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Macromolecules 1986, 19, 2541-2544
Dynamic Mechanical Study of the 0-Relaxation in Poly(tetrafluoroethy1ene) Howard W. Starkweather, Jr. Central Research and Development Department, Experimental Station, E. I. du Pont de Nemours and Company, Wilmington, Delaware 19898. Received April 21, 1986 ABSTRACT The dynamic mechanical properties of Roly(tetrafluoroethy1ene)were measured at frequencies from 0.033 to 90 Hz. Abrupt changes in the distribution of relaxation times are associated with the crystalline transitions at 19 and 30 "C. The activation energies are 24.5 kcal/mol below 19 "C, 122 kcal/mol between the transitions, and 7.5 kcaljmol above 30 "C. These effects are seen most clearly in a sample made by extruding virgin polymer at 50 "C.
Introduction The @-relaxationnear room temperature in poly(tetrafluoroethylene) (PTFE) is attributed to motions in the crystalline regions which undergo first-order transitions near 19 and 30 OC.I On the basis of creep experiments, Nagamatsu, Yoshitomi, and Takemoto2 concluded that there is a discontinuity in the distribution of relaxation times at 20 "C. They found that a plot of modulus vs. log (time) was steeper below that temperature and that the apparent activation energy changed in a complex way. Illers and JenckeP suggested that fragments of different loss peaks are observed at temperatures below and above the transitions. This results in a variety of shapes for the overall @-relaxationloss peak depending on the degree of crystallinity, the frequency, and so forth. We have explored these effects through dynamic mechanical measurements on samples of maximum crystallinity. Experimental Section Two samples of PTFE were used. One was made from granular polymer of relatively low molecular weight which had been used in previous studies4" where it was important to achieve a high degree of crystallinity with little or no tendency to form voids. Its standard specific gravity was 2.184. The sample was cooled slowly from the melt. The other sample was made by extruding a high molecular weight virgin granular polymer through a rectangular die 0.250 in X 0.050 in. (6.35 mm X 1.27 mm) at 50 "C to form a coherent extrudate. The DSC data in Table I show that this process caused little if any change in crystallinity. Scans over the room-temperature transition at several heating rates indicated that the temperature of the endothermal peak extrapolated to a zero heating rate was 17.4 "C. This type of extrudate has substantial orientation of the polymer chains in the direction of extrusion.' Both samples were studied by means of the Polymer Laboratories dynamic mechanical thermal analyzer (DMTA), which operates at fixed frequencies of 0.033,0.1,0.33,1,3, 10, 30, and 90 Hz. This was done either by scanning the temperature at a heating rate of 5 "C/min at a fixed frequency or by making isothermal measurements at the various frequencies. Measurements on PTFE Cooled Slowly from the Melt Temperature scans at constant frequency were run on the sample that had been cooled slowly from the melt to increase its crystallinity. This material exhibited an endothermal peak a t 22.6 O C in a DSC scan taken a t 20 OC/min. The temperatures of the dynamic mechanical loas peaks at various frequencies are shown in Table 11. The largest peak in both tan 6 and the loss modulus, E", re+ Contribution
No. 4058.
Table I DSC Data on Virgin PTFE" Dowder extrudate transition, "C 21.1 20.8 AH,cal/g 3.0 2.2 Tm, "C peak end iw,, caVg % crystallinity
344.3 352
17.9 81
344.9 355 16.9 76
"Heating rate: 20 "C/min Table I1 &&laxation Loss Peaks for Slow-Cooled PTFE temp, "C fres, Hz tan Lax E'".. 0.033 0.1 0.33 1 3 10 30 90
20 22 22 23, 28 23.5, 29 30 33
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29 29
mained at 22-23 OC for frequencies from 0.1 to 10 Hz. A second peak in tan 6 a t 28 O C appeared in a scan a t 1Hz and moved to higher temperatures with increasing frequency, reaching 34.5 "C a t 90 Hz. This peak was also resolved in scans of E" at 30 and 90 Hz. As explained by Illers and J e n ~ k e lthe , ~ dynamic mechanical loss peak at 22-23 O C reflects a discontinuity in the properties at the first-order transition, which was seen at 22.6 "C in the DSC scan. At intermediate frequencies, only the low-temperature side of a peak associated with the low-temperature phase and the high-temperature side of the peak associated with the high-temperature phase are seen. These fragments combine to give a rather sharp peak right a t the transition which does not shift with frequency. At higher frequencies, the temperature of the relaxation associated with the high-temperature phase is sufficiently far from the temperature of the transition to be seen as a separate peak. The data in Table I1 for this higher temperature phase correspond to an activation energy of 122 kcal/mol.
