Thermal conductivity behaviour of polymers around glass transition and crystalline melting temperatures

Accepted Manuscript Thermal conductivity behaviour of polymers around glass transition and crystalline melting temperatures W.N. dos Santos, J.A. de Sousa, R. Gregorio PII:

S0142-9418(13)00104-9

DOI:

10.1016/j.polymertesting.2013.05.007

Reference:

POTE 4062

To appear in:

Polymer Testing

Received Date: 9 April 2013 Accepted Date: 16 May 2013

Please cite this article as: W.N. dos Santos, J.A. de Sousa, R. Gregorio Jr., Thermal conductivity behaviour of polymers around glass transition and crystalline melting temperatures, Polymer Testing (2013), doi: 10.1016/j.polymertesting.2013.05.007. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Material Behaviour THERMAL CONDUCTIVITY BEHAVIOUR OF POLYMERS AROUND GLASS TRANSITION AND CRYSTALLINE MELTING TEMPERATURES

Department of Materials Engineering Federal University of São Carlos

RI PT

W. N. dos Santos*, J. A. de Sousa, R. Gregorio Jr.

Rodovia Washington Luiz, Km 235,CP 676, São Carlos, CEP 13565-905, São Paulo, Brazil

[email protected] [email protected]

M AN U

ABSTRACT

SC

[email protected]

The thermal conductivity of five semi-crystalline and four amorphous polymers was determined within a wide range of temperature, starting at room temperature and going up to temperatures above the polymer melting point (Tm) for semi-crystalline polymers or above the glass transition temperature (Tg) for amorphous polymers. Two transient techniques were employed in the experimental investigation: the hot wire technique for the group of amorphous polymers, and the laser flash technique for the semicrystalline

TE D

polymers. As expected, the experimental results show that Tg exerts a measureable influence on the thermal conductivity of amorphous polymers. In the case of semicrystalline polymers, a singular behaviour of the thermal conductivity is observed within the Tm range. In order to explain the anomalous behaviour, the influence of these

EP

transition temperatures on the thermal conductivity behaviour with temperature has been analysed in terms of a phonon conduction process and temperature variations of

AC C

specific heat and modulus of elasticity of the analyzed polymers,. Keywords:

Thermal transition temperatures, thermal conductivity, phonons heat

conduction, hot wire and laser flash techniques.

ACCEPTED MANUSCRIPT

*Corresponding author. INTRODUCTION Modelling heat-energy transfer problems under steady state or transient conditions is of fundamental importance in engineering design as well as for tailoring of

RI PT

thermal and mechanical behaviour of materials. Thermal conductivity, diffusivity and specific heat capacity are three important thermo-physical properties of a material that

are needed for heat transfer calculations. Detailed knowledge of such properties becomes crucial in many situations when heat is added or removed from a material.

Thermal conductivity (k) is the property that determines the working

SC

temperature levels of a material, determining the temperature gradient inside this

material, and so it is an important parameter in problems involving steady state heat

M AN U

transfer. This property assumes a critical role in the performance of materials in high temperature applications. Low thermal conductivity values are required when the purpose is to minimize heat losses. On the other hand, when heat transfer from one site to another is desirable, materials with higher thermal conductivities must be chosen. Therefore, reliable thermal conductivity values are essential for material selection criteria in order to get the best performance of the material in a specific application. However, it is one of the physical quantities that is difficult to measure and requires

TE D

high precision in the determination of the parameters involved in its calculation. Moreover, many factors can affect the thermal conductivity of a material [1-3]: temperature, density, porosity, moisture, degree of crystallinity, orientation of grains, size of molecules, impurities, etc.

