Low temperature dependence of the strength of polyimide fibres

Low temperature dependence of strength of polyimide fibres

11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

2781

kristallov (Physics and Chemistry of the Solid State of Organic Crystals) p. 114, Mir, Moscow, 1967 Yu. I. ALEKSANDROV, Toehnaya kriometriya organicheskikhveshchestv (Precision Cryometry of Organic Substances). 160 pp, Khimiya, Leningrad, 1975 S. ALFORD and M. DOLE, J. Amer. Chem. Soc. 77: 4774, 1955 Yu. K. GODINSKII, Toplofizicheskiye metody issledovaniya polimerov (Thermophysical Methods of Investigating Polymers). 215 pp, Khimiya, Moscow, 1976 U. WENLAND, Termicheskiye metody analiza (Thermal Methods of Analysis). p. 261, Mir, Moscow, 1978 S. V. MASTRANGELO and K. W. DORNTE, J. Amer. Chem. Soc. 77: 6200, 1955 B. V. LEBEDEV and L B. RABINOVICH, Vysokomol. soyed. BIB: 416, 1976 (Not translated in Polymer Sci. U.S.S.R.) ldem., Dok. Akad. Nauk SSSR 237: 641, 1977 I. B. RABINOVICH and B. V. LEBEDEV, Vysokomol. soyed. A21: 2025, 1979 (Translated in Polymer Sci. U.S.S.R. A21: 9, 2234, 1979) B. V. LEBEDEV, Dissert. Doct. Chem. Sci., Mosk. Gos. Univ., Moscow, 1979 G. H. GIBBS and A. E. DIMARZIO, J. Chem. Phys. 28: 373, 1958 P. A. SMALL, Trans. Faraday Soc. 51: 1717, 1955

Polymer ScienceU.S.S.R. Vol. 26, No. 12, pp. 2781-2788, 1984 Printed in Poland

0032-3950/84 $10.00+.00 © 1986PergamonPress Ltd.

LOW TEMPERATURE DEPENDENCE OF THE STRENGTH OF POLYIMIDE FIBRES* S. V. BRONNIKOV, V. I. VETTEGREN', L. N. KORZHAVIN a n d S. YA. FRENKEL' Institute of High Molecular Weight Compounds, U.S.S.R. Academy of Sciences

(Received 11 March 1983) The authors have investigated the temperature dependence of strength a(T) of 14 oriented polyimide fibres of varied chemical structure in the temperature interval 100-650 K and established that in the region of low temperatures T< 00/3 (0a is the effective Debye temperature) the dependence of strength on temperature is non-linear. It is assumed that the cause of the non-linearityof a(T) is the variability of the thermal expansion coefficient in this temperature range as is confirmed by the results of spectroscopic investigations. ZHURKOV [1] has shown that the d e s t r u c t i o n of solids is based o n the a n h a r m o n i s m o f the t h e r m a l v i b r a t i o n s o f the atoms. He o b t a i n e d a relation l i n k i n g the strength o f a * Vysokomol. soyed. A26: No. 12, 2483-2488, 1984.

S.V. BRONmKOVet al.

2782

solid to Young's modulus E and the thermal expansion coefficient

Ee,(

a=--

r

1

~lnz/r0 ) T =~o-flT, 3e,

(1)

where r is the coefficient of mechanical overload; 8, is the limiting relative elongation at which the interatomic bond loses stability and is d e s t r o y e d , is the durability of the E~ solid; % is the period of vibration of the atoms of the solid; ~o = - - is the athermal lg 0~E z component of strength; fl = - - l n - is the temperature coefficient of strength. 3x % It is known that in the classical temperature region the thermal expansion coefficient does not depend on temperature and hence fl=const and the strength falls linearly with temperature for a fixed time of the tests ,. However, in the region of low temperatures at T < 0D where 0o is the characteristic Debye temperature, the thermal expansion coefficient ~ falls while at T-~0 the magnitude also tends to zero. It is also known that the changes in 0care d~te to fall in the thermal capacity C at low temperature since the thermal expansion coefficient is linked with the thermal capacity by the relation [2] CG ~ = ~-77~,

