Thermal density-fluctuations in rejuvenated and aged polycarbonate

Thermal Density-Fluctuations in Rejuvenated and Aged Polycarbonate

J. MfJLLER and J. H. WENDORFF, Deutsches Kunstsfoff-Institut, Darmstudt, West G e m n y

INTRODUCTION

It is a characteristic property of the glassy state that its properties depend on thermal history and in many cases also on mechanical hi~tory.';~ Examples in case are the dependence of viscoelastic properties on the cooling rate by which the glassy state is approached from the melt or the dependence on the pressure applied during cooling? The reason for such coupling of macroscopic properties to the previous history of the material is that the glassy state corresponds thermodynamically to a nonequilibrium state. This manifests itself by the phenomenon of physical aging, i.e., by the occurrence of relaxations of thermodynamic quantities such as the volume or the enthalpy towards their equilibrium values. Aging gives rise to an increase of the relaxation times characteristic of the glassy state, which in turn influences macroscopic mechanical or electrical properties.'-4

It has been reported that the effects of aging may be totally or at least partially erased by subjecting the glassy material to a strain.'*6-8 This gives rise to a decrease of the relaxation time and it is for this reason that this effect has been called rejuvenation. The decrease of the relaxation time, on the other hand, gives rise to an enhanced aging of the rejuvenated samples, which is obvious from density measurements and calorimetric samples, as well as from investigations on dynamic mechanical properties.'*6-8 This enhanced aging has been tentatively attributed to strain-induced formation of free volume, although compressional strain leads to similar effects as tensile strain. It is obvious that our knowledge on the process of rejuvenation and a subsequent aging is still very much restricted.

The present paper is concerned with this topic for the particular case of cold-drawn polycarbonate. The techniques applied comprise absolute small-angle X-ray studies on thermal density fluctuations: and in addition, calorimetric studies on enthalpy variations as well as dilatometric studies of volume variations.

EXPERIMENTAL

The experiments were performed on polycarbonate. Polycarbonate has the ad- vantage that uniaxial extensions or compressions can be achieved rather easily within the solid state. We used for our investigations Makrolon samples obtained from Bayer AG, West Germany. The samples were deformed in the majority of cases at room temperature and total deformation amounted to about 100%. In some instances the deformation was performed at elevated temperatures within the glassy state,

The calorimetric investigations were done by means of a Perkin Elmer DSC 4 and the dilatometric measurements with a glass dilatometer, using mercury. The thermal density fluctuations were determined by means of absolute small-angle X-ray scattering studies. A Kratky compact small-angle X-ray camera was used in combination with

Journal of Polymer Science: Part C: Polymer Letters, Vol. 26, 421-427 (1988) 0 1988 John Wiley & Sons, Inc. CCC 0360-6384/88/l00421-07$04.00

422 m E R AND WENDORFF

a position-sensitive counter. The absolute intensity was established by means of a moving slit device.

Thermal Density Fluctuatio~ in the Glassy State

It has repeatedly been shown that one approach towards modelling the nonequilibrium glassy state, including its dynamical properties, and particularly its rejuvenation and aging properties, is based on the free volume c ~ n c e p t . ' - ~ ~ ~ - ~ So, in order to gain a detailed understanding of the dynamic properties of both the molten and glassy states, including physical aging, it would be highly important to be able to measure the free volume directly. The problem is that there is no direct way of measuring this quantity.

One is, however, able to measure a quantity which is related at least to its distribution. This is the mean square value of the thermal density fluctuation?,'5-20 It represents the half width of such a distribution. This value is experimentally available from absolute small-angle scattering experiments, such as X-ray or light scattering e~periments . '~* '~*~'*~~ Statistical mechanical treatments predict for the case of an equilibrium state that the mean-square value of the thermal density fluctuations is directly controlled by the thermal energy kT and the isothermal ~ompressibility:~

where N is the number of particles, K ( T ) the isothermal compressibility, and the particle density.

