. In the
first stage, a linear background was determined based on the intensity level at
small and large Results
angles and
and subtracted
discussion
from the diffraction curves. Next, the
curves of all the samples were normalResults and
andized
discussion
to the same of
value
integralcurves
inten- into compo
The analysis
decomposition
the ofWAXS
sity scattered by a sample over the whole
calculations were performed using WAXSFIT [6], a new version of
range of scattering angles recorded in
The analysis and decomposition
of the
WAXS
curves
into component
and all thebased
the stage,
experiment.
Finally,
the peaks
diffraction
program.
In the
first
a linear
background
was determined
curves
wereversion
resolvedthe
into
crystalline
calculations were performed small
using and
WAXSFIT
[6], aand
new
Optifit
[7] computer
large angles
subtractedoffrom
the
diffraction
curves. N
peaks and amorphous scattering. To this
program. In the first stage, a samples
linear background
wasadetermined
based
on
intensity
level at sca
were normalized
to the same
value
of
integral intensity
aim,
theoretical
curve
wasthe
constructed,
composed
of
functions
related
to
indismall and large angles and subtracted
diffractionangles
curves.
Next, the
curves
of all theFinal
the whole from
rangethe
of scattering
recorded
in the
experiment.
vidual crystalline peaks and amorphous
samples were normalized to were
the same
valueinto
ofhalos.
integral
by
over To
resolved
crystalline
peaksscattered
andcurve
amorphous
scattering.
Theintensity
theoretical
wasa sample
fitted
theexperiment.
experimental
using
arelated
multic-tocurves
the whole range of scattering curve
angleswas
recorded
intothe
the diffraction
constructed,
composed Finally,
ofone
functions
individua
riterial optimization procedure and a hywere resolved into crystalline
peaks
and
amorphous
scattering.
To
this
aim,
a
theoretical
amorphous halos.brid
The
theoretical
wasa fitted
system
[8] that curve
combines
geneticto the exp
curve
was
constructed,
composed
of
functions
related
to
individual
crystalline
peaks and
algorithm
and
the
classical
optimization
multicriterial
Figure 1. WAXS pattern of linear polyethylene standard resolved into crystalline
peaks and optimization procedure and a hybrid system [8] th
method
of
Powell.
Both
crystalline
peaks
amorphous scattering.
amorphous halos. The theoretical
was classical
fitted tooptimization
the experimental
one
using a Both
algorithmcurve
and the
method
of Powell.
and amorphous
halos were
represented
multicriterial optimization procedure
hybrid
system
[8]
combines
a genetic
by
a represented
linear
combination
of
Gauss and
amorphousand
halosa were
by athat
linear
combination
of Gauss a
Lorentz
profiles:
algorithm and the classical optimization method of Powell. Both crystalline peaks and
amorphous halos were represented by a linear combination of Gauss
Lorentz profiles:
2
 and
 2( x − xoi )  
(1 − f i )
Fi ( x ) = f i H i exp− ln 2
 +
w
(x − x
[
+
1
2
i


 
2

 2( x − xoi )  
(1 − f i )H i
Fi ( x ) = f i Hwhere:
i exp − ln 2 
 +
2
(1)

 wi
  1 + [2( x − xoi ) / wi ]
(1)
where:
where:
x – scattering angle 2θ, Hi – peak height, wi – width at half height, xoi
x – scattering angle 2θ, Hi – peak height,
fi – shape factor, fiwequals
0 for
profile
1 forpoGauss profile
at Lorentz
half height,
xoi and
– peak
i – width
sition,
f
–
shape
factor,
f
equals
0
for
x – scattering angle 2θ, Hi – peak height, wi – width at half
height, xoi – peak
position
i
i
Lorentz profile and 1 for Gauss profile.
fi – shape factor, fi equals 0 for
Lorentz
profile
andof1 the
for crystalline
Gauss profile.
The
starting
values
peak positions were calculated
The
starting
values
of
the crystalline
peak
unit cell dimensions. In contrast to other
similar investigations,
th
positions were calculated using the polyThe starting values of the crystalline
peak
positions
were
calculated
using
the
polyethylene
recorded and analysed
in aunit
broad
θ range: 4°–60°
covering not on
ethylene
cell 2dimensions.
