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Low-temperature relaxation behaviour of heat-stable polymers
Low-temperature relaxation behaviour of heat-stable polymers
2923
REFERENCES 1. M. T. BRYK, Polimerizatsiya na tverdoi poverkhnosti neorganicheskikh veshchestv (Polymerization on Solid Surfaces of inorganic Materials), p. 240, Naukova Dumka, Kiev, 1981 2. S. S. IVANCHEV and A. V. DMITRENKO, Uspekhi khimii 31: 1178, 1982 3. G. C. EASTMOND, C. NGUYEN-HUU and W. H. PIRET, Polymer 21: 598, 1980 4. C. E. SCHILDKNECHT, High Polymers. Polymer Processes 29: 244, 1977 5. S. S. IVANCHEV, N. S. YENIKOLOPYAN, B. V. POLOZOV, A. V. DMITRENKO, V. A. DEMIDOVA and A. K. LITKOVETS, Vysokomol. soyed. A23: 2064, 1981 (Translated in Polymer Sci. U.S.S.R. 23: 9, 2248, 1981) 6. V. A. POPOV, A. N. GRISHIN, Yu. A. ZVEREVA, T. V. PALAYEVA, V. A. FOMIN and S. S. IVANCHEV, Vysok0mol. soyed. A25: 760, 1983 (Translated in Polymer Sci. U.S.S.R. 25: 4, 883, 1983) 7. A. V. OLENIN, A. K. ANDRIANOV, E. A. KASHUTINA, A. A. ZHDANOV, V. P. ZUBOV and V. A. KABANOV, U.S.S.R. Pat. 935511. Publ. in Byull. Izob., 22, 102, 1982 8. C. H. BAMFORD, P. A. CROWE and R. P. WAYNE, Proc. Roy. Soc. London A284: 455, 1965 9. C. H. BAMFORD, P. A. CROWE, J HOBBS and R. P. WAYNE, Proc. Roy. Soc. London A292: 153, 1966 10. E. A. KASHUTINA, A. A. ZHDANOV, A. V. OLENIN, A. K. ANDRIANOV, V. P. ZUBO'V, and V. A. KABANOV, Soviet Pat. 935508. PubL in Byull. Izob., 22, 102, 1982 11. A. V. OLI~NIN, A. L. KHRISTYUK, V. B. GOLUBEV, V. P. ZUBOV and V. A. KABANOV, Vysokomol. soyed. A25: 423, 1983 (Translated in Polymer Sci. U.S.S.R. 25: 2, 495, 1983) 12. F. W. BILLMAYER and C. B. de THEN, J. Amer. Chem. Soc. 77: 4763, 1955 13. A. K. ANDRIANOV, A. V. OLENIN, V. P. ZUBOV, R. A. KASHUTINA, A. A. ZHDANOV and V. A. KABANOV, Vysokomol. soyed. A25: 1987, 1983 (Translated in Polymer Sci. U.S.S.R. 25: 9, 2314, 1983)
Polymer Science U.S.S.R. Vol. 26, No. 12, pp. 2923-2931, 1984 Printed in Poland
0006-3509/84 $10.00+ .00 © 1986PergamonPress Ltd.
LOW-TEMPERATURE RELAXATION BEHAVIOUR OF HEAT-STABLE POLYMERS* R. B. BANYAVICHYUS, Z. B. MIGONENE a n d A. A. ASKADSKil Antapas Snechkus Polytechnical Institute, Kaunas
(Received 13 June 1983) Relaxation transitions occurring in aromatic polymers of structurally dissimilar types have been investigated by stress relaxation and creep methods. At low temperatures significant degrees of deformation were observed for these polymers. The range of mechanical durability has been determinef or the polymers, taking low temperature relaxation processes into account. * Vysokomol. soyed. A26: No. 12, 2604-2610, 1984.
2924
R . B . BANYAVICHYU$et al.
SPECIAL structural characteristics of heat-stable polymers determine their high heat resistance, thermal stability and cold resistance [1-3]. Heat-stable polymers are widely used as constructional materials capable of withstanding high temperatures [3, 4]. Detailed studies have accordingly been made of the high-temperature mechanical behaviour of heat-stable polymers under loads of various types [2]. It is known [3, 5-8] that heat-stable polymers are also noted for their marked ability to withstand cryogenic temperatures: their high deformation values even at - 2 7 0 ° are referred to in [6]. In view of this polymers of this type important constructional applications from a cryogenic standpoint and are of definite interest as cold-resistant materials. However, it appears that very little study has been made o f features o f the low-temperature mechanical behaviour of heat-stable polymers. Our aim in the present investigation was to study features of the low-temperature viscoelastic behaviour o f heat-stable polymers and to determine their mechanical durability, taking relaxation processes into account. To do so we took as examples two structurally dissimilar polymers, polybenzoxazole (PBO) and polyoxadiazole (POD). Heat stable polymers of Soviet origin,* viz. Niplon-1 (POD) [9] and Niplon-2 (PBO) [10] were used as model study objects in the investigation. Relaxation properties of these polymers were investigated at high temperatures in papers [11, 12]. Low temperature studies (under isothermic conditions) of stress relaxation and creep were carried out, using bulk microsamples measuring 3 × 5 x 6 ram. Samples were prepared by hot pressing at 360 (POD) and 380° (PBO) under specific pressure of 75 MPa. The ready-made samples underwent heat treatment at 100° for 72 hr, and before use were kept in an exsiccator. Low temperature experiments were performed on the 1253U-2-2 equipment using a specially developed reversor and extensometer [13]. The temperature interval extended from 20 to -145°; the ranges of stress and deformation extended from minimal values in the area of linen r viscoelasticity to levels determined by the maximum (limiting) deformation and stress values for mechanical softening of the polymer at a given test temperature. Experiments took 90 rain to perform. Stress relaxation and creep. Studies of stress relaxation and creep in PBO and POD showed that relaxation processes in these polymers are clearly evident even in the low temperature region. It is clear from an analysis of the results of stress relaxation experiments that in the entire temperature interval examined (from 20 to - 1 4 5 °) an increase in the degree of deformation is accompanied by displacement of the relaxation curves towards high stress. In addition, there is a marked acceleration of relaxation in the initial period as the deformation increases. This is exemplified by the relaxation curves for PBO at - 75 ° (Fig. 1) at different initial degrees of deformation. A temperature drop down to - 145 ° leads to a significant retardation of relaxation processes. A similar pattern of change in relaxation processes is revealed by investigation of the behaviour of the studied polymers under conditions of creep. Figure 2 shows the creep curves for P O D at - 120 ° under various initial stresses. It can be seen that an increase
* POD and PBO were kindly provided for test purposes by A. Ya. Chernikhov of the Plastmassy Scientific & Industrial Research Association.
