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Measurement of thermal conductivity of polymers using an improved Lee's Disc apparatus
PII:
Polymer Testing 16 (1997) 203-223 Copyright 0 1997 Elsevier Science Ltd Printed in Great Britain. All rights reserved
SO142-9418(96)00043-S
0142.9418/97/$17.00
ELSEVIER
TEST APPARATUS/MATERIAL PROPERTIES Measurement of Thermal Conductivity of Polymers using an Improved Lee’s Disc Apparatus N. Sombatsompop”sb
& A. K. Wood”,*
“Polymer Science and Technology Group, Manchester Materials Science Centre, University of Manchester and UMIST, Grosvenor Street, Manchester Ml 7HS, UK ‘Also at the Faculty of Energy and Materials, King Mongkut’s Institute of Technology Thonburi (KMITT), Bangkok 10140, Thailand (Received
7 June 1996; accepted 5 August 1996)
ABSTRACT An improved Lee’s Disc apparatus was designed and utilised to measure the thermal conductivity of various commercial polymers such as low-density polyethylene, polystyrene, polypropylene and poly(ether ether ketone) over a wide range of test temperatures from 40 to 400°C. The measurements were carried out under vacuum such that convective heat losses were minimised. It was found that the thermal conductivity of semi-crystalline polymers, below melting temperature (T,), was dependent on their density and degree of crystallinity and, above T,, on the chain mobility and degradation effects. The thermal conductivity of the amorphous polymer was dependent on mobility of polymer chains below the glass transition temperature (T,) and on the density above T,. The effect of density, degree of crystallinity and heating/cooling were also separately investigated and found to influence the thermal conductivity of the polymers used. 0 1997 Elsevier Science Ltd.
NOTATION the rate of flow of heat (W) the surface area across which the heat flows (m*) temperature (K) glass transition temperature (“C)
*To whom correspondence
should be addressed.
203
204
TlIl AT TP T, d KP
N. Sombatsompop,
A. K. Wood
melting temperature (“C) the temperature difference between the two surfaces (K) the temperature of the tested polymer (melt) (K) the temperature of the ceramic ring (K) the thickness of the slab (m) the thermal conductivity of the tested polymer (W m-l “C-1) the thermal conductivity of the ceramic ring (W m-l “C- -1 ) the cross-section area of the tested polymer (m2) the cross-section area of the ceramic ring (m2) current measured from the heater (A) voltage across the terminals (V) heat radiation coefficient of copper, 1.254 W rnp2 Kw4 density (g cmp3) heat radiation energy of the object i (W me2) area of surface of the object i (m2)
1 INTRODUCTION The thermal conductivity (K) of a material is essentially a constant of proportionality between the conductive heat flux and the temperature gradient driving the heat flux. Generally, the thermal conductivity of a typical polymer melt is quite low, around 10-l Wm-’ K-i, this being a thousand times less than most metals such as copper and aluminium.‘*2 The low thermal conductivity of polymer melts can generate a number of problems related to the processing of the materials such as non-uniform cooling and shrinkage, those causing frozen-in stress, shrink voids, warpage and melt instabilities. Knowledge of thermal conductivity enables engineers to design the machines, screw and dies in order to achieve the desired product. For instance the thermal conductivity can aid the assessment of heating and cooling rates and the development of temperature and velocity profiles for flowing polymer melts in a confined duct.3 The thermal conductivity of solid polymers and polymer melts depends on the molecular structure and is influenced by polar and non-polar groups, the degree of crystallinity, molecular orientation and other physical properties of the polymers. A number of techniques have been used to determine the thermal conductivity of polymers, these being the Hot-Line method,4,5 GuardedHot-Plate,6*7 Lee’s Disc method8 and the DSC.g Due to difficulties in controlling the test conditions such as the contact area between the polymer and the apparatus (thermal contact resistance), heat losses and the accuracy of temperature measurements, significant errors occur in the values of thermal
Measurement of polymers using Lee’s Disc apparatus
205
conductivity obtained. These techniques also present difficulties in terms of sample preparation and polymer degradation, for example in the Hot-Line method it is necessary to use a new wire for each experiment. Sheldon and Lane’OJ l used a cylindrical cell technique based on Fourier’s equation for steady-state conditions and obtained some useful information about the change in thermal conductivity of amorphous and crystalline polymers with temperature, over a range of 15-98”C, and density. They explained the variation of the thermal conductivity in terms of the change in the level of crystallinity with temperature and the additives in the polymer. Kline6 reported the thermal conductivity of amorphous and crystalline polymers and showed that the thermal conductivity of the polymers changed significantly at the glass transition and the melting temperatures due to the greater mobility of the polymer molecules. Yue et ~1.’ investigated the thermal conductivity of low density polyethylene melts between 130 and 240°C using the Lee’s Disc method and found that in this temperature range the thermal conductivity increased slightly with increasing temperature. They related this phenomenon to the increased segmental mobility of the polymer chains, this effect being greater than that resulting from the reduction in density. This result was in good agreement with that of Fuller and Fricke12 who used a concentric cylinder cell method and also suggested that the thermal conductivity decreased with increased complexity of the polymer structure. However they showed that errors in determining wall temperature, measuring total heat input and the presence of radiant heat transfer were significant. Underwood and Taylor’ used the Hot-Line technique to determine the thermal conductivity of various polymers by concentrating on time measuring corrections. In addition, they also indicated that different results could be obtained when using different types of thermocouple. Lobo and Cohen5 utilised the same method to measure the thermal conductivity of various polymers over a temperature range from room temperature to 200°C. Their work indicated that a higher degree of crystallinity results in larger values of thermal conductivity and that, except at the melting and glass transition temperatures, there appeared to be no major variation in thermal conductivity with temperature. Data concerning the thermal conductivity has been of great significance in recent investigations regarding polymer processing such as temperature and velocity profile measurements, heat transfer studies3 polymer degradation and stabilisation, the investigation of cooling and heating processes in injection moulding3 and the thermoplastic insulating industry. However, the thermal conductivity data available has been found to be limited, in particular few attempts have been made to measure the thermal conductivity of polymer melts at temperature above 300°C and the effect of heating and cooling on the measurement of thermal conductivity is still unclear. In addition, a number of the techniques and apparatus used to generate the existing data seem to
N. Sombatsompop,
206
A. K. Wood
give results with significant errors due to the thermal contact resistance and heat losses as mentioned above. The current work investigated the thermal conductivity as a function of test temperature for several commercial polymers, these including low-density polyethylene, polystyrene, polypropylene and poly(ether ether ketone) (PEEK) using an improved Lee’s Disc apparatus. A variety of different test conditions were used. These include sample form, effect of cooling and heating, polymer density and degree of crystallinity. One of the purposes of this investigation was to measure the thermal conductivity of various commercial polymers at exceptionally high temperatures. For example PEEK has a very high glass transition and melting temperature, these being about 143 and 334°C respectively l5 PEEK is normally processed at temperatures of around 360400°C.13914The apparatus used in this work was specially designed and manufactured such that the thermal conductivity of materials could be determined over a wide range of test temperatures, from 40 to 400°C, with the minimum thermal contact resistance, heat losses and accuracy in measuring gradients and total heat input. In addition, an experimental model’ for deriving the thermal conductivity was also reviewed and the results generated were then compared with existing results from the literature.
