# Thermal Conductivity of High-Strength Polyethylene Fiber and

Authors: Atsuhiko Yamanaka; Tomoaki Takao
Journal: ISRN Materials Science
 (2011)

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## Abstract

The local temperature rise of the tape is one of instabilities of the
conduction-cooled high temperature superconducting (HTS) coils. To prevent the
HTS tape from locally raising a temperature, high thermal conductive fiber
reinforced plastic was applied to coil bobbin or spacer for heat drain from HTS
tape. The thermal conductivity of ramie fibers increases by increasing
orientation of molecular chains with drawing in water, and decreases by chain
scission withγ-rays irradiation or by bridge points in
molecular chains with vapor-phase-formaldehyde treatments. Thermal conductivity
of high strength ultra-high-molecular-weight (UHMW) polyethylene (PE) fiber
increases lineally in proportion to tensile modulus and decreases by molecular
chain scissions with γ-rays irradiation. This result
suggested the contribution of the long extended molecular chains due to high
molecular weight on the high thermal conductivity of high strength UHMW PE
fiber. Thermal conductivity of high strength UHMW PE fiber reinforced plastics
in parallel to fiber direction is proportional to the cross sectional ratio of
reinforcement oriented in the conduction direction. Heat drain effect of high
strength UHMW PE fiber reinforced plastic from HTS tape is higher than that of
glass fiber reinforced plastic (GFRP) and lower than that of aluminum nitride
(AlN). In the case of HTS coil, the thermal stability wound on coil bobbin made
of high strength UHMW PE fiber reinforced plastic is good as that of AlN, and
better than that of GFRP.


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## Body

## 1. Introduction

In applications of polymeric materials, the thermal conductivity has been an
important property, for example, for a cool/warm sensation for clothing fiber or
wood product, or in the thermal insulation of plastics including styroforms [1–4]. With the recent development of superconducting and electronic
engineering technologies, thermal conductivities of structural and insulating
materials used as composites in cryogenic and heat-releasing materials in electrical
equipment have become more important. Furthermore, the desired features vary,
depending upon the application, from insulation for use in cryostat [5] to high-thermal conductivity for use in
superconducting coils [6] and electronic
engineering [7]. For example, the thermal
conduction between a superconductor and the cold head of a refrigerator is important
for the stability of a conduction-cooled superconducting coil, because this
connection is the only heat-flow-pathway for cooling superconductor [8].Thermal conductivities of most of polymer materials are lower than those of metals
as shown in Figure1. From previous studies
of polymer materials, it is well-known that the thermal conductivities of amorphous
polymers are smaller than those of metals and semiconductors [9, 10]. Therefore, these
have principally been used as heat insulators. However, other reports have shown
that polymeric crystals possess high thermal conductivity in the direction in which
the molecular chains are covalently bonded, polyethylene crystals being an example
[11, 12]. Thus, high-crystallized and high-oriented polymers exhibit high
thermal conductivity [10–15]. For example, highly crystallized polymer
materials including high-strength polyethylene (PE) fiber [15–18] and
high-strength polypara-phenylene-benzo-bis-oxazole (PBO) fiber [16] are known to possess high thermal
conductivity similar to those of metals as shown in Figure 2. The high-strength PE fiber and PBO fiber shown in Figure
2 are Dyneema® SK-60 (hereinafter
abbreviated to DF) and Zylon® HM (TOYOBO CO.) [18–20].Figure 1
Thermal conductivities of industrial materials.Figure 2
Thermal conductivities of high-thermal-conductive polymer fibers [18].In this paper, we report the thermal conductivity of high-strength PE fiber and
application of the high-strength PE fiber reinforced plastics for conduction-cooled
high-temperature superconducting (HTS) coil.