EP

Thermal diffusivity (α) is a measure of the rate of heat propagation through a material. It is an important property in all problems involving non-steady state heat

AC C

conduction. In the extrusion and injection moulding processes, knowledge of the precise values of both the thermal conductivity and diffusivity and their temperature dependence is essential for heat-energy transfer calculations in both heating and cooling cycles of polymer processing operations. In cooling operations, thermal conductivity variations can induce non-uniform cooling and shrinkage problems and, thereby, cause frozen-in stresses, delamination, shrink voids in extrudate profiles and injection mouldings [2, 3]. The specific heat (cp - heat capacity per unit mass) is a thermodynamic quantity that determines the amount of heat necessary to raise by one degree the temperature of a unit mass of a material and is, therefore, associated with the energy consumption in

ACCEPTED MANUSCRIPT

heating processes. In the polymer melting process, the value of cp increases substantially due to the fact that the high heat absorbed by the semi-crystalline material is used up as latent heat of fusion and does not contribute towards a temperature variation. The anomalous thermal conductivity variations verified for both crystalline and

RI PT

amorphous thermoplastics in the temperature range around both Tg and Tm of these polymers, although well documented in published polymer processing literature [1-3],

has seldom been analyzed in terms of the actual phonon heat conduction theory used for

ceramic materials [4]. Hence in this work, the influence of thermal transition temperatures (Tg and Tm) on the behaviour of the thermal conductivity with

SC

temperature is determined and analysed in terms of the phonon conduction process. The

thermal conductivity of five semi-crystalline and four amorphous polymers was

M AN U

determined within a wide range of temperature, starting at room temperature. Two transient techniques were employed in the experimental investigation: the hot wire technique for the group of amorphous polymers and the laser flash technique for the semicrystalline polymers. The reasons for the choice of these two distinct thermal measurement techniques is detailed in the experimental procedure section. THEORICAL CONSIDERATIONS

TE D

The equation relating the thermal conductivity (k, W/m K), thermal diffusivity (α, m2/s), specific heat at constant pressure (cp, J/kg K) and the bulk density (ρ, kg/m3) is given by:

(1)

EP

k = α ρ cp

Heat conduction in insulating solids (ceramics and polymers) may be considered either as the propagation of anharmonic elastic waves through a continuum or as the

AC C

interaction between quanta of thermal energy called phonons (lattice thermal conduction) [4]. At high temperatures, another mechanism of conduction must be considered: the photon conductivity. However, since this process of conduction is proportional to the fourth power of temperature, it is usually neglected at low temperatures (< 500 0C). For insulating solids, the thermal conductivity is proportional to the Cp and ρ of the material, and to the mean speed (v) and the mean free path (λ) of the phonons, according to the following equation [5]:

ACCEPTED MANUSCRIPT

1 k = ρ Cp v λ 3

(2)

For pure crystalline ceramic material, when temperature increases, specific heat also increases to an approximately constant value, and the phonons mean free path

RI PT

decreases, since it is proportional to T-1. For temperatures not so low (T > -2200C), the net effect is a decrease in the thermal conductivity. Experimental results indicate that,

for pure crystalline materials, the thermal conductivity may be represented by an equation of the form [4]:

A +B T

SC

k=

(3)

M AN U

where T is the absolute temperature and A and B are constants to be determined. The temperature dependent term is interpreted as the intrinsic thermal conductivity due to the Umklapp process (an anharmonic phonon-phonon scattering process), and the temperature independent term as conductivities due to the collective contribution of all point defect scattering terms [6]. The conductivity decreases with temperature increase because the anharmonic Umklapp process becomes more frequent, and hence the phonon mean free path decreases. Umklapp scattering is the dominant process for

TE D

thermal conductivity at high temperatures for low defect crystals. For amorphous ceramic materials, the mean free path may be considered approximately constant and, when temperature increases, thermal conductivity increases in proportion to the specific heat. In this case, the thermal conductivity may be

k = CT + D

(4)

AC C

EP

represented by an equation of the form [4]:

where C and D are also experimental constants to be determined, with the same

meaning of A and B given previously. If a material is a combination of crystalline and glassy phases, the temperature

dependence of the thermal conductivity may be represented by the equation [4]:

k=

1 AT + B +

C T

where A, B and C are also experimental constants to be determined.

(5)

ACCEPTED MANUSCRIPT

Although the previous equations are also valid for polymers, since phonons are mainly responsible for heat transfer, polymeric materials have some particularities which make the structure of such materials different from that of ceramic structures. The polymer thermal conductivity is also dependent on molecular weight distribution,

RI PT

crystallite orientation, degree of crystallinity, macromolecule size, thermo-mechanical history and other structural features [1-3]. The glass transition temperature (Tg), exerts a measureable influence on the thermal conductivity of amorphous polymers [7, 8]. This influence is experimentally hardly detectable for semicrystalline polymers. However,

within the melting temperature range.

