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�
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
Kwith 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
Kwith 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
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
Kappear only at very low temperatures.
0-
TEMPERATURE ( KlIn figure 2 we show the
temperature variation of
Kfor Fig.1. Temperature variation of
Kin 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).
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 -
Abecomes 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
av-~. Combined with a specific heat varying as T~ this leads to
K a