MONOLAYERS AND MULTILATERS OF POLAR HYDROCARBOX MOLECULES
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This would be capable of ionizing to give two potassium ions and a silicate ion with a double charge. Actually, of course, the situation is more complicated. Part of the silicate is present in the form of multicharged ionic micelles (4). In addition, there is little hydrolysis. While these factors affect the degree of condensation, the basic cross-linkage mechanism would be the same. The concentration of the added salt will determine to a considerable extent the degree of cross-linkage. Higher concentrations of salt would increase the number of linkages and increase the strength of the bond. The condensation-polymerization is a relatively slow process. The addition of acids or acidic materials induces a much more rapid type of polymerization. However, we believe that too much reduction in pH is undesirable, first, because the bond thus formed is weaker and, second, because the process becomes much more difficult to control. Some reduction to decrease the time required for the formation of a good screen may be worth while. Studies on this are under way. The effects of various factors in screen formation are being studied. We hope t o report on these in a later paper. REFEREKCES (1) ADAM,S . K.: T h e Physics and Chemistry of Surfaces, 3rd edition, pp. 202-4. Oxford University Press, London (1941). (2) EDELBERG, R . , A N D HAZEL. F.: Trans. Electrochem. Sac. 96, 13-20 (1949). (3) HAZEL, F . : Unpublished work. (4) MCBAIN, J. W., A N D SALMON, C. S . : J. Am. Chem. SOC.42, 426-60 (1920). (5) SADOFSKY, MEIER:Trans. Electrochem. Sac. 95, 112-18 (1949).
O S T H E STRGCTURE OF RlOSOLAYERS AKD MLLTILAYERS O F POLAR HYDROCARBOX MOLECULES O S SOLID SUBSTRATES H . T. E P S T E I S ' Department of Physics, Unzversaty of Machzgan, Ann Arbor, Machzgan Receaued October 20, 1949 I. INTRODUCTIOX
The many studies (1, 5 , 12) of monolayers and multilayers of polar hydrocarbon molecules on solid substrates have not yet resulted in knowledge of the detailed arrangement of the molecules in such layers. The properties of the layers are sufficiently characteristic so that it has not been possible to infer the structure from the properties. Some of the properties peculiar to these layers are as follows: ( a ) the layers are simultaneously hydrophobic and oleophobic; ( b ) the layers are closePresent address: Departments of Biophysics and Physics, Cniversity of Pittsburgh, Pittsburgh, Pennsylvania.
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E. T. EPSTEIN
packed, but the molecules are randomly situated on the substrate; (c) the molecules have their axes tilted at random away from the normal to the substrate, and the tilts take on all values up to a maximum value characteristic of the molecule; (d) the binding energy per atom in the layers is greater than the binding energy per atom in crystals of the same molecules, according to the first, relatively rough measurements of the binding energy. There are many questions raised by a consideration of the observed properties of these layers. The origin of the tilting of the molecules must be found. It must be explained how randomly situated molecules, having random tilts of their axes, can be closely packed, and indeed, so closely packed that their binding energy is probably greater than when the same molecules are in a crystalline array. Further, it is necessary to ask why the usual crystal array ever occurs, if the monolayer structure has a binding energy greater than that of the crystal. This paper will describe the attempts to obtain answers to some of these questions by the use of electron microscopic observation of the layers. 11. EXPERIMENTAL DETAILS
The monolayers and multilayers considered in this paper are composed of molecules of the normal fatty acid series. Most of the work has been done with the eighteen-carbon-atom molecule, stearic acid, and it will be used as prototype throughout the discussion. The layers have been deposited on glass microscope slides by either of two methods: the Langmuir-Blodgett dipping technique or the oleophobic technique. The latter method involves placing a drop of stearic acid dissolved in, say, hexadecane on the slide; the drop then rolls over the slide, leaving a single layer of molecules on the surface. The former method requires that a drop of a solution of stearic acid (e.g., in benzene) be placed on a water surface. The drop spreads out to form a monolayer of stearic acid on the surface. Insertion and withdrawal of a slide result in the deposition of a single layer of molecules during each insertion and withdrawal after the first immersion of the slide. By adjusting the pH of the water according to the standard recipes of Blodgett and Langmuir (4) the monolayer can be made to contain any arbitrary proportion of stearate molecules, e.g., barium stearate, if a barium salt is added. Once the layers are formed, they are shadow cast with platinum, palladium, or uranium. The preshadowed replica technique (14) is used to prepare the layers for examination in the electron microscope. It should be pointed out that the contrast of the layers with the substrate is so low that the study is impossible without the enhanced contrast afforded by the shadow-casting technique. 111. RESULTS AND DISCUSSION
A . Layer heights It was necessary first to ascertain whether the shadow-casting procedure has any effect on the layer structure. This check can be made, to some extent, by
3IOh-OL.SSERS d S D SIT.LTIL.4YERS
OF POL SR HYDRO CAR BOA^ MOLECCLES
10%
measuring the height of the layers, for the layer height of bariuy stearate molecules is knolvn, from optical measurements (4); to be nearly 25 .$. per layer. The attempt to make or t o find holes in the monolayers was not successful. Ilo\vever. holes can be obtained in multilayers simply by making the successive
FIG 1 . lclectron micrograph of thiee layers of stearic acid.
