Abstract
X-ray diffraction has been used to measure the separation of the molecular axes as a function of temperature, lamella thickness, and comonomer concentration in copolymers of tetrafluoroethylene and hexafluoropropylene. These data show that the increase of separation with increasing concentration of perfluoromethyl groups is a consequence of inclusion of the groups in the crystals and not an artifact associated with lamella thickness or crystal transition temperature. This conclusion is supported by the fact that diffuseness of some of the x-ray reflections in the copolymers indicates the presence of molecular disorder which might be expected from inclusion of the perfluoromethyl groups in the crystals. The lamellas in the copolymers are thinner than those in the typical homopolymer and this aspect of the structure is the primary cause of the lower density in the copolymers. Analysis of the available data indicates that this is also the situation in copolymers of ethylene and propylene. For both copolymer series, the density of the lamellas is apparently increased by the inclusion of the methyl groups in the crystals as defects.
1. Introduction
In an earlier article [1],1 evidence was presented that copolymers of tetrafluoroethylene and hexafluoropropylene form lamellar crystals with the perfluoromethyl groups within the crystals as point defects. Part of this evidence was the fact that the copolymer exhibited a larger separation of the molecular axes than did polytetrafluoroethylene. This result, which disagrees with a report of no change of separation [2], is subject to a question arising from the fact that polytetrafluoroethylene undergoes first-order, crystal-crystal transitions at about 290 and 305 °K [3, 4]. These transitions, at which both the lattice parameters and the thermal coefficients of expansion increase [3, 5] occur at lower temperatures in the copolymers. Thus, it can be asked whether the lattice of the copolymer is larger than that of polytetrafluoroethylene at 296 °K merely because the copolymer is at a temperature which is further removed from the phase transition.
Another question arises from the fact that the lamella thickness was observed to decrease with increasing concentration of perfluoromethyl groups [1]1 (the same effect has also been observed in ethylene-propylene copolymers [6, 7]). It might be argued that at the lamella surface there is strain and an increase of the unit cell size. Then it can be asked whether the lattice of the copolymer is larger not because of inclusion of perfluoromethyl groups but because the lamella surfaces are more numerous and therefore exert a stronger influence on cell size.
This article presents data and analyses as evidence that the larger separation of the axes in the copolymer is a result of inclusion of the perfluoromethyl groups in the crystals and not an artifact associated with transition temperature or lamella thickness. Also presented are data and analyses concerning the density, lamella thickness, and unit cell dimension of tetrafluoroethylene-hexafluoropropylene and ethylene-propylene copolymers. These indicate that the thinner lamellas of the copolymers rather than “amorphous defects” of reduced density around the methyl [8] or perfluoromethyl groups are primarily responsible for the reduction in density from that of the homopolymer.
2. Experimental Procedures
Wide angle x-ray diffraction measurements were made as a function of temperature using Cu radiation filtered by Ni and a cryostat that provided temperature control in the range 4 to 300 °K [9, 10]. The present measurements for polytetrafluoroethylene and a copolymer similar to the intermediate one of reference [1] were made above to 80 °K only, since this temperature was found to be well below the transition temperature. Measurements were made at approximately 10 deg intervals with increasing temperature and a wait of about 50 min at each temperature. In the temperature range of the transition, the temperature intervals were shortened to 5 deg with a wait of 40 min. Temperatures were measured with a Au-2.1 percent Co versus Cu thermocouple [9] and are subject to an uncertainty of about 1 deg.
Since the polymers, especially the copolymer, did not yield suitable diffraction at large angles, they could not be used to aline the goniometer [11]. Therefore, silicon which had been measured previously [11] was pressed into asperities on the front surface of the polymer and diffraction from the {111}, {220}, {311}, {400}, {331}, {511}, and {440} planes was used to aline that surface.2 Because the surface responded to contraction of both the sample, which was about 1 mm thick, and the apparatus, alinement was carried out at the lowest temperature after 2 hr were allowed for the attainment of thermal equilibrium. Subsequently, the alinement was checked at each temperature using diffraction from only the first planes above, and more were used only if realinement was necessary. Over the present temperature range, the expansion of silicon is very small, corresponding to a total change of less than 2 × 10−3 A in the dimension of the unit cell [12].
