APPLICATION OF X-RAY ANALYSIS TO THE STUDY OF RUBBER, VULCANIZED RUBBER, GELATIN, ETC. *

J. J. Trillat, Paris

I. Study of Rubber by Means of X-Rays

Rubber, used in everyday life to such a great extent, is a substance about which we possess very scant information. Its composition and the cause of its elasticity, the phenomena of vulcanization, and the Joule effect upon stretching present problems which at the present time have not received a definite solution; however, an important discovery made by Katz opened a new stage in this question, and the application of X-ray diffraction to rubber has made it possible to construct new hypotheses that have advanced our conception of the structure of this substance far forward.

It is known that, under deformation, rubber has a noticeable temporary birefringence; it would be interesting to learn how this substance behaves with respect to X-rays, applying the very same methods that have led to such great progress in our knowledge of crystals. These investigations were carried out chiefly in Germany and Holland—by Katz, Binns, Hauser, Mark, Rosbaud, Lock, and Günemorder; in Switzerland—by Ott; and in the United States—by Clark.

1. Study of Unstretched Rubber

If, following the Debye–Scherrer method, an undeformed specimen of rubber is illuminated with a beam of monochromatic X-rays of long wavelength (for example, \(K\alpha\) Cu \(= 1.54\ \text{Å}\)), then on a photographic plate one obtains a diagram analogous to those given by liquids; in the present case this diagram consists of two concentric rings [Hauser and Rosbaud (2), Fig. 1]. Without entering into a detailed interpretation of these “amorphous” diagrams, it is sufficient to say that, by means of the classical

* From the book by J. J. Trillat, Les applications des Rayons X; see U.F.N. XI, 493, 595, 847, 1931; XII, 215, 1932.

according to Bragg’s formula, or according to the following formula [[unclear: reference]],

\[ a=\frac{5.12\lambda}{4\pi \sin \frac{\theta}{2}}, \]

where \(\lambda\) is the wavelength, and \(\theta\) is the angle of diffraction, it is possible to relate the diameter of these rings (measured between the places of maximum intensities) to the distance between the centers of the diffracting particles.

For rubber it turns out that the outer ring corresponds to a distance of \(6.05\ \text{\AA}\), and the inner one to a distance of \(134.8\ \text{\AA}\). The distances that are connected with the positions of the maxima of the intensity of the rings correspond to the most probable, or most frequently occurring, arrangement of the centers of diffraction. From the fact that between these two rings there is still a zone of darkening, it follows, according to Zernike’s theory, that distances intermediate between those that have been calculated are also possible, although less probable. In any case, the absence of higher orders of reflection shows that in this state there is no regular structure, as in crystals, and, even if one admits in unstretched rubber the preliminary formation of some micelles, this state must be considered irregular in comparison with a crystalline lattice.

The amorphous state is the basic case for rubber not subjected to deformation; all rubbers give analogous diagrams. Similar diagrams are given by synthetic rubber from isoprene, which speaks for its kinship with natural rubber, whereas differences exist between the diagrams of natural rubber and rubber obtained synthetically from butadiene and dimethylbutadiene (Katz)\(^1\).

However, there is one important exception to this basic case: when studying stale rubber (a sample of the grade called “skokedshits”), which had become hard and brittle, and “frozen rubber,” Hauser and Rosbaud\(^2\) observed, instead of “amorphous” rings, Debye-Scherrer rings, indicating the presence of a large number of disorderly oriented microscopic crystals; this same rubber, heated in hot water, kneaded, or stretched many times and left at rest (without deformation), again became amorphous.

2. Study of stretched rubber

If one takes a sample of unvulcanized rubber, which gives only the rings characteristic of amorphous substances, and subjects it to stretching, a very important phenomenon is observed, discovered by Katz\(^3\) and also studied by Hauser, Rosbaud, Mark, Clark, and others\(^4\). With increasing stretching [[unclear: continuation cut off]]

as seen in general, upon elongation from 80 to 1000% (Fig. 1), noticeable interference spots, etc. If one continues the stretching, this picture of crystalline interference becomes increasingly intense, and its distinctness reaches the same degree as that observed for well-crystallizing organic substances. These interference spots are situated exactly on the Debye rings of frozen rubber; during stretching they do not change their positions, only their intensity changes, increasing with the stretching. As for the amorphous ring (6 Å), it remains in the same place, but gradually weakens, so that in the end it almost disappears at strong stretches.

After stretching, rubber that has returned to its original state no longer gives traces of crystalline interference, and again the “amorphous” diagrams observed before stretching are obtained.

Together with these principal observations it is necessary to make the following further remarks:

a) frozen rubber, which gives, as has already been said, complete Debye-Scherrer rings, can, if it is carefully stretched, also give interference spots located on these rings, spots which gradually lose their intensity with increasing stretching;

b) the rate of stretching (Gauzer, Roseveare, and Ghenemorder)2 is of great importance (Fig. 1 at the end of the article),—by operating at very low rates, rubber can be stretched quite isotropically—so that it almost gives no interference phenomena, and this important result is in agreement with the stretching curves, which, as Roseveare and Smith5 have shown, are quite different at different rates of stretching;

c) there is a correspondence between the time of stretching and the time of recording the diagram; indeed, molecules oriented as a result of stretching have a tendency to lose this orientation and slowly return to a disordered arrangement. It is precisely for this reason that sharply stretched rubber, kept under tension and having acquired a fibrous structure, after several hours again becomes completely amorphous;

d) finally, Feuchter6 indicated a method for preparing rubber stretched by 10 thousand %; this rubber has the appearance of a thread similar to a violin string. These threads give intense diagrams with spots identical with those given by stretched rubber. But if they are heated in warm water, they return to their original amorphous state.

3. Hypotheses on the structure of rubber

What conclusions can we draw from the phenomena described? First of all, the fundamental fact is the circumstance that for sufficient stretches everything happens as though crystals were formed, oriented parallel to a definite

to the direction of tension and capable, consequently, of giving the same diagrams as in the case of other materials, and cellulose, owing to the presence of a predominant direction.

We shall see below whether here it is really a question of the formation of true crystals, or only of the appearance of a quasicrystalline structure; first of all, the question arises whether these crystalline or pseudocrystalline cells exist in rubber before it has been subjected to deformation.

According to Katz, these cells are formed during stretching; rubber, consequently, is a strongly deformed crystalline lattice, which stretching brings into order. Most likely, the initially unorganized elements form a lattice, perhaps because in that form they occupy a minimal volume.

