Macromolecules 1986,19, 2538-2540
2538
Research Corp., Dow Chemical, and the National Science Foundation (Grant DMR-8513271). In addition, acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. M.D.E. thanks Professor H. Yu for useful discussions. We thank Mr. H. Tominaga and Mr. N. Ota at the Toyohashi University of Technology for their help in the preparation and characterization of the polymer. Registry No. Polyisoprene, 9003-31-0; 9,10-bis(bromomethyl)anthracene, 34373-96-1;9,1@dimethylanthracene,781-43-1.
References and Notes
(6) Viovy, J. L.; Monnerie, L. Polymer, in press. (7) Moog, R. S.; Ediger, M. D.; Boxer, S. G.; Fayer, M. D. J. Phys. Chem. 1982,86,4694. ( 8 ) Hall, C. K.; Helfand, E. J. Chem. Phys. 1982, 77, 3275. (9) Bendler, J. T.; Yaris, R. Macromolecules 1978, 11, 650. (10) Williams, G.; Watts, D. C. Trans. Faraday SOC.1971, 66, 80. (11) Bendler, J. T.; Shlesinger, M. F. Macromolecules 1985,18,591. (12) Ediger, M. D.; Domingue, R. P.; Fayer, M. D. J. Chem. Phys. 1984, 80, 1246. Miller, R. J. D.; Pierre, M.; Fayer, M. D. J . Chem. Phys. 1983, 78,5138. Moog, R. S.; Kuki, A.; Fayer, M. D.; Boxer, S. G. Biochemistry 1984, 23, 1564. (13) Fayer, M. D. Annu. Reo. Phvs. Chem. 1982. 33, 63. (14) Ne-lson, K. A,; Miller, R. J. D.; Lutz, D. R.; Fayer, M. D. J . Appl. Phys. 1982,53,1144. (15) Nemoto, N.; Landry, M. R.; Noh, I.; Yu, H. Polym. Commun. 1984. 15. 141. I
Ricka, J.; Amsler, K.; Binkert, Th. Biopolymers 1983,22,1301. Phillips, D. Polymer Photophysics: Luminescence, Energy Migration, and Molecular Motion in Synthetic Polymers; Chapman and Hall: London, 1985. Viovy, J. L.; Monnerie, L.; Merola, F. Macromolecules 1985, 18, 1130. Viovy, J. L.; Monnerie, L.; Brochon, J. C. Macromolecules 1983,16,1845. Viovy, J. L.; Frank, C. W.; Monnerie, L. Macromolecules 1985, 18, 2606.
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(16) ingeneral, the probe is diffracted by both an amplitude and phase grating (see ref 13). Conditions for these experiments have been chosen so that the phase grating contribution is negligible. (17) Wahl, P. Biophys. Chem. 1979, 10, 91. (18) Bevington, P. R. Data Reduction and Error Analysis for the Physical Sciences; McGraw-Hill: New York, 1969; p 237. (19) Hatada, K.; Kitayama, T.; Terawaki, Y.; Tanaka, Y.; Sato, H. Polym. Bull. (Berlin) 1980, 2, 791. (20) Weber, T. A.; Helfand, E. J. Phys. Chem. 1983, 87, 2881.
Dynamic Mechanical Study of the a-Relaxation in Poly(oxymethylene)t Howard W. Starkweather, Jr. Central Research and Development Department, Experimental Station, E. I. du Pont de Nemours and Company, Wilmington, Delaware 19898. Received March 15, 1986
ABSTRACT: The dynamic mechanical properties of poly(oxymethy1ene) were measured in the region of the a-relaxation at frequencies from 0.033 to 90 Hz. Isothermal data were taken at temperatures from 100 to 150 "C to form master curves of the dependence of tan 6, the storage modulus ( E ' ) ,and the loss modulus (E") on frequency. The frequency-temperature shifts corresponded to an activation energy of 22 i 1kcal/mol, in agreement with the findings of Gray for temperatures below 70 O C . A two-dimensional shift was required for the modulus functions. The activation entropy of this relaxation is close to zero, suggesting that the internal motion has little cooperative character.
Introduction The a-relaxation in poly(oxymethy1ene) is generally attributed to motions within the crystalline regions. Widely scattered values, from 20 to 92 kcal/mol, have been reported for the activation In a careful study based on measurements of creep and dynamic compliances, Gray' concluded that the activation energy is 21 f 1 kcal/mol below about 70 "C. Above that temperature, it increased gradually, reaching 33 f 2 kcal/mol at 120 O C . We have adapted his methods to the Polymer Laboratories dynamic mechanical thermal analyzer (DMTA). This instrument measures dynamic mechanical properties using a flexural deformation and a defined strain amplitude and frequency.
Experimental Section The sample was an injection-molded bar of Delrin acetal resin 5 in. X 'Iz in. X in. It was first annealed at 150 O C for 15 min. The latent heat at the melting point was 182 J/g, corresponding to 56% crystallinity. Temperature scans at constant frequency were run on the DMTA using a heating rate of 5 OC/min. In a separate series of experiments, data were taken isothermally at intervals of 10 O C from 100 to 150 "C. All available frequencies were used 0.033, Contribution No. 4028.
0024-9297/86/2219-2538$01.50/0
0.1, 0.33, 1, 3, 10, 30, and 90 Hz.