2 EXPERIMENTAL 2.1 Raw materials
and sample preparation
Four commercial polymers, a low-density polyethylene (LDPE, Exxon Chemical (Belgium) Ltd, LDlOOBW), polystyrene (PS, LACQRENE, 1540/l), polypropylene (PP, MOPLEN 3400MNl) and PEEK, (15OP, without carbon fibre) and APC-2 (with 61% by volume of carbon fibre, ICI) were used. The specimens were prepared in the form of a disc, 70 mm in diameter and 1 mm thick, by compression moulding. The temperatures and pressures used for the compression moulding were based on thermal data obtained using differential scanning calorimetry (DSC) and given in Table 1. Table 2 shows density and crystallinity data for five samples of low-density polyethylene (LDlOOBW). The variation in density and crystallinity was achieved by: (1) Compression moulding the polymer at 5000 kPa and 160°C for 2 min. (2) Cooling the melt to 105°C. (3) Holding the melt at this temperature for a time period varying from 0 to 360 min. (4) Crash cooling the material to room temperature using water at the end of this time period.
Measurement of polymers using Lee’s Disc apparatus
207
TABLE 1 Compression moulding conditions for sample preparation Polymers
Density
T, or T, (“C)
Compression conditions
(g cm-9 Pressure (kPa)
Temperature f”C)
LDPE PS PP PEEK (without CF*) PEEK (with CF)
0.91 1.05 0.92 1.44 1.60
112 97 152 344 341
150 5000 150 5000 185 5000 400 5000 Supplied in sheet form
* Carbon fibre.
Data for low-density polyethylene Sample name
A B C D
TABLE 2 (LDlOOBW) as a function of crystallisation
Crystallisation times (min)
Density at 23°C
0 120 240 360
0.911 0.918 0.925 0.929
time at 110°C
Crystallinity level (%)
tg cm--‘)
34.0 40.2 44.0 46.9
The Pycnometer (Method B of IS0 RI 183) and wide-angle X-ray scattering (WAXS) techniques were employed to measure the density and degree of crystallinity of the polymers, respectively. The accuracy of determining the density and degree of crystallinity was estimated to be f2.5% and f3% respectively. 2.2 Experimental design and apparatus Figure 1 shows the arrangement of the Lee’s Disc apparatus designed and manufactured for this work. Discs A, B and C were made from copper. A cast aluminium heater was placed between discs A and B. The total power consumed by the heater, this being the rate of energy input to the apparatus, was measured using a power meter via a temperature controller. In order to measure the thermal conductivity of a polymer melt, a housing ring, made from ceramic material with thermal conductivity of 1.45 W m-r”C-1,16 was used to retain the sample in the position between discs B and C. The temperature of each of the copper discs and the ambient temperature were measured
208
N. Sombatsompop,
A. K. Wood
using three platinum resistance sensors, the temperatures being displayed on a temperature indicator. The error in the temperature measurement was f2%. One of the problems of thermal conductivity measurement when using the Lee’s Discs technique at elevated temperature is convective heat losses to the surrounding atmosphere, this results in variations in the thermal conductivity determined. The apparatus was therefore placed in a vacuum oven, the oven being evacuated during testing. The assembly of the apparatus involved the sequential positioning of all the components using three ceramic bars, 10 mm in diameter and 100 mm long, as shown in Fig. 1, these being removed after assembly. The ceramic bars were removed in order to minimise heat losses due to conduction. The apparatus was positioned on three ceramic pillars, 20 mm in diameter and 25 mm long, and clamped together using another ceramic rod, 20 mm in diameter and 25 mm long, this bar being tightened using a bolt. 2.3 Experimental procedure The apparatus and its components were arranged according to Fig. 1. Two samples, 1 mm thick, were inserted between discs B and C and the test rig was then placed in the vacuum oven, the oven being pumped down to 20 mm Hg. The heater was turned on, the temperature being controlled using the temperature controller. When the desired temperature was reached and the temperature of the various components of the apparatus had stabilised, the current and voltage across the heater were determined using the power meter. The temperature indicator was used to measure the temperatures of the copper discs. The thermal conductivity was calculated using eqn (6), shown in Section 2.4.8 The test temperature was then altered, further measurements being taken once the temperature of the components of the apparatus had stabilised. 2.4 Experimental study and modelling of thermal conductivity measurement The thermal conductivity is usually known and defined for steady state conditions by Fourier’s law of heat conduction in eqn (1): q = K.S.$
The thermal conductivity measured in this work was based on the heat supplied to the apparatus in the steady state, this being equal to the energy emitted from the exposed surfaces. The can be expressed in the form of:
Fig. 1. The experimental
TemperatureIndicator
Controller
~OSPHERIC
arrangement of the Lee’s Disc apparatus.
I
CONLMTa
9’
6
09
IV. Sombatsompop,
210
q=
A. K. Wood
VI=CE,A;
(2)
The determination of thermal conductivity was based on eqn (1) and the assumptions made in previous work’ are that the temperature of the sample was the mean of those of discs B and C: all elements of the apparatus are at a uniform temperature and the heat through the sample and the ceramic ring is the sum of the heat emitted from disc C and half the heat emitted from the ring. The expression used to calculate the thermal conductivity was given as follows:
+ EPJP, 2
E
p
P
=
K.&.TJ + Wp.Sp.Tp)
PC
d
(3)
When a steady state is reached in the situation without and with a polymer sample, the heat supplied to the apparatus can be determined using eqns (4) and (5), respectively.
IpVp= EpnApa + EpxApx + EpbApb + EplApr+ EpPpc
(5)
where the subscripts refer to the element of apparatus (a, b and c for the copper discs, x for the heater and r for the ceramic ring). By combining eqns (3), (4) and (5), the thermal conductivity of the polymer sample can be determined as shown in eqn (6).
