ADA L. RYLAND E. I. d u Pont d e Nemours & Co., Inc., Polychemicals Department, Wilmington, Delaware
IN RECENT years X-ray diffraction has become an increasingly important technique for qualitative and quantitative analyses as well as for fundamental studies of the properties and structures of polymers. The nondestructive nature of the technique makes it particularly valuable because one frequently needs to obtain a large amount of information about a relatively small sample of material. The unique feature of X-ray diffraction as a technique for qualitative analysis is that components are identified as specific compounds. It has been used in this laboratory to identify a wide variety of inorganic and organic compounds. It might appear that the technique is not generally applicable to organic analysis because of the necessity of working with crystalline compounds. However, when organic compounds cannot be identified directly (if they are liquids, for example) it is frequently possible to convert them to crystalline derivatives which have characteristic patterns. Many of the classical derivatives can he used for X-ray identification, and standard patterns of a number of derivatives have been published (1-7). Standard samples have been prepared, and the X-ray patterns of a large number of organic compounds have been obtained in this laboratory. Among the applications which have been made of the technique to organic analysis are identification of dibasic acids directly, identification of aldehydes and ketones as 2,4-dinitrophenylhydrazones,fatty acids as gbromoanilides, and amines as picrate derivatives. Recent studies on two binary derivative systems, acetic and propionic pbromoanilides and acet- and propion- 2,4dinitrophenylhydrazones were made in this laboratory (8). These studies indicated that X-ray techniques could be used satisfactorily for semiquantitative estimation of composition as well as for identification of the derivatives. QUANTITATIVE ANALYSIS
Although X-ray diffraction has received primary emphasis as a tool for qualitative analysis, it is readily adaptable to quantitative applications because the intensities of the diffraction peaks of a given compound in a mixture are proportional to the fraction of the material in the mixture. I n practice the method does not work quite as smoothly as this statement would seem to indicate. Direct comparison of the intensity of a diffraction peak in the pattern obtained Presented as part of the Symposium on An Analy~isGroup in an Industrial Research Organization before the Divisions of Chemical Education and Analytical Chemistry a t the 130th Meeting of the American Chemical Society, Atlantic City, September, 1956.
from a mixture with the intensity of the same peak in the pattern of the pure material does not give the most reliable analysis. It is frequently necessary to make corrections for the differences in absorption coefficients between the compound being determined and the matrix. Considerable effort must sometimes be exerted to prevent the establishment of preferred orientation which may seriously distort the intensity ratios. A method was recently developed for determining the graphite content in blends of graphite and Teflonv' tetrafluoroethylene resin. The integrated intensities of the graphite crystalline peak and the crystalline peak and amorphous halo of Teflon were measured. A correction was applied to eliminate the effect of the varying crystallinity of the Teflon in different samples. At the 10% level, the graphite could be determined with a precision of about *0.5% absolute. Probably an ultimate in quantitative analysis by Xray diffraction was reported a few years ago by Black (9). An elegant arrangement permitted the simultaneous determination of six mineral components in bauxite a t the rate of eighty samples a day with a precision and accuracy which compared favorably with chemical measurements. Notably, the various components were individually distinguishable in the mixture. Frequently, when complex mixtures are analyzed, a separation of some sort must be effected before the individual components can be adequately identified. Very often separations can be made on the basis of different colors or textures of the components. In other cases good separations can be made by a flotation method which takes advantage of density differences among the various compounds. COMBINATION WITH OTHER TECHNIQUES
X-ray diffraction frequently can he combined with other techniques to provide a simple solution t o a relatively complex problem. For example, a convenient method was devised for determining beryllium in a complex beryllium organic compound. The compound was wet ashed using sulfuric acid, and the ash was identified as BeSOa by X-ray diffraction. I n some instances, other techniques are of great value in differentiating compounds for which the diffraction patterns are quite similar. This situation occurs relatively frequently in inorganic systems. A notable example is the case of FeO, COO and Cu10 which have virtually identical "d" spacings although the intensities of the spacings are different. Emission spectrography is the most valuable technique for identifying metallic constituents, and it is used routinely in these laboratories to complement the X-ray results, particularly when complex mixtures are being analyzed. JOURNAL OF CHEMICAL EDUCATION
One of the principal values of X-ray diffraction for qualitative analysis is the ability to analyze very small samples. Our laboratory was asked to identify a minute flake-like contaminant in a polymer sample. The particle, which was about I mm. long and 0.2 rnm. thick, was excised from the polymer with the help of a binocular microscope. The tiny fragment was then stuck on a short length of wire, and an X-ray pattern was ohtained using a powder camera. Two crystalline components, TiOn (rutile) and anhydrous CaSO4 were readily identified from the diffraction pattern. Additional evidence obtained with the infrared "microscope" led to the conclusion that the particle was a paint fragment. POLYMER STRUCTURE STUDIES