In contrast
to
other
similar
investigations,
the
WAXS
unit cell dimensions. In contrast
to
other
similar
investigations,
the
WAXS
patterns
were phas
(110) peaks but all the peaks characteristic of the crystalline
patterns were recorded and analysed in a
recorded and analysed in a broad
range:
4°–60° covering
not was
only approximated
the highest (200) and
angles.2θThe
amorphous
broad 2θ scattering
range: 4°–60°
covering not onlyby two br
(110) peaks
but all the
peaks
characteristic
crystalline
phase,
located
at from
higher
Figure 2. WAXS pattern of the EO6 sample resolved
into crystalline
peaks
and
amorphous
the
highest
(200) and
(110)
peaks
but
all the2θintermaximum,
locatedof
atthe
lower
diffraction
angles,
results
scattering, assuming a two-phase structure.
the
peaks
characteristic
of
the
crystalangles. The amorphous scattering
was
by two
broad
maxima.
The first
the second
oneapproximated
observed at higher
angles
results
from intra-molecular
line phase, located at higher 2θ angles.
maximum, located at lower diffraction
angles, The
results
frommaxima
the scattering
inter-molecular
scattering
and
amorphous
was approxicase of polyethylenes,
the
are located
at 2θ ≈ 19–20°
mated
by
two
broad
maxima.
The
first
the second one observed at higher
anglescurve
results
intra-molecular
scattering is
[9,shown
10]. Ininthe
diffraction
of from
LPE resolved
into components
Fig. 1.
maximum, located at lower diffraction
case of polyethylenes, the maxima are located
at
2
θ
≈
19–20°
and
2
θ
≈
39–40°.
The
angles, results from the inter-molecular
scattering
andinthe
second
one observed
diffraction curve of LPE resolved into components
is shown
Fig.
1.
at higher angles results from intra-molecular scattering [9, 10]. In the case of
polyethylenes, the maxima are located at
2θ ≈ 19–20° and 2θ ≈ 39–40°. The diffraction curve of LPE resolved into comFigure 3. Width at
ponents is shown in Figure 1.
half height of the first
amorphous maximum
during cooling for
LPE and two chosen
copolymers EO2 and
EO7 [4]. The dotted lines indicate the
melting temperatures.
58
In the first trials, the diffraction curves were
resolved into components assuming an ideal two-phase structure of the investigated
polymers. In the 2θ range, 10°–30°, the experimental curve was approximated by two
FIBRES & TEXTILES in Eastern Europe January / December / B 2008, Vol. 16, No. 6 (71)
peaks representing (200) and (110) crystalline reflections and a broad peak representing the first amorphous maximum. However, for all the samples, the quality of fit
was poor. An example is given in Figure 2,
which is related to the sample EO6. The
differential plot shows considerable differences between the experimental and theoretical curves in the 2θ range corresponding
to the considered peaks.
These problems with fitting are consistent with the results of our previous studies [4], which have indicated a composed
structure of the amorphous scattering in
the WAXS patterns of LPE and ethylene1-octene copolymers. It was shown that
the position, the width at half height and
the shape of the first amorphous maximum change with the temperature of a
polymer and the most sudden changes
occur during melting or crystallization.
In a solid state, the value of the angular
position 2θ of the amorphous maximum
as well as its width at half height are considerably higher than the values expected
from the extrapolation of the respective
data for molten polymer (Figure 3 [4]).
Figure 4. WAXS pattern of the EO6 sample resolved into components. One additional peak
represents a partially ordered phase.
The abruptly changing width and the sudden change in the shape of the amorphous
maximum, as well as the shift in its position, suggest that the amorphous phase
contains two contributions and the total
amorphous scattering is composed of two
parts. One part is related to a typical liquid-like amorphous phase and the other
one to better-ordered and denser regions.
The changes observed during cooling and
heating can be interpreted as being caused
by the originating and disappearing of
those partially ordered regions.