FIG.3 . Twenty-one layer film of stearic :tcicl-l)ariuni stearate after immersion in Iienzene (a) for 2 s e e . and ( t i ) for 1 min. Layers prepared a t pH 6.4.
FIG.2. Twenty-one layers of stearic acid-barium stearate (a) before and (b) after immersion in henzene for 1 min. From t o p to bottom, layers prepared at pH's of 5 . 8 . 6.4, 7 . 3 . and i . 9 .
dips of the slide more rapidly than is suitable for smooth layer deposition. The speed used was about one dip per second. A typical preparation is shown in figure 1. The preparation was shadow cast so that the layer height was one-third the shadow Tvidth; from this datum and knoiring the magnification of the pic-
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H. T. EPSTEIN
4.
ture, the layer height is found to be about 50 Measurements on two dozen such preparations gave an average height of 45 A. As has been previously mentioned, two molecules are deposited when the slide is inserted and withdrawn from the water, so that the height per molecule is half the measured value, or 23 A. The height of the layers studied in the electron microscope should be a little less than that of the layers studied by Blodgett and Langmuir, for the present study measures the height of a stearic acid molecule, and it is known to be tilted away from the normal more than is the barium stearate molecule studied by Blodgett and Langmuir. The agreement of the layer heights with that determined by the optical measurements is taken as evidence that shadow casting has little effect on the orientation of the molecules, though it cannot be stated that the grouping of the molecules has not been affected.
B. Skeletonized jilms By dipping a multilayer-covered slide in benzene for about 30 sec. Blodgett and Langmuir (4) were able to reduce the refractive index of the multilayer from about 1.5 to 1.3 with practically no change in the measured thickness of the film. It is known that benzene selectively dissolves the stearic acid in these layers and leaves the barium stearate molecules. Thus, it was thought that it might be possible to learn something about the distribution of the acid in the layers by observing the pattern of the holes in the film with the electron microscope. It is not possible to obtain sharp micrographs of films as thick as those used by Blodgett and Langmuir in their studies of skeletonization. Their films averaged about 170 molecularolayers; this number of layers corresponds to a film thickFess of about 4000 8.In the present study, a film of 21 layers (about 500 A.) was selected as a thickness which would probably show the effects of skeletonization and which is still thin enough to allow fairly sharp micrographs to be obtained. The films were prepared on mater having pH values of 5.8, 6.4, 7.3, and 7.9. The films on which Blodgett and Langmuir made most of their observations were prepared a t pH 6.4. Figure 2 shows the effects of dipping the series of layers in the benzene. The first column contains micrographs of the layers before they were immersed in benzene for 1 min. Layers deposited at pH 5.8 are simply reduced in thickness by a rather extensive dissolving of the entire film. Rather deep holes are made in the layers deposited a t the other pH values. There appear to be fewer holes in the layer deposited a t pH 7.9 than in the other two layers in which holes appear, as might be expected because there is less acid in the layers, the higher the pH. One set of observations \vas made on the effect of dipping a layer in benzene for different lengths of time. A layer prepared at pH 6.4 was dipped for 2 sec. The micrograph of this preparation (figure 3a) is s h o m beside the preparation dipped for 1 min. (figure 3b). The total area of the holes in the 2-sec. preparation seems not particularly different from the hole area in the 1-min. prepara-
MOSOLAYERS AND MULTIL.4YERS OF POLAR HYDROCIRBON MOLECULES
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tion. However, there seem t o be more and smaller holes in the 2-sec. preparation. The implication of the difference between these two preparations is that there must be considerable mobility of the stearate molecules in the layers so that the small holes are brought together. The stearate molecules have this mobility, of course, only while the layers are immersed in the solvent. X suggestion concerning the mechanism of skeletonization can be obtained from the fact that the total hole area remains roughly constant while the average density of the film decreases, according to the measurements of Blodgett and Langmuir. Because the hole area remains constant, it is suggested that the removal of a large fraction of the molecules probably occurs by a mechanism, perhaps diffusion, which brings the acid molecules from the inside of the film to the holes. Once in the holes, the molecules are removed by the solvent. Furthermore, since the hole area seems to be established practically at the first contact of the solvent with the film, the formation of the holes probably occurs by a simple mechanism. Now, when the slide is first immersed in benzene, the
FIG.4
FIG. 5
FIG 1 Schematic representation of a skeletonized multilayer FIG 5 Cross-section of a stearic acid micelle on water
solvent sees only that a certain fraction of the molecules of the top layer is stearic acid, and these acid molecules are taken out into solution. Of the molecules in the second layer which are revealed by the extraction of the acid molecules in the top layer, the same fraction, on the average, is stearic acid. Presumably, the acid molecules in the second layer are likewise dissolved out, and the solvent then attacks the acid molecules in the third layer, and so on. This picture of the action of the solvent is indicated schematically in figure 4, which has been sketched, for simplicity, for the conditions at pH 6.6 at which there are equal amounts of acid and stearate in the layers. Since half the top layer is stearic acid, this half is removed by the solvent, and the removed area is indicated by the cross-hatched portion of the layer. Half of the molecules underneath the cross-hatched portion are stearic acid, and these too are removed, as indicated, and so on. The average thickness of the film of figure 4 can be calculated by a simple numerical integration, as follows: Let tl be the thickness of the film before skele-
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H. T. EPSTEIN
tonization and ZZ be the average thickness after skeletonization. 1 is the thickness of one layer of molecules, and N is the number of layers in the film. The calculation is done for unit width of film perpendicular to the paper; the length of the portion of the film considered is s. The expressions for tl and & are:
Nl
ti
si, = NZ;
+ ( N - l ) Z + ( N - 2)Z +
Thus :
&
1
tl- = 2 + -
( N - 1) + (N - 2) + 4N 8N
...