Kp
d L&V, = 2s,.(
- (E,a,
+ EprApx +
E,bA,,)+ E,P,,l
TP
(6) where the heat radiation of the coppers (E) can be obtained from eqn (7):
E=
c[&J4
(7)
Measurement
of polymers using Lee’s Disc apparatus
211
3 RESULTS AND DISCUSSION 3.1 Thermal conductivity of low density polyethylene Figure 2 shows thermal conductivity of the LDPE tested using sample B (Table 2) over the temperature range 40-4OO”C, the value being between 0.209-0.269 W m-l OC-‘. The accuracy of the determination is estimated to be f2.5%. The data can be observed to be composed of four regions over the range of temperature tested. In region (a) the thermal conductivity gradually decreases from 0.245 to 0.235 W m-l ‘C-l due to a reduction in the density of the polymer with increasing temperature. In region (b) it was found that the conductivity of the polymer dropped sharply from 0.235 to 0.215 W m-’ ‘C-l. This was associated with the destruction of crystallites in the solidmolten transition range and results in an increase in free volume.i7 The increase in free volume increases the distance between the polymer chains and thus increases the resistance to energy transfer between the polymer molecules. The thermal conductivity of the LDPE progressively increases in region (c) as the temperature increases due to the increasing segmental mobility of the polymer molecules. This effect is believed to be more dominant than the density effect in this region, this view being supported by previous workers.8,‘2 Finally, the conductivity falls from 0.259 to 0.223 W rn-’ ‘C-’ in region (d) as the temperature increases up to 300°C. This may be due to possible crosslinking and degradation effects which are indicated by the DSC curve as shown in Fig. 3. An exothermic peak started to occur between 320 and 375°C this peak indicating the crosslinking and degradation of the polymer. The degradation and crosslinking processes are exothermic and so the simple energy balance assumed in the analysis of the data obtained on the apparatus no longer exists. The temperature of the molten sample will probably be higher than that assumed in the analysis, that it is half the sum of the temperatures of plates B and C. Thus the thermal gradient will be reduced, to some extent, related to the rate of degradation and so the rate of heat conduction through the polymer will be reduced as will the corresponding value of thermal conductivity. 3.2 Effect of prepared sample form on thermal conductivity measurements In Section 3.1 it was mentioned that the contact area between the polymer sample and the copper surface influenced the thermal conductivity values obtained. Therefore, an experiment was carried out to measure the conductivity using two samples of LDPE; one, prepared by compression moulding, in sheet form and the other being in a granular form. The results are shown
0.19
0.27
0.29
0
100
Fig. 2. Thermal conductivity
50
in low density
150
LDlOOBW,
(“C)
Temperature
polyethylene,
250
200
as a function
300
Regibn
400
of temperature.
350
D
450
Measurement of polymers using Lee’s Disc apparatus
213
214
N. Sombatsompop,
A. K. Wood
in Fig. 4. It was found that the conductivity of compression moulded sample was higher than that of granular system by about 11% over the temperature range 40-120°C and by about 2% beyond 120°C. The reduced contact area found in the case of the packed granular system, produced a reduction in the heat transfer and thus an apparent reduction in the thermal conductivity. Above 12OT, the polymer is molten and it can be seen that the values of thermal conductivity obtained are very similar, within the limits of experimental error, with those obtained using the compression moulded sample. The granules clearly melted and fused to give an air-free molten mass of the same form as that produced when the compression moulded sample melted. 3.3 Thermal conductivity influenced by density and level of crystallinity Four samples with different densities and degrees of crystallinity prepared as indicated in Section 2.1 were used to determine the thermal conductivity as a function of test temperature from 40-250°C the results being shown in Fig. 5. It was found that at 40°C the data for the polymer samples with the different degrees of crystallinity are very close together and are within the limits of experimental error. It is therefore, difficult to determine whether or not the degree of crystallinity affects the thermal conductivity other than that any such effects are small. Similarly at 140°C the data is within the limits of experimental error, no differences between the samples being expected as the samples will have completely melted. It is interesting to note that the differences occurred in the melting temperature region, the fall in thermal conductivity being less pronounced for the higher original degree of crystallisation. 3.4 Effect of heating and cooling processes on the measurement In practice, polymer processing involves heating the materials, deforming and shaping and cooling them down in order to obtain a desirable product. The physical properties of the product are very dependent on the thermal-history during processing. Work was carried out, using compression moulded samples of LDlOOBW, to investigate the effect of thermal-history, heating and cooling processes, on thermal conductivity values. Figure 6 shows the thermal conductivity measured using the same sample at three conditions, these being (a) heating the sample from 100 to 225’C, (b) cooling down to 1OO’C and (c) re-heating to 225°C. The results show that there are differences between these conditions. It is thought that the observed effects may arise for two reasons. Firstly in the solid state, due to the cooling regime imposed the degree of crystallinity of the sample cooled in the apparatus is likely to be higher than
Measurement of polymers using Lee‘s Disc apparatus
215
216
N. Sombatsompop, A. K. Wood
a
0
Measurement
of polymers using Lee’s Disc apparatus
217
218
N. Sombatsompop, A. K. Wood
that found in the original. Whilst the previous evidence above suggests that the degree of crystallinity has a limited effect, the degree of crystallinity found in this case may be significantly higher than that in the case above due to the slow cooling. The second reason arises due to the requirement to have an initial sample which is slightly thicker than the height of the ledge on the spacing ring in order to ensure good thermal contact between the polymer and the copper discs. As the polymer sample is heated it melts and expands and this expansion leads to a limited, small amount of leakage out of the gap between the copper discs. On cooling, as the melt contracts, the thickness of the sample will become smaller, this giving rise to an apparent small increase in thermal conductivity. Similarly in the solid state, due to the higher degree of crystallinity following cooling, the specimen thickness is likely to be less than that of the original specimen and so the apparent thermal conductivity will be higher. Table 3 shows the degrees of crystallinity of the LDlOOBW before and after experiencing the heating and cooling stages, these values being determined using the WAXS method. It was found that the degree of crystallinity after the heating-cooling stage is higher than that prior to the initial heating stage. However, in the early stage of re-heating the thermal conductivities are close to those of the cooling path and a difference starts to appear at higher temperature (about 6% compared to cooling stage and 16% compared to the initial heating stage). This arises because of the change in polymer density and the effect of mobility of polymer chains. In addition, it is interesting to note that the difference in the values of thermal conductivity between the initial heating and cooling stages was more pronounced than that in the values of thermal conductivity between the cooling and re-heating stages. 3.5 Dependence of polymer molecular structure on thermal conductivity Figure 7 shows a comparison of the thermal conductivity values of polyethylene, as mentioned in Section 3.1, with other commercial thermoplastics such as polypropylene and polystyrene over the temperature range of 40-300°C. The thermal conductivity of the PP is less than that of the LDPE over the
