Radiation Effect on the Thermal Conductivity andDiffusivity of Ramie Fibers in a Range of Low
Temperatures by ␥ Rays
Atsuhiko Yamanaka,1 Yoshinobu Izumi,2 Takaya Terada,2 Kimiko Ema,2 Masayuki Tsutsumi,1Muneatsu Nakamura,1 Takeshi Oohazama,1 Tooru Kitagawa,1 Hiroyuki Fujishiro,3 Shunzo Abe,1
Shigehiro Nishijima2
1

Research Center, Toyobo Company, Limited, 2-1-1, Katata, Ohtsu, Shiga 520-0292, Japan
Department of Nuclear Engineering, Graduate School of Engineering, Osaka University, Yamadaoka 2-1, Suita, Osaka
565-0871, Japan3
Department of Materials Science and Technology, Faculty of Engineering, Iwate University, Ueda 4-3-5, Morioka 0208551, Japan
2

Received 30 June 2005; accepted 3 October 2005
DOI 10.1002/app.23838
Published online in Wiley InterScience (www.interscience.wiley.com).
ABSTRACT: To understand the inﬂuence on the thermal
conductivity by the length of the molecular chain in thepolymer ﬁber, the thermal conductivity and thermal diffusivity of ramie ﬁbers and those irradiated by ␥ rays, which
induced molecular chain scission of cellulose, were investigated in a range of low temperatures. The degrees of polymerization, crystallinities, and orientation angles of ramieﬁbers and those irradiated by ␥ rays (␥-ray treatment) were
measured by the solution viscosity method, solid-state
NMR, and X-ray diffraction. Only the degree of polymerization decreased with the ␥-ray treatment, and the crystallinities and orientation angles were almost independent of the
␥-ray treatment. The thermal conductivities of the ramieﬁbers with and without ␥-ray treatments decreased withdecreasing temperature. The thermal diffusivities of theramie ﬁbers and those irradiated by ␥ rays were almost
constant from 250 to 100 K, increased slightly with thetemperature decreasing from 100 to 50 K, and increased
rapidly with the temperature decreasing below 50 K. The
thermal conductivity and thermal diffusivity of the ramieﬁbers decreased with the ␥-ray treatment. The mean freepath of the phonon in the ramie ﬁbers was reduced by the
␥-ray treatment. This decrease of the thermal diffusivity andthermal conductivity was explained by the reduction of themean free path of the phonon by molecular chain scission
with ␥ rays. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100:

INTRODUCTION

tial to enable the formation of technologies for designing polymeric materials that possess the required thermal conductivity.
From previous studies of polymeric materials, it iswell known that the thermal conductivity of amorphous polymers is smaller than that of metals andsemiconductors.8,9 Therefore, these have principally
been used as heat insulators. However, other reports
have shown that polymeric crystals possess a highthermal conductivity in the direction in which themolecular chains are covalently bonded, polyethylene
crystals being an example.10 –17 The thermal conductivity of electrical insulators is considered to be attributable to phonons,10,12 and the heat in polymers is
conducted in the direction of covalently bonded molecular chains, whereas conduction in the direction tointermolecular chains bonded by van der Waals forces
is much less. Therefore, the thermal conductivity depends on the crystallization, orientation, crystal size,and defects in the polymer crystal material. Thus,
high-crystallization and high-orientation polymers exhibit high thermal conductivity.11–17 For example,

Thermal conductivity is an important property in applications of polymeric materials, such as a cool/warm sensation for clothing ﬁber or wood products
and the thermal insulation of plastics, including styroforms.1– 4 With the recent development of superconducting and electronic engineering technologies, thethermal conductivity of structural and insulating materials used as composites in cryogenic and heat-releasing materials in electrical equipment has become
more important. Furthermore, the desired features
vary, depending on the application, from insulation
for use in cryostats5 to high thermal conductivity foruse in superconducting coils6 and electronic engineering.7 The investigation of the factors that affect thethermal conductivity of polymeric materials is essenCorrespondence to: A. Yamanaka (Atsuhiko_Yamanaka@
kt.toyobo.co.jp).
Journal of Applied Polymer Science, Vol. 100, 5007–5018 (2006)© 2006 Wiley Periodicals, Inc.

5007–5018, 2006

Key words: chain; ﬁbers; radiation; thermal properties

5008

YAMANAKA ET AL.

highly crystallized polymeric materials, including
high-strength polyethylene ﬁber11,17–19 and highstrength poly(para-phenylenebenzobisoxazole) ﬁber,18
are known to possess high thermal conductivity similar to that of metals. The thermal conductivity ofpolymers, therefore, ranges from high to low, depending on the crystal structure or morphology.
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 on the surface of the material,
the grain boundaries, or intracrystal or interphonon
dispersion in the material.20 Therefore, in polymers,
the crystal or amorphous boundary, defects, ends, andentanglements of the molecular chains can scatterphonons and interfere with the thermal transmittance.
Therefore, in the case of the thermal conduction ofpolymer ﬁbers in the ﬁber direction, the mean freepath of phonons is inﬂuenced not only by the crystallization or orientation but also by the length of molecular chains and the bridge structure. The changes in
the mean free path of phonons result in changes in thethermal conductivity. In this report, the dependence ofthe thermal conductivity on the length of the molecular chain in the polymer ﬁbers is described.
It is well known that ﬁbers mainly made of cellulose, including ramie and cottons, undergo main-chain
scission by irradiation with ␥ rays.21 It is also known
that the crystallinity is not reduced by irradiation with␥ rays in the case of an appropriate dose rate.21 In thisarticle, we report the changes in the thermal conductivity and thermal diffusivity of ramie ﬁbers by chain
scission with the radiation of ␥ rays.
EXPERIMENTAL
SampleIn this work, the thermal conductivity and diffusivityof ramie ﬁbers and those irradiated with ␥ rays (␥-ray
treatment) were measured in a range of low temperatures. The sample preparations are described in thefollowing.
Ramie fibers
The ramie ﬁber samples used in this work were madein China. The ramie ﬁbers were scoured and bleached.
The density and ﬁneness of the ramie ﬁbers were 1.54
g/cm3 and 4.3 dtex, respectively.
Irradiation with ␥ rays
The purpose of this work was the investigation of therelation between the thermal conductivity and lengthof the molecular chain. For this purpose, ramie ﬁbers
made of short molecular chains were prepared withchain scission in the ramie ﬁbers by irradiation with ␥
rays. Irradiation was carried out with Co-60 ␥ rays at
the Institute of Scientiﬁc and Industrial Research (Sanken) at Osaka University at the ambient temperatureand in air. The absorbed dose rate and irradiation time
were 0.5 kGy/h and 2 h, 1.0 kGy/h and 2 h, and 16.7
kGy/h and 6 h. The total absorbed doses were 1, 2,
and 100 kGy, respectively. These are abbreviated toramie (1 kGy), ramie (2 kGy), and ramie (100 kGy),
respectively. The densities of the ramie ﬁbers with␥-ray treatments were 1.54 g/cm3. Those densities
were measured by a pycnometer after drying at 383 K
for 8 h.
Characterization
The lengths of the molecular chains of ramie ﬁbers
with ␥-ray treatments were measured by the degree ofpolymerization (DP). The DPs of ramie ﬁbers with the
␥-ray treatment for chain scission were measured by
the solution viscosity method. The thermal conductivity and diffusivity depended on not only the length ofthe molecular chain, which was expected to inﬂuence
the mean free path of the phonon, but also the changes
in the crystallinity and orientation angle by the ␥-ray
treatment.11–17 To clarify the changes in the ramieﬁbers, the crystallinities were measured by solid-state,high-resolution NMR, and the orientation angles were
measured by X-ray diffraction. Those measurements
are described in the following.
DP
DPs of the ramie ﬁbers with and without the ␥-ray
treatment were measured by the viscosity methodwith a copper ethylene diamine (CED) solution, as
shown in the following.22,23 Copper hydroxide (II) was
dissolved in a 4.5N ethylene diamine aqueous solution
at a concentration of 55 g/500 mL. A CED solution
was prepared via the stirring of this solution for 2 h atroom temperature. The ramie ﬁbers with and without
␥-ray treatments were dissolved in the CED solution
at a concentration of 0.008 g/25 mL, and those solutions were stirred for 30 min at room temperature. The
relative viscosities (t/t0) at 293 K of the sample solutions were measured with Ubbelohde viscometers in athermostat. The DPs of the ramie ﬁbers with andwithout the ␥-ray treatment were estimated from themeasured viscosities. The parameters t and t0 are deﬁned as the dropping times of the CED solution withand without the dissolution of ramie ﬁbers, respectively. The DPs of the ramie ﬁbers were estimated by
t/t0.
Crystallinity
The crystal and amorphous parts have different chemical shifts of the C4 and C6 carbon peaks in the solid-

DIFFUSIVITY OF RAMIE FIBERS

5009

Figure 1 Schematic diagram of the thermal conductivity and diffusivity measurement system.

state 13C-NMR spectrum of cellulose (e.g., ramie).24 –26
Therefore, it is possible to obtain the ratio of crystal
and amorphous parts by peak separation in the NMR
spectrum. It is also possible to study the molecularmotions of the crystal and amorphous parts by the
analysis of the relaxation time of the crystal and amorphous peaks in the NMR spectrum, respectively.27,28 It
is also known that the chemical shifts of cellulose insolid-state 13C-NMR spectra are different through thedifference of the crystal structure (e.g., celluloses I and
II).24,25,29,30 The relations between the chemical shifts
and torsion angles of the molecular chain in cellulose
crystal have been reported.26 The changes in the crystal structures and crystallinities of cellulose ﬁbers bymercerization or a liquid ammonia treatment werestudied by solid-state NMR.31,32 In this work, thechanges in the crystal structure and crystallinity by the
␥-ray treatment were investigated with solid-state
NMR. The crystallinities were estimated by the peakseparation of the C4 carbon.
Solid-state NMR measurements were carried out on
Bruker Avance 300 (13C, 75.5 MHz) (Rheinstetten, Germany). NMR spectra were measured by the crosspolarization (CP), high-power proton decoupling,
magic-angle-spinning (MAS) method. The pulse
width was 4 ␮s, and the MAS rate was 4.5 kHz.
Orientation angle
The orientation angle of the crystalline phase to theﬁber axis was estimated by X-ray diffraction. The samples were prepared in the form of a bundle of about 30

ﬁlaments in parallel, and they were ﬁxed at both ends.
A Rigaku RU-200 (40 kV and 100 mA) (Akishima,
Tokyo, Japan) was used with X-ray diffraction on
Ni-ﬁltered Cu K␣ (␭ ⫽ 0.1548 nm). The intensity distribution of the (002) diffraction spot was used for
estimating the orientation angles.

Measurements
In this work, the thermal conductivities and thermal
diffusivities in the ﬁber direction of the ramie ﬁbers
prepared as shown in the previous section were measured. The tensile modulus of those ramie ﬁbers withand without the ␥-ray treatment were measured toinvestigate the contribution of the sound velocity to
the thermal conductivity and diffusivity. The measurements of the thermal conductivity, thermal diffusivity, and tensile modulus are described in the following.

Thermal conductivity
The thermal conductivity was measured by asteady-state heat ﬂow method.18,33 The measurements of the thermal conductivity were carried out
on an automated measuring system with a thermal
controller of a Gifford–MacMahon (GM) cycle helium refrigerator (Sumitomo Heavy Industries, Shinagawa, Tokyo, Japan) as a cryostat.33 A schematic
diagram of the thermal conductivity measurement
system is shown in Figure 1.

5010

YAMANAKA ET AL.

Figure 2 Schematic diagram of the sample space in the thermal conductivity and diffusivity measurement system with aclosed-cycle helium refrigerator.

The ﬁber samples were stored in a desiccator for
more than 3 weeks. The ﬁber samples were preparedby the bundling f about 6000 monoﬁlaments with alength of 25 mm. Both ends of the ﬁber bundle were
ﬁxed with the adhesive Stycast GT (Emerson & Cuming, Co., Atsugi, Kanagawa, Japan) for uniform cooling and heating among the ﬁlaments. One end of thebundle was attached to the cold stage of a GM refrigerator via mechanical pressing with indium metal andthe adhesive Stycast GT. A small resistance heater (1k⍀) was attached to the other end of the bundle with
GE7031 varnish (Nilaco, Co., Chuo-ku, Tokyo, Japan).
The intermediate positions at which thermocouples
were contacted were bound by ﬁne (0.1 mm) Cu wireto keep the temperature uniform in the perpendicular
direction of the ﬁbers. The Cu wire and ramie Au (0.07
atom % Fe)– chromel thermocouples were used asthermometers and were attached by GE7031 varnish.
The sample space was evacuated below 10⫺3 Pa by anoil diffusion pump for heat insulation. A schematic
diagram of the sample space in the thermal conductivity measurement system is shown in Figure 2.
The automated measuring system of the thermal
conductivity was operated from 10 to 150 K. The measurements were started after the sample space was
kept in a high vacuum below 10⫺3 Pa for 24 h to dry
up the sample. The thermal conductivity was estimated as follows: ␬ (mW/cmK) ⫽ (Q/⌬T)(L/S),
where ␬ is the thermal conductivity, Q is the heat ﬂow
per second, ⌬T is the temperature difference between
thermometers, L is the distance between the thermometers, and S is the cross section of the bundle. The

details of the determination of the thermal conductivity are described elsewhere.18,19
Thermal diffusivity
The thermal diffusivity was measured by a nonsteady-state heating method.18,33 The measurementsof the thermal diffusivity were carried out on the same
system as that used for the measurements of the thermal conductivity, as shown in Figures 1 and 2. In thismethod, the time evolutions of the temperature at two
measurement points that were intermediate positions
between the cold head and 1-k⍀ heater were recorded
after the application of a heat pulse from the heater,
and the measured temperature changes were compared for various thermal diffusivity values via ﬁtting
to the one-dimensional diffusion equation dT/dt⫽ D(d2T/dx2),33 where D is the thermal diffusivity, T
is the temperature, t is the time, and x is the length in
the measured direction. The ﬁber samples were prepared and were set to the sample space in the sameway used for the measurements of the thermal conductivity, as previously mentioned. The sample space
was evacuated below 10⫺3 Pa by an oil diffusion
pump for heat insulation and was kept for 24 h before
the measurements for drying up the sample. The automated measuring system of the thermal diffusivity
was operated from 10 to 150 K. The details of thedetermination of the thermal diffusivity are described
elsewhere.18,19
To measure the water contents of the samples usedin the measurements of the thermal conductivity andDIFFUSIVITY OF RAMIE FIBERS

Figure 3 DP of ramie ﬁbers irradiated with ␥ rays.

thermal diffusivity, the samples were stored in a highvacuum below 10⫺3 Pa for 24 h in the sample space inthe same way used for the measurement of the thermal conductivity. The weights of those samples weredeﬁned as W. The dried samples were obtained by thedrying of those samples at 383 K for 8 h in vacuo at 1
Pa, as described elsewhere.34,35 The weights of thedried samples were deﬁned as Wd. The water contentsof those samples were estimated by the difference
between W and Wd.