Low-temperature relaxation behaviour of heat-stable polymers
2925
in the applied stress, where the test temperature is kept constant, leads to a uniform displacement of the curves towards larger deformations. Moreover relaxation p r o c esses become more definite and clear-cut as the Stress increases. A drop in temperature is accompanied by a significant diminution of the creep, though it is fairly marked a t - 50 and - 75 °. ~, MPa
2
2
0
~
5 .o.
_~
,
~ 2
140 <"
0
I
I
30
I
~O I
t
I
;
i
60
BO '
Time, rain FIG. 1. Stress relaxation curves for PBO at - 75 ° and initial deformations of 4 (1), 6 (2),
8 (3), 9 (4) and 10~o (5).
e,% f 18 ,0
0
3
aoo..oo.o
o
,
DO'O-O-o"O
0
0
I
30
I
Time, min
l
GO
2 ! t
0
l
90
FIG. 2. Creep curves for POD at -120 ° under initial Stresses of 120 (1), 180 (2), 220 (3), 260 (4) and 290 MPa (5). Temperature dependences of acr-T and e,,~-T plotted at different d e f o r m a t i o n s or stresses (ac, and eer being the stress and the deformation developing in the course o f an experiment lasting 90 min) may be used as generalizing characteristics reflecting the influence of temperature on relaxation processes. These plots appear in Fig. 3 for the PBO and P O D polymers. It can be seen that over a wide range of low temperatures the relaxation stress a¢,, which is a function of the applied deformation, varies significantly with temperature. As the temperature rises one can pick out two temperature regions where the stress relaxation rates differ: in the case of 8 % deformation the re-
2926
R . B . BANYAVICHYU$et al.
'
gions are 20- - 75 ° and - 75- - 145 °. The position of the transitional region does not depend on the magnitude of the applied deformation. An analysis of the e c r - T plots in the low temperature region (Fig. 3) shows that large deformations are typical for heat-stable polymers. It is clear from these data that the creep deformation, the extent of which is a function of the applied stress, varies only slightly with temperature over a wide range of low temperatures. Under relatively low degrees of stress (Fig. 3, curve 1) there is only one section of the curve that relates to a low rate of creep. As the stress increases the ecr-T curves feature two portions with differing rates of creep. With the level of stress increasing the transitional region is displaced towards higher temperatures. O-cr ~ MPcI 5 230 -
~'cr,Z
4
15
130
-
120
-60
0
Fro. 3. Temperature dependences of the relaxing stress (r~, for PBO and those of creep deformation ecr for POD at stresses of 120 (1), 200 (2) and 230 MPa (3) and deformations of 4 (7), 6 (6), 9 (4) and I 0 ~ (5).
d(t)MPa ~
240
80~ I "~2 l
l
~
l
6
-
L
l
10eo,%
£[o. 4. ]sochronal dependences of the relaxing stress for PBO at 20 (D, - 5 0 (H), - 7 5 (HI), - 1 2 9 (IV) and - 1 4 5 ° (V). Times of relaxation processes: 3 (1) and 90 min (2).
Isochronal curves plotted on the basis of the creep and the stress relaxation data show that a wide interval of linear viscoelasticity is a characteristic feature of the studied polymers at low temperatures. This is exemplified by the curves in Fig. 4 plotted f o r PBO. The hatched regions relate to extremes in duration of the relaxation processes
Low-temperature relaxation behaviour of heat-stable polymers (3 min and 90 min). Acceleration of relaxation accompanying increase: in the applied deformation or stress leads to the curvilinear character of.the isochronal plots. It should be noted that a maximtun does appear on isochronal curves o f the relaxing stress, though it is less well defined than the high temperature maxima [11]. Coordinates of the maxima on the isochronal curves characterize critical levels of stress act and deformation ec~.Mechanical softening of the material follows whenever these levels are exceeded [2], No maxima appear on the isochronal curves plotted on the basis of the creep data, though there is a clear-cut inflexion. Values of ecr and tr, viz. critical limits above which the onset of a major acceleration of the creep appears, may be determined fromthe coordinates of the point of intersection of two tangents to branches of the isochronal curve. Thus it appears that high deformations at low temperatures are typical for PBO and POD. At low temperatures it is normal for viscous breakdown (mechanical softening) occurring in polymeric materials to be replaced by a rapid growth of cracks, leading to loss of soundness of the material. Changes in polymer properties occurring in the cooling process are the result of diminished segmental and group mobility of the macromolecules as well as diminution of the amount of free volume in the material [5, 6]. However, the free volume is only slightly affected by a fall in temperature where rigidity is a property of the chains of the heat-stable polymers [7, 8]. This means that if group mobility of the macromolecules is maintained in the cryogenic temperature region changes in their thermoviscoelastic properties during cooling processes are less marked than those occurring in flexible polymers (traditional thermoplasts). Relaxation transitions in the low-temperature region. A temperature change in the region of Tg for heat-stable polymers is normally accompanied by a change in the rate of the relaxation processes and by the appearance of relaxation transitions. Such transitions have been reported for a number of heat-stable polymers by authors investigating their relaxation behaviour in the high temperature region [2, 11, 12]. Let us consider the matter of low temperature relaxation transitions in some detail. An analysis of the results of the stress relaxation investigations shows that the magnitude of critical stresses a~r is a function of the time of relaxation processes t r. Figure 5 shows the temperature dependence of critical stress levels plotted for different values of rr. It can be seen that over the entire temperature interval examined an increase in t~ is accompanied by a reduction in ~ r . TO determine the position of relaxation transitions temperature dependences of the critical stresses were replotted using the coordinates critical stress tr¢~-relaxation time tr. Figure 6 shows these plots for PBO at various temperatures. Over the entire temperature interval (from 20 to - 145 °) a linear relationship between log t~ and log a , is maintained. It is known that the absolute value of the tangent of the angle of slope ~o of the linear portion of a log t~ vs. log act plot is a kinetic indicator of the relaxation rates of polymers [14]. The temperature dependence of parameter Cto for PBO is represented in Fig. 7. It is seen that the curve can be subdivided into two portions. In the interv~ 2 0 - - 70 ° there is no significfint change in ~o. A fall in temperature in the interval - 70- 145 ° marks the onset of a rapid rise in 0Co.The higher the value of 0Co,the less marked is the degree of stress relaxation. A fall in temperature leads to a very significant change
2928
R.B.