Based on these results, we assumed a
3-phase structure of the investigated
polymers and tried to account for the
third phase in the deconvolution of the
diffractogram. At the beginning, we employed a 4-peak approximation in the 2θ
range 12°–30°: 2 crystalline reflections
(110) and (200), the amorphous maximum and the fourth peak were related
to the intermediate phase. Such an approach is equivalent to the assumption of
a quasi-hexagonal structure of the third
phase. Unfortunately, the quality of fitting did not increase satisfactorily – the
differential plot still showed clearly visible errors in the fitting of the curves. A
plot obtained for the sample EO6 is given
in Figure 4. For this reason, we adopted
the ideas of Baker and Windle[11] in
our further analysis. Investigating sev-
Figure 5. WAXS pattern of the EO6 sample resolved into components. Two additional peaks
represent a partially ordered phase.
eral polyethylenes with a broad range
of branching, Baker noticed that the unit
cell parameters refined from the fitting
of the theoretical curve just to the (110)
and (200) reflections were clearly larger
than those refined from the higher angle
reflections. The extent of the discrepancy was higher, the more branched the
polyethylenes were. Baker has found
that such an effect is caused by a clear
asymmetry of the peaks (110) and (200).
He indicated the excess scattering on
the left, low-angle side of these peaks.
Baker proposed that the excess scattering
is produced by a third, partially ordered
component of the polymer structure.
FIBRES & TEXTILES in Eastern Europe January / December / B 2008, Vol. 16, No. 6 (71)
Based on the difference plot between the
theoretical and experimental curves, he
showed that the scattering produced by
the third component contains two peaks,
which are broader, clearly smaller and
shifted towards lower angles with respect
to the “true” crystalline (110) and (200)
reflections. Because of a lower degree of
order, the contribution of the third phase
to the weaker, higher angle crystalline reflections is negligible [11].
Adopting the suggestions of Baker, we decomposed the WAXS patterns, introducing
two additional peaks related to the partially
ordered component. This time, the quality
59
a)
b)
Figure 6. WAXS pattern of the EO7 and LPE sample resolved into components. The peaks
related to the transition phase are denoted as “(110)” and “(200)”; a) LPE sample, b) E07
sample.
of fit was much better. The result of decomposition for the sample EO6 is shown in
Figure 5 (see page 59). In Figures 6.a and
6.b, similar plots but in a narrower angular range are shown for the samples LPE
and EO7. Two additional peaks related to
the transition phase are denoted by quotation marks: “(110)” and “(200)”. It is seen
that their shift with respect to the crystalline
reflections (110) and (200) is much higher
for the samples with high 1-octene content
than for LPE. This means that the higher
the degree of branching of a copolymer,
the more loosely packed are the molecular
chains in the transition regions. The calculated positions of the “(110)” and “(200)”
Figure 7. Angular positions of the “(110)” and “(200)” peaks versus the
number of CH3/1000, calculated for all the investigated samples.
60
peaks versus the number of CH3 groups
per 1000 carbon atoms in the main chain
are shown in Figure 7. Based on these
angular positions and assuming a “quasiorthorhombic” structure of the transition
component, the a and b unit cell parameters
and the density of this phase were estimated. In this estimation, it was assumed
that the height of the unit cell (c edge) is
the same as in crystalline polyethylene.
The obtained results are shown in Figure 8.
The density of the transition phase continuously decreases. In the case of LPE,
it is close to the density of the crystalline
phase of PE at room temperature (25 °C):
0.999 g/cm3 [12]. For the sample with high
1-octene content, the density tends to the
values typical of the amorphous phase:
0.851 g/cm3 [12]. As can be seen in Figure 8,
the values obtained for the last two samples (EO7 and EO8) were estimated below
this level. These errors are caused by the
fact that the crystalline peaks in the WAXS
patterns of these samples are broad and
weak (see Figure 6.b). As a consequence,
the deconvolution of these patterns into
component peaks may cause an incorrect
estimation of their angular positions. Nevertheless, the trend in the observed changes in the density of the transition phase is
clear and understandable. Most probably,
the transition phase is located on the border between the crystalline and amorphous
phases. It is formed of stretched sectors of
molecular chains emerging from the surfaces of crystallites and partially retaining
the alignment and order typical of the crystalline phase. In the case of linear polyethylene, the degree of packing of the chains
in the transition regions, and consequently
its density, is not too much less than in the
crystallites. However, in the samples with
a high concentration of branches formed
of the 1-octene comonomer, the chains
Figure 8. Density and weight fraction of the third transition phase
versus the number of CH3/1000.