Er o

(2)

where G is the Gruneisen parameter; ro is the equilibrium interatomic distance. Fall in the thermal capacity, in turn, is due to the "freezing out" of the vibrations with high values of frequency (change in the quantuart numbers of filling of the phonon states) [3]. These propositions also apply to polymers [4]. If it is assumed that the strength equation (1) also remains valid at low temperatures then from the fall in ~ one must expect that the temperature strength coefficient fl will be variable and the dependence of strength on temperature will become non-linear. Non-linear dependence of the strength of polymers on temperature was obtained for an oriented polyimide BZF film by Bessonov et al. [5] and for polycaproamide and Teflon fibres by Slutsker et al. [6, 7]. In the last two studies disturbance of the linearity of the temperature dependence of strength at low temperatures is also explained by the change in the filling numbers of the phonon states. We would note that earlier a link between change in the filling numbers of the phonon states at low temperatures and strength characteristics was postulated by Salganik [81 and Gilman [9]. The present work investigates the temperature dependence of strength over a wide temperature range (100-650 K) for a number of oriented polyimide fibres (Table). The strength of the fibres was determined with the UMIV-3 unit at a constant stretching rate (5 ram/rain). The samples studied had the following dimensions: length 15 ram, diameter " 20/zm. The temperature fluctuations in the course of thermostatting and deformation of the samples on stretching did not exceed +_1 K. At each temperature of the experiment not less than 10 strength tests were run and the arithmetical mean determined.

27'8~

L o w t e m p e r a t u r e d e p e n d e n c e o f s t r e n g t h o f p o l y i m i d e fibres C H E M I C A L STRUCTURE OF MONOMER U'NIT~ AND EFFECTIVE DEBYE TEMPERATURE OF POLYIMIDE FIBRES

Polyimide No.

Chemical structure

Oa, K

t350 CI--I= at,

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o0

t125.

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oc

\OC

\

t350

O I

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1245

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2784

S . V . BRONNIKOV et al.

The spectroscopic investigations of the oriented polyimide films with a thickness = 2 0 / t m were with the DS 403 G I R spectrophotometer (JASCO). The absorption bands - 1020 c m - 1 corresponding to the skeletal vibrations of the polyimides were investigated. The time of recording the spectra a n d the width of the spectral slit chosen were optimal. The conditions of thermostatting were the same as for the mechanical tests.

As an example Fig. 1 gives the typical temperature dependence of the strength of the fibres studied. It will be seen that in the region of moderate temperatures the strength rises linearly with fall in temperature. However, in the region of low temperatures appreciable deviations from linearity are observed: the function a(T) becomes ever more sloping with fall in temperature with change in the parameter ft. Figure 2a, presents the temperature dependence of this coefficient calculated by differentiating the curves a(T) by temperature. It will be seen that at low temperatures the magnitude fl rises with increase in temperature reaching a certain limiting value at T= T* and then remains constant. According to formulae (1) and (2) such a course of the function fl(T) may be explained by change in the thermal capacity at low temperature the value of which is directly proportional to the thermal expansion coefficient ~. cT, 10-2MPo

! P Mpa//~

15

o

vi ) cm'l

]9

6 1008

\',.5 ~z~

5

S

-

I

200

600 T,K

--5

lOZ2

-

1006

f020

\ l

I

2oo

Goo T, K

FIG. 1

I

200

I

I "~'q

600 77,/f

FIG. 2

FIG. 1. Temperature dependence of the strength of polyimide fibres. In all the figures the numerals next to the curves correspond to the potyimide numbers. FIG. 2. Temperature dependence of parameter [3=B(r/c3T(a) and shift of maxima of I R absorption

bands (b). To check this assumption we used the results of IR spectroscopy. As is known from theory [10] the relative shift ( v ° - v J v ° of the maximum of the ith absorption band v~ of solids is linked with the relative deformation of the interatomic bonds e by the Gruneisen mode parameter G~ vo _ v i -

o

vi

~-Gi e

(3)

I f the bonds are deformed as a result of the thermal influence, then the equation (3) may

Low temperature dependence of strength of polyimide fibres

2785

be rewritten thus:

V°-v~ (4)

v iO ~-Gi~tT.

where ~ is the thermal expansion coefficient of the monomer units; v~o is the value of the maximum of the ith absorption band at 0 K. %-0"

~0 o-a-

o~.[0sK -I (2

V

2

b

OXO~eO~OX

_

ox

} ~"

•

I

200

600

02

I

o

'1//" -

"

0.4,

0,6'

v/~,lO a

FIG. 3

~:~

a 6

• 6'

'~'

1

200

I

I

600 T,K

FIo. 4

FIG. 3. Temperature dependence of thermal expansion coefficients of interatomic bonds in skeleton of macromolecules (a) and comparison of the relative fall in strength with relative shift of the maximum of the IR absorption bands (b). FIG. 4. Comparison of experimental (numerals without apostrophes) and temperature dependence of strength of polyimide fibres calculated from IR spectroscopy (numerals with. apostrophes).