By comparing the experimentally obtained value for 8 w 2 / N and the value predicted by eq. 1, one is directly able to decide whether a given material is in its equilibrium state. The finding for a glnssy state is, for instance, that the mean-square value of the thermal density fluctuations may be represented, to a first approximation, by:l5,l6

in the neighborhood of the glass transition temperature, where K ( % ) is the compressibility of the material in the melt at the glass transition. This behavior has been treated both experimentally and theoretically in some detai1.'7-25

A rather surprising finding is the insensitivity of the thermal density fluctuations on the aging history.'6,20 The observation was that the mean square value of the thermal density fluctuations changed only insignificantly during annealing in the glassy state (the variation becomes larger at temperatures very close to the glass transition temperature) despite the fact that thermodynamic quantities such as the volume or the enthalpy showed considerable relaxations. One possible interpretation is that the relaxation time characteristic of the volume relaxation differs drastically from that characteristic of the thermal density fl~ctuations'~ and another explanation is that the free volume decreases, as the observed volume, while the average hole volume increases during aging?'

This somewhat strange result obtained for the aging properties of thermal fluctuations in isotropic systems motivated us to investigate the effect of a rejuvenation and the induced enhancement of aging which results from deformations such as uniaxial extension or uniaxial compression of materials ih their glassy state. The experimental results of such studies are reported below.

Table I represents the mean square value of the thermal density fluctuations of unaged isotropic polycarbonate as well as of samples which were aged at various temperatures. The finding is that aging has no appreciably effect on the absolute value of the thermal density fluctuations, independent of the aging time and aging temperature. This is obvious from the fact that the room temperature values of unaged

REJUVENATED AND AGED POLYCARBONATE 423

TABLE I Room temperature values for the mean square value of the thermal density ductuations

for isotropic and cold drawn samples of polycarbonate for various thermal histories

Sample history sIv2/Iv (lor3)

Isotropic, unaged Isotropic, aged at 55OC ( t , variable) Isotropic, aged at 70°C ( t , variable) Isotropic, aged at 125°C ( t , up to 40 days) Drawn at 23"C, unaged Drawn at 23"C, aged at 60°C

Drawn at W"C, unaged Drawn at 12OOC

16 h

6.1 6.1

6.1

6.1 6.64 6.40

6.15 6.08

samples and samples which were aged at elevated temperatures for prolonged times agreed very well. This finding is again in agreement with results published in the literature.'3* l4

The corresponding result obtained for a polycarbonate sample which was uniaxially drawn at room temperature is also displayed in Table I. It has to be pointed out that the thermal density fluctuations were found to be isotropic for the drawn samples in the sense that the value obtained experimentally did not depend on the direction along which the X-ray intensity was determined relative to the drawing direction. The obvious r d t is that drawing has increased the absolute value of the thermal density fluctuations considerably. No such increase of the absolute value of the thermal density fluctuation is observed,

if the drawing is performed within the glassy state at elevated temperatures. This is evident from the results displayed in Table I. The values obtained for higher deformation temperatures correspond to the ones found for the isotropic state at the same temperature.

The reason apparently is that the increased thermal density fluctuations resulting from drawing are able to relax as a function of time, in contrast to the case of isotropic samples. This is apparent from Figure 1. It displays the variation of the small angle X-ray intensity resulting from the density fluctuations as a function of the aging time. The rate with which the relaxation takes place is, however, a strong function of temperature. No aging effects occur up to 45°C and one is no longer able to resolve the relaxation by means of small angle X-ray scattering for temperatures surpassing about 80°C.

This is apparently the reason why one is not able to induce an increase of thermal density fluctuations by drawing at temperatures above this temperature range. It has to be pointed out that the fast relaxation taking place at increased temperatures never leads to values for the mean-square value of the thermal density fluctuations which are below the ones observed for isotropic samples.

Finally it has to be pointed out that one is not able to determine the temperature dependence of the thermal density fluctuations over a large temperature range due to the onset of the relaxation process. Nevertheless, from studies in a limited temperature range it became obvious that the increase per temperature interval is approximately identical to the one observed for isotropic samples or for samples which were drawn at elevated temperatures. In the following we will analyze in which way the relaxation properties of thermal density fluctuations agree with those of the volume and the enthalpy.

424

1.70 -

1.66-

MULLER AND WENDORFF

( orb. unts 1 0

0

0 .