Degree of crystallinity
TABLE 3 of LDPE before and after heating and cooling stages
Sample
Degree of crystallinity (%)
Before measuring (unprocessed polymer) After measuring (after the heating and cooling)
34.0 44.8
Measurement of polymers using Lee’s Disc apparatus
219
220
N. Sombatsompop,
A. K. Wood
whole temperature range tested. This may be due to differences in molecular structure and subsequently the energy transfer along and between the molecules. The thermal conductivity of the PP decreases as the temperature increases, the trend being similar to that of the LDPE up to their melting temperatures (152°C for the PP). In the case of the PP the thermal conductivity beyond the melting point is fairly stable. The results obtained were in good agreement with the work carried out by Lobo and Cohen5 and Boenig.17 PS, an amorphous polymer, with a glass transition temperature of around 97”C, had the lowest thermal conductivity when compared to the LDPE and PP. According to Fuller and Fricke this is due to the more complex structure of the PS molecule.” It can be seen that the thermal conductivity of PS increases up to around lOO”C, this being close to its Tg. This increase is because of the increased molecular movement in glassy state as the temperature increases and hence so does the intermolecular energy transfer.17*18Above the Tg the free volume increases more rapidly, which results in increased molecular separation and thus the energy transfer is poorer, with the thermal conductivity gradually falling. Figure 8 shows the thermal conductivity as a function of temperature of the PEEK with and without 61% by volume of carbon fibre as a function of test temperature. It was found that the thermal conductivity of the sample without carbon fibre appears to be independent of temperature up to 250°C test temperature, the average value being 0.219 W m- ’ ‘C-l. Above this temperature, the thermal conductivity increases from 0.226 to 0.262 W m-l OC-l from 250°C up to 400°C. This is due to the increased segmental mobility of the polymer chains. The molecular structure of PEEK is more complex than for polymers such as PP and PS and its thermal conductivity is higher. This is due to the PEEK molecules being stiff due to the ring structures in the backbone of the polymer as compared to polystyrene whose ring structures are pendant. This leads to more efficient energy transfer along the polymer chains. For carbon fibre reinforced PEEK, the thermal conductivity measured in the transverse direction to the fibre orientation is strongly affected by temperature, the conductivity progressively increasing with test temperature. The results show that the thermal conductivity increases from 0.468 W m-i ‘C-l to 0.804 W m-l OC-’ over the temperature range of 40-4OO”C as indicated in Fig. 8. The values of thermal conductivity are lOO-300% higher than that found with the PEEK without carbon fibre. It can be concluded here that thermal conductivity of PEEK is dramatically influenced by the presence of carbon fibre.
Measurement of polymers using Lee’s Disc apparatus
0
I I
v
221
N. Sombatsompop,A. K. Wood
222
4 CONCLUSIONS
(1) The improved Lee’s Disc apparatus designed in this work was found to be a reliable and accurate technique for the determination of the thermal conductivity of various polymers over the temperature range of 40400°C. The results obtained for the thermal conductivity were as follows: (a) 0.2094.269 W m-l “C-l for low density polyethylene between 40 and 400°C; (b) 0.185-0.215 W m-l ‘C-l for polypropylene between 40 and 300°C; (c) 0.147-0.185 W m-l ‘C-l for polystyrene between 40 and 300°C; (d) 0.213-0.262 W m-l ‘C-l for PEEK without carbon fibre between 40 and 400°C; (e) 0.4684.804 W m-l ‘C-l for PEEK with 61% by volume of carbon fibre between 40 and 400°C. It was found that the thermal conductivity of the polymers was influ(2) enced by density, level of crystallinity, polymer molecular structure, thermal contact resistance and thermal-history of the polymers tested. (3) The effect of polymer density seemed to be more pronounced on the determination of thermal conductivity below the melting temperature whereas the segmental mobility of polymer chains had a greater effect above the melting point in the semi-crystalline polymers. This phenomenon was found to be opposite when testing the amorphous polymer.
REFERENCES 1. Rental, C., Polymer Extrusion. Hanser Publisher, New York, 1990. 2. Yue, M. Z., Investigation of melt temperature profiles and shear heating effects in polymer processing. Ph.D Thesis, University of Manchester, UMIST, 1994. 3. Sombatsompop, N. and Wood, A. K., Effect of processing variables in the velocity and temperature profiles of flowing polymer melts in the injection moulding process. In ASME Fluids Engineering Conference Forum on Flow Measurements and Instrumentation, FED-Vol. 239(4), San Diego, California, 1996, pp. 385390. 4. Underwood, W. M. and Taylor, J. R., The thermal conductivity of several plastics determined by an improved line-source apparatus. Poly. Eng. Sci., 1978, N(7), 558. 5. Lobo, H. and Cohen, C., Measurement of thermal conductivity of polymer melts by the line-source method. Poly. Eng. Sci., 1990, 30(2), 65. 6. Kline, D. E., Thermal conductivity studies of polymers. J. Poly. Sci., 1961, L,
441.
Measurement of polymers using Lee’s Disc apparatus
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7. Foreman, P. J., SPE ANTEC’92 Tech. Papers, 1125, 1992.
8. Yue, M. Z., Wood, A. K. and El-Rafey, E., Thermophysical characterization of polyethylene. J. Appl. Poly. Sci., 1994, 55, 105. 9. Khanna, Y. P., Taylor, T. J. and Chomyn, G., A new differential scanning calorimetry based approach for the estimation of thermal conductivity of polymer solids and melts. Poly. Eng. Sci., 1988, 28, 1038. 10. Sheldon, R. P. and Lane, S. K., Thermal conductivity of polymers 1: polyvinyl chloride. Polymer, 1965, 6, 77-83. 11. Sheldon, R. P. and Lane, S. K., Thermal conductivity of polymers 2: polyethylene. Polymer, 1965, 6, 205-212. 12. Fuller, T. R. and Fricke, A. L., Thermal conductivity of polymer melts. J. Appl. Poly. Sci., 1971, 15, 1729. 13. Cogswell, F. N., Thermoplastic Aromatic Polymer Composites. Butterworth Heinemann Ltd, 1992. 14. Tay, H. K., The mechanical properties of multiple-layer carbon fibre/PEEK laminates. M.Sc dissertation, University of Manchester, UMIST, 1993. 15. Brown, R. P., Handbook of Plastics Test Methods. George Godwin Ltd, New York, 1981. 16. RS components Ltd, Part 3: Mechanical Products and Tools. RS, 1996, pp. 32055. 17. Boenig, H. V., Structure and Properties of Polymers. Georg Thieme Publishers, Stuttgart, Chapter 7, 1973, pp. 191-192. 18. Hands, D., The thermal transport properties of polymers. Rubb. Chem. Tech., Vol., 1977, 50, 480.