BANYAVICHYUS
et al.
in the segmental a n d g r o u p mobility o f the macromolecules, a n d in the final analysis this is reflected in the relaxation rate. Thus the temperature dependence o f ~o enables us to detect a low temperature relaxation transition at - 70 ° for P B O and to identify n o t only this one in the low temperature region, but also subregions in which relaxation processes take place at different rates. ~c. ,M P a
180 2
-120
-60
0
T°
Fxo. 5. Temperature dependences of critical stresses crc, for PBO. Times of the relaxation process: 0-5 (1), 3 (2), 30 (3) and 90 rain (4).
lo9 .Cseol 22
3"25
°
1.75 I
2'I
I
23
I
1
1N o'cr[MPa]
Fro. 6
FIe. 7
FIe. 6. Plots of time of the relaxation process for PBO vs. critical stresses at 20 (1), - 50 (2), - 75 (3), - 120 (4) and - 145° (5). Fro. 7. Temperature dependences of fl-1 (1-3) and 6o (4) for PBO. Time of relaxation processes 3 (1), 30 (2) and 90 rain (3); 8 % deformation. The p o s i t i o n o f the relaxation transition m a y be determined with the aid o f a simplified indicator, viz. the relative degree o f decay in the rcla~'ng stress 1
(gin
B
oio-o(t)
Low-temperature relaxation behaviour of heat-stable polymers
2929
where oq. is the initial stress developing at the moment when the deformation is no longer apl~lied, and a(t) is the relaxing stress at a moment o f time t. Figure 7 shows the temperature dependences of parameter fl- t for PBO for the various relaxation times. It can be seen that the relaxation transition determined from the temperature dependence of fl- i is scarcely dependent at all on the duration o f the relaxation process, and coincides with the transition determined from the *t0(T) plot. It is clear therefore that the simplified parameter fl- ~ may be used to determine the position o f relaxation transitions for heat-stable polymers in the low-temperature region. This parameter was also used as a means o f comparative analysis of the relaxation behaviour of a number of heat-stable polymers in the high-temperature region [14, 15]. Mechanical durability. A kinetic indicator of the mechanical durability of polymers under conditions o f stress relaxation is the length of time t~ during which a critical stress relaxation is the length of time tr during which a critical stress trcr is preserved [14]. To approximate the dependence of t~ on Crorwe have the relation t, = B o ' ~ ~°
where B and *to are empirical parameters.
VPa 320
1I0 ~
-120
-60
31
.
0
T°
FIG. 8. Regions of mechanical durability for POD (1, 3, 6) and PBO (2, 4, 5) under isothermal conditions based on stress (1-4) and deformation (5, 6) determined from the forced elastic limit under compression (1, 2) and from the critical stresses and deformation in the case of creep (3, 6) and relaxation (4, 5). Parameter *to is the tangent o f the angle of slope of the log tr (log oct) plots. According to Fig. 7 relations between *to and T change at a relaxation transition temperature o f - 7 0 °. Now the temperature dependence of *to may be described by the following correlations: *to
( a -- k T ~al - kl T
when when
T >I Tt, T~< rtr
It appears from the results of the experiments and calculations that the temperature
2930
R.B. BANYAVICHYUSet al.