FIBRES & TEXTILES in Eastern Europe January / December / B 2008, Vol. 16, No. 6 (71)
emerging from the crystallites lose their
alignment and order at much smaller distances from the surfaces of the crystallites
and consequently the density of the transition regions tends to the density of the
amorphous phase.
The mass fraction of the transition phase
(TX) was calculated as the ratio of the total area of the “(110)” and “(200)” peaks
to the total area of the WAXS pattern
after the background subtraction. In the
same way, the mass fractions of crystalline (CX) and amorphous (AX) phases
were calculated. The results of the calculations are given in Table 2 (see page 62).
As one can see, the mass fraction of the
transition phase continuously decreases
when the degree of branching increases.
This result is fully consistent with that
obtained in our first paper, resulting from
the measurements of the angular position
of the first amorphous maximum [4].
The mass fractions of all three phases
were also determined using the method of
Strobl and Hagedorn [5], which is based
on the analysis of Raman spectra. In this
method, the Raman spectra of the investigated samples are resolved into three components originating from the orthorhombic
crystalline phase, a liquid-like amorphous
phase and a third, partially ordered phase.
According to Strobl and Hagedorn [5], the
third phase is of a disordered, anisotropic
structure, where the chains are stretched
but have lost their lateral order. The mass
fractions of these three phases are calculated directly from the integral intensities
of characteristic bands.
The total, integral intensity of the CH2
twisting vibrations range (1250-1350 cm-1)
is independent of the degree of crystallinity and for this reason can be used as
a standard with which the intensities of
other bands can be compared [5]. This
range contains a narrow band localized at
1295 cm-1 arising from the crystalline phase and a much broader band at
1303 cm-1 coming from the liquid-like
amorphous phase. The narrow band at
1416 cm-1 is a part of the CH2 bending range,
which is split into two component branches
at 1416 cm-1 and 1440 cm-1 by the crystal
field. For this reason, the band is related to
the orthorhombic crystalline phase.
The mass fractions of the crystalline (CR),
liquid-like amorphous (AR) and transition
(TR) phases contained in the investigated
samples were calculated using the following formulas:
a)
3.4
1295
3.2
3.0
2.8
2.6
2.4
1439
2.2
1129
2.0
1.8
1061
1.6
1.4
1.2
1460
1416
1.0
0.8
0.6
1305
0.4
1368
0.2
1550
1500
1450
1400
1350
1300
1250
1169
1200
1150
1100
1050
cm-1
b)
2.1
2.0
1.9
1.8
1.7
1437
1.6
1295
1.5
1.4
1.3
1.2
1.1
1457
1.0
1061
0.9
0.8
1128
1305
0.7
0.6
1081
0.5
0.4
1416
0.3
1366
0.2
1169
0.1
1550
1500
1450
1400
1350
1300
1250
1200
1150
1100
1050
cm-1
c)
1.4
1.3
1.2
1.1
1.0
1451
1436
0.9
0.8
1305
0.7
0.6
0.5
1295
0.4
1060
0.3
1416
0.1
1550
1129
1367
0.2
1062
1500
1450
1400
1350
1300
1250
1200
1150
1100
1050
cm-1
Figure 9. Raman spectrum of the sample resolved into individual bands: a) EO1, b) EO5,
c) EO8.
FIBRES & TEXTILES in Eastern Europe January / December / B 2008, Vol. 16, No. 6 (71)
61
Table 2. Mass fractions of amorphous (A), crystalline (C) and transition (T) phases
determined with WAXS and Raman methods.