The circumstance that in amorphous substances there are at the same time observed phenomena corresponding to oriented crystalline powders leads to the conclusion that there are simultaneously present two components, differing more or less in their physical state: one of them is amorphous, the other tends to form a crystalline structure. Various authors have, moreover, already arrived at this assumption of two different phases. Ostwald[^17] considers it probable that within the spheres of a colloid there exists another substance, having a looser consistency and a lower degree of polymerization than the envelope. Freundlich and Hauser[^7] proved this by an ingenious method of microsections. Schenew and Gehl[^8] assumed states of this kind, at least implicitly, in their investigation of the stretching curve; the beginning of this curve corresponds to deformation of an easily deformable component, the middle part to simultaneous stretching of both, and the end to deformation of only the hard phase. Katz does not share the opinion of these authors concerning the existence from the very beginning of two components; he himself supposes that one of them is formed during stretching, at the expense of the other.

His hypothesis also takes into account the rather peculiar details of the stretching curve of rubber, which is unlike the usual form of this curve for other substances. Hooke’s law (the proportionality of deformation to the acting force) is justified only at the beginning and at the end of the curve. Whereas metals are drawn into wire if the elastic limit is exceeded, i.e. before rupture itself, rubber, by contrast, is stretched most easily when the loads are small. The deformations become relatively smaller in the region of large elongations.

If one supposes that the structure gradually passes into the crystalline one as stretching proceeds, then these phenomena are naturally explained by the fact that crystals are less deformable than an amorphous substance, and that the proportion of these latter gradually decreases as stretching proceeds. This crystalline or pseudocrystalline phase Katz named his “nerve”; indeed, experiments carried out with...

If one also measures the intensity of the spots upon reflection from other planes (200, 220, 111), curves are obtained that are similar to one another, and at the same time almost parallel to one another (Fig. 3), but not passing through the origin; moreover, the ratio of the intensities of the spots obtained upon reflection from different planes does not remain constant as elongation increases. If one investigates how the intensity of the interference changes not as a function of elongation, but as a function of the corresponding stress, curves are obtained that are entirely different from the preceding ones, as was to be expected (Fig. 4).

Hauser and Mark showed that, in the case of continuous growth of crystals, the intensity increases proportionally to the square of the elongation, whereas in the case of a doubling of the number of identical crystals the intensity likewise only doubles (assuming that the particles are sufficiently small so as not to produce any appreciable absorption). This is precisely what takes place in the case of rubber: we do not observe in it the growth of already existing crystals, but see how, around new nuclei, new crystallites grow in proportion to the degree of elongation.

Fig. 4. Intensity of diffraction as a function of stress, rubber.

Fig. 5. Intensity of the amorphous ring as a function of elongation (rubber).

In the case of NaCl, the ratio of intensities remains constant if the number of crystals subjected to the action of elongation increases. This is not the case for rubber, for which the ratio of intensities changes with elongation. On the basis of arguments that we cannot develop here, Hauser and Mark came to the conclusion that the force holding a lattice particle in its equilibrium position increases with the degree of elongation and that the crystalline structure gradually becomes stronger as the crystallite grows.

As for the intensity of the amorphous ring, it decreases in proportion to the stretching (Fig. 5).

These experimental results allow one to conclude that the interference observed under stretching has a very great similarity to the interference from crystals, though with certain differences. All this leads to the conclusion that we are dealing with already existing aggregates of definite dimensions [[unclear: text continues beyond visible page]].

If one also measures the intensity of spots upon reflection from other planes (200, 220, 111), then curves similar to one another are obtained, and moreover almost parallel to one another (Fig. 3), but not passing through the origin; in other words, the ratio of the intensities of spots obtained upon reflection from different planes does not remain constant as elongation increases. If one investigates how the intensity of the interference changes not as a function of elongation, but as a function of the corresponding stress, curves are obtained that are quite different from the preceding ones, as indeed was to be expected (Fig. 4).

Hauser and Mark showed that, in the case of continuous growth of crystals, the intensity increases in proportion to the square of the elongation, whereas in the case of a doubling of the number of identical crystals the intensity is only doubled (assuming that the particles are small enough not to produce any appreciable absorption). This is precisely what takes place in the case of rubber: we do not observe in it the growth of already existing crystals, but see how new crystallites grow around new nuclei in proportion to the degree of elongation.

Fig. 4. Diffraction intensity as a function of stress in rubber.

Fig. 5. Intensity of the amorphous ring as a function of elongation (rubber).

In the case of NaCl, the ratio of intensities remains constant if the number of crystals subjected to the action of the radiation increases. This is not the case for rubber, for which the ratio of intensities changes with elongation. On the basis of arguments that we cannot develop here, Hauser and Mark came to the conclusion that the force holding a lattice particle in its equilibrium position increases with the degree of elongation, and that the crystalline structure gradually becomes stronger as the crystallite grows.

As for the intensity of the amorphous ring, it decreases in proportion to the stretching (Fig. 5).

These experimental results make it possible to conclude that the interference observed during stretching has a very great similarity to the interference from crystals, with, however, certain differences. All this leads to the conclusion that we are dealing with already existing aggregates of definite sizes.

Why, then, do these aggregates not manifest themselves in unstrained rubber? Recent investigations of the structure of various organic compounds—for example, the celluloses—compelled us to classify them as “quasi-homogeneous” substances, owing, for instance, to their properties in the dissolved state. X-ray investigations have shown that swelling or dissolution is not limited to the particular surface on which the action takes place, but proceeds simultaneously throughout the entire crystal. We find analogous phenomena when heating benzophenone almost to its melting point; at this moment, although the crystals observed under the microscope still appear well formed, we are unable to obtain X-ray photographs. In both cases the cause is the same: excessively strong vibrational motions of the molecules do not permit the formation of distinct interference. Crystals formed by strongly polymerized hydrocarbons of rubber are in the swollen state, while weakly polymerized hydrocarbons are the swelling-producing substances. Until such a state is reached, the amplitude of the molecules’ vibrations is too great for the formation of distinct interference, and the X-ray photographs show nothing except rings characteristic of amorphous substances. If rubber is stretched and then returned to its former state, the substance tends to assume its original equilibrium state. This naturally leads to the disappearance of the interference. Thus the appearance of interference in rubber is a consequence of a peculiar process, caused by stretching, that is the reverse of swelling; and to explain these phenomena it is necessary to assume the presence of two phases with different degrees of polymerization.

