Some Applications of X-Rays

J. J. Trillat, Paris

The Application of X-Rays to the Study of Colloids

Several years ago X-rays were successfully applied to the study of colloids and highly polymerized substances. The results obtained, whose theoretical interpretation is often very difficult, nevertheless provide very important new information.

Even the study of double refraction led to the idea that the structural elements of biological forms are in fact crystals [starch, fibers of animal tissues (muscles, tendons), cellulose fibers]. This point of view was confirmed by the experiments of Ambronn¹, who relied on Wiener’s investigations of the double refraction of rods. The results were then confirmed with the aid of X-rays.

In fact, Debye and Scherrer showed that, for the study of systems in two phases, the interference phenomena that are obtained when X-rays fall on crystals can readily be used: here one is dealing with systems having two phases, one of which is crystalline, as is the case for a large number of colloidal solutions or gels.

In what follows we shall give several noteworthy examples of various applications of this new method.

1. The Crystalline Structure of Colloidal Substances

On the basis of the work of Zsigmondy², Scherrer³ succeeded in showing that colloidal gold, as well as colloidal silver, actually consists of separate

small crystallites; the same is true for silicic-acid gels, stannic acid, glutine hydroxide, and the same should be true for a large number of colloids.

Among organic compounds, the majority of precipitates usually regarded as amorphous are in fact “cryptocrystalline,” and a large number of substances with large molecules also have a crystalline structure [polysaccharides such as starch, cellulose, inulin, certain sugars: mannose, xylose, chitin, proteins, such as the substance of silk threads, soaps, and certain artificial or natural rubber-like substances].

On the other hand, among the polysaccharides glycogen is amorphous, as is also mannose obtained from an extract of Salep. Crystallized albuminoids, hemoglobin, edestin, and a number of other substances still give diagrams of amorphous bodies, although not only their appearance but also their double refraction speak in favor of their crystalline structure. Here it is quite possible that we are dealing with shortcomings of the experiment, since day by day substances enjoying the reputation of being amorphous turn out in reality to possess a microcrystalline structure.

2. Determination of the Average Sizes of Crystallites

The study of interference rings makes it possible, as Scherrer showed, to draw conclusions about the relative magnitude of the elementary microcrystallites. For this it is necessary to know the width of the interference band: the width of the interference rings is connected with the sizes of the particles of the microcrystalline powder, or of the colloidal particles, subjected to the action of X-rays. Here we have something analogous to what is observed with ordinary gratings; the position of the maxima of light depends only on the wavelengths, whereas the intensities of the maximum and its width are inversely proportional to the number of rulings of the grating.

The width of the interference rings depends on the number

of the individual elements acting simultaneously, and, in the case of a single crystal, on the number of atoms of the crystal lattice participating in the interference. If this number is large, the lines are very sharp and clear; if it is small, they become weaker.

This method enabled Scherrer to show that in some preparations of colloidal gold there exist crystalline particles containing only a few atoms of the metal, i.e., formed by the combination of a very small number of elementary crystalline cells.

At such an extreme degree of subdivision, the substance is still in a truly crystalline state.

In Germany, Herzog[^4] determined the sizes of cellulose crystallites; the values he found, in the case of cotton for example, were of the order of 100 Å (10 mμ). In addition, this author also showed that if, with certain precautions, cellulose is converted into nitrocellulose while preserving the fibrous structure of the former, crystalline nitrocellulose can be obtained, whose crystallites have the very same dimensions as the crystallites of cellulose (see below). Determination of the particle size of colloidal solutions of nitrocellulose by the diffusion method, for example, gives the same values. Thus it turns out that the size of the particles of colloidal solutions is the same as that of the crystallites of cellulose.

Finally, it is appropriate to note here that the relation derived by Scherrer also makes it possible, in favorable cases, to determine the orientation of the axes of crystallites1.

3. Nucleation and transformation of crystallites

Haber[^5] studied in detail the phenomena occurring at the moment of crystallization, using the method of X-ray spectroscopy. It turned out that these phenomena depend, on the one hand, on the rate at which molecules come into contact and group together (the rate of aggregation), and, on the other hand, on the rate at which they are distributed (the rate of placement).

It is necessary to consider 2 cases: the first, when the aggregation rate \((CA)\) is considerably greater than the rate of arrangement \((CP)\):

\[ CA > CP, \]

and the second, when the aggregation rate is almost equal to the rate of arrangement:

\[ CA = CP. \]

At high rates of aggregation and arrangement, amorphous particles are obtained at first, which little by little crystallize. If, however, \(CP\) is very large, this state is not observed. Precipitates that form rapidly are usually amorphous; precisely this occurs in the case of rapidly precipitating deposits, such as the precipitates \(\mathrm{Al(OH)_3}\) and \(\mathrm{Fe(OH)_3}\). In contrast to this, those precipitates for which \(CP\) is small, for example those slowly obtained by hydrolysis of the salts \(\mathrm{Al_2O_3}\) and \(\mathrm{Fe_2O_3}\), are crystalline; the same is observed for silica gel and beryllium oxide hydrate: silica extracted from animal organisms is always amorphous, as are inorganic substances contained in bones. Particles of \(\mathrm{HgS}\), \(\mathrm{ZnS}\), \(\mathrm{CdS}\), \(\mathrm{HgCl}\), \(\mathrm{AgBr}\), \(\mathrm{AgJ}\), having a clearly expressed dipolarity, are crystalline, whereas the hydrates of Zn and Th, with a weakly dipolar character, are amorphous.

If cellulose is treated with acetic acid, while preserving the fibrous structure (D. R. P. No. 183, 209), the preparation is at first amorphous; then, little by little, the appearance of interference can be observed, which becomes more and more intense. It is highly probable that here there occurs a gradual separation and elimination of impurities.

Phenomena of recrystallization have hitherto been observed only for crystalline aggregates of metals. It may be stated with certainty that these phenomena also occur in the formation and transformation of bodies which until now have been regarded as amorphous; it is also possible that the phenomenon known as the aging of colloids may be explained by recrystallization.

In the same way, adsorption phenomena can be explained when studied by means of X-rays. Characteristic examples are provided by zeolites (Pinne)\(^{6}\), which retain ions of mercury, water, alcohol, and iodine without any change in the dimensions of the crystal lattice or in the intensity of the interferences, and by crystals capable of adsorbing a certain amount of water of crystallization.

The method of X-ray analysis has also been successfully applied to the study of the influence of treatment upon silk. It has been observed that all treated silks give the phase diagrams of untreated silks, at least in their most intense part: the fibrous structure undergoes no changes under the action of foreign substances. The substances used for treatment give their own, well-defined diagrams, which are superimposed upon the diagram of the silk.

Silks treated with tin phosphate or soluble potassium silicate give several interference rings, the intensity of which increases with the amount introduced. In some cases the mordant gathers into crystallites in the form of a sheath (around the thread), so that the Debye–Scherrer rings are replaced by Laue spots. Silks treated with iron mordant, potassium cyanide, and sodium silicate give intense circles, among which the diagrams of the silk can still be distinguished; in those cases where the mordant substance is amorphous, blurred circles appear instead of thin rings. Adsorbents, such as silk is here, always retain the crystalline structure, while the absorbed bodies (mordants), not entering into chemical reaction with the substance of the silk, have either an amorphous or a crystalline form.

This example is of very great interest for the following reasons.

Natural silk, i.e. the thread forming the silk fiber, consists of crystalline aggregates arranged parallel to one another along the thread, and of amorphous substances, which constitute a kind of cement fastening together the separate bricks of the wall (the role of bricks*

here the crystallites play a role). The mordant substance, which can be introduced into the threads in large quantity, enters there, as X-ray analysis shows, without chemical changes. Apparently one may think that the substances accompanying the principal crystalline substance absorb the mordant substances and serve as colloidal buffers.

Processes of this kind are very numerous in the organism and are very often encountered in industry, for example in tanning or dyeing, where they acquire exceptional importance. In addition, it is undoubtedly of interest to reveal clearly, for the first time, the absorption of quasi-crystalline bodies.

4. Phenomena of swelling of colloids

X-ray analysis also makes it possible to study the mechanism of swelling of colloidal substances by solvents; these investigations were carried out chiefly by Katz and Mark.^7

Two following cases may be distinguished.

1. The substance causing swelling penetrates between the crystallites and is absorbed by cracks or fissures in the crystals, forming amorphous parts of the system. The crystalline lattice in this case does not change: this, for example, was found for cellulose in salt solutions.

2. The agent causing swelling reacts chemically with the crystalline substance. In this case the dimensions of the lattice and the position of the rings change.

However, not all the predicted phenomena are always observed; thus it was noticed that inulin, swelling from water, gives only one crystalline modification, whereas several of them might have been expected. The same is true for mercerized cellulose.

5. Determination of crystalline forms

The determination of the crystalline structure of the microcrystals composing colloids presents a fairly

great difficulties and could be carried out successfully only in a very limited number of cases. In essence, the method consists in the study of Debye–Scherrer rings and measurements of intensity; where this is possible, it is of great interest to obtain fiber diagrams (fiber diagrams).

As an example of determinations of this kind one may cite Scherrer’s experiments on colloidal gold and silver, and those of Herzog and Polanyi on cellulose, silk fibers, chitin, nitro- and acetocellulose, and on gels.

6. Orientation of crystals in the colloidal substance itself

The position and orientation of crystallites can also be studied quite clearly by the method of fiber diagrams, according to Polanyi and Weisenberg.

To the same extent that the study of metals has shown that knowledge of their structure is of great importance for understanding their strength, this knowledge is likewise of great interest in the case of the fine structure of gels consisting of cryptocrystalline particles.

For this purpose the method of X-ray analysis has also been applied. A number of investigations were carried out on fibers of natural or artificial cellulose and on animal tissues. It is evident that the two-phase structure of these substances determines their physical properties.

A simple fiber structure—the axes of the crystallites parallel to the axis of the fiber—was found in cellulose fibers and natural silk. In a layered structure, similar, for example, to the structure of sheet iron, the crystallites are parallel to one another or at least subdivided into several parallel groups; this type of orientation also occurs in a large number of organic substances (fatty acids, soaps, etc.) in crystalline aggregates of biological nature, in worked metals, and finally in many fibers that are cryptocrystalline or finely crystalline.

These formations, which are encountered very often in

in nature, owe their origin to the conditions of crystal growth, and it may be said that this kind of fibrous texture arises chiefly under drawing, stretching, and slow cooling; this hypothesis has received completely precise confirmation in the work of Katz on rubber and of Herzog, Mark, and Trillat on stretched cellulose.