## 2. Thermal Conductivity of High-Strength Polyethylene Fiber

### 2.1. Thermal Conductivity of Polymer Fiber

The thermal conductivity of solid, electrical insulating materials is introduced
attributable to phonons [12, 13], and the heat in polymers is conducted
in the direction of covalently bonded molecular chains, whereas conduction in
the direction to intermolecular chains bonded by Van der Waals forces is much
less. It is known that thermal conductivities of PE, polyethyleneterephtalate,
and polypropylene toward to the direction of molecular chain increase by the
increasing crystallinity and orientation of crystal [11, 13–17, 21, 22]. In the case of
amorphous polymers, it is also known that thermal conductivities of
polymethylmethacrylate and polystyrene increase by the orientation of molecular
chain [16, 23, 24].The thermal conductivity of solid electrically insulating materials is affected
by the scattering of phonons. The phonon scattering is considered to be
introduced by imperfections in the material. For example, crystal or amorphous
boundary, defects, chemical bridge points, and the ends and entanglements of the
molecular chains can scatter phonons and interfere with the thermal
transmittance in polymer materials. Dependence of thermal conductivity on
molecular weight has been reported about polystyrene film [25].In the case of polymer fibers, the thermal conductivity in fiber direction
depends on the crystallinity, orientation, crystal size, length of molecular
chains, chemical bridge points, and morphologies composed of crystal and
amorphous.For example, thermal conductivity of ramie fiber in fiber direction changes by
the following treatments, drawing in water (water treatment), irradiation withγ-rays (γ-rays treatment), and
vapor-phase-formaldehyde treatments (VP-HCHO treatment). Those treatments induce
the extension, chain scission, and bridging to molecular chains as shown in
Figure 3 [26–28]. The thermal
conductivities of the ramie fibers before and after those treatments are shown
in Figure 4 [26–28].Figure 3
Schematic diagram of molecular chains of cellulose with drawing,γ-rays treatment, and VP-HCHO treatment.Figure 4
Thermal conductivities of ramie fibers with water treatment, g-rays
treatment, and VP-HCHO treatment [26–28].It is reported that the tensile modulus is increased by the increasing of
orientation degree of molecular chains in the amorphous region of ramie fiber by
water treatment [31]. It is also known
that tensile modulus of ramie fiber increases by water treatment [31]. Thermal conductivity of ramie fiber in
the fiber direction increases by water treatment as shown in Figure 4 [26]. In this water treatment, ramie fibers were drawn by the stress
of 17.4 kg/mm2 in the water. The tensile modulus of the ramie
fiber doubles by this water treatment. The increasing of thermal conductivity by
water treatment is inferred to be caused by the extension of molecular chains in
the amorphous region as shown in Figure 3
[26].It is well known that fibers mainly made of cellulose, including ramie and
cottons, undergo main chain scission byγ-rays treatment
[32] as shown in Figure 3. And it is also known that the
crystallinity is not decreased by irradiation with γ-rays
in the case of appropriate dose rate [27,
32]. Thermal conductivity of ramie
fiber in fiber direction decreases by γ-rays treatment as
shown in Figure 4 [27]. It is reported that the decreasing of thermal
conductivity of ramie fiber by γ-rays treatment agrees to
the decreasing of the degree of polymerization (DP) of ramie fibers. In this
case, shown in Figure 4, the irradiation
was carried out with Co-60 γ-rays and the total absorbed
dose was 100 kGy [27]. The DP of
ramie fibers decreases from 1700 to 220 by this γ-rays
treatment. The decreasing of thermal conductivity by
γ-rays treatment is inferred to be caused by molecular
chain scission. That is to say, thermal conductivity of ramie fibers depends on
the length of molecular chain [27].Fibers mainly made of cellulose, including ramie and cottons, are well known for
being bridged with formaldehyde (HCHO) [31, 37, 39–44], for
example, by VP-HCHO treatment [39] as
shown in Figure 3. This technology is
employed for stabilizing the conformity of cellulose fibers and is used
practically in clothing materials such as wash and wear shirts [40, 42–45]. Thermal
conductivity decreases to about 20–25% by VP-HCHO treatments as
shown in Figure 4 [28]. It is reported that the thermal conductivity decreases
by increasing the concentration of bound HCHO [28]. In this case, shown in Figure 4, the concentration of bound HCHO of the VP-HCHO-treated ramie
fiber was 1.6% [28]. The decreasing
of thermal conductivity of ramie fiber by VP-HCHO treatment is inferred to be
caused by scattering of phonon at bridge points combined with HCHO [28].In this way, the thermal conductivity of ramie fibers increases by increasing
orientation of molecular chains and decreases by chain scission or by bridge
points in molecular chains [26–28]. That is to say
that the thermal conductivities of polymer fibers depend on the structures, for
example, orientation, length (molecular weight), and bridge points of molecular
chains.


### 2.2. Thermal Conductivity of High-Strength Polyethylene Fiber

#### 2.2.1. High Thermal-Conducting Polymer Fiber

As above mentioned, high-strength PE fiber has a high thermal conductivity
in fiber direction [18–20]. DF shown in Figure 2 is one of the high-strength
ultra-high-molecular-weight (UHMW) PE fibers made by gel spinning method
[46–51]. In this section, the mechanism of high thermal
conduction of DF is reported.It is well known that the random-oriented crystal region composed of folding
UHMWPE chains changes to highly oriented crystal region composed of extended
chains by gel spinning as shown in Figure5 [29, 46–51]. Therefore, it is considered that heat conduction
of the extended chains in the direction covalent-bonded chain axis in
crystal regions contributes to the high thermal conductivity of DF [18–20].Figure 5
Schematic diagram of molecular chains in UHMW-PE [29].The relationship between the thermal conductivity and the structure of DF is
reported in the following.


#### 2.2.2. Dependence of Thermal Conductivity on Tensile Modulus of
High-Strength Polyethylene Fiber [20]

Thermal conductivities of high-strength UHMW PE fibers (hereinafter
abbreviated to PEFs) made by gel spinning method with different draw ratios
are shown in Figure6 [20]. They have different modulus shown
as follows: A: 15 GPa, B: 51G Pa, C(DF): 85 GPa, and D:
134 GPa. Thermal conductivity increases with increasing tensile
modulus of PEF, and all of them increase with increasing temperature as
shown in Figure 6. The relations
between thermal conductivity and tensile modulus of the PEFs are shown in
Figure 7. Thermal conductivity of
PEFs increases lineally in proportion to tensile modulus.Figure 6
Thermal conductivities of high-strength PE fibers having different
modulus [20].Figure 7
Relationship between the thermal conductivities and tensile module of
high-strength PE fibers.The relationship between the thermal conductivities and tensile modulus of
PEFs was explained by the fiber structure illustrated in the mechanical
serial-parallel model (Takayanagi model), which consists of a
crystalline/amorphous structure as shown in Figure8 [20]. This
mechanical model is composed of the following two parts by parallel
combination. One of them is continuous crystal part composed of extended
molecular chains, and the other is series combination part of crystal and
amorphous. In this mechanical model composed of continuous crystal region
and series combination part composed of crystal and amorphous, thermal
conductivity of the PEF in fiber direction is dominated by that of
continuous crystal region composed of extended molecular chains [20].Figure 8
Schematic diagram showing the structure of high-strength PE fiber by
mechanical model [20].