The mechanism must be as follows (Hauser, Mark, and Rosbaud). Stretching begins to orient the particles, and at the same time these particles reduce the degree of swelling; at maximum elongation all such particles become oriented parallel to one another; they become crystalline in exactly the same way as cellulose, which can be made to swell in alkalis and then removed and “dried.” It is precisely then that the appearance of fiber diagrams is observed. If the tension in stretched rubber is relaxed, the reverse process occurs.

In the case of hardened rubber, it should be assumed that, owing to prolonged storage or under the action of cold, a process has occurred that is the reverse of the swelling of the particles and has again led to the crystalline phase. The particles are arranged at random and, in a monochromatic beam of X-rays, give complete Debye–Scherrer rings passing through the positions of the spots of the fiber diagram.

If hardened rubber is kneaded or stretched many times, a mixture of two phases is formed; particles with a low degree of swelling begin to swell again and give the diffraction pattern of amorphous bodies; the very same effect can also be obtained by heating, including for stretched rubber.

This ingenious theory explains the elastic properties of rubber by assuming an equilibrium between polymerized hydrocarbons and, at least, one hydrocarbon of the same chemical structure but less polymerized. It, moreover, agrees with certain conclusions obtained otherwise. Nevertheless, it is by no means invulnerable to criticism: one of the fundamental objections concerns the influence of the rate of stretching of rubber on the formation and intensity of interference. Above we indicated that, under very slow stretching, the amorphous structure is preserved, which is an objection to a theory from which proportionality of the intensities and elongation follows.

It is necessary to operate at a strictly definite rate and, moreover, to take diagrams over extremely short intervals of time, taking into account the possibility of a process of “slipping” of particles.

In addition, one cannot vouch that there is not present here a change in the degree of polymerization due to stretching; moreover, it is not necessary that such a modification be accompanied by a change in the dimensions of the cell, which would cause a displacement of the spots. One may, in general, assume that heat and mastication cause depolymerization of rubber, accompanied, in particular, by changes occurring in its physical (stretching curves) and chemical (acetone extraction, rubber-lubricant) properties.

Incidentally, Mark and Susich⁴ and Meyer and Mark¹¹ (1928) have recently put forward new hypotheses concerning this problem. In the opinion of these authors, it is well substantiated that, upon stretching, the atoms composing rubber become oriented and are arranged in a lattice, giving rise to crystallites, whose accumulation forms micelles. Such crystallites should have a length of from 300 to 600 Å, while their thickness and width should be from 10 to 200 Å, and they should contain from 10 to 20 thousand elementary cells, or from 80 to 150 thousand C₅H₈.

From the circumstance that the substance of rubber acquires a definite orientation as a consequence of stretching, it may be concluded that the micelle in this state has the form of an elongated box and that, at least by 80%, rubber acquires a crystalline structure owing to stretching.

The large molecule of rubber thus possesses a regular internal arrangement of atoms and groups, and becomes a crystal capable of diffracting X-rays. The elementary groups are connected by secondary valences, forming sufficiently weak bonds, allowing easy displacements and making it possible for the structure constructed in this way to assume various forms. In this, apparently, lies the explanation of the easy deformability of rubber.

Of course, these results are very approximate, since it is difficult to say whether all crystallites have identical …

sizes and what their actual shape is. It is interesting to note that here we have again arrived at constructions analogous to those which we made in the case of cellulose, where we had to admit the existence of elementary cells, a grouping of elementary cells or crystallites, a grouping of crystallites or micelles, entailing intermolecular diffraction as a result of the regular arrangement of the principal valence groups.

The second interesting observation made by Meyer and Mark (loc. cit.) is as follows. The orientation which occurs during stretching proceeds extremely rapidly, as can be established by direct observation on a fluorescent screen. But it may also be a question of slow crystallization. When the tension is removed, complete disorientation of the chains takes place, accompanied by the disappearance of interference. This disorientation, however, does not lead to a complete destruction of the bonds between the individual \(C_5H_8\)-groups; measurements of osmotic pressure show that a certain number of chains always remain joined into micelles.

Following Mark and Meyer, the cause of the elasticity of rubber should be sought in the existence of a double bond in the isoprene radical, which may be written in the form:

\[ \ldots — CH_2 — \underset{CH_3}{C} = CH — CH_2 — \ldots \]

Indeed, if it is assumed that the chains of the principal valences have a tendency to bend or curl up owing to the regular arrangement of the double bonds, it is clear that the elastic properties of rubber should be attributed to these chains; this is all the more probable since Langmuir and Lecomte du Noüy\(^ {18*}\) point to the possibility of such deformations in many substances with double bonds (oleic acid, sodium oleate, etc.). This principal cause, connected with the structure of the chains, may, of course, be strengthened by secondary bonds appearing as a result of the micellar structure of rubber.

5. Determination of the elementary cell

The diagrams obtained make it possible to draw certain conclusions regarding the structure of the crystalline phase of rubber. However, we must make the same reservations as in the case of cellulose.

Indeed, from Polanyi’s equation it is possible to calculate the lattice parameter in the direction of stretching; thus

* Concerning elasticity, see also the latest memoir of Meyer [[unclear: citation continues]].

one obtains \(c = 7.68\) Å; it remains, however, to find two other parameters so that the corresponding indices can be assigned to each of the spots. If it is assumed that the two equatorial points situated nearest to the center correspond to the indices \((110)\) and \((200)\), then for the two other axes one obtains \(a = 8.0\) Å and \(b = 8.6\) Å. The quadratic form for \(\lambda = 1.54\) Å, under the assumption of rhombic symmetry, is obtained in the form (Gauzer and Mark):

\[ (\mathrm{Cu}\ K\alpha)\ \sin^2 \frac{\theta}{2} = 0.00921\,h^2 + 0.0097\,k^2 + 0.00997\,l^2, \]

an equation into which the obtained results fit well: the calculated and experimentally found positions of the spots coincide.

The product \(a \times b \times c\) gives the volume of the elementary cell \(V = 529\) Å\(^3\).

Assuming an average density equal to 0.920, one can determine the number of groups \(\mathrm{C}_5\mathrm{H}_8\) entering into the cell:

\[ M = 529 \cdot 0.92 \cdot 10^{-24}\, g = n \cdot 68\, \frac{10^{-23}}{6.06} \]

(\(68\) is the molecular weight of the \(\mathrm{C}_5\mathrm{H}_8\) group), whence: \(n = 4.12\).

Thus the elementary cell must contain 4 isoprene groups \(\mathrm{C}_5\mathrm{H}_8\). We would arrive at a different conclusion under the assumption of a monoclinic or triclinic elementary-cell symmetry; according to Ott (12), in this case we would obtain \(n = 6\).

