This document describes a study using rheo-optical near-infrared (NIR) spectroscopy to analyze the molecular-level deformation of low-density polyethylene (LDPE) during mechanical tensile testing. NIR spectra were collected from an LDPE sample under increasing strain. Two-dimensional correlation analysis with projection was used to filter out spectral changes from baseline fluctuations caused by sample thickness changes, in order to reveal deformation-related spectral features. The analysis identified predominant extension of amorphous tie chains followed by rotation of crystalline lamellae, corresponding to elastic and plastic deformation of the LDPE.

1. Vibrational Spectroscopy 70 (2014) 53–57
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Vibrational Spectroscopy
journal homepage: www.elsevier.com/locate/vibspec
Rheo-optical near-infrared (NIR) spectroscopy study of low-density
polyethylene (LDPE) in conjunction with projection two-dimensional
(2D) correlation analysisଝ
Hideyuki Shinzawaa,∗
, Wataru Kanematsua
, Isao Nodab
a
National Institute of Advanced Industrial Science and Technology (AIST), Nagoya 463-8560, Japan
b
Department of Materials Science and Engineering, University of Delaware, Newark DE 19716, USA
a r t i c l e i n f o
Article history:
Received 29 October 2013
Received in revised form 5 November 2013
Accepted 5 November 2013
Available online 21 November 2013
Keywords:
Rheo-optics
Tensile test
Neat-infrared (NIR)
Two-dimensional (2D) correlation
spectroscopy
Projection 2D correlation
Low-density polyethylene (LDPE)
a b s t r a c t
A rheo-optical characterization technique based on near-infrared (NIR) spectroscopy is developed specif-
ically to probe the submolecular-level deformation caused during a mechanical test. An illustrative
example of the mechanical deformation of low-density polyethylene (LDPE) is provided to show how
it can be utilized. A set of NIR spectra of the polymer sample were collected by using an acousto-optic
tunable filter (AOTF) NIR spectrometer coupled with a tensile testing machine as an excitation device.
While the substantial level of variation of spectral intensity was readily captured during the mechanical
deformation of the LDPE, main feature of the NIR spectra was overwhelmed by the contribution from
the baseline change. Projection 2D correlation analysis was then applied to selectively extract the signal
contribution from the baseline fluctuation. The 2D correlation spectra revealed the predominant exten-
sion of amorphous tie chains followed by the rotation of crystalline lamellae, which induce elastic and
plastic deformation of the LDPE, respectively.
© 2013 Elsevier B.V. All rights reserved.
1. Introduction
Mechanical properties of polymeric materials are of consider-
able importance to their engineering applications. The increased
need for a better understanding of the mechanisms involved in
polymer deformation has led to the search for new experimen-
tal techniques to characterize transient structural changes during
mechanical processes [1]. Simultaneous vibrational spectroscopic
and mechanical measurements have been developed as a very
informative probe to study the submolecular-level deformation
and relaxation phenomena in polymer films. For example, Siesler
pioneered the rheo-optical studies of polymer samples under var-
ious deformation modes by using an infrared probe to establish
the correlation between macroscopic and molecular dynamics of
polymers [2–5]. Such rheo-optical study of solid polymeric mate-
rials has been mainly challenged by the strong absorption in the
mid IR region [4–6]. The use of IR light often faces a serious obsta-
cle in analysis where substantially thick samples are required for
ଝ Selected paper presented at 7th International Conference on Advanced Vibra-
tional Spectroscopy, Kobe, Japan, August 25–30, 2013
∗ Corresponding author at: National Institute of Advanced Industrial Science and
Technology (AIST), Nagoya 463-8560, Japan. Tel.: +81527367563.
E-mail address: h-shinzawa@aist.go.jp (H. Shinzawa).
mechanical integrity during the deformation. Thus, there is a strong
incentive to expand the rheo-optical measurement to near-infrared
(NIR) region with much less intense absorption.
Polyethylene polymer consists of seemingly very simple chem-
ical structure but is one of the most basic and important
polymers. The crystalline and amorphous phases of polyethyl-
ene readily undergo substantial variation to generate different
supermolecular structures when the external forces (e.g., temper-
ature, mechanical force, etc.,) are applied [7–9]. The development
of different structures, in turn, provides different physical prop-
erty of the polyethylene. For example, Watanebe et al. have
studied temperature-dependent behavior of polyethylene by NIR
spectroscopy. They revealed that the different density of the
polyethylene (i.e., branching) provides different variation of NIR
spectral features when the samples undergo temperature-induced
alternation [7,10]. In this study, a rheo-optical characterization
technique based on the combination of NIR spectroscopy and
mechanical analysis was carried out to measure strain-dependent
NIR spectra as well as tensile stress of a low-density polyeth-
ylene (LDPE) sample. A set of NIR spectra were collected by
using an acousto-optic tunable filter (AOTF) NIR spectrometer
coupled with a tensile testing machine as an excitation device.