ing the third phase are introduced. The
additional peaks are located close to the
crystalline reflections (110) and (200),
WAXS
Raman
Mole % of
on the left sides of these reflections. As a
Sample
CH
/1000
3
1-octene
AX
CX
TX
AR
CR
TR
consequence, the third phase is treated as
HDPE
+
+
32
53
15
31
65
4
a quasi-orthorhombic one. Based on the
LPE
0
0
33
55
12
31
68
1
angular positions of these peaks, found
from the decomposition of the WAXS
EO1
0.8
3.9
43
48
9
43
48
9
patterns, the density of the third phase
EO2
1.77
8.4
56
37
7
54
31
15
was estimated. The obtained results show
EO3
4.34
19.2
66
31
3
66
14
20
that, when the number of side branches
EO4
5.42
23.3
67
30
3
68
17
15
in a polyethylene chain increases, the
EO5
5.5
23.6
69
28
3
70
13
17
density smoothly decreases from the valEO6
6.64
27.7
70
28
2
69
13
18
ues close to the density of the crystalline
EO7
9.15
35.9
88
10
2
90
5
5
phase, in the case of linear polyethylene,
EO8
11.27
42.1
92
8
91
2
7
to the values close to the density of the
amorphous phase, for the copolymers
I1303
I1303scopic methods differ considerably. On with high 1-octene content. The crystalI1416
I1416
(2)
TR = 1 − (AR T
+RC=R 1) − (AR + CR (2)
)
AR =
AR =
CR =
CR =
0.46 ⋅ I tw 0.46 ⋅ I tw
I tw
(2) I tw the other hand, the mass fractions of the linity and mass fraction of the transition
I1303
phase - also decrease continuously with
liquid–amorphous phase
simi-1 are very -1
(2)
=where
TRand
= 1I−integral
(ARare
+ Cthe
I1303
are
the
intensities
intensities
the bands
of
located
thecorrelation
bands
at 1416
located
cm
atand
1416
1303
cmresults
cm
and
1303
cm
where
I1416 and
I1416
R ) integralof
1303
increasing
1-octene content.
lar.
The
between
the
I tw
1
1
obtained
for this
parameter
is asshown
and
I1303
are
integral
in- vibrations
, Itw is thewhere:
integral
, Itw isI1416
the
intensity
integral
ofintensity
the the
whole
of
twisting
the
whole
twisting
region
vibrations
used
region
as
a
standard
used
and
a
standard
and
-1
tensities of the
bandsoflocated
at 1416
cmat
and 1303
tensities
the bands
located
1416
cm-1 cm in Figure 10. It is evident that the “de- A comparison of the mass fractions of all
0.46 is a scaling
0.46 is
coefficient
a scaling obtained
coefficient
forobtained
a completely
for a completely
crystalline polyethylene.
crystalline polyethylene.
andvibrations
1303 cm-1region
, Itw is the
integral
intensity andgrees of amorphicity” determined with three phases determined with the WAXS
hole twisting
used
as a standard
TheofRaman
The
spectra
Raman
were
spectra
decomposed
wereregion
decomposed
into individual
into bands
individual
bands
a methods
least-squares
using coina least-squares
method and the Raman spectroscopic
the WAXS
and using
Raman
the whole
twisting
vibrations
or a completely
crystalline
polyethylene.
method shows that the total amounts of
cide
very
well
with
each
other.
In
other
used
as
a
standard
and
0.46
is
a
scaling
curve fittingcurve
method
fitting
implemented
method implemented
in the computer
in theprogram
computer
GRAMMS,
program GRAMMS,
universally universally
used in
used in
coefficient
obtained
omposed into
individual
bands for
usinga acompletely
least-squareswords, the total mass fraction of the crystalline and transition phases estithe analysiscrystalline
the
of analysis
infrared
spectra.
of infrared
Thespectra.
bands were
The bands
approximated
were approximated
by
linear combination
byordered
a linear phases
combination
of theis mated
of the with these two methods agree very
polyethylene.
ordered
anda partially
the computer program GRAMMS, universally used inestimated similarly with the two meth- well. However, the values obtained for
Gauss and Lorentz
Gauss and
functions.
LorentzThree
functions.
examples
Threeofexamples
Raman spectra
of Raman
for spectra
the EO1,forEO5
the and
EO1,EO8
EO5 and EO8
The Raman spectra
were
decomposed
ands were approximated
by a linear
combination
of theods; however, the individual fractions each individual phase do not coincide.
samples areinto
samples
shown
inareFig.
shown
9 a)–c).
in Fig.