Because of beam penetration into the sample, alinement of the front surface yields a small error in the determined spacings and a very small correction was made for this effect. However, comparison of the spacings determined for the two samples is not altered significantly by omission of this correction for the following reasons: the effect is small, measurements for the two samples were made in the same angular range, the difference in density of the two samples is about 5 percent only, and the variation of density over the temperature range of interest is about 5 percent only [13]. There are other sources of possible error, and the determined spacings are subject to an estimated uncertainty of about 0.02Å. Most of this uncertainty is the result of systematic errors and because of similarity of the samples and the experimental procedures for each, is also not relevant to a comparison of the results for each. In order to minimize unwanted surface orientation effects [14], the samples were cooled slowly from the melt. Orientation in the surface layers of the samples was examined by x-ray diffraction with a Norelco micro camera and a 100-μ beam of Cu radiation filtered by Ni. Transverse sections were cut from the samples and diffraction patterns were obtained with the beam parallel to the surface and incident upon the top 50 to 100μ of surface.
Wide-angle x-ray diffraction measurements were made at about 296 °K as a function of comonomer concentration and lamella thickness with a Norelco diffractometer and Cu radiation filtered by Ni. Samples about 0.3 mm thick were carefully placed at the same position in the same sample holder and at the same position in the diffractometer. With the slowest speed of the diffractometer and four recordings for each of the one to three positionings of each sample, this procedure yields average angles of the diffraction maxima which are subject to standard deviations corresponding to less than 2×10−3Å in the unit cell dimension. This value is small enough that, together with the small differences in densities and in angles of the diffraction maxima of the different samples, it permits comparative measurements for the samples without use of an internal standard. The validity of this technique is supported by the fact that for two of the samples, the difference between the cell dimensions was reproduced with a powder camera. Similarly, the difference between cell dimensions of two other samples did not differ significantly from that measured by the technique described in the previous paragraph.
Samples with comonomer concentrations of approximately 0, 3, 4, 5.75, 6.2, 7, 7.6, and 8 CF3 units per 100 main chain carbon atoms were used. Lamella thickness was varied by isothermal crystallization for about one week at different supercoolings followed by slow cooling. Thinner lamellas were produced by quenching thin films of melt in ice water. Lamella thickness was measured with Cu radiation and a small-angle diffractometer.
3. Results and Discussion
A number of papers have discussed various aspects of the crystal structure of polytetrafluoroethylene [3, 5, 15–19]. With the present sample, diffraction from more than five (hk0) planes could be observed in addition to that from several other planes at all temperatures. When the separation of the molecular axes (cell dimension a) was determined from each of the various hk0 reflections at 327 °K, there were small variations which were probably contributed to by variations in both the background of the scattering curve and the beam penetration of the sample with angle. These variations were not large enough to hamper comparisons with the copolymer and the 100 reflection was selected for comparison since it was the strongest of the hk0 reflections that could be observed readily in the copolymer. At temperatures below the transition temperature, the lateral packing of the molecules is not quite hexagonal [19] and an average of the nearest neighbor distances is given.
Data for intermolecular distance, which are presented in figure 1, show a transition to occur at about 225 °K in the copolymer. The scatter of the data gives a measure of the reproducibility and may be sufficient to mask the small [19] transition that occurs near 305 °K in polytetrafluoroethylene. Below 225 °K, as well as above, the spacing of the molecular axes in the copolymer is larger than in polytetrafluoroethylene.3 The difference increases slightly at 225 °K and above but the increase is only a small portion of the total difference for two reasons. First, the increase in spacing at the transition is not too great. Second, the difference between the average values of the expansion above and below the transition is only about 1.2 × 10−4 Å/°K. Thus, it seems reasonable to conclude that the larger separation of the molecular axes in the copolymer is real and that the answer to the first question raised in the introduction is negative. That is, at 296 °K, the greater part of the increase of separation of the axes in the copolymer is not an anomaly associated with transition temperature.