dependence of B is described by the formula B=AeV/Rr,
,'~
where A and U are empirical parameters, R is the universal gas constant, and T is the absolute temperature. For BPO the above parameters are: a = 65, k = 0.13; a~ = 131, k l = 0.146; log A = - 3 2 ; U = 5 1 3 kJ/mole. The found values of the parameters make it possible to predict the relaxation behaviour of PBO, and its mechanical durability in the low-temperature region. Temperature dependences of the critical stresses trcr and deformations 2 give an objective descriptions of the mechanical durability of polymers allowing for relaxation processes that occur in the latter. Figure 8 shows the curves in question for PBO and P O D under conditions of stress relaxation and creep. In our case the time during which act and e , were determined is the maximum period of time for the experiment, i.e. 90 min. A comparative analysis of regions of mechanical durability of PBO and P O D (Fig. 8) based on stress ( a - T ) , taking account of relaxation processes, and also neglecting the latter, shows that the studied polymers are reasonably well able to withstand considerable stress at low temperatures. At the same time range of durability of the polymers is significantly lower, over the entire temperature interval examined, when account is taken of the relaxation processes. Translated by R. J. A. HENDRY REFERENCES
1. V. V. KORSHAK, Khimicheskoye stroyenie i temperaturnye kharakteristiki polimerov (Chemical Structure and Temperature Characteristics of Polymers). p. 420, Nauka, Moscow, 1970 2. A. A. ASKADSKII, Struktura i svoistva teplostoikikh polimerov (Structure and Properties of Heat-stable Polymers). p. 320, Khimiya, Moscow, 1981 3. Termoustoichivost' plastikov konstruktsionnogo naznacheniya (Heat Resistance of Plastics Intended for Constructional Uses). (ed. by Ye. B. Trostyanskaya) p. 240, Khimiya, Moscow, 1980 4. A. Ya. CHERNIKI-IOV, D. A. SOLOVYKH, M. P. YAKOVLEV, V. A. ISAYEVA, N. V. LEONTEVA, R. V. MARKINA, V. P. POPOVA and B. Ye. VOSTORGOV, Plast. Massy, 7, 40, 1977 5. D. A. WRIGLEY, Mekhanicheskie svoistva materialov pri nizkikh tetnperaturakh (Mechanical Properties of Materials at Low Temperatures). (Trans. from English, ed. by L. K. Gordenko) p. 374, Mir, Moscow, 1974 6. T. I. SOGOLOVA and M. I. DEMINA, Mekhanika polimerov, 3, 387, 1977 7. L 1. PEREPECHKO, Svoistva polimerov pri nizkikh temperaturakh (Low Temperature Behaviour of Polymers). p. 272, Khimiya, Moscow, 1977 8. L 1. PEREPECHKO and Ye. B. VOLOSHILOV, Vysokomol. soyed. A19: 1620, 1977 (Translated in Polymer Sci. U.S.S.R. 19: 7, 1856, 1977) 9. A. Ya. CHERNIKHOV, L. A. RODIVILOVA, Ye. I. KRAYEVSKAYA,L. I. GOLUBENKOVA, B. M. KOVARSKAYA, S. N. NIKONOVA, Ts. N. TSVETKOV, L. D. PERTSOV and T, Ts. BOGACHEV, Plast. Massy, 4, 24, 1973 10. A. Ya. CHERNIKHOV and V. A. ISAYEVA, Sintez i svoistva i primenenie polibenzoksazolov (Synthesis and the Properties and Applications of Polybenzoxazoles). Obzorn. inform, seriya: Plasticheskie massy i sinteticheskie smoly (Plastics and Synthetic Resins). p. 36, NIITEKHIM, ,Moscow, 1980
Description of glass-transitions (~-transitions)
293I
11. R. B. BANYAVICHUS, A. I. MARMA and A. A. ASKADSKII, Vysokomol. soyed. A21:1383 1978 (Translated in Polymer Sci. U.S.S.R. 21: 6, 1519, 1978) 12. A. A. ASKADKSH, Z. S. VIKHAUSKAS, R. B. BANYAVICHYUS and A. I. MARMA, Vysokomol, soyed. A25: 203, 1983 (Translated in Polymer Sci. U.S.S.R. 25: 1, 236, 1983) 13. R.B. BANYAVICHYUS, A. V. AMBRAZYAVICHYUS and A. A. ASKADSKII, Zavodsk. lab. 50: 86, 1984. 14. A. A. ASKADSKII, Deformatsiya polimerov (Deformation of Polymers). p. 448, Khimiya, Moscow ,1973. 15. A. A. MAVRICHEVA, A. A. ASKADSKII and V. Ye GUL', Vysokomol. soyed. A 1 9 : 2379, 1977 (Translated in Polymer Sci. U.S.S.R. 19: 10, 2733, 1977)
Polymer Science U.S.S.R. Vol. 26, No. 12, pp. 2931-2939, 1984
Printed in Poland
0006-3509/84 $10.00+ .off © 1986 PergamonPress Ltd.
DESCRIPTION OF GLASS-TRANSITIONS (~-TRANSITIONS) USING A NONLINEAR MODEL OF A POLYMER BODY* Y u . I. MATVEYEV a n d A. A. ASKADSKII Kuibyshev Civil Engineering Institute, Moscow (Received 13 June 1983) The relaxation time spectra of a nonlinear model of a polymer body have been used to determine the relations between temperatures of glass transition, melting and the onset of rapid degradation as well as parameters of elements of the model. Relations between coordination numbers in the amorphous and the crystalline states and thermal characteristics of the polymer have been determined. An expression similar to the Williams-Landel-Ferry equation has been derived with its coefficients expressed in terms of the model.
EARLIER p a p e r s o f ours [1, 2] describe a n o n l i n e a r m o d e l which we p r o p o s e d in o r d e r t o describe the viscoelastic b e h a v i o u r o f p o l y m e r b o d i e s u n d e r large [1] a n d small [2] def o r m a t i o n s . W e were able to show t h a t even in the case o f small d e f o r m a t i o n s two A l e k s a n d r o v - L a z u r k i n t y p e m o d e l s j o i n e d t o g e t h e r at a p a r t i c u l a r angle will give a r e l a x a t i o n t i m e s p e c t l u m due to n o n l i n e a r effects. On the basis o f the d a t a in p a p e r s [1, 2] we have n o w to a n a l y z e s o m e new results t h a t follow f r o m this model, which m a y be verified b y experiments. W e will s h o w t h a t with the a i d o f the m o d e l one is a b l e to describe t h e p r i n c i p a l t r a n s i t i o n t o the glasslike state.