For the layers studied by Blodgett and Langmuir, N is about 170, and the integration intervals are a little different from the simple 4 2 , 44, s/8, etc., of the expression given above for a layer prepared at pH 6.6. The result of the calculation for the layers studied by Blodgett and Langmuir is: L/tl
=
0.990
This figure is t o be compared with the experimentally found value, 0.992. The apparent agreement of the experimental and calculated values of &/tl should probably not be taken too seriously until some optical experiments have been done on thinner films than those used by Blodgett and Langmuir. The calculation is relatively insensitive to the number of layers, if the number is large. Finally, it should be mentioned that the mobility of the stearate molecules (while the film is in the solvent) prevents obtaining information about the distribution of the acid and stearate molecules within the layers.
C . The characteristic grouping and tilt of the molecules One of the more striking features of the monolayers and multilayers as revealed by the electron micrographs is the apparent grouping of the molecules into clusters, which, for stearic acid, are about 100 A. in diameter. I t was thought at first that the clustering is due to the roughness of the substrate. Both glass and collodion are known to have irregularities in their surfaces of the same order of magnitude as the cluster diameter. It was later realized that the observed cluster size remained approximately constant, although layers were deposited on substrates cleaned in a variety of ways. The constancy of the cluster size led to experiments designed to test the hypothesis that the molecular clustering is a property of the monolayer structure and is not entirely a feature caused by the roughness of the substrates. The obvious way of testing the above hypothesis is by depositing the layers on smooth substrates. The finding of a smooth substrate is, however, one of the unsolved problems which generated the present work. A long series of experiments by Williams and Backus (14) and by the writer has ended in the conclu-
MONOLhYERS A S D MULTIL.4YERS O F P O L h R HYDROC.iRBOS MOLECULES
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sion that none of the methods tried has produced a smooth glass or collodion substrate. I t is true that the heights of the irregularities of glass microscope slides have been reduced by polishing with rouge so that the slopes of the irregularities are probably less than 10”. The diameters of the irregularities have not been reduced, however, so that the slides cannot be considered smooth enough to permit a definite statement to be made that the molecular clustering is a characteristic property of the monolayers. Accordingly, the evidence for the existence of characteristic clustering of the monolayer molecules must be obtained from other experiments to be described below. Langmuir (11) has used the idea of clusters of molecules in monolayers to explain the properties of expanded layers. He called these groups micelles, and this name will be adopted for the clusters seen with the electron microscope. Langmuir’s explanation of the existence of micelles starts from the experimental finding that the cross-section of the hydrated carboxyl groups is much greater than the cross-section of the hydrocarbon tails. The arrangement of the molecules within a micelle is believed to be as indicated by the sketch in figure 5 . The circle represents the carboxyl group; the straight line represents the hydrocarbon tail. It occurred to the writer that even the unhydrated carboxyl groups might be larger in cross-section than the hydrocarbon tails. h search of the literature reveals that Adam (1) has already suggested such a possibility. The data which Adam has obtai2ed for the cross-sections of the unhydrated acid molecules give an area of 20.4 .1.*for all the long-chain acid molecules. Th: area of the hydrocarbon tails has been measured by Muller (13) and is 18.4 .%.* The explanation generally given for the difference between the two areas just described is that the acid molecules are all tilted by the same angle (about 26’) away from the normal to the water surface. Adam pointed out that it was equally possible to explain the area difference by saying that the cross-section of the acid is dettrmined by the area of the carboxyl group, which is then taken to be 20.4 A.