Fig. 6. Diagram of rubber stretched into a thin strip with simultaneous rotation. The diagram consists of two superposed fiber diagrams (according to Mark and von Susich).

Finally, the latest works of Mark and V. Susich\(^4\) and of Meyer and Mark\(^ {11}\), in which these authors photographed diagrams from rubber in two mutually perpendicular directions (Fig. 6), make it possible, as it were, to determine all three parameters exactly:

\[ \begin{aligned} c &= 8.1\ \text{Å} \quad \text{(direction of stretching)}\\ b &= 8.3\ \text{Å}\\ a &= 1.8\ \text{Å} \end{aligned} \]

Hence the following quadratic form is obtained:

\[ \sin^2 \theta = 0.00392\,h^2 + 0.00857\,k^2 + 0.00890\,l^2 \quad (\text{for Cu }K\alpha) \]

(orthorhombic symmetry).

The number of \(C_5H_8\) groups in the elementary cell is equal to 8; their arrangement was studied by these authors (Figs. 7 and 8); the \(C_5H_8\) groups are oriented parallel to the direction \(C\), and may, moreover, rotate about this direction. This representation seems at the present time to be the closest to reality.

Fig. 7. Elementary cell of rubber
(after Meyer and Mark).

Fig. 8. Elementary cell of rubber.
Schematic section perpendicular to the axis of the chains of the main valences (fiber axis).

6. The anomalous Joule effect in rubber

(Double refraction)

It is of interest to compare these results with earlier observations and to see how they are interrelated.

In 1857 Joule showed that rubber is heated when stretched under the action of a large load, whereas other substances are cooled under the very same conditions; at small extensions rubber behaves normally.

If this fact is compared, as Katz notes, with the circumstance that in a supercooled body heat is evolved during crystallization, it may be supposed that the cause of heat evolution, beginning with certain elongations, should be sought in the crystallization of the initially amorphous substance of rubber; for smaller loads normal cooling should be observed. Thus an explanation is found for this previously incomprehensible phenomenon; the anomalies of the stretching curve depend on the same cause.

Finally, let us explain how these phenomena may be connected with the long-known fact of double refraction occurring upon stretching.

It is known that rubber, like a great many substances such as gelatin and fish glue, becomes birefringent upon stretching like a uniaxial crystal.

It is further known that the ratio

\[ \lambda = \frac{\text{increase of double refraction}}{\text{increase of length}} \]

has smaller values for small deformations than for large ones.

This observation is in good agreement with the circumstance that at the beginning of stretching there are no crystals, but there exists an orientation of the molecules or particles of which the substance is composed (orientation of swollen particles), whereas toward the end of stretching the substance almost completely assumes a crystalline structure; the birefringence of the crystals must, of course, be expressed much more intensely than for amorphous substances.

These observations may be compared with those that were made concerning the birefringence of fibers or films of stretched cellulose, in which it was not possible to obtain complete crystallization, but only a very good orientation of the molecules, revealed under strong stretching by the appearance of elliptical rings in X-rays and by an intensification of intensity in certain directions (Herzog, Jancke, Iodl, Mark, W. Susich, Trillat) (see the preceding chapters).

To summarize: by the experiments of Katz, Hauser, Mark, Rosbaud, Meyer, and others it has been experimentally proved that, during the stretching of rubber, certain elements become oriented; these elements turn out to be of the same order of magnitude as hydrocarbon molecules. This orientation is apparently accompanied at the same time by an orientation of micelles, although there still exist certain doubts as to the structure of the latter.

7. Study of Vulcanized Rubber

(Influence of ingredients)

Until now we have considered only the case of natural pure rubber, stretched or unstretched; what, then, is found if we study commercial rubber subjected to vulcanization?

Katz1 took up this problem and found that, for every vulcanization product, it is necessary to attain a certain critical elongation in order to obtain phase diagrams (diagrams of individual spots): about 225% with a low sulfur content, and 275% with a longer vulcanization and the same sulfur content. With increasing sulfur content this critical elongation increases. With a sulfur content of up to 20%, clear phase diagrams are obtained at once, whereas for strongly vulcanized rubber (25% S, 130 min at 132°) the interference spots become diffuse. In all cases the positions of the interference spots remain the same as for raw rubber.

Ostromyslensky’s theory, according to which vulcanization is a swelling process in which rubber with sulfur is the medium in which unchanged rubber swells, seems to be confirmed by the results of X-ray analysis. In any case, sulfur hinders the crystallization of the hydrocarbons of rubber. Microscopic investigations by Polanyi and Ren…2

show that in vulcanized rubber there is more likely pure sulfur than rubber-sulfur.

According to the theory of Hauser, Mark, and Rosbaud, vulcanization causes the hardening of an initially only slightly polymerized medium and, in this way, hinders the phenomenon of “swelling” of the particles. The same complication of “swelling” (“drying”) also appears in the presence of other additives; in such a case vulcanization consists in the colloidal dispersion of sulfur in rubber.

Finally, according to the latest investigations of Meyer, Mark, and B. Susich^4,11, the reversible stretching of pure rubber can be explained by the properties of the chains of the principal valences: they stretch out and in this state have a tendency to bend. On stretching, the spherical micelle is transformed into a kind of elongated box (see above). The circumstance that the interference pattern is the same for vulcanized and non-vulcanized rubber means that the internal structure of these particles has not changed. In non-vulcanized rubber after stretching there is a continuous flow, accompanied by the disappearance of interference; this means that the micelles have shifted relative to one another during relaxation; it is known that this phenomenon is not observed in vulcanized rubber. It is natural to suppose that, as a result of vulcanization, the bonds between the micelles are somehow strengthened.

Studying the process of vulcanization more closely, Meyer and Mark* expressed the supposition that the reaction of sulfur chloride with rubber (cold vulcanization) develops on the surface of the micelle; part of the reagent is used for the formation of bridges between olefin groups in one and the same micelle (!), another part serves to bind the double bonds of neighboring micelles and thus to increase the forces of mutual linkage. Vulcanization must therefore consist partly in addition, partly in adsorption of sulfur; the greater the percentage of sulfur, the lower the elasticity (ebonite), which is in agreement with the preceding hypotheses.

It is obvious that these investigations are still quite new and must necessarily be supplemented in the direction of detecting these supposed compounds of sulfur with rubber. The problem, at the same time, is becoming an industrial problem as well, the solution of which may lead to very important results.

The influence of additives was investigated by Katz and Bingon^15. It is known that the various additives used in the rubber industry have different properties; while most of them are simple additions, some impart to rubber special properties which we note without very clearly understanding the mechanism of their action. The authors investigated whether, under the action of stretching, those crystalline substances which are introduced into the resin under test are also oriented. To note such a phenomenon would be of no little interest.