Consequently, in line with equation (4) knowing the temperature dependence of the shift in the maximum of the absorption band it is possible to determine the temperature course of the thermal expansion coefficient ~(T). The values of the Gruneisen mode parameter Gl were calculated by the technique in reference [11 ]. Figure 2b, presents the temperature dependence of the absorption bands 1020 cm- 1 for some polyimides. It is worth noting that in the region of moderate temperatures these relations are linear, while over the low temperature interval the deviations from linearity are appreciable. From comparison of Figs. 1 and 2b, it may be concluded that the temperatures of the start of the appreciable deviations in the functions tr(T) and v~(T) are close. Differentiating by temperature vl(T) in line with the equation (4) we obtain the temperature dependence of the thermal expansion coefficient ~(T) which is presented in Fig. 3a. As supposed, in the region of classical temperatures ct=const and then on passing to the quantum region ~ falls with fall in temperature. To establish the presumed link between the temperature changes in strength and the thermal expansion coefficient we transform equations (1) and (4) as follows tro-tr a0

-

lnT/% v°i-vi v°-vi 3Gie~ v0 =A-°---'vi

(5)

2786

S.V. BROI~IKOVet al.

lnz/ro . is a parameter not depending on temperature. 3Gi e, Consequently, if it assmned that the reason for the experimentally observed low temperature deviations in the function a(T) lies in the variability of the thermal expansion coefficient in this temperature range, then in line with equation (5) in the coordinates where A -

Oo

-

ao

v ° -

v,

(--V/Y-) a direct prOpOrtiOnal relatiOn must be °btained" This is well cOn"

firmed by Fig. 3b. Another way of checking the above assumption is to compare the experimental function a(T) with that calculated from relation (5) from the temperature course of the shift of the maximum of the IR absorption band. For the calculation we took e.=0.16 for all the polyimides; G,=0.28 (polyimide 4); 0.19 (polyimide 5) and 0.24 (polyimide 6). The functions a(T) for the different polyimides and also the experimental points obtained from the mechanical tests are given in Fig. 4. Good agreement of the experimental and calculated values of the ratio a/ao is obvious. Thus, the spectroscopic data confirm the assumption that the cause of the non-linearity of the functions a(T) is the variability of the thermal expansion coefficient ~. Let us try to find an approximate analytical formula for a(T) in the low temperature range. As Fig. 2 shows, the dependence expressed by the relation fl(T)=aa(T)/OT is linear. From this it may be assumed that the function a(T) in the low temperature region is quadratic. Deviations from linearity in the region of low temperatures are also observed in the temperature course of another characteristic of a solid body - Young's modulus E. This phenomenon is known both for classical solids (metals, crystals) [12] and for polymers [13]. In reference [12] it is shown theoretically that the function E(T) in the low temperature region has the following form: E-~ Eo - ~ T 2,

(5')

where r/is the temperature coefficient of Young's modulus (r/= OE(T)/OT) at high (classical) temperatures; Eo is the value of Young's modulus at 0 K; 0D is the characteristic Debye temperature. In reference [14] we showed that in the low temperature region relation (5') holds for polyimide fibres. In line with equation (1) the strength is directly proportional to Young's modulus. In fact, as may be seen from Fig. 5a, at all temperatures of the experiment including the low temperature range direct proportionality is observed between the ratios a/go and E/Eo. From all this we assume that the low temperature course of strength may be described by a relation similar to formula (5') fl---T2 a ~ a ° - - Oo

(6)

To check this assumption let us reconstruct the experimental functions a(T) depicted

Low temperature dependence of strength of polyimide fibres

2787

in Fig. 1 in the coordinates In ( a ~ - a ) = f l n T) where a~ is the strength value obtained on continuing the non-linear functions a(T) to 0 K. The results of such a construction axe given in Fig. 5b. It will be seen that at low temperatures the experimental points lie on straight lines the tangent of the angle of slope of which is roughly equal to two and hence in the low temperature region the course of strength may be described by the relation (6). We would note that the representations of the dependences of strength on temperature presented in references [5-7] in the coordinates in Fig. 5b, also shows that they are satisfactorily described by expression (6). In references [8, 15] for the analytical description of a(T) at low temperatures stricter expressions axe used. However, if the temperature is not too low according to reference [12] they may be interpolated by a quadratic function given in this work.