* Then there is no necessity for assuming that the molecules are all tilted away from the normal. The assumption of tilted molecules on water has not been supported by any accepted arguments or experiments to make plausible that there should be any tilt a t all, or that there should be a single tilt angle for all the molecules of the fatty acid series. At the time of Adam’s writing, however, it’ \vas not important to know which, if either, of the explanations of the difference in cross-section was correct, so Adam carried the discussion no further than the mere suggestion of the alternative explanation. Adam’s suggestion leads to a calculation of the size of the stearic acid micelles found on solid substrates which is in reasonable agreement with the size observed with the electron microscope. This calculation will now be presented. First, Langmuir’s condition for limiting the size of the micelles can be restated in a somewhat more usable form. The condition suggested by Langmuir is that the tails are forced so far apart that they cannot bind the molecules to each other. Here we shall say that the binding energy of the molecules decreases as the molecules tilt, the energy decrease arising from the fact that the molecules
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slip along each other as indicated in figure 5 . Then, the condition for limiting the size of the micelle is taken to be the decrease in binding energy by some definite amount, perhaps of the order of the binding between each pair of carbon atoms. When the binding energy has decreased by this amount, it is then energetically more stable to form a second micelle than to continue the growth of the first micelle. Although the limiting decrease of binding energy is not known, an equivalent quantity can be calculated from the data on the size of micelles on water. This quantity is the tilt of the outermost molecules in the micelle. The limiting angle of tilt on water will be calculated and applied to the case of the molecules on a solid substrate. If the molecule is taken to h y e a cylindrical shape, the radius of the hydrocarbon tail is 41= 2.42 A. Similarly, the radius of the hyGrated carboxyl group is 42% = 2.88 A. The difference in the radii is 0.46 A. If two molecules come together, the angle between them is approximately given by the difference in the diameters of the opposite ends of the molecules divided by the length of the molecule: 0.92124.4 = 0.038 radian. according to Langmuir's diagram of the way the molecules are arranged in a micelle, there are about two or three molecules per micelle radius, for stearic acid. Since the tilt per molecule is 0.038 radian, the tilt of the outermost molecules is, say, 2.5 times this angle, or nearly 0.1 radian, which is nearly 6". The unhydrated carboxyl group has already been mentioned as having a crosssection of 20.4 A.2 The difference inodiameter of the polar group and the hydrocarbon tail in this case is only 0.26 A. The angle between two molecules is then 0.26/24.4 = 0.01 radian. Thus, if the limiting angle of tilt is 0.1 radian, there must be 10 molecules in the radius of a micelle on a solid substrate where the molecule is not hydrated. The micelle then has a diameter of ZO molecules, or 20 x 5 = 100 A , since the diameter of a molecule is about 5 A. This value for the micelle diameter is the same as that found with the electron microscope for the clusters of stearic acid on glass and collodion substrates. Further, it should be observed that the calculated limiting angle of tilt is in agreement with the characteristic limiting tilt angle found for stearic acid by electron diffraction techniques, within experimental error. Because the calculation just presented can correlate three hitherto unrelated experiments, and because it leads to predictions of the micelle diameter and characteristic tilt angle which are in reasonable agreement with experiment, it is felt that there is a strong possibility that the molecules in a monolayer are really grouped together in micelles. Further evidence suggesting the reality of the micelles will be presented below. The experiments on the wetting temperatures of oleophobic layers yield desorption energy values which can be interpreted as indicating that the monolayer molecules are arranged in clusters. Zisman and coworkers (2, 3) found that the binding energy per carbon atom of the molecule is either about 1200 cal./ mole or about 200 or 300 cal./mole, depending on which, if either, of their two calculations is correct.