7. Determination of the Polymerization Index of Substances with High Molecular Weight

Analysis of crystals by X-rays provides a means of determining the degree of polymerization. Indeed, for crystalline and microcrystalline substances it is possible, by means of X-ray analysis, to determine the elementary parallelepiped of the crystal; this elementary parallelepiped, which must contain at least one molecule, reproduces the crystal itself by successive superposition. Spectrographic determination can be used to determine molecular weight: in fact, if for a given elementary cell the space occupied in it by a certain group of atoms is known, we have a measure for finding the upper limit of the degree of polymerization. Ott⁸ attempted to apply this method to certain organic substances of this kind, such as cellulose, rubber, amylose, etc. The reasoning followed by this author may be summarized as follows.

According to Bragg, an atom always has almost one and the same diameter in a crystal, whatever other atoms may surround it. The magnitude of this diameter is characteristic of the atom: one may imagine atoms as spheres of a certain radius; the crystal is reproduced by the closest packing of these spheres.

For organic substances, such as cellulose, rubber, etc., the atomic radii were determined by Bragg and have the following values:

Atom	Atomic radius
Carbon	0.77 Å
Hydrogen	0.75 Å
Oxygen	0.66 Å

If we consider, for example, the group \(C_6H_{10}O_5\), its volume is determined, according to Ott, in the following way.

An atom of radius \(r\) is contained in a cube with side \(2r\) and volume \((2r)^3 = 8r^3\). Thus the full volume of the group \(C_6H_{10}O_5\) will be equal to:

\[ \begin{aligned} \text{volume of 6 atoms } \ldots\ C &= V_C = 48r_C^3 === 22\ \text{\AA}^3 \\ \text{” 10 ” } \ldots\ H &= V_H = 80r_H^3 == 31\ \text{\AA}^3 \\ \text{” 5 ” } \ldots\ O &= V_O = 40r_O^3 \phantom{==} 11\ \text{\AA}^3 \\ \hline \text{Volume } C_6H_{10}O_5 &= V = V_C + V_H + V_O = 64\ \text{\AA}^3 \end{aligned} \]

The atomic group \(C_6H_{10}O_5\) thus fills a volume of about \(64\ \text{\AA}^3\). The first part of the problem is thereby solved; it is now necessary to determine the volume of the elementary parallelepiped.

But the majority of organic substances crystallize in classes of low symmetry, and do not form any strict crystallographic forms. If we turn to the diagrams of very finely powdered materials (the Debye–Scherrer method), the rings prove to be weakly expressed; this makes a complete determination of the structure difficult.

It is nevertheless possible to find the order of magnitude of the elementary volume, and thus to determine the upper limit of the degree of polymerization. This method, proposed by Ott\(^{8}\), although it has met with much criticism, may nevertheless have certain applications.

Bragg’s equation

\[ d=\frac{\lambda}{2\sin\theta} \]

shows that, for rings of the first order, the maximum \(d\) is obtained for the minimum values of \(\theta\). Consequently the line closest to the center of the diagram corresponds to the greatest distances between nets, which are usually equal to the characteristic elementary spacings (in the case of a cube) (Ott).

Thus, from the dimensions of the innermost ring itself, one can obtain the value of the characteristic maximum distance and, from this, the upper limit of the length of the edge

of an elementary parallelepiped. The cube calculated from this edge gives the upper limit of the volume of the elementary cell; dividing this volume by the volume found theoretically for a chemical group (for example, 64 ų for \(C_6H_{10}O_5\)), we obtain the limit of the degree of polymerization of the substance under study.

Using these considerations, Ott arrived at the following results.

Substance	Probable formula	Maximum distance between nets	Maximum possible formula for the elementary cell
Diamylose . . .	\((C_6H_{10}O_5)_2\)	11.35 Å	\((C_6H_{10}O_5)_{22}\) ?
Tetramylose . .	\((C_6H_{10}O_5)_4\)	9.02 »	\((C_6H_{10}O_5)_{12}\) ?
Octamylose . . .	\((C_6H_{10}O_5)_k\)	15.98 »	\((C_6H_{10}O_5)_{63}\) ?
Triamylose . . .
Hexamylose . .	\((C_6H_{10}O_5)_h\)	7.27 »	\((C_6H_{10}O_5)_6\)
Inulin . . . .		7.34 »	\((C_6H_{10}O_5)_6\)
Cellulose . . .	\((C_6H_{10}O_5)_4\)	6.01 »	\((C_6H_{10}O_5)_4\)
Lichenin . . .		7.69 »	\((C_6H_{10}O_5)_7\)
Amyloid . . .	\((C_6H_{10}O_5)_2\)	5.21 »	\((C_6H_{10}O_5)_3\)

Most of these results do not agree with those which chemistry gives for the degree of polymerization. The polymerization indices given by chemistry are considerably smaller. It should be noted that this calculation raises doubts: on the one hand, the innermost ring often falls out of spectrographic analysis, and, on the other hand, it is hardly correct to take into account only the maximum distances between nets for constructing the elementary cell. However, the results obtained with the aid of X-rays and by chemistry sometimes differ from one another also because the concept of the index of polymerization is not one and the same in these two cases.

Study of polyoxymethylenes

At the present time the problem of studying organic microcrystals and polymers has been solved by a more rational method by Staudinger[^10], Meyer, and Hengstenberg[^11]. These authors turned to the study of polyoxymethy-

lenes and acetates of polyoxymethylenes, specially prepared for these investigations in the form of highly polymerized formaldehyde products, in order to obtain a visual model of cellulose.

Staudinger\(^{10}\) and his collaborators proposed that natural colloidal products are formed by polymerization of substances that are essentially monomeric. Polymerization occurs along “principal valences,” which are “physically determined” by the fact that the forces corresponding to them are considerably greater than those which lead to the formation of a crystal from individual molecules. The size of the molecule need not necessarily be identical with the size of the particles or crystallites; it determines them only insofar as the terminal group (acetyl, for example) separates the individual tiers of the structure formed by successive superposition of the basic units. The synthesis of polymerized compounds of this kind does not lead to the formation of entirely definite substances: rather, mixtures appear, from which it is difficult to isolate definite substances because of the extraordinary similarity of their physical properties.

Proceeding from the idea that the study of an unknown basic unit, and hence also of the course of the polymerization process, is an impossible task for natural complex substances, Staudinger\(^{10}\) attempted to verify this theory by taking, as an example, polymerized formaldehyde and its chemical derivatives, since this proved possible.

Hengstenberg, Mark\(^{11}\), and Ott\(^{12}\), for their part, also studied these substances by the method of X-ray spectroscopy. It is precisely these investigations that we shall now summarize.

Polyoxymethylenes have the formula

\[ \mathrm{H}-\mathrm{O}-\mathrm{CH}_{2}-(\mathrm{O}-\mathrm{CH}_{2})_{x}-\mathrm{O}-\mathrm{CH}_{2}-\mathrm{O}-\mathrm{H}. \]

Their average degree of polymerization, as determined by chemists, is of the order of 60; in addition to this there exist other modifications, denoted \(\beta\), \(\gamma\), \(\delta\). With the aid of these substances one can form diacetyl esters:

$$ \mathrm{CH_3—C—(O—CH_2)_x—O—C—CH_3} $$

$$ \begin{array}{cc} \| & \| \\ \mathrm{O} & \mathrm{O} \end{array} $$

These esters can be prepared with an average degree of polymerization that is quite well defined, and can contain from 1 to 22 groups of \(\mathrm{CH_2O}\); they are liquid when the number of groups is from 1 to 7 and solid if the number of groups is greater than 7; these latter were studied by means of X-rays. It goes without saying that the various products obtained in this way are not pure substances, but mixtures which are formed from substances with average and higher degrees of polymerization.

In order to obtain phase diagrams that make it possible to measure periods of identity which cannot be obtained from powder diagrams, Tengenberg and Me resorted to pressure in order to bring about a static arrangement of the crystallites; in this process there occurred a phenomenon of orientation of the crystallites analogous to that which takes place for fatty acids, and it proved possible to obtain intense bands or arcs of circles corresponding to a certain crystallographic direction and, in some cases, even layer lines (Schichtlinien).

The crystallites obtained have dimensions too large to produce broadening of the bands (size \(> 0.5\)); for all the products studied it was not possible to establish correlations between particle size and physical properties, contrary to what is usually obtained for other highly polymerized substances; this shows that in the present case the size of the molecule has nothing in common with the size of the particles: particles and crystallites have no chemical significance for the polymerization of formaldehydes.

Investigation by means of X-rays and comparison of the diagrams obtained lead to the following important results: the lines occupy one and the same position and possess one and the same intensity, whatever the modification under study may be\(^1\). Consequently the elementary substance is the same for all polymers; slight differences in thick—

tion and intensity of the lines can be connected only with the possibility of small changes in the positions of the atoms, but are insufficient for explaining the chemical results.

The study of polyoxymethylene diacetates, more definitely characterized chemically, makes it possible to draw interesting conclusions. In addition to the fact that the lines or rings do not change

Fig. 1. Spectra of polyoxymethylenes.
1 — polyoxymethylene ($d = 25$ mm) (paraformaldehyde gives the same spectrum);
2 — polyoxymethylene diacetate ($f = 93—95^\circ$) — ($d = 51$ mm);
3 — polyoxymethylene diacetate ($f = 31—34^\circ$) — ($d = 51$ mm);
4 — polyoxymethylene diacetate ($f = 52—54^\circ$) — ($d = 51$ mm).

with the polyoxymethylene lattice, near the center there appears a series of rings corresponding to successive orders of reflection on lattice planes located at large distances from one another (exactly as for fatty acids or triglycerides); the diameter of these rings decreases with increasing degree of polymerization; this means that the addition of a $CH_2O$ group to the molecule increases the distance between the lattices (Fig. 1).

(pressed powders). The molecules of the diacetates prove to be arranged normally to these net planes, which contain terminal acetyl groups

\[ -\mathrm{C}-\mathrm{CH}_3 \]
\[ \Vert \]
\[ \mathrm{O} \]

Under these conditions the elementary volume (calculated for diacetates with index 9), according to Meyer and Hengstenberg, is equal to

\[ 25 \cdot 8.3 \cdot 4.47\ \text{\AA} = 935\ \text{\AA}^3 . \]

The molecular volume from the density (1.353) and molecular weight is \(451\ \text{\AA}^3\). Thus the number of molecules in the elementary cell is \(=2\).

The same number is also obtained for the higher diacetates; the symmetry is pseudohexagonal.