The utilization of the AOTF, which is a wavelength tunable fil-
ter based on high-frequency transducer, offers a clear advantage
over the conventional grating-monochromator or interferometer
0924-2031/$ – see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.vibspec.2013.11.005

2. 54 H. Shinzawa et al. / Vibrational Spectroscopy 70 (2014) 53–57
based approach in terms of high speed data acquisition, especially
when the variation of the system occurs in a relatively short time
scale [11]. In fact, such short time scale is true to the mechanical
deformation of the ductile LDPE polymer caused during the tensile
test. Consequently, side-by-side comparison between the spectral
feature and the corresponding stress or strain behavior provides
the key information on the evolution of supermolecular structure
essentially governing the macroscopic deformation of LDPE.
While the rheo-optical NIR measurement readily captures the
molecular-level deformation caused by the applied strain, the main
feature of the spectra can also be influenced by physical changes
of the sample dimension and morphology. For example, tensile
test of the sample induces the substantial decrease in the thick-
ness and subsequent change in the NIR light scattering, which both
inevitably provide unwanted fluctuations of the spectral intensi-
ties. In addition, the limited resolution and assignment of NIR bands
have also been the obstacles for extracting meaningful information
on the deformation phenomenon. Two-dimensional (2D) correla-
tion analysis in conjunction with projection treatment was used
to selectively filter out such unwanted portion of the information
of spectral data [12,13]. A notable feature of the projection tech-
nique lies in the fact that selective rejection or augmentation of
a certain correlational feature becomes possible by utilizing the
projecting vector from various sources, including a part of original
spectral data or even the perturbation variables themselves. Impor-
tantly, such selective attenuation is also available as an effective
baseline correction method by utilizing a part of original spectral
data, predominantly reflecting spectral intensity change caused by
the change in the sample thickness and light scattering. Substantial
level of detailed changes in the spectral feature was readily eluci-
dated when the strain-dependent NIR spectra were subjected to the
projection 2D correlation analysis [14]. The 2D correlation spectra
revealed the seemingly complicated variation of the spectral inten-
sity associated with crystalline and amorphous structures of the
LDPE, which in turn, provide useful insight into the deformation
mechanism of the LDPE.
2. Theory
2.1. 2D correlation spectra
Assume the spectral data matrix A consists m rows of spectra
with n columns of spectral variables. We define a set of dynamic
spectra by subtracting a reference spectrum, typically the average
spectrum. The synchronous and asynchronous correlation spectra,
and , are obtained as
˚ =
1
m − 1
˜AT ˜A (1)
« =
1
m − 1
˜AT
N ˜A (2)
the superscript T denotes the transpose operation of the matrix and
N is the so-called Hilbert–Noda transformation matrix [15,16].
2.2. Vector projection
Projection 2D correlation operation [12] is a useful data pre-
treatment technique to sort out dynamic spectra into two separate
sets: one which is fully aligned with a chosen projecting vector and
the other which is orthogonal to the same vector. For the given
vector y, the projection matrix Ry is defined as
Ry = y(yT
y)
−1
yT
(4)
where the superscript −1 stands for the inverse operation of the
matrix. The m-by-m matrix Ry acts as a projector for the space
spanned by y. The projected data matrix AP is obtained by the
multiplication of Ry with A,
AP = RyA (5)
the projected data Ap represents the projection of A onto the
abstract space spanned by y. The portion of dynamic spectra pro-
jected onto the space spanned by such a projecting vector y will
have the same trend of y. Thus, all signals contained in the projected
dataset are fully synchronized.
The corresponding null-space projection is carried out as
AN = (I − Ry)A = A − AP (6)
where I means m-by-m identity matrix. The null-space projected
data matrix AN represents the projection of A onto the space
spanned by the vectors orthogonal to y. AN is the residual after the
removal of AP from A by using the information contained within
y. The null-space projection selectively eliminates the portion of
dynamic spectra which is synchronized with the projecting vector.
Finally 2D correlation spectra generated from the projected or null-
space projected data are given by substituting AP or AN into Eqs. (1)
and (2).
There are several options to choose the source of the projector. In
most cases, a single column is selected as a projector vector y from
the data matrix. For example, it was demonstrated by the projec-
tion 2D IR correlation analysis of a poly(methyl methacrylate) film
under a small amplitude deformation by using the intensity con-
tribution of the side group ester as a source of the projector [13].
Importantly, it is also possible to utilize the baseline fluctuation as
a source of the projector. For example, Shinzawa et al. [14] reported
that the unwanted baseline change can be removed by utilizing the
spectral intensity change at a certain wave number, representing
baseline fluctuation, as a projection vector.