* Vysokomol. soyed. A26i No. 12, 2611-2617, 1984.
2923
REFERENCES 1. M. T. BRYK, Polimerizatsiya na tverdoi poverkhnosti neorganicheskikh veshchestv (Polymerization on Solid Surfaces of inorganic Materials), p. 240, Naukova Dumka, Kiev, 1981 2. S. S. IVANCHEV and A. V. DMITRENKO, Uspekhi khimii 31: 1178, 1982 3. G. C. EASTMOND, C. NGUYEN-HUU and W. H. PIRET, Polymer 21: 598, 1980 4. C. E. SCHILDKNECHT, High Polymers. Polymer Processes 29: 244, 1977 5. S. S. IVANCHEV, N. S. YENIKOLOPYAN, B. V. POLOZOV, A. V. DMITRENKO, V. A. DEMIDOVA and A. K. LITKOVETS, Vysokomol. soyed. A23: 2064, 1981 (Translated in Polymer Sci. U.S.S.R. 23: 9, 2248, 1981) 6. V. A. POPOV, A. N. GRISHIN, Yu. A. ZVEREVA, T. V. PALAYEVA, V. A. FOMIN and S. S. IVANCHEV, Vysok0mol. soyed. A25: 760, 1983 (Translated in Polymer Sci. U.S.S.R. 25: 4, 883, 1983) 7. A. V. OLENIN, A. K. ANDRIANOV, E. A. KASHUTINA, A. A. ZHDANOV, V. P. ZUBOV and V. A. KABANOV, U.S.S.R. Pat. 935511. Publ. in Byull. Izob., 22, 102, 1982 8. C. H. BAMFORD, P. A. CROWE and R. P. WAYNE, Proc. Roy. Soc. London A284: 455, 1965 9. C. H. BAMFORD, P. A. CROWE, J HOBBS and R. P. WAYNE, Proc. Roy. Soc. London A292: 153, 1966 10. E. A. KASHUTINA, A. A. ZHDANOV, A. V. OLENIN, A. K. ANDRIANOV, V. P. ZUBO'V, and V. A. KABANOV, Soviet Pat. 935508. PubL in Byull. Izob., 22, 102, 1982 11. A. V. OLI~NIN, A. L. KHRISTYUK, V. B. GOLUBEV, V. P. ZUBOV and V. A. KABANOV, Vysokomol. soyed. A25: 423, 1983 (Translated in Polymer Sci. U.S.S.R. 25: 2, 495, 1983) 12. F. W. BILLMAYER and C. B. de THEN, J. Amer. Chem. Soc. 77: 4763, 1955 13. A. K. ANDRIANOV, A. V. OLENIN, V. P. ZUBOV, R. A. KASHUTINA, A. A. ZHDANOV and V. A. KABANOV, Vysokomol. soyed. A25: 1987, 1983 (Translated in Polymer Sci. U.S.S.R. 25: 9, 2314, 1983)
Polymer Science U.S.S.R. Vol. 26, No. 12, pp. 2923-2931, 1984 Printed in Poland
0006-3509/84 $10.00+ .00 © 1986PergamonPress Ltd.
LOW-TEMPERATURE RELAXATION BEHAVIOUR OF HEAT-STABLE POLYMERS* R. B. BANYAVICHYUS, Z. B. MIGONENE a n d A. A. ASKADSKil Antapas Snechkus Polytechnical Institute, Kaunas
(Received 13 June 1983) Relaxation transitions occurring in aromatic polymers of structurally dissimilar types have been investigated by stress relaxation and creep methods. At low temperatures significant degrees of deformation were observed for these polymers. The range of mechanical durability has been determinef or the polymers, taking low temperature relaxation processes into account. * Vysokomol. soyed. A26: No. 12, 2604-2610, 1984.
2924
R . B . BANYAVICHYU$et al.
SPECIAL structural characteristics of heat-stable polymers determine their high heat resistance, thermal stability and cold resistance [1-3]. Heat-stable polymers are widely used as constructional materials capable of withstanding high temperatures [3, 4]. Detailed studies have accordingly been made of the high-temperature mechanical behaviour of heat-stable polymers under loads of various types [2]. It is known [3, 5-8] that heat-stable polymers are also noted for their marked ability to withstand cryogenic temperatures: their high deformation values even at - 2 7 0 ° are referred to in [6]. In view of this polymers of this type important constructional applications from a cryogenic standpoint and are of definite interest as cold-resistant materials. However, it appears that very little study has been made o f features o f the low-temperature mechanical behaviour of heat-stable polymers. Our aim in the present investigation was to study features of the low-temperature viscoelastic behaviour o f heat-stable polymers and to determine their mechanical durability, taking relaxation processes into account. To do so we took as examples two structurally dissimilar polymers, polybenzoxazole (PBO) and polyoxadiazole (POD). Heat stable polymers of Soviet origin,* viz. Niplon-1 (POD) [9] and Niplon-2 (PBO) [10] were used as model study objects in the investigation. Relaxation properties of these polymers were investigated at high temperatures in papers [11, 12]. Low temperature studies (under isothermic conditions) of stress relaxation and creep were carried out, using bulk microsamples measuring 3 × 5 x 6 ram. Samples were prepared by hot pressing at 360 (POD) and 380° (PBO) under specific pressure of 75 MPa. The ready-made samples underwent heat treatment at 100° for 72 hr, and before use were kept in an exsiccator. Low temperature experiments were performed on the 1253U-2-2 equipment using a specially developed reversor and extensometer [13]. The temperature interval extended from 20 to -145°; the ranges of stress and deformation extended from minimal values in the area of linen r viscoelasticity to levels determined by the maximum (limiting) deformation and stress values for mechanical softening of the polymer at a given test temperature. Experiments took 90 rain to perform. Stress relaxation and creep. Studies of stress relaxation and creep in PBO and POD showed that relaxation processes in these polymers are clearly evident even in the low temperature region. It is clear from an analysis of the results of stress relaxation experiments that in the entire temperature interval examined (from 20 to - 1 4 5 °) an increase in the degree of deformation is accompanied by displacement of the relaxation curves towards high stress. In addition, there is a marked acceleration of relaxation in the initial period as the deformation increases. This is exemplified by the relaxation curves for PBO at - 75 ° (Fig. 1) at different initial degrees of deformation. A temperature drop down to - 145 ° leads to a significant retardation of relaxation processes. A similar pattern of change in relaxation processes is revealed by investigation of the behaviour of the studied polymers under conditions of creep. Figure 2 shows the creep curves for P O D at - 120 ° under various initial stresses. It can be seen that an increase
* POD and PBO were kindly provided for test purposes by A. Ya. Chernikhov of the Plastmassy Scientific & Industrial Research Association.