#### 2.2.3. Radiation Effect on Thermal Conductivity of High-Strength
Polyethylene Fiber byγ-Ray [30]

The contribution to thermal conductivity by the length of the molecular
chains in high-strength PEF is reported in this section. It is known that
polyethylene undergoes main chain scission by irradiation withγ-rays (γ-rays treatment)
in the presence of oxygen [52].Thermal conductivities of PEFs withγ-rays treatments
are shown in Figure 9 [30]. The used PEF was DF. Irradiation
was carried out with Co-60 γ-rays, and the total
absorbed dose was 0.5 MGy; that is hereinafter abbreviated to DF
(γ-rays treatment). The DF without
γ-rays treatment is abbreviated to DF (Blank).
Thermal conductivity of DF decreases to 50% by
γ-rays treatment at every temperature [30].Figure 9
Thermal conductivity of high-strength PE fiber withγ-rays treatment [30].The measured molecular weight of DF (Blank) was
2.0 × 106. It decreased to
2.6 × 104 by 0.5 MGy irradiation.
This result shows the main chain scission of DF by the
γ-rays treatment. On the other hand, the change
of the crystal structure of DF by γ-rays treatment
could not be observed. Therefore, the decrease of thermal conductivity of DF
by γ-rays treatment was explained by the molecular
main chain scission as similar to the case of ramie described in the above
mentioned. This result suggested the contribution of the length of extended
molecular chains due to high molecular weight on the thermal conductivity of
DF [30].


#### 2.2.4. Summary

With aforementioned, high-strength PE fiber has a high thermal conductivity
in fiber direction, and this high thermal conductivity is explained by the
mechanical series-parallel model composed of crystal and amorphous including
continuous crystal region composed of long extended molecular chains [20, 30].


### 2.3. Thermal Conductivity of High-Strength Polyethylene Fiber Reinforced
Plastics [18, 53]

In order to apply the PEFs to the cryogenic use, for example, coil bobbin or
spacer of superconducting coils, thermal conductivities of PEF-reinforced
plastics are important as described in the following sections. In this section,
the PEF used as the reinforcement is DF. Hereinafter, DF-reinforced plastics is
abbreviated to DFRP. The schematic diagram of unidirectional (UD) DFRP is shown
in Figure10.Figure 10
Schematic diagram of UD-DFRP.Thermal conductivities of UD-DFRP in parallel and perpendicular to fiber
direction are shown in Figure11 [18]. Thermal conductivity of DFRP in
parallel to fiber direction shows about medium value between those of DF and
epoxy resin. Dependence of thermal conductivity on volume fraction (Vf) of DF in
UD-DFRP is shown in Figure 12. Thermal
conductivity of UD-DFRP is proportional to Vf of DF as shown in Figure 12 [18]. Therefore, thermal conductivity of DFRP in parallel to fiber
direction is proportional to the cross-sectional ratio of DF oriented in the
conduction direction [18].Figure 11
Thermal conductivities of DF and DFRP [18]. ●: DF in parallel to the fiber direction,
○: DFRP in parallel to the fiber direction, △: DFRP in
perpendicular to the fiber direction, □: Epoxy.Figure 12
Vf dependence of thermal conductivity of UD-DFRP on fiber direction.Thermal conductivity of UD-DFRP in the perpendicular to fiber direction is one
order magnitude smaller than that in the parallel to fiber direction [18].It is known that the thermal conductivity of hybrid FRP including DF can be
expressed by the law of mixtures [53].


