Thermal Conductivity of High Strength Polyethylene Fiberin Low Temperature
ATSUHIKO YAMANAKA,1 HIROYUKI FUJISHIRO,2 TOSHIHIRO KASHIMA,3 TOORU KITAGAWA,4 KIMIKO EMA,5YOSHINOBU IZUMI,5 MANABU IKEBE,2 SHIGEHIRO NISHIJIMA5
1

Advanced Textile R & D Center, Research Center, Toyobo Co., Ltd., 2-1-1, Katata, Ohtsu, Shiga 520-0292, Japan2

Department of Materials Science and Technology, Faculty of Engineering, Iwate University, Ueda 4-3-5,
Morioka 020-8551, Japan

3

Hamamatsu Technopolis, Shizuoka University, H amamatsu, Shizuoka 431-3215, Japan

4

Polymer Institute, Toyobo Research Center Co., Ltd., 2-1-1, Katata, Ohtsu, Shiga 520-0292, Japan

5

Department of Nuclear Engineering, Graduate School of Engineering, Osaka University, Yamadaoka 2-1,
Suita, Osaka 565-0871, Japan

Received 26 November 2004; revised 25 January 2005; accepted 26 January 2005
DOI: 10.1002/polb.20428
Published online in Wiley InterScience (www.interscience.wiley.com).

ABSTRACT: High strength polyethylene ﬁber (Toyobo, Dyneema1 ﬁber, hereinafter
abbreviated to DF) used as reinforcement of ﬁber-reinforced plastics for cryogenic use
has a high thermal conductivity. To understand the thermal conductivity of DF, therelation between ﬁber structure and thermal conductivity of several kinds of polyethylene ﬁbers having different modulus from 15 to 134 GPa (hereinafter abbreviated toDFs) was investigated. The mechanical series-parallel model composed of crystal andamorphous was applied to DFs for thermal conductivity. This mechanical model was
obtained by crystallinity and crystal orientation angle measured by solid state NMR
and X-ray. Thermal conductivity of DF in ﬁber direction was dominated by that of thecontinuous crystal region. The thermal conductivity of the continuous crystal part estimated by the mechanical model increases from 16 to 900 mw/cmK by the increasing
temperature from 10 to 150K, and thermal diffusivity of the continuous crystal partwas estimated to about 100 mm2/s, which is almost temperature independent. The phonon mean free path of the continuous crystal region of DF obtained by thermal diffusivity is almost temperature independent and its value about 200 Å. With the aforementioned, the mechanical series-parallel model composed of crystal and amorphous
C 2005 Wiley Periodicals, Inc.
regions could be applied to DFs for thermal conductivity. V
J Polym Sci Part B: Polym Phys 43: 1495–1503, 2005

Keywords:

thermal conductivity; polyethylene ﬁber; low temperature

INTRODUCTION
The thermal conductivity of amorphous polymers
is believed to be lower than that of metals or
Correspondence to: A.
yamanaka@kt.toyobo.co.jp)

Yamanaka (E-mail:atsuhiko_

Journal of Polymer Science: Part B: Polymer Physics, Vol. 43, 1495–1503 (2005)
C 2005 Wiley Periodicals, Inc.
V

semiconductors.1,2 Therefore, polymers are frequently used as heat insulators. However, in thecase of polyethylene crystals, reports have been
produced suggesting that crystalline polymers
possess high-thermal conductivity toward the
direction of the molecular chain axis.3–9 The thermal conductivity of electrical insulators can be
due to phonons.3,5 Therefore, the thermal conduc1495

1496

YAMANAKA ET AL.

