THE STRUCTURE OF CELLULOSE IN LIGHT OF X-RAY ANALYSIS1

William H. Bragg, London

A detailed study of the chemical compounds occurring in nature shows that a predominant role in them is played by quite definite atoms, molecules, and combinations of molecules, whereas other atoms, molecules, and combinations occur comparatively rarely. The part of the universe known to us is built up of 50% oxygen, 27% silicon, and 8% aluminum; the remainder consists almost entirely of iron and certain other elements, while the overