choy 1975
Post on 02-Jun-2018
215 Views
Preview:
TRANSCRIPT
-
8/10/2019 Choy 1975
1/11
The low-temperature thermal conductivity of a semi-crystalline polymer, polyethylene
terephthalate
This article has been downloaded from IOPscience. Please scroll down to see the full text article.
1975 J. Phys. C: Solid State Phys. 8 3121
(http://iopscience.iop.org/0022-3719/8/19/012)
Download details:
IP Address: 129.174.55.245
The article was downloaded on 27/06/2012 at 15:58
Please note that terms and conditions apply.
View the table of contents for this issue, or go to thejournal homepagefor more
ome Search Collections Journals About Contact us My IOPscience
http://iopscience.iop.org/page/termshttp://iopscience.iop.org/0022-3719/8/19http://iopscience.iop.org/0022-3719http://iopscience.iop.org/http://iopscience.iop.org/searchhttp://iopscience.iop.org/collectionshttp://iopscience.iop.org/journalshttp://iopscience.iop.org/page/aboutioppublishinghttp://iopscience.iop.org/contacthttp://iopscience.iop.org/myiopsciencehttp://iopscience.iop.org/myiopsciencehttp://iopscience.iop.org/contacthttp://iopscience.iop.org/page/aboutioppublishinghttp://iopscience.iop.org/journalshttp://iopscience.iop.org/collectionshttp://iopscience.iop.org/searchhttp://iopscience.iop.org/http://iopscience.iop.org/0022-3719http://iopscience.iop.org/0022-3719/8/19http://iopscience.iop.org/page/terms -
8/10/2019 Choy 1975
2/11
J. Phys. C : Solid State Phys., Vol. 8, 1975. Printed in G rea t Britain. @ 1975
The low-temperature thermal conductivity
of
a
semi-crystalline
polymer, polyethylene terephthalate
C
L
Choy? and D Greig
Department of Physics, The University of Leeds, Leeds LS2 9JT
Received 22 May 1975
Abstract. Th e thermal conductivity,
K
of seven samples
of
polyethylene terephthalate (PET )
with volume fraction crystallinity varying from
0
to 0.51 has been m easured between
1 5
and
70
K. The am orp hou s sample exhibits the characteristic plateau region between
4
and 9 K .
Above
30 K, K
increases with crystallinity, but there is a cross-over near 20
K so
that K
decreases with crystallinity at lower temperatures. This peculiar behaviour can be und erstood
on
the basis of the acoustic mismatch theory of Little by considering a semi-crystalline
polymer as composed of crystalline regions dispersed in an amorphous matrix. As the
temperature is lowered, the thermal boundary resistance due to acoustic mismatch at
amor phous-crystalline interfaces increases and
thus
the thermal conductivity of the crystal-
line samples is reduced relative to th at of amorph ous PET .
1. Introduction
The low-temperature behaviour of the thermal conductivity
K
of amorphous solids has
now been well established experimentally (Choy et a 1970, Zeller and Pohl 1971,
Stephens et a 1972, Burgess and Greig 1974). Below 1 K, I
T 8;
as
T
increases the
temperature dependence decreases, until in the range
of
5 to 10K,
K
is independent of
temperature (plateau region). At higher temperatures, I again increases with
T
and
becomes proportional to the specific heat above 60 K. Two classes of models have been
proposed to explain this behaviour. The first class explains the T 1 8dependence by
assuming resonant scattering by tunnelling states (Phillips 1972, Anderson et d 1972)
and the plateau by similar scattering of a different band of localized states at higher
frequencies (Dreyfus
et a
1968). The second class of models (Klemens 1965, Morgan and
Smith 1974) assumes that scattering of phonons is due
to
fluctuations in the properties
of the solid from one point to another. In the most recent attempt by Morgan and Smith
(1974), the characteristic
T1 *
ependence can be accounted for by assuming a correla-
tion length of the order of 3000A, while the plateau is explained by the increasing
importance with rising temperature of a short-range correlation of the order of lOA.
Although more experimental investigations such
as
light scattering and spectroscopic
measurements are required to establish the relative merits of these models, they seem to
provide a plausible explanation for the temperature dependence of K.
The situation for semi-crystalline solids is much more uncertain. No plateau region has
been observed, and
K
exhibits a
T 1 - T 3
dependence between 0.1 and 10 K (Chang and
t On leave from the D epartment of Physics, The Ch inese Un iversity of Hong
K o n g
Shatin, NT, Hong Kong.
3121
-
8/10/2019 Choy 1975
3/11
3122
C L
Choy
and
D
Greig
Jones 1962, Anderson et a 1963, Reese and Tuc ker 1965, Kolou ch and Brown 1968,
Scott et a 1973, Burgess and Greig 1975). M ost mea suremen ts on semi-crystalline solids
had been made before the resonant-scattering and correlation-length models were
advance d. In th e analyses of these data, a semi-crystalline solid is treated as a com posite
with crystalline regions dispersed in an amorphous matrix, and phonons are therefore
scattered by a combination of two processes
:
structu re scattering (Klemens 1951) due
to the amorphous matrix characterized by a frequency-dependent mean free path,
given by U- and scattering by internal boundaries characterized by a frequency-
independent mean free path. It was thought at the time that K U- would be the correct
frequency dependence for the mean free path of phonons in an amorphous material.
How ever, it has since been sho wn (Cho y et al 1970, Zeller and Poh l 1971) that structu re
scattering gives the wrong te mp eratu re dependence ( K K T below 1 K) even for amo rph -
ous
solids, so the use of this form to describe scattering
in
the amorphous matrix of a
semi-crystalline solid is certainly not justified. Thus it is doubtful that the frequency-
independ ent m ean free path extracted from these analyses has any physical meaning.
Recently, Anderson and Rauch (1970) studied the therm al conductivity of a dispersion
of 15ym copper powder in a grease (an amorphous insulator). It was found that the
results could be explained o n the basis of Littles (1959) acou stic mismatch model wh ich
predicted that the mismatch of the elastic constants at the interface of two dissimilar
materials gave rise to strong ph ono n scattering. At low temperatures, this model gives a
thermal boundary resistance rb at the interface proportional to
T -3 .
The thermal
conductivity m easurem ents of G ar ret t and R osenberg (1972) on compo sites ma de from
epoxy resin filled with crystalline coru ndu m (A120 3), rystalline quartz, glass spheres and
diamond powder were also found to be in agreement with this model.
It would therefore seem to be of interest to investigate whether Littles model is
applicable to sem i-crystalline solids. Since the density and sou nd velocity in the am or ph -
ous
and crystalline regions are different, acoustic mismatch at the interface is expected.
The m ain ob stacle to th e application of this model to a semi-crystalline solid lies in the
fact that the thermal conductivity of the corresponding amorphous phase is usually
not known. Most semi-crystalline polymers cannot be transformed to the amorphous
state even by fast cooling from the melt. However, there is one polymer, polyethylene
terephthalate (PET), which can be quenched to the am orphous stat e; then, by annealing
at different temperatures for different periods of time, six semi-crystalline samples with
volume fraction of crystalline regions ranging from 0.09 to 0.51 were prepared. The
thermal conductivities of all the samples were then measured between
1.5
and
70
K. and
Littles model was used to analyse the dat a.
2.
Experimental techniques
All the samples used in the me asureme nts were prepared from a quenched sheet of PE T
kindly supplied by Professor I M Ward of the Department of Physics, University of
Leeds. Six other semi-crystalline samples were prepared by annealing at different
tem pera tures fo r different periods of time. The densities, p, of all samples were measured
using a density gradien t colu mn, an d the volume fraction crystallinity
X
was calculated
from the expression X p
pa)/@, pa).
where the densities of the crystalline and
amo rphous phases,
p,
and pa are 1.455 and 1.335 g c m -j , respectively, from the litera-
ture (D aub eny and Bunn 1954). The thermal treatment, density and crystallinity of these
samp les are given
in
table 1.
-
8/10/2019 Choy 1975
4/11
The thermal conductivity of P E T 3123
Table
1
Physical properties of PET samples.
Sample Thermal treatment
Density Crystallinity f
(g
cm-.)
x
so
Quenched 1,337 0.015 __
s 1
Annealed at
100C
for 45 min
1,346 0.09 0.33
s 2 Annealed at 100C for 75 min 1,35 6 0.17 0.59
s3 Annealed at
100C
for
100
min
1.365
0.25
0.81
s4 Annealed at 100C for 17 h 1.370 0.29 0.86
s5 Annealed at
170C
for
30
min
1.382 0.39
0.90
S6 Annealed at 210C for h 1.396 0.51 0.93
The thermal conductivity measurements were made between 1.5 and 70
K
using the
steady-heat-flow method, in a double-enclosure cryostat immersed in a bath of liquid
helium. Since full details of the method have been given elsewhere (Burgess and Greig
1974), only a brief description of the essential features will
be
given here. The measure-
ments made use of inward radial heat flow in disc-shaped samples approximately
2.5 m
n diameter and 0.3 m hick. Thermal contact to the cryostat was made by a
1 0 ~ ~crew threaded into the central axis of the disc, while a 2 5 0 0 heater of 46 SWG
manganin wire wound uniformly on the outer rim and glued with GE7031 varnish
provided the heat required. A further length of
2
m
of
manganin wire was sufficient to
make the heat loss negligible. During the experimental runs, the sample chamber was
always evacuated to better than
The temperature gradient along the direction of heat flow and the absolute tempera-
ture of one point on the specimen were measured by Au-Fe/chromel thermocouples,
with the temperature
of
helium bath used as the reference in the latter case. Since the
diameter of the thermocouple wire used was 0.008 cm, about 14 m and 10 cm of Au-Fe
and chrome1 wires, respectively, were required to ensure negligible heat loss by conduc-
tion. The thermocouple voltages were opposed by the output of a Tinsley Diesselhorst
potentiometer stepped down in the ratio 1000:1,ana the null point detected by a Tinsley
galvanometer amplifier. The temperatures and temperature gradients were obtained
from calibration tables published by Rosenbaum (1968) and Medvedeva et a (1971).
A comparison of these two sets of tables together with checks in our laboratory showed
that, for the thermocouples actually used, both tables agreed to about 1 between
-5 and 30 K, Rosenbaums being the better below K and Medvedevas the more
satisfactory above 30
K.
The greatest uncertainties were at very low temperatures,
-
K,
where errors could be as great as 4
%.
Torr.
With the sample geometry given above, the thermal conductivity is given by
where L is the sample thickness,
r l
and rz are the inner and outer radii between which
the temperature gradient AT is measured, and 0 is the power generated in the heater.
The absolute accuracy of K is largely determined by the geometrical factors in (1) and
is estimated to be 4 . The relative accuracy for any one sample or among different
samples in this series is much better (
-
%) since all samples have similar geometrical
factors.
-
8/10/2019 Choy 1975
5/11
3124 C L Choy and D
Greig
I I
I
3. Results
and discussion
The results of our measurements are shown in figures1and 2 while values of K at selected
temperatures are given in table 2. Even though the quenched sample has a small crystal-
linity of
0.015,
it shows the characteristic plateau region between 4 and 9 K. Henceforth,
we will regard this sample as amorphous and denote its thermal conductivity by
IC .
Above 30 K, all the crystalline samples have higher conductivities than the amorphous
T(K )
Figure 1
The thermal conductivity of
PET
between
1 5
and
70
K.
-
8/10/2019 Choy 1975
6/11
The thermal
conduc tivity of P E T
3125
Table 2
Experimental thermal conductivity
of PET at
selected temperatures (mW cm - K -
I)
T(K)
SO s1 s 2 s 3 s 4 s 5 S 6
1.5 0.268
0.177 0,117 0.056 0.047 0.030 0.020
2 0,305
0.215
0.136 0,070
0.060 0.040
0.030
3 0.353 0.265 0,174 0.097
0.088 0.066 0.052
4
0.375
0.295 0.206 0.125 0.116 0.095 0.081
5 0.388
0.320 0.236 0.158 0.149 0.129 0.117
6 0.400 0.342 0.266 0.191 0.181 0.166 0.156
8
0.431 0.388 0.327 0.258
0.248 0.242
0.236
10 0.470 0.435 0.385 0.310 0.320
0.325 0.340
15 0.590
0.575 0.550 0.490 0.510 0.530 0.570
20 0.710 0,705 0.705 0.680
0.690 0.740
0.790
30
0.940
0,950 0.960 0.970 0,980
1.08 1.18
40 1.12
1.14 1.16 1.19 1.22 1.34 1.45
50 1.28
1.33 1.38 1.42 1.44
1.55 1.70
60 1.41
1.46 1.54 1.58
1.60 1.73 1.90
70 1.51 1.56 1.62 1.68 1.74 1.88 2.02
sample, and I increases with crystallinity. However, below 10
K
this trend is reversed,
and at 1 5 K, the conductivity of the sample with X 0.51 is more than one order of
magnitude less than IC .
As a preliminary to any discussion, it seems worthwhile to give a brief description
of the morphology of a semi-crystalline polymer. Such a material consists of crystalline
units called lamellae dispersed in an amorphous matrix. Each lamella, typically
60-100
thick in the case of PET (Overton and Haynes 1973), is made up of chains folded back
and forth between the lamella surfaces. In an isotropic polymer, these lamella are
randomly oriented and they may arrange themselves end-to-end to form a ribbon-like
structure. If a sample is allowed to crystallize, the ribbons normally grow out from
nucleating centres to form spherulites. The material which fills the space between the
ribbons is amorphous and thus on a microscopic scale the structure can be visualized as
alternate regions of crystalline and amorphous phases.
With this picture as a basis, we shall now consider whether our results can be under-
stood in the light of Littles acoustic mismatch model applied to the interfaces between
amorphous and crystalline regions. Little (1959) has shown that, when the vibrational
spectrum is given by the Debye approximation, the thermal boundary resistance rb at
the interface of two media is
T - 3 ,
h 3
where h is Plancks constant, k is Boltzmanns constant, vL is the velocity of longitudinal
phonons,
vT
is the velocity of transverse phonons, r, is the transmission coefficient of
longitudinal phonons, rT s the transmission coefficient of transverse phonons,
and 8, is the Debye temperature. At sufficiently low temperatures where
8,lT
%
1,
f is a constant and equation (2) becomes
-
8/10/2019 Choy 1975
7/11
3126
C L Choy and D Greig
The contribution of this resistance therefore depends strongly on temperature and.
at high temperatures, is expected to be small. Since, in general, Crystalline regions have a
much higher conductivity than amorphous regions, it follows that when the thermal
boundary resistance is negligible then the more-crystalline polymers should have the
higher thermal conductivity. This is in agreement with our measurements above 30 K.
As the temperature decreases, r, increases and, at some temperature (15-25 K in our
case), the contribution from rb more than compensates for any increase in heat con-
duction due to the presence of the crystalline regions. At this temperature, a cross-over
in the K curves will occur. This trend increases until finally, at
1.5
K, the conductivity
of the sample with X
0.51
is more than ten times lower than K,.
It is also easily seen that the slope of the K versus T curves below 10 K increases with
crystallinity. This is the direct result of a combination of scattering
in
the amorphous
regions and the amorphousxrystalline interfaces (and neglecting the weak scattering
in the crystalline regions). Since experimentally,
K
cc
To
for the amorphous polymer,
we expect cc
TY
where
0.5 < < 3)
for the crystalline samples.
As
the crystallinity
increases, there will be more surfaces for scattering, so the contribution of boundary
scattering becomes more important and an increase in expected.
In order to make a more quantitative comparison with theory, the arrangement of
crystalline and amorphous regions along the direction of heat flow is assumed to be that
shown in figure
3 .
That is, for each cross-sectional areaA perpendicular to the direction
Heat
f l ow
morphous
eg ions
Figure 3.
A
schematic model for the arrangement of the am orpho us and crystalline regions
in semi-crystalline
PET.
of heat flow, a fractional area 1 ) A is completely occupied by amorphous material.
In the remaining area,
4,
crystalline and amorphous material is stacked
in
alternate
layers. The thickness
d
of the crystalline regions represents the effective thickness of the
lamellae along the direction of heat flow. Since the lamellae are on average inclined at
an angle, say
45 ,
to the direction of heat flow,
d
is taken to be
1 5 0 A
(approximately
100 J2&. If we neglect the small resistance due to the crystalline regions, then it
is
-
8/10/2019 Choy 1975
8/11
The thermal
conductivity of
P E T
3127
easily shown that
The low-temperature expression for
rb in
equation
(3)
can be evaluated if the densities
and sound velocities of the amorphous and crystalline phases are known. The densities,
as mentioned above, are
pa 1.335
and
p c 1.455
g ~ m - ~ ,
o p J p , rr 1.09.
The
transverse sound velocity
vT
of the amorphous phase calculated from low-temperature
shear modulus measurements (Armeniades and Baer
1971)
is
1.1
x
lo5
cm s- . while
uL N 2vT,
a relation generally valid for polymers (Athougies
et al 1972).
The velocities
in the crystalline phase are not known. There are data of Young's modulus both along
and perpendicular to the polymer chains (Holliday and White
1971)
which can be used
to give an estimate of the longitudinal velocity, but it is obvious from equation
(3)
that
the transverse velocity term is the dominant one. From the data of shear modulus versus
crystallinity (Armeniades and Baer
1971),
it is estimated that the ratio of the velocities
of the crystalline and amorphous phases is about 1.8. With these ratios for the densities
and velocities, the transmission coefficients can be obtained from Little's article (1959).
Since the transmission coefficients for phonons going from crystalline to amorphous
phases are different from those going in the opposite direction, the appropriate average
is taken, leading to a value of rT
rL 0.2.
Substitution of these estimated values of
v
and
I
into equation
(3)
results in a thermal boundary resistance of an amorphous-
crystalline interface given by
rb 1.3 x T-'
cm2s K4 erg-
.
Using this expression
for
rb
and taking
d
to be
150 A,f
is adjusted to fit equation
(4)
to the experimental data.
The results as shown in figure
4
show good agreement between theory and experiment
in the range
1.5
to
5
K. Near
1.5 K,
the fit is very sensitive to
(1
- j ince it is the
dominant term for all samples. The values ofJ; shown in table
1,
increase rapidly with
increase in X but become saturated when
X
reaches
0.29.
Between X =
0.29
and
X
0.51, f
increases by less than
10
%. When X
0.51,
=
0.93,
indicating that most
of the area perpendicular to heat flow is blocked by crystalline lamellae. This is the
physical situation expected when the plate-like lamellae embedded
in
an amorphous
matrix reach a volume fraction of
0.51.
For the more crystalline samples X >
0.29),
the dominant term near
4
K
is the one containing the factor
rb/d,
and any change
in
this
factor produces a similar fractional change in the theoretical values. Since the assigned
value for
d
of
150A
is a reasonable estimate of the effective thickness of the lamellae,
it cannot be changed by more than a factor of
2
without producing
an
unreasonable
physical picture. Thus the magnitude of
rb
is correct to within a factor
2,
and the good
agreement between theory and experiment
in
the whole temperature range also justifies
the validity of the T - 3 dependence. Both these factors support our contention that the
important phonon scattering mechanism in semi-crystalline polymers at low tempera-
tures is caused by acoustic mismatch at amorphous-crystalline interfaces.
Above
5
K, the theoretical values rise above the experimental ones and this deviation
becomes larger at higher temperatures, as is clearly shown in figure
5
(curve
1)
for the
sample with
X
=
0.51.
This reveals the inadequacy of equation
(3)
at higher temperatures
and the full expression
in
equation
(2)
should then
be
used. However, there is not enough
information known on the vibrational spectrum of PET to allow the evaluation off( 7 ).
As an estimate of the effect of f r),he Debye temperature
8
is assumed to be
60
K,
a value not unreasonable for a polymer with a complicated structure (Wunderlich and
Baur 1970). The expression in equation (2) can then be combined with equation (4) to
give curve
I1
in figure
5.
Even with this crude approximation of the vibrational spectrum,
-
8/10/2019 Choy 1975
9/11
3128
C
L
Choy and D Greig
0.01
I
2
IO 20
40
60 100
*5 2 3 4 5
T
K)
T ( K )
Figure 4 Theo retical fits to the therma l conductivity Figure 5 Theoretical fit to the thermal conductivity
of PET between
1.5
and K. Th e poin ts repr esen t of the sample of P ET of crystallinity
0.51.
Curve
I
is
the smoo thed experim ental da ta while the full curves calculated using equations (3) and (4) while curve I
are calculated using equations (3) and
(4).
The broken
is
calculated according to equations (2) and
(4).
The
curve denotes th e therm al conduc tivity of th e points denote the experimental da ta. The broken
amorp hous sample.
curve represents the thermal conductivity of the
amorp hous sample.
quite a large part of the discrepancy has been removed, and between 1-5 and 70 K the
agreement with experiment is within 20z t is conceivable that if the actual vibrational
spectrum were used, even better agreement would be possible.
The above calculation also gives us a rough estimate of the relative importance of
the interface boundary resistance. Sincef 0.93, the sample can be treated as approxi-
mately a series arrangement of crystalline and amorphous regions, and the total thermal
resistance is just the sum of the resistances of the crystalline (assumed negligible) and
amorphous regions and the boundary resistances. Then the application of equation (2)
shows that even at
70
K the boundary resistance still accounts for about 20 % of the total
resistance. Although the resistance of the crystalline regions can no longer be neglected
at higher temperatures, it is still only a small fraction of the total. Since both 1 / ~ ,nd
Tb
decrease very slowly with temperature and have approximately the same temperature
dependence, we see that near 300
K,
boundary resistance may still amount to l0-20
of the total resistance. This must be taken into account in any model for the thermal
conductivity of semi-crystalline polymers.
It should be noted that the expression for Yb in equation (2) is only valid when the
dominant phonon wavelength is smaller than the dimensions of the lamellae. With
vT 1.1 x
lo5
cm s-l, the wavelength of the dominant transverse phonons at 1.5K
is N k44 .3 kT N
80
A. This is about half the effective thickness of the lamellae and
thus we expect equation
(2)
to be valid above 1.5 K. However, it would be interesting to
-
8/10/2019 Choy 1975
10/11
The thermal
conductivity of P ET
3129
extend the measurements to lower temperatures to clarify the situations where phonon
wavelength is either comparable to or much larger than lamella thickness.
Finally, we want to emphasize two important points in the model employed. First,
the basic scattering units are assumed to be the lamellae. This is contrary to most
previous works on semi-crystalline polymers which associate a constant mean free path
of the order of 1-10 pm with the average dimension of the spherulites. As mentioned
above, a spherulite is made up of ribbons of twisted lamellae with amorphous regions in
between,
so
it is rather unreasonable to expect phonons not to suffer scattering as they
go across amorphous-crystalline interfaces while traversing a spherulite. Secondly,
even though the lamellae are the basic scattering units, they do not lead to a constant
mean free path equal to the lamella thickness. This is because the average transmission
coefficient is approximately equal to 0-2 (the maximum possible value is 0.9, so that
phonons have a finite probability
of
crossing any amorphous-crystalline interfaces.
4.