M AN U

MATERIALS AND METHODS

SC

for this class of polymers, a singular behaviour of the thermal conductivity is observed

As stated before, two experimental techniques were employed in this work: the hot wire technique for the amorphous polymers and the laser flash technique for the semicrystalline polymers. Thermal conductivity results obtained by using both techniques are perfectly compatible for polymeric materials, and discrepancies verified lie within the accuracy of each technique, as reported elsewhere by the authors [9]. The hot wire technique permits direct measurement of thermal conductivity of

TE D

materials. However, due to larger sample (~1.5 kg) requirements for this test, the thermal equilibrium is achieved only after relatively long periods (~6 h) of polymer exposure to heat, and also the measurements are severely hampered in the melting temperature range of semicrystalline polymers. The high and rapid heat expansion of

EP

semicrystalline polymers in their melting temperature range aggravates the surface contact problem between the sample material and the thermal sensor and, thereby,

AC C

severely hampers the stability of the measurements being made in experimental runs of 10 to 15 minutes duration. Furthermore, restrictions due to economic or other technical aspects also restrict the use of this technique for some materials. However, the hot wire technique permits precise measurements of thermal conductivity variations in the temperature range around Tg of polymers. Details of the hot wire technique and samples preparation were given in many occasions elsewhere [10 - 13]. In the laser flash technique, the use of much smaller samples (~50 mg) simplifies sample preparation, and the thermal equilibrium is quickly attained (1-2 min), permitting measurements both in the solid and molten states and even in the narrow crystalline melting interval of semicrystalline polymers. However, this technique

ACCEPTED MANUSCRIPT

measures the thermal diffusivity and not the thermal conductivity, which can then be derived from equation (1) shown earlier, provided that the specific heat and density data of the sample are also determined as a function of temperature. Details of the laser flash technique and sample preparation were given on many occasions elsewhere [14 - 17].

RI PT

In this work, the hot wire technique was adopted for the amorphous polymers and the thermal conductivity was directly determined in the temperature interval starting from room temperature and going up to temperatures above the Tg of the analyzed polymers. In the case of the semicrystalline polymers, the laser flash technique was

utilized to determine the thermal diffusivity, starting from room temperature up to

SC

temperatures above the crystalline melting point of these materials. The thermal conductivity data was then derived using the experimental values of both the polymer

M AN U

density and specific heat as a function of temperature.

The specific heat dependence with temperature was determined by modulated differential scanning calorimetry (DSC- Q100, TA Instruments) according to ASTM E 1269-90 and with a heating rate of 5 oC/min. The glass transition Tg and Tm (crystalline melting endotherm maximum) temperatures along with the percentage degree of crystallinity of the semicrystalline polymers were determined by DSC according to ASTM D3418 with a heating rate of 10 oC/min. The density at room temperature was

TE D

determined by picnometry using ethanol, according to ASTM D 792, and its dependence with temperature was evaluated by using the thermal expansion coefficient. Samples were prepared in the shape of discs, 10 mm in diameter and 0.3 to 1 mm in thickness for the laser pulse technique. For the hot wire technique, the samples were

EP

prepared through extrusion starting from powder or pellets of the solid polymer, using a special mould of stainless steel with inner dimensions of 220x100x65 mm in the shape Before each measurement, a dwell time at each

AC C

of a rectangular parallelepiped.

temperature is required in order to get the thermal equilibrium: ∼6 hours for the hot wire

technique (large samples) and 1-2 minutes for the laser flash technique (small samples). In both techniques, the thermal property measurements were carried out in the heating mode.

RESULTS AND DISCUSSIONS Table 1 displays the polymer sample details along with the data on glass transition (Tg) and crystalline melting point (Tm – crystalline melting endotherm

ACCEPTED MANUSCRIPT

maximum) and the percentage degree of crystallinity of the semi-crystalline polymers as determined by DSC.

