Macromolecules 1992,25, 7069-7070
Large Deformation of Polycarbonate near the Glass Transition Temperature' Tadashi Inoue,' Hirotaka Okamoto, and Kunihiro Osaki Institute for Chemical Research, Kyoto University, Uji, Kyoto 611, Japan Received April 6, 1992 Revised Manuscript Received September 25, 1992
When a large stress is created in a glassy polymer, the polymer starts to deform plastically. By elongating a specimen at a constant rate, such large stresses can be produced. The stress-strain curve depends on the type of polymer species, and many examples of these curves are documented in the literature.' Polystyrene (PS),which is one of the most familiar amorphous polymers, breaks before yielding at room temperature. Consequently, PS is sometimes referred to as "brittle". On the other hand, Bisphenol A polycarbonate (PC) is known as a "ductile" polymer and shows the necking phenomenon even though it is not a crystalline polymer. In a previous study,2 we showed that the birefringence measurement performed simultaneously with the stress test is a convenient method to investigatethe stress-strain relation at large deformation. The birefringence, An, in melts can be related to the stress with the stress-optical rule (SOR).3 However, SOR does not hold well in the glass-to-rubber transition or glassy zones. Some modifications of SOR have been proposed.44 The modified stress-optical rule (MSOR) proposed by the authors led to a rather simple interpretation of the stress-strain relation for PS near the glass transition temperature.2 MSOR for tensile stress, f , can be written as
f ( t )= f G ( t ) + f R ( t ) An(t) = Cd~(t) + CR~R(~)
(1) (2)
where CG and CR are the stress-optical coefficients associated with two components of stress, f~ and f ~ , respectively? CR is equal to the ordinary stress-optical coefficient for the polymer melts. Equations 1 and 2 can be solved simultaneously for f~ and f ~ The . estimated R component of PS increased monotonously with increasing strain and did not show noticeable nonlinear behavior. On the other hand, the G component showed a yield phenomenon and a remarkable nonlinear strain dependence. The complicated behavior of the tensile stress due to large deformation can be attributed mainly to the nonlinearity of the G component. These results are in accord with the interpretation that the R component is the entropy elasticity arising from the orientation of chainse6 The birefringence and stress have been well described with MSOR for a number of polymers, PC, poly(amethylstyrene), and so on in small deformation^.^^^ In the present study, we analyze the stress and birefringence of PC under uniaxial extension up to about 100% strain near the glass transition temperature. Bisphenol A polycarbonate, poly(oxycarbonyloxy-1,4phenyleneisopropylidene-1,4-phenylene),was supplied by the Idemitsu Petroleum Chemical Co., Ltd. The weightaverage molecular weight, M,, and the number-average molecular weight, M,,were measured as M, = 7.5 X lo4 Part 6 of the aeries "Birefringence of Amorphous Polymers".
7069
and M, = 4.2 X lo4with gel permeation chromatography. Test films, 0.1 mm thick, of PC were cast from solution in dichloromethane on a hot plate and dried for a few days under vacuum at 150"C before making the measurements. DSC measurement showed that the glass transition temperature was 147 "C. The modified stress-optical coefficients, CR and CG,of PC were determined as 6.0 X 10-9 and 3.2 X lo-" Pa-l with dynamic measurements, respectively.8 The details of our tensile tester equipped with a simple optical system were reported previously.2 The specimen was attached to the clamps of the apparatus with one end free and kept at 180 "C to remove the remaining birefringence. The temperature was lowered to the measuring temperature at the rate of 1 "C/min, and the free end of the specimen was clamped. The elongation measurement was performed 1h later. After the measurement, the test specimen was checked with a polarizing microscope. Necking and crazing were not observed. The tensile stress, f , and the birefringence, An, were measured under a constant speed of elongation. The initial elongation rate, eo, ranged from 0.1 to 7.4X s-l. Since the elongation ratio, X = 1 + eot, was large (up to about 2 for each measurement), the rate of elongation, e ( t ) = eo/h, was not constant during the experiment. An example of the measured quantities is shown as f and An/CR in Figure 1. The temperature was 151 "C, that is, higher than the glass transition temperature. The stress is a complicated function of time with a sudden change of slope at several points, while the birefringence increases monotonously with t. One can see that SOR, which is applicable to melts, An = CIJ, holds well over a certain time range of 400 < t / s < 800. The G and R components of stress calculated from eqs 1 and 2 are also shown in , differs from An/ Figure 1. The R component, f ~scarcely CR and is a simple function of time. The G component, f ~ is, a complicated function: It increases more rapidly with elongation than the R component does at very short times and then begins to decrease. At about t l s = 400,the G component vanishes and remains zero until it appears again at about t l s = 800. The G and R stress components at various elongation speeds are shown as a function of X in Figure 2. The R component increases simply with increasing extension ratio s-l. except in the range of X > 2 at eo = 7.4 and 1.9 X The fracture occurs at about X = 2.25 when eo = 7.4 X 5-1. In the range of e o = 0.1 X 10-3-1.0X s-l, the G component vanishes at about h = 1.4. It reappears at a higher A, which varies with elongation speed, and then increases. The ordinary stress-opticalrule holds well over this limited range of elongation ratio where the G component remains zero. This means that the tensile stress consists of only the R component that presumably is due to the entropy elasticity due to the orientation of main chains. One may say that the system is close to the rubbery state. and 1.9 X lod3s-l, the G component A t 40 = 7.4X never falls down to zero. However, it decreases rapidly around X = 1.4. Probably the mechanism supporting the G component of stress in the small-strain region breaks down at about h = 1.4. The reason for nonvanishing of the G component at high elongation speeds may be an early onset of strain hardening that will be discussed later. The result presented here should be compared with that for PS. The results obtained on PS in ref 2 are replotted against X in Figure 3. Comparing with Figure 2, one sees a remarkable difference in the behavior of the G component contrasting with the similarity of the R component. The
0024-9297/92/2225-7069$03.00/00 1992 American Chemical Society
Macromolecules, Vol. 25, No. 25, 1992
7070 Communications to the Editor
/i
200
0
LOO
600
800
1200
1000
1400
tis
Figure 1. Example of the stress and birefringence measurements. The temperature is 151 O C , and the elongation speed, eo, is 1.0 X
8-l.