Polymer Testing 16 (1997) 203-223 Copyright 0 1997 Elsevier Science Ltd Printed in Great Britain. All rights reserved
SO142-9418(96)00043-S
0142.9418/97/$17.00
ELSEVIER
TEST APPARATUS/MATERIAL PROPERTIES Measurement of Thermal Conductivity of Polymers using an Improved Lee’s Disc Apparatus N. Sombatsompop”sb
& A. K. Wood”,*
“Polymer Science and Technology Group, Manchester Materials Science Centre, University of Manchester and UMIST, Grosvenor Street, Manchester Ml 7HS, UK ‘Also at the Faculty of Energy and Materials, King Mongkut’s Institute of Technology Thonburi (KMITT), Bangkok 10140, Thailand (Received
7 June 1996; accepted 5 August 1996)
ABSTRACT An improved Lee’s Disc apparatus was designed and utilised to measure the thermal conductivity of various commercial polymers such as low-density polyethylene, polystyrene, polypropylene and poly(ether ether ketone) over a wide range of test temperatures from 40 to 400°C. The measurements were carried out under vacuum such that convective heat losses were minimised. It was found that the thermal conductivity of semi-crystalline polymers, below melting temperature (T,), was dependent on their density and degree of crystallinity and, above T,, on the chain mobility and degradation effects. The thermal conductivity of the amorphous polymer was dependent on mobility of polymer chains below the glass transition temperature (T,) and on the density above T,. The effect of density, degree of crystallinity and heating/cooling were also separately investigated and found to influence the thermal conductivity of the polymers used. 0 1997 Elsevier Science Ltd.
NOTATION the rate of flow of heat (W) the surface area across which the heat flows (m*) temperature (K) glass transition temperature (“C)
*To whom correspondence
should be addressed.
203
204
TlIl AT TP T, d KP
N. Sombatsompop,
A. K. Wood
melting temperature (“C) the temperature difference between the two surfaces (K) the temperature of the tested polymer (melt) (K) the temperature of the ceramic ring (K) the thickness of the slab (m) the thermal conductivity of the tested polymer (W m-l “C-1) the thermal conductivity of the ceramic ring (W m-l “C- -1 ) the cross-section area of the tested polymer (m2) the cross-section area of the ceramic ring (m2) current measured from the heater (A) voltage across the terminals (V) heat radiation coefficient of copper, 1.254 W rnp2 Kw4 density (g cmp3) heat radiation energy of the object i (W me2) area of surface of the object i (m2)
1 INTRODUCTION The thermal conductivity (K) of a material is essentially a constant of proportionality between the conductive heat flux and the temperature gradient driving the heat flux. Generally, the thermal conductivity of a typical polymer melt is quite low, around 10-l Wm-’ K-i, this being a thousand times less than most metals such as copper and aluminium.‘*2 The low thermal conductivity of polymer melts can generate a number of problems related to the processing of the materials such as non-uniform cooling and shrinkage, those causing frozen-in stress, shrink voids, warpage and melt instabilities. Knowledge of thermal conductivity enables engineers to design the machines, screw and dies in order to achieve the desired product. For instance the thermal conductivity can aid the assessment of heating and cooling rates and the development of temperature and velocity profiles for flowing polymer melts in a confined duct.3 The thermal conductivity of solid polymers and polymer melts depends on the molecular structure and is influenced by polar and non-polar groups, the degree of crystallinity, molecular orientation and other physical properties of the polymers. A number of techniques have been used to determine the thermal conductivity of polymers, these being the Hot-Line method,4,5 GuardedHot-Plate,6*7 Lee’s Disc method8 and the DSC.g Due to difficulties in controlling the test conditions such as the contact area between the polymer and the apparatus (thermal contact resistance), heat losses and the accuracy of temperature measurements, significant errors occur in the values of thermal
Measurement of polymers using Lee’s Disc apparatus
205
conductivity obtained. These techniques also present difficulties in terms of sample preparation and polymer degradation, for example in the Hot-Line method it is necessary to use a new wire for each experiment. Sheldon and Lane’OJ l used a cylindrical cell technique based on Fourier’s equation for steady-state conditions and obtained some useful information about the change in thermal conductivity of amorphous and crystalline polymers with temperature, over a range of 15-98”C, and density. They explained the variation of the thermal conductivity in terms of the change in the level of crystallinity with temperature and the additives in the polymer. Kline6 reported the thermal conductivity of amorphous and crystalline polymers and showed that the thermal conductivity of the polymers changed significantly at the glass transition and the melting temperatures due to the greater mobility of the polymer molecules. Yue et ~1.’ investigated the thermal conductivity of low density polyethylene melts between 130 and 240°C using the Lee’s Disc method and found that in this temperature range the thermal conductivity increased slightly with increasing temperature. They related this phenomenon to the increased segmental mobility of the polymer chains, this effect being greater than that resulting from the reduction in density. This result was in good agreement with that of Fuller and Fricke12 who used a concentric cylinder cell method and also suggested that the thermal conductivity decreased with increased complexity of the polymer structure. However they showed that errors in determining wall temperature, measuring total heat input and the presence of radiant heat transfer were significant. Underwood and Taylor’ used the Hot-Line technique to determine the thermal conductivity of various polymers by concentrating on time measuring corrections. In addition, they also indicated that different results could be obtained when using different types of thermocouple. Lobo and Cohen5 utilised the same method to measure the thermal conductivity of various polymers over a temperature range from room temperature to 200°C. Their work indicated that a higher degree of crystallinity results in larger values of thermal conductivity and that, except at the melting and glass transition temperatures, there appeared to be no major variation in thermal conductivity with temperature. Data concerning the thermal conductivity has been of great significance in recent investigations regarding polymer processing such as temperature and velocity profile measurements, heat transfer studies3 polymer degradation and stabilisation, the investigation of cooling and heating processes in injection moulding3 and the thermoplastic insulating industry. However, the thermal conductivity data available has been found to be limited, in particular few attempts have been made to measure the thermal conductivity of polymer melts at temperature above 300°C and the effect of heating and cooling on the measurement of thermal conductivity is still unclear. In addition, a number of the techniques and apparatus used to generate the existing data seem to
N. Sombatsompop,
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give results with significant errors due to the thermal contact resistance and heat losses as mentioned above. The current work investigated the thermal conductivity as a function of test temperature for several commercial polymers, these including low-density polyethylene, polystyrene, polypropylene and poly(ether ether ketone) (PEEK) using an improved Lee’s Disc apparatus. A variety of different test conditions were used. These include sample form, effect of cooling and heating, polymer density and degree of crystallinity. One of the purposes of this investigation was to measure the thermal conductivity of various commercial polymers at exceptionally high temperatures. For example PEEK has a very high glass transition and melting temperature, these being about 143 and 334°C respectively l5 PEEK is normally processed at temperatures of around 360400°C.13914The apparatus used in this work was specially designed and manufactured such that the thermal conductivity of materials could be determined over a wide range of test temperatures, from 40 to 400°C, with the minimum thermal contact resistance, heat losses and accuracy in measuring gradients and total heat input. In addition, an experimental model’ for deriving the thermal conductivity was also reviewed and the results generated were then compared with existing results from the literature.