0 0

cold drawn Sample

1.50

Variation of small-angle X-ray scattering due to thermal density fluctuations with time 2 .o 2.5 3.0 3.5 4.0 4.5 5.0 logIt,/sl

Fig. 1. at an aging temperature of 55°C. Samples cold drawn at 23°C.

Volume Relaxation

The volume relaxation was determined for an isotropic unaged polycarbonate sample as well as for a cold-drawn sample at 45OC. The result is displayed in Figure 2. It is obvious that the volume decreases linearly with the logarithm of the aging time for both kinds of samples. It is, however, also apparent that the rate of volume relaxation is at least one order of magnitude larger for the cold drawn sample. This happens despite the fact that cold drawing was found to lead to a decrease of the volume by about 0.3%, in agreement with results published in the literature?' Defining a volume relaxation rate" as:

- r = ( l /u) du/d log( t , / s )

one obtains the result that the rate is about 1.3 X at 45°C for the isotropic sample (in agreement with ref. 11) and about 3.3 X for the cold drawn sample. An increase of the aging temperature leads to a slight reduction of the rate for the anisotropic sample (2.1 x and a noticeable increase for the isotropic sample (3.3 x An enhancement of the volume relaxation in cold-drawn polycarbonate was also reported by Pixa et al?' The obvious conclusion is that cold working has


0

- 2 . 0

- 4 . 0

- 6 . 0

- 8 . o

-10 .0 I I I I I 1 - -0.5 0 0.5 1 . 0 1 . 5 2 . 0 2 . 5 l o g ( t / h l

Fig. 2. Variation of the normalized volume of Av/v with the aging time for an isotropic and for a cold drawn sample of polycarbonate.

increased the mobility and one possible reason is that free volume has been increased during drawing. This topic will be reconsidered below.

Calorimetric Investigations on Enthalpy Variations

Aging is known to give rise to an endothermic peak for isotropic samples at about the glass transition temperature if the aged sample is heated in a calorimeter.' The magnitude of the peak usually increases linearly with the logarithm of the aging time. The aging of an isotropic sample of polycarbonate which is annealed at a temperature of 45°C is apparently too slow to give rise to such an endothermic peak even for aging times amounting to 19 days. This is apparent from Figure 3.

Figure 3, on the other hand shows that the same aging history leads to dramatic changes in the DSC heating trace, both of cold-drawn and of cold-pressed polycarbonate, in agreement with similar results reported in the lite~-ature>~*'~ The DSC trace is characterized by an endothermic peak at temperatures well below the glass transition temperature, by an exothermic contribution above this temperature, and exothermic and endothermic contributions in the glass transition regime.

Without going into details, it is obvious that the dynamic state of the cold-drawn sample has to differ markedly from that of the isotropic sample. The various features showing up in the DSC trace of the drawn material have been discussed in terms of an increase of the molecular mobility and of the memory effects resulting from such an in~rease.'~.'~ Again an increase of the free volume accompanying the drawing step is a m b l e interpretation.

DISCUSSION

A straightforward interpretation for the increase of the rate of volume relaxation, the Occurrence of the memory effects in the calorimetric investigations, and for the increase of the thermal density fluctuations due to drawing may be based on the

426

i

MULLER AND WENDORFF

T c

80 100 120 1co 160 180 200'C Fig. 3. DSC traces obtained for isotropic (3), cold pressed (1) and cold drawn (2) polycarbonate

after aging at 45°C for 19 h.

assumption that the application of a mechanical stress during drawing results in an increase of the free volume, since the Poisson ratio is below 0.5. Experimental results are reported in the literature which have shown this assumption to be ~ o r r e c t . ~ , ~ ~ This is in agreement with our own dilatometric experiments performed as a function of the applied stress. We have to conclude from our X-ray scattering results that it is not only the free volume but also width of the distribution of the free volume which increase in response to the applied stress.

The removal of the stress after the uniaxial elongation or compression evidently does not give rise to a total relaxation of the induced variations of the free volume and of their fluctuations. The result is that the free volume has probably been increased relative to that in the original unstretched state and certainly the fluctuations of the density increase. This happens despite the fact that the actual volume of the sample decreases by as much as 0.3% due to the deformation.