Low-temperature relaxation behaviour of heat-stable polymers
2925
in the applied stress, where the test temperature is kept constant, leads to a uniform displacement of the curves towards larger deformations. Moreover relaxation p r o c esses become more definite and clear-cut as the Stress increases. A drop in temperature is accompanied by a significant diminution of the creep, though it is fairly marked a t - 50 and - 75 °. ~, MPa
2
2
0
~
5 .o.
_~
,
~ 2
140 <"
0
I
I
30
I
~O I
t
I
;
i
60
BO '
Time, rain FIG. 1. Stress relaxation curves for PBO at - 75 ° and initial deformations of 4 (1), 6 (2),
8 (3), 9 (4) and 10~o (5).
e,% f 18 ,0
0
3
aoo..oo.o
o
,
DO'O-O-o"O
0
0
I
30
I
Time, min
l
GO
2 ! t
0
l
90
FIG. 2. Creep curves for POD at -120 ° under initial Stresses of 120 (1), 180 (2), 220 (3), 260 (4) and 290 MPa (5). Temperature dependences of acr-T and e,,~-T plotted at different d e f o r m a t i o n s or stresses (ac, and eer being the stress and the deformation developing in the course o f an experiment lasting 90 min) may be used as generalizing characteristics reflecting the influence of temperature on relaxation processes. These plots appear in Fig. 3 for the PBO and P O D polymers. It can be seen that over a wide range of low temperatures the relaxation stress a¢,, which is a function of the applied deformation, varies significantly with temperature. As the temperature rises one can pick out two temperature regions where the stress relaxation rates differ: in the case of 8 % deformation the re-
2926
R . B . BANYAVICHYU$et al.
'
gions are 20- - 75 ° and - 75- - 145 °. The position of the transitional region does not depend on the magnitude of the applied deformation. An analysis of the e c r - T plots in the low temperature region (Fig. 3) shows that large deformations are typical for heat-stable polymers. It is clear from these data that the creep deformation, the extent of which is a function of the applied stress, varies only slightly with temperature over a wide range of low temperatures. Under relatively low degrees of stress (Fig. 3, curve 1) there is only one section of the curve that relates to a low rate of creep. As the stress increases the ecr-T curves feature two portions with differing rates of creep. With the level of stress increasing the transitional region is displaced towards higher temperatures. O-cr ~ MPcI 5 230 -
~'cr,Z
4
15
130
-
120
-60
0
Fro. 3. Temperature dependences of the relaxing stress (r~, for PBO and those of creep deformation ecr for POD at stresses of 120 (1), 200 (2) and 230 MPa (3) and deformations of 4 (7), 6 (6), 9 (4) and I 0 ~ (5).
d(t)MPa ~
240
80~ I "~2 l
l
~
l
6
-
L
l
10eo,%
£[o. 4. ]sochronal dependences of the relaxing stress for PBO at 20 (D, - 5 0 (H), - 7 5 (HI), - 1 2 9 (IV) and - 1 4 5 ° (V). Times of relaxation processes: 3 (1) and 90 min (2).
Isochronal curves plotted on the basis of the creep and the stress relaxation data show that a wide interval of linear viscoelasticity is a characteristic feature of the studied polymers at low temperatures. This is exemplified by the curves in Fig. 4 plotted f o r PBO. The hatched regions relate to extremes in duration of the relaxation processes
Low-temperature relaxation behaviour of heat-stable polymers (3 min and 90 min). Acceleration of relaxation accompanying increase: in the applied deformation or stress leads to the curvilinear character of.the isochronal plots. It should be noted that a maximtun does appear on isochronal curves o f the relaxing stress, though it is less well defined than the high temperature maxima [11]. Coordinates of the maxima on the isochronal curves characterize critical levels of stress act and deformation ec~.Mechanical softening of the material follows whenever these levels are exceeded [2], No maxima appear on the isochronal curves plotted on the basis of the creep data, though there is a clear-cut inflexion. Values of ecr and tr, viz. critical limits above which the onset of a major acceleration of the creep appears, may be determined fromthe coordinates of the point of intersection of two tangents to branches of the isochronal curve. Thus it appears that high deformations at low temperatures are typical for PBO and POD. At low temperatures it is normal for viscous breakdown (mechanical softening) occurring in polymeric materials to be replaced by a rapid growth of cracks, leading to loss of soundness of the material. Changes in polymer properties occurring in the cooling process are the result of diminished segmental and group mobility of the macromolecules as well as diminution of the amount of free volume in the material [5, 6]. However, the free volume is only slightly affected by a fall in temperature where rigidity is a property of the chains of the heat-stable polymers [7, 8]. This means that if group mobility of the macromolecules is maintained in the cryogenic temperature region changes in their thermoviscoelastic properties during cooling processes are less marked than those occurring in flexible polymers (traditional thermoplasts). Relaxation transitions in the low-temperature region. A temperature change in the region of Tg for heat-stable polymers is normally accompanied by a change in the rate of the relaxation processes and by the appearance of relaxation transitions. Such transitions have been reported for a number of heat-stable polymers by authors investigating their relaxation behaviour in the high temperature region [2, 11, 12]. Let us consider the matter of low temperature relaxation transitions in some detail. An analysis of the results of the stress relaxation investigations shows that the magnitude of critical stresses a~r is a function of the time of relaxation processes t r. Figure 5 shows the temperature dependence of critical stress levels plotted for different values of rr. It can be seen that over the entire temperature interval examined an increase in t~ is accompanied by a reduction in ~ r . TO determine the position of relaxation transitions temperature dependences of the critical stresses were replotted using the coordinates critical stress tr¢~-relaxation time tr. Figure 6 shows these plots for PBO at various temperatures. Over the entire temperature interval (from 20 to - 145 °) a linear relationship between log t~ and log a , is maintained. It is known that the absolute value of the tangent of the angle of slope ~o of the linear portion of a log t~ vs. log act plot is a kinetic indicator of the relaxation rates of polymers [14]. The temperature dependence of parameter Cto for PBO is represented in Fig. 7. It is seen that the curve can be subdivided into two portions. In the interv~ 2 0 - - 70 ° there is no significfint change in ~o. A fall in temperature in the interval - 70- 145 ° marks the onset of a rapid rise in 0Co.The higher the value of 0Co,the less marked is the degree of stress relaxation. A fall in temperature leads to a very significant change
2928
R.B.