0"8

~' a

x4

"5

In(G ~-~ ~MPa]

06

b

×

_

0"4

/

x o I

0.4

1

I

0.8 E / E o

3

I

4.5

5.5 InT[K]

FIG. 5. Comparison of relative strength with relative modulus (a) and dependence of In (a~-~r) on In T (b). To describe the temperature course of thermal capacity and the thermal expansion coefficient of solids a very successful idea was to introduce the Debye temperature as the temperature above which the thermal capacity and thermal expansion coefficient assume classical (constant). values [3, 4]. Taking into account the experimental errors, as noted in references [3, 12], practically already at T=OD]2--Oo/4 one may consider that these parameters have classical values. The magnitudes 0D may be determined as in reference [14] for the temperature dependence of Young's modulus: from comparison of the tangents of the angles of slope ~/in the coordinates E = f ( T ) (in the region of classical temperatures) and rlE/Oo in the coordinates E = f ( T 2) (in the region of low temperatures (equation (5)). Performing such an operation with the temperature dependence of strength we obtained the effective Debye temperatures given in the Table. They are 900-1400 K and are close to the Debye tempeiatures calculated from the temperature dependence of the modulus [14]. Comparing the values of 0o determined by us with the start of the appreciable deviations of the functions a(T) from linearity (in Fig. 1 these temperatures T= T* are denoted by arrows) we established that the linear dependence of strength on temperature becomes quadratic at T* - 0D/3. We would note that knowledge of the magnitudes 0o and temperature dependence of strength in the classical temperature region helps to calculate it with good accuracy also

2788

s.v.

BRONNIKOVet al.

at low t e m p e r a t u r e s . F r o m the a b o v e r e m a r k s we a s s u m e t h a t the linear d e p e n d e n c e o f s t r e n g t h passes into q u a d r a t i c at T*~-Oo/3. U s i n g the f u n c t i o n tr(T) at T>Oo/3 f r o m f o r m u l a (6) we c a l c u l a t e d the t e m p e r a t u r e c o u r s e o f s t r e n g t h at T < 0D/3. T h e f u n c t i o n a ( T ) thits c a l c u l a t e d is s h o w n in Fig. 1 b y a b r o k e n line. I t will b e seen t h a t the l o w t e m p e r a t u r e c o n t i n u a t i o n o f the t e m p e r a t u r e d e p e n d e n c e o f strength with g o o d a c c u r a c y is d e s c r i b e d b y the r e l a t i o n (6).

Translated by A. CRoz'¢ REFERENCES

1. S. N. ZHURKOV, Fizika tverd, tela 22: 3344, 1980 2. A. I. ANSEL'M, Vvedeniye v teoriyu poluprovodnikov (Introduction to the Semiconductor Theory). 6t6 pp, Nauka, Moscow, 1978 3. L. D. LANDAU and Ye. M. LIFSHITS, Statisticheskaya fizika (Statistical Physics). 564 pp, Nauka, Moscow, 1976 4. V. WUNDERLICH and G. BAUER, Teployemkost' lineinykh polimerov (Thermal Capacity of Linear Polymers). 240 Pla, Mir, Moscow, 1972 5. N. P. KUZNETSOV, M. I. BESSONOV and N. A. ADROVA, Vysokomol. soyed. A15: 1886, 1973 (Translated in Polymer Sci. U.S.S.R. A15: 8, 2128, 1973) 6. Kh. AIDAROV and A. I. SLUTSKER, Idib. A26- 1823, 1984 (Translated in POlymer Sci.U.S.S.R. A26: 2034, 1984) 7. A. I. SLUTSKER and Kh. AIDAROV, Aktual'nye problemy prochnosti (Current Problems of Strength). Izhevsk, 1982 8. R . L . SALANIK, Fizika tverd, tela 12: 1336, 1970 9. I. I. GILMAN and H. C. TONG, J. Appl. Phys. 42: 3479, 1971 10. O. MADELUNG, Teoriya tverdogo tela (Solid Body Theory). 416 pp, Nauka, Moscow, 1980 I I. V. I. VETTEGREN', N. R. PROKOPCHUK, S. Ya. FRENKEL' and M. M. KOTON, Dokl. Akad. Nauk SSSR 230: 1343, 1976 12. G. LEIBFRIED and B. LUDWIG, Teoriya angarmonicheskikh effektov v kristallakh (Theory of Anharmonic Effects in Crystals). 232 pp, Inost. lit., Moscow, 1963 13. N. I. PEREPECHKO, Svoistva polimerov pri nizkik.h temperaturakh (Properties of Polymers at Low Temperatures). 272 pp, Khimiya, Moscow, 1977 14. S. V. BRONNIKOV, V. I. VETTERGEN', A. A. KUSOV and L. H. KORZHAVIN, Vysokomol. soyed. B25: 241, 1983 (Not translated in Polymer Sci. U.S.S.R.) 15. A. I. SLUTSKER and Kh. AIDAROV, Fizika tverd, tela 25: 777, 1983