* Loc. cit.

As is known from the example of metals, whiskers, etc., together with the orientation of the elements of an elastic substance in a given direction, its resistance in this direction also increases.

The investigations were carried out on specimens with 25% additives, 4 S, and vulcanized for 35″ at 131°. The rubber strips were subjected to a 7-fold elongation, as compared with the initial length, and in this state had a thickness of 1 mm. Whereas ZnO, MgO, SO₄Ba, Ag₂S, Pb₃O₄, PbO, and graphite exhibited no orientation or exhibited it only very weakly, magnesium oxide, on the contrary, showed a distinct orientation. Here, probably, its needle-like microcrystalline structure played a role; substances whose particles are spherical are, of course, not inclined to orient themselves. This orientation does not appear in the photographs for elongations of less than 300%; up to this value only Debye–Scherrer ring diagrams are obtained.

Here there is a certain lag in the orientation. This fact is analogous to similar phenomena in rubber, which even before stretching possesses a partially crystalline structure and in which small crystallites orient themselves parallel to one another only at sufficiently large elongations.

In the case of rubber with a high sulfur content, very distinct Debye–Scherrer rings are obtained; these disappear when the sulfur is dissolved by acetone, but do not break up into segments even at large elongations.

All these observations show that the additives experience difficulty in orienting themselves in rubber under the action of a tensile force.

It is equally interesting to note that, in the case of MgO, ZnO, PbO, the interference rings in all parts represent uniform blackenings. With graphite and barium sulfate, points are also observed, indicating the presence of large crystals. A phenomenon of the same kind is found for specimens with 30% sulfur content. Such a picture shows that sulfur, introduced at first in a state of extreme dispersion, crystallizes in this case into large crystals.

This method should thus reveal reactions proceeding during vulcanization and show whether they lead to the formation of crystalline substances by reaction of sulfur with the additive, for example, or by recrystallization. It is likewise possible to hope to clarify the influence of the size of the additive grains on the ease with which the latter can orient themselves, as well as the relation between this orientation and the stress–strain curves and wear during friction; it is also possible, if this is of interest from the technical point of view, to give the additive material a form that would allow it to orient itself.

8. Study of gutta-percha and balata

Gutta-percha and balata give Debye–Scherrer rings, thereby showing that already in their natural form these bodies are in a crystalline or pseudocrystalline state, as is the case for hardened rubber. Clark,^4bis Brogden and Lanyon showed that these two substances, examined in the state of rest, give somewhat different diagrams.

But whereas hardened rubber is still elastic to a certain degree, balata and gutta-percha are almost entirely inelastic, and it is not possible to impart to their particles any appreciable orientation in order to obtain fiber diagrams. However, Midgley^20 succeeded in showing that at temperatures of 35–40° it is possible to draw these substances into extremely hard strips possessing, in the direction of stretching, a fibrous structure; these strips give good spot diagrams, from which one can estimate the lattice parameter in the direction of the stretching axis. Both diagrams are very similar, and the parameter calculated for balata and gutta-percha is equal to 9.40 Å (Hauser, Gutmann and Rosbaud).^2

According to the hypothesis of Hauser and Mark, it must be assumed, in the case of the substances under consideration, that the swelling medium here is much harder than for raw rubber; in its properties it approaches rather the state in hardened rubber, with, however, still weaker elasticity.

On the basis of these observations one can at the same time explain the peculiarities of balata and gutta-percha; the difference in the physical properties of rubber, gutta-percha and balata is explained, according to Midgley, not by a difference in their molecular weights, but by the greater uniformity of the individual carbons in the first of these substances.

II. Study of resins, gelatin, proteins, etc.

1. Study of resins

Natural and artificial resins give either amorphous or crystalline diagrams. Thus, colophony shows hints of crystallization; this crystallization is manifested more distinctly in Sumatra benzoin, Siam resins, and Elem resins. However, the diagrams obtained vary with the age and viscosity of the substance being studied: from whether amorphous rings or crystalline rings are obtained, one can judge the age of the resin. Clark and Lanyon^12 studied shellac as a function of the degree of its polymerization; they established that natural shellac is definitely crystalline (Fig. 9): the diagram consists of a series of concentric rings corresponding to the principal spacing of 3.9 Å; an amorphous phase is also detected, characterized by a broad ring which may be assigned to molecular distances of 4.9 Å. If shellac is completely

polymerized prolonged heating or artificial aging. The Debye–Scherrer ring disappears, and in its place a broad ring appears, strengthening and retaining its initial position. This result shows that the crystals which existed at the beginning, in all probability, combine into a more complex molecule, analogous to that which already existed in the amorphous phase.

Clark also established that gudron, as well as films of siccative, behave in an analogous manner; the diameter of the amorphous rings of these substances, however, is sensitive to polymerization, and its dimensions may serve as a qualitative indicator of this internal structure of the substance.

Herzog-Jabo[^18] investigated a series of resins in a similar way and divided them into amorphous and crystalline.

Recently Trillat has studied the change in the structure of bakelite as a function of the degree of polymerization. It is known that in state A bakelite easily melts and dissolves; in state B (first heating) it is no longer very soluble; in state C (second heating) it is hard, brittle, does not melt and is insoluble; it is precisely in this latter state that it is used as an insulator. Diagrams taken with the aid of molybdenum \(K\alpha\)-rays passing through a piece \(2\ \mathrm{mm}\) thick gave, in all three cases, concentric amorphous rings; microphotometry of the negatives showed that the first of these rings remains constant regardless of the degree of polymerization, while the second undergoes changes.

It is evident that successive condensation leads to a closer arrangement of the diffracting groups, which agrees well with the changes in the physical properties of bakelite. However, these changes are still not so substantial that the great difference between states A and C could be attributed to them; it remains to explain precisely what the nature is of the diffracting groups which, in our view, must be very small elementary groups containing several carbon atoms—groups whose combination in one number or another gives molecules of various degrees of polymerization, which in turn group into a micelle. Here the field for applying X-ray investigation is still almost untouched and requires systematic development.

2. Study of Gelatin and Collagens

Gelatin and collagens. Gelatin at rest, like rubber, gives a diagram characteristic of an amorphous substance. However, if it is stretched, the resulting diagrams change and show an increase of intensity in certain directions; but, unlike rubber, no crystalline phase appears, located outside the region of the amorphous ring and superposed upon the latter: the sectors of great intensity do not have the form of spots, but remain more or less intense bands situated on the amorphous ring.

