Abstract
Lecture delivered at the Royal Institution of Great Britain on January 16 of this year.
Full Text
STUDY OF THE PROPERTIES OF THIN LAYERS USING X-RAYS1
William H. Bragg.
There exists a whole series of questions of the greatest importance that are being solved, or can be solved, by studying so-called “thin layers.” The connecting link among all these questions is the circumstance that the course of most reactions between different bodies is determined chiefly by boundary conditions and therefore depends on the nature of their surfaces. What is inside bodies often has far less significance than the composition and state of the surface layer. Examples may be found in the problems of surface tension in their endless variety, on the one hand, and the phenomena of catalysis, friction, and lubricating action on the other.
Although the surface layer is thus of great importance, its thickness is usually very small and lies beyond the limits accessible to direct optical observation. With the aid of X-rays one can measure smaller distances than with the aid of a microscope, and the question naturally arises whether they cannot help us advance further. True, with their aid we measure only the thickness of periodically repeating layers, and such periodic repetition is impossible if we have only a single layer or film. Consequently, X-rays cannot be applied directly to the study, say, of the black spot on a soap bubble. Indirectly, however, they can still bring us substantial benefit by clarifying questions of molecular arrangement, for all these manifestations of surface forces are directly dependent on the arrangement of atoms and molecules at the surface. Moreover, those properties of substances whose manifestations in individual thin layers are of greatest interest often prove to be repeated many times in crystals, which in fact can be studied with the aid of X-rays.
Soap bubbles and soap films have repeatedly attracted the attention of investigators by their beauty and fascination. Since the magnitude of the surface in this case is especially large in comparison with the volume content of the body, these formations are particularly convenient objects for studying the action of surface forces. The variety of phenomena observed here is so great that in the last few years new and exceedingly interesting discoveries have been made in this field. It will be useful first to touch on some of them, since they may serve as an explanation of what follows.
When a soap bubble approaches the end of its existence, a black spot often appears on it, and soon after this the bubble bursts. This spot appears black because it is so thin that it reflects only very little light. One might suppose that the appearance of the “black spot” indicates some destruction of the structure of the bubble, which is the precursor of rupture. In reality, the black spot is a fairly stable formation: under suitable conditions it can be preserved for hours and days, as James Dewar liked to demonstrate. Reynolds and Rucker, Relly, Johannot, and many others were extremely interested in the sharpness of its boundaries, its thinness, and the uniformity of its structure. They found two degrees of “blackness” of the spot, as Newton, incidentally, had already done long before them, and assumed that these two degrees correspond to a certain single layer and its doubling. They also succeeded in measuring the thickness of these layers, which they found to be approximately equal to 60 Angstrom units in the case of the thinner layer and approximately twice as great in the case of the thicker layer.
If the film is properly prepared and mounted, the black spot appears at once in the upper part of the film, with a horizontal line sharply separating it from the rest of the film with its horizontal colored bands. Small black spots are continuously formed at various points of the colored film and quickly rise upward to merge with the main spot; of course, the essence of the phenomenon here lies in the downward motion of the surrounding liquid, which causes these spots to move in the opposite direction. From time to time luminous points appear, moving over the surface, most often along the edges of the black spots; in all probability these are water droplets.
When observations of this kind are made under quiet laboratory conditions with small films, which are easier to handle, a variety of details can be discovered that cannot be followed on a screen. We owe our knowledge of these details to Perrin’s excellent work, published in 1918.
and repeated by Wells in 1920. Briefly summarizing Perrin’s conclusions, we may say that the two possible thicknesses which had been observed from the very beginning correspond to a certain very thin homogeneous layer and to its doubling, as has already been shown; that the three further stages observed by Johannot correspond to further repetitions of the same layer, and, finally, that careful investigation has revealed the existence of dozens of such layers, whose thickness is a multiple of the fundamental thickness. In the very black spot there was only one layer, and this formation was, strange as it may seem, the most stable of all. It was possible to detect that other similar layers were superposed upon this initial one, like sheets of paper of identical thickness, until a film was obtained sufficiently thick to reveal all the richness of the colors of Newton’s rings, which we usually see on soap bubbles.