tivity of crystalline polymer materials depends ontheir crystallinity and orientation, that is, highlycrystalline and highly-oriented polymers should
exhibit high thermal conductivity.4–9 Furthermore, there are high-crystallinity and highstrength ﬁbers that possess thermal conductivity
almost as high as metals; these include highstrength polyethylene5,10,11 and high-strength
polybenzobisoxazole ﬁbers.10 Thermal conductivity of crystal polymer, for example, polyethylene,
was analyzed by a mechanical model composed of
crystal and amorphous.4,7–9,12–14
Meanwhile, the importance of polymer materials as electrical insulating or structural materials
has been recognized in those areas of cryogenic
engineering that require super conducting technology, such as superconducting power equipment, magnetic levitated transportation, medical
diagnosis equipment, or nuclear fusion reactors
and so on. To apply polymer materials to theseareas, their thermal properties, and in particular
their coefﬁcient of linear expansion and their
thermal conductivity, have been importantparameters to study. For example, high-strength
polyethylene ﬁber (Toyobo, Dyneema1; DF)15–17
and composite materials that use DF as a reinforcing ﬁber (DFRP),16,18 possess a negative coefﬁcient of linear expansion toward the direction of
the ﬁber axis. Typical applications for these materials are as coil bobbins19–29 and spacers23,28,30,31
for super conductors.
Furthermore, in the ﬁeld of high-temperature
superconducting coils, highly thermal conductive
and electrical insulating materials need to be
developed to protect superconducting materials
from heat burn up.32,33 Because DFRP-basedmaterials possess high-thermal conductivity10
and are highly insulating,34 their application tothis system has been expected. Practical reports
have been produced concerning the heat-radiation effects of high-temperature superconducting
tape materials.32,33 These indicate that the thermal conductivity of these insulators as well as
their negative expansivity are important characteristics when considering their application in
the ﬁeld of cryogenics.
In this article, we investigate the relationshipbetween the thermal conductivity and the structure of polyethylene ﬁbers (hereafter DFs) having different tensile modulus (from 15 to 134GPa) to understand the thermal conductivity ofDF, which is used as reinforcing ﬁber in the
cryogenic composite material DFRP. Previous
reports showed that these DFs exhibited higher

thermal conductivity with increasing tensile
modulus.11 Furthermore, a previous report elucidated that DF with higher tensile modulus
showed higher negative thermal expansivity,
and this relationship was explained by the ﬁber
structure illustrated in the mechanical serialparallel model (Takayanagi-model), which consists of a crystalline/amorphous structure.17 In
this article, we apply this mechanical model
introduced in our previous report17 to the DFs
for thermal conductivity. This mechanical model
is composed of the following two parts by parallel combination. One of them is the continuous
crystal part, and the other is the series combination part of crystal and amorphous. We estimate
the thermal conductivity and thermal diffusivityof the continuous crystal part in DF on themechanical model.

EXPERIMENTAL
SampleFour kinds of DFs (Toyobo, Dyneema1, DF (A–D)
with different draw ratio16 were used.17 They
have different modulus17 shown as follows:
DF(A): 15GPa, DF(B): 51GPa, DF(C): 85GPa, andDF(D): 134GPa.
Measurements
Thermal Conductivity
Thermal conductivity (j) was measured by asteady-state heat ﬂow method.10 The measurements of j were carried out on the automatedmeasuring system with thermal controller of a
Gifford-MacMahon (GM) cycle helium refrigerator as a cryostat.35 The ﬁber samples were prepared by bundling about 6000 monoﬁlamentswith a length of 45 mm.10,11 The diameters of
DFs were about 12  25 lm. The direction of
measurements of j was parallel to the ﬁber
direction. Details of the determination of j aredescribed eleswhere.10,11
Crystallinity
Crystallinities of DFs were estimated by peakseparation of solid state high resolution NMR.
Solid state NMR measurements were carried out
on a Varian XL-300 (13C, 75.5MHz). NMR spectra
were measured by the Cross-Polarization (CP)high power proton dipole decoupling (DD) magicHIGH STRENGTH POLYETHYLENE FIBER IN LOW TEMPERATURE

1497

Figure 1. The temperature dependence of thermal conductivity of DF(A–D) in theﬁber direction.

angle spinning (MAS) method. Pulse width was 5
ms, dipole DD power was 50 kHz, and MAS rate
was 3.5 kHz. Details of NMR measurements were
described in a previous article.17
Orientation Angle
Orientation angle of crystallic phase in DFs wasestimated by intensity distribution of X-ray diffraction spots as described in a previous
article.17 A Rigaku RU-200 (40 kV  100 mA)
was used with X-ray diffraction on Ni-ﬁltered
Cu Ka (k ¼ 0.1548 nm).

ductivity in the amorphous region is much lower
than that in the crystal region in the chain axis.8
From these results, the relation between the thermal conductivity and tensile modulus of DFs in
the ﬁber direction is inferred to be caused by the
crystallinity and orientation angles.
The crystallinities and orientation angles of
DFs are measured by solid state high resolution
NMR and X-ray diffraction in the following sections. From those results, the parameters of themechanical series-parallel model are estimatedto explain the thermal conductivity of DFs.