Figure 1. Temperature dependence of the change of average intermolecular distance with respect to an arbitrary reference.
The solid points represent a copolymer of tetrafluoroethylene and hexafluoropropylene with about six perfluoromethyl groups per 100 main-chain carbon atoms. The copolymer exhibits a phase change near 225 °K. Open points represent polytetrafluoroethylene.
Variation of intermolecular distance with comonomer concentration is shown in more detail in figure 2. Between the samples with 0 and 3 perfluoromethyl units per hundred main chain atoms, there is a dotted line which is intended to guide the eye rather than represent the detailed variation of intermolecular distance. As noted above, part of this variation (~0.013 Å) is a consequence of the fact that at about 296 °K, polytetrafluoroethylene is not completely above the transitions [19] whereas the copolymer is. In the range of perfluoromethyl concentration between 3 and 8 percent, the intermolecular distance increases approximately uniformly with concentration at an average rate of about 1.4×10−2 Å per 1 percent change in concentration. The intermolecular distance in the copolymer is evidently not the same as that in the homopolymer as has been reported [2].
Figure 2. Change of intermolecular distance with the ratio of perfluoromethyl groups to main-chain carbon atoms (concentration).
The reference point is polytetrafluoroethylene at about 296 °K. The numbers in brackets give the approximate lamella thickness for each sample.
On figure 2 the approximate lamella thickness is given next to each point. These show the basis of the possibility that the variation of intermolecular distance with concentration might be caused by the variation of lamella thickness. However, as figure 3 shows for two concentrations of perfluoromethyl groups, when thickness is varied at constant concentration, there is little discernible variation of intermolecular distance for a thickness variation of about 200 Å. (The latter is greater than the variation of thickness when concentration varies from 0.03 to 0.08, cf. fig. 2.) This conclusion is supported by statistical analysis which yields a rate of change of intermolecular distance with thickness of − 2×10−6Å/Å with a standard deviation of 1.2×10−5Å/Å. Therefore, it is concluded that the answer to the second question in the introduction is negative. That is, the greater part of the change of intermolecular distance with comonomer concentration is not a consequence of the change of lamella thickness.4
Figure 3. Change of intermolecular distance with approximate lamella thickness for samples with two different concentrations of perfluoromethyl groups (upper curve 0.076, lower curve 0.062).
The reference is 0.10 Å. on fig. 2 and the data were obtained at 296 °K. Data represented by open points were obtained with a diffractometer and the data represented by the solid points were obtained with a powder camera.
On the basis of the results in the last two paragraphs, it is concluded that the increase of intermolecular distance with concentration of perfluoromethyl groups is primarily the consequence of inclusion of the groups within the crystals. This concept is supported by an aspect of the data other than the increase of cell dimension; that is, the diffuse nature of the diffraction from certain planes. The 107, 108, 1, 0, 15, and 0, 0, 15 reflections could be observed readily in polytetrafluoroethylene at room temperature but the corresponding ones were very broad and diffuse in the copolymer. Even at the lowest experimental temperatures, these reflections (or the corresponding ones below the transition temperature) remain diffuse as shown in figure 4. While this effect can be the consequence of surface orientation in quenched samples [14], wide angle x-ray diffraction shows that this is probably not the case in the present, slowly cooled sample. As shown in figure 5, patterns obtained with the beam parallel to the surface and intercepting the top 50 to 100μ of surface show little preferential orientation. While the absence of orientation is difficult to confirm positively, patterns similar to figure 5 were obtained with several geometries of beam and sample. Also, one long exposure did not show orientation in the diffuse 0, 0, 15 reflection.
Figure 4. Intensity in arbitrary units as a function of approximate diffraction angle (20) for polytetrafluoroethylene at 278 °K and for a copolymer at 78 °K.
These are the same samples as in figure 1. The curve for polytetrafluoroethylene has been arbitrarily displaced to higher intensities.