Conclusion
While the thermal conductivity of PET at 30K and above increases with increasing
crystallinity, the values below about 10K show the opposite trend. At 1.5K the con-
ductivity of a 50 crystalline sample is an order of magnitude less than that of the
amorphous material. We have interpreted these conflicting tendencies as follows.
Crystalline material will always have a higher intrinsic conductivity than amorphous,
and at high temperatures the presence of crystalline regions will simply increase the net
conductivity of the polymer. At low temperatures, on the other hand the acoustic
mismatch at the amorphous-crystalline boundaries provides the dominant thermal
resistance, and the total conductivity is reduced rapidly as the number of such boundaries
becomes large. We have applied a theory due toLittle to a schematic model of a semi-
crystalline polymer, and have shown how these ideas can account for the experimental
observations. As a final comment, we should like to emphasize that this analysis is not
restricted to the particular polymer studied here, but is of quite general validity.
Acknowledgments
We are grateful to Professor
I
M Ward for supplying the quenched sheet of PET and for
taking part in many enlightening discussions. One of us (CLC) would like to thank the
Chinese University of Hong Kong for partial financial support during the period of this
work. Thanks are also due to Mr J Dale for his technical assistance.
References
Anderson P W , Halperin B I and Varma C M 1972 Phil. M a g .
25
1-9
Anderson A C and Rauch R B 1970
J .
Appl .
Phys .
41 3648-51
Anderson A
C,
Reese W and W heatley J
C
1963 Rev. Sci. Instrum.
34
1386-90
Armeniades C D and Baer E 1971
J .
Polymer Sei. A-2 9 1 3 4 5 4 9
Athougies A D, Peterson B T, Salinger G L and Swartz C P 1972 Cryogenics
12
125-8
Burgess
S
and Greig D 1974 J .
Phys.
D: Appl .
Phys.
7 2051-7
1975 J .
Phys.
C:
Solid St. Phys .
1 6 3 7 4 8
Chang G K and Jones R E 1962
Phys.
R ev . 126 2055-8
-
8/10/2019 Choy 1975
11/11
3130
C L Choy and D Greig
Choy C L , Salinger G
L
and Chiang Y C 1970
J .
Appl. Phys.
41
597-603
Daubeny R de P and Bunn C W 1954
Proc. R . Soc. A226
5 3 1 4 2
Dreyfus B, Fernandes
N C
and M aynard R 1968 Phys. Let t . 12 647-8
Garrett K W and R osenberg H M 1972 Pro c. 4th In ?. Cryogenic Engineering Conference pp 267-9
Holliday
L
and White
J N
1971 Pure App l. Chem.
6
545-82
Klemens P G 1951 Proc. R . Soc. A208 108--33
__
Kolouch R
J
and Brown R G 1968
J .
Appl. Phys.
39
3999-4003
Little W A 1959 Can. J . Phys . 37 3 3 4 4 9
Medvedeva L
A
Orlova M P and R abinkin
A
G 1971 Cryogenics
11
316-37
Morgan G J and Smith D 1974 J . Phys. C : Solid St . Phys. 7 649-64
Overton J R and Haynes S K 1973 J . Polymer Sci. C 43 9-17
Phillips W A 1972
J .
Low-Temp. Phys. 7 3 5 1 4 0
Reese W and Tucker J E 1965
J .
Chem. Phys. 43 105-14
Rosenbaum R L 1968
Rev. Sci. Instrum. 39
890-9
Scott T
A
de Bruin
J,
Giles
M
M and Terry
C
1973
J .
Appl. Phys. 1212-6
Stephens R B, Cieloszyk G S and Salinger G L 1972 Phys. Let t . 3 215-6
Wunderlich B and B aur H 1970 Adv . Polymer Sci.
7
151-368
Zeller R
C
and Pohl R
0
1971
Phys . Rev.
B
4
2 6 2 9 4 1
1965
Physics
of
Non-Crystalline Solids
(Netherlands: North -Holla nd) pp 162-78
top related