The most interesting fact is the regular increase of the length of the period, which, according to Meyer and Hengstenberg, represents the length of the molecule. Depending on the index of polymerization, we obtain the following values:

\(n\) (degree of polymerization)	8	9	10	12	14	15	16	17	19
\(d\) in angstroms	23.7	25.2	27.2	32.1	34.6	36.8	38.5	40.4	43.7

which, owing to the existence of a mixture, represent only average values. The constant increase per \(\mathrm{CH}_2\mathrm{O}\) group reaches approximately \(1.9\ \text{\AA}\). From this,\(^{12}\) the interest of this result is obvious: a simple calculation of the magnitude of the identity period makes it possible in this case to determine the degree of polymerization.

The determination of the principal elementary nucleus of the higher polymers was also carried out by Meyer and Hengstenberg by means of a simple calculation; with the aid of fiber diagrams one can calculate the dimensions and consequently also the volume of the elementary cell, if one uses fibrous compounds or presses the substance in such a way as to impart to it a fibrous structure. The volume of \(\mathrm{CH}_2\mathrm{O}\) thus obtained is equal to \(33.2\ \text{\AA}^3\); we obtain the number of \(\mathrm{CH}_2\mathrm{O}\), dividing the volume of the elementary cell by \(33\ \text{\AA}^3\).

Thus, diacetates, methyl ethers, etc., of polyoxymethylenes (slightly polymerized) are compounds with well-defined molecules; investigation by X-rays shows that the molecule serves as the structural element in the construction of the crystal, i.e., the lattices here are molecular; the length of the molecule is a linear function of the degree of polymerization and determines various physical properties, such as density, solubility, ability to crystallize, and the size of the crystallites. Identical results have been obtained for dimethyl ethers of polyoxymethylenes. As in the case of fatty acids, it is possible to reveal the internal structure of the molecule (the periodicity of the CH₂O group).

a — polymerized    b — normal
Fig. 2. Diagram of “shellac” resin.

As for the higher polymers, they do not form such well-defined molecular lattices, since they contain, like a mixture, molecules of very different lengths; but these elongated molecules are arranged parallel to one another, like rods of different sizes.

In two directions perpendicular to the main axis of the molecule, a regular network-like arrangement is obtained, and it is precisely the CH₂O groups, by their regular sequence in the molecule and along the axis, that give rise to such an arrangement. The forces between the terminal groups (methyl-,

acetyls, etc.) disappear are small in comparison with the forces of the group CH₂O. We thus have to do with real crystals (Meyer and Hengstenberg), where the greater distance between the networks is no longer manifested, owing to the irregular alternation of terminal groups, which form only isolated lattice defects; the period of identity of the CH₂O lattice proved to be equal to 17.35 Å.

From the numerous parallels between polyoxymethylene and cellulose one may conclude that the latter also possesses a highly polymerized molecule. According to Staudinger, polymerized formaldehyde may be taken as a model of cellulose, and the latter may be regarded as the product of polymerization of some unknown basic substance; we must assume—this follows from previous work—that in the \((\mathrm{CH}_2\mathrm{O})_x\) network the forces in one direction have the character of chemical forces and thus are sufficient for the formation of long molecules.

For a substance considerably more complex, the existence of chemical bonds in different directions is entirely possible—bonds of such a kind that the whole crystallite becomes a sort of gigantic molecule.

As regards the question of determining the index of polymerization, so important from the chemical and biological point of view, at present its final solution by means of X-ray spectrography is still impossible; nevertheless, knowledge of the dimensions of the elementary cell, on the one hand, and of the primary groups and colloidal particles, on the other, should lead to the solution of this problem.

It should be pointed out that between the results obtained by physical and chemical methods there is a constant difference—a difference that is rooted in the fact that the two methods essentially deal with different elements, and also in the fact that we still do not know precisely what physical meaning the expression “index of polymerization” has.

BIBLIOGRAPHY

Application of X-rays to the study of colloids

1. Ambronn, Koll. Zeit., 6, 144, 1910; 13, 103, 200, 1913; 8, 80, 90, 73, 1916; 20, 173. 1917.

2. Zsigmondy, Kolloidchemie, Leipzig, 1920.

3. Sherrer, see Kolloidchemie by Zsigmondy, p. 387, Leipzig 1920.
   Determination of particle size in gold sols.

4. Herzog, Svensk Pappers Tidning, No. 8, p. 19, 1927. Study of cellulose by means of X-rays. Journ. of Phys. Chem., 30, 457, 1926.
   The nature of the structure of cellulose and its significance in chemical transformations.

5. Haber, Ber. d. deutsch. chem. Ges. 55, 1717, 1922. See also Böhm and Niclasson, Zeit. f. anorg. Chem., 132, 1, 1923.

6. Rinne, Fortschr. d. Min. Krist. und Petrogr., 3, 159, 1923.

7. Katz and Mark, Phys. Zeit., 25, 321, 431, 1924; Zeits. f. Elektrochem., 105, 1925.
   Katz, Naturwissenschaften, 3, 316, 1924; 4, 154, 1925.

8. Ott, Phys. Zeit., p. 174, 1926.

9. Ott, Naturwiss., 14 320, 1926. Size of rubber molecules.

10. Staudinger, Johner, Signor, Zeits. phys. Chem., 126, 425, 1925.

11. Mie and Hengstenberg, Zeit. phys. Chem., 126, 425, 1927.
    Hengstenberg, Ann. d. Phys., No. 18, 1927.

12. Ott, Helv. Chim. Acta, 5, 1, 300, 1928.

Other bibliographic references

Study of colloids by means of X-rays

Katz and Sammwell, Naturwiss., H. 30, S. 592, 1929. New views on the form of the cellulose molecule and its polymers.

Herzog and Weissenborg, Koll. Zeit. 46, 277, 1928. Thermal, mechanical, and roentgenographic analysis of cellulose.

Katz, Zeit. f. phys. Chem. 125, H. 5/6, 1927. Influence of polymerization on roentgenograms.

Herzog, Koll. Zeit., p. 345. Dec. 1925. Application of X-ray spectrography to the study of colloidal systems.

Kurt Meyer, Zeit. f. angew. Chemie, No. 34, 1928. New ways in the study of the structure of organic compounds and in the investigation of highly polymerized compounds.

Clark, Applied X-Rays, p. 174.

Freundlich, Zeit. f. angew. Chem., p. 1329, 1927. Structure and formation of colloidal particles.

Mark, Koll. Zeit., 38, 351, 1926. Experimental methodology of the roentgenography of colloidal systems.

Mark, Die Verwendung der Röntgenstrahlen in Chemie und Technik, Bredig.

Clark, Ind. and Eng. Chem., Febr. 1929. Application of X-rays to the study of polymerization problems.

Trillat, Rev. Coll., mars, avril, septembre 1928; Journal de Physique, Octobre, 1928.

Structure of Colloids

Duclaux, 2-e Congrès Solvay, Bruxelles, avril 1925; Revue des Colloïdes, No. 61, p. 9, 1929. Structure of colloidal substances in the solid state.

Arsem, J. Phys. Chem., p. 306, mars 1926.

Obrist, Rev. gen. Coll., août 1927. On phenomena accompanying mastication.

Andrejeow, Koll. Zeit., Sept. 1927. A new method for studying colloidal systems.

Kuhn, Koll. Zeit., p. 365, 1925. Methods for determining the size of colloidal particles.

Sheppard, Nietz and Keenan. Ind. and Eng. Chem., 21, 126, 1929. The supermolecular state of polymerized substances.

Investigation of Cellulose and Its Derivatives

Several years ago, Herzog and his collaborators, Katz, Meyer, Clark, Scherrer, and Trillat, carried out a large number of investigations on cellulose and its derivatives by means of X-rays (see the bibliography).

In view of the importance of the results obtained, in this chapter we shall give a detailed résumé of these works, which are of interest both from the theoretical and from the practical point of view.

I. Fibers of Natural Cellulose

Natural fibers, as well as cellulose precipitated from dispersed solutions, prove to consist of small crystals arranged more or less regularly. In its natural state (ramie, cotton, hemp fibers, etc.) cellulose consists of crystalline aggregates analogous to those found in

fibers of bark, in the coverings of seeds, and in other plant or animal tissues.

In bark fibers the crystallites are often arranged in such a way that their axes are parallel to the axis of the fiber, or at least the crystallites of one and the same layer form a definite angle with the axis of the fiber; in cotton they are arranged spirally with respect to this axis. It may be said that observations made with the aid of double refraction and explained by Nägeli’s1 micellar hypothesis or by Weier’s theories were fully confirmed by means of X-ray analysis.

Fig. 3. Schematic diagram of cellulose (after Herzog).

Diagrams obtained, for example, from a ramie fiber in a direction perpendicular to the axis of the fiber are analogous to those that would be given by a single crystal rotating about one of its axes, which plays the role of the fiber axis: they are characterized by spots lying on hyperbolas (Fig. 3) in the case of a flat plate, or on parallel straight lines in the case of a cylindrical film with the specimen at the center. The method of investigation consists in illuminating a bundle of fibers, fastened in some manner, with monochromatic X-rays (the K-α rays of copper or iron); this bundle can be placed in various positions with respect to

directions of the incident X-rays, which makes it possible to obtain various fiber diagrams.* These experiments showed that different varieties of natural cellulose (ramie, hemp, flax, wood, cotton boll, cotton, etc.) have a crystalline structure and, moreover, belong to one and the same crystalline system; only the degree of orientation changes: ramie, for example, has a very regular arrangement of crystallites along the axis of the fiber, whereas cotton, on the contrary, is much less regular (Figs. 4 and 5).

Fig. 1. Diagram of cellulose.
Fiber diagram of cellulose according to Herzog (Cu \(K\alpha\) and \(K\beta\) rays).
Fiber diagram of natural cellulose (ramie) according to Mark (Cu \(K\) rays).

The presence of veils and circles compels one to assume the presence of amorphous substances; the chemical nature of these substances is still unknown, but it may be supposed that they contain cellulose in an amorphous form, the existence of which was noted by Hess and Trogus[^2].

Thus, according to the views of Herzog, Weimarn[^3] and D’yuklo[^4], cellulose has a crystalline structure; this is a result of primary importance. But the study of X-ray photographs allows one to go much further; the number of spots (the dotted character) of the various circles, and their intensities, make it possible, with the aid of certain hypotheses—

determine the crystalline system of cellulose; this is an extremely difficult problem, quite impossible to solve in the case when only rings appear in the diagrams (the microcrystals are not oriented), and is made easier in some cases by the appearance of spots arranged partly on rings and partly on hyperbolas or parallel straight lines.

Fig. 3 presents a schematic diagram of a cellulose fiber possessing a perfect orientation of the crystallites (Herzog); much more often, however, even if the microcrystals are all oriented, only Debye–Scherrer rings are observed, more or less complete.