5011

and amorphous components.24 –26 The peaks of thecrystal part are sharp, and those of the amorphouspart are broad. The crystallinity can be estimated by
the peak separation of those resonance lines. In particular, the peak separation of the C4 resonance is easy
because the difference between the crystal peak at 88.8
ppm and the amorphous peak at 83.7 ppm is larger
than that of the C6 resonance. Therefore, the C4 resonance peak is used for the estimation of the crystallinity.
First, the solid-state NMR spectra of ramie ﬁbers
with and without ␥-ray treatments are compared toinvestigate the changes in the crystal structure bythese treatments. The solid-state NMR spectra oframie ﬁbers with and without ␥-ray treatments areshown in Figure 5. The peak assignments are shown in
Figure 3. All the NMR spectra show the same peak
shape and chemical shifts. This result shows that the
crystal structure of the ramie ﬁber does not changewith ␥-ray treatments. Comparing the crystal andamorphous resonance peaks of C4 and C6 carbons, we
ﬁnd that the peak intensities do not change so muchby ␥-ray treatments.
To discuss the crystallinities quantitatively, the C4
resonance peaks are separated into crystal and amorphous peaks. The C4 peak separations of ramie ﬁbers
with and without ␥-ray treatments are shown in Figure 6. The crystal resonance of the C4 carbon splits
into two peaks.25 As shown in the ﬁgure, peak separation of the C4 resonance into crystal and amorphous

Tensile modulus
The tensile test of a single ﬁber was carried out on asmall Tensilon Toyo Sokki UTM-II (Yokohama, Kanagawa, Japan). The span length was 10 mm, and thecrosshead speed was 10 mm/min.
RESULTS AND DISCUSSIONDPThe DPs of ramie ﬁbers with and without ␥-ray treatments, estimated by the measurements of the solution
viscosity, are shown in Figure 3. This ﬁgure showsthat DP of the ramie decreases with irradiation with ␥
rays. This result shows the main-chain scission of theramie ﬁber by the ␥-ray treatment. The crystallinity
and orientation angle of the ramie ﬁbers with andwithout the ␥-ray treatment are reported in the following section.
Crystallinity
The CP–MAS, solid-state 13C NMR spectrum of ramieﬁber is shown in Figure 4. The assignments of theresonance lines are also shown in the ﬁgure. The crystal structure of ramie is cellulose I type.25,36 –38 The
resonance lines of C4 and C6 carbons split into crystal

Figure 4 CP–MAS, solid-state, high-resolution 13C-NMR
spectrum of ramie.

5012

YAMANAKA ET AL.

Figure 5 CP–MAS, solid-state, high-resolution 13C-NMR
spectra of ramie ﬁbers irradiated with ␥ rays.

components is possible. The peak shape and chemical
shifts do not change with the ␥-ray treatment as all the
spectra shown in Figure 5. The ratio of the crystal peakFigure 7 Relation between the crystallinity and absorbed
dose of irradiation with ␥ rays of ramie ﬁbers.

and amorphous peak does not change so much by the
␥-ray treatment. The crystallinities of those ramie ﬁbers are estimated by the ratio of the area of the peaks
separated into crystal and amorphous components
quantitatively. The estimated crystallinities are shownin Figure 7. The crystallinity of the ramie ﬁber does
not change with the ␥-ray treatment. Therefore, thethermal conductivity of the ramie ﬁber is expected tochange not so much by the change in the crystallinity
with the ␥-ray treatment.
In the following section, the orientation angles oframie ﬁbers with and without ␥-ray treatments arereported.
Orientation angle

Figure 6 Line-shape analysis for C4 peaks of ramie cellulose irradiated with ␥ rays in CP–MAS, solid-state 13C-NMR
spectra. The solid lines indicate observed curves, and thebroken lines indicate the estimated curves of crystal components and amorphous components.

The orientation angles of crystals were estimated by
the azimuthal intensity distribution of the (002) diffraction spot. X-ray diffraction proﬁles of the (002)
spot of the ramie ﬁbers are shown in Figure 8. Thisﬁgure shows that the half-width of the diffraction
peak changes not so much by ␥-ray treatments. The
orientation angles are estimated by the half-width ofthe diffraction peak, and the orientation degrees are
estimated with the orientation angles with the following formula:28,39

DIFFUSIVITY OF RAMIE FIBERS

5013

Figure 8 X-ray diffraction proﬁle of ramie ﬁbers irradiatedby ␥ rays: the azimuthal direction of the (002) spot.

␾ ⫽ 关共180 ⫺ ␤ 兲/180兴 ⫻ 100

this method. On the other hand, the observed thermal
conductivities are independent of the number of ﬁlaments in the temperature range below 150 K when thenumber of ﬁlaments is greater than 6000. The independence of the observed thermal conductivity fromthe number of ﬁlaments in the lower temperature
range shows that the inﬂuence of bundling ﬁbers andthermal radiation can be neglected in this measurement.
The water concentrations of the ramie ﬁbers withand without the ␥-ray treatment used in this work areless than 0.1%. The thermal conductivities of the ramie
samples before and after a dry treatment at 383 K for
8 h in vacuo at 1 Pa were not different. Therefore, theinﬂuence of the thermal conductivity of 0.1% water isneglected in this article. The details are described in aprevious article.40
The temperature dependence of the thermal conductivity of the ramie ﬁbers with ␥-ray treatments inthe ﬁber direction from 10 to 150 K is shown in Figure
10. The thermal conductivities of all the samples decrease with decreasing temperature. Ramie is an electrical insulator. Therefore, it is thought that the thermal conduction of ramie ﬁbers is caused by phonon
conduction, like most polymeric materials.