Figure 5. Diffraction pattern obtained with the x-ray beam parallel to the surface and incident upon the top 50 to 100 μ of surface of the copolymer sample in figure 1.
The beam of CuKa radiation is 100-μ in diameter. Because the beam is near the horizontal surface, radiation diffracted upward encounters a different path-length (and absorption) than that diffracted downward. Therefore, one-half of the film is more strongly exposed than the other and two prints are presented in order to show the equivalence of the essential details in each half.
Another possible cause of the effect is disorder. Although a certain amount of caution must be exercised in interpreting the present limited number of reflections (especially those with l=15 since they are intrinsically weak [19]), some observations can be made. For example, for l= 15 (or 13 at low temperature) the reflections are governed by a zero-order Bessel function and therefore diffuseness would not result from rotational disorder about the chain axis but would result from disorder along the axis [17, 19]. Longitudinal disorder would probably be the cause of diffuseness for l=7 and 8 (or 6 and 7) but since these reflections are governed by a first-order Bessel function, diffuseness could result from rotational disorder. Thus, subject to the caution above, the diffuse nature of the reflections suggests longitudinal disorder along and possibly rotational disorder about the chain axis. Small disordering in rotation and translation might be expected from inclusion of the perfluoromethyl groups within the crystals.5
The density of the copolymers in figure 2 ranged from 2.155 to 2.133 g/cm3 at 296 °K. These are smaller than typical homopolymer values which can be greater than 2.22 g/cm3. However, it would be incorrect to assume that lamella thickness is largely independent of copolymer concentration and then to attribute lowering of the density directly to reduced density [8] around the comonomer units without first considering the known tendency for lamella thickness to decrease with increasing comonomer content [1, 6, 7]. Since mispacking of the folds of adjacent lamellas lowers the gross density [20, 21], copolymers should be less dense than the homopolymer simply because lamellas of the latter are often an order of magnitude thicker than the 350 to 500 Å lamellas of the copolymers in figure 2 [22]. However, greater supercooling of the polytetrafluoroethylene melt produces samples with thinner lamellas. Data obtained by electron microscopy indicate that such samples with densities somewhat less than 2.18 g/cm3 would have lamellas less than 500 Å thick [23]. Also, light scattering yielded a structural dimension of 260 Å for a sample with density of 2.13 g/cm3 [24].
These densities are in the range of those for copolymers with similar lamella thickness. Therefore, to provide a more direct comparison and avoid systematic differences in thickness and density as determined by different techniques, a quenched sample of polytetrafluoroethylene was prepared and measured by the present techniques. This yielded a sample with lamella thickness of 550 to 600 Å and density of 2.139 g/cm3 which is less than the values of 2.151 and 2.155 for the copolymer samples with the 500 Å lamellas. Reduced lamella thickness of the copolymer apparently accounts for the usual reduction of density. In fact, the data indicate that for copolymer and homopolymer samples with lamellas of equal thickness, the copolymer would be more dense.
Consideration of the increase of mass associated with the comonomer units together with the increase of cell volume suggests that the density of the lamellas is increased slightly by the comonomer units.6 This type of analysis is based upon results from calculations for point and slightly larger centers of dilation in an elastic continuum [25–27] After introduction of the defects, the fractional dilations of the macroscopic and cell volumes are equal if no new substitutional sites are introduced. Experimental verification of the effect has been obtained for a number of examples in atomic solids [26, 28, 29]. While the present analysis may be subject to errors, the increase of lamella density would remove almost completely the discrepancy noted above for the density of copolymer and homopolymer samples with similar lamella thickness.