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I t will be shown in appendix A that there is an error in the calculation which leads to the smaller value for the binding energy. When the calculation is corrected, the resulting binding energy value is in good agreement with the larger of the two values given by Zisman and coworkers. If the larger binding energy per carbon atom (1200 cal./mole) is correct, it is necessary t o ask what molecular configuration could give a greater binding energy than the crystal array, and also to ask why the monolayer configuration OC the molecules is not adopted in the three-dimensional arrangement of the molecules. The answer to the latter question must be that it is not possible to continue the monolayer configuration into the third dimension. The arrangement of fatty acid molecules in the crystal is indicated schematically in figure 6a. The angle by which the tails of the molecules are tilted away from the surface normal is about 35" (6). When the molecules are in a monolayer,
a
b
5
FIG.6
FIQ.7 FIG. 6. The arrangement of polar hydrocarbon molecules in crystals and in oriented monolayers. FIG.7 . Oriented layer configuration continued into the third dimension
they are known to be oriented to within, say, 10" of the surface normal, as suggested in figure 6b. However, the binding ehergy per carbon atom is no more in the arrangement of figure 6b than it is in the arrangement of figure 6a, unless the tails are closer together in the monolayer array. The tails can be closer together in the monolayer in at least two ways. The first way requires that the effective diameter of the carboxyl group be smaller in the direction of the C-OH bond than it is in the horizontal direction in figure 6a. The possibility of this configuration must be discarded, because there seems to be no reason why a three-dimensional array could not be built with this arrangement of the molecules. The second way for the tails to get closer together is for the tails to tilt toward each other, as indicated in figure 6c. This configuration satisfies the requirement that it is an arrangement which cannot be continued into the third dimension,
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H. T. EPSTEIN
as indicated in figure 7. I t is seen that the carboxyl groups of the second layer are nonplanar; the nonplanarity can only become worse by building more layers on top of these two layers. Thus, the above argument tends to support the idea that the molecules are arranged in clusters whose size must eventually be limited by the slip of the molecules on their inner neighbors in the micelles. The argument for the existence of micelles can be stated somewhat differently, and in a way which seems to be independent of the actual arrangement of the molecules within the micelles. One can say that the molecules in a monolayer must be arranged in micelles containing one molecule, more than one molecule, or all the molecules in the monolayer. If the number of molecules per micelle is unity, it is difficult to understand how there can be a greater binding energy per carbon atom than there is in the crystalline array. If all the molecules are in one micelle, it is difficult to understand how the molecules can be randomly situated on the surface and tilted at random up to a maximum value. Therefore, it seems probable that each micelle contains more than one molecule and considerably fewer than a large fraction of all the molecules in the monolayer. There is a recent experiment by Karle (9) which yields results which have been interpreted as indicating a micellar grouping of the molecules in oleophobic monolayers. Karle studied the rate of evaporation of monolayers of cerotic acid and n-octadecylamine deposited on glass from melts of the pure compounds. He also took electron diffraction pictures of the layers throughout the course of the evaporation. It was found that when the relative amount of material evaporated is small, the characteristic tilt of the molecules in the monolayers does not change appreciably. This result was interpreted as indicating that the monolayer exists as what Karle called patches on the surface, the evaporation taking place mainly from the edges of the patches. Further, Karle was able to analyze his data in terms of the energy necessary to remove a molecule from the monolayer and he found that it is about one-third the average binding energy of a molecule in the monolayer as determined from the data of Bigelow, Glass, and Zisman. This result is taken as further evidence that the evaporation takes place mainly on the edges of the patches, because the evaporation energy is only a fraction of the average binding energy, and therefore it would appear likely that only a fraction of the bonds needs to be broken in order for the evaporation to occur. There is one more experiment to be discussed at this point which probably offers support to the suggestion that the molecules in a monolayer are collected together in small groups which have a characteristic tilt associated with their outermost molecules. The experiment is the electron diffraction study of rubbed multilayers. It has been interpreted by Germer and Storks (8) as indicating that the multilayer molecules are left on top of the first layer in the form of crystals which are inclined up against the direction of rubbing by about 8".The thickness of the crystals is believed to be somewhat less than 200 b. Because a thickness of 200 A. is easily observed with the electron microscope if the preparation is shadow cast, it seemed worthwhile to attempt to photo-
YOSOLAYERS A K D MULTILAYERS OF. POLAR HYDROCARBON MOLECULES
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graph the rubbed multilayers in order to discover if the crystal structure could be seen directly. There is difficulty in deciding just what Germer and Storks meant by “light rubbing,” but a number of preparations were rubbed with varying amounts of pressure. No crystals are visible. As a rule, the rubbing appeared to wipe off all the multilayer except what appeared to be the first layer-a result which had been obtained by Germer and Storks. Mr. W. C. Bigelow obtained electron diffraction patterns t o verify that the first layer remained on the substrate after rubbing, and he found the usual monolayer patterns. The finding that there are no crystals large enough to be seen in the microraphs is interpreted as indicating that the crystals must be less than, say, 200 . in diameter. On the basis of this finding, the following suggestion is made concerning the structure of rubbed multilayers. Because the electron diffraction pattern indicates crystals tilted up against the direction of rubbing, the upward tilting must be due to a structure in the first layer which is repeated in distances of the order of 100 A. This distance between repeated structures in the first layer is derived from the finding that crystals of this size show the same upward tilting. Furthermore, the structure probably has a cylindrical symmetry, because the layer can be rubbed in any direction and the same result obtained, as far as the interpretation of the electron diffraction pattern is concerned. The crystals are fairly firmly wedged against some structure, because they are not easily dislodged by rubbing in the same direction as the original rub, though very