This observed phenomenon differs from what is observed in rubber, and therefore requires another explanation.

The study of stretched and unstretched gelatin by means of X-rays was carried out by Katz and Gerngross,\(^{21,22}\) on the one hand, and (partly) by Herzog and Gonell,\(^{23}\) Clark and Lannon,\(^{19}\) and others, on the other.

In order to obtain strong stretching of gelatin, Katz proceeded as follows. A 20–30% gelatin gel in water is taken, left for 24 hours in 60% alcohol, dried, and stretched in a special apparatus with constant moistening by 60% alcohol. In this way elongations on the order of 50–100% are obtained. Elongations up to 400% can be obtained with glycerin–gelatin gels, which are strongly stretched and from which the glycerin is then extracted by placing them under tension in absolute alcohol.

The diagrams obtained by Katz under these conditions show contraction of the amorphous ring into sharp sectors: one equatorial, the other located at a greater distance and in the direction of stretching. At an elongation of 300%, the samples give spectra close to the spectra of natural fibrous collagen (bull Achilles tendon). Thus an amorphous substance such as gelatin can, exclusively as a result of stretching, yield characteristics inherent in other substances whose molecules possess a regular arrangement; without being able to assert definitely the existence of a crystalline phase, one must suppose that in this state these substances possess a mesomorphic structure, intermediate between amorphous and crystalline structure; this question has still not been resolved up to the present time. As can be seen, the result is close to that obtained for the stretching of cellulose films (see the preceding chapter).

The results of Clark and Lannon agree with Katz’s results*: according to these authors, pure isoelectric gelatin, freed from mineral substances and unstretched, gives a broad amorphous ring corresponding to spacings of 4.2 Å (Fig. 10) and, in addition, outer very sharp ones corresponding to spacings of 2.8 Å, which Clark attributes to the crystalline phase. For gelatin that has not been brought to the isoelectric point, this ring does not appear; it is possible that the difference between the results of Katz and Clark arose because of the nonidentity of the initial materials or of the methods of their preparation.

Clark, Herzog, and Gonell, working with pure isoelectric gelatin freed from mineral impurities, found that for elongations of 50% the “crystalline” rings break up into two crescents located along the axis of stretching, thus indicating a predominant orientation of the—

* See also Meyer’s work\(^{16\ \mathrm{bis}}\), p. 272: “Zerreibungen von Sehnen und Muskeln” and Krishnamurti’s work on the study of gelatin and dextrin.\(^{24}\)

residual crystals. For elongations up to \(100\%\), however, only two pairs of large maxima of intense elliptical form remain; one of these groups corresponds to a spacing of \(10\) Å, the second to \(5.5\) Å (Fig. 10).

Similar results were obtained with collagens such as Achilles tendon.

Apparently, the method of preparing the substance under investigation plays an essential role here; indeed, Gerngross and [[unclear: name]], working with collagens of various origins (connective tissue, cartilage), obtained more or less distinct diagrams in which the amorphous and crystalline phases were combined; this latter was the same for all such substances (see above).

It goes without saying that it is impossible to determine the crystalline system of this phase; in all cases one can only conclude, as has already been noted for cellulose and rubber, that the elementary cell must contain a volume of material much smaller than that corresponding to [[unclear: formula or name]] Prolydron: \(\mathrm{C}_{22}\mathrm{H}_{34}\mathrm{O}_{13}\mathrm{N}_{6}\) or \(\mathrm{Eukon\ C}_{24}\mathrm{H}_{40}\mathrm{O}_{13}\mathrm{N}_{6}\), if it contains three [[unclear: words]]. [[unclear: several damaged lines concerning the dimensions and relation of the cell to chemical composition]]. Thus, in any case, cellulose and rubber differ sharply from this case, since the results obtained by these two methods refer to two completely different, although interconnected, individual entities.

Glues. Glues freed from mineral impurities by the same methods as gelatin give, according to Katz and Mark, diagrams identical with the diagrams of gelatin (an amorphous ring relating to \(4.2\) Å and without any crystalline interference).

Pieces and dried films of glue give identical diagrams; hence it follows that the adhesive properties of these glues are explained by the simple solidification of a gel around the matrices of the fibers, as is evidenced, on the other hand, by study with the aid of microphotographs.

3. Study of albumins and proteins

Egg albumin can be obtained crystallized according to Sørensen in a solution of \(P_{\mathrm{H}} = 5.08\) by the gradual addition of a saturated solution of ammonium sulfate over eight days. Microcrystalline preparations were studied in the presence of a small amount of ammonium sulfate in colloidal tubes with thin walls; since evaporation should, if possible, be avoided. The diagrams obtained consist of three regular circles, sprinkled with Laue spots caused by sulfate, and are entirely different from the diffraction figures of amo-

… of type \((\mathrm{OTr})^{24}\); the protein is thus present, in some sense, not in a non-crystalline, but in a genuinely crystalline state.

Herzog and his co-workers\(^25\), studying X-ray diagrams of natural albumin fibers in the state of rest and stretching, came to the conclusion that they consist of small microscopic crystallites composed only of the substance; this crystalline phase was called by them “skeletin.” Silk fiber, muscle fibers, and cartilage appear to be composed of comparatively small elementary cells, leading likewise to a smaller molecular weight.

Assuming, as a first approximation, a cubic symmetry, Herzog was able to obtain the product \(nM\) from the known formula

\[ V=N\cdot n\cdot \frac{M}{x}, \]

where \(N—6.06\cdot 10^{23}\), \(x\)—density, \(V\)—volume of an individual cell, \(n\)—the number of molecules entering into the cell, \(M\)—the molecular weight. The figures obtained in this way are found in the 3rd column of the preceding table.

According to Herzog, the product \(nM\), from the physical point of view, represents the upper limit of the “molecular weight,” while the latter may be some fraction \((1/2—1/4—1/8)\) of the weight calculated in this way. These results here again come into contradiction with the ideas of very large molecules which are obtained in the study of hydrolysis products, always composed of a large number of various amino acids, and also with the molecular weights obtained by the usual methods (cryoscopy and osmotic pressures)*.

It is obvious that these results—not to mention that they rest on certain a priori assumptions—needed supplementation and verification by other methods; this is precisely what Herzog attempted to do\(^25\), undertaking cryoscopic measurements with resorcinol and metacresol as solvents, making it possible to avoid hydrolysis. Thus for silk fibroin a value of 300 was found, representing one half of that which is obtained from X-ray diagrams; chemical study of the products separated by treatment with phenol should show whether fibroin, or that part of it which dissolves in phenols (and this is the greater part), possesses the same simplicity of structure as the hydrolysis products, as is assumed in order to explain such small molecular weights.