Fig. 5. Diagram of flax according to Herzog.

The classical Bragg formula

\[ n\lambda = 2d \sin \theta \]

(\(n\) is the order of reflection, \(\lambda\) the wavelength, \(\theta\) the value of the angle of selective reflection from planes situated at distances \(d\)) together with Polanyi’s equality (phase diagrams) makes it possible to determine the distance between the planar lattices.

Table 1 gives a summary of the principal results obtained for cellulose (Herzog).

It would be very difficult to draw a conclusion about the crystalline system of cellulose on the basis of these data alone: these measurements can rather serve as a starting point for checking the purity of a substance or for detecting a new crystalline form, which in our opinion constitutes one of the most interesting practical results.

TABLE 1

Reflection angles for interference spots

Material
Cotton	7°28′	10°15′	11°26′	17°28′
Ramie	7°20′	10°19′	11°25′	17°34′
Hemp	7°26′	10°19′	11°25′	17°32′
Flax	7°24′	10°12′	11°25′	17°36′
Bark of pink laurel	7°25′	10°19′	11°27′	17°36′
Mulberry bark	7°27′	10°15′	11°27′	17°9′
Grapevine bark	7°28′	10°18′	11°25′	17°28′
Rye straw	7°32′	10°20′	11°25′	17°32′
Animal cellulose	7°14′	10°14′	11°20′	17°18′
Cellulose (according to Ott)	7°21′30″	11°13′30″	14°58′	17°11′30″

The complete determination of the elementary cell was carried out by Herzog^5 and his collaborators, and quite recently by Meyer and Mark^6 on the basis of Polanyi’s calculations for fiber diagrams.

Indeed, X-ray photographs make it possible to calculate the lengths of the edges of the elementary crystalline cell; by this means one can find not only their ratio—which can be found for microcrystals with the aid of a goniometer—but also measure these lengths in absolute units.

These determinations are very risky and delicate in the case of powder diagrams; but if the substance has a fibrous structure, i.e. if it is formed by crystallites whose axes are parallel to the fiber axis (according to Duclaux—the structure of a “brick tube”), the determination of the edge length in the direction of this axis of orientation becomes considerably easier.

According to Polanyi, there is a simple relation between the distances of the various hyperbolas or parallel straight lines on which the spots are grouped, and the period of identity in the direction of the axis (these hyperbolas, or straight lines, are called “Schichtlinien,” Figs. 6, 3, 4, and 5).

This period of identity for the various celluloses giving fiber diagrams was initially found to be equal to 10.38 Å (Herzog). But for the complete determination of the elementary cell, two more measurements of edge lengths are necessary, which are very doubtful, since there is no

there is no way to orient the crystals in the direction of two other axes, i.e. to obtain a complete macrocrystal.

One has to resort to hypotheses based on the relations used in crystallography for determining the geometrical properties of a crystal; this relation, called the “quadratic equation of the lattice,” is obtained between the coordinates of the various periods of identity in combination with Bragg’s fundamental equation.

Fig. 6. \(O\)—the point of incidence of the primary X-ray beam; \(A\)—the specular reflection; I, II, III, IV—lines of layers; \(A_1, A_2, A_3\), etc.—positions of interference (after Herzog).

The quadratic form changes depending on the symmetry of the crystal and characterizes it; it makes it possible to explain all the phenomena of X-ray interference in a crystal and to calculate the various angles corresponding to the interferences, i.e. to assign them to a system of plane nets, or, in crystallographic terms, to determine the indices.

The quadratic form of cellulose was first determined by Polanyi \(^{7}\).

The period of identity along the fiber axis was determined, as we have already said, from the distances between the layer lines. To determine the elementary dimensions in other directions it was necessary to assume, a priori, rhombic symmetry; this hypothesis is based on data from the stereochemical structure of cellulose.

The quadratic form obtained under these conditions by Polanyi and Herzog is as follows:

\[ 4\sin^{2}\frac{\theta}{2}=0.031h^{2}+0.03923k^{2}+0.02275l^{2}. \]

This equation makes it possible to calculate the values of \(b\) corresponding to the different values of the indices \(h,k,l\); the agreement between these results and the results found for \(b\) experimentally makes it possible to judge to some extent the correctness of the hypothesis of a rhombic structure.

The calculations, carried out by Herzog for the various spots of the diagram of cellulose fiber (Fig. 3), showed satisfactory agreement with experiment and made it possible to assign the following values to the edges of the elementary parallelepiped:

\[ \begin{aligned} a &= 8.60 \cdot 10^{-8}\ \mathrm{cm},\\ b &= 7.78 \cdot 10^{-8}\ \mathrm{cm},\\ c &= 10.22 \cdot 10^{-8}\ \mathrm{cm}, \end{aligned} \]

whence the volume \(V\) of the elementary cell is

\[ V = 684 \cdot 10^{-24}\ \mathrm{cm}^{3}. \]

On the other hand, from the formula for the volume of the elementary cell

\[ V = \frac{Mn}{Nd}, \]

where
\(M\)—the molecular weight of the group \(C_{6}H_{10}O_{5}\), \(162\),
\(N\)—Avogadro’s number \(= 6.06 \cdot 10^{23}\),
\(d\)—the density of cellulose \(= 1.52\),
\(n\)—the number of groups \(C_{6}H_{10}O_{5}\) in the cell,

one can find \(n\). It turned out that \(n = 4.03\), i.e. the cell contains 4 radicals \(C_{6}H_{10}O_{5}\).

According to other authors, it should contain 2 or 6 groups \(C_{6}H_{10}O_{5}\).

Taking into account the hypotheses that underlie all these determinations, there is no need to discuss this discrepancy; the question cannot be resolved with sufficient rigor until a cellulose single crystal has been obtained, sufficient for a spectrographic investigation of its dimensions.

It should be noted that some of the interference spots cannot be identified with the values obtained on the basis of the above quadratic form;

according to Janke, if these anomalies cannot be explained by the presence of a second crystalline substance, they are caused rather by deformations of the cellulose lattice during growth.

It should likewise be noted that the diagrams of these substances are not sufficiently distinct for exact measurements; here, of course, there is a certain uncertainty, which should not be forgotten. Finally, there is a second form of the quadratic equation that gives results agreeing fairly well with experimental observations (Meyer and Mark6).

However that may be, it can be said that at present the structure of cellulose, if not determined absolutely, has nevertheless been established to a high degree of approximation, thanks to the excellent work of Polanyi, Herzog, and their collaborators.

The latest work of Mark and Meyer, concerning the question of the structure of cellulose6, seems to give an even closer solution1.

Fig. 7. Elementary cell of cellulose (after Mark). Small circles denote oxygen atoms; the hatched portions correspond to rotation by 180° relative to the unhatched ones (glucose residues).

Fig. 7 gives the structure of the elementary cell at which these latter authors arrived.

The hexagons represent “residues” of glucose (not counting the six C atoms and the hydroxyl groups). These glucose residues are arranged in chains; oxygen is included between them as points; these chains constitute the “chains of principal valences,” which, by their grouping, create a crystallite owing to the existence of association forces. In general, spectrographic investigations on the basis of certain other arguments of a chemical nature, belonging in particular to Hess5, make it possible to construct the cellulose fiber according to the following idea, which agrees sufficiently well with the representa-

by Dzochlo: on the outer parts there is an amorphous layer, more or less thin, which can be removed by weak acetic acid; inside are elongated crystals (Fig. 8), the axes of which are parallel to the axis of the thread and which can be separated from one another (Hess, loc. cit.). It is very probable that amorphous cellulose, which constitutes a kind of medium in which the crystals are found, likewise plays the role of a cement between these crystals.

Fig. 8. Diagram of a cellulose fiber.

Here we find new evidence for the existence of cellulose in two phases, which seem necessary for explaining the phenomena of swelling and dispersion.

Before concluding the study of cellulose fibers, it is not useless to point out that the results obtained with the aid of X-rays concerning the magnitude of the molecule or the value of the degree of polymerization of colloidal substances, such as cellulose, acetocellulose and nitrocellulose, rubber, gelatin, etc., differ substantially from those obtained by physical or chemical methods. In fact, the crystallographic cell is a kind of geometric function; X-rays give the dimensions not of the entire molecule, but only of the elementary cell, which for these substances is much smaller than the chemically complete molecule or micelle: the elementary constituents thus prove to be considerably simpler than what is given by investigation with the aid of colloid or organic chemistry. Thus it would be incorrect to say that the cellulose molecule consists of 4 groups \(C_6H_{10}O_5\). The complete molecule should rather be regarded either as an aggregate bound by secondary valences, or, proceeding from the assumption of periodicity of the structure within some weakly bound compound, capable of reflecting X-rays as if it were

it consisted of separate layers, similar to layers of fatty substances (Trillat¹⁶, Katz⁹). It is precisely this conception that we shall develop in the second part of this chapter; however, it is necessary first to emphasize the fundamental difference between chemical and roentgenographic results, a difference whose misunderstanding may lead to endless disputes between chemists and physicists.

II. The Effect of Chemical Treatment on Cellulose Fibers

Up to now we have dwelt on results obtained for natural, pure cellulose and on its crystalline form; X-rays likewise make it possible to study its various transformations under the action of different chemical substances. Here we shall summarize the principal investigations in this field.

a) Cellulose Hydrates. Investigations of Mercerization

As is known, if an alkaline solution is allowed to act on cellulose fiber, the fiber contracts; if this contraction is prevented by stretching, the thread becomes lustrous and forms a product that has very wide application in the textile industry (mercerization).

After thorough washing, threads treated in this way give diagrams that differ from the diagrams of the cellulose from which they were obtained. This difference is the more noticeable the more complete the mercerization. In threads mercerized without stretching, a curvature of the particles occurs, and the spots of the fiber diagrams are transformed into rather indistinct arcs of circles. By classifying the diagrams obtained, one can follow the process of gradual mercerization of cellulose (Fig. 9).

It turns out that the proper diagrams of very pure cellulose disappear for alkali concentrations equal to that which corresponds to the break in the absorption curve (Fiver and Hesser), i.e., to the formation of the complexes $(\mathrm{C}_6\mathrm{H}_{10}\mathrm{O}_5)_2\mathrm{NaOH}$ and $(\mathrm{C}_6\mathrm{H}_{10}\mathrm{O}_5)\mathrm{NaOH}$. A new interference

always occurs in the same places, independently of which alkali was used: sodium, potassium, or even lithium; this shows that the action of the alkalis can transform cellulose into isomer (Katz, Mark, and Fiver).

In the diagrams of pure and mercerized cellulose the following differences are observed (Herzog).

After treatment.      Before treatment.