As we know, the color of a film makes it possible for us to determine its thickness. Thus, for example, the color changes from black to gray, becoming lighter and lighter as the thickness increases, until it passes into an almost pure white, then into straw-yellow, yellow, orange-red and dark red, and then into violet; the latter coloration is very sensitive to changes in thickness and thus gives us a definite stage. For water the thickness in this case reaches 2100 Å. Perrin counted 37 or 38 stages, by means of which the layers superposed one upon another ultimately give a total thickness corresponding to the violet coloration. He also made a series of measurements with monochromatic light and ultimately came to the conclusion that the thickness of the unit layer is equal to 52 Å. Wells found a somewhat smaller value, namely 42 Å. Perrin and Wells, on the basis of data which we cannot discuss here, came to the conclusion that the unit layers consist of two molecules of oleic acid, formed as a result of the hydrolysis of sodium or potassium oleate dissolved in water.
Let us now recall that Rayleigh, Devaux, and, more recently, Langmuir, Hardy, and Adam measured the thickness of a layer of oleic acid spreading over the surface of water1. It must apparently be accepted that in the case of fatty acids such as stearic or palmitic acid, when the surface is filled, the long chain stands vertically, its carboxyl end being attached to the water, which strongly attracts it, while the methyl ends are directed outward. The length of an oleic-acid molecule is approximately 23 Å.
It is clear that such a length is in full agreement with the assumption put forward by Perrin. His layer, 52 Å thick, or, according to Wells, 42 Å, must consist of two layers of molecules of oleic acid, whose carboxyls meet in the middle. The molecules hold on to one another by their sides, forming a strong film, while the methyl groups give a surface that can exert only a very weak action on objects situated outside.
The investigation of crystals by means of X-rays shows that the peculiar arrangement of molecules in films on the surface of water is in many cases also extended to solid crystals and may be regarded as characteristic of the structure of a numerous and important class of bodies. It is observed first of all in solid fatty acids, hydrocarbons, alcohols, and other molecules with long chains. These substances were investigated by Piper in Bristol and by Müller (A. Müller) and Shearer in the Davy-Faraday Laboratory. A year ago I had already touched on some of these results. The number of examples has greatly increased during the last twelve months, and the data obtained can already be published.
If a small quantity of one of these substances is applied to a plate of glass or mica, by melting it or simply by pressing it on, a series of layers is obtained, especially in the latter case, for pressure and mechanical treatment apparently favor the uniform arrangement of the molecules and the regularity of the layers obtained. After this one may place the object under investigation on the table of an X-ray spectrometer and take a photograph by the rotating-crystal method. The photographic plates usually reveal a series of lines which clearly correspond to reflections of different order from the plane of the layers. In this way the thickness of the layer can be measured with an accuracy of approximately one percent. Spectra up to the tenth order and higher are often observed. The cleavage planes of many crystals, especially those belonging to the class described, give spectra of several orders, but usually in much smaller number than in this case; other reflecting surfaces may give one or, at most, two higher-order spectra of medium intensity, while most often all the spectra, with the exception of the first-order spectrum, are very weak. This phenomenon is undoubtedly entirely analogous to the fact, known from optics, that gratings give many higher-order spectra when the lines are fine and sharp. In our case the “lines” correspond to a clearly expressed discontinuity in the distribution of scattering centers, which are observed at the ends of long molecules; the presence of hydrogens of the methyl group
causes a deficiency, the presence of oxygens of the carboxyl group—an excess in these centers. We may suppose that the planes which divide the layer of molecules are thereby well marked, while otherwise the distribution along the entire molecule may be regarded as sufficiently uniform.
If we plot the distances between layers in each substance as a function of the number of carbon atoms in the chain, we at once see that the points obtained, provided the chain is not too short, lie exactly on one straight line. This was proved by Müller and Shearer for fatty acids, hydrocarbons, alcohols, ketones, and in other cases, and the regularity of the data obtained leaves no room for doubt about these facts. The increase in the chain length for each carbon atom is equal either to 1.0 Å or to 1.3 Å, the first number being observed, for example, in the case of fatty acids, and the second—in the case of their esters. If we may suppose that the molecules are arranged perpendicular to the planes of the layers, then the numbers found for the thicknesses will indeed correspond to molecular lengths, and there is some basis for assuming that this is often actually so. However, the molecules, of course, may also not be arranged normally to the plane of the layers, and in that case the length of the molecule will exceed the thickness of the layers. Undoubtedly this case, too, is sometimes observed in reality. Small crystals of substances of this group were obtained and successfully investigated in our laboratory by Gibbs. Despite the fact that each of them weighed only about one-hundredth of a milligram, Gibbs found that these crystals are monoclinic prisms.