RI PT

Table 1

Figures 1 to 5 show, respectively, the results obtained for the group of semicrystalline polymers studied: high density polyethylene (HDPE), low density polyethylene (LDPE), polypropylene (PP), nylon 6 (PA6) and polyvinylidene fluoride

SC

(PVDF). The traced vertical lines were included in the figures in order to indicate the

M AN U

crystalline melting temperature interval defined by DSC analysis.

Figures 1 to 5

Figure 6 shows the experimental results obtained for the group of amorphous polymers studied: polymethylmethacrilate (PMMA), high impact polystyrene (HIPS), crystal polystyrene (PS) and polycarbonate (PC). In these figures, the Tg values

TE D

obtained from DSC analysis are also indicated by arrows.

Figure 6

For the group of semi-crystalline polymers (Figures 1 to 5), the thermal

EP

conductivity displays a smooth decrease as temperature rises, from room temperature up to the beginning of the melting process, as predicted by equation (5). This behavior may

AC C

be explained using equation (2), in terms of two mechanisms of opposite effects: the specific heat increases slightly when temperature rises, but the thermal diffusivity reduces due to the decrease in the phonon mean free path. The reduction in the polymer density (bulk density) with temperature also contributes to k values reduction. The net effect of these mechanisms is a smooth decrease of the thermal conductivity with temperature rise, except for PA6. In this case, the steeper slope of cp curve with increasing temperature contributes towards a slight rise in k values. In the beginning of the melting process, the thermal conductivity exhibits an abrupt increase as temperature rises; reaches a maximum and then decreases, following the behaviour of the specific heat within the melting temperature interval.

ACCEPTED MANUSCRIPT

For the amorphous polymers, (Figure 6) the dependence of the thermal conductivity with temperature is quite different from that foreseen by equation (4) for amorphous ceramic materials. The glass transition temperature exerts a detectable influence on the thermal conductivity behaviour with temperature, and two distinct

RI PT

regions may be considered: in the glassy state before Tg and in the rubbery state after Tg. In the glassy state region, the thermal conductivity increases with temperature as predicted by equation (4). This is due to the specific heat increase effect, since phonon mean free path is considered practically constant with temperature for amorphous materials. Starting in the rubbery region, an abrupt decrease of the thermal conductivity

SC

is observed. As a result, a peak is attained close to the Tg. This sudden drop may be

explained in terms of molecular mobility, since in the temperature interval in the

M AN U

neighborhood of Tg the polymer passes from a rigid and brittle glassy state to the soft rubbery state. In the rubbery state, the large-scale mobility of atoms and macromolecules increases and chain segments undergo intensive thermal motion and torsional rotations. This disorder introduced in the material structure contributes to the scattering center phonons and, thereby, decreasing the thermal conductivity. A sudden drop of the thermal diffusivity of amorphous PET in Tg's region was also observed by

as follows.

TE D

Chen et al using the flash method [18]. Physically, this phenomenon may be explained

For amorphous materials, the phonon mean free path is practically independent of the temperature. When the lateral dimensions are much less than the wavelength, an extensional wave is propagated and the phonon mean speed (v) is proportional to the

AC C

i.e.:

EP

square root of the ratio of the elasticity modulus (E) and the bulk density of the material,

v∝

E ρ

(6)

Although the density decreases with temperature rise, the elasticity modulus experiences a sudden and intense drop above Tg, as shown schematically in Figure 7. This figure displays the sudden drop of E after the Tg for semi-crystalline and amorphous polymers. This sudden drop in E is much more pronounced (2-3 orders of magnitude) in amorphous than in semi-crystalline polymers. The net effect is a decrease in the phonon speed, which according to equation (2) leads to a corresponding decrease

ACCEPTED MANUSCRIPT

in the thermal conductivity. After this sudden drop, the thermal conductivity displays a smooth variation with temperature, as shown in Figure 6.