## 2.1. Thermal Conductivity of Polymer Fiber

The thermal conductivity of solid, electrical insulating materials is introduced
attributable to phonons [12, 13], and the heat in polymers is conducted
in the direction of covalently bonded molecular chains, whereas conduction in
the direction to intermolecular chains bonded by Van der Waals forces is much
less. It is known that thermal conductivities of PE, polyethyleneterephtalate,
and polypropylene toward to the direction of molecular chain increase by the
increasing crystallinity and orientation of crystal [11, 13–17, 21, 22]. In the case of
amorphous polymers, it is also known that thermal conductivities of
polymethylmethacrylate and polystyrene increase by the orientation of molecular
chain [16, 23, 24].The thermal conductivity of solid electrically insulating materials is affected
by the scattering of phonons. The phonon scattering is considered to be
introduced by imperfections in the material. For example, crystal or amorphous
boundary, defects, chemical bridge points, and the ends and entanglements of the
molecular chains can scatter phonons and interfere with the thermal
transmittance in polymer materials. Dependence of thermal conductivity on
molecular weight has been reported about polystyrene film [25].In the case of polymer fibers, the thermal conductivity in fiber direction
depends on the crystallinity, orientation, crystal size, length of molecular
chains, chemical bridge points, and morphologies composed of crystal and
amorphous.For example, thermal conductivity of ramie fiber in fiber direction changes by
the following treatments, drawing in water (water treatment), irradiation withγ-rays (γ-rays treatment), and
vapor-phase-formaldehyde treatments (VP-HCHO treatment). Those treatments induce
the extension, chain scission, and bridging to molecular chains as shown in
Figure 3 [26–28]. The thermal
conductivities of the ramie fibers before and after those treatments are shown
in Figure 4 [26–28].Figure 3
Schematic diagram of molecular chains of cellulose with drawing,γ-rays treatment, and VP-HCHO treatment.Figure 4
Thermal conductivities of ramie fibers with water treatment, g-rays
treatment, and VP-HCHO treatment [26–28].It is reported that the tensile modulus is increased by the increasing of
orientation degree of molecular chains in the amorphous region of ramie fiber by
water treatment [31]. It is also known
that tensile modulus of ramie fiber increases by water treatment [31]. Thermal conductivity of ramie fiber in
the fiber direction increases by water treatment as shown in Figure 4 [26]. In this water treatment, ramie fibers were drawn by the stress
of 17.4 kg/mm2 in the water. The tensile modulus of the ramie
fiber doubles by this water treatment. The increasing of thermal conductivity by
water treatment is inferred to be caused by the extension of molecular chains in
the amorphous region as shown in Figure 3
[26].It is well known that fibers mainly made of cellulose, including ramie and
cottons, undergo main chain scission byγ-rays treatment
[32] as shown in Figure 3. And it is also known that the
crystallinity is not decreased by irradiation with γ-rays
in the case of appropriate dose rate [27,
32]. Thermal conductivity of ramie
fiber in fiber direction decreases by γ-rays treatment as
shown in Figure 4 [27]. It is reported that the decreasing of thermal
conductivity of ramie fiber by γ-rays treatment agrees to
the decreasing of the degree of polymerization (DP) of ramie fibers. In this
case, shown in Figure 4, the irradiation
was carried out with Co-60 γ-rays and the total absorbed
dose was 100 kGy [27]. The DP of
ramie fibers decreases from 1700 to 220 by this γ-rays
treatment. The decreasing of thermal conductivity by
γ-rays treatment is inferred to be caused by molecular
chain scission. That is to say, thermal conductivity of ramie fibers depends on
the length of molecular chain [27].Fibers mainly made of cellulose, including ramie and cottons, are well known for
being bridged with formaldehyde (HCHO) [31, 37, 39–44], for
example, by VP-HCHO treatment [39] as
shown in Figure 3. This technology is
employed for stabilizing the conformity of cellulose fibers and is used
practically in clothing materials such as wash and wear shirts [40, 42–45]. Thermal
conductivity decreases to about 20–25% by VP-HCHO treatments as
shown in Figure 4 [28]. It is reported that the thermal conductivity decreases
by increasing the concentration of bound HCHO [28]. In this case, shown in Figure 4, the concentration of bound HCHO of the VP-HCHO-treated ramie
fiber was 1.6% [28]. The decreasing
of thermal conductivity of ramie fiber by VP-HCHO treatment is inferred to be
caused by scattering of phonon at bridge points combined with HCHO [28].In this way, the thermal conductivity of ramie fibers increases by increasing
orientation of molecular chains and decreases by chain scission or by bridge
points in molecular chains [26–28]. That is to say
that the thermal conductivities of polymer fibers depend on the structures, for
example, orientation, length (molecular weight), and bridge points of molecular
chains.


## 2.2. Thermal Conductivity of High-Strength Polyethylene Fiber

### 2.2.1. High Thermal-Conducting Polymer Fiber

As above mentioned, high-strength PE fiber has a high thermal conductivity
in fiber direction [18–20]. DF shown in Figure 2 is one of the high-strength
ultra-high-molecular-weight (UHMW) PE fibers made by gel spinning method
[46–51]. In this section, the mechanism of high thermal
conduction of DF is reported.It is well known that the random-oriented crystal region composed of folding
UHMWPE chains changes to highly oriented crystal region composed of extended
chains by gel spinning as shown in Figure5 [29, 46–51]. Therefore, it is considered that heat conduction
of the extended chains in the direction covalent-bonded chain axis in
crystal regions contributes to the high thermal conductivity of DF [18–20].Figure 5
Schematic diagram of molecular chains in UHMW-PE [29].The relationship between the thermal conductivity and the structure of DF is
reported in the following.


### 2.2.2. Dependence of Thermal Conductivity on Tensile Modulus of
High-Strength Polyethylene Fiber [20]

Thermal conductivities of high-strength UHMW PE fibers (hereinafter
abbreviated to PEFs) made by gel spinning method with different draw ratios
are shown in Figure6 [20]. They have different modulus shown
as follows: A: 15 GPa, B: 51G Pa, C(DF): 85 GPa, and D:
134 GPa. Thermal conductivity increases with increasing tensile
modulus of PEF, and all of them increase with increasing temperature as
shown in Figure 6. The relations
between thermal conductivity and tensile modulus of the PEFs are shown in
Figure 7. Thermal conductivity of
PEFs increases lineally in proportion to tensile modulus.Figure 6
Thermal conductivities of high-strength PE fibers having different
modulus [20].Figure 7
Relationship between the thermal conductivities and tensile module of
high-strength PE fibers.The relationship between the thermal conductivities and tensile modulus of
PEFs was explained by the fiber structure illustrated in the mechanical
serial-parallel model (Takayanagi model), which consists of a
crystalline/amorphous structure as shown in Figure8 [20]. This
mechanical model is composed of the following two parts by parallel
combination. One of them is continuous crystal part composed of extended
molecular chains, and the other is series combination part of crystal and
amorphous. In this mechanical model composed of continuous crystal region
and series combination part composed of crystal and amorphous, thermal
conductivity of the PEF in fiber direction is dominated by that of
continuous crystal region composed of extended molecular chains [20].Figure 8
Schematic diagram showing the structure of high-strength PE fiber by
mechanical model [20].


