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(11) (12) (13) (14) (15)
JOLIBOIS, P.: Compt. rend. 172, 809 (1021). OLMER,F.: “Reduction des oxydes de fer”, Thesis, Rey, Lyon, 1941, p. 15. SABATIER, P.: La catalyse, p. 29. Paris. SAITO,H.: Science Repts. TGhoku Imp. Univ. 16, 186 (1927). SAUERWALD, F.: Z. anorg. Chem. 122, 277 (1922); Z. Elektrochem. 29, 79 (1023); 30,
(16) (17) (18) (19)
176 (1924). SCHENK, R . , .4ND ZIMYERMAKN, F.: Ber. 36, 1232 (1903). SLADE, R. E., AKD HIGSOK, G. J.: J . Chern. SOC.116, 205 (1919). TROPSCH, H., AND PHILIPPOYICH, A . v . : Abhandl. Kenntniskohle 7, 44 (1929). VALLET,P.: “Methode d’6tude des systhmes chirniques d temperature va,riable”. Thesis, Jouve, Paris, 1936.
ORIENTATIOS O F AIICELLES IN S0.4P FIBERS SYDXEY ROSS Department of Chemistry, Stanford Unzuerszty, Californza Receivod LVovemberIS, 1941
The ease with which molecules of soaps and fatty acids orient themselves is a well-known and characteristic property. Investigation by x-rays has indicated fibrillation when the material is either pressed into rods (l), or smeared on metallic surfaces (lo), or picked up from aqueous surfaces by the Langmuir and Blodgett technique (2), or spun into threads from concentrated gels (7). The fiber structure thus revealed by x-rays may well be expected to exhibit features in common with other fibers composed of organic molecules linked to one another along a polymeric chain. The exhaustive x-ray researches already applied with such valuable results to the study of cellulose could be used as a guide for further studies of the nature of soap fibers. However, soap fibers differ in one respect from the polymeric fibers in that the molecules lie transverse to the fiber axis (8) and are not linked together by anything more than “crystal” forces, whereas in all other natural and synthetic fibers the macromolecules lie along the fiber axis. Fiber photographs can be obtained by pressing the powdered material into capillary tubes, so the presence of micelles in the soap fiber need not be assumed merely by analogy with the case of the cellulose fibers. I t would be impossible to suppose that the original particles lose their separate identity after orientation. That the micelles are oriented is immediately evident from the x-ray picture. The positions of the intensity maxima on the fiber diagram indicate the direction of the orientation, and the sharpness of the localized maxima can be used to ascertain how nearly the orientation is completed. The arrangement of the soap molecules inside the micelle has already been derived from x-ray data by Thiessen and his collaborators (7, 8, 9). The next step in the elucidation of the fiber structure,-the orientation of the micelles in the fiber,-can also be revealed by x-ray diffraction photographs. The purpose
ORIEPiT.%TIOS O F MICELLES 1s SOAP FIBERS
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of the present contribution is to correlate data already provided by x-ray studies with those from the electron microscope, in order to obtain a preliminary picture of the fiber structure. There is no doubt that further studies by both methods will reveal more structural detail, especially concerning type and degree of orientation, comparisons of fibers produced by the various methods, and variations introduced by homologs and polymorphs. The x-ray photographs printed by Dr. P. A. Thiessen (9) for monoclinic soap fibers show strong equatorial diffraction from the (001) planes when the incident beam is perpendicular to the fiber axis. This means that the (001) planes are parallel to the fiber axis, which is the long axis of the micelle. A qualitative picture of the degree of orientation can be obtained by assuming that the distribution of the micelles around the pencil of x-rays is proportional to the intensity distribution around any one of the (001) diffraction rings. This is strictly analogous to the method used by Sisson and Clark (6) to obtain a comparison of micelle orientation in cellulose fibers. Examination of Dr. Thiessen's photographs reveals a very pronounced degree of orientation for his samples 1 If the (001) planes are parallel to the fiber axis, then the actual soap molecule (c-axis of the unit cell) must be perpendicular to the fiber axis (b-axis of the unit cell). Inspection of the electron-microscope photographs of Marton, McBain, and \'old (4),in the light of the knowledge of fiber structure already provided by x-ray diffraction, shows that though the whole process of fiber formation took place in only a fex moments, yet an oriented structure of macroscopic size had actually formed. Measurements of the widths of the fibers indicated an unquestionable tendency to assume values that are integral multiples of approximately twice the length of the soap molecule. In most of the fibers, therefore, the (001) planes are revealed not only as parallel to the fiber axis but with a degree of selective orientation placing them at right angles to the plane of the photograph. If a random orientation of these planes had been the case, then a random distribution of v a l y s for the fiber width would have been discovered. Marton and Schiff (5) have more recently measured the thickness of the soap fibers from th,e intensity distribution of the electronic image. They have found a value of 115 A. in the direction parallel to the optical axis of the electron microscope. Out of three hundred and thirty-five measurements of the widt? of the fiber, perpendicular to the optical axis, onlxone gives dimensions of 110 A,, three give dimensions of 120 A.,and six give 130 A. If the (001) planes were capable of rotational positions around the fiber axis, we would expect a much greater number of values in the region of 115 A , deriving from those cases where the fibers are twisted by 90" around the b-axis, added on to the values in the same region that represent the third integral multiple of the double molecular length. This corroborates the original deduction that the soap fibers reveal selective unaxial orientation in the electron-microscope photographs. It is, perhaps, to be 1 Experiments conducted in this laboratory by Alev de Bretteville indicate that the type of orientation is independent of crystal structure and depends only on the method of preparing the sample