Crystallinity of DFs

RESULTS AND DISCUSSION
Thermal Conductivity of DFs
The temperature dependence of thermal conductivity of DFs in the ﬁber direction is shown in Figure 1. Thermal conductivity increases withincreasing tensile modulus of DF, and all of themincrease with increasing temperature. It is known
that thermal conduction of polyethylene is causedby phonon conduction and that thermal conductivity is higher in the chain axis combined by covalent bonding than perpendicular to the chain axis
combined by van der Waals interaction in the crystal region.3,7,14 It is also known that thermal con-

It is known that the crystal and amorphous ofpolyethylene have different chemical shifts in solidstate 13C NMR spectra.36–40 This means that it ispossible to estimate the crystallinity by peak separation of the 13C NMR spectra of polyethylene.36–40
In this way, the crystallinities of DFs were estimated by the measurements of solid state 13C
NMR spectra in a previous work.17 The details of
estimation of crystallinities were discussed in aprevious article.17 The crystallinities of DFs areshown in Figure 2. It is shown that crystallinity
is higher in DFs of higher modulus. Relations
between the thermal conductivities at 20, 50, 80,
and 100K and crystallinities of DFs are shown in1498

YAMANAKA ET AL.

Figure 2. Crystallinity and tensile modulus ofDF(A–D).

Figure 3. It is shown that thermal conductivity of
DF increases with increasing crystallinity. Thissuggests a contribution of the crystal region to
the high thermal conductivity of DF. But thermal
conductivities between DF(A) and DF(B) aremuch different in spite of a small difference of
crystallinities. Therefore, the increasing thermal
conductivity cannot be explained only by crystallinities of DFs. In the following section, orientation angles of DFs are reported.

Figure 4. Orientation angles and tensile modulus ofDF(A–D).

The orientation angles of DFs are shown in
Figure 4.17 The orientation angle is smaller;

the tensile modulus is higher. Relations
between the thermal conductivities at 20,50,80,
and 100K and orientation angles of DFs
are shown in Figure 5. Therefore we foundthat highly oriented DF has a high thermal
conductivity.
But every DF has a small orientation angle
from 1.9deg to 6.1deg, which is nearly equal to 0.
In this section, the contribution of the orientation
angle to the thermal conductivity of the DFs isestimated. Thermal conductivity of the crystal
region in the ﬁber direction (jcf) is described in eq
1 by that in the chain axis (jc(chain)) and the crystal orientation angle /.

Figure 3. Relation of crystallinities and thermal
conductivities at 20, 50, 80, and 100K of DFs.

Figure 5. Relation of orientation angles and thermal conductivities at 20, 50, 80, and 100 K of DFs.

Orientation Angles of DFs

HIGH STRENGTH POLYETHYLENE FIBER IN LOW TEMPERATURE

1499

Table 1. Parameter of DF(A – D) in the Mechanical Model

DF(A)
DF(B)
DF(C)
DF(D)

E
(GPa)

Crystallinity
(%)

xIIc

xIIa

yI

yII

15
51
85
134

79.5
82.7
94.7
99.0

0.782
0.781
0.918
0.978

0.218
0.219
0.082
0.022

0.058
0.213
0.354
0.544

0.942
0.787
0.646
0.455

jcf ¼ jcðchainÞ cos /ð1Þ

The jcf of DFs are estimated as follows by eq 1:
jcf (A) ¼ 0.994jc(chain), jcf (B) ¼ 0.998jc(chain), jcf(C) ¼ 0.999jc(chain), and jcf (D) ¼ 0.999jc(chain).
With the aforementioned, the difference ofdistribution to the thermal conductivity by the
crystal orientation angles among the DFs issmall in spite of a large difference of thermal
conductivities. Therefore, the difference of thermal conductivities among the DFs cannot be
explained only by orientation angles. From thoseresults, all DFs are considered as nearly perfectoriented ﬁbers and the chain axes in the crystal
regions are considered as ﬁber axes to discuss
thermal conductivity.
In the following section, we use those results
to introduce the mechanical series-parallelmodel to DFs.