(1)

where ␾ is the orientation degree and ␤ is the orientation angle.
The dependence of the orientation angle and orientation degree on the absorbed dose from ␥-ray irradiation is shown in Figure 9. The orientation angle andthe orientation degree do not change with the ␥-ray
treatment in the case of an absorbed dose from ␥-ray
irradiation below 100 kGy.
As previously mentioned, the radiation effects on
the DP, crystallinity, and orientation degree by ␥ rays
were investigated. The results are shown in Table I.
Those results show that only DP changes and that the
crystal structure, crystallinity, and orientation degree
do not change with the ␥-ray treatment in the case of
the ramie ﬁbers used in this work.
Thermal conductivity
The inﬂuence of the thermal radiation effect, ﬁber
bundling, and water in the ﬁbers on the measurementof the thermal conductivity are discussed before thediscussion of the change in the thermal conductivity
with the ␥-ray treatment. The dependence of the observed thermal conductivity on the number of ﬁlaments was reported in a previous article.40 In thetemperature range over 200 K, the observed thermal
conductivities depend on the number of ﬁlaments. It
has been inferred to be caused by a thermal radiation
effect. Therefore, it is difﬁcult to observe the thermal
conductivity at a temperature higher than 200 K with

Figure 9 Dependence of the orientation angle and orientation degree on the absorbed dose of irradiation with ␥ raysof ramie ﬁbers.

5014

YAMANAKA ET AL.

TABLE I
DP, Crystallinity, and Orientation Degree of the Ramie Fibers Irradiated by ␥ Rays

SampleAbsorbed doseof irradiation
with ␥ rays

DP

Crystallinity(%)

Orientation
angle (°)

Orientation
degree (%)

Ramie blank
1 kGy ramie
2 kGy ramie
100 kGy ramie

0
1
2
100

1700
660
610
220

56
58
57
57

12.7
11.3
11.9
11.9

92.9
93.7
93.4
93.4

We have investigated the effect of the ␥-ray treatment on the thermal conductivity. The thermal conductivity of ramie ﬁbers decreases with the ␥-ray
treatment very much. The reduction of the thermal
conductivity is inferred to be caused by the change inthe crystallinity, crystal structure, and orientation degree and the reduction of the mean free path of thephonon by chain scission with the ␥-ray treatment.
However, the crystal structure does not change, andthe crystallinity and the orientation degree do notdecrease with the ␥-ray treatment, as described in theprevious sections. Therefore, the reduction of the thermal conductivity by the ␥-ray treatment is inferred tobe caused by the reduction of the mean free path of thephonon with molecular chain scission.
To clarify the relation between the thermal conductivity and the length of the molecular chain, that is,DP, the relation between the thermal conductivity at
120, 100, 80, and 60 K and DP in the ramie ﬁbers isshown in Figure 11. The DPs of the ramie ﬁbers do notchange with cooling. Therefore, the DP values measured at 293 K can be used in the following discussion.
As shown in this ﬁgure, the thermal conductivity at
every temperature decreases with decreasing DP. It isthought that the decrease in the thermal conductivity

Figure 10 Temperature dependence of the thermal conductivities of ramie ﬁbers irradiated with ␥ rays.

of ramie by the ␥-ray treatment is dominated by thechain scission of molecular chains. To clarify the relation between the thermal conductivity and chain scission, the relation between the thermal conductivity
and mean free path of the phonon is discussed in thefollowing. The relation between the thermal conductivity and the mean free path of the phonon is shownin the following formula, and the relation between thethermal diffusivity reported in the following and themean free path of the phonon is shown in the following formula:17–19

␬ ⫽ C p␳ D

(2)

D ⫽ 共1/3兲vl(3)

where ␬ is the thermal conductivity in the ﬁber direction, Cp is the heat capacity at a constant pressure, ␳ isthe density of the ramie ﬁber, D is the thermal diffusivity in the ﬁber direction, v is the sound velocity inthe ﬁber direction, and l is the mean free path of thephonon in the ﬁber direction. From formulas (2) and(3), the thermal diffusivity of the ramie ﬁber is also

Figure 11 Relation between the DP and thermal conductivity of ramie ﬁbers irradiated with ␥ rays.

DIFFUSIVITY OF RAMIE FIBERS

Figure 12 Temperature dependence of the thermal diffusivities of ramie ﬁbers treated by ␥ rays.

expected to decrease by the ␥-ray treatment, like thethermal conductivity, if the decrease of the thermal
conductivity of the ramie ﬁber by the ␥-ray treatment
is caused by the reduction of the mean free path of thephonon by molecular chain scission. Therefore, for thecertiﬁcation of this assumption, the thermal diffusivityof the ramie ﬁbers and those with the ␥-ray treatment
is investigated in the following section.
Thermal diffusivity
It is reported in a previous article40 that the behaviorof thermal diffusivity is almost independent of thenumber of measuring ﬁlaments. Therefore, the inﬂuence of thermal radiation and ﬁber bundling on themeasurement of the thermal diffusivity can be neglected.
The water concentrations in the ramie ﬁbers are lessthan 0.1%, and the inﬂuence of the water on the thermal conductivity can be neglected, as previously mentioned. The change in the heat capacity by 0.1% water
has been estimated to be about 0.25% according to therelation between the heat capacity and water contents.41 Therefore, it is also thought that the change inthe thermal diffusivity by 0.1% water can be neglectedaccording to formula (2).
The temperature dependence of the thermal diffusivities in the ﬁber direction of ramie ﬁbers with andwithout the ␥-ray treatment is shown in Figure 12. The
thermal diffusivities of all the ramie ﬁbers are almost
constant from 250 to 100 K, increase slightly as thetemperature decreases from 100 to 50 K, and increase
rapidly as the temperature decreases below 50 K. The
phonons are scattered by the end of the molecular
chain, the crystal or amorphous boundary, and defects. Therefore, the mean free path of the phonon is5015