Results Data from isothermal experiments are shown in Figures 1-3 for tan 6, the storage modulus ( E r ) ,and the loss modulus (E"), respectively. At all temperatures, tan 6 and E" increased at 30 and 90 Hz, presumably because of the proximity of a mechanical resonance. Only the data for E at these frequencies were used in the analysis of frequency-temperature relationships. The tan 6 curves were shifted along the log (frequency) axis to form a master curve with a reference temperature of 130 "C as shown in Figure 4. The points at the bottom of the chart indicate the position off = 1Hz in the original curves. The corresponding frequencies on the master curve define the shift factors, a, as a function of temperature. For E' and E", the real and imaginary parts of the complex modulus, it was necessary to make two-dimensional shifts of log-log plots of E vs. f to form master curves. The curves for log E'vs. log f from Figure 2 were shifted horizontally by the same factors that has been used for the tan 6 data. They were then shifted vertically to form the master curve which is shown in Figure 5. As in Figure 4, the reference temperature is 130 "C. The points along the vertical axis indicate the positions of E ' = lo9 P a in the original curves. The vertical displacements 0 1986 American Chemical Society
Macromolecules, Vol. 19, No. 10, 1986
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define a shift parameter, b, which is a function of temperature. The same shift parameters, a and b, were applied to the data for the loss modulus in Figure 3 to form the master curve for log E” vs. log f shown in Figure 6. In this case, the points along the vertical axis indicate the positions of E” = IO8 Pa in the original curves.
Determination of the Activation Energy An Arrhenius plot of the temperature shift factor, a, in Figure 7 corresponds to an activation energy of 22 kcal/ mol. As stated above, this was based on shifting the tan 6 data along the log (frequency) axis to form a master curve, which was than used to define the frequency-temperature relationship for the other functions. Alternatively, the curves for log E’or log E”vs. log f can be shifted two-dimensionallywithout reference to other data to form master curves. When this was done, the values of a,determined independently for tan 6, E‘, and E‘’, gave an
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activation energy of 21 kcal/mol with somewhat more experimental scatter than is shown in Figure 7. Both of these approaches give activation energies in good agreement with the value of 21 f 1kcal/mol obtained by Gray’ using data from 20 to 70 “C and up to 100 “C for one method of analyzing creep data. He concluded that the activation energy increased a t higher temperatures, reaching 33 kcal/mol a t 120 “C. On the other hand, our activation energy of 21-22 kcal/mol is based on measurements a t 100-150 OC. In earlier work? we have discussed a class of “simple” relaxations in which the activation entropy is close to zero. For such phenomena, the relationship between the Arrhenius activation energy, E,, and the absolute temperature of the relaxation at a frequency of 1Hz, T’, is given by the following equation: E, = RT’[l + In (kT’/27rh)] = RT’[22.922 + In T’]
In a temperature scan at 1Hz, the maximum in E” for the a-relaxation occurred a t 104 “C. For a “simple”relaxation
2540 Starkweather 9.2
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Macromolecules, Vol. 19, No. 10, 1986
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Figure 8. Complex plane plot normalized to 130 "C.
2
Figure 6. Master curve for the loss modulus. a t this temperature, E , would be 21.6 kcal/mol, within experimental uncertainty of our value and Gray's. This indicates that there is little cooperative character in the fundamental motion assocd. with cy-relaxation. Certain crystalline relaxations in polyethylene and poly(ch1orotrifluoroethylene) were also found to have activation entropies near zero.3
Limiting Moduli As a material crosses a relaxation, the modulus changes from one limiting value to another. The high, unrelaxed modulus is approached a t low temperatures and high frequencies, while the low, relaxed modulus is approached a t high temperatures and low frequencies. In some cases, such as the a-relaxation in poly(oxymethylene), the limiting moduli themselves depend on the temperature. The complex plane plot of E" vs. E' in Figure 8 was formed by cross-plotting the data in the master curves in Figures 4 and 6. Extrapolating to the high-modulus intercept with the E'axis leads to the conclusion that the unrelaxed modulus, E,, is 1.01 GPa a t 130 "C. Values at other temperatures can be determined from the vertical shift factors from Figure 5 and are given in Table I.
temp, "C 100 110 120 130 140 150
Table I Shift Factors log a log b 1.04 -0.192 0.95 -0.105 0.40 0 -0.22 -0.45
-0.045 0 0.060 0.156
E,,, GPa 1.57 1.29 1.12 1.01 0.88 0.705
To determine the relaxed modulus, E,, one would need data at lower frequencies (longer times) or higher temperatures. The latter approach is impeded by the onset of partial melting. One possibility, indicated by the dashed line in Figure 8, is that E, is close to zero. This line defines a constant ratio between E"and E', i.e., a constant limiting value of tan 6 a t low frequencies. The data in Figures 1 and 4 are consistent with this possibility. On the other hand, Gray's master curve for tan 6 shows a maximum with a decline at low frequencies, suggesting that E, has a finite value. Registry No. Delrin, 9085-38-5.
References and Notes (1) Gray, R. W. J. Muter. Sci. 1973,8, 1673. (2) Enns, J. B.; Simha, R. J. Mucromol. Sci., Phys. 1977, B13,25. (3) Starkweather, H. W. Macromolecules 1981, 14, 1277.
