• Aucun résultat trouvé

THE THERMAL CONDUCTIVITY OF SEMICRYSTALLINE POLYMERS AT VERY LOW TEMPERATURES

N/A
N/A
Protected

Academic year: 2021

Partager "THE THERMAL CONDUCTIVITY OF SEMICRYSTALLINE POLYMERS AT VERY LOW TEMPERATURES"

Copied!
4
0
0

Texte intégral

(1)

HAL Id: jpa-00221288

https://hal.archives-ouvertes.fr/jpa-00221288

Submitted on 1 Jan 1981

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

THE THERMAL CONDUCTIVITY OF

SEMICRYSTALLINE POLYMERS AT VERY LOW TEMPERATURES

D. Greig, N. Hardy

To cite this version:

D. Greig, N. Hardy. THE THERMAL CONDUCTIVITY OF SEMICRYSTALLINE POLYMERS AT VERY LOW TEMPERATURES. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-69-C6-71.

�10.1051/jphyscol:1981621�. �jpa-00221288�

(2)

JOURNAL DE PHYSIQUE

CoZZoque C6, supptdment au n012, Tome 42, de'cembre 1981 page C6-69

THE THERMAL C O N D U C T I V I T Y OF S E M I C R Y S T A L L I N E POLYMERS A T VERY LOW TEMPERATURES

D. Greig and N.D. Hardy

Department o f Physics, University o f k e d s , Leeds LS2 9J2: England

Abstract. - For polyethylene the temperature dependence of thermal conduct- ivity decreases below a temperature T* -- in this case 1 K -- from

T~

to T. We now present experimental results on a lightly modified form of polyethylene for which T* is raised to between 3 K and 9K. There appears to be a correlation between T* and the microcrystalline structure and we

speculate that for semicrystalline polymers in this temperature range structure scattering is more important than 2-level tunnelling.

The general trends of the temperature dependence of the thermal conductivity,

K ,

of semicrystalline polymers have been well-established between

?.

2 K and room

temperature

I

. We have studied in detail the influence of (i) cr?stallinity2 and (ii) crystallite orientation

3

, and have found that above and below * 20K the

variations in

K

with these two parameters are completely different. At the higher end of the range the conductivity increases both with crystallinity and with

orientation. At low temperatures, on the other hand, the specimens with the greatest crystallinity have the lowest conductivity with values at

".

2 K roughly an order of magnitude lower than those found "universally" for all amorphous polymers 4 . These

low values, furthermore, are to be more or less independent of crystallite orientation.

This rather dramatic difference in behaviour is attributed to the conditions arising at low temperatures when the phonon mean free path, R, becomes larger than the dimension of the structural units. As the difference in density between

crystalline and amorphous regions can be as great as 20% the "structure scattering"

of the composite polymer gives rise to a thermal resistance that is considerably greater than that of the amorphous material alone. For these materials this structure scattering argument seems preferable to the 2-level phonon scattering explanation that has been applied so successfully to materials that are completely

5 6 amorphous .

At still lower temperatures it i s found that for polyethylene (PE) the

variation of

K

with T undergoes a sharp decrease in slope, changing at a temperature T* from a dependence of about T ~ to a variation that is almost linear. The anomaly, ' ~ although towards the lower end of the temperatures, has been clearly established7'*"

-

and has been explained by the dominant phonon wavelength,

A ,

becoming greater than the thickness of the crystallites. In the latest study it has been found to occur

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981621

(3)

C6-70 JOURNAL DE PHYSIQUE

at a higher value of T* in a specimen of PE that had been extruded. It therefore appears that we can define an "ultra-low" temperature range in which the orientation properties of the crystallites are again of importance.

We are now reporting on some systematic srudies of this effect by making measurements on a modified form of PE, Rigidex 40, for which the values of T* are conveniently rather higher. Rigidex 40 is an ethylene-propylene co-polymer containing 5 methyl side groups per thousand main chain atoms

We have obtained 2 sets of measurements both showing very marked effects. In the first (figure

1)

we show the

temperature variation of K in the extrusion direction for a set of samples for each of which the extrusion ratio was 15 but which were extruded at 75Oc, 10oO~, and

1 1 0 ~ ~ . Corneliussen and peterlin1° have shown that increasing the drawing tempera- ture of PE from 40°c to 1 4 0 ~ ~ results in a dramatic increase in long period, L, with values rising from about 170 21 to nearly 400 2.

Although there are no published data on extruded Rigidex 40, pre- liminary experiments by ~ o ~ e l l have shown the same trend. The most important feature of figure 1 is that the changes in

K

appear only at very low temperatures.