RI PT

Figure 7

The much higher thermal conductivity values observed for PC in Figure 6, in comparison to those of other amorphous polymers, is probably due to the fact that PC

exhibits high molecular stiffness below Tg, with the presence of two p-phenylene groups in its macromolecular skeleton, and thus contributing towards higher phonon

SC

conduction [19]. It is also possible to observe in Figure 6 that the sudden drop in

thermal conductivity for PMMA takes place at around 86 ºC, which is considerably

M AN U

lower than the temperature verified for the Tg of this polymer, as determined by the conventional calorimetric technique (112 ºC). This fact may be explained having in mind the long dwell time (up to 6h) before each measurement of thermal conductivity in order to get the thermal equilibrium in the hot wire test. After this elapsed time, part of the polymeric mass would reach the rubbery state, even at a temperature below the classical Tg, resulting in a decrease of the thermal conductivity. In order to confirm this hypothesis, two DSC runs with the PMMA samples are provided in Figure 8. Initially,

TE D

the sample (8 mg) remained at 86 ºC for a short dwell time of 5 minutes and was then heated up to 140 ºC, as shown on Figure 8 (2nd heating run). This curve was then compared to the one obtained in the determination of Tg, from room temperature up to

Figure 8

AC C

EP

140 ºC (1st heating run). In both cases the heating rate was 10 ºC/min.

It is evident from Figure 8 that the variation of the base line decreased after

PMMA sample was held at 86 ºC for five minutes. This behavior is an indication that part of the polymeric mass had already attained the rubbery state. As a consequence, a drop in its thermal conductivity is observed at this temperature, several degrees before the Tg value determined by DSC. This fact may be explained having in mind that the conventional Tg is a kinetic (rate-dependent) manifestation of an underlying thermodynamic phenomenon, and corresponds to the temperature at which the forces that keep the connected chain segments of a solid polymer are overcome by the thermally induced movement within the experimental time scale. Hence, the value of

ACCEPTED MANUSCRIPT

such a property depends on the heating rate and the time that the material remains at a fixed constant temperature. Figure 8 shows that, for PMMA, the actual glass transition temperature in the hot wire thermal conductivity technique is attained at around 86 0C, and not at 112 0C as determined by the classical differential scanning calorimetry, as

RI PT

shown in Table 1. For the other amorphous polymers, this behavior was not detected. The variation of the base line remains approximately constant even when such a

material remained for a time time below its classical Tg value, which indicates that this

time interval was not enough to lead the polymer to a rubbery state. This difference in the behaviour between amorphous polymers is associated with the type and stiffness of

SC

each structure. The effects of number-average molecular weight, chain stiffness and

M AN U

cohesive forces on the value of Tg are different from each other.

CONCLUSIONS

The glass transition temperature exerts a noticeable influence on the thermal conductivity of amorphous polymers, exhibiting a peak around this temperature. This effect is hardly detectable for semi-crystalline polymers, since only the amorphous phase is responsible for this behaviour, and the crystalline phase overrides this influence. However, for semi-crystalline polymers, the specific heat introduces a

TE D

singular behaviour on the thermal conductivity temperature dependence in the temperature range of the polymer melting. This singular behavior of the thermal conductivity around the crystalline melting temperature can be attributed to the specific heat variation of semi-crystalline polymers. The thermal conductivity variations

EP

registered around Tg of amorphous polymers can be explained by considering the

AC C

reduction in the phonons velocity above this glass transition temperature.

ACKNOWLEDGEMENTS The authors acknowledge to FAPESP (Proc. 2011/02943-4) for the financial

support and to Prof. Elias Hage Jr. for the valuable discussions.

REFERENCES 1. H. Lobo. Thermal conductivity and diffusivity of polymers. Handbook of Plastics Analysis, Marcel Dekker Inc. 2003. 2. C. Rauwendaal. Polymer extrusion, Carl Hanser Verlag. 2001.

ACCEPTED MANUSCRIPT

3. D. G. Baird and D. I. Collias. Polymer processing – principles and design. WileyInterScience Publi. 1998. 4. W.D. Kingery and M.C. McQuarrie. Thermal conductivity: I - concepts of measurement and factors affecting thermal conductivity of ceramic materials. Journal of

RI PT

the American Ceramic Society 1954; 37 (2): 67. 5. W.D. Kingery, H.K. Bowen and D.R. Uhlmann. Introduction to ceramics. 2nd ed. John Wiley & Sons. 1976.