The use of X-ray diffraction to determine the configuration of molecules is its most familiar application. Application of the techniques to studies of high polymer molecules presents some unique problems because of the extreme difficulty of preparing large single crystals of polymers. The low symmetry of polymer molecules (structures simpler than orthorhombic are nonexistent) makes direct interpretation of the nonoriented powder pattern virtually impossible. However, if a highly oriented crystalline fiber can be prepared, a
A.,
ethylene, has a repeat distance of 19.5 corresponding to 15 CF2 units. This strongly suggests that each CF2group is twisted slightly out of the plane, forming a helix which requires 15 CF2groups to make a complete turn. Some information can be deduced, even if tentatively, on the basis of the repeat distance alone. The next step in the structural analysis is the derivation of the unit cell dimensions, and finally, by consideration of the relative intensities of the reflertions, the position of all the atoms in the unit cell. Complete analyses are tedious and time-consuming, and in only a few cases have polymer structures actually been worked out completely (10). I n general, in this laboratory, only unit cell dimensions are calculated. This, however, does permit calculation of the number of monomer units in the unit cell and the theoretical crystalline density. In the past few years electron diffraction has been recognized as a valuable supplement to X-ray diffraction in the determination of structures. Russian investigators, particularly Pinsker (II), have done the majority of the work in this field Electron diffraction has several advantages over the X-ray method. Very small crystals can be examined. The extremely short wave length of the electron beam produces a great many more spacings in the electron diffraction pattern than are normally observed in X-ray patterns. This makes indexing the unit cell considerably simpler. On the other hand, complete analysis of electron diffraction patterns with respect to intensity is still in a primitive state. Electron diffraction results will undoubtedly be used to an increasing extent in polymer structure studies. m D A M E N T A L POLYMER PROPERTIES
Figure 1.
Fiber Diagram of Polyethylene
great deal of information can be ohtained from the fiber diagram. Figure 1 shows a fiber diagram of polyethylene. The center row of spots in the pattern is called the equator and the horizontal rows parallel to the equator are called layer lines. I n general, polymer fiber patterns show a larger number of layer lines than the polyethylene pattern. The equator spots arise by diffraction from lattice planes which are parallel to the fiber axis. The layer line spots arise by diffraction from planes which intersect the fiber axis. The easiest information obtained from the fiber pattern is the repeat distance along the polymer chain. This value is calculated from the distances of the layer lines from the equator and their separation from one another. I n the simplest cases, the repeat distance will correspond to that of a fully extended chain of the known chemical constitution. In the case of p2lyethylene, for example, the repeat distance is 2.54 h., which is the repeat of a fully extended planar zigzag carbon chain. On the other hand, polytetrafluoroethylene, which might be expected to have a structure similar to polyVOLUME 35, NO. 2, FEBRUARY, 1958
In addition to the structural and analytical applications, X-ray diffraction is of value in studying fundamental polymer properties, such as crystallinity, crystallite size, orientation, phase changes and melting points. The extent of crystallinity is one of the most important variables of plastics and one that has considerable bearing on physical properties. In most polymers which crystallize at all, the crystalline regions are small, and one molerule may pass through several crystallites and their neighboring amorphous regions. In general, higher crystallinity increases stiffness, but decreases
1A
POLYTETRAFLUOROETHYLENE POLYETHYLENE POLYETHYLENE TEREPHTHALAT E
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DIFFRACTION ANGLE, 2 e Fig-
2.
X-ray Difiaction Patterns of Polymnrr
0
10
20
30
40
DIFFRACTION ANGLE
Figure 3.
Amorphous content of Teflon TetraBuoloethylene Renin
toughness, so that an optimum value of crystallinity will give the proper balance of physical properties for given applications. As a consequence one of the first questions asked about a new polymer is "Is it crystalline?" Qualitatively, the extent of crystallinity can be estimated from the number and sharpness of the diffraction maxima. Totally amorphous polymers such as polymethyl methacrylate and polyvinyl acetate have X-ray patterns which show only broad diffuse halos. typical of the noncrystalline material. Twical patGins of a few crystaliine polymers are shownin ~ i g u r e 2. These patterns were obtained using a Geiger counter diiractometer. In all these patterns there are crvstalline diffraction ~ e a k su~erim~osed s on the amorpgous halos. It is dbvious ihat ihese are partially crystalline polymers also apparentthat the polyethylene and polytetrafluoroethylene are more crystalline than the nylon and polyethylene terephthalate. ~ ~ ~ ~ information t i t ~ ton i crystallinity ~ ~ often is necessary. 1f the polymer has a pattern like ~ ~ ktrafluoroethylene resin or polyethylene, with the amorphous halo resolved from the crystalline peaks, it is comparatively simple to determine the crystallinity quantitatively, ~i~~~~ illustrates the method developed in this laboratory for determining the crystalliuity of ~ ~ f ~h~ l ~areas ~ under . the crystalline peak and amorphous halo are measured with a polar planimeter, and the weight percentage of amorphous rial is as shown. ~h~ factorof 1.8 torrects the intensities for polarization, diffraction angle, temperature effects, and density. rn general, it has heen noted that specificvolume is a
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EXTRAPOLATED VALUE: d, = 2.30 2 0.01 g m . l c c . BY I R : d, = 2.306 t 0 . 0 0 4 g m . l c c .