151
10
(-)
f; (* * *) An/CR; (I
I
I
12
14
16
* *
-1 f ~(- ;
-) fc.
I
1
I
1
18
20
22
24
A
Figure 2. Two componenb of stress, f~ and fR, for PC plotted against the elongation ratio at various elongation speeds. The temperature is 151 O C . Thick lines represent f~ and thin lines f ~ The . dotted line overlaps the abscissa at large A. .) e o = 0.1 x 10-3, (-. .-) 0.5 x 10-3, (-. -) 1.0 x 10-3,(- -) 1.9 x 10-3, (e
(-)
-
7.4 x 10-3 S-1.
I
I
I
I
I
decrease of f~ for PC over X = 2 at e o = 7.4 X 10-3 s-1 is possibly the result of the stretch comparable with the maximum stretching of chains between entanglement points. At a lower elongation speed, the level of the R component at X = 2 is lower owing to the relaxation. Since f~ depends on the elongation speed and temperature, a strict comparison between two polymers may be difficult. However, the difference of X, suggests that the segments between entanglement points of PC would orient more highly than those of PS, and the nonlinear viscoelasticity of the R component for PC would be more remarkable at the same elongation ratio. The difference of X, may also affect the behavior of the G component. The secondary increase of the G component at large X might be related to the so-called strain hardening.' It should be noted that the origin of the R component is force due to entropy and does not include the energetic one. When the chain is highly oriented, not only the entropy force but also the energetic one may arise because of bending or torsion of the chain. The energetic forces would be observed as the G component. The secondary increase of the G component seems to start at a lower extension level at a higher elongation speed. The beginning of the secondary increase may be related to the orientation degree of the main-chain backbone, i.e., the . the starting point of the secondary strength of f ~ At increase, the value of f~ seems to be about 5 MPa. Thus, the behavior of PC under large deformation near the glass transition temperature is qualitatively different from that of PS. In particular, the G component of PC vanishes over the range of certain extension ratio. The R components of two polymers are similar to each other and do not show remarkable nonlinearity. However, the maximum extension ratio of PC is about 2 times smaller than that for PS, and this causes the orientation hardening of PC. These features near the glass transition temperature cannot be directly related to the behavior a t lower or room temperatures. The analysis with MSOR a t those temperatures may be significant. Acknowledgment. This study was supported by a Grant-in-Aid for Scientific Research (02453101) of the Ministry of Culture, Science, and Education of Japan.
L
n
12
16
14
18
20
A
Figure 3. Two components of stress, fc and f ~for, PS plotted against the elongation ratio at various elongation speeds. The temperatureis 98 "C. Thick lines represent f~ and thin lines f ~ . (-. .-1 eo = 0.6 x 10-3, (-. -) 1.1 x 10-3, (- -) 1.4 x 10-3, (-) 2.0 x 10-3s-1.
G component of PS remains nonzero over the whole range of measurements. Thus, the nonlinear viscoelasticity of the G component strongly depends on the polymer species. For the case of PC, the fracture occurs at about X = 2.25 when eo = 7.4 X s-l. This X agrees well with the elongation ratio A, at which chains between entanglement points are fully stretched. The value of Xe estimated by Dettenmaier is 2 for PC and 4.1 for PS in which estimation of the relaxation of the orientation is not c~nsidered.~ The
References and Notes (1) See, for example: Relaxation Phenomena in Polymers; Matauoka, S., Ed.; Hanser Publishers: New York, 1992. (2) Okamoto,H.; Inoue, T.; Osaki, K. Macromolecules 1992,25, 3413. (3) See,for example: Janeschitz-Kriegl,H.PolymerMelt Rheology and Flow Birefringence; Springer-Verlag: Berlin, 1983. (4) Pries, L. S.; Vishnyakov, I. I.; Pavlova, I. P. Znt. J. Polym.
Mater. 1980,8, 85.
(5) Read, B. E.Polym. Eng. Sci. 1983,23, 835. (6) Inoue, T.; Okamoto, H.; Osaki, K. Macromolecules 1991,24, 5670. (7) Inoue, T.;Hwang, E. J.; Osaki, K. J. Rheol., in press. (8) Hwang, E. J.; Inoue, T.; Osaki, K. J.Polym.Eng. Sci., in press. (9) Dettenmaier, M. Intrinsic Crazes in Polycarbonate: Phe-
nomenology and Molecular Interpretation of a New Phenomenon. Advances in Polymer Science; Springer-Verlag: Berlin, 1983; Vol. 52/53.