0

-

TEMPERATURE ( Kl

In figure 2 we show the

temperature variation of

K

for Fig.1. Temperature variation of

K

in the extrusion direction for samples of extrusion various values of A in samples ratio 15 extruded at: u , 7 5 O ~ ; 0 , 1 0 0 ~ ~ ; that have all been extruded at + 1lOOC.

100°C. Hope has obtained some indication of a reduction in L with increasing

A,

but we must also consider an increase in the number of intercrystalline bridges created during the extrusion process. From figure 2 we see that the conductivity is changed both above 20 K

@

at "ultra-low" temperatures.

Very generally we may argue that the change in slope at

T*

with falling

temperature indicates a transition to a regime in which the mean free path is

relatively long; that is, as the dominant phonon wavelength, - A, becomes longer,

phonon scattering is reduced. The results indicate that this occurs at the highest

temperatures for material that has been (a) extruded at low extrusion temperatures

(figure 1) and (b) extruded to the greatest possible extrusion ratio (figure 2).

(4)

This is entirely in accordance with the observation that both of these processes give rise to long periods that are

relatively small, with an implication that the crystalline structure is then most broken up. This results in less scattering for 2 possible reasons. (1) When -

A

becomes greater than the dimensions of the crystal- line units some form of Rayleigh

scattering takes place. When the density of scattering sites is large interference occurs between scattered wavefronts giving a relationship R

a

v-~. Combined with a specific heat varying as T~ this leads to

K a

T in agreement with the experimental results. (2) On a more qualitative argument orientation will tend to

'homogenize' the polymer making the amorphous material more dense and the crystalline component less so. The specimen will thus behave more like an amorphous solid with fluctuations in properties over a length

%

100 g. Morgan and smith12 have shown that this leads to

Fig.2. Temperature variation of

K

for samples extruded at 100°C with

extrusion ratios

:

n, lO(measured perpendicular to the extrusion a temperature variation of

K

of exactly - direction); @(isotropic; 0,5; A,10;

X,15; 1 , 1 7 ; -,20 (all measured the form that we have found.

parallel to the extrusion direction).

We should like to thank Dr P.S.Hope

and Professor I.M. Ward for their interest in the work and the SERC for continued financial support.

References

1. See, for example, C.L. Choy, Polymer, 18, 984 (1977).

2. C.L. Choy and D. Greig, J.Phys.C: 8, 3121 (1975).

3. A.G. Gibson, D. Greig, M. Sahota, I.M. Ward, and C.L. Choy, J.Polym.Sci:Polym.

Letts.Edn., 15, 183 (1977)

4. R.B. Stephens, Phys.Rev.B., 8, 2896 (1973).

5. P.W. Anderson, B.I. Halperin, and C.M. Varma, Phil.Mag., 5, 1 (1972).

6. W.A. Phillips, 3.Low Temp.Phys., 7, 351 (1972).

7. M. Giles and C. Terry, ~hys.~ev.~ztts., 2, 882 (1969).

8. A. Bhattacharyya and A.C. Anderson, J.Low.Temp.Phys., 2, 64 (1979).

9. D.M. Finlayson, P. Mason, J.N. Rogers, and D. Greig, J.Phys.C: 12, L185 (1980).

10. A. Peterlin, J.Polym.Sci: Part C, 18, 123 (1967) 11. P.S. Hope, Thesis, University of ~ G d s , U.K. (1978).

12. G.J. Morgan and D. Smith, J.Phys.C: 1, 649 (1974).

Références

Documents relatifs

During these many years, Comeille Jest was accompa ni ed a long the path s of Nepal by Sarkiman Majhi , from Parse I village in Kabhre Palangco k.. Photography in lI,e

Better behaviour of the strained devices has been observed for many electrical parameters at 10 K operation: lower threshold voltage, smaller access

While these individual resonant layers are properly defined solutions of the MHD equations, their physical relevance is not obvious a priori since their narrow width might

A simple kinetic model of the solar corona has been developed at BISA (Pier- rard & Lamy 2003) in order to study the temperatures of the solar ions in coronal regions

At IOW temperatures both the initial local susceptibility and the dependence of the saturation hyperfine field on applied field indicate a small reduction of the Fe moment.. A

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des

We define a partition of the set of integers k in the range [1, m−1] prime to m into two or three subsets, where one subset consists of those integers k which are < m/2,

An infinitesimal increase of the volume ∆v brings an increase in p int , so that the piston moves until another equilibrium point with a bigger volume. On the other hand, a