BANYAVICHYUS
et al.
in the segmental a n d g r o u p mobility o f the macromolecules, a n d in the final analysis this is reflected in the relaxation rate. Thus the temperature dependence o f ~o enables us to detect a low temperature relaxation transition at - 70 ° for P B O and to identify n o t only this one in the low temperature region, but also subregions in which relaxation processes take place at different rates. ~c. ,M P a
180 2
-120
-60
0
T°
Fxo. 5. Temperature dependences of critical stresses crc, for PBO. Times of the relaxation process: 0-5 (1), 3 (2), 30 (3) and 90 rain (4).
lo9 .Cseol 22
3"25
°
1.75 I
2'I
I
23
I
1
1N o'cr[MPa]
Fro. 6
FIe. 7
FIe. 6. Plots of time of the relaxation process for PBO vs. critical stresses at 20 (1), - 50 (2), - 75 (3), - 120 (4) and - 145° (5). Fro. 7. Temperature dependences of fl-1 (1-3) and 6o (4) for PBO. Time of relaxation processes 3 (1), 30 (2) and 90 rain (3); 8 % deformation. The p o s i t i o n o f the relaxation transition m a y be determined with the aid o f a simplified indicator, viz. the relative degree o f decay in the rcla~'ng stress 1
(gin
B
oio-o(t)
Low-temperature relaxation behaviour of heat-stable polymers
2929
where oq. is the initial stress developing at the moment when the deformation is no longer apl~lied, and a(t) is the relaxing stress at a moment o f time t. Figure 7 shows the temperature dependences of parameter fl- t for PBO for the various relaxation times. It can be seen that the relaxation transition determined from the temperature dependence of fl- i is scarcely dependent at all on the duration o f the relaxation process, and coincides with the transition determined from the *t0(T) plot. It is clear therefore that the simplified parameter fl- ~ may be used to determine the position o f relaxation transitions for heat-stable polymers in the low-temperature region. This parameter was also used as a means o f comparative analysis of the relaxation behaviour of a number of heat-stable polymers in the high-temperature region [14, 15]. Mechanical durability. A kinetic indicator of the mechanical durability of polymers under conditions o f stress relaxation is the length of time t~ during which a critical stress relaxation is the length of time tr during which a critical stress trcr is preserved [14]. To approximate the dependence of t~ on Crorwe have the relation t, = B o ' ~ ~°
where B and *to are empirical parameters.
VPa 320
1I0 ~
-120
-60
31
.
0
T°
FIG. 8. Regions of mechanical durability for POD (1, 3, 6) and PBO (2, 4, 5) under isothermal conditions based on stress (1-4) and deformation (5, 6) determined from the forced elastic limit under compression (1, 2) and from the critical stresses and deformation in the case of creep (3, 6) and relaxation (4, 5). Parameter *to is the tangent o f the angle of slope of the log tr (log oct) plots. According to Fig. 7 relations between *to and T change at a relaxation transition temperature o f - 7 0 °. Now the temperature dependence of *to may be described by the following correlations: *to
( a -- k T ~al - kl T
when when
T >I Tt, T~< rtr
It appears from the results of the experiments and calculations that the temperature
2930
R.B. BANYAVICHYUSet al.