9 a)–c).
individual
bands
using
a least- are different. Such discrepancies may The discrepancies may be caused by a
xamples of Raman spectra for the EO1, EO5 and EO8
different
be
caused
by
the
the transition
fitting
method
implementThesquares
resultscurve
The
of the
results
calculations
of
the calculations
are
given inare
Table
given
2. in
The
Table
comparison
2. fact
Thethat
comparison
shows
that shows
the
that
the “perception” of the transition
ed in the computer program GRAMMS, phase is “seen” differently in these two phase in these methods and by problems
mass fractions
massoffractions
the transition
of the
transition
crystalline
phases
crystalline
determined
phasesMoreover,
determined
with the X-ray
diffraction
the X-ray
with the isolation of the “crystalline” band
methods.
towith
calculate
thediffraction
theand
analysis
ofand
infras are given universally
in Table 2. used
The in
comparison
shows
that the
at 1416 cm-1 in the Raman spectra of the
mass
fraction
of
the
crystalline
phase
in
red
spectra.
The
bands
were
approximatand Raman and
spectroscopic
Raman spectroscopic
methods differ
methods
considerably.
differ considerably.
On the otherOnhand,
the other
the mass
hand,fractions
the mass fractions
rystalline phases
with the X-ray
ed by determined
a linear combination
of the diffraction
Gauss the Raman method, we have to isolate samples with high 1-octene content.
of the liquid–amorphous
of the liquid–amorphous
phase are very
phase
similar.
are very
Thesimilar.
correlation
The correlation
between -1thebetween
results obtained
the results
obtained
CH2
and
Lorentz
functions.
Three
examples
fer considerably. On the other hand, the mass fractionsthe band 1416 cm from a broad
-1
range
(1430-1550
cm ) ofcomof
spectra
EO1,
for this parameter
forRaman
this is
parameter
shownforinisthe
Fig.
shown
10.EO5
inIt Fig.
isand
evident
10. bending
It is
thatevident
the
“degrees
that
theof“degrees
amorphicity”
amorphicity”
ry similar. The
between
results 9.a-c
obtainedposed of 4 bands. In the case of samples
EO8correlation
samples are
shown the
in Figure
determined determined
with the WAXS
with the
andWAXS
Raman and
methods
Raman
coincide
methods
very
coincide
well with
veryeach
wellother.
with each
In other
other. InReferences
other
(see pagethat
61).the “degrees of amorphicity”with medium and low crystallinity (see
10. It is evident
1. McFaddin D., Russel K., Wu G., Heydig
words, the words,
total mass
the total
fraction
massof fraction
the ordered
of the
andordered
partially
ordered
partially
ordered
is estimated
phasesmay
is estimated
Figureand
9),
such aphases
decomposition
an methods The
coincide
very
wellcalculations
with each other.
In otherresult in an underestimation of this band
R.J. Polym. Sci. (1993), 31, 175.
results
of
the
are
given
similarly with
similarly
the two
withmethods;
the two however,
methods; the
however,
individual
the individual
fractions are
fractions
different.
are Such
different. 2.
Such
Simanke A., Alamo R.G., Galland G.,
2. Theordered
comparison
that and as a consequence of too low a mass
he ordered in
andTable
partially
phasesshows
is estimated
Mauler R.S. Macromolecules (2001),
discrepancies
discrepancies
may
be
caused
may
by
be
the
caused
fact
that
by
the
the
fact
transition
that
the
phase
transition
is
“seen”
phase
differently
is
“seen”
in
differently
these
in
these
the mass fractions of the transition and fraction of the crystalline phase and,
34, 6959.
owever, the individual fractions are different. Suchin turn, too high a mass fraction of the
crystalline
phases
determined
with fraction
the
two methods.
twoMoreover,
methods.
to
Moreover,
calculate
tothecalculate
mass
the mass
of the
fraction
crystalline
of the phase
crystalline
in thephase
Raman
in the Raman
3. Sajkiewicz P., Hashimoto T., Saijo K.,
phase (see Equation 2). -1
ct that the transition
phase is “seen”
differently
in thesetransition
X-ray diffraction
and Raman
spectroGradys
A. Polymer (2004), 46, 513.
-1
-1
-1
method, wemethod,
have to we
isolate
havethe
to band
isolate
1416
the cm
band
1416acm
from
broad
from
CHa2 bending
broad CHrange
(1430range
cm –(1430 cm
– S. Fibres&Text. (2005), 5, 30.
