Die Makromolekulare Chemie 177,271-277 (1976)

Department of Physics, University of Umei, S-901 87 U m d , Sweden

Pressure Dependence of the Thermal Conductivity of Some Polyamides

Per Anderson

(Date of receipt: May 5 , 1975)

SUMMARY: The pressure dependences of the thermal conductivities of five polyamides (nylons)

have been determined in a cylindrical geometry at 300K and in the pressure range &25 kbar. The conductivities increase strongly with pressure, the values a t 25 kbar being higher by the factors 1,83, 1,90, 1,89, 2,07, and 2,03 for, respectively, nylon 66, nylon 610, nylon 6, nylon 11, and nylon 12, than those at atmospheric pressure. The results are compared with other experimental results and with theoretical calculations. The difference in conductivity response to pressure between the different varieties is discussed.

ZUSAMMENFASSUNG: Die Abhangigkeit der Warmeleitfahigkeit vom Druck wurde bei funf Polyamiden

(Nylon) in einer zylindrischen Geometrie bei 300K und im Druckbereich von G 2 5 kbar gemessen. Die Warmeleitfahigkeit steigt stark an mit zunehmendem Druck. Bei 25 kbar sind die Werte fur Nylon 66 ~ 1,83, Nylon 610 - 1,90, Nylon 6 - 1,89, Nylon 11 - 2,07 und fur Nylon 12 - 2,03 ma1 so hoch wie bei atmospharischem Druck. Die Ergebnisse werden mit anderen experimentellen Ergebnissen und mit theoretischen Berechnungen verglichen. Die unterschiedliche Abhangigkeit der Warmeleitfahigkeit vom Druck dieser funf Polyamide wird diskutiert.

Introduction

There are relatively few reports on experimental studies of the thermal conductivity of polymers under pressure. Some of these are from this labora- tory '). In the present work different varieties of polyamides were chosen as a suitable material for establishing a relationship between the thermal conductivity response to pressure and the chemical structure of polymers. To our knowledge, the only reported experiments of the influence of pressure on the thermal conductivity of nylon are those of ,%he2).

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Experimental Part

The experiments described below were performed in a belt type of high-pressure apparatus. The construction of the high pressure cell is shown in Fig. 1 of ref.’). The nylon sample is made up of three short cylinders and is fitted into a pyrophyllite matrix. The sample is heated along the axis by means of a manganin spiral, the power being measured by voltage taps. The temp. difference (AT) between two points at different radii, r l and r 2 , is measured by a chromel-alumel thermocouple. A power density of 0,2 W/cm typically yields A T z 3 K. For calibration we use a coaxial Ce-Bi wire, produced by extrusion. The calibration wire is placed in a single turn around the sample. The resistance of the manganin heater is used for obtaining a continuous pressure scale. Assuming radial and stationary flow of heat in a cylinder, the thermal conductivity A may be calculated from Eq. (I) ,

where Q is the heating power and I is the axial length of the sample. The pressure distribution in the high-pressure cell was investigated in separate measure-

ments a t 25 kbar by observing the synchronism of the Bi 1-11 transition in different partsofthe cell. The pressure difference between the peripheral region, where the calibration ring is situated, and the central region of the sample was found to be ca. 3 kbar for increasing pressure. However, the pressure inhomogeneity in the sample was found to be less than 1 kbar. The pressure scale was corrected according to these measurements.

The purpose of the present work was to determine only the relative value, A(P)/L(O). Therefore, there is no need to know accurately the ratio r2/rl, but only its variation with pressure. Since the sample is essentially homogeneous, the ratio r2/r1 is simply supposed to be constant, when pressure is applied.

However, the length I of the specimen will change strongly with pressure P, and the greatest uncertainty in these measurements of A is, no doubt, due to incomplete knowledge of the pressure variation of I.