dependence of B is described by the formula B=AeV/Rr,
,'~
where A and U are empirical parameters, R is the universal gas constant, and T is the absolute temperature. For BPO the above parameters are: a = 65, k = 0.13; a~ = 131, k l = 0.146; log A = - 3 2 ; U = 5 1 3 kJ/mole. The found values of the parameters make it possible to predict the relaxation behaviour of PBO, and its mechanical durability in the low-temperature region. Temperature dependences of the critical stresses trcr and deformations 2 give an objective descriptions of the mechanical durability of polymers allowing for relaxation processes that occur in the latter. Figure 8 shows the curves in question for PBO and P O D under conditions of stress relaxation and creep. In our case the time during which act and e , were determined is the maximum period of time for the experiment, i.e. 90 min. A comparative analysis of regions of mechanical durability of PBO and P O D (Fig. 8) based on stress ( a - T ) , taking account of relaxation processes, and also neglecting the latter, shows that the studied polymers are reasonably well able to withstand considerable stress at low temperatures. At the same time range of durability of the polymers is significantly lower, over the entire temperature interval examined, when account is taken of the relaxation processes. Translated by R. J. A. HENDRY REFERENCES
1. V. V. KORSHAK, Khimicheskoye stroyenie i temperaturnye kharakteristiki polimerov (Chemical Structure and Temperature Characteristics of Polymers). p. 420, Nauka, Moscow, 1970 2. A. A. ASKADSKII, Struktura i svoistva teplostoikikh polimerov (Structure and Properties of Heat-stable Polymers). p. 320, Khimiya, Moscow, 1981 3. Termoustoichivost' plastikov konstruktsionnogo naznacheniya (Heat Resistance of Plastics Intended for Constructional Uses). (ed. by Ye. B. Trostyanskaya) p. 240, Khimiya, Moscow, 1980 4. A. Ya. CHERNIKI-IOV, D. A. SOLOVYKH, M. P. YAKOVLEV, V. A. ISAYEVA, N. V. LEONTEVA, R. V. MARKINA, V. P. POPOVA and B. Ye. VOSTORGOV, Plast. Massy, 7, 40, 1977 5. D. A. WRIGLEY, Mekhanicheskie svoistva materialov pri nizkikh tetnperaturakh (Mechanical Properties of Materials at Low Temperatures). (Trans. from English, ed. by L. K. Gordenko) p. 374, Mir, Moscow, 1974 6. T. I. SOGOLOVA and M. I. DEMINA, Mekhanika polimerov, 3, 387, 1977 7. L 1. PEREPECHKO, Svoistva polimerov pri nizkikh temperaturakh (Low Temperature Behaviour of Polymers). p. 272, Khimiya, Moscow, 1977 8. L 1. PEREPECHKO and Ye. B. VOLOSHILOV, Vysokomol. soyed. A19: 1620, 1977 (Translated in Polymer Sci. U.S.S.R. 19: 7, 1856, 1977) 9. A. Ya. CHERNIKHOV, L. A. RODIVILOVA, Ye. I. KRAYEVSKAYA,L. I. GOLUBENKOVA, B. M. KOVARSKAYA, S. N. NIKONOVA, Ts. N. TSVETKOV, L. D. PERTSOV and T, Ts. BOGACHEV, Plast. Massy, 4, 24, 1973 10. A. Ya. CHERNIKHOV and V. A. ISAYEVA, Sintez i svoistva i primenenie polibenzoksazolov (Synthesis and the Properties and Applications of Polybenzoxazoles). Obzorn. inform, seriya: Plasticheskie massy i sinteticheskie smoly (Plastics and Synthetic Resins). p. 36, NIITEKHIM, ,Moscow, 1980
Description of glass-transitions (~-transitions)
293I
11. R. B. BANYAVICHUS, A. I. MARMA and A. A. ASKADSKII, Vysokomol. soyed. A21:1383 1978 (Translated in Polymer Sci. U.S.S.R. 21: 6, 1519, 1978) 12. A. A. ASKADKSH, Z. S. VIKHAUSKAS, R. B. BANYAVICHYUS and A. I. MARMA, Vysokomol, soyed. A25: 203, 1983 (Translated in Polymer Sci. U.S.S.R. 25: 1, 236, 1983) 13. R.B. BANYAVICHYUS, A. V. AMBRAZYAVICHYUS and A. A. ASKADSKII, Zavodsk. lab. 50: 86, 1984. 14. A. A. ASKADSKII, Deformatsiya polimerov (Deformation of Polymers). p. 448, Khimiya, Moscow ,1973. 15. A. A. MAVRICHEVA, A. A. ASKADSKII and V. Ye GUL', Vysokomol. soyed. A 1 9 : 2379, 1977 (Translated in Polymer Sci. U.S.S.R. 19: 10, 2733, 1977)
Polymer Science U.S.S.R. Vol. 26, No. 12, pp. 2931-2939, 1984
Printed in Poland
0006-3509/84 $10.00+ .off © 1986 PergamonPress Ltd.
DESCRIPTION OF GLASS-TRANSITIONS (~-TRANSITIONS) USING A NONLINEAR MODEL OF A POLYMER BODY* Y u . I. MATVEYEV a n d A. A. ASKADSKII Kuibyshev Civil Engineering Institute, Moscow (Received 13 June 1983) The relaxation time spectra of a nonlinear model of a polymer body have been used to determine the relations between temperatures of glass transition, melting and the onset of rapid degradation as well as parameters of elements of the model. Relations between coordination numbers in the amorphous and the crystalline states and thermal characteristics of the polymer have been determined. An expression similar to the Williams-Landel-Ferry equation has been derived with its coefficients expressed in terms of the model.
EARLIER p a p e r s o f ours [1, 2] describe a n o n l i n e a r m o d e l which we p r o p o s e d in o r d e r t o describe the viscoelastic b e h a v i o u r o f p o l y m e r b o d i e s u n d e r large [1] a n d small [2] def o r m a t i o n s . W e were able to show t h a t even in the case o f small d e f o r m a t i o n s two A l e k s a n d r o v - L a z u r k i n t y p e m o d e l s j o i n e d t o g e t h e r at a p a r t i c u l a r angle will give a r e l a x a t i o n t i m e s p e c t l u m due to n o n l i n e a r effects. On the basis o f the d a t a in p a p e r s [1, 2] we have n o w to a n a l y z e s o m e new results t h a t follow f r o m this model, which m a y be verified b y experiments. W e will s h o w t h a t with the a i d o f the m o d e l one is a b l e to describe t h e p r i n c i p a l t r a n s i t i o n t o the glasslike state.
* Vysokomol. soyed. A26i No. 12, 2611-2617, 1984.