Fig. 9. Change in the cellulose diagram upon mercerization (27% NaOH and washing) according to Katz.

1. The quadratic form determined for non-mercerized cellulose is suitable only as a first approximation; if one assumes that the elementary cell of mercerized cellulose contains 4 groups and has rhombic symmetry (as does cellulose), the quadratic equation obtained from the diagrams would be as follows:

\[ 4\sin^{2}\frac{\theta}{2}=0.03080\,h^{2}+0.03660\,k^{2}+0.024430\,l^{2}. \]

A comparison of the results found for fibers of pure cellulose and mercerized cellulose makes it possible to compile the following table (Herzog).

Table 2

Reflection angle \(\theta\)

Pure cellulose	\(7^\circ26'\)	\(10^\circ19'\)	\(11^\circ25'\)	\(17^\circ34'\)
Mercerized ramie (strands)	\(6^\circ8'\)	\(10^\circ\)	\(10^\circ59'\)	\(18^\circ6'\)
Mercerized (fibers)	\(6^\circ8'\)	\(10^\circ4'\)	\(11^\circ3'\)	\(18^\circ10'\)

If one compares the dimensions of the unit cell of untreated cellulose and of mercerized cellulose, it turns out that the length \(c\) (along the fiber axis) changes from \(10.22\ \text{Å}\) (pure cellulose) to \(9.88\ \text{Å}\), which corresponds to a contraction of \(3\%\) in this direction; this figure is somewhat higher at the end of mercerization. At the same time the dimensions \(a\) and \(b\) increase from 8.60 to 8.88 and from 7.78 to \(8.05\ \text{Å}\).

For the volume \(V\) of the unit cell we obtain

\[ V = 706\ \text{Å}^3, \]

which agrees well with the values obtained from the molecular weight and density \((V = 704\ \text{Å}^3)\). This volume is somewhat greater than the volume of cellulose \((V = 684\ \text{Å}^3)\).

1. On the equator, the points \(A_3\) and \(A_4\) have different intensity ratios; for mercerized cellulose these points have almost the same intensity, whereas for pure cellulose their intensities are in the ratio \(1/3\) to 5.

2. Two equatorial points, which are not obtained from the quadratic equation of cellulose, disappear after sufficiently complete mercerization.

3. On the equator a new point appears, which is located closer to the center and which cannot be explained by the quadratic form of cellulose.

Discussion of these results leads to the following two possibilities:

a) a complete change of the quadratic form,

b) anomalous interference[^4] should be attributed to the presence of a new crystalline substance.

The first hypothesis seems to be in better agreement with the experimental data; it leads to the construction of a new quadratic form characterizing mercerized cellulose, the form which we indicated above.

As for the second hypothesis, it encounters the same difficulties as in the case of pure cellulose: indeed, it is not clear why the new crystalline substance manifests itself only by one or two anomalous points and does not cause the appearance of new interference spots—

chains located on new lines (lattice rows), in the event that this new substance likewise possesses a fibrous structure.

Diagrams of mercerized cellulose are obtained whenever cellulose is made to swell. They are also obtained in the case of the disperse form from sols of cellulose and its derivatives; cellulose regenerated from various “solvents” gives diagrams of hydrocellulose.

If precautions are not taken and work is not carried out under simultaneous stretching, the fibrous structure in turn disappears, and only complete Debye–Scherrer rings are obtained, indicating the disappearance of all traces of orientation. All artificial silks based on cellulose give diagrams of mercerized cellulose (dissolution in zinc chloride and washing, etc.). Consequently, diagrams of cellulose hydrate appear whenever cellulose reaches a certain degree of swelling (Figs. 9 and 10).*

The question that now arises is to determine what causes the changes observed in the diagrams of mercerized cellulose. The results obtained (Table 2) make it possible to conclude that mercerization consists in a new arrangement of atoms within the unit cell; these modifications may be effected both by regrouping groups of atoms in the unit cell and by introducing new atoms into it. Assuming this latter case, we must note that the change produced by the intrusion of new atoms is insignificant, especially if one considers that the density remains almost constant (natural cellulose—1.58; hydrocellulose—1.52); it is precisely this, according to Herzog, that leads to the idea that during mercerization there occurs a wedging-in of atoms

* The manner in which progressive mercerization is formed can be studied by obtaining diagrams at suitably short intervals of time. The technique for obtaining such diagrams was recently proposed by Mark and Susich, 1929.

into the elementary cell, caused either by the wedging-in of chains \(C_6H_{10}O_5\) into one another, or by an internal regrouping of the groups \(C_6H_{10}O_5\).

These conclusions, purely geometrical or crystallo-

Fig. 10.

B) Oscillocellulose.
E) Acetylcellulose (maximum heterogeneous).

C) Hydrocellulose.
H) Mercerized acetate (40 and below) according to Trillat.

graphic, can be fully verified if the observed difference has a physical (mechanical deformation, for example) or chemical (new compounds) character.

Gonell’s observations\(^5\), it would seem, established the existence of a chemical process alongside mechan-

for threads mercerized with soda or treated with nitric acid.

As is evident from all the preceding considerations, the question is still not entirely clear; however, it is of great interest both from a purely scientific point of view and from a practical point of view.

b) Lignin, hydrocellulose, and oxycellulose

The investigations of Karrer^10 and his collaborators showed that a close kinship must exist between lignin and cellulose. These substances behave in such a way that they can possibly be identified from the chemical and physicochemical points of view; the difference appears in the action of agents that cause hydrolysis, such as mineral acids and enzymes. Whereas cellulose is insoluble in water, lignin is capable of giving a kind of colloidal solution in water; on the other hand, lignin is converted into sugar much more rapidly than cellulose.

These differences may be caused either by equal structure, or by different dispersion, or by a different degree of polymerization; investigations with the aid of X-rays make it possible to shed some light on these questions.

Using the Debye–Scherrer method (copper \(K_{\alpha}\) radiation), Ott^11 succeeded in showing that cellulose and lignin give different diagrams (Table 4).

Table 4.

Cellulose	Cellulose	Lignin	Lignin
\(7^\circ 21'30''\)	strong	\(5^\circ 45'\)	weak
\(11^\circ 13'30''\)	strong	\(10^\circ 06'\)	strong
\(14^\circ 53'\)	weak	\(13^\circ 42'\)	weak
\(17^\circ 11'30''\)	strong	\(17^\circ 19'30''\)	weak

Of course, this is insufficient to decide completely the question of whether this difference in the diagrams is caused by a difference in chemical structure or by a difference in crystalline structure.

Further, upon examining cellulose precipitated in a definite manner by phosphoric acid, we obtain exactly the same diagrams as for lignin. The same is true for oxycellulose prepared from viscose treated with potassium permanganate, and for hydrocellulose likewise prepared from viscose by dissolution and precipitation (Table 5).

Table 5

Cellulose precipitated with phosphoric acid		Oxycellulose		Hydrocellulose
5°48′	weak	5°48′	weak	5°48′	weak
10°06′	bright	10°09′	bright	10°09′	bright
13°42′	weak	13°45′	weak	13°42′	weak
17°19′30″	weak	17°19′30″	weak	17°21′30″	weak

The identity of the crystalline particles of the precipitated cellulose, of the precipitated oxy- and hydrocellulose, with lignin is thus fully revealed, and at the same time we find confirmation of the conception of the close kinship between lignin and cellulose; if cellulose, under the action of such diverse methods of treatment, always proves to have been brought into the form of lignin, then it must be assumed that the transformation is reduced to a simple transition from one form into another, modified one; an explanation by means of chemical rearrangement would be little intelligible.

From these investigations it follows, finally, that the structural crystalline particle is one and the same in hydrocellulose, oxycellulose, and lignin alike.

Herzog, who also studied these questions, justly observes that one should distinguish reactions which occur in a homogeneous medium from those which occur in a heterogeneous medium: in the first case dissolution precedes the reaction; in the second case local chemical rearrangements are obtained (a topochemical reaction, according to Kohlschütter) without change in the form of the fibers. This latter process is possible thanks to the presence of small, strongly elongated crystallites, lying—

…together and capable of swelling; the crystalline grains thus change little by little, beginning from the outer parts toward the inner ones.

The formation, from hydro- and oxycellulose, of a mixture in which part of the cellulose has been chemically transformed and part has remained unchanged ought, according to this author, to have yielded amorphous products, consequently producing no sharp interference of X-rays.*

A little further on we shall give diagrams of the crystals which we obtained for these substances and which show, on the contrary, that these substances are fully crystalline.

c) Aceto- and nitrocelluloses

For a long time nitro- and acetocellulose were considered to be substances that were completely amorphous; only quite recently has it proved possible to obtain crystalline X-ray diagrams for them.

It is known that films of nitrocellulose, subjected to strong stretching, possess double refraction; Ambronn and Duclaux also found birefringence in preparations of nitrocellulose and acetocellulose prepared in a special manner.** Investigations by means of X-rays have shown that the crystalline structure of these substances can be detected if they are prepared specially, while preserving the fibrous structure,\(^{12}\) i.e. by reaction in a heterogeneous medium not accompanied by dissolution. In this way fiber diagrams are obtained, on the basis of which Herzog, Jäncke, and Naray-Szabo\(^{13,24}\) were able to characterize these substances (Figs. 11 and 12).

In the main, threads of acetocellulose and nitrocellulose give fiber diagrams different from the fiber diagrams of cellulose and characteristic for each of the substances.

The various angles of reflection are reproduced exactly for nitrocelluloses containing different percentages of nitrogen [from

* Herzog, Svensk Pappers Tidning 8, 1927.
** See also Herzog and Jäncke\(^{23}\), Ueda\(^{24}\), Mark and Susich\(^{25}\), Susich and Naray-Szabo\(^{26}\), Trillat\(^{22}\).

6.91% (mononitrate) to 11.08% (dinitrate) and higher (trinitrates)], the thread diagrams are distinct; nevertheless it turns out that the number of spots is considerably greater for nitrocelluloses with 12.8% than for nitrocelluloses with 6.9%, 9.46%, and 11.8% nitrogen.*

Here it is also possible to calculate the quadratic form corresponding to the observed diagrams. For trinitrocellulose, Narai-Szabó, assuming rhombic symmetry, found that one unit cell also contains 4 groups of \( \mathrm{C}_6\mathrm{H}_{10}\mathrm{O}_5(\mathrm{NO}_3)_3 \).

The dimensions of the unit cell of these bodies prove to be approximately as follows (Herzog).