2 EXPERIMENTAL 2.1 Raw materials
and sample preparation
Four commercial polymers, a low-density polyethylene (LDPE, Exxon Chemical (Belgium) Ltd, LDlOOBW), polystyrene (PS, LACQRENE, 1540/l), polypropylene (PP, MOPLEN 3400MNl) and PEEK, (15OP, without carbon fibre) and APC-2 (with 61% by volume of carbon fibre, ICI) were used. The specimens were prepared in the form of a disc, 70 mm in diameter and 1 mm thick, by compression moulding. The temperatures and pressures used for the compression moulding were based on thermal data obtained using differential scanning calorimetry (DSC) and given in Table 1. Table 2 shows density and crystallinity data for five samples of low-density polyethylene (LDlOOBW). The variation in density and crystallinity was achieved by: (1) Compression moulding the polymer at 5000 kPa and 160°C for 2 min. (2) Cooling the melt to 105°C. (3) Holding the melt at this temperature for a time period varying from 0 to 360 min. (4) Crash cooling the material to room temperature using water at the end of this time period.
Measurement of polymers using Lee’s Disc apparatus
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TABLE 1 Compression moulding conditions for sample preparation Polymers
Density
T, or T, (“C)
Compression conditions
(g cm-9 Pressure (kPa)
Temperature f”C)
LDPE PS PP PEEK (without CF*) PEEK (with CF)
0.91 1.05 0.92 1.44 1.60
112 97 152 344 341
150 5000 150 5000 185 5000 400 5000 Supplied in sheet form
* Carbon fibre.
Data for low-density polyethylene Sample name
A B C D
TABLE 2 (LDlOOBW) as a function of crystallisation
Crystallisation times (min)
Density at 23°C
0 120 240 360
0.911 0.918 0.925 0.929
time at 110°C
Crystallinity level (%)
tg cm--‘)
34.0 40.2 44.0 46.9
The Pycnometer (Method B of IS0 RI 183) and wide-angle X-ray scattering (WAXS) techniques were employed to measure the density and degree of crystallinity of the polymers, respectively. The accuracy of determining the density and degree of crystallinity was estimated to be f2.5% and f3% respectively. 2.2 Experimental design and apparatus Figure 1 shows the arrangement of the Lee’s Disc apparatus designed and manufactured for this work. Discs A, B and C were made from copper. A cast aluminium heater was placed between discs A and B. The total power consumed by the heater, this being the rate of energy input to the apparatus, was measured using a power meter via a temperature controller. In order to measure the thermal conductivity of a polymer melt, a housing ring, made from ceramic material with thermal conductivity of 1.45 W m-r”C-1,16 was used to retain the sample in the position between discs B and C. The temperature of each of the copper discs and the ambient temperature were measured
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using three platinum resistance sensors, the temperatures being displayed on a temperature indicator. The error in the temperature measurement was f2%. One of the problems of thermal conductivity measurement when using the Lee’s Discs technique at elevated temperature is convective heat losses to the surrounding atmosphere, this results in variations in the thermal conductivity determined. The apparatus was therefore placed in a vacuum oven, the oven being evacuated during testing. The assembly of the apparatus involved the sequential positioning of all the components using three ceramic bars, 10 mm in diameter and 100 mm long, as shown in Fig. 1, these being removed after assembly. The ceramic bars were removed in order to minimise heat losses due to conduction. The apparatus was positioned on three ceramic pillars, 20 mm in diameter and 25 mm long, and clamped together using another ceramic rod, 20 mm in diameter and 25 mm long, this bar being tightened using a bolt. 2.3 Experimental procedure The apparatus and its components were arranged according to Fig. 1. Two samples, 1 mm thick, were inserted between discs B and C and the test rig was then placed in the vacuum oven, the oven being pumped down to 20 mm Hg. The heater was turned on, the temperature being controlled using the temperature controller. When the desired temperature was reached and the temperature of the various components of the apparatus had stabilised, the current and voltage across the heater were determined using the power meter. The temperature indicator was used to measure the temperatures of the copper discs. The thermal conductivity was calculated using eqn (6), shown in Section 2.4.8 The test temperature was then altered, further measurements being taken once the temperature of the components of the apparatus had stabilised. 2.4 Experimental study and modelling of thermal conductivity measurement The thermal conductivity is usually known and defined for steady state conditions by Fourier’s law of heat conduction in eqn (1): q = K.S.$
The thermal conductivity measured in this work was based on the heat supplied to the apparatus in the steady state, this being equal to the energy emitted from the exposed surfaces. The can be expressed in the form of:
Fig. 1. The experimental
TemperatureIndicator
Controller
~OSPHERIC
arrangement of the Lee’s Disc apparatus.
I
CONLMTa
9’
6
09
IV. Sombatsompop,
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q=
A. K. Wood
VI=CE,A;
(2)
The determination of thermal conductivity was based on eqn (1) and the assumptions made in previous work’ are that the temperature of the sample was the mean of those of discs B and C: all elements of the apparatus are at a uniform temperature and the heat through the sample and the ceramic ring is the sum of the heat emitted from disc C and half the heat emitted from the ring. The expression used to calculate the thermal conductivity was given as follows:
+ EPJP, 2
E
p
P
=
K.&.TJ + Wp.Sp.Tp)
PC
d
(3)
When a steady state is reached in the situation without and with a polymer sample, the heat supplied to the apparatus can be determined using eqns (4) and (5), respectively.
IpVp= EpnApa + EpxApx + EpbApb + EplApr+ EpPpc
(5)
where the subscripts refer to the element of apparatus (a, b and c for the copper discs, x for the heater and r for the ceramic ring). By combining eqns (3), (4) and (5), the thermal conductivity of the polymer sample can be determined as shown in eqn (6).