### 2.2.3. Radiation Effect on Thermal Conductivity of High-Strength
Polyethylene Fiber byγ-Ray [30]

The contribution to thermal conductivity by the length of the molecular
chains in high-strength PEF is reported in this section. It is known that
polyethylene undergoes main chain scission by irradiation withγ-rays (γ-rays treatment)
in the presence of oxygen [52].Thermal conductivities of PEFs withγ-rays treatments
are shown in Figure 9 [30]. The used PEF was DF. Irradiation
was carried out with Co-60 γ-rays, and the total
absorbed dose was 0.5 MGy; that is hereinafter abbreviated to DF
(γ-rays treatment). The DF without
γ-rays treatment is abbreviated to DF (Blank).
Thermal conductivity of DF decreases to 50% by
γ-rays treatment at every temperature [30].Figure 9
Thermal conductivity of high-strength PE fiber withγ-rays treatment [30].The measured molecular weight of DF (Blank) was
2.0 × 106. It decreased to
2.6 × 104 by 0.5 MGy irradiation.
This result shows the main chain scission of DF by the
γ-rays treatment. On the other hand, the change
of the crystal structure of DF by γ-rays treatment
could not be observed. Therefore, the decrease of thermal conductivity of DF
by γ-rays treatment was explained by the molecular
main chain scission as similar to the case of ramie described in the above
mentioned. This result suggested the contribution of the length of extended
molecular chains due to high molecular weight on the thermal conductivity of
DF [30].


### 2.2.4. Summary

With aforementioned, high-strength PE fiber has a high thermal conductivity
in fiber direction, and this high thermal conductivity is explained by the
mechanical series-parallel model composed of crystal and amorphous including
continuous crystal region composed of long extended molecular chains [20, 30].


## 2.2.1. High Thermal-Conducting Polymer Fiber

As above mentioned, high-strength PE fiber has a high thermal conductivity
in fiber direction [18–20]. DF shown in Figure 2 is one of the high-strength
ultra-high-molecular-weight (UHMW) PE fibers made by gel spinning method
[46–51]. In this section, the mechanism of high thermal
conduction of DF is reported.It is well known that the random-oriented crystal region composed of folding
UHMWPE chains changes to highly oriented crystal region composed of extended
chains by gel spinning as shown in Figure5 [29, 46–51]. Therefore, it is considered that heat conduction
of the extended chains in the direction covalent-bonded chain axis in
crystal regions contributes to the high thermal conductivity of DF [18–20].Figure 5
Schematic diagram of molecular chains in UHMW-PE [29].The relationship between the thermal conductivity and the structure of DF is
reported in the following.


## 2.2.2. Dependence of Thermal Conductivity on Tensile Modulus of
High-Strength Polyethylene Fiber [20]

Thermal conductivities of high-strength UHMW PE fibers (hereinafter
abbreviated to PEFs) made by gel spinning method with different draw ratios
are shown in Figure6 [20]. They have different modulus shown
as follows: A: 15 GPa, B: 51G Pa, C(DF): 85 GPa, and D:
134 GPa. Thermal conductivity increases with increasing tensile
modulus of PEF, and all of them increase with increasing temperature as
shown in Figure 6. The relations
between thermal conductivity and tensile modulus of the PEFs are shown in
Figure 7. Thermal conductivity of
PEFs increases lineally in proportion to tensile modulus.Figure 6
Thermal conductivities of high-strength PE fibers having different
modulus [20].Figure 7
Relationship between the thermal conductivities and tensile module of
high-strength PE fibers.The relationship between the thermal conductivities and tensile modulus of
PEFs was explained by the fiber structure illustrated in the mechanical
serial-parallel model (Takayanagi model), which consists of a
crystalline/amorphous structure as shown in Figure8 [20]. This
mechanical model is composed of the following two parts by parallel
combination. One of them is continuous crystal part composed of extended
molecular chains, and the other is series combination part of crystal and
amorphous. In this mechanical model composed of continuous crystal region
and series combination part composed of crystal and amorphous, thermal
conductivity of the PEF in fiber direction is dominated by that of
continuous crystal region composed of extended molecular chains [20].Figure 8
Schematic diagram showing the structure of high-strength PE fiber by
mechanical model [20].


## 2.2.3. Radiation Effect on Thermal Conductivity of High-Strength
Polyethylene Fiber byγ-Ray [30]

The contribution to thermal conductivity by the length of the molecular
chains in high-strength PEF is reported in this section. It is known that
polyethylene undergoes main chain scission by irradiation withγ-rays (γ-rays treatment)
in the presence of oxygen [52].Thermal conductivities of PEFs withγ-rays treatments
are shown in Figure 9 [30]. The used PEF was DF. Irradiation
was carried out with Co-60 γ-rays, and the total
absorbed dose was 0.5 MGy; that is hereinafter abbreviated to DF
(γ-rays treatment). The DF without
γ-rays treatment is abbreviated to DF (Blank).
Thermal conductivity of DF decreases to 50% by
γ-rays treatment at every temperature [30].Figure 9
Thermal conductivity of high-strength PE fiber withγ-rays treatment [30].The measured molecular weight of DF (Blank) was
2.0 × 106. It decreased to
2.6 × 104 by 0.5 MGy irradiation.
This result shows the main chain scission of DF by the
γ-rays treatment. On the other hand, the change
of the crystal structure of DF by γ-rays treatment
could not be observed. Therefore, the decrease of thermal conductivity of DF
by γ-rays treatment was explained by the molecular
main chain scission as similar to the case of ramie described in the above
mentioned. This result suggested the contribution of the length of extended
molecular chains due to high molecular weight on the thermal conductivity of
DF [30].


## 2.2.4. Summary

With aforementioned, high-strength PE fiber has a high thermal conductivity
in fiber direction, and this high thermal conductivity is explained by the
mechanical series-parallel model composed of crystal and amorphous including
continuous crystal region composed of long extended molecular chains [20, 30].