3. Experiment
3.1. Sample preparation
The sample film was prepared from LDPE provided by Alfa
Aesar. Pellets of LDPE were melted and pressed at 120 ◦C to form a
5 × 5 cm2 piece of approximately 800 ␮m thick sheet.
3.2. Rheo-optical NIR measurement
Fig. 1 illustrates a schematic illustration and images of an AOTF-
NIR spectrometer (Systems Engineering Inc., Tokyo) equipped with
a tensile testing machine MX2-2500N (Imada Co. Ltd., Aichi).
The polymer sample was gradually deformed by the mechani-
cal stretcher while being probed with NIR beam. The sample was
stretched at the speed of 0.1 mm/min. A set of NIR spectra was
collected every 4 s by co-adding 64 scans over the 1200–1900 nm
region, and the corresponding stress and strain were also recorded
simultaneously.
4. Results and discussion
4.1. Tensile test
Fig. 2 shows a stress–strain curve of the LDPE sample. At the
onset of the tensile test, the stress gradually increases, reflecting the
elastic deformation of the sample. Further stretching of the sam-
ple causes the plastic deformation, which results in the irreversible
variation of the structure. The deformation finally ends up with
the breaking of the sample. Semicrystalline polyethylene samples,
prepared from the melt, often show a complex supermolecular
structure consisting of folded-chain crystal lamellae embedded in

3. H. Shinzawa et al. / Vibrational Spectroscopy 70 (2014) 53–57 55
Fig. 1. (A) Schematic illustration of a rheo-optical NIR spectrometer and (B) its actual
image.
Fig. 2. Stress–strain curve of LDPE sample.
a liquid-like amorphous matrix. It is believed that adjacent lamel-
lae are linked with the so-called amorphous tie-chain molecules
[17–19]. Because of differences in their mechanical properties, even
under a common macroscopic deformation, each phase is often
subjected to a different level of local mechanical stimuli. For exam-
ple, crystalline structure generally makes a material strong, but it
also makes it brittle. The amorphous structure, on the other hand,
gives the polymer it’s toughness , i.e., the ability to bend without
breaking. The generation of such different deformation behaviors
may be closely associated with the co-existence of the crystalline
and amorphous structures. Thus, the analysis of the corresponding
NIR spectra becomes important to derive the in-depth understand-
ing of deformation at the submolecular level.
4.2. Projection 2D correlation analysis
The strain-dependent NIR spectra of the LDPE sample are shown
in Fig. 3(A). This region of the NIR spectrum of LDPE is dominated by
the overtone and combination modes associated with CH2 groups
of LDPE. The corresponding second derivative spectra are also
Fig. 3. (A) Strain-dependent NIR spectra of LDPE sample and (B) corresponding
second derivative spectra.
provided as reference in Fig. 3(B). A peak observed around 1730 nm
is assigned to the first overtone of antisymmetric stretching mode
of CH2 group having the electric dipole-transition moment in the
direction perpendicular to that of the polymer backbone [10,20].
Although it is not readily identified, the amorphous component
also provides spectral intensity change at around 1710 nm [10,20].
It is important to point out that the spectra show gradual decrease
in the intensity over the region. The baseline changes from one
spectrum to the other, and the fluctuations caused by the macro-
scopic changes of the sample are much larger than those caused by
the molecular level structural changes caused by the mechanical
deformation, making the identification of pertinent feature diffi-
cult. Such baseline changes are mostly arising from the decrease
in the thickness of the LDPE sample induced by stretching. Impor-
tantly, such predominant baseline change causes some difficulties,
especially in the practice of 2D correlation analysis. Fig. 4 shows
(A) synchronous and (B) asynchronous correlation spectra directly
calculated from the raw NIR spectra shown in Fig. 3. The plot of the
reference spectrum is placed at the top and side of the contour map.
Negative correlation intensity areas of the contour map are repre-
sented by the shading. The problem caused by the baseline change
is especially acute for the asynchronous correlation spectrum. Base-
line fluctuations tend to have strong asynchronous elements with
respect to intensity changes arising from molecular level responses
of the system. In fact, all the correlation features associated with
the amorphous and crystalline peaks are obviously overshadowed
by the intense variation caused by the baseline change, generating
meaningless artifacts in the 2D correlation spectrum.

4. 56 H. Shinzawa et al. / Vibrational Spectroscopy 70 (2014) 53–57
Fig. 4. (A) Synchronous and (B) asynchronous correlation spectra derived from
strain-dependent NIR spectra shown in Fig. 3.
One reasonable solution to improve the quality of the 2D cor-
relation spectra is to selectively remove the portion of the spectra
which is synchronized with the baseline change. A simple offset
correction may be considered as one of such possible approaches.