Parameters of the Mechanical Series-Parallel
Model
A schematic diagram of the mechanical seriesparallel model composed of crystal/amorphous is

Figure 6. Schematic diagram showing the structureof DF by mechanical model.

shown in Figure 6. The chain axis in the crystal
region is extended and aligned to the ﬁber axis
in this mechanical model, because the orientation angles of DFs are nearly 0 as shown in theearlier sections. As shown in Figure 6, DFs arecomposed of part I and part II by parallel combination in this model.17 Part I is continuous crystal, and part II is composed of crystal and amorphous by series combination.17
The parameters of the mechanical model aredeﬁned as follows: E, total tensile modulus in
ﬁber direction; EI, tensile modulus of part I in
ﬁber axis; EII, tensile modulus of part II in ﬁber
axis; Ec, tensile modulus of crystal in chain axis;
Ea, tensile modulus of amorphous; yI, width ofpart I; yII; width of part II; xIIc; length of crystal
part in part II; xIIa; length of amorphous part inpart II; va ¼ xIIayII, volume fraction of amorphous. So, crystallinity is shown as 1- xIIayII.
Those deﬁnitions are also shown in Figure 6.
The relation formulas between those parameters
are shown in Figure 6. E of DFs are experimental values. Ec is 235GPa obtained by Nakamae
and coworkers,41 and Ea is 0.3GPa obtained byChen and colleagues.42 The volume fractions ofamorphous va ¼ xIIayII are estimated by solidstate NMR measurements as mentioned above.
The parameters of the mechanical model (xIIc,
xIIa, yI, and yII) were estimated by the substitutionof the numerical values aforementioned into theequations shown in Figure 6. The estimated values
are shown in Table 1 and Figure 7.17

Figure 7. Schematic diagram of DF(A–D) estimatedby the mechanical model.

1500

YAMANAKA ET AL.

The Relation Between the Thermal Conductivity
and Mechanical Model of DFs
In this section, the mechanical model obtainedin the front section is applied to DFs for thermal
conductivity. Thermal conductivity of DF in theﬁber direction is deﬁned as j. Thermal conductivity of part I (continuous crystal region) shownin Figure 6 in the chain axis is deﬁned as jI,
and that of part II shown in Figure 6 in theﬁber direction as jII. j, jI, and jII are shown in
the following eqs 2 and 3:
j ¼ yIKI þ yIIKIIð2Þ

From yI þ yII ¼ 1 as shown in Figure 6,
j ¼ ðjI  jII ÞyI þ jII

ð3Þ

The thermal conductivity of the crystal region
in the chain axis is deﬁned as jc, and that of theamorphous region as ja. Because the orientation
angles are nearly 0 as mentioned above, we canneglect contributions by thermal conduction perpendicular to the chain direction. Therefore, therelation between jI, jII, and jc, ja is shown by
eqs 4 and 5 as follows:jI ¼jcð4Þ

jII ¼ ðjc ja Þ=ðja XIIc þ jc XIIa Þð5Þ

It is known that ja is lower than 2 mw/cmK
below 150 K.8 Meanwhile, thermal conductivityof DF(D) is 500 mw/cmK at 150 K, as shown in
Figure 1. Therefore, jc is guessed to be higher
than 500 mw/cmK, namely, jc  ja. This meansthat jI  jII. From this inequality, eq 3 can betreated as the following eq 6::
j¼: jI yI þ jII

ð6Þ

In this mechanical model, eq 6 shows that
thermal conductivity (j) of DF in the ﬁber direction is dominated by that of part I (jI). The
value of thermal conductivity in the ﬁber direction (j) is expected to depend on that of thecrystal region in the chain axis (jc(¼ jI)) andthe volume fraction of the continuous crystal
region (yI). This approximation was applied tothe highly oriented polyethylene for thermal
conductivity elsewhere.12,14

Figure 8. Thermal conductivity of DF(A–D) as functions of yI in the mechanical model at 20, 50, 80, and
100 K.