In this case, therefore, the molecule does not stand upright, but is inclined. It is difficult to suppose that the molecules were inclined in one direction in films of oil on water, for in that case it would probably be possible to detect in these films the existence of one direction distinct from all the others. It is possible that the explanation should be sought in the fact that molecules in reality may be arranged in two or even several ways. Gibbs found, along with the monoclinic form, an orthorhombic form, and Müller observed that hydrocarbons give a somewhat different value for the lattice constant at a temperature lying only a few degrees below the melting point. The external appearance is also different in both cases. In the second case the whole mass is translucent; usually, however, it is opaque, probably owing to the presence of microscopic voids, which form during cooling as a result of the decrease in volume. Perhaps this same thing is the cause of the change that we see when observing cooling candle tallow: for some time it remains transparent and then suddenly becomes cloudy.
Until the angle of inclination of the molecules with respect to the cleavage planes has been finally determined, we cannot be certain-
... certain that we are measuring the actual length of the molecules; but one may hope that this question will soon be clarified.
Molecules of fatty acids (but not of hydrocarbons) are arranged in double layers. We can prove this in two ways. First, the actual increase in the thickness of the layer for each carbon atom is in one case twice as great as in the other. Secondly, the spectra of even orders for fatty acids are very weak in comparison with the spectra of odd orders.
In an optical grating the same result can be achieved by alternating white and black lines on a gray background. When strong and weak black lines are alternated, the even spectra are intensified; replacing black lines of one kind by white ones, however, leads to a change in the sign of the effect that depends on them. One can construct gratings that would serve to illustrate these relations. If oppositely directed molecules are joined by their carboxyl ends, then the methyl ends of the molecules will be poorer scattering centers than the whole molecule on average, while the places where the carboxyl groups meet will, obviously, scatter more strongly than the whole molecule on average.
Scherrer found another analogous example in the case of hydrocarbons, which give a single layer and can be converted into ketones if two hydrogens are replaced by oxygen at some point in the chain. If the substitution takes place in the middle of the chain, then at this point there will be an excess of scattering centers, and we shall again have the conditions that lead to an intensification of spectra of odd order. If, however, the substitution does not take place in the middle of the chain, then the spectra of odd order will no longer be intensified in comparison with the spectra of even order.
Thus, in these layered structures, which we investigate with the aid of X-rays, we find the very same formations that Perrin observed in liquid films. It turns out that in all cases the molecules are extended along their entire length and are linked together by their carboxyl ends. Scherrer found that the length of the double molecule of oleic acid is approximately \(36\mathring{A}\), a value that may be compared with the value \(52\mathring{A}\) found by Perrin and \(42\mathring{A}\) found by Wells.
The factors that lead to the formation of films on the surface of water and to the appearance of layering in fatty acids and other similar bodies act in the same way in the case of many other, more solid crystals. The result is, as it were, a scaly structure, since the crystal very readily splits into thin layers that slide over one another without difficulty, as a consequence of which the crystal often seems greasy to the touch.
Examples of this kind may be naphthalene and anthracene. Their molecules are long and narrow and are arranged side by side, like molecules of oleic acid on water. The arrangement of the molecules in each layer is like ears of grain in a field; but they overlap one another as ears do when the wind blows. They are not perpendicular to the plane of the layer. The bonds that force the molecules to remain side by side must be stronger than those that attach them at the ends, since the individual layers can be very easily separated from one another. The naphthalene molecule consists of two hexagonal rings of carbon atoms, while the anthracene molecule is further lengthened by the addition of a third ring, so that the thickness of the layer in this case is greater. In both cases the molecule possesses a center of symmetry, and in each layer the molecules, according to their arrangement, may be divided into two classes. Each molecule belonging to one class is in some way connected with several (probably four) molecules of the other class, which form its immediate environment in the layer; apparently, such a system of cross-coupling both holds the layer together and gives it its strength.
It is very probable that many other substances are built in the same way. Even in those cases where no attempt has yet been made to investigate them by means of X-rays, crystallographic data point to this. In other substances a similar external form is achieved by means of a somewhat more complex internal arrangement. The molecule of the substance may itself have no center of symmetry, indeed may possess no elements of symmetry at all; in this case, to construct a monoclinic prismatic element of the lattice, twice the number of molecules is required. To this group belong, for example, benzoic acid and, probably, many of its derivatives. But in this case too the same scale-like character is observed, which can be reduced to the same causes: 1) the general arrangement of the molecules, which lie across the plane of the layer, and 2) the presence of hydrogen atoms at the ends of the molecules. In all these cases we observe that the crystal is held together by bonds that extend from each molecule to its neighbors with another possible arrangement; apparently, this is one of the fundamental features of the structure of crystals. Of course, it cannot be traced down to the very lowest type of symmetry, where in general there exists only one possible orientation and each molecule is arranged in a way completely analogous to all the others. However, although such a structure can be imagined, it is doubtful whether examples of this kind are known. In any case, Asbury has shown that calcium thiosulfate, which was usually cited as the sole example, probably has symmetry of class 2 (two orientations connected by a center of symmetry). Whether this is so or not, in any case
Undoubtedly, in the overwhelming majority of cases cross-linking is a very important factor. It probably also has great significance in determining the faces that appear on a crystal. The plane of a face will naturally contain within it specimens of different molecular orientations, owing to which the elements of the face can be firmly bound to one another. Thus, for example, in naphthalene, as in many other cases, the majority of the commonly occurring faces contain equal numbers of molecules with both orientations; knowing the formula of the crystal, one can even predict their arrangement.