determined by those concentrations in this temperature range.15 Those concentrations of the end of themolecular chain, crystal or amorphous boundary, anddefects are independent of the temperature. Almost
temperature-independent thermal diffusivity has beenreported about other amorphous and crystal polymers.15,42 On the other hand, increasing the thermal
diffusivity via cooling below 50 K is considered to be
due to the mean free path of the phonon increasing
with decreasing phonon scattering. Increasing thethermal diffusivity by cooling is considered to becaused by two factors. One is the increasing soundvelocity with increasing tensile modulus of the amorphous region by cooling. The other is the increasing
phonon mean free path with decreasing phonon scattering caused by decreasing lattice vibration at a lowtemperature. In this case, it is not thought that thetensile modulus increases rapidly below 50 K, like theglass transition.
The change in the thermal diffusivity by the ␥-ray
treatment is investigated in the following. The thermal
diffusivity from 250 to 50 K decreases with the ␥-ray
treatment, like the thermal conductivity. With the results in the previous section, it is thought that decreasing thermal diffusivity is caused by the reduction of
the phonon mean free path by the molecular chain
scission with the irradiation of ␥ rays. To clarify the
relation between the molecular chain length and thermal diffusivity of ramie, the relation between the thermal diffusivity at 240 K and DP is shown in Figure 13.
The thermal diffusivity of ramie at 240 K decreases
with increasing absorbed dose from ␥-ray irradiation.
The thermal diffusivities of ramie (1 kGy) and ramie (2kGy) are not so different. The DPs of ramie (1 kGy)

Figure 13 Relation between the thermal diffusivity at 240 K
and DP of ramie ﬁbers treated by ␥ rays.

5016

YAMANAKA ET AL.

and ramie (2 kGy) are 610 and 660, respectively. These
are also not so different. The small difference in thethermal diffusivities is inferred to be due to the small
difference in the DPs, that is, the small difference inthe average length of the molecular chain between
ramie (1 kGy) and ramie (2 kGy). The reduction of thethermal diffusivity of the ramie ﬁber by the ␥-ray
treatment agrees with the reduction of DP. This reduction of the thermal diffusivity with the reduction of
DP agrees with that of thermal conductivity mostly.
Next, the change in the mean free path of the phonon by the ␥-ray treatment is investigated. The crystal
region and amorphous region are mixed in the ramieﬁber used in this work. The mean free path of thephonon in the crystal region and that in the amorphous region are different. Therefore, it is difﬁcult to
discuss the absolute value of the phonon mean freepath in the crystal region in this work, so the relativechange in the average behavior of the phonon mean
free path in the mixture of crystal and amorphousparts by molecular chain scission by the ␥-ray treatment is discussed in this work. The tensile modulus in
the ﬁber direction of the ramie ﬁber is 61 GPa. The
tensile moduli of ramie (1 kGy), ramie (2 kGy), andramie (100 kGy) are 55, 53, and 69 GPa, respectively.
The densities of those samples are 1.54 g/cm3. The
sound velocity in the ﬁber direction is estimated withthe tensile modulus and density with the following
formula:v ⫽ 共E/ ␳ 兲 1/2(4)

where v is the sound velocity, E is the tensile modulus,and ␳ is the density of ramie.
By the substitution of the numerical values of E and␳ into formula (4), the sound velocities of ramie(blank), ramie (1 kGy), ramie (2 kGy), and ramie (100kGy) have been estimated to be 6400, 5000, 5900, and6800 m/s, respectively. The thermal diffusivities of
those ramie ﬁbers show almost constant values from50 to 250 K, as shown in Figure 12. Therefore, thethermal diffusivities of the ramie ﬁbers at room temperature are expected to be equal to those at 240 K.
The mean free path of the phonon in the ramie ﬁbers
with the ␥-ray treatment can be compared with that in
the blank ramie ﬁber relatively with formula (3) andthe sound velocity estimated by formula (4) under theassumption that the thermal diffusivities at room temperature are equal to those at 240 K. The relative
dependence of the phonon mean free path on DP isshown in Figure 14. The mean free path of the phonon
decreases with decreasing DP. It is inferred that thethermal diffusivity and thermal conductivity decrease
with the reduction of the phonon mean free path bymolecular chain scission with the irradiation of ␥ rays.
The reduction of the thermal conductivity, thermal
diffusivity, and phonon mean free path by the ␥-ray

Figure 14 Relation between the ratio of the phonon mean
free path in the ﬁber direction of ramie ﬁbers treated by ␥rays to that of blank ramie ﬁber [l/l(blank)] and DP.