Kp
d L&V, = 2s,.(
- (E,a,
+ EprApx +
E,bA,,)+ E,P,,l
TP
(6) where the heat radiation of the coppers (E) can be obtained from eqn (7):
E=
c[&J4
(7)
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of polymers using Lee’s Disc apparatus
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3 RESULTS AND DISCUSSION 3.1 Thermal conductivity of low density polyethylene Figure 2 shows thermal conductivity of the LDPE tested using sample B (Table 2) over the temperature range 40-4OO”C, the value being between 0.209-0.269 W m-l OC-‘. The accuracy of the determination is estimated to be f2.5%. The data can be observed to be composed of four regions over the range of temperature tested. In region (a) the thermal conductivity gradually decreases from 0.245 to 0.235 W m-l ‘C-l due to a reduction in the density of the polymer with increasing temperature. In region (b) it was found that the conductivity of the polymer dropped sharply from 0.235 to 0.215 W m-’ ‘C-l. This was associated with the destruction of crystallites in the solidmolten transition range and results in an increase in free volume.i7 The increase in free volume increases the distance between the polymer chains and thus increases the resistance to energy transfer between the polymer molecules. The thermal conductivity of the LDPE progressively increases in region (c) as the temperature increases due to the increasing segmental mobility of the polymer molecules. This effect is believed to be more dominant than the density effect in this region, this view being supported by previous workers.8,‘2 Finally, the conductivity falls from 0.259 to 0.223 W rn-’ ‘C-’ in region (d) as the temperature increases up to 300°C. This may be due to possible crosslinking and degradation effects which are indicated by the DSC curve as shown in Fig. 3. An exothermic peak started to occur between 320 and 375°C this peak indicating the crosslinking and degradation of the polymer. The degradation and crosslinking processes are exothermic and so the simple energy balance assumed in the analysis of the data obtained on the apparatus no longer exists. The temperature of the molten sample will probably be higher than that assumed in the analysis, that it is half the sum of the temperatures of plates B and C. Thus the thermal gradient will be reduced, to some extent, related to the rate of degradation and so the rate of heat conduction through the polymer will be reduced as will the corresponding value of thermal conductivity. 3.2 Effect of prepared sample form on thermal conductivity measurements In Section 3.1 it was mentioned that the contact area between the polymer sample and the copper surface influenced the thermal conductivity values obtained. Therefore, an experiment was carried out to measure the conductivity using two samples of LDPE; one, prepared by compression moulding, in sheet form and the other being in a granular form. The results are shown
0.19
0.27
0.29
0
100
Fig. 2. Thermal conductivity
50
in low density
150
LDlOOBW,
(“C)
Temperature
polyethylene,
250
200
as a function
300
Regibn
400
of temperature.
350
D
450
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in Fig. 4. It was found that the conductivity of compression moulded sample was higher than that of granular system by about 11% over the temperature range 40-120°C and by about 2% beyond 120°C. The reduced contact area found in the case of the packed granular system, produced a reduction in the heat transfer and thus an apparent reduction in the thermal conductivity. Above 12OT, the polymer is molten and it can be seen that the values of thermal conductivity obtained are very similar, within the limits of experimental error, with those obtained using the compression moulded sample. The granules clearly melted and fused to give an air-free molten mass of the same form as that produced when the compression moulded sample melted. 3.3 Thermal conductivity influenced by density and level of crystallinity Four samples with different densities and degrees of crystallinity prepared as indicated in Section 2.1 were used to determine the thermal conductivity as a function of test temperature from 40-250°C the results being shown in Fig. 5. It was found that at 40°C the data for the polymer samples with the different degrees of crystallinity are very close together and are within the limits of experimental error. It is therefore, difficult to determine whether or not the degree of crystallinity affects the thermal conductivity other than that any such effects are small. Similarly at 140°C the data is within the limits of experimental error, no differences between the samples being expected as the samples will have completely melted. It is interesting to note that the differences occurred in the melting temperature region, the fall in thermal conductivity being less pronounced for the higher original degree of crystallisation. 3.4 Effect of heating and cooling processes on the measurement In practice, polymer processing involves heating the materials, deforming and shaping and cooling them down in order to obtain a desirable product. The physical properties of the product are very dependent on the thermal-history during processing. Work was carried out, using compression moulded samples of LDlOOBW, to investigate the effect of thermal-history, heating and cooling processes, on thermal conductivity values. Figure 6 shows the thermal conductivity measured using the same sample at three conditions, these being (a) heating the sample from 100 to 225’C, (b) cooling down to 1OO’C and (c) re-heating to 225°C. The results show that there are differences between these conditions. It is thought that the observed effects may arise for two reasons. Firstly in the solid state, due to the cooling regime imposed the degree of crystallinity of the sample cooled in the apparatus is likely to be higher than
Measurement of polymers using Lee‘s Disc apparatus
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N. Sombatsompop, A. K. Wood
a
0
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218
N. Sombatsompop, A. K. Wood
that found in the original. Whilst the previous evidence above suggests that the degree of crystallinity has a limited effect, the degree of crystallinity found in this case may be significantly higher than that in the case above due to the slow cooling. The second reason arises due to the requirement to have an initial sample which is slightly thicker than the height of the ledge on the spacing ring in order to ensure good thermal contact between the polymer and the copper discs. As the polymer sample is heated it melts and expands and this expansion leads to a limited, small amount of leakage out of the gap between the copper discs. On cooling, as the melt contracts, the thickness of the sample will become smaller, this giving rise to an apparent small increase in thermal conductivity. Similarly in the solid state, due to the higher degree of crystallinity following cooling, the specimen thickness is likely to be less than that of the original specimen and so the apparent thermal conductivity will be higher. Table 3 shows the degrees of crystallinity of the LDlOOBW before and after experiencing the heating and cooling stages, these values being determined using the WAXS method. It was found that the degree of crystallinity after the heating-cooling stage is higher than that prior to the initial heating stage. However, in the early stage of re-heating the thermal conductivities are close to those of the cooling path and a difference starts to appear at higher temperature (about 6% compared to cooling stage and 16% compared to the initial heating stage). This arises because of the change in polymer density and the effect of mobility of polymer chains. In addition, it is interesting to note that the difference in the values of thermal conductivity between the initial heating and cooling stages was more pronounced than that in the values of thermal conductivity between the cooling and re-heating stages. 3.5 Dependence of polymer molecular structure on thermal conductivity Figure 7 shows a comparison of the thermal conductivity values of polyethylene, as mentioned in Section 3.1, with other commercial thermoplastics such as polypropylene and polystyrene over the temperature range of 40-300°C. The thermal conductivity of the PP is less than that of the LDPE over the