It can be argued that each case must be considered separately and therefore it is of interest that the available data indicate that the same effects occur in copolymers of ethylene and propylene. For slowly cooled samples, the measured density decreases ca. 8×10−3 g/cm3 for each methyl group per 100 main chain atoms [8]. Slowly cooled copolymers with methyl group concentrations between 0 and 1.5 percent exhibit a decrease of lamella thickness of about 55 Å for each percent of methyl groups [6].7 Together with the variation of density of the homopolymer with lamella thickness [20] these data yield a calculated decrease of ca. 10×10−3 g/cm3 for each percent of methyl groups. While all these data were not available for a coherent set of samples as were the data presented above for the fluorocarbons, the density decrease calculated from lamella thickness again appears to be greater than that actually observed. However, taking the data for cell dimension and comonomer concentration given in reference [8] and calculating the density of the lamellas again removes most of the discrepancy.
The decrease of density of both copolymer series is apparently a result primarily of decreasing lamella thickness and not of reduced density around the comonomer units. Indeed, lamella density based on comonomer concentration and cell size is increased by the comonomer units and this result tends to agree with the experimental data. However, this latter fact cannot be established unambiguously without a rather formidable set of very accurate measurements of density, unit cell, and lamella thickness on a series of copolymer samples which have accurately known, different comonomer concentrations and which have been isothermally crystallized at different supercoolings. In any event, there are no data for small scale techniques which unambiguously indicate extensive amorphous disorder around the methyl groups and so gross a measurement as density is a poor one to use in the resolution of small scale structural details such as the nature of the disorder around the groups.
4. Conclusions
Measurements of the separation of molecular axes have been made as a function of comonomer concentration, temperature and lamella thickness in copolymers of tetrafluoroethylene and hexafiuoropropylene. These give evidence that the increase of separation with concentration is primarily the consequence of inclusion of the perfluoromethyl groups in the crystals. This conclusion is supported by the fact that the diffuseness of some of the x-ray reflections in the copolymers indicates the presence of molecular disorder which might be expected from inclusion of the perfluoromethyl groups in the crystals. The density of the copolymers is lower than that of the homopolymer primarily because the former have thinner lamellas and not because of “amorphous defects” of lower density around the perfluoromethyl groups. The same statement applies to copolymers of ethylene and propylene at low methyl group concentrations. For both copolymer series, the density of the lamellas is apparently increased by the inclusion of the methyl groups in the crystals as defects.
Acknowledgments
The authors express their thanks to W. A. Zisman and Marianne K. Bernett of the U.S. Naval Research Laboratory for providing samples of copolymers. Also, they want to thank E. S. Clark of the DuPont Experimental Station and J. P. Colson and their other colleagues at the National Bureau of Standards for helpful discussions and encouragement. Helpful discussions with Professor R. W. Balluffi are gratefully acknowledged.
Footnotes
Abstract in Bull. Am. Phys. Soc. 10, 354 (1965); NBS Tech. Note 236, 56 (1963); and NBS Tech. Note 260, 47 (1965).
Figures in brackets indicate the literature references at the end of this paper.
The silicon had initially been placed on the front surface with a silicone grease. The pressing technique was used after it was observed that the grease crystallized at about 230 °K.
Only a few data were taken with polytetrafluoroethylene for purposes of comparison here since precise measurements have been published [19]. The present results for 298 °K do agree with these but there does not seem to be any reason to expect exact agreement in the range of the transitions which varies with rate of heating, polymer sample, etc. [4,13].
Although 99 percent confidence limits on the change of intermolecular distance with lamella thickness are somewhat larger, they are too small to invalidate the conclusion just made. We wish to note also that for both copolymers the three samples with thickest lamellas exhibited a trend toward increasing spacing with decreasing lamella thickness. Although this trend is too small to be considered significant in our data, it tends to be reproducible. Also, it is always vitiated by the data for the quenched (thinnest lamellas) samples. Such a trend could result from a number of possible causes ranging from artifact to real physical effect and they have not been pursued.
This type of disordering cannot be adequately described by the word amorphous which implies liquid-like disorder.
The concentration of perfluoromethyl groups in the lamellas is taken as that in the whole polymer.
Although data over a wider range of concentration are available, they have been obtained on samples which were not slowly cooled. These show the same general trend in lamella thickness with the rate of decrease becoming smaller at higher concentrations.
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