Table 6

Nitrocellulose (in thread form)	Acetylcellulose (in thread form)
\(a = 10.1\ \text{Å}\)	\(a = 9.2\ \text{Å}\)
\(b = 8.6\ \text{Å}\)	\(b = 7.1\ \text{Å}\)
\(c = 10.8\ \text{Å}\)	\(c = 9.8\ \text{Å}\)

From this we conclude that the elementary volume in the first case is equal to \(935\ \text{Å}^3\), and in the second to \(636\ \text{Å}^3\)—values very close to the value of the elementary volume of cellulose.

It should be noted that the X-ray photographs of cellulose disappear entirely or almost entirely even if only part of the substance has been transformed. This, as has already been noted, occurs because the reaction is heterogeneous: the action on the crystal takes place in successive layers, beginning from the outer parts of the thread toward the inner parts; the scheme

* These results were recently obtained by Mark and Susich\(^{25}\), as well as by Susich and Narai-Szabó\(^{26}\), who found that nitrocelluloses and acetylcelluloses are mixtures of trinitro- and triacetylcellulose with pure, unchanged cellulose. Objections to these views are raised by Meyer and Kreck\(^{27}\), Brunschwig\(^{28}\), and Docq and Nodzu\(^{29}\), who support the hypothesis that the substances under investigation are mixtures of compounds with different percentage contents of nitrogen or acetyl acetic acid.

of the cellulose thread, which we gave above, makes it possible to understand this mechanism.

Network planes of cellulose compounds are formed very rapidly; moreover, acids, penetrating along the cracks or gaps separating cellulose crystals, cause swelling and disintegration of the cellulose, which to some extent may explain the weakening or disappearance of the spectra of the latter.

Let us now turn to the much more important case of acetyl- and nitrocelluloses obtained by homogeneous reactions. There are at present very few works in this field; the authors note that in this case rings of amorphous substances are obtained—rings whose interference nature is still being debated; nevertheless, it turns out that it is precisely from this side that we may expect to obtain results of the greatest interest from the point of view of colloidal structure.

Here one may again cite a work by Ott,^14 in which an attempt was made to elucidate the crystalline character of cellulose triacetate prepared by Karrer;^16 working with strongly compressed specimens, this author showed that the diagrams he obtained resemble the diagrams of crystalline substances composed of extremely small crystals. The results found are presented in the following table.

Table 7

Diameter of the rings for the working distance of 51 mm (from the plate)	Angles
14.6 mm	4° 4′30″
19.3 ″	5°21′30″
24.0 ″	6°37′
32.0 ″	8°42′30″
42.6 ″	11°20′
52.0 ″	13°30′30″

The figures, in our opinion, are very approximate, since they were obtained for broad rings and very indistinctly

…photographs. To say, on the basis of these data, that the substance is crystalline would be a somewhat bold extrapolation. Undoubtedly, part of the acetocellulose investigated is crystalline, but the greater part of the substance is in any case in an amorphous state.

Other authors have sought a solution to this problem by attempting to obtain microscopic crystals of acetocellulose; these excellent investigations were carried out by Hess^25 only for acetocellulose; crystallization of nitrocellulose has still not been achieved.

As Hess showed, it is in fact possible to obtain crystals of cellulose diacetate and triacetate of macroscopic dimensions. This crystallization must proceed extremely slowly from benzene + alcohol for the diacetate and from carbon tetrachloride for the triacetate. Cellulose triacetate crystallizes as needles up to a centimeter long, thus repeating the form of threads; these needles are unstable and, if left standing, gradually transform into good tetrahedral crystals. These crystals are hard and can be ground into powder; they contain solvent and deteriorate in air. Specimens obtained in this way are not entirely amorphous and sometimes give X-ray spectra (long exposure).

An X-ray study of large crystals yielded very strange facts: indeed, the lines obtained are either very weak or do not appear at all, which contradicts everything known about the diffraction of X-rays by crystals. The explanation of this phenomenon is not yet fully known: it is connected with the swelling property of these substances, by virtue of which they always retain solvent; consequently, molecular motion may exist within the crystal, disrupting the lattice structure; it is also possible that this effect is caused by the presence of stresses. Below we shall indicate the results at which we arrived in our investigations of these substances.

Stretching of colloidal gels of aceto- and

nitrocellulose. The author recently showed (Trillat),^22 that, if films of nitrocellulose or acetocellulose are strongly stretched (up to 300%), the structure of these films passes from the original amorphous state into a state very close to crystalline. Indeed, when diagrams are taken in three mutually perpendicular directions, it is observed in two of these directions that the rings are deformed into ellipses and become very intense in the equatorial and polar parts. These intensifications coincide exactly with the positions of the most intense spots of crystalline aceto- or nitrocellulose (fiber diagrams); stretching thus oriented the molecules, and they became arranged at the lattice nodes, with the same lattice as that of these substances crystallized in the fibrous state.

Results of a similar kind have been published by Eda (Heda, Z. Phys. Chemie, vol. 133, nos. 5/6, 1928) for celluloid, by Herzog and Jancke (Herzog und Jancke, Z. f. Phys., vol. 52, nos. 11 and 12, 1929) for mercerized cellulose, and by Mark and Susich (Susich) (Z. f. phys. Chemie, vol. 4, no. 6, 481) for cellulose.

These phenomena explain both the mechanical properties of rolled films (resistance to tearing, etc.) and certain physicochemical properties, such as the fixation of dyes. Indeed, if the film is stretched, small quantities of coloring substance are retained on its surface owing to the orientation of active groups, such as the OH group.

III. Cycle of cellulose transformations

The author carried out a series of investigations^16 in order to trace the various stages of cellulose transformations under conditions of a homogeneous or heterogeneous medium; these investigations led precisely to a strict separation of cellulose acetates having an amorphous and a pseudoamorphous structure.

The method of investigation consists in the use of radiation.

copper; a special device makes it possible to investigate the powder or the product under study without enclosing it in a celluloid or glass tube (sheath), which always gives its own interfering diffraction rings.

The series of transformations studied may be represented by the following table:

	Cellulose	(Linter C) (X-rays) Miles method: acetic acid + sulfuric acid
	↓
	Hydrocellulose	(X-rays)
washed and dried		not dried
↓		↓
Heterogeneous phase		Homogeneous phase
Acetic anhydride + benzene + sulfuric acid or catalyst		Acetic anhydride + catalyst (sulfuric acid)
↓		↓
Acetate with maximum acetylation, retaining the form of the thread (X-rays)		Acetate with maximum acetylation in collodium + acetic anhydride.
↓		↓
Dissolve: 1) in acetic acid and precipitate with water 2) in carbon tetrachloride and precipitate with alcohol		Subject to hydrolysis, 10–20% solution in water. During hydrolysis, with increasing time, acetates precipitate, all more and more deacetylated (10·acetates, whose percentage contents vary from 59 to 30) (X-rays)
↓	↓	↓
In this way a homogeneous product is obtained with maximum saturation with acetic acid, which can be subjected to hydrolysis and precipitated with water (X-rays)		Action of alkali ↓ Cellulose (Hydrocellulose) (X-rays)

The results obtained may be briefly summarized as follows.

1. Cellulose (cotton linter) gives rather indistinct diagrams of the crystalline structure of the fibers; narrow rings can be detected, corresponding to very small lattice distances of the order of (1, 2 Å) (Fig. 10).

2. Oxycelluloses and hydrocelluloses give very good—

still diagrams of crystalline structure, identical with diagrams of cellulose; the orientation of the crystals disappears in almost all cases (regular rings). This shows that these substances are formed mainly from the same elements as cellulose itself, which agrees with chemical observations (Fig. 10).

1. Hydrocelluloses give diagrams of crystalline structure different from the diagrams of cellulose; the diagrams remain the same for regenerated products (such as denitrated nitrocellulose, deacetylated cellulose acetate, etc.) prepared from the homogeneous phase. This result corresponds to an altered form of cellulose (undoubtedly by physical agents) (Fig. 10).

2. Cellulose treated with alkali has diagrams rich in rings; these diagrams are analogous to those of hydrocellulose, but the lattice is somewhat enlarged (swelling); in addition, here one can detect the formation of compounds of cellulose with alkalis in stoichiometric proportions (Fig. 10).

3. Cellulose acetates obtained in non-dissolving media (threads) possess a very distinct crystalline portion scattered within the amorphous phase. Their dissolution and conversion into homogeneous acetates leaves this structure unchanged for members with a high percentage content of acetic acid. As hydrolysis gives products with an ever decreasing content of acetic acid, the appearance of the diagrams changes; the crystalline portion gives way to the amorphous phase. The rings have a structure that likewise changes with the percentage content of acetic acid; the principal ring of the amorphous phase corresponds in position to the rings of the crystalline phase, which indicates a close relationship between the crystalline and amorphous phases; the former is undoubtedly inherent in a quite definite substance (triacetate) (Fig. 10).

4. It proved possible, thanks to microphotometry, to trace changes in the structure of the rings in the course of acetylation. It was observed that the principal ring corresponds to an intermolecular distance of the order of 5.2 Å, and the outer one—to a distance-

of the order of 2 Å; at the moment of transition into the dissolved state (in acetone) the crystalline part disappears, and the rings become broader—this means that the molecules were arranged in a more irregular manner and more randomly. Further, as the percentage of acetylation decreases, the molecules are arranged closer to one another, and the inner ring becomes sharper, while the outer one disappears; this structure is retained up to the most highly hydrolyzed acetates (Fig. 10).

1. A hypothesis has been put forward for the structure of solid colloidal gels formed, for example, by cellulose acetates; according to this hypothesis, the molecules must be arranged with a certain regularity, just as is assumed for liquids. In the case of a colloid, the medium has an extremely high viscosity and offers resistance to molecular motion.

2. Finally, the study of the diagrams makes it possible to accept or reject the results of chemical analysis and therefore provides a very interesting means of control over the manufacture of these substances.

IV. Determination of the size of the particles of cellulose and its derivatives

In order to complete the study of cellulose, we shall also indicate how it is possible to determine, even if only approximately, the size of the crystallites of cellulose and its derivatives.

We have already seen that the elementary cell of these substances can be determined. We have said that this elementary cell has chiefly a geometrical meaning. By superposing such cells one reproduces, as we know, a crystal. In cellulose these crystallites are too small to be called crystallites: the question that now arises is the determination of their average dimensions. This determination can be made on the basis of the work of Scherrer, who established the relationship between the width of interference lines or spots and the dimensions of the particles.

This method was used by Herzog* to determine the dimensions of crystallites in konofil fiber; he found two values, 117 Å and 66 Å (Herzog^17, Parray–Dzabo^13).

It turned out that, in the colloidal state, the dimensions of the particles are the same as in these crystallites. From this one may conclude that dispersion upon transition to the colloidal state consists only in the separation of the crystallites.