## 2.3. Thermal Conductivity of High-Strength Polyethylene Fiber Reinforced
Plastics [18, 53]

In order to apply the PEFs to the cryogenic use, for example, coil bobbin or
spacer of superconducting coils, thermal conductivities of PEF-reinforced
plastics are important as described in the following sections. In this section,
the PEF used as the reinforcement is DF. Hereinafter, DF-reinforced plastics is
abbreviated to DFRP. The schematic diagram of unidirectional (UD) DFRP is shown
in Figure10.Figure 10
Schematic diagram of UD-DFRP.Thermal conductivities of UD-DFRP in parallel and perpendicular to fiber
direction are shown in Figure11 [18]. Thermal conductivity of DFRP in
parallel to fiber direction shows about medium value between those of DF and
epoxy resin. Dependence of thermal conductivity on volume fraction (Vf) of DF in
UD-DFRP is shown in Figure 12. Thermal
conductivity of UD-DFRP is proportional to Vf of DF as shown in Figure 12 [18]. Therefore, thermal conductivity of DFRP in parallel to fiber
direction is proportional to the cross-sectional ratio of DF oriented in the
conduction direction [18].Figure 11
Thermal conductivities of DF and DFRP [18]. ●: DF in parallel to the fiber direction,
○: DFRP in parallel to the fiber direction, △: DFRP in
perpendicular to the fiber direction, □: Epoxy.Figure 12
Vf dependence of thermal conductivity of UD-DFRP on fiber direction.Thermal conductivity of UD-DFRP in the perpendicular to fiber direction is one
order magnitude smaller than that in the parallel to fiber direction [18].It is known that the thermal conductivity of hybrid FRP including DF can be
expressed by the law of mixtures [53].


## 3. Application of High-Strength Polyethylene-Fiber-Reinforced Plastics for
Conduction-Cooled High-Temperature Superconducting Coil

### 3.1. Instability of HTS Coil by Local Temperature Rise of HTS Tape

When the cooling power of a refrigerator exceeds the loss in HTS coil and
conduction heat along the current leads, steady state operation of
conduction-cooled coil is possible [54].
However, if a cooling condition of the HTS tape in the coil is partly
insufficient, a local hot spot occurs in the conduction-cooled coil during
operation of the coil [55]. The local
temperature rise of the tape is one of instabilities of the conduction-cooled
HTS coils. To prevent the HTS tape from locally raising a temperature, it is
necessary to drain heat from HTS tape to electrical insulation materials in the
coil effectively. For effective heat drain from HTS tape to electrical
insulation materials, high-thermal-conduction electrical insulator is necessary
for coil bobbin or spacer [6].Usually, glass-fiber-(GF-) reinforced plastics (GFRP) were used as electrical
insulation materials for HTS coil, for example, coil bobbin or spacer. However,
GFRP is a thermal insulator. Therefore, heat drain from HTS tape to GFRP is
insufficient. On the other hand, aluminum nitride (AlN) is known as an
electrical insulator and a thermal conductor. However, the AlN is hard and
brittle, and, hence, difficult for coil makers and users to process the
electrical insulation parts in the coil, for example, spacers [6].In the following sections, effect of heat drain of PEF-reinforced plastics for
electrical insulation material of HTS coils is reported. DFRP reinforced plastic
is used as a PEF-reinforced plastic in the following sections.


### 3.2. Important Physical Properties of High-Strength
Polyethylene-Fiber-Reinforced Plastics for HTS Coil

Important physical properties of DFRP except for thermal conductivity are
reported in this section in order to report the HTS coils in the following
sections. Frictional coefficients, surface spark voltages, and thermal
contraction by cooling of DFRP are shown in Figures13,  14 and 15. DFRP has a lower
frictional coefficient and higher spark voltage than those of GFRP [33, 34]. DFRP has a negative thermal expansion coefficient in fiber
direction [35, 36]. Therefore, DFRP expands in fiber direction by cooling
down from room temperature to liquid nitrogen temperature as shown in Figure
15 [35, 36].Figure 13
Frictional coefficients of DFRPs and GFRPs [33].Figure 14
Surface spark voltage in Liq. He [34].Figure 15
Thermal strain of UD-FRP in fiber direction by cooling down [35, 36].


### 3.3. Heat Drain Effects from HTS Tapes to High-Strength
Polyethylene-Fiber-Reinforced Plastics [38]

In this section, the heat drain effect of the DFRP with a steady-state current to
the HTS tape is reported. The schematic illustration of experimental arrangement
is shown in Figure16. Bi-2223 is used
as a HTS tape in this section. DFRP, GFRP, and AlN were used as structural
materials in Figure 16. Volume fraction
of fiber of DFRP and GFRP were 50% (hereinafter abbreviated to DFRP-50 and
GFRP-50). The structural materials were used as clamping materials.
Specifications of the clamping materials and the Bi tape are listed in Table
1. The set of the clamping
materials, the clamped tape, and the weight is on a cold head of a refrigerator
and is cooled down to 77 K. A steady current of 60 A, which equaled to
the critical current of the Bi tape, was applied to the tape, and the voltage
between the tapes was observed [38].Table 1
Specifications of Bi-2223 tape and clamping materials.
Bi2223 tape
Clamping materials
Width (mm)
4.1
9
Thickness (mm)
0.21
9
Length (mm)
150
124
Ag ratio
2.2
Ic at 77 K
60 A
Material
Ag, Bi-2223
DFRP, GFRP, AlNFigure 16
The schematic illustration of experimental arrangement [37].The voltages of the tape clamped by GFRP-50, DFRP-50, and AIN are shown in Figure17. As shown in Figure 18, when the clamping material is the AlN,
the voltage keeps relatively low, that is to say, the temperature rise of the
tape is very slow [38]. On the contrary,
the voltage of the GFRP-50 took off within a short time from the current start,
and the temperature rise of the tape was fast [38]. DFRP-50 shows the middle behavior between GFRP-50 and AlN. The
voltage rise is caused by temperature rise induced by joule heating. Thermal
conductivity of DFRP-50 is higher than that of GFRP-50 and lower than that of
AlN. Therefore, the difference of the data in the GFRP-50, DFRP-50, and AlN is
due to thermal conductivity of the clamping materials and heat transfer from the
Bi tape to the clamping materials [38].
It is known that the voltage rise becomes slower by increasing content ratio of
DF and contact stress to Bi tape in the case of DFRP [38]. It is considered that the negative thermal expansion
of DFRP contributes to increasing contact stress in the HTS coil. The stability
of HTS coil is reported in the next section.Figure 17
The voltages of the tap clamped by GFRP-50, DFRP-50, and AIN [38].Figure 18
Schematic illustration of HTS coil [8].