Measurements on Extruded Virgin PTFE In earlier work,8p9 it had been shown that the dynamic mechanical behavior of this kind of sample is dominated by the crystalline @-relaxation.The a-and y-relaxations, which are associated with motions in amorphous regions,' are either absent or greatly altered. The dependence of the storage modulus, E', and tan 6 at 1Hz on temperature is shown in Figure 1.
0024-929718612219-2541$01.50/0 0 1986 American Chemical Society
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Figure 1. Dynamic mechanical properties of extruded virgin PTFE.
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Figure 3. Master curve for tan 6 of virgin PTFE below the 19 "C transition.
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Figure 4. Master curve for the loss modulus of virgin PTFE below the 19 "C transition.
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Figure 2. (3-Relaxationsin virgin PTFE. The ideas of Illers and Jencke13 are applied to this sample in Figure 2. The maximum in tan 6 at 21 "C is not the peak of a relaxation but rather a discontinuity associated with the crystal transition. At 1 Hz, one observes only the low-temperatureside of the loss peak which is characteristic of the low-temperature phase. The rest of the peak is imaginary, because it lies beyond the transition. This is indicated by a dashed line. Similarly, above the transition, only the high-temperature side of the peak is seen. The crystal transitions at 19 and 30 "C are indicated by vertical lines. The maximum in E ''occurs at a lower temperature than the maximum in tan 6 and is seen in the figure as a rounded peak at 4 "C. At this frequency, only the high-temperature tail of the relaxation which occurs above 30 "C is seen. As mentioned above, the relaxation maximum above 19 "C appears in data taken at higher frequencies. Between 20 and 30 "C,there is an abrupt transition between the pattern for the lowand high-temperature relaxations. Master curves for tan 6 and log E"obtained by shifting isothermal scans of frequency taken between -40 and +15 "C along the log (frequency) axis are shown in Figure 3 and 4. The reference temperature was 0 "C. The points along the horizontal axis indicate the position of the data for f = 1Hz before shifting. Only the high-frequency side of the peak is seen in the data for tan 6. For E", the maximum occurs at a frequency of about 0.25 Hz at 0 "C. From an Arrhenius plot of the temperature shift factors (Figure 5 ) , an activation energy of 24.5 kcal/mol was
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Figure 5. Arrhenius plot of the temperature-frequency shift factors for the (3-relaxation in virgin PTFE below the 19 "C transition. calculated from data taken from -30 to +15 "C. There is good agreement between the temperature shift factors for tan 6 and E". A maximum in E"a1ways occurs at a lower temperature or a higher frequency than a maximum in tan 6. In a narrow range of conditions, one or the other may provide a better picture of a relaxation. The use of the loss modulus, E", is attractive, because it is closely related to the distribution of relaxation times and because it is proportional to the energy absorbed per cycle when the dynamic
Macromolecules, Vol. 19, No. 10, 1986 I
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Figure 8. Loss modulus data for virgin PTFE from high and low temperatures shifted to 20 "C. I
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Figure 6. Master curve for the loss modulus of virgin PTFE for data taken between 19 and 30 "C.
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Figure 9. Master curve for tan 6 data taken on virgin PTFE at temperatures between 30 and 100 "C.