light rubbing in the opposite direction easily removes them. I t seems likely that the structure against which the crystals are wedged must be the source of the characteristic upward tilting by about 8”. If we put together the suggestions of the previous paragraph, they seem to indicate the existence of cylindrically symmetrical groupings of molecules in a monolayer. The groupings are of the order of 100 A. in diameter, and the outermost molecules are tilted about 8’ away from the surface normal. The discussions of this section, thus far, may be summarized as follows: (1) The electron micrographs of monolayers on solid substrates indicate the grouping of the molecules into clusters which we call micelles. @) A suggestion as to the energy condition which determines the size of the micelles on water leads to calculations of the micelle diameter and characteristic tilt of the micelle molecules on solid substrates which are in agreement with the experimentally found micelle diameter and characteristic tilt of stearic acid monolayers. (3) Four other independent experiments have been shown to have a consistent interpretation in terms of a micelle structure for the monolayer molecules. In consequence of the satisfactory results of the calculations presented in the first part of this section, an attempt has been made to formulate a theory which can predict the dependence of the characteristic tilt angle and micelle diameter on the length of the molecule. This theory will be presented in appendix B. The theory predicts that both the micelle diameter and the characteristic tilt angle vary inversely with the length of the molecule, the tilt varying more
1
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H. T. E P S T E I N
strongly than the micelle diameter. The details of the experiments designed to test these predictions will be published later; the first results are that both predictions are fulfilled. The fact that the micelle size is found to vary systematically with molecule length is further evidence that the micelle is a characteristic feature of the monolayer itself. IV. DISCUSSION O F ELECTRON DIFFRACTION E X P E R I M E N T S ON T H E BASIS O F T H E MICELLE MODEL FOR MONOLAYERS
On the basis of the existence of micelles within monolayers it is possible to understand the finding that the monolayer molecules are closely packed but randomly placed on the substrate. This finding was based on observations on layers of stearic acid. The micrographs show that the micelles themselves are closely packed and randomly situated on the substrate so that their constituent molecules are primarily arranged in a similar manner. However, it is possible that there should be an orderly arrangement of molecules within a micelle. An orderly arrangement of the molecules would seem to be more possible the more nearly equal are the cross-sections of the polar group and the hydrocarbon tail, as is the situation in barium stearate films. In the patterns from stearate films, Germer and Storks observed a very few spots on the bands, indicating an orderly arrangement of molecules of not too extensive a nature. The micellar grouping of monolayer molecules is also one by means of which it appears possible to have an oriented film in which the tilts of the molecules are randomly directed around the surface normal, and still have a closely packed layer. Furthermore, the model explains the observation of Karle and Brockway (10) that the patterns seemed to indicate that the number of molecules tilted a t any angle appears to increase with the angle of tilt. The development of multilayers is also more clearly understandable on the basis of the existence of micelles. Germer and Storks (7) noted that the threelayer diffraction pattern is composed of both a monolayer and a crystalline pattern, and that the monolayer pattern shows the tilt angle to be less than it would have been before the upper layers were deposited. The change of the tilt of the molecules will be explained with the aid of the sketches in figures 5, 7, and 8. Figure 5 represents a monolayer micelle. When the second layer is added, as indicated in figure 7, the carboxyl groups would have to be nonplanar if the first layer were to remain undisturbed. It is probable that there would be a decrease in the binding energy if the nonplanarity were very great, so it is not unreasonable to suppose that there is a decrease for all nonplanar configurations. Thus, it is indicated that there may be some tendency to alter the configuration toward that in figure 8. Furthermore, when the third layer is deposited, the molecules of the second and third layers have been shown to form a crystalline array. Thus there will be an even greater tendency to straighten up the tilted molecules of the first layer and to rearrange them into the regular crystal positions. The deposition of even more layers should give a crystal structure increasingly closer to the naturally occurring crystal structure, owing to the strengthening of the tendency of the upper layers to rearrange the molecules of the first layer.
MONOLAYERS AND MULTILAYERS OF POLAR HYDROCARBON MOLECULES
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The fact that the regular crystal structure is not found for a three-layer film indicates both that the first-layer molecules are not regularly spaced and that the surface formed by the ends of the tails is not planar, for if these conditions were met, the second and third layers could form as regular an array as they do on Resoglae, according to Germer and Storks. Furthermore, it is indicated that the randomness of the positions of the first-layer molecules is not the randomness of separated molecules but rather that these molecules have some sort of stable configuration. This conclusion is based on the idea that it would probably be easy to rearrange the molecules if they were not in a stable configuration already. In many of the micrographs which have already been shown, the micellar structure can be seen to persist through many layers. This result may be interpreted as showing that the crystal built on top of each micelle tends to grow separately from the crystals which are developing on top of the other micelles.
FIG.8 FIQ.9 FIG.8. Effect of depositing a second layer of molecules on top of a monolayer FIG.9. Relation of limiting tilt angle to slip of molecules on each other
If this interpretation of the micrographs is correct, then the various planes of one crystal need not be oriented parallel to the corresponding planes of the other crystals. The electron diffraction pattern from such an array of crystals should show all orientations of the crystal planes with respect to the surface normal, unless there is some other factor tending to orient the planes. In the barium stearate multilayers there appears to be no such factor, and the crystal planes have been found by Germer and Storks to be randomly oriented with respect to each other. I n the stearic acid crystals, however, there exists an orienting factor. As indicated previously, the molecules in such crystals are tilted about 35" away from the surface normal. Germer and Storks pointed out that there should therefore be a strong tendency to line up these crystal tilts in the direction in which the slide is dipped to form the multilayer, and they observed the results of such a factor.