### 3.4. Evaluating Cooling Performance of High-Strength
Polyethylene-Fiber-Reinforced Plastics in Conduction-Cooled HTS Coils [8]

In this section, thermal stabilities of HTS coils composed of DFRP, GFRP, and AlN
bobbins shown in Figure18 are reported.
DFRP and GFRP bobbins were pipes shown in Figure 19, and those were made by filament winding (FW) method.
The specimens of coil and superconductor are shown in Table 2. FW angles of DFRP pipes were 30, 45,
and 60 deg. Those are denoted as DFRP60, DFRP30, and DFRP45,
respectively. If the angle is larger than 45 degrees, the bobbin expands
radially when cooled [36]. When is
smaller than 45 degrees, on the other hand, the bobbin contracts when cooled
[36]. FW angle of GFRP was 60deg. AlN
and GFRP bobbins do not expand when cooled.Table 2
Specifications of coil, coil bobbins, and Bi-2223 tapes in the HTS sample
coils shown in Figure19.
Coil and bobbin
Height (mm)
50
Inner diameter of bobbin (mm)
40
Outer diameter of bobbin (mm)
55
Turn/layer
4 turns and single layer
Winding tension
10 N at room temperature
Conductor
Superconductor
Bi-2223
Sheath
Silver alloy
Width (mm)
3.3
Thickness (mm)
0.7
Silver ratio
2.2
Ic at 77 K
86AFigure 19
Bobbin shape and fiber angle in bobbin [8].The time profiles of voltage tape signals of those coils are shown in Figure20. Applied current to the HTS coil
corresponds to 86A (Ic). The voltage profile of the AlN coil is almost same as
that of the DFRP60 coil even though the thermal conductivity of AlN is more than
twice of DFRP60 [56]. The reason is the
heat transfer from the tape to the bobbin. The DFRP60 bobbin expanded, and,
hence, its heat transfer became better [57]. The AlN bobbin, on the other hand, contracted, and its heat
transfer became worse. The thermal conductivity of GFRP is lower than that of
the other four materials used in the experiment, and the heat transfer of the
GFRP coil is bad because the material contracts when cooled. This is why the
measured thermal stability was worst for the coil wound on the GFRP bobbin.
Therefore, the thermal stability of the coils depended not only on the thermal
conductivity of the bobbin but also on the heat transfer from the tape to the
bobbin. Thus, DFRP60 would be a good heat sink material for the bobbin of a
conduction-cooled coil [8].Figure 20
The time profiles of voltage tap signals of HTS coils wound on DFRP,
GFRP, and AlN bobbins [8].


## 3.1. Instability of HTS Coil by Local Temperature Rise of HTS Tape

When the cooling power of a refrigerator exceeds the loss in HTS coil and
conduction heat along the current leads, steady state operation of
conduction-cooled coil is possible [54].
However, if a cooling condition of the HTS tape in the coil is partly
insufficient, a local hot spot occurs in the conduction-cooled coil during
operation of the coil [55]. The local
temperature rise of the tape is one of instabilities of the conduction-cooled
HTS coils. To prevent the HTS tape from locally raising a temperature, it is
necessary to drain heat from HTS tape to electrical insulation materials in the
coil effectively. For effective heat drain from HTS tape to electrical
insulation materials, high-thermal-conduction electrical insulator is necessary
for coil bobbin or spacer [6].Usually, glass-fiber-(GF-) reinforced plastics (GFRP) were used as electrical
insulation materials for HTS coil, for example, coil bobbin or spacer. However,
GFRP is a thermal insulator. Therefore, heat drain from HTS tape to GFRP is
insufficient. On the other hand, aluminum nitride (AlN) is known as an
electrical insulator and a thermal conductor. However, the AlN is hard and
brittle, and, hence, difficult for coil makers and users to process the
electrical insulation parts in the coil, for example, spacers [6].In the following sections, effect of heat drain of PEF-reinforced plastics for
electrical insulation material of HTS coils is reported. DFRP reinforced plastic
is used as a PEF-reinforced plastic in the following sections.


## 3.2. Important Physical Properties of High-Strength
Polyethylene-Fiber-Reinforced Plastics for HTS Coil

Important physical properties of DFRP except for thermal conductivity are
reported in this section in order to report the HTS coils in the following
sections. Frictional coefficients, surface spark voltages, and thermal
contraction by cooling of DFRP are shown in Figures13,  14 and 15. DFRP has a lower
frictional coefficient and higher spark voltage than those of GFRP [33, 34]. DFRP has a negative thermal expansion coefficient in fiber
direction [35, 36]. Therefore, DFRP expands in fiber direction by cooling
down from room temperature to liquid nitrogen temperature as shown in Figure
15 [35, 36].Figure 13
Frictional coefficients of DFRPs and GFRPs [33].Figure 14
Surface spark voltage in Liq. He [34].Figure 15
Thermal strain of UD-FRP in fiber direction by cooling down [35, 36].