From these investigations Herzog concluded that skelet—

* See also the subsequent work of Meyer (16 bis).

…from the point of view of structure, different from simple ions. For our part, however, we confine ourselves to the observation that the significance of molecular weight for colloidal systems needs clarification, since in some cases it refers to the weight of an actually existing complex molecule, and in others to the weight of an aggregate of groups entering into this or that particle, which may be much simpler in comparison with the molecule as a whole. The contradictions obtained among all these results, in our opinion, can be eliminated if one defines precisely what is to be understood by the molecular weight of a colloidal substance, the index of polarization, the elementary group, the molecule, and the micelle*.

III. The Universality of Orientation Phenomena in Biotic Formations

From what we have learned in this and in the preceding chapter it follows that orientation phenomena are encountered to an extremely high degree in products obtained from living nature, such as: wool, cotton, spider silk, gelatin, muscles, tendons, and so forth. The notion of these substances as amorphous must be shaken to a considerable degree, since, as crystallographic technique improves, fewer and fewer substances prove to be in an actually amorphous state.

Thus the majority of colloidal substances, as soon as they are not swollen by some liquid wetting them, are in fact composed of crystalloid-like elements. Even those of them which give amorphous diagrams, under the orienting action of such factors as stretching, prove, often under the conditions of natural growth, capable of revealing, if not a completely crystalline state, then at any rate one close to it—an intermediate state, which was anticipated by Ambronn when he proposed that the formation of a colloidal micelle begins with certain crystalline elements.

Orientation phenomena are thus observed in a very large number of natural formations. We have described only some of them; we again encounter them in a hidden form in sea-lion hairs, where the orientation is so perfect that monocrystalline diagrams are obtained (Laue spots); in the mineral needles of sponges, in spider web, in shells, in shrimp shells, and in the elytra of beetles—in this last case each layer is composed of parallel-oriented crystals, the orientation of which differs from the orientation in the neighboring layer. Tooth enamel, in the arrangement of its crystallites, resembles rolled metallic films of a complex fibrous structure.

All the various cases of orientation encountered in metals—single crystals, crystals strictly oriented in a definite crystallographic direction (simple phase—

* See the bibliography index.

structure); a complex fibrous structure, crystals or aggregates forming a simple fibrous structure; a peculiar crystalline structure—all this is found in various organic products. Depending on the case, and perhaps on the physical properties of these substances, they possess one structure or another, which is the expression of some general law of nature that is still looming before us.

It is obvious that the presence of small crystals and their arrangement determine the physical properties of the substances containing them. Just as the resistance of a metallic thread depends on the arrangement of the crystallites within it, so too the resistance of fibers is almost determined by the very same factors. A change in orientation determines not only physical but also chemical properties. It is understandable that the orientation, in a certain direction, of molecules having groups capable of reacting with some reagents may prove most favorable for the course of this reaction. There is a whole series of descriptive facts confirming such a point of view: for example, strongly stretched artificial-silk threads do not dye in the same way as in the unstretched state; even the formation of emulsions from oils in water containing mono- or divalent soaps—all these are phenomena of adsorption, and perhaps also of catalysis, which is probably caused by surface orientation.

Devaux20, in his interesting investigations of the orientation of molecules in thin films, also came to the conclusion that the walls of the cells have an oriented structure, which makes it possible to explain their semipermeability as depending on the different arrangement of the groups on one side and on the other.

Here we stand face to face with a very important problem, which, for its solution, requires the improvement of X-ray technique and other methods.

Finally, one should reflect on the causes giving rise to these important phenomena. From the investigations of Ambronn and his pupils, as well as of Tscher over the dichroism of dyed gels, it would seem to follow that fine cracks or capillaries are capable of causing the orientation of crystallization nuclei and thereby determining the arrangement of the crystals; in the gel itself, inorganic crystallites included in organic gels (mother-of-pearl) are arranged in networks or layers, following the direction of the slits. Thus, whenever small crystallites occur in an organic substance—and this happens more often than is usually thought—their position is connected with growth and has a significance that has not yet been deciphered.

The key to these phenomena, so important for our understanding of secondary processes, will be found through the joint application of the X-ray and polarization methods.

LITERATURE

A. Rubber

1. Katz, Selman, Lotze, Das Problem der Polymerisierung und der Kautschuk-Elastizität, Koll. Zs., 215, June 1927.

2. Hauser and Rosbaud, Röntgenographische Studien an Kautschuk und verwandten Substanzen, Kautschuk H. 1, January 1927.

See Hauser, Haemmerle and Rosbaud, Neuere röntgenographische Untersuchungen an Kautschuk und verwandten Substanzen, Kautschuk, p. [[unclear: page]], June 1927.

1. Katz, Koll. Zs. 25, 300, 1925 and 37, 19, 1925; Naturwiss. 13, 410, 1925. Katz and Bing, Zs. angew. Chem. 38, 438, 1925.

2. Mark and V. Susich, Über geregelte Mizellarstrukturen von Kautschuk, Koll. Zs., B. XLVI, H. 1, 1928; Hauser and Rosbaud, loc. cit.; Hauser and Mark, Röntgenographische Studien an Kautschuk, Gummi Ztg. 40, p. 2000, June 1926.

3. Müller, Kautschuk-Ztg., p. 106—187.

4. Rosbaud and Schmidt, Dehnungsversuche an Rohkautschuk. Zs. f. techn. Phys. 8, 1928.

5. Staudinger, Koll. Chem. Beihefte, XXI, 1925.

6. Freundlich and Hauser, Koll. Zs. 36, 15, 1925.

Schönberger, Röntgenographische Studien an Metastyrol, Kautschuk, Hartgummi.

Katz, Ist die Synthese des Kautschuks schon gelungen, Kölnische Zeitung (Jubilee issue), 384, 1926.

1. Hock, Rev. gen. Col. 767, September 5, 1927; Kautschuk 126, [[unclear]].

2. Hauser and Mark, Zur Kenntnis der Struktur gedehnter Kautschukproben, Kautschuk-Beihefte, B. XXII, H. 3–5, 63, 1926; Mark and V. Susich, loc. cit.

3. Meyer and Mark, Über den Kautschuk. Ber. d. Deutsch. Chem. Ges., [[unclear: volume]], 8, p. [[unclear]], 1928.

Neue Wege in der organischen Strukturlehre und in der Erforschung hochpolymerer Verbindungen, Zs. angew. Chem. 34, 1928.