Fig. 11. Schematic diagram of nitrocellulose (12.5% bound N) according to Parray-Dzabo and Sponzu.
Obtained from the initial substance—nitrated ramie.

Fig. 12. Phase diagram of acetylcellulose (37%) according to Parray-Dzabo and Sponzu.
Obtained from the initial substance—acetylated ramie.

In fact, the diameter of the colloidal particles in konofil fiber treated with nitric acid, calculated from the diffusion coefficient by the formulas of Einstein^18 or Eiler and Ogalm^13, is 74 Å; in the solid state, for these same particles, if their dimensions are investigated from the width of the interference lines, 100 and 58 Å are obtained. The dimensions of the crystallites of colloidal threads, determined by the same method, are 117 and 66 Å. These results po-

* See also Meyer’s memoir^19.

show equally (Herzog) that chemical transformations take place inside the crystallites without their decomposition into isolated groups \(C_6H_{10}O_5\).

Thus it proves possible to determine the magnitude of cellulose crystallites from the sizes of colloidal particles in solutions of nitrocellulose.

Treatment of cellulose with such reagents as acids or strong alkalis causes a decrease in the sizes of the particles in solutions of nitrocellulose; the size of the particles of mercerized viscose after nitration approximately corresponds to the decrease in size that occurs during the phenomenon of ripening, which takes place in the manufacture of mercerized viscose.

As an example we shall dwell on the results obtained by Narai–Szabo (loc. cit.), on the one hand, and by Krüger, on the other,—by the method of X-ray diagrams and by determining the diffusion coefficient according to Euler’s formula—results which differ slightly from the data given above.

Table 8

Nitrocelluloses	Particle size according to X-diagrams	Particle size according to diffusion coefficients
Ramie	130 Å	82 Å
Flax	90 Å	66 Å
Hemp	86 Å	74 Å

Thus these investigations seem to show that the number of radicals \(C_6\) contained in one crystallite does not change, despite chemical transformations and the transition to the disperse state (colloid). The forces that hold the elements of the crystal together exist, despite chemical transformations, almost in the same way as in the benzene molecule, in which the joining of hydrogen atoms with other atoms or radicals is possible without destruction of the carbon ring. This picture makes it understandable why some chemists regard cellulose crystallites or colloidal particles of the same magnitude as the molecule of cellulose itself, despite the fact that these

representations contradict the very meaning of the word “molecule.” Conclusions of this kind are at present somewhat premature, but it is precisely by these methods that one can most likely judge their correctness and thereby bring clarity into our knowledge of cellulose and its derivatives (see Meyer ⁶).

V. Artificial silk and fibers used in the textile industry

All artificial silks, with the exception of silks treated with acetic acid, give X-ray photographs of crystalline bodies. These diagrams consist of interference bands and rings; measurements show that the diagrams of artificial silks correspond to the diagrams of mercerized cellulose in everything concerning the position and intensity of the interference maxima; thus the crystalline substance of mercerized cellulose is contained in artificial silks.

The difference between diagrams obtained by different methods consists only in the greater or lesser size of the sectors into which the arcs of the rings break up, i.e., in a more or less regular arrangement of the crystallites with respect to the axis of the thread. Of course, there is some difference in the sharpness of the interference rings, as well as in the sizes of the particles.

Below are the results obtained for several artificial silks (Fig. 13).

a) Cuprammonium silk

Primary material . . . . . . .	Diagrams closest to fiber diagrams, weak conversion of points into lines
Primary material: cellulose.	Points are more pronounced in lines than in the preceding case
Artificial . . . . . . . . .	The diagram is a ring with weak intensifications where points would appear under ideal orientation

b) Fibers of artificial viscose

Silk obtained by the usual method or with the aid of centrifuges	Ring diagram, in many cases with a weak orientation effect
Viscose	The points degenerate into bands

c) Nitrocellulose silks (denitrated)

Obtained by the dry method	Ring diagrams with a noticeable orientation effect
From wet fibers	The same

d) Silks with cellulose acetate (or nitrocellulose)

Silk treated with acetic or nitric acid	Diagram of an amorphous body; there are no lines, only circles around the center

Other natural fibers, changing their form like silk and wool, were also studied and gave a diagram of crystalline substances.

From these results it follows that, depending on the process of fiber manufacture, the fibers may consist either of irregularly arranged crystallites, or of regularly arranged crystallites, or of colloidal micelles without any preferential orientation. It turns out that, for viscose silk, the orientation effect disappears under prolonged preliminary treatment if the finally obtained thread is not stretched in the wet state; the best orientation is obtained if the silk is made from young viscose. The strongest orientation is obtained for cuprammonium silk after treatment by stretching.

As for nitro-silk, or cellulose acetates not denitrated or not freed of acetic acid, they give, as the author has established, the diagram of amorphous bodies, which, however, is of interest from the point of view of intermolecular distances and the quantities of acid present in the bound state. In the process of preparing yarn by drawing, an intensification of the circles in the equatorial direction is obtained (Fig. 13); thus in substances of this kind it is possible to induce a fairly strong orientation. The resulting structure approaches one in which the crystallites are arranged along a certain direction.

The great interest of these investigations is obvious. In fact, in this way a quantitative assessment becomes possible of the phenomenon of orientation, which is directly connected with a large number of other properties, such as, for example, tensile strength, water absorption, dyeing, etc. These results make it possible to indicate in what direction the treatment process should be changed in order to obtain the required qualities.

Viscose silk (DuPont)  Cellophane  Acetate silk (Oxford)

Cellulose acetate not drawn  Acetate silk (Dreyfuss)  Natural silk

Fig. 13. Diagrams of artificial silk (according to Mark).

What, then, is the actual cause of the formation of this fibrous or oriented structure? According to Herzog, the colloidal particles (primary particles) contained in the dissolved state in the spinning dope gather into agglomerates during coagulation, and each particle is thus transformed into a cellulose crystal. The only cause that can produce orientation of the crystals during the formation of the thread is stretching. It acts on the colloidal particles during crystallization in such a way that a very high rate of crystallization arises in the direction of the fiber. In contrast to this, when a solid fiber is stretched, or a fiber that has already been finally treated, most likely in this—

in the particles themselves, which form the thread, sliding occurs in the direction of the thread during the agglomeration of colloidal particles or crystallites.*

It may be assumed that this first case is realized in the process of preparing yarn by drawing (cuprammonium silk), whereas the second case predominates in the manufacture of viscose; however, these two processes cannot be strictly differentiated from this point of view.

Apparently, a phenomenon analogous to that which takes place in obtaining yarn by drawing also occurs in the formation of natural fiber: thus there must exist a colloidal solution of cellulose (or a solution of a colloidal substance yielding cellulose in the process of fiber formation). From these particles there is formed an aggregate of oriented crystals under the influence of forces analogous to tensile forces. The second hypothesis consists in the supposition that the crystallites are formed from a crystalline solution; agglomeration and orientation thus occur very rapidly and successfully under the influence of this drawing or of some other causes producing orientation.

Dyeing of cellulose and its derivatives

The dyeing of fibers by salts was studied by Bihon²¹ with the aim of investigating the still so little known degree of fixation of coloring substances. The X-ray diagrams obtained by this author make it possible to draw the following conclusion.

1. Dyeing by means of such elements as gold, silver, selenium, tellurium.** Dyeing occurs owing to an absolutely regular distribution of small submicroscopic crystals within the thread. In some cases (Au, Ag), however, side by side with this regular distribution, partial orientation appears.

* An explanation of mechanical deformations in a crystalline thread was given by Mark.

** By impregnating the fiber with a solution of a metal salt and subsequent reduction.

1. In threads colored gray by mercury, the metal is in the liquid state.

2. With iodine, which seems to be present in an absorbed state, the roentgenograms of this latter metalloid do not appear.

3. Dyed preparations obtained with organic dyes do not give the interference rings of the coloring substance, even when the latter themselves produce them. If a thread is dyed with lead salts of coloring substances, it is observed that their interference properties likewise disappear; here, too, it appears, we are dealing with absorption or else with dissolution of the micelle surface.

4. In the process of dyeing, the size of the crystallites of the thread changes owing to coagulation or crystallization; the width of the interference bands makes it possible to estimate these changes.

An increase in the size of the thread crystallites is usually observed in baths containing hot salt solutions. Hot baths containing only the coloring substance have almost no effect.

It seems that here, too, roentgenographic study has brought some clarity to the phenomena of dyeing threads; of course, the phenomenon of preferential orientation must play a significant role here, and it is precisely in this direction that new possibilities are opening up. In fact, orientation is caused by the preferential arrangement of certain chemical groups; if these groups have an affinity for the coloring substance, absorption becomes more significant; thus it was observed that threads or films of cellulose acetate, prepared by stretching, are dyed much better than unstretched ones.

In the same way, other physicochemical properties (resistance, permeability, etc.) also prove to be altered. A complete study of these phenomena of orientation is of great importance for a large number of problems of a scientific and technical character.

Bibliography

Study of Cellulose and Its Derivatives

1. Naegeli, Sitzungsber. Akad. Wiss. München, 9, 389, 1879.

2. Hess und Trogus, Ber. der Deutsch. Chem. Ges., 8, 1982, 1928.

3. Weimarn, Zsigmondy Festschrift, 1927; Koll. Zeit. 42, 134, 1927.

4. Duclaux, 2-e Congrès Solvay, Bruxelles, p. 91. Structure of colloidal substances in the solid state.

5. Herzog, Svensk. Pappers Tidning, 8, 1927. Investigation of cellulose with the aid of X-rays.

Herzog, Journ. Phys. Chem., 30, 457, 1926. The nature of the structure of cellulose and its significance in chemical transformations.

Herzog, Pulp and Paper Mag. Can. 24, 821, 1926. Investigations of cellulose with the aid of X-rays.

Herzog, Cellulosechemie 6, No. 3, 1925. Probable hypotheses concerning the structure of cellulose.

Herzog, Papier-Fabrik, 24, 137, 1926. Progress in the study of fibers.

Herzog und Gonell, Koll. Zeit. 35, No. 201, 1924; Cellulosechemie, 7, 26, 1926. Microscopic structure of fibers.

Herzog und Jancke, Zeit. f. Phis., 49, 27, 1928. X-ray observations on cellulose.

1. Meyer und Mark, Ber. der Deutsch. Chem. Ges., p. 593, 1928. On the structure of the crystalline part of cellulose.

Meyer, Zeit. f. angew. Chem., No. 4, 1928. New paths in the study of organic structures and in the investigation of high-polymer compounds.