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H. T. EPSTEIN
The stearic acid multilayer diffraction patterns can be interpreted without there being micelles, but the barium stearate multilayer patterns seem to require the existence of micelles. V. SUMMARY
Monolayers and multilayers of the normal fatty acids have been prepared on solid substrates and examined by electron microscopy and electron diffraction. The main result is the observation that the molecules are grouped into twodimensional micelles, about 100 A. in diameter. On the basis of the existence of micelles, it is shown to be possible to explain and correlate a number of experimental results of previous workers. Several inconsistencies and errors in previous work are resolved and corrected. An order of magnitude theory of micelle structure is developed, and preliminary experiments indicate that its predictions are at least qualitatively correct. The theory relates the micelle diameter, the observed maximum tilt of molecules in a monolayer, and the length of the molecule. Skeletonized films are examined, and it is observed that deep holes develop in such films. A mechanism for skeletonisation is proposed and is found not to be inconsistent with the very limited amount of data available on skeletonized filma. The writer would like to express his gratitude to Professor R. C. Williams, who suggested this problem and guided the research so helpfully. I t is a pleasure to acknowledge the many discussions with Professors L. 0. Brockway and E. Katz. Finally, thanks are expressed to Mr. W. C. Bigelow for doing the electron diffraction work needed in conjunction with the research and also for supplying all the purified chemicals. REFERENCES (1) ADAM:The Physics and Chemietry of Surfaces, 3rd edition. Oxford University Press, London (1941). (2) BIGELOW, GLASS,AND ZISMAN: J. Colloid Sci. 2, 563 (1947). (3) BIGELOW, PICKETT, AND ZISMAN: J. Colloid Sci. 1, 513 (1946). AND LANGMUIR: Phys. Rev. 61, 964 (1937). (4) BLODGETT AND KARLE: J. Colloid Sci. 2, 277 (1947). (5) BROCKWAY AND STORKS: Proc. Natl. Acad. Sci. U.S. 23, 390 (1937). (6) GERMER (7) GERMER AND STORKS: J. Chem. Phys. 6,280 (1938). (8) GERMER A N D STORKS: Phys. Rev. 66, 648 (1939). (9) KARLE: J. Chem. Phys. 17, 500 (1949). (10) KARLEAND BROCKWAY: J. Chem. Phys. 16, 213 (1947). (11) LANGMUIR: J. Chem. Phys. 1, 756 (1933). (12) LANGMUIR: Proc. Roy. SOC.(London) 170, 1 (193Y). (13) MULLER: Proc. Roy. SOC.(London) 114,542 (1927). (14) WILLIAMS AND BACKUS: J. Applied Phys. 20,98 (1949). APPENDIX A
Correction of theoretical treatment of oleophobic layers The deposition of monolayers by the oleophobic techniques has given the possibility of measuring U ,the energy of adsorption (or desorption) of the molecules, by raising the temperature until the molecules no longer form an oleo-
MONOL.4YERS AND MULTILAYERS OF POLAR HYDROCARBON MOLECULES
1067
phobic layer. Zisman and coworkers (2, 3) developed theoretical arguments to show that dU/dN, the binding energy per carbon atom of the molecules, is 1200 cal./mole or 200 cal./mole, depending on which of their two theoretical developments is used. N is the number of carbon atoms in a molecule. It was suggested in the main part of this paper that the larger of the two values is correct, and the larger value was used to offer an additional reason for believing that the monolayer molecules associated into micelles. I t will be shown that there is an error in the second calculation by Zisman and his group, and a value of the order of 1200 cal./mole/carbon atom will be shown to be correct for dU/dN. The authors measured I, the wetting temperature for deposition of monolayers from solutions of the pure molten acids, from which they calculated a a quantity b2, defined as b2 = U/Rr. This quantity was determined for the acids, alcohols, amines, and amides, and was found to be constant within about 15 per cent; the value is about 15. Thus, dU/dN can be obtained by differentiation to be dU/diV = b2R dr/dN Since R and bZ are known, and since d r / m can be determined from the data from pure molten compounds, dU/dN can be calculated, and is found to be 212 cal./mole/carbon atom at N = 18. A similar calculation was carried out for the amines, amides, and alcohols. The value of 336 cal./mole/carbon atom for the amines was considered to be in good agreement with a value of 400 cal./mole/ carbon atom found from the desorption energy data as outlined above. The value 400 cal./mole/carbon atom was obtained from the desorption energies for the amines with ten and eighteen carbon atoms. However, it must be remarked that the desorption energies of the amines with six and ten carbon atoms lead to a value of 1200 cal./mole/carbon atom for dU/dN. I n pointing out the agreement of the numbers 336 and 400 for the amines, the Zisman group ignored the fact that the corresponding numbers for the acids are 212 and 1200. The error is a simple one. In evaluating the constant b2, these authors first showed that it is really a constant by evaluating it from the data from the acids, alcohols, amines, and amides. The resultant values for b2 differed from each other by less than 15 per cent. However, an inspection of the evaluation reveals that the data were all from molecules eighteen carbon atoms long. Thus, the possibility that b2 depends on the chain length, N , is not ruled out, as tacitly assumed by the authors. The derivative db2/dN can be evaluated from their data, and is found to be of the order of unity; the value actually obtained is 1.5. The relation giving the energy increment per carbon atom is then modified to: dU/dN = Rb2 dr/dN
+ R r dbZ/dN
Inserting the values for the various quantities, we obtain: dU/dN = 212
+ 1100 = 1312 cal./mole/carbon atom
This value agrees with the 1200 cal./mole/carbon atom found by the other of their theoretical developments.