We investigate the relation between yI and thermal conductivity (j). Thermal conductivity of DF(A–D) as a function of yI in the mechanical model
shown in Table 1 and Figure 7 at 20, 50, 80, and100K is shown in Figure 8. Thermal conductivityof DF(A, B, C, D) increases linearly in proportion
to yI. This result shows that eq 3 can be approximated to eq 6. And it also suggests that thermal
conductivity of the continuous crystal region (jI¼ jc) of every DF is nearly equal. From this section, the mechanical series-parallel model shownin Figure 7 can be applied to DF (A, B, C, D) having different modulus prepared by the same raw
material for thermal conductivity.
Thermal Conductivity of Continuous Crystal Regionin DFsIn this section, thermal conductivity of the continuous crystal region (part I) (jI) is estimated. The
parameters of eq 3 can be obtained by linear line
approximation of k and yI in Figure 8. jI ¼ jc
can be estimated by extension of the approximated linear line to yI ¼ 1.0, namely, jI can be
estimated by substitution of yI ¼ 1.0 into eq 3
obtained by linear line approximation. The estimation of jI is carried out by every 10 degrees
from 10 to 150K. Temperature dependence of jI¼ jc is shown in Figure 7, with observed thermal
conductivity of DFs shown in Figure 1. The jc of
DF increases from 16 to 900mw/cmK by theincreasing temperature from 10 to 150K. jc
increases slowly by increasing temperature.

HIGH STRENGTH POLYETHYLENE FIBER IN LOW TEMPERATURE

1501

From the thermal diffusivity in part I estimated as aforementioned, the mean free pathof phonon in the ﬁber axis of the continuous
crystal region in DF is obtained in the following
way. The mean free path of phonon l is estimated in eq 8.
l ¼ 3k=v

ð8Þ

In this formula, v is deﬁned as sound velocity.
In this case, it is sound velocity in the chain
axis in crystal. The v in the chain axis in crystal
is estimated by using Ec and q in eq 9.
v ¼ ðEc=qÞ1=2
Figure 9. Temperature dependence of thermal conductivity of DF(A–D) and crystal of DF.

Thermal Diffusivity and Phonon Mean Free Path ofContinuous Crystal Region in DF
In this section, we estimate thermal diffusivity(k) of the continuous crystal region in DF. The
relation between thermal diffusivity and thermal conductivity is shown in eq 7:
k ¼ j=Cpq

ð7Þ

In this equation, Cp is deﬁned as heat capacityand q as density of polyethylene. Temperaturedependence of the thermal diffusivity k of the continuous crystal region (part I) is estimated by eq 7.
The crystalline density of polyethylene is 1.00 g/cc,
which is used as the numerical value of q.43 The
reported heat capacities43 of polyethylene crystal
are used as numerical values of Cp. The Cp isalmost orientation independent.43 The values of jI¼ jc shown in Figure 9 are used as j. k is estimatedby the substitution of the numerical values of jc,
Cp, and q into eq 7. Temperature dependence ofthermal diffusivity k of part I obtained as aforementioned is shown in Figure 10. The obtained k isabout 100 mm2/s at 150 K and nearly temperature
independent. The k increases very slightly withtemperature decreasing from 150 K to 40 K, shows
minimum value at about 20 K, and increases
markedly with temperature decreasing from 20 K
to 10 K. In the case of the temperature range under
20 K, both j and Cp converge to 0 with temperature approaching 0 K. Therefore, the experimental
error of k ¼ j/Cpq becomes large in this temperature range, so we could not discuss the temperature dependence of k under 20 K.

ð9Þ

Tensile modulus of the crystal region in chain
direction Ec is assumed as 235Gpa, reported as
the experimental value about DF.41 And temperature independence of Ec is also reported.41 On theother hand, estimations of temperature dependence of Ec by calculation are reported.44–47 So,
more detailed discussion will be necessary for
accurate consideration. In this report, the experimental value observed for DF41 is used as Ec. The
density of the crystal region (q) is 1.00 g/cc.43 The
sound velocity of the crystal in DF (v) is estimatedas 15,300 m/s by substitution of the numericalvalues of Ec and q into eq 9. In the case of DF(C),the sound velocity of DF(C) reinforced plastics
was measured, and it almost agrees to that estimated tensile modulus.48,49
The mean free path l of phonon of the continuous crystal region of DF in the ﬁber direction
is estimated by the substitution of thermal diffu-

Figure 10. Temperature dependence of thermal diffusivity of the crystal part in DF.