As the pressure is increased, the length of the sample is affected not only by the compressibility of the specific polymer, but also by the plastic &formation of the sample, as the conditions in the cell are non-hydrostatic. The deformation was, therefore, investi- gated experimentally in the following way. A coil of manganin wire was wound around the cylindrical surface of the sample, and the resistance of the coil was measured up to 25 kbar. From the pressure coefficient of resistance of manganin3), the variation of the sample diameter was then calculated. These experiments showed that the sample is strongly distorted during the first pressure increase, and therefore thermal conductivity results for the first run were always disregarded. The average result for the second pressure increase of several measurements was that the sample diameter increased at a rate of 0,04%/kbar. The compressibility data needed for the final calculation of I under pressure, were kindly supplied by Wurfield4). His measurements were carried out on nylon samples obtained from the same commercial stocks which we used in our conductivity experiments. Fig. 1 shows his compression data, which are in the

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Pressure Dependence of the Thermal Conductivity of Some Pol yamides

range up to 9 kbar. For comparison are also shown compression data’) on nylon 66 and nylon 610 up to higher pressures. The data of Warfield had to be extrapolated up to 25 kbar. As can be judged from the approximate parallelism of the compression curves at pressures above 5 kbar, the extrapolation seems justified.

Fig. 1 . Compression data of different polyamides. From ref.4), (A): nylon 66, (0): nylon 610, (0 ) : nylon 6, (m): nylon 11 and (v): nylon 12; From ref.’), (a): nylon 66 and (0): nylon 610. The data from ref.4) are extrapolated to 25 kbar using the results of ref.’). For clarity some of the measuring points and compression curves are omitted

Tab. 1. Properties of the tested polyamides

A 10 20 30

Pressure in kbar OO

Polyamide Trade name Density Densities Volume e:) e:) crystal- -- and in g/cm3

producer g ~ m - ~ g cm-3 Iinity xc

Nylon 66 Ultramid A 3K BASF, Ludwigshafenph., Germany Ultramid S 3K BASF, Ludwigshafenph., Germany

Stockholm, Sweden Rilsan

Stockholm, Sweden Nordbergs Tekniska,

Sweden

Nylon 610

Nylon 6 Andrtn & Soner,

Nylon 1 1 Andren & Soner,

Nylon 12 Sundbyberg,

1,143 1,076 1,246 0,43

1,084 1,046 1,196 0329

1,131 1,0846 1,236 0,32

1,028 1,016 1,15, 0,13

1,009 0,996 1,077 0924

a) e,: density of the amorphous part. b, e,: density of the crystalline part.

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P. Anderson

- m E 2 1,50

.- P d m

c

c

h

1,oo

The properties of the tested polyamides are summarized in Tab. 1. The volume crystal- linity X, was estimated from the relation Eq. (2),

- 0

0 Fig. 2. Thermal conductivity 0 data for one sample (nylon 66)

vs. pressure, obtained from the 0 second pressure increase (s.

0

0

0 1 I Exptl. Part)

~

where e , and ,pa are the densities of the crystalline and amorphous parts, resp., while e is the density of the semi-crystalline polymer. The values of e, and ec were obtained from refs. 6, '! The density values were determined by direct measurement and weighing.

Results

In Fig. 2 are shown results for the thermal conductivity A obtained from the second pressure increase on one sample (nylon 66). The pressure dependence is most pronounced at low pressures, a tendency which is applicable to all the polymers.

0

0

0

0

x 2,oo c u 3 '0 c 0 $ 1 u

Pressure in kbar

Tab. 2. Ratio of the thermal conductivity at 25 kbar to that at atmospheric pressure, 1(25)/2(0), for the tested polyamides

Polyamide 425)lW) uncorrected corrected

Nylon 66 Nylon 610 Nylon 6 Nylon 11 Nylon 12

1,42 0,Ol 1,46 f 0,02 1,47 f 0,02 1,54 f 0,02 1,52 f 0,02

1,83 f 0,03 1,9OfO,04 1,89 f 0,04 2,07 f 0,04 2,03 f 0,04

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Pressure Dependence of the Thermal Conductivity of Some Polyamides

For each material three different samples were examined. Tab. 2 shows the average fractional change of 1, from atmospheric pressure to 25 kbar for the tested polymers. The errors represent the maximum variation in results.