6. W.N. dos Santos, R. Taylor. Effect of porosity on the thermal conductivity of alumina. High Temperatures-High Pressure 1993; 25:89.

SC

7. A.B. Bashirov and T.D. Shermergor. Mekhanika polimerov 1976; 3, 5538. 8. P. Dashora and G. Gupta. Polymer 1996; 37(2): 231.

M AN U

9. W.N. dos Santos, J.N. dos Santos, P. Mummery, A. Wallwork. Thermal diffusivity of polymers by modified Angström method. Polymer Testing 2010; 29: 107. 10. A.L. Schieirmacher, Wiedemann. Ann Phys. 1888; 34: 38.

11. E.F.M. Van Der Held, F.G. Van Drunen. A method of measuring the thermal conductivity of liquids. Physics, 1949; 15(10):865.

12. W.N. dos Santos. O método do fio quente: técnica em paralelo e técnica de superfície. Cerâmica 2002; 48(306):86.

TE D

13. W.N. dos Santos, Thermal properties of melt polymers by the hot wire technique. Polymer Testing 2005; 24, (7): 932.

14. W.J. Parker, R.J. Jenkins, C.P. Butter, G.L. Abbot. Flash method of determining

1679.

EP

thermal diffusivity, heat capacity, and thermal conductivity. J. Appl. Phys. 1961; 32:

15. W.N dos Santos, P. Mummery, A. Wallwork. Thermal diffusivity of polymers by

AC C

the laser flash technique. Polym. Test.2005; 24 (5): 628. 16. C. Y. Iguchi, W.N. dos Santos, R. Gregorio Jr. Determination of thermal properties of pyroelectric polymers, copolymers and blends by the laser flash technique . Polym. Test 2007; 26 (2):788. 17. W. N. dos Santos, C. Y. Iguchi; R. Gregorio Jr. Thermal properties of the poly(vinilidene fluoride) in temperature range from 25 to 210oC. Polym. Test. 2008; 27:204. 18. F. C. Chen, Y. M. Poon, C. L. Choy. Thermal diffusivity of polymers by flash method. Polymer 1977; 18: 129. 19. J. A. Brydson. Plastics materials. 7th ed. Butterworth public.1999.

ACCEPTED MANUSCRIPT

Table 1. Polymer samples details with their respective properties.

HDPE

Braskem

HI760UV

Crystalline melting temperature Tm (oC) 136

LDPE

Braskem

PB608

103

PP

Braskem

H503

163

Nylon-6

BASF

Ultramid 8200HS

223

PVDF

Atochem

F4000HD

169

PMMA

Unigel

Acrigel

-

HIPS

BASF

PS495F

-

PS

BASF

PS145D

-

PC

Sabic

Lexan grade

Glass transition temperature Tg (oC) -135

60 28

-18

38

47

30

-35

49

112

-

93

-

90

-

145

-

SC

-125

M AN U

TE D EP AC C

-

Crystallinity (%)

RI PT

Resin Supplier

Code

Material

ACCEPTED MANUSCRIPT

Figure Captions

Figure 1. Specific heat, thermal diffusivity and thermal conductivity as a function of temperature for HDPE.

RI PT

Figure 2. Specific heat, thermal diffusivity and thermal conductivity as a function of temperature for LDPE.

Figure 3. Specific heat, thermal diffusivity and thermal conductivity as a function of temperature for PP.

Figure 4. Specific heat, thermal diffusivity and thermal conductivity as a function of

SC

temperature for PA6.

Figure 5. Specific heat, thermal diffusivity and thermal conductivity as a function of

M AN U

temperature for PVDF.

Figure 6. Thermal conductivity as a function of temperature for PS, PC, PMMA and HIPS (the arrows indicate the Tg values for each one of the polymers). Figure 7. Schematic variation of modulus of elasticity as a function of temperature for semicrystalline and amorphous polymers.

Figure 8. DSC curves for PMMA: heating rate 10 ºC/min; 2nd heating after the specimen

AC C

EP

TE D

remained for 5 minutes at 86 ºC.