1. Ost. Sur le grandeur moléculaire du caoutchouc et de la gutta-percha. Naturwiss., H. 15, 14, 1926.

2. Katz, Gummi-Ztg. 41, 2035, 1927.

3. Regnault, Études micrographiques de caoutchouc vulcanisé montrant l’évolution du soufre libre, Chimie Industrie, p. 397, 1927.

4. Katz and Bing, Röntgenographische Beobachtungen an Kautschuk und anorganischen Beimischungen, Zs. f. angew. Chem., p. 515, 18 June 1927.

5. Michael, Kautschuk, p. 230, 1927.

16bis. Meyer, Fier Feinbau, Festigkeit und Kontraktilität tierischer Gewebe. Biochem. Beihefte, B. 214, H. 4, 1926; Neue Wege in der organischen Strukturlehre und in der Erforschung hochpolymerer Verbindungen, Zs. f. angew. Chem., 34, 1928.

1. Ostwald, Zur Theorie des Röntgenflekiges gespannter Gele, im besonderen des Kautschuks, Koll. Zs., B. LX, H. 1, 1926.

2. Lecomte du Nouy, Équilibre superficiel des solutions colloidales, Masson, Paris, 1929.

B. Additional literature on the question of the structure of rubber

Fric, La structure du caoutchouc étudiée au moyen des rayons X, Gén. du caoutchouc, 1927.

Olivier, Nos connaissances actuelles sur la constitution de la molécule des caoutchoucs, C. R. Chimie Ind., VII Congrès, p. 557.

Katz, Neue Bahnen in der Röntgenspektrographie des Kautschuks. Kautschuk-ähnlichen dehnbaren Substanzen, Chemiker Ztg., 21 [[unclear]], 1927.

[[unclear: author]], Sind die Doppelbindungen des Kautschuks? Gummi Ztg., No. 24 [[unclear]], 1927.

Katz, Stäbcheninterferenzen im Kautschuk und anderen Polymeren, [[unclear: journal]], No. 38, p. [[unclear]], 1927.

Katz, P. Van Kempen, Synthetische Kautschuke und natürliche [[unclear]], Chem. Ztg., No. 6, p. [[unclear]], January 22, 1927.

Sheppard, Nietz, Keenan, État supermoléculaire de substances polymérisées, Ind. and Eng. Chem. XXI, No. 2, p. 126, 1929.

Katz, Einfluss der Polymerisierung auf das Röntgendiagramm. Zs. Chem., vol. 125, II. 125, no. 5/6, 1927.

Clark, X-Ray Contribution to the problem of Polymerization. Ind. and Chem., February 1929, p. 125.

Hauser, Nouvelle hypothèse sur la structure du caoutchouc, basée sur les recherches récentes par les rayons X, Caoutchouc et Gutta-percha, p. 14, 1927; Ind. Eng. Chem., 19, 165, 1927.

Pulverer, La constitution du caoutchouc, Kautschuk, pp. 233—237.

Seoim, Constitution du caoutchouc, Les caoutchoucs synthétiques, Rev. du caoutchouc, p. 3, May 1928.

P. Bari, Contribution à la connaissance de la structure du caoutchouc. Rev. gén. de caoutchouc, 11, no. 20, p. 5; no. 21, p. 3, 1926.

Schob, Kautschuk als Werkstoff, Zs. des Ver. deutsch. Ing., vol. 71, 23 April 1927.

Dannenberg, Étude ultramicroscopique de la vulcanisation, Kautschuk, pp. 104—308, 1927.

Dugué, Observations anciennes et hypothèses nouvelles sur les caoutchoucs. Rev. gén. du caoutchouc, no. 40, March—April, 1928.

B. Resins, gelatin, etc.

1. Clark et Lanyon, Applied X-Rays, p. 194.

2. V. Naray-Szabo, Röntgenographische Untersuchungen an Harzen, I Chem. Zs., vol. 185, no. 1/3, 1927.

3. Katz u. Gerngross, Gélatine und Kollagen, Naturwiss., no. 44, year, p. 900, 1925.

4. Katz u. Gerngross, Über die Herstellung sehr stark gedehnter Gelatinepräparate und deren Röntgendiagramm, Gelatine und Kollagen, Koll. Zs. vol. 3, no. 2, 1926.

5. Herzog u. Gonnell, Berichte, 58, 2228, 1925.

6. Ott, Über röntgenometrische Untersuchungen an Eiweisskristallen. Kolloidchemische Beihefte (Ambronn Festschrift), 1926.

7. Herzog, Zur Erkenntnis der Skleroproteine, Helv. Chim. Acta, vol. XI, 2, March, 1928.

8. Devaux, Structure moléculaire de la cellule et des tissus vivants, J. de Phys., 2 March, 1928, no. 258, p. 34.

9. Krishnamurti, On the Nature of Dextrine of, Gelatine, and Sodium oleates as revealed by Ray Diffraction, Indian Journ. of Physics, 30 November, 1928.

I. Additional literature on the question of the structure of resins, gelatin, etc.

Gerngrosse u. Katz, Röntgenographische Untersuchungen über die Hitzekontraktion von ungegerbeten und formaldehydgegerbeten Sehnen, Kolloidchemische Beihefte (Ambronn Zeit.), p. 368, 1926.

Herzog et Gonnell, De la systématiques de la formation des structures inorganiques dans les organismes. Zsigmondy-Zeit., Dresden 1925.

W. Bragg, La cristallisation imparfaite des choses courantes, Nature, 24 June, 1926.

Clark, Théorie de la contraction musculaire avec diagrammes de diffraction X des muscles contractés et détendus, Amer. J. Physiol., 83—181, 194, 1927.

Lutenbacher, La structure des muscles striés d’après leurs propriétés optiques, C. R. Acad. Sciences, 23 January, 1928.

Herzog u. Jancko, Röntgenographische Untersuchungen von Spinnenseide. Hoppe Seyler’s Zeit. für phys. Chemie, vol. 164, no. 4/6, p. 306, 1627.

Meyer u. Mark, Über den Aufbau des Chitins, Ber. d. Deutsch. Ges., no. 8, p. 1930, 1928; Über den Aufbau des Seiden-Fibroins, Ber. d. Deutsch. Ges., no. 8, p. 1132, 1928.

Sheppard, Niets, Keenan. État supermoléculaire de substances polymérisées. Ind. and. Eng. Chem., XXI, no. 2, p. 126, 1929.

Bergmann et Jacobi, Sur l’augmentation de solidité conférée par étirage aux pellicules de gélatine. Koll. Zeit. 1928, p. 46.