Thus, if we do not focus on the main features of the numerous class of scaly crystals, we shall see that Langmuir monomolecular layers, Perrin’s repeated layerings, and in general the whole field of “thin layers” have much in common with the solid representatives of this class. There are, however, characteristic differences as well. Apparently, by studying the features of similarity and difference, it will be possible to shed light also on some properties of the more “liquid” films. Having these data before us, we may perhaps give a somewhat more detailed theory of the black spot on soap films. An ordinary thick film is bounded on both sides by monomolecular layers of oleic acid. In these layers there is undoubtedly a regular arrangement. Adam studied especially thoroughly the phenomena of compression of these layers under the action of external forces, and his observations and conclusions agree well with the supposition that in this case there exists a regular palisade, as was to be expected. However, the crystalline structure of these layers is imperfect. They are compressible to some degree and during compression behave like a two-dimensional gas. The perfect crystals of this class, however, we have in the layers studied by Müller and Shearer, and in the miniature crystals measured by Gibbs. In a perfect crystal of oleic acid the variety of orientations is twice as great as in layers of oleic acid on water; on water there are molecules directed only one way, whereas to complete the structure molecules with the reverse arrangement are also necessary.
Suppose, however, that the layers of oleic acid situated on both sides of the film somewhere come into contact; all the conditions for the appearance of a crystalline structure are now present. The carboxyl groups now not only meet but also interlock, each molecule of the upper layer binding two or four molecules of the lower layer and conversely. Such an arrangement will undoubtedly be much more stable than that which existed in the single layer. The outer monomolecular layers, once having touched at one point, will tend to increase the area of contact and to expel the water lying between them.
The layer that is thereby obtained will already be a true crystal, since it contains all the molecular orientations. The black spot is thus the thinnest possible scale of oleic acid. It is true that oleic acid melts at \(11^\circ\text{C}\), but here we have a crystalline structure in a mobile state. The solution can now no longer be forced to enter the space between the two surfaces, joined in the manner of a crystal. Other films can form and float on this layer, held by the weak attractive forces that act between the methyl groups; the pressure of the air will also facilitate their possible adhesion. These additional layers will slide easily over the surface; they too are crystals of oleic acid, probably containing no water.
The difference between the properties and the structure of the black spot, on the one hand, and of the adjacent thick layer, on the other, is so great that we need not be surprised at the sharpness of the boundary and at the enormous change in thickness that is observed there: on one side the thickness may be hundreds of times greater than on the other.
When black spots appear and rise through the thick part of the film in order to merge with the main black surface in the upper part of the film, they leave behind a trace—they look like tadpoles swimming upward. When the motion becomes less intense, the remaining tails gather into small round spots. On the other hand, if a piece of the thick layer is driven by the general vortex into the middle of a black spot, it also tends to assume the shape of a circle.