ACCEPTED MANUSCRIPT

Figure 1

20000

15000

10000

5000

0 25

50

75

100

125

150

175

200

0

Temperature ( C)

-7

2

Thermal Diffusivity (x10 m /s)

HDPE 2.5

2.0

1.5

1.0

0.5 25

50

75

100

125

150

175

200

M AN U

3.0

225

250

0

EP

1.5

1.0

0.5

0.0

AC C

Thermal Conductivity (W/mK)

HDPE 2.0

TE D

Temperature ( C) 2.5

25

50

75

100

125

150 0

Temperature ( C)

175

SC

Specific Heat (J/kgK)

RI PT

HDPE

25000

200

225

ACCEPTED MANUSCRIPT

Figure 2

5000 4000

3000 2000

1000 40

60

80

100

120

140

160

180

200

0

LDPE

-7

2

Thermal Diffusivity (x10 m /s)

1.6 1.4 1.2 1.0 0.8 0.6 25

50

75

100

125

150

175

0

0.4

LDPE

0.3

0.2

0.1

0.0 25

50

EP

Thermal Conductivity (W/mK)

200

TE D

Temperature ( C)

M AN U

Temperature ( C)

75

100

125

150

0

AC C

Temperature ( C)

175

SC

LDPE

6000

Specific Heat (J/kgK)

RI PT

7000

200

ACCEPTED MANUSCRIPT

PP

8000

6000

4000

2000 75

100

125

150

175

200

M AN U

50

0

PP

−7

2

Thermal Diffusivity (10 m /s)

Temperature ( C)

1,2

1,0

0,8

50

75

100

TE D

0,6

25

125

150

175

200

0

Temperature ( C)

PP

EP

0,4

0,3

0,2

AC C

Thermal Conductivity (W/mK)

0,5

0,1

0

25

50

75

100

125

150 0

Temperature ( C)

.

175

SC

Specific Heat (J/kgK)

10000

RI PT

Figure 3

200

225

ACCEPTED MANUSCRIPT

9000

PA6

Specific Heat (J/KgK)

8000 7000 6000 5000 4000 3000 2000 1000 50

75

100

125

150

175

200

225

250

275

0

PA6

1,6 1,4

-7

2

Thermal Diffusivity (x10 m /s)

M AN U

Temperature ( C)

1,2 1,0 0,8 0,6

50

100

TE D

0,4 0

150

200

250

300

0

Temperature ( C) 0,60

PA6

0,50

EP

0,45 0,40 0,35 0,30 0,25

AC C

Thermal Conductivity ( W/mK)

0,55

0,20 0,15

0

50

100

150

200 0

Temperature ( C)

SC

RI PT

Figure 4

250

300

ACCEPTED MANUSCRIPT

RI PT

Figure 5

9000 8000

PVDF

6000 5000 4000 3000

SC

Specific Heat (J/kgK)

7000

2000 1000 0 50

75

100

125

150

175

PVDF

-7

2

Thermal Diffusivity (x10 m /s)

1,2

200

M AN U

0

Temperature ( C)

1,0

0,8

25

50

75

100

TE D

0,6

125

150

175

200

225

0

Temperature ( C)

PVDF

EP

0,6 0,5 0,4 0,3

AC C

Thermal Conductivity (W/mK)

0,7

0,2 0,1

25

50

75

100

125

150 0

Temperature ( C)

175

200

225

ACCEPTED MANUSCRIPT

Figure 6

0.35

SC

0.30 0.25 0.20 0.15 0.10 20

M AN U

Thermal conductivity (W/mK)

0.40

RI PT

PS PC PMMA HIPS

0.45

40

60

80

100

120 0

AC C

EP

TE D

Temperature( C)

140

160

180

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

Figure 7

ACCEPTED MANUSCRIPT

-1,50

0

86 C st

1 run nd 2 run

PMMA

-2,00

SC

-2,25 -2,50 -2,75 -3,00 -3,25 85

90

95

M AN U

Heat Flow (W/g)

-1,75

RI PT

Figure 8

100

105

110

115

0

AC C

EP

TE D

Temperature ( C)

120

125

130