For example, Fig. 5(A) represents the offset-corrected spectra of the
LDPE sample. Note that the offset treatment was carried out by sub-
tracting the spectral intensities at 1650 nm. Despite the elimination
of the offset deviation, the spectra still show gradual downward
shift. The fluctuation becomes especially acute in the longer wave-
length region, revealing the contribution from the baseline change
due to the multiplicative scatter factor. Fig. 5(B) illustrates the
intensity variations at 1710 (crystalline), 1730 (amorphous), and
1800 nm along strain direction derived from the offset-corrected
spectra shown in Fig. 5(A). The intensity variation at 1800 nm
mostly reflects the baseline increase arising from the multiplica-
tive scatter factor. It should be noted that the entire features of the
crystalline and amorphous bands result in a very similar pattern
with that at 1800 nm, suggesting that the baseline change provides
overwhelming contribution to the intensity variations in the whole
spectral region. It is important to point out here that the intensity
variation at 1800 nm in the offset spectra purely reflects the sig-
nal contribution from the multiplicative scatter factor. Thus, the
attenuation of the portion, which is synchronized with this trend,
leads to the highly selective removal of the contribution from the
multiplicative scatter factor in the whole spectral region.
Fig. 5(C) represents projection-corrected spectra calculated
from the offset spectra by the projection onto the space spanned
Fig. 5. (A) Offset-corrected spectra, (B) spectral intensity variations at 1710, 1730,
and 1800 nm, and (C) Projection-corrected spectra derived from offset-corrected
spectra onto null-space of their signals at 1800 nm.
orthogonal to the intensity variation at 1800 nm. The projection-
corrected spectra contain contributions from all other constituents
except for the baseline fluctuation, while the spectra are now
free from the intensity contribution from the intensity varia-
tion related to the multiplicative scatter factor. Such selective
attenuation becomes useful, especially for the subsequent 2D
correlation analysis. For example, Fig. 6 shows (A) synchronous
and (B) asynchronous correlation spectra calculated from the
projection-corrected NIR spectra. The entire plane of the syn-
chronous correlation spectra is covered with positive correlation
peaks of LDPE, reflecting the same deformation trend in the
variation within this NIR region. On the other hand, in the asyn-
chronous correlation spectrum, the influence of overwhelming

5. H. Shinzawa et al. / Vibrational Spectroscopy 70 (2014) 53–57 57
Fig. 6. (A) Synchronous and (B) asynchronous correlation spectra derived from
projection-corrected spectra shown in Fig. 5(C).
predominance of the baseline change is removed, and small fea-
tures overshadowed by the intense baseline change now becomes
clearly visible. The cross peak at the coordinate (1710, 1730) reveals
the different behavior of the crystalline and amorphous bands in the
variation of the spectral intensity, which is not readily identified
in the original set of one dimensional spectra. The development
of the positive correlation peak suggests that, at the onset of the
tensile testing, the deformation of the amorphous structure occurs
predominantly before that of the crystalline structure.
It is believed that the elastic properties of polyethylene is closely
associated with the interlamellar bridges, providing high elasticity
to the semicrystalline polymer [18,19]. Thus, the sequential order of
the event revealed by the 2D correlation analysis, in turn, provides
an even clearer picture to the mechanical deformation induced by
the tensile test. Fig. 7 schematically summarizes a possible defor-
mation mechanism proposed by the rheo-optical analysis. Initially
the LDPE sample consists of the crystalline lamellae oriented in
many directions. The deformation is mainly achieved by the exten-
sion of the amorphous tie chains. Such extension of the tie chains
results in the elastic deformation. Further stretching of the tie chain
induces the rotation and eventual breakup of the lamellae, lead-
ing to the irreversible plastic deformation. Consequently, it was
demonstrated that the rheo-optical NIR spectroscopy coupled with
Fig. 7. A possible deformation mechanism of LDPE under tensile test.
projection 2D correlation analysis can probe fine details of the sub-
molecule deformation of the polymer sample.
5. Conclusion
A rheo-optical characterization technique based on the com-
bination of NIR spectroscopy and mechanical analysis was
demonstrated in this study. A set of strain-dependent NIR spec-
tra as well as tensile stress of a LDPE sample were collected using
an AOTF NIR spectrometer coupled with a tensile testing machine
as an excitation device. While the substantial level of variation
of spectral intensity was readily captured during the mechanical
deformation of the LDPE, the main feature of the NIR spectra was
overwhelmed by the contribution from the baseline change. Projec-
tion 2D correlation analysis was applied to selectively separate the
signal contribution of interest from the baseline fluctuation. The 2D
correlation analysis of the spectra revealed that submolecular-level
deformation mechanism of the LDPE, namely the extension of the
tie chains and subsequent rotation of the lamellae, which induces
elastic and plastic deformation of the LDPE, respectively.
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