treatment is smaller than that of DP. It is thought thatthe probability of molecular chain scission by the
␥-ray treatment in the crystal region is different fromthat in the amorphous region and that the molecular
chain scission in the amorphous region contributes tothe change in the thermal conductivity not so much incomparison with that in the crystal region. A moredetailed discussion including structural analysis will
be necessary for the quantitative discussion of therelation between the thermal conductivity and ␥-ray
treatment.
Next, the change in the thermal diffusivity by molecular chain scission by the ␥-ray treatment at a lowtemperature is investigated. As previously mentioned,
the thermal diffusivities of all the ramie samples increase with cooling. The thermal diffusivities increaseslightly with the temperature decreasing from 100 to
50 K and increase rapidly with the temperature decreasing below 50 K. To compare the temperaturedependence of the thermal diffusivity, the thermal
diffusivities divided by that at 240 K from 250 to 10 K
are shown in Figure 15. Those are relative values tothe thermal diffusivity at 240 K. All the curves show
almost the same behavior. That is, the temperaturedependence of the thermal diffusivities of all the samples shows similar behavior, although the thermal
diffusivity values of the ramie ﬁbers are different, asshown in Figures 12 and 13. Therefore, it is thoughtthat only the change in the phonon mean free pathinﬂuences the thermal diffusivity of the ramie ﬁber at
all temperature in the case of molecular chain scission
by radiation.

DIFFUSIVITY OF RAMIE FIBERS

5017

6. The mean free path of the phonon in ramie was
reduced by the ␥-ray treatment. From those results, the reduction of the thermal conductivity
and thermal diffusivity was explained by the
reduction of the phonon mean free path by molecular chain scission.
7. The temperature dependence of the thermal diffusivities of the ramie ﬁbers with and without the
␥-ray treatment showed similar behavior at a lowtemperature.

Figure 15 Temperature dependence of D/D(240 K) oframie ﬁbers treated with ␥ rays. D is the thermal diffusivity,
and D(240 K) is the thermal diffusivity at 240 K.

CONCLUSIONSThe thermal conductivity, thermal diffusivity, ﬁber
structure, and DP were measured for ramie ﬁbers andthose irradiated by ␥ rays, for which the absorbed
doses were 1, 2, and 100 kGy [ramie (1 kGy), ramie (2kGy), and ramie (100 kGy), respectively]. The effects
of molecular chain scission with radiation on the thermal conductivity and thermal diffusivity were investigated. The following conclusions were drawn:
1. Only DP decreased with the ␥-ray treatment (theabsorbed doses were 1, 2, and 100 kGy). The
crystal structure, crystallinity, and orientation
degree did not change with the ␥-ray treatment.
The molecular chain scission of the ramie ﬁber by␥ rays was estimated by the change in DP.
2. The thermal conductivities of the ramie ﬁbers
and those with ␥-ray treatments decreased withdecreasing temperature.
3. The thermal conductivity of the ramie ﬁbers decreased with increasing absorbed from ␥-ray irradiation. The reduction of the thermal conductivity of the ramie ﬁbers by the ␥-ray treatment
agreed with the reduction of DP.
4. The thermal diffusivities of the ramie ﬁbers withand without ␥-ray treatments were almost constant from 250 to 100 K, increased with the temperature decreasing from 100 to 50 K, and increased very much with the temperature decreasing below 50 K.
5. The thermal diffusivity of the ramie at 240 K
decreased with increasing absorbed dose from␥-ray irradiation. The reduction of the thermal
diffusivity of the ramie ﬁber by the ␥-ray treatment agreed with the reduction of DP.

As previously mentioned, the thermal conductivity
and thermal diffusivity decreased with a reduction of
the mean free path of the phonon by molecular chain
scission with the ␥-ray treatment, although the crystallinity and orientation degree did not decrease.
Those results suggest that the thermal conductivity ofpolymeric ﬁbers can be controlled by the control of thelength of the molecular chain.
Many thanks are due to Mr. Atsushi Hamai (Fiber Business
Unit, Toyobo) for obtaining ramie samples. The authors’
gratitude is also expressed to Dr. Fumitaka Horii (Professorof Kyoto University), Dr. Seichi Ochi (Research and Development Department, Toyobo), Dr. Masao Murano (Professorof Saga University), and Dr. Atsushi Kaji as well as Dr. Yuji
Shimizu (Toyobo) for their valuable advice and referenceswith respect to cellulose and its structural analysis. Thanks
are also due to Dr. Hiroshige Sugiyama and Dr. Sonoko
Ishimaru (Toyobo) for their advice and references on theengineering applications of thermal conductivity. The authors express their appreciation to Ms. Sayuri Nagao(Toyobo) and Mr. N. Nakajima (JEMS Co.), who were very
helpful with the experiments. They also thank Manabu
Ikebe (Professor of Iwate University), Dr. Hiroshi Hirahata,
Dr. Yukihiro Nomura, and the members of their group(Toyobo Functional Fiber Group), and Mr. Toshiyuki Matsui(manager), Tokuichi Maeda, and other members of the
Toyobo Dyneema Division, in addition to Dr. Takaharu
Ichiryu (Zylon Business Unit), Dr. Keiji Yukimatsu (President of Nippon Dyneema), and Dr. Masatoshi Yoshikawa(Textiles Products Development Center, Toyobo) for theirsupport.