We shall now turn to another very important surface phenomenon, namely to friction, or, speaking of the reciprocal quantity, to slipperiness. All these scaly substances are usually slippery and greasy to the touch. The greasy sensation apparently depends on the ease with which the scales separate from the main mass of the body and then slide over it. Graphite is a clearly expressed example of the scaly state, and although its inclusion in the group of substances that we are studying would be somewhat artificial, we see that in graphite too, in each layer, the atoms are very strongly bound to one another, whereas between neighboring layers there exists only a very weak bond. Apparently the combination of these two properties also accounts for good lubricating substances. In all the substances that we have studied, the same properties are present to a greater or lesser degree: thus, for example, the molecules of stearic acid are bound to one another much more strongly along their length than at those ends where the methyl groups are located. Thus every time there is a clearly expressed layered structure, the same results are obtained as in the case of graphite. Usually a layered structure
imperfect; this is evident if only from the fact that large and defect-free crystals of stearic acid are never obtained. Pressure is one of the factors contributing to the formation of layers; therefore, by pressing on a piece of stearic acid or another material, we thereby already create conditions favorable to slipping. As I have already mentioned, Scherrer and Müller observed that the substance under investigation, having been melted on a plate of glass or mica and placed on the spectrometer table in such a position that it ought to have given reflections from planes parallel to the surface of the glass, often exhibited this ability only to a comparatively slight degree. On the other hand, in this case, on all the plates one could detect clear signs of the presence of two recurring distances, corresponding to the transverse dimensions of the molecules and not depending on their length. But it was enough to press on the substance or to rub it on the plate for the lines corresponding to the complex structure to appear, while the others disappeared, showing us the nature of the rearrangement that takes place in this process. It may be that this phenomenon also explains other properties of fats. We must acknowledge, however, that the layers existing in the crystal are not always ready to slide, since otherwise, under the slightest pressure, they would begin to slide one relative to another, like cards in a deck. There exists some retarding friction, which must be overcome in exactly the same way as in graphite. As to its nature, one can only make suppositions: perhaps it depends on molecular forces, and slipping occurs only when the bonds, already weak without that, are weakened still further, as when approaching the melting point; perhaps, however, it depends on the imperfection of the structure of the crystal.
It is probable that under the best conditions the capacity for sliding in these cases must be almost complete. Indeed, between two perfectly constructed methyl layers the friction should be very small, or there should even be none at all. The most perfect form of a methyl layer we have in the surface of the black spot in soap films, and numerous investigators have noted that one such layer very easily slides over another. Perrin drew attention to this remarkable phenomenon, which is especially clearly visible in the Brownian motion of ruptures of one layer lying and sliding on the surface of another.
In some experiments by Sir William Hardy and Miss Doubleday, conditions of almost ideal sliding were realized. Their brilliant work on the lubricating action of very thin layers led to the establishment of some surprisingly simple regularities. They found cases in which friction almost disappears, and in agreement with what has been said above, this phenomenon is observed
then, when the solid lubricating substance is almost completely removed and wiped from the surface, there probably remains a very thin layer with a regular layered structure. Not only the phenomena of surface tension and lubrication, but also the phenomena of catalysis, must be closely connected with the actual arrangement of molecules. Stereochemistry is considered to be the science concerned with the question of the mutual relations between atoms in a molecule, their arrangement and orientation. In order to pass to the phenomena listed above, it is necessary to broaden the domain of stereochemistry so that it includes questions concerning not only the mutual arrangement of atoms, but also of molecules. We see that one cannot speak of molecules as of a sphere acting according to the laws of attraction; even for atoms such an approximation is inadequate, except in the case of substances with an ionic structure, such as common salt. If some cosmic observer wished to draw conclusions from phenomena observed on the surface of the earth concerning the nature of human beings, to whom he would attribute these phenomena, and if, being unable to detect by the methods available to him any one of these beings, he were to say: “Let us suppose that a human being is a sphere possessing identical properties in all directions and devoid of special points of attraction,” then he would have made little progress toward a satisfactory solution of the question. It would already be a success if he discovered the existence of two types of opposite sign and thus laid the foundation of an ionic theory of a heteropolar compound; but even in that case he would still be very far from the truth. In the same way, in trying to explain the phenomena of surface tension as a consequence of the mutual attraction of spherical atoms or molecules, we cannot count on great successes.
Indeed, proceeding along this path, we often arrive at conclusions that seem unexpected, as, for example, in the case when we measure the attraction between molecules on the basis of the energy that must be expended in order to remove molecules from the surface in the process of evaporation, and conclude from this that pressures of thousands of atmospheres exist in the middle of a liquid. In the same way we could measure the force needed to tear off the end link in a piece of iron chain, ascribe it to the mutual attraction between the links, and on this basis come to the conclusion that an enormous pressure exists in the chain.
Only by assuming that on the surface of the catalyst there are active centers, whose mutual arrangement and magnitude are such that two dissimilar wandering molecules, attracted by these centers, can in a definite manner be brought into contact, can we obtain some notion of the character of the action of the catalyst. It is necessary to regard as the basis
surface phenomena, the possible arrangements of molecules on the surface—both those which actually exist and those which have a chance of being realized. This idea runs like a red thread through the works of all those investigators—Langmuir, Harkins, Hardy, Adam, Perrin, and others—who have achieved such successes in recent years; the X-ray method confirms this point of view and provides a whole series of quantitative data by means of which it can be clarified and supplemented.