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T-flon T.trdu0roethyl.n. Resin: Amaphova cont-nt
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Figure 5.
Fiber Diagrama of Teflon TetrafluoroethdancRasin ,.. ..... . . . ..
A , 14'C: B. 25-C.
linear function of crystallinity for polymers. Figure 4 the 'peeific a group of Teflon plotted against the amorphous contents as measured by the X-ray method. The value of the crystalline by extrapolating the line $0 0 f density l ~obtained ~ morphous content is 2.30 0.01 g./cc. This is in excellent agreement with the crystalline density of 2.306 + 0.004 g./cc. determined by infrared studies. Once this linear relationship has been established a polymer, a measurement can be wed to give a measure of the crystallinity of that polymer. The recent development of density-gradient tubes provides a rapid and precise method for determining the density (18) and, consequently, the crystallinity of a polymer Some polymers undergo fundamental changes in crystalline structure which may have profound effects on ~hysical~ r o ~ e r t i e sX-ray . methods are vartitularly %I adaitedto studies of these phase changes. Figure 5 shows the X-ray patterns of Teflon taken a t 14°C. and a t room temperature. The transition between these two forms takes place a t about 20°C. and is accompanied by about a 1% volume change. Below 20' the pattern indicates a highly ordered helical structure, which is probably triclinic, and has a repeat distance corresponding to 13 CF2 groups. Above 20°, some of the order along the chain is lost, as indicated by the comparative fuzziness of the layer lines. The cell is hexagonal-shaped, with a repeat distance of 19.5 A., corresponding to 15 CF2 groups. Studies of this transition and the structures of the two forms are still in progress in our laboratories ( I S ) .
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JOURNAL OF CHEMICAL EDUCATION
High temperature X-ray techniques have been applied to studies of polymer melting behavior, and to the determination of crystallinity as a function of temperature. The melting point is determined by observing the temperature of disappearance of the crvstalline diffraction ueaks. Crvstallinitv can be dLtermined a t tempera&res below- the melting point. Typical data for a sample of Alathon@10, a polyethylene with 2.2 CHa groups per 100 carbon atoms and a linear polyethylene are shown in Figure 6. The obvious difference is the excellent retention of cnistallinitv of the linear polymer a t temperatures up to 1 0 0 ~ ~ . It is this property which accounts for the greater stiffness of linear polyethylene and permits its use in high temperature applications for which the branched polymer is unsuited. The melting point of the linear polymer is much higher than that of Alathon 10, ae one would expect. The examples given here illustrate the versatility of X-ray diffraction in solving analytical problems as well as in supplying fundamental knowledge of the structure and properties of polymers. LITERATURE CITED (1) "Alphahetical and Grouped Numerical Index of X-ray Diffreetion Data," Special Technical Publication No. 4&E, American Society for Testing Matmisls, Philadelphia, 1955.
G. L., W. I. &YE, AND T. D. PARKS,Ind. Eng. Chem., Anal. Ed., 18,310 (1946). (3) DE LANQE, J. J., AND J. P. W. HOUTXAN, Ree. Trav. Chim., (2) CL&,
(4)KAUFMAN, H. S..
AND
I. FANKUCHEN, Anal. Chem.. 26, 31
(1954). (5) MATTHEWS,F. W., G. G. WARREN, AND Anal. Chern., 22, 514 (1950).
VOLUME 35, NO. 2, FEBRUARY, 1958
J. H. MICBELL,
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I uNEAR PowETHYLENt
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(6) POST,B., A N D I. FANKUCHEN, Anal. Chem., 28, 591 (1956). (7) WARREN, G. G., AND F. W. MAITHEWS,Anal. Chem., 26, 1985 (1954). (8) MITCHELL, J., JR.,AND A. L. RYLAND, Mikrochim. Ach, 1-6, 422 (1956). BLACK,R. H., Anal. Chem., 25, 743 (1953).
BWNN,C. W., in R. HILL, ed., "Fibres from Synthetic Polymers," Elsevier Publishing Co., Amsterdam, 1953, nn. 287-300. PINSKER,Z. G., "Electron Diffraction," tr. by J. A. SPINK A N D E. FEIQL, Butterworth's Scientific Publicahions, London, 1953. VOTER,R. C., J. CHEM.EDUC.,35, 83 (1958). PIERCE,R. H. H., JR., E. 5. CLARK, J. F. WHITNEY, AND W. M. D. BRYANT, "Crystal Structure of Polytetrafluoroethylene," presented before the Division of Polymer Chemistrv a t the 130th Meetine" of the American Chemical Society, Atlantic City, September, 1956.
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