References
1. Yoneda, M.; Kawabata, S. J Text Machinery S Jpn 1981, 34, 183.
2. Yoneda, M. J Text Machinery S Jpn 1982, 35, 365.
3. Kawabata, S. J Text Machinery S Jpn 1984, 37, 131.
4. Nishijima, S.; Okada, T.; Niihara, K. Key Eng Mater 1999, 161,
535.
5. Hand Book of Superconductivity and Cryogenic Engineering;
Cryogenic Association of Japan: Oumusha, Japan, 1993.
6. Takao, T.; Kawasaki, A.; Yamaguchi, M.; Yamamoto, H.; Niiro,
A.; Nakamura, K.; Yamanaka, A. IEEE Trans Appl Supercond
2002, 13, 1776.
7. Agari, Y.; Kamiyama, T. Plastics 2003, 54, 49.
8. Bhowmick, T.; Pattanayak, S. Cryogenics 1990, 30, 116.
9. Jackel, M.; Muller, M.; Claverie, A. L.; Arndt, K. F. Cryogenics
1991, 31, 228.

5018

10. Choy, C. L.; Wong, S. P.; Young, K. J Polym Sci Polym Phys Ed
1985, 23, 1495.
11. Choy, C. L.; Leung, W. P. J Polym Sci Polym Phys Ed 1983, 21,1243.
12. Mergenthaler, D. B.; Pietralla, M.; Roy, S.; Killian, H. G. Macromolecules 1992, 25, 3500.
13. Burgress, S.; Greig, D. J Phys C: Solid State Phys 1975, 8, 1637.
14. Gibson, A. G.; Greig, D.; Sahota, M.; Ward, I. M.; Choy, C. L. J
Polym Sci Polym Lett Ed 1977, 15, 183.
15. Choy, C. L. Polymer 1977, 18, 984.
16. Choy, C. L.; Luk, W. H.; Chen, F. C. Polymer 1978, 19, 155.
17. Yamanaka, A.; Fujishiro, H.; Kashima, T.; Kitagawa, T.; Ema, K.;
Izumi, Y.; Nishijima, S. J Polym Sci Part B: Polym Phys 2005, 43,1495.
18. Fujishiro, H.; Ikebe, M.; Kashima, T.; Yamanaka, A. Jpn J Appl
Phys 1997, 36, 5633.
19. Fujishiro, H.; Ikebe, M.; Kashima, T.; Yamanaka, A. Jpn J Appl
Phys 1998, 37, 1994.
20. Kittel, C. Introduction to Solid State Physics; Academic: New
York, 1974.
21. Phillips, G. O.; Arthur, J. C., Jr. In Cellulose Chemistry and Its
Applications; Nevell, T. P.; Zeronian, S. H., Eds.; Wiley: New
York, 1985; Chapter 12, p 290.
22. Cyclopedia of Cellulose; Cellulose Society Japan, Ed.; Academic:
Asakura Shoten, Japan, 2000.
23. Klemm, D.; Philipp, B.; Heinze, T.; Heinze, U. Comprehensive
Cellulose Chemistry; Wiley-VCH: Weinheim, 1998; Chapter 1, p
168.
24. VanderHart, D. L.; Atalla, R. H. Macromolecules 1984, 17, 1465.

YAMANAKA ET AL.

25. Horii, F. In Nuclear Magnetic Resonance in Agriculture; Pfeffer,
P. E.; Gerasimowicz, W. V., Eds.; CRC: Boca Raton, FL, 1989;
Chapter 10, p 311.
26. Horii, F.; Hirai, A.; Kitamaru, R. Polym Bull 1982, 8, 163.
27. Sakaguchi, Y.; Tsutsumi, M.; Kaji, A.; Abe, S. Senni-Gakkaishi
2002, 58, 321.
28. Abe, S.; Tsutsumi, M.; Yoshikawa, M.; Sakaguchi, Y. J Text
Machinery S Jpn 2000, 53, 1.
29. Dudley, R. L.; Fyfe, C. A.; Stephenson, P. J.; Deslandes, Y.;
Hamer, G. K.; Marchessaulft, R. H. J Am Chem Soc 1983, 105,2469.
30. Horii, F.; Hirai, A.; Kitamaru, R. Macromolecules 1987, 20, 2117.
31. Yamato, H.; Horii, F.; Odani, H. Macromolecules 1989, 22, 4130.
32. Abe, S.; Ohta, S.; Yamanaka, A.; Nagara, N. J Text Machinery S
Jpn 1996, 49, 290.
33. Fujishiro, H.; Ikebe, M.; Naito, T.; Noto, K. Cryog Eng 1993, 28,533.
34. Wada, M.; Heux, L.; Isogai, A.; Nishiyama, Y.; Chanzy, H.;
Sugiyama, J. Macromolecules 2001, 34, 1237.
35. Miyake, H.; Nagura, M. Text Res J 2001, 71, 645.
36. Woodcock, C.; Sarko, A. Macromolecules 1980, 13, 1183.
37. Ishikawa, A.; Sugiyama, J.; Okano, T. Wood Res 1994, 81, 16.
38. Earl, W. L.; VanderHart, D. L. Macromolecules 1981, 14, 570.
39. Abe, S.; Ohta, S.; Tsutsumi, M. J Text Machinery S Jpn 1997, 50,
109.
40. Yamanaka, A.; Yoshikawa, M.; Abe, S.; Tsutsumi, M.;
Oohazama, T.; Kitagawa, T.; Fujishiro, H.; Ema, K.; Izumi, Y.;
Nishijima, S. J Polym Sci Part B: Polym Phys 2005, 43, 2754.
41. Hatakeyama, H.; Hatakeyama, T. Thermochim Acta 1998, 308, 3.
42. Morikawa, J.; Tan, J.; Hashimoto, T. Polymer 1995, 36, 4439.