## 3.3. Heat Drain Effects from HTS Tapes to High-Strength
Polyethylene-Fiber-Reinforced Plastics [38]

In this section, the heat drain effect of the DFRP with a steady-state current to
the HTS tape is reported. The schematic illustration of experimental arrangement
is shown in Figure16. Bi-2223 is used
as a HTS tape in this section. DFRP, GFRP, and AlN were used as structural
materials in Figure 16. Volume fraction
of fiber of DFRP and GFRP were 50% (hereinafter abbreviated to DFRP-50 and
GFRP-50). The structural materials were used as clamping materials.
Specifications of the clamping materials and the Bi tape are listed in Table
1. The set of the clamping
materials, the clamped tape, and the weight is on a cold head of a refrigerator
and is cooled down to 77 K. A steady current of 60 A, which equaled to
the critical current of the Bi tape, was applied to the tape, and the voltage
between the tapes was observed [38].Table 1
Specifications of Bi-2223 tape and clamping materials.
Bi2223 tape
Clamping materials
Width (mm)
4.1
9
Thickness (mm)
0.21
9
Length (mm)
150
124
Ag ratio
2.2
Ic at 77 K
60 A
Material
Ag, Bi-2223
DFRP, GFRP, AlNFigure 16
The schematic illustration of experimental arrangement [37].The voltages of the tape clamped by GFRP-50, DFRP-50, and AIN are shown in Figure17. As shown in Figure 18, when the clamping material is the AlN,
the voltage keeps relatively low, that is to say, the temperature rise of the
tape is very slow [38]. On the contrary,
the voltage of the GFRP-50 took off within a short time from the current start,
and the temperature rise of the tape was fast [38]. DFRP-50 shows the middle behavior between GFRP-50 and AlN. The
voltage rise is caused by temperature rise induced by joule heating. Thermal
conductivity of DFRP-50 is higher than that of GFRP-50 and lower than that of
AlN. Therefore, the difference of the data in the GFRP-50, DFRP-50, and AlN is
due to thermal conductivity of the clamping materials and heat transfer from the
Bi tape to the clamping materials [38].
It is known that the voltage rise becomes slower by increasing content ratio of
DF and contact stress to Bi tape in the case of DFRP [38]. It is considered that the negative thermal expansion
of DFRP contributes to increasing contact stress in the HTS coil. The stability
of HTS coil is reported in the next section.Figure 17
The voltages of the tap clamped by GFRP-50, DFRP-50, and AIN [38].Figure 18
Schematic illustration of HTS coil [8].


## 3.4. Evaluating Cooling Performance of High-Strength
Polyethylene-Fiber-Reinforced Plastics in Conduction-Cooled HTS Coils [8]

In this section, thermal stabilities of HTS coils composed of DFRP, GFRP, and AlN
bobbins shown in Figure18 are reported.
DFRP and GFRP bobbins were pipes shown in Figure 19, and those were made by filament winding (FW) method.
The specimens of coil and superconductor are shown in Table 2. FW angles of DFRP pipes were 30, 45,
and 60 deg. Those are denoted as DFRP60, DFRP30, and DFRP45,
respectively. If the angle is larger than 45 degrees, the bobbin expands
radially when cooled [36]. When is
smaller than 45 degrees, on the other hand, the bobbin contracts when cooled
[36]. FW angle of GFRP was 60deg. AlN
and GFRP bobbins do not expand when cooled.Table 2
Specifications of coil, coil bobbins, and Bi-2223 tapes in the HTS sample
coils shown in Figure19.
Coil and bobbin
Height (mm)
50
Inner diameter of bobbin (mm)
40
Outer diameter of bobbin (mm)
55
Turn/layer
4 turns and single layer
Winding tension
10 N at room temperature
Conductor
Superconductor
Bi-2223
Sheath
Silver alloy
Width (mm)
3.3
Thickness (mm)
0.7
Silver ratio
2.2
Ic at 77 K
86AFigure 19
Bobbin shape and fiber angle in bobbin [8].The time profiles of voltage tape signals of those coils are shown in Figure20. Applied current to the HTS coil
corresponds to 86A (Ic). The voltage profile of the AlN coil is almost same as
that of the DFRP60 coil even though the thermal conductivity of AlN is more than
twice of DFRP60 [56]. The reason is the
heat transfer from the tape to the bobbin. The DFRP60 bobbin expanded, and,
hence, its heat transfer became better [57]. The AlN bobbin, on the other hand, contracted, and its heat
transfer became worse. The thermal conductivity of GFRP is lower than that of
the other four materials used in the experiment, and the heat transfer of the
GFRP coil is bad because the material contracts when cooled. This is why the
measured thermal stability was worst for the coil wound on the GFRP bobbin.
Therefore, the thermal stability of the coils depended not only on the thermal
conductivity of the bobbin but also on the heat transfer from the tape to the
bobbin. Thus, DFRP60 would be a good heat sink material for the bobbin of a
conduction-cooled coil [8].Figure 20
The time profiles of voltage tap signals of HTS coils wound on DFRP,
GFRP, and AlN bobbins [8].



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*Source: 718761-2011-10-05.xml*