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Figure 7. Arrhenius plot for the temperature-frequency shift factors for data on virgin PTFE taken between 19 and 30 "C.
mechanical experiment is performed at a constant strain amplitude as is the case with the DMTA.' A master curve for loss modulus data taken between 19 and 30 "C is shown in Figure 6. For a reference temperature of 25 "C,the maximum in E"occurs near 500 Hz. Figure 7 is an Arrhenius plot of the corresponding shift factors. The slope corresponds to an activation energy of 122 kcal/mol. The same value was found for the higher temperature peak in measurements on the sample that had been cooled slowly from the melt. This large activation energy indicates that the relaxation is a highly cooperative process at these temperatures. It may also reflect the diffuse character of the first-order transitions. If the second derivative of the loss modulus with respect to log (frequency) is small, the distribution of relaxation times can be approximated by' H ( 7 ) = (2/a)G"(u) where 7 = 1 / w = 1/2af. In Figure 8, the loss modulus vs. frequency data from both temperature regions have been shifted to a reference temperature of 20 "C. The corresponding scales for the relaxation times, 7 , and the distribution, H ( T ) ,are also shown. The maximum occurs at a higher frequency for the data taken a t 20-30 "C. The relaxation time distribution function is larger for the data taken below 20 "C,in agreement with the work of Nagamatsu and co-workers.2
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Figure 10. Arrhenius plot for frequency-temperature shift factors from tan 6 data on virgin PTFE taken between 30 and 100 "C.
There is also a discontinuity at the 30 "C transition, which shows up principally in the temperature dependence of the dynamic mechanical properties. Figure 9 is a master curve for tan 6 data taken between 30 and 100 "C and plotted with a reference temperature of 50 "C. Only the low-frequency,high-temperature side of the peak is seen. The Arrhenius plot of the frequency-temperature shift factors (Figure 10) indicates an activation energy of 7.5 kcal/mol for data taken between 40 and 100 "C. The failure of the data taken at 30 and 35 "C to follow this relationship may be due to the diffuse character of the 30 "C transition. The corresponding data for E''were too far
Macromolecules 1986,19, 2544-2550
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out on the low-frequency side of the peak to be useful in determining shift factors. Nagamatsu and co-workers2also reported changes in the apparent activation energy at temperatures near the crystal transitions. They gave values of 53 kcal/mol below 19 "C, 29 kcal/mol at 19-22 "C, a maximum of 90 kcal/mol at 25 "C, and a gradual decrease from 64 kcal/mol at 30 "C to 25 kcal/mol at 60 "C. Krum and Muller detected the ,&relaxation in dielectric measurements at frequencies from lo3 to lo5 Hz'O Eby and Sinnott did dynamic mechanical measurements at 1.2 X 10' Hz and observed the corresponding loss peak at 140 "C.ll When these data were combined with earlier dynamic mechanical work, at 1-100 Hz,an activation energy of 34 kcal/mol was obtained. We find apparent activation energies of 24.5 kcal/mol between -40 and +15 "C, 122 kcal/mol at 20-30 "C, and 7.5 kcal/mol at 40-100 "C. In both this work and that of Nagamatsu and co-workers, maximum values were found between the two first-order crystal transition. Their work was based on stress relaxation in tension on a sample of commercial film that presumably had a lower crystallinity because of its meltprocessing history. Our measurements used a dynamic
flexural technique on a specimen of virgin PTFE that had been extruded at 50 "C. This process resulted in the retention of a very high level of crystallinity and produced a high degree of longitudinal ~rientation.~ Registry No. PTFE, 9002-84-0. References and Notes (1) McCrum, N. G.; Read, B. E.; Williams, G. Anelastic and Di-
electric Effects in Polymeric Solids; Wiley: New York, 1967. (2) Nagamatsu. K.: Yoshitomi., T.:, Takemoto. T. J. Colloid Sci.
19&, 13, 257. ' (3) Illers, K. H.: Jenckel. E. Kolloid 2. 1958. 160. 97.