1. Polanyi, Naturwiss. 9, 288, 337, 1921.

2. Hess, Ambronn Festschrift, p. 93. On the question of cellulose.

Hess, Zeit. f. angew. Chem., 37, 792, 993, 1924; Cellulosechemie, 5, 115, 1924; 6, No. 3, 1925; Pulp Paper Mag. Can., 23, 795, 1925. Recent results of cellulose investigations.

Hess, Naturwiss. 14, 435, 1926; Cellulosechemie, 7, 174, 1926. The latest results of cellulose investigations in the light of Nägeli’s micellar theory.

Hess, Papier-Fabrik, 23, 327, 1925. Report on the chemistry of cellulose.

1. Katz, Cellulosechemie, 6, No. 3, 1925. Results of investigations of cellulose with the aid of X-rays, showing that celluloses exist with various degrees of polymerization.

Katz, Cellulosechemie, 6, No. 3, 1925. Results of X-ray investigations of cellulose and of alkali adsorption during the swelling of cellulose under the action of various alkaline media.

Katz, Cellulosechemie, 7, 136, 1926. Comparisons of the heat evolution that takes place during swelling and mercerization of cellulose with the results of adsorption experiments and X-ray spectroscopic observations.

Katz und Vieweg, Zeit. f. Elektrochemie, 35, 157, 1925; Cellulo-

sechemie, 6, No. 8, 1925. Comparison of X-ray spectrographic observations of the absorption of alkalis during the swelling of cellulose in aqueous and alcoholic solutions of soda.

Katz und Mark, Phys. Zeit., p. 431, 1924. Investigations by means of X-rays of the swelling of certain substances that give diagrams under the action of X-rays.

Katz und Mark, Zeits. f. Elektrochem., 31, 105, 1925. Radiogram of cellulose hydrates. The form which it assumes during experiments with regeneration.

1. Karrer, Kolloidforschung in Einzeldarstellungen, Zsigmondy. 1925. Introduction to the chemistry of polymeric coal hydrates.

2. Ott, Phys. Zeit. p. 174, 1926. X-ray investigations of high-polymeric substances for the purpose of determining their molecular weights.

3. Hess und Schultze, Naturwiss., 13, 1008, 1925; Cellulosechemie, 7, No. 2—3, 1926. Crystalline acetylcellulose.

Hess, Schultze und Messmer, Liebigs Ann. Chem., 111, 268, 1925; Cellulosechemie, 6, 196, 1925. Crystalline acetylcellulose.

1. Herzog und Naray-Szabo, Zeit. f. Physl. Chem. (Cohen Festband), 1927.

Herzog, Svensk Pappers Tidning, 30, 231, 1927.

Jancke, Koll. Zeit., 42; 1927. X-ray observations on one technical specimen of acetylcellulose.

1. Ott, Helv. Chim. Acta, 9, 2, 1926. Demonstration of the crystalline character of cellulose.

2. Karrer, Polymere Kohlenhydrate, p. 176, Leipzig, 1925.

3. Trillat, C. R. Acad. Sc., p. 859, 1928. Study of cellulose and its acetates by means of X-rays.

Trillat, Rev. gén. des Colloides, No. 53, 57, 1928; No. 54, 89, 1928. Investigations of cellulose and its derivatives.

1. Herzog, Svensk Pappers Tidning, No. 8, 19, 1927. Investigations of cellulose by means of X-rays.

Herzog, Journ. of Phys. Chemistry, 30, 466, 1926. The nature of the structure of cellulose and its significance in chemical transformations.

1. Einstein, Ann. Phys. (4), 19, 303, 1906.

2. Oeholm, Medd. Vetenskaps Nobel Institut, 2, 23, 1912.

3. Herzog und Gonnell, Koll. Zeit., p. 201, 1924. On the structure of artificial silk.

Herzog, Kunstseide, J. Springer, Berlin, 1927.

Herzog, Zeit. f. angew. Chemie, 41, 531, 1928. On the chemistry and physics of artificial silk.

1. Bion, Helv. Chim. Acta, 10, 1, 1928. X-ray investigations of dyed cellulose. Communication on the theory of dyeing.

2. Trillat, C. R. Acad. Sc. 188, 1246, 1929; J. d. Physique, oct. 1929. Phenomena of orientation and pseudocrystallization occurring under the action of stretching of colloidal gels.

1. Herzog und Jancke, Zeit. f. Phys., 52, H. 11—12, 1929. Studies of deformation in fibrous substances.

2. Ueda, Zeit. f. Phys. Chem., 133, H. 5/6, 1928. X-ray studies of cellulose.

3. Mark und Susich, Zeit. für Phys. Chem., 4, 431, 1929. Structure of the crystalline part of cellulose.

4. Naray-Szabo und von Susich, Zeit. f. Phys. Chem., 134, H. 3/4, 1928. Roentgenograms of nitrocellulose and acetylcellulose.

5. Miles und Craik, Nature, p. 82, 1929. Composition of nitrocellulose.

6. Brunswik, Zeit. ges. Schiess. und Sprengstoff, 23, 337, 1928. Nature of nitrocellulose.

7. Duclaux et Nodzu, Rev. des colloïdes, No. 66, 241, 1929. Methods of fractionating cellulose esters.

Other bibliographic references.

Hydro-, oxy- and alkali-cellulose

Herzog, Koll. Zeit., 39, 98, 1926; Cellulosechemie, 7, 148, 1926; Papier Fabrik, 24, 226, 1926. Swelling of cellulose.

Herzog und Krüger, Naturwiss., 13, 1040, 1925; Cellulosechemie, 7, 13, 1926. Depolymerization or dispersion of cellulose.

Hess, Papier-Fabrik, 23, No. 9, 1925. Zeit. Elektrochem., 31, 1925; Cellulosechemie, 6, No. 12, 1925. Hydro- and oxycellulose. Do chemical changes in the grouping occur during mercerization?

Hess und Schultze, Lieb. Ann. Chemie, 450, 1926; Cellulosechem., 7, Jan., 1927. Composition of cellulose.

Heuser, Niethamer und Bartunek, Cellulosechemie, 6, 1925. Febr., 1925; 7, Dec., 1926.

Kruger, Papier-Fabrik, 23, No. 48, 1925. Magnitude of the particles of cellulose; of wood.

Micheel und Reich, Lieb. Ann. Chem., 450, 59, 1926; Cellulosechemie, 7, Jan. 1927. Recognition of foreign substances in cellulose fiber.

Pringsheim, Leibowitz, Schreiber, Karsten, Lieb. Ann. Chem., 448, 1926; Cellulosechemie, 7, Sept. 1926. Composition of cellulose.

Möhring und Reix, Koll. Chem. Beihefte, 23, 1926; Cellulosechemie, 7, Dec. 1926. Double refraction of fibers of natural cellulose and chitin.

Bergman, Herzog, Jancke, Naturwiss., H. 22, 464, 1928. X-ray studies of cellulose anhydride.

Katz und Hess, Zeit. f. Phys. Chem., 122, 1926. On the swelling and mercerization of natural fibers in nitric acid.

Sponsler, Ind. Eng. Chem., 1060, 1928. Structure of cellulose fibers with the aid of X-rays.

Katz, Zeit. f. Phys. Chem., 124, H. 5/6, 1927. On the roentgenogram of Gladstone’s alkali-cellulose.

Herzog, Ber. d. Deutsch. Chem. Ges. H. 2, 600, 1927. X-ray photograph of hydrocellulose.

Hess und Katona, Ann. Chem. 455, 1927. Oxycellulose.

Clark, Lanyon, Freundenthal, Kulp. See Applied X-Rays, p. 196.

Hess, Zeit. Elektrochem, No. 11, 1925. Note on Heuser’s work on the depolymerization of cellulose.

Herzog und Jancke, Zeit. angew. Chem, 34, 385, 1921. Study by means of X-rays of organic compounds with high molecular weights.

Herzog und Kruger, Koll. Zeit., 39, 250, 1925; Cellulosechemie 7, 149, 1926. Experiments on the diffusion of cellulose solutions in copper-ammonia solutions.

Hess, Cellulosechemie, 7, No. 11, 1926. Dissolution and degradation of cellulose. Naturwiss., 12, 1150, 1924; Cellulosechemie, 6, No. 3, 1925. On the capacity which cellulose possesses, in the solid or dissolved state, for molecular reactions, independently of the degree of dispersion.

Hess und Messmer, Koll. Zeit. 36, 260, 1925; Cellulosechemie, 6, No. 7, 1925. Studies on the solubility of cellulose in copper-ammonia liquid.

Hess, Weltzien und Messmer, Lieb. Ann. Chem. 435, 1923. Copper-ammonia solutions of cellulose.

Heuser und Hiemer, Cellulosechemie, 6, Aug., Sept., Nov. 1925, 7, No. 4, Apr. 1926. Depolymerization of cellulose.

Mark, Melliand Textilberichte, Heidelberg, No. 9, 1929. The structure of cellulose and its technical processing.

Meyer, Zeit. f. angew. Chem., No. 4, 1928. New paths in the study of organic structures and in the investigation of high-polymer compounds.

Acetates and Other Cellulose Ethers

Aparci, Rev. Coll., No. 54, 1928. On the metallic complexes of cellulose nitrates.

Hess und Müller, Lieb. Ann. der Chem., 455, 205, 1927. Crystalline triethylcellulose.

Hess und Pichlmay, Lieb. Ann. d. Chem., 450, 29, 1926. Crystalline trimethylcellulose.

Hess und Friese, Lieb. Ann. d. Chem., 450, 40, 1926. Acetolysis of cellulose.

Hess und Schultze, Lieb. Ann. d. Chem., 448, 89, 1926. Cryoscopic behavior of crystalline ethylcellulose.

Herzog, Helv. Chim. Acta, 10, No. 9, 1926; Cellulosechemie, 7, No. 2, 1927. Notes on the crystalline structure of acetylcellulose and nitrocellulose.

Ueda, Zeit. f. Phys. Chem., 153, H. 5/6, 1928. X-ray investigations of celluloid.

Sheppard, Nietz, Keenan, Ind. and Eng. Chem., 21, 126, 1929. The supramolecular state of polymerized substances.

Clark, Ind. and Eng. Chem., Febr. 1929. Study of the problem of polymerization by means of X-rays.

Meyer, Biochem. Beihefte, 214, H. 4/6, 1929. On the fine structure, strength, and compressibility of animal tissues.

Freundlich, Zeit. f. angew. Chem. 40, Nov. 1927. Structure and formation of colloidal particles.

Katz und Sammwel, Naturwiss., H. 30, 592, 1929. A new view of the form of the molecules of cellulose and its polymers.

1. Nägeli. ↩↩

2. A fiber diagram is the type of diagram obtained when fibrous substances are irradiated with X-rays. ↩