1502

YAMANAKA ET AL.

decreasing temperature. This means that thesound velocity and k increase with temperature
decrease. The detailed discussion about the morphology and temperature dependence of Ec of
DF will be necessary to clear the slight temperature dependence of k and l.

CONCLUSIONS

Figure 11. Temperature dependence of the mean
free path of phonon in the crystal part in DF.

sivity k shown in Figure 10 and sound velocity
v ¼ 15,300 m/s into eq 8. Temperature dependence of the mean free path of phonon (l) in thecontinuous crystal region is shown in Figure 11.
The estimated l is nearly temperature independent and its value about 200 Å. This almost constant l indicates that phonons are mainly scattered by domain wall-like barriers over theentire temperature range. The phonon scattering is inferred to be due to phonon heat conduction in the crystal region. The slight temperature dependence of k and l shown in Figures 10
and 11 is discussed in the following.
The k and l were estimated on the following
assumptions as aforementioned. The DFs arecomposed of only two components; crystal andamorphous, and the tensile modulus of the crystal region (Ec) is temperature independent. But
more detailed discussion will be necessary toclear the temperature dependence of Ec as
aforementioned. The change of Ec reported byother articles44–47 is 4  60GPa by cooling from300 K to 4 K. This increasing of Ec means aslight increasing of sound velocity and k.
On the other hand, it is reported that polyethylene has many components, for example,
intermediate regions between crystal and amorphous.38–40 In the case of DF, it was reported
that the crystalline signal of DF in NMR is composed of several components.39,40 Therefore, thecrystal region in the mechanical model in thisarticle is able to contain the components’ amorphous-like crystal or crystal-like amorphous to
add to the crystal region. The tensile modulus of
those components is able to increase with

Thermal conductivity, crystallinity, and orientation angles were measured for several kinds ofhigh strength polyethylene ﬁber (DF (A–D)) having different modulus, which were 15–134GPa.
And a mechanical series parallel model composedof extended crystal and amorphous (the Takayanagi model) was applied to DFs for thermal conductivity. The following conclusions were drawn:
1. Thermal conductivity increases withincreasing tensile modulus of DF.
2. In this mechanical model composed of acontinuous crystal region and a series combination part composed of crystal andamorphous, thermal conductivity (j) of DF
in the ﬁber direction is dominated by thatof the continuous crystal region.
3. The thermal conductivity of the continuous
crystal region in DF increases from 16 to
900 mw/cmK by increasing temperaturefrom 10 to 150 K.
4. The thermal diffusivity of the continuous
crystal region in DF is about 100 mm2/s
and is almost temperature independent.
5. The phonon mean free path of the continuous crystal region of DF obtained by thermal diffusivity is almost temperature independent and its value about 200 Å.
With the aforementioned, the mechanical series-parallel model composed of crystal and amorphous could be applied to DFs for thermal conductivity.
The authors thank Dr. Yasuo Ohta and Dr. Tadao Kuroki of Toyobo Co., Ltd. for preparing DF samples. The
authors also thank professor Dr. Masakatsu Takeo of
Kyushu University, professor Dr. Tomoaki Takao ofSophia University, and professor Dr. Kenji Hosoyamaof the High Energy Accelerator Research Organization
for useful suggestions about the importance of thermal
conductivity of materials for applied superconductivity.
Thanks to professor Dr. Yuichi Okuda and Dr. Ryuji
Nomura of the Tokyo Institute of Technology for usefulsuggestion about the sound velocity of DF. Thanks also
to the experimental assistant group of the Polymer

HIGH STRENGTH POLYETHYLENE FIBER IN LOW TEMPERATURE

Institute in Toyobo Research Center Co., Ltd. for experimental assistance. Thanks to Dr. Hiroshi Hirahata,
Dr. Yukihiro Nomura, and members in the advanced
textiles R and D center of Toyobo, Co, Ltd. for useful
discussions. Thanks to the Dyneema Department of
Toyobo, Co, Ltd. for encouragement.

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