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H. T. EPSTEIN
APPENDIX B
A theory of the variation of micelle structure with molecule length The limiting tilt angle can be calculated from the amount that one molecule slips on its inner neighbor owing to the tilt. From figure 9 it is seen that the limit angle is given by the relation: tan
e
=
slip distance intermolecular spacing
_ -X -
5.1
(1)
The slip distance is not known, but it can be evaluated in terms of the decrease in binding energy due to the slip. The assumption is made that the binding energy decrease is the same for all the fatty acid molecules, regardless of their length. This assumption leads to the relation
N , As, = N , As,
(2)
where A6 is the slip energy (binding energy decrease) per carbon atom, n is the number of carbon atoms in the molecule, and i and j refer to molecules of different chain lengths. The variation of the slip energy with distance, x,along the chain is not known, but will be assumed to be representable in first approximation by an exponential relation :
kx"
(3) The exponent m is an adjustable constant, and is the only such constant in the theory, inasmuch as the factor k cancels out when equation 3 is introduced into equation 2. The value of m may be obtained if the characteristic tilt of any molecule, in addition to that of stearic acid, can be measured. Brockway and Karle ( 5 ) have made a few electron diffraction measurements of the characteristic tilt of the acid with twenty-six carbon atoms, cerotic acid. However, it will develop that the value of m is very sensitive to the exact value of the tilt angles for the longer chain molecules, so it seems better to use the data for the tilt of a molecule shorter than stearic acid. Electron diffraction experiments were carried out in Professor Brockway's laboratory by Mr. W. C. Bigelow to determine the characteristic tilt of myristic acid (fourteen carbon atoms). Myristic acid is the shortest chain fatty acid for which the pattern is sufficiently sharp to permit measurement of the tilt angle. The characteristic tilt angle for myristic acid was found to be about 14".Using this datum and a value of 5.7' (0.1 radian) for the stearic acid tilt angle, the exponent m can be evaluated, as follows: First, equations 2 and 3 are substituted into equation 1 to give A€ =
tan 8 = xJ5.1 = (x,/~.~)(N,/N,)~/" For N
=
18, tan 8 = 8 = 0.1,so that x = 0.51 A. Thus,
tan 0
=
(0.51/5.1)(18/N,)1/m
MONOLAYERS AND MULTILAYERS OF POLhR HYDROCARBON MOLECULES
I069
For
N,
=
14, tan 0 = tan 14’ = 0.25
Then, 0.25 = (0.51/5.1)(18/14)1’m Taking logs :
+
-0.6 = - 1 (l/m) log (1.29) 0.4 = (l/m)(0.109) l/m = 4 m = 1/4 Thus, finally: tan 0 = (1/10)(18/N)4
(4)
The micelle diameter can also be calculated. Because the tangents of the tilt angles are small, for all the tilts which have been measured, the angle, in radians, may be substituted for the tangent in equation 4. The number of molecules in the micelle radius is approximately given by the ratio of the limiting tilt angle to the tilt per molecule. The micelle diameter, D,, is then twice this number of molecules times the diameter of a molecule (5.1 A.):
D
= 2
X 5.1 X
e ow (10.2)(L/0.26)(1/10)(18/N)4 =
=
3.4L ( 1 8 / ~ V ) ~
Since L = (4/3)N, where L is the length of the molecule,
D
=
4.E1(18)~/rV’~
(5)
It should be remarked that the exponent m is not 2 , as might have been expected for an equilibrium configuration. The fact that it is not 2 means only that the figure given for m is probably an average value holding over the range of slip distances used in the calculation. The writing down of equations 4 and 5 is not meant to imply that the calculation presented above has, as yet, a sufficiently quantitative character to warrant more than qualitative deductions from the equations. In order to avoid ambiguity on this point, the results which the writer feels can be extracted from the theory will be stated explicitly: ( I ) equation 4 predicts that the characteristic tilt angle varies inversely with the length of the molecules, probably varying more strongly than with the first power of the length; (2) equation 5 predicts that the micelle diameter also varies inversely with the length of the molecules but less strongly than does the characteristic tilt angle,