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expected that orientation should be noticed when only a few fibers are considered, but a knowledge of the nature of the orientation thus observed is of value in building a picture of the orientation of lal*ger fiber bundles. No close correspondence in the type of orientation is claimed in the present essay between fibers obtained by the various methods and the interlaced ribbons revealed by the electron microscope, but a general structural relationship clearly holds for all.* It is tempting to seek for further correlations between information already furnished by x-ray investigation and the electron-microscope photographs. For instance, it is not unreasonable to suppose that the externally visible form of the fiber will exhibit a face inclined a t the monoclinic angle to the b-c plane. If the fiber is oriented with the b-c plane perpendicular to the optical axis of the electron microscope, the monoclinic angle could be easily verified by measuring the variation of the intensity distribution of the electronic image along the c-axis of the fiber. In this way the microphotometer record across the width of the fiber would provide a ready means of obtaining the monoclinic angle. If the fiber were not oriented, the rotational angle could be calculated by a trigonometrical formula: a = tan-'
sin fl cost.cos (j3 - t )
1
where a is the angle calculated from the microphotometer record, /3 is the monoclinic angle, and t is the rotational angle between the b-c plane of the fiber and a plane perpendicular to the optical axis of the electroh microscope. There is but little doubt that the electron microscope in its present form (3) is capable of producing a record sufficiently free from optical defects t o justify the accuracy of such a calculation. The dimensions af the phenomenon sought are within the l i i t s of present-day electron microscopy? Tentative microphotometer records made of the electron-microscope photographs of Marton, McBain, and Vold (4) indicated optical aberrations of sufficient magnitude t o invalidate measurements of a. But such records were not made on the original micrographs, *hich were not available, and hence do not permit a decision on whether the theory is significant or not. It must be borne in mind that previous micrographs were not made with the object of investigating thk phenomenon. It is t o be expected, of course, that with the production of finer instruments present difficulties will disappear. SUMMARY
1. The oriented nat.ure of the soap fibers photographed by the electron micro-
scope is pointed out, and 8 correlation is sought between this orientation and that revealed by x-ray diffraction photographs. 2 In this connection it is significant to recall the pseudo-crystals of Miiller (Proc. Roy. 800. (London) All4, 556 (1927)),in which orientation along the b-aXis waa discovered for similar long-chain carbon compounds. In 8ome cases there was also present some preferred orientation along another crystal axis. a Private communication from Professor L. Marton.
QENERAL THEORY OF THE ISOELECTRIC POINT
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2. The electron microscope is here proved a powerful instrument for the detection of selective orientation, a phenomenon previously discovered by x-ray diffraction only after considerable investigation. Further applications are suggested. The author is indebted to Professor James W. McBain for his interest, sustained with unusual fortitude while recovering from a serious automobile accident. REFERENCES BECKER, K., AND JANCKE, W.: Z. physik. Chem. 99,242 (1921). CLARK, G.L., AND LEPPLA,P. W.: J. Am.Chem. SOC.68,2199 (1936). MARTON, L.: Phys. Rev. 68,57 (1440). MARTON, L., MCBAIN,J. W., AND VOLD,R . D.: J. Am. Chem. SOC.63,1990 (1941). (5) MARTON, L., AND SCHIFF, L. I.: J. Applied Phys. 19,759 (1941). (6) SISSON,W.A,, AND CLARK, G. L.: Ind. Eng. Chem., Anal. Ed. 6,296 (1933). (7) THIESSEN, P . A.,AND EHRLICH, EVA:Z. physik. Chem. 186, 453 (1933). (8) THIESSEN, P . A,, AND SPYCHALSKI, R . : Z. physik. Chem. 166,442 (1931). (9) TAIESSEN,P. A., AND STAUFF,J.: Z. physik. Chem. 176, 397 (1936). (10) TRILLAT, J. J.: Rev. Sei. 64,552 (1926) : Ann. phys. 10, 5 (1926). (1) (2) (3) (4)
GENERAL THEORY OF T H E ISOELECTRIC POINT TERRELL L. HILL Department of Chemistry, University of California: Berkeley, California Received August 18, lO4l
The concept of the isoelectric point derives most of its significance from the occurrence a t this hydrogen-ion concentration of r n w a in certain properties of aqueous solutions of ampholytes. Considerab1e;experimental work has been done on this problem, but the theory is rather incomplete. Levene and Simms (4)have derived an expression for the isoelectric point, making certain simplifying assumptions, and on the same basis have shown that the hydrogen-ion concentration a t which an ampholyte exhibits minimum ionization coincides with its isoelectric point. Hitchcock (3) obtained an exact expression for the isoelectric point of an ampholyte, but apparently no attempt has been made t o consider the properties of the isoelectric point from this point of view. In the present paper we attempt a general treatment of the problem, extending the concept to include solutions of any number of ampholytes-such complex solutions being of the type which actually occur in biological systems. The more important special cases all may be derived from this single discussion. THE ISOELECTRIC POINT
We take as our general system of interest an aqueous (an analogous treatment can be made for other solvents) solution of p ampholytes, of which those num-