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(4) Starkweather, H. W. Polym. Sci., Poly& Phys. Ed. 1982,20, 2159. (5) Starkweather, H. W. J . Polym. Sci., Polym. Phys. Ed. 1985,23, 1177. (6) Starkweather. H. W.: Fereuson. R. C.: Chase. D. B.: Minor. J. M. Macromolecules 1985: 18, 1684. ' (7) Starkweather, H. W. J . Polym. Sci., Polym. Phys. Ed. 1979,17, 73. (8) Sasuga, T.; Takehisa, M. J . Polym. Sci., Polym. Phys. Ed. 1974, 12, 1889. (9) Starkweather, H. W.; Zoller, P.; Jones, G. A,; Vega, A. J. J . Polym. Sci., Polym. Phys. Ed. 1982, 20, 751. (10) Krum, F.; Mliller, F. H. Kolloid 2. 1959, 164, 81. (11) Eby, R. K.; Sinnott, K. M. J. Appl. Phys. 1961, 32, 1765.
Dynamics of Macromolecular Chains in Solution. A Model of Local Motion in a Polycarbonate Piotr Tekely Laboratoire d'Etude des Solutions Organiques et Colloidales, U.A. C.N.R.S. 406, Universite' de Nancy I, 54506 Vandoeuvre les Nancy Ceden, France. Received October 11, 1985 ABSTRACT: A semimolecular-level model permitting interpretation of local motion in a polycarbonate chain and giving good agreement between experimental results obtained by certain authors and calculated results for spin-lattice NMR relaxation times for 'H and 13Cnuclei over a wide range of frequencies has been considered. The model assumes modulation of the dipole-dipole interaction by (i) specific conformational reorientation s and T~ s, respectively. of single bonds and (ii) isotropic motion, with correlation times In addition, phenyl and methyl groups are assumed to execute fast internal rotation with a correlation time r2 10-l' s. The characteristic autocorrelation function derived from molecular-level specificity of the polycarbonate chain is compared with Hall and Helfand's general orientational autocorrelation function. In general, the data suggest that conformational transitions in polycarbonate, as revealed by the NMR method, do not occur necessarily as cooperatively as implied by crankshaft theories and can simply be bond rotations between isomeric transition states.
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Introduction The precise nature of local motion of the main chain of macromolecules in dilute solution and in condensed systems is still not fully understood. Today, spectroscopic techniques are a very useful tool for experimental studies of the problem. NMR allows one to obtain information about autocorrelation functions of the molecular motion, but it is not simple to relate the experimental data to the individual type of motion. This is due to the variety of motion types that may contribute to relaxation through modulation of the dipole-dipole interaction. Because of the frequencies applied, the nuclear relaxation time Tlis mainly sensitive to relatively high-frequency motion connected with conformational changes in the chain (often termed segmental motion). It has been found with certainty to be independent of molecular mass, which proves that the recorded motions are of local nature and therefore highly dependent on the local chemistry of the polymer. For many years local conformational changes in a polymer chain, even in dilute solutions, were treated by 0024-9297/86/2219-2544$01.50/0
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the majority of authors as proceeding through a crankshaft-like In recent years, several models of local conformational jumps have been suggested4+ in which it has been assumed that neighboring chain fragments remain in the same position and orientation, in common with the crakshaft mechanism. They all lead to a similar decrease of the autocorrelation function and satisfactorily describe experimental data obtained from fluorescence depolarization, dielectric relaxation, and nuclear relaxation.',* However, some data suggest that the existence of such motionsg should be questioned, and in fact such motions obviously cannot be the only possible local motion mechanism occurring in the macromolecule chain.lOJ1 Simulation of experimental data by means of various distributions of correlation timed2provides another approach to the problem. None of the interpretations mentioned above are satisfactory, as they provide little information about the individual molecular processes responsible for relaxation. The dielectric relaxation measurements of Mashimo, Nakamura, and Chiba13 in dilute 0 1986 American Chemical Society