Discussion

Heat conduction in polymers is brought about by lattice vibrations. These vibrations consist of interchain vibrations which are mainly governed by van der Waals forces between the chains, and intrachain vibrations which are governed by covalent forces along the chains. The anharmonicity of potential is much larger for the interchain vibration, and therefore properties such as the Gruneisen constant and the thermal expansion, which are related to anharmonicity, may be determined in terms of interchain vibrations. Further- more, Wuda et al.*) have pointed out that the heat conduction is mainly governed by interchain lattice waves. As shown in a previous paper’), the kinetic formulation of thermal conductivity makes possible a calculation of the initial change of the relative thermal conductivity, q, with pressure, P. We get

where B , is the zero pressure isothermal bulk modulus and y o is the Griineisen constant as determined from the pressure dependence of the bulk modulus.

These parameters were obtained from experimental compressibility data4), using a technique described in ref.”). The corresponding values of q are shown in comparison with our experimental results in Tab. 3. The calculated value of y o for nylon 12 is surprisingly low. The experimental results are about a factor of two lower than the theoretical ones. The discrepancy is larger for the more crystalline materials.

No attempt was made to measure the absolute values of 1 at atmospheric pressure for the various nylon materials. However, there are minor differences reported in the literature”). The conductivity of nylon 66 is higher than that of nylon 610 and the conductivity of nylon 6 is higher than that of nylon 12. The differences may partly be due to different degrees of crystallinity. The crystalline parts show a higher thermal conductivity than the amorphous parts. However, when pressure is applied the most crystalline material, nylon

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P. Andersson

Tab. 3. The initial values of the isothermal bulk modulus, B,, the lattice Gruneisen constant, yo, and q=(dl/dP)/l, (cf. Eq. (3))

Polyamide BO kbar

Y o

Nylon 66 33 5,O 15,7 6S Nylon 610 23 5,7 25,5 7,8 Nylon 6 44 3,9 9 2 5,5 Nylon 11 32 3,9 12,7 7 3 Nylon 12 40 2,8 7,4 6,3

66, shows the smallest relative pressure response, while the most amorphous material, nylon 11, shows the highest relative pressure response. It should also be noted that nylon 11 is the most compressible material, and as can be judged from Fig. 1 and Tab. 2, high compressibility favours high pressure response in conductivity.

The differences in conductivity and its pressure dependence may partly be due to different crystal structure in the various polymers. The general structure consists of planar zig-zag carbons chains, which are held parallel to each other by hydrogen-bonds between CO and NH-groups in neighbouring chains. The distance between these interchain bonds, which varies with the kind of the polyamide, strongly affects the physical properties of the polyamides, such as the melting point, and it seems quite reasonable that it also affects the thermal conductivity and its pressure dependence.

Lohe2) has measured the thermal conductivity of molten polymers at 1 bar and 300 bar. At 225°C his value of (dA/dP)/& for nylon 6 is approximately 13%/kbar, which is about twice as high as our result for this polymer at 300 K.

Theauthor would like to thank Dr. Robert W. Warfield for kindly supplying compressibi- lity data on the tested polyamides.

') P. Andersson, B. Sundqvist, J. Polym. Sci., Polym. Phys. Ed. 13, 243 (1975)

3, R. J. Zeto, H. B. Vanfleet, J. Appl. Phys. 40, 2227 (1969) 4, R. W. Warfield, private communication

P. Lohe, Kolloid-Z. Z. Polym. 203, 115 (1965)

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Pressure Dependence of the Thermal Conductivity of Some Polyamides

5 , P. W. Bridgman, Proc. Amer. Acad. Arts Sci. 76, 71 (1948) ‘) D. W. van Krevelen, “Properties of Polymers, Correlations with Chemical Structure”,

7, D. W. van Krevelen, private communication ’) Y. Wada, A. Itani, T. Nishi, S. Nagai, J. Polym. Sci., Part A-2, 7, 201 (1969) 9, L. Bohlin, P. Anderson, Solid State Commun. 14, 711 (1974)

lo) R. W. Warfield, Makromol. Chem. 175, 3285 (1974)

Elsevier, Amsterdam 1972, pp 47, 49

S. Floberg, “Polvmerteknologi II”, FB-Forlag, Bor& 1969, D 276

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