2 bending
4. Rabiej
the mass -1
fraction of the
crystalline phase in the Raman
5. Strobl R.G., Hagedorn W. J.Polym. Sci.
1550 cm
cm-1) of
) 1550
composed
composed
4 bands. of
In 4the
bands.
case In
of the
samples
case of
with
samples
medium
with
andmedium
low crystallinity
and low crystallinity
-1
Polym. Phys. Ed. (1978), 42, 1181.
416 cm from110a broad CH2 bending range (1430 cm-1– Conclusions
(see Fig. 9),(see
such
Fig.
a decomposition
9), such a decomposition
may result may
in anresult
underestimation
in an underestimation
of
this band
ofand
thisas
band
a and6.asRabiej
a
M., Rabiej S. “Analiza rent100
The
existence
of
a
third,
transition
phase
A
=1.027*A
2.18
R=0.9976
the case of samples
with medium and low crystallinity
genowskich krzywych dyfrakcyjnych
90
is intermediate
in and,
the
order
consequenceconsequence
of too low aofmass
too low
fraction
a mass
of the
fraction
crystalline
of that
the phase
crystalline
and, in
phase
turn,
toodegree
in
high
turn,
aofmass
too
high a mass
polimerów za pomocą programu kommay result in an80 underestimation of this band and as abetween the crystalline and amorphous
puterowego WAXFIT”, Publishing House
70
fraction of the
fraction
transition
of thephase
transition
(see equation
phase (see
(2)).
equation (2)).
ATH, Bielsko-Biała 2006.
60
on of the crystalline
phase and, in turn, too high a massphases has already been proved in several papers dedicated to the structure of
7. Rabiej M. Polimery (2002), 47, 423.
50
uation (2)).
8. Rabiej M. Fibres&Text. (2003), 5, 83.
40
polyethylenes. In this work, we tried to
Conclusions
Conclusions
9. Monar K., Habenschuss A. J. Polym.
30
determine how to account for the third
Sci. Polym. Phys. Ed. (1999), 37, 3401.
20
component in the analysis of the WAXS
10. Bartczak Z., Gałęski A., Argon A.S., CoConclusions 20 30 40 50 60 70 80 90 100
diffraction
curves
of of
polyethylenes.
It between
The existence
Theofexistence
a third, transition
of a Athird,
phase
transition
that isphase
intermediate
that
is intermediate
in the
degree
in
the
order
degree
between
of order
hen R.E. Polymer (1996), 37, 2113.
,%
was shown that the best fit of the theo- 11. Baker A.M.E, Windle A.H., Polymer, 42,
the crystalline
the and
crystalline
amorphous
and amorphous
phases has already
phases has
been
already
provedbeen
in several
proved
papers
inexperimental
several
dedicated
papersdata
todedicated(2001),
to
retical
curves
to the
667.
hase that is Figure
intermediate
in the degree
of order
between
10. Comparison
of the mass
fractions
was
obtained
when
the
suggestions
of
12.
Swan
P.R.
J. Polym. Sci. (1960), 42, 525.
the structure
the
of
structure
polyethylenes.
of
polyethylenes.
In
this
work,
In
we
this
tried
work,
to
determine
we
tried
to
how
determine
to
account
how
for
to
account
the
third
for
the
third
of the amorphous phase determined with
has alreadythe
been
proved
in several
WAXS
method
(AX) andpapers
with thededicated
Raman toBaker [11] were adopted. In this apcomponentspectroscopic
component
in the analysis
inmethod
the
of analysis
the
diffraction
WAXS curves
diffraction
polyethylenes.
curves
of polyethylenes.
It wasrepresentshown
It was shown
(A WAXS
). of the
Received 23.05.2008
Reviewed 21.11.2008
proach,oftwo
additional
peaks
work, we tried to determine how toR account for the third
that the best
that
fit the
of the
besttheoretical
fit of the theoretical
curves to the
curves
experimental
to the experimental
data was obtained
data waswhen
obtained
the when the
AXS diffraction
FIBRES & TEXTILES in Eastern Europe January / December / B 2008, Vol. 16, No. 6 (71)
62 curves of polyethylenes. It was shown
suggestionssuggestions
of Baker [11]
of Baker
were adopted.
[11] were
In adopted.
this approach,
In thistwo
approach,
additional
twopeaks
additional
representing
peaks representing
rves to the experimental data was obtained when the
R
AX, %
X
R