Now, the presence of an excess free volume and possibly also the existence of a broader distribution of the free volume gives rise to increased mobility, in agreement with the free volume theory. This increased mobility manifests itself, for instance, by volume relaxations which are'at least one magnitude of order more rapid than in the case of isotropic samples and by the memory effects which slow up in calorimetric investigations.

It is therefore not surprising that the thermal density fluctuations also show relaxations, even at such low temperatures as 55°C. The interesting finding is, however, as in the case of the relaxation behavior of isotropic samples, that the volume and enthalpy relaxations are decoupled from the relaxation of the thermal density fluctuations. The relaxation of the thermal density fluctuations is characterized by the fact that negligible effects occur below a temperature of about 50°C and that the relaxation


happens within a short time above a temperature of about 80°C. The final value obtained is in all cases the one characteristic of the isotropic sample.

This contrasts with the case both of the volume relaxation and of the enthalpy relaxation. They occur in a broad temperature range, they do not depend very strongly on the annealing temperature and they go beyond the values characteristic of the unaged isotropic state. A possible interpretation is again that i t is primarily the increase of the average hole size and its subsequent relaxation which controls the variation of the thermal density fluctuations during rejuvenation and aging whereas the relaxation of the volume depends on the decay of the free volume. Further studies are in progress which are aimed at investigating this particular problem.

References

1. L. C. E. Struik, Physical Aging in Amorphus Polymers and Other Makriuls, Elsevier,

2. A. J. Kovacs, Fortschr. Hochpolym. Forsch., 3, 394 (1963). 3. A. J. Kovacs, J. J. Aklonis, J. M. Hutchinson, and A. R. Ram-, J.Polym. Sci. Polym.

4. S. Matsuoka,Poly., Eng. Sci., 25, 907 (1981). 5. C. Price, Polymer, 16, 585 (1975). 6. T. L. Smith, Polymer, 26, 1979 (1985). 7. T. L. Smith, T. Ricco, G. Levita, and W. K. Moonan, Plost. Rubb. Proc. AppL, 6, 81

8. C. Bauwens-Crowet and J. C. Bauwens, Polymer, 28,1863 (1987). 9. L. D. Landau and E. M. Lifschitz Statistical Mechanics, Vol. 5, Pergamon Press, 1974.

10. C. A. Pampillo, and L. A. Davis, J . Appl. Phys., 42, 4674 (1971). 11. L. C. E. Struik, Polymer, 28, 1869 (1987). 12. R. Pixa, B. Grisoni, and D. Froelich, Polymer B&tin, 16, 361 (1986). 13. A. R. Berens and I. A. Hodge, Macromolecules, 16,756 (1982). 14. I. A. Hodge, Macromolecules, 16, 898 (1983). 15. J. H. WendortT and E. W. Fischer, Kolloid Z.Z. Polymers, 261, 876, (1972). 16. J. H. WendortT, J. Polym. Sci. Polym. Lett. Ed., 17, 765 (1979). 17. R. E. Robertson, J . Poly. Sci. Polym. Phys. Ed., 17,597 91979). 18. J. J. Curro, R. R. Lagasse and R. Simha, Macromolecules, 16, 1621, (1982). 19. T. S. Chow, J . Chem. Phys., 79, 4602 (1983). 20. J. J. Curro and R. J. Roe, Polymer, 25, 1424 (1984). 21. H. Lee, A. M . Jamieson and R. Simha, Colloid Polym. Sci., 268,545 (1980). 22. W. Ruland, Pure Appl. Chem., 49,905 (1977). 23. C. M. Balik, A. M. JamiesOn, and R. Simha, Colloid Polym. Sci,, 260, 477 (1982). 24. R. E. Robertson, J . Polym.. Phys. Ed., 19, 1227 (1981). 25. R. J. Roe, Macromolecules, 14, 1586 (1981). 26. J. M. Powers and R. M. Caddell, Polym. Eng. Sci., 12,432 (1972).

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Phys. Ed., 17, 1097 (1975).

(1986).

Received March 18,1988 Accepted April 13, 1988

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Thermal density-fluctuations in rejuvenated and aged polycarbonate