Degree of crystallinity
TABLE 3 of LDPE before and after heating and cooling stages
Sample
Degree of crystallinity (%)
Before measuring (unprocessed polymer) After measuring (after the heating and cooling)
34.0 44.8
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whole temperature range tested. This may be due to differences in molecular structure and subsequently the energy transfer along and between the molecules. The thermal conductivity of the PP decreases as the temperature increases, the trend being similar to that of the LDPE up to their melting temperatures (152°C for the PP). In the case of the PP the thermal conductivity beyond the melting point is fairly stable. The results obtained were in good agreement with the work carried out by Lobo and Cohen5 and Boenig.17 PS, an amorphous polymer, with a glass transition temperature of around 97”C, had the lowest thermal conductivity when compared to the LDPE and PP. According to Fuller and Fricke this is due to the more complex structure of the PS molecule.” It can be seen that the thermal conductivity of PS increases up to around lOO”C, this being close to its Tg. This increase is because of the increased molecular movement in glassy state as the temperature increases and hence so does the intermolecular energy transfer.17*18Above the Tg the free volume increases more rapidly, which results in increased molecular separation and thus the energy transfer is poorer, with the thermal conductivity gradually falling. Figure 8 shows the thermal conductivity as a function of temperature of the PEEK with and without 61% by volume of carbon fibre as a function of test temperature. It was found that the thermal conductivity of the sample without carbon fibre appears to be independent of temperature up to 250°C test temperature, the average value being 0.219 W m- ’ ‘C-l. Above this temperature, the thermal conductivity increases from 0.226 to 0.262 W m-l OC-l from 250°C up to 400°C. This is due to the increased segmental mobility of the polymer chains. The molecular structure of PEEK is more complex than for polymers such as PP and PS and its thermal conductivity is higher. This is due to the PEEK molecules being stiff due to the ring structures in the backbone of the polymer as compared to polystyrene whose ring structures are pendant. This leads to more efficient energy transfer along the polymer chains. For carbon fibre reinforced PEEK, the thermal conductivity measured in the transverse direction to the fibre orientation is strongly affected by temperature, the conductivity progressively increasing with test temperature. The results show that the thermal conductivity increases from 0.468 W m-i ‘C-l to 0.804 W m-l OC-’ over the temperature range of 40-4OO”C as indicated in Fig. 8. The values of thermal conductivity are lOO-300% higher than that found with the PEEK without carbon fibre. It can be concluded here that thermal conductivity of PEEK is dramatically influenced by the presence of carbon fibre.
Measurement of polymers using Lee’s Disc apparatus
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I I
v
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4 CONCLUSIONS
(1) The improved Lee’s Disc apparatus designed in this work was found to be a reliable and accurate technique for the determination of the thermal conductivity of various polymers over the temperature range of 40400°C. The results obtained for the thermal conductivity were as follows: (a) 0.2094.269 W m-l “C-l for low density polyethylene between 40 and 400°C; (b) 0.185-0.215 W m-l ‘C-l for polypropylene between 40 and 300°C; (c) 0.147-0.185 W m-l ‘C-l for polystyrene between 40 and 300°C; (d) 0.213-0.262 W m-l ‘C-l for PEEK without carbon fibre between 40 and 400°C; (e) 0.4684.804 W m-l ‘C-l for PEEK with 61% by volume of carbon fibre between 40 and 400°C. It was found that the thermal conductivity of the polymers was influ(2) enced by density, level of crystallinity, polymer molecular structure, thermal contact resistance and thermal-history of the polymers tested. (3) The effect of polymer density seemed to be more pronounced on the determination of thermal conductivity below the melting temperature whereas the segmental mobility of polymer chains had a greater effect above the melting point in the semi-crystalline polymers. This phenomenon was found to be opposite when testing the amorphous polymer.
REFERENCES 1. Rental, C., Polymer Extrusion. Hanser Publisher, New York, 1990. 2. Yue, M. Z., Investigation of melt temperature profiles and shear heating effects in polymer processing. Ph.D Thesis, University of Manchester, UMIST, 1994. 3. Sombatsompop, N. and Wood, A. K., Effect of processing variables in the velocity and temperature profiles of flowing polymer melts in the injection moulding process. In ASME Fluids Engineering Conference Forum on Flow Measurements and Instrumentation, FED-Vol. 239(4), San Diego, California, 1996, pp. 385390. 4. Underwood, W. M. and Taylor, J. R., The thermal conductivity of several plastics determined by an improved line-source apparatus. Poly. Eng. Sci., 1978, N(7), 558. 5. Lobo, H. and Cohen, C., Measurement of thermal conductivity of polymer melts by the line-source method. Poly. Eng. Sci., 1990, 30(2), 65. 6. Kline, D. E., Thermal conductivity studies of polymers. J. Poly. Sci., 1961, L,
441.
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7. Foreman, P. J., SPE ANTEC’92 Tech. Papers, 1125, 1992.
8. Yue, M. Z., Wood, A. K. and El-Rafey, E., Thermophysical characterization of polyethylene. J. Appl. Poly. Sci., 1994, 55, 105. 9. Khanna, Y. P., Taylor, T. J. and Chomyn, G., A new differential scanning calorimetry based approach for the estimation of thermal conductivity of polymer solids and melts. Poly. Eng. Sci., 1988, 28, 1038. 10. Sheldon, R. P. and Lane, S. K., Thermal conductivity of polymers 1: polyvinyl chloride. Polymer, 1965, 6, 77-83. 11. Sheldon, R. P. and Lane, S. K., Thermal conductivity of polymers 2: polyethylene. Polymer, 1965, 6, 205-212. 12. Fuller, T. R. and Fricke, A. L., Thermal conductivity of polymer melts. J. Appl. Poly. Sci., 1971, 15, 1729. 13. Cogswell, F. N., Thermoplastic Aromatic Polymer Composites. Butterworth Heinemann Ltd, 1992. 14. Tay, H. K., The mechanical properties of multiple-layer carbon fibre/PEEK laminates. M.Sc dissertation, University of Manchester, UMIST, 1993. 15. Brown, R. P., Handbook of Plastics Test Methods. George Godwin Ltd, New York, 1981. 16. RS components Ltd, Part 3: Mechanical Products and Tools. RS, 1996, pp. 32055. 17. Boenig, H. V., Structure and Properties of Polymers. Georg Thieme Publishers, Stuttgart, Chapter 7, 1973, pp. 191-192. 18. Hands, D., The thermal transport properties of polymers. Rubb. Chem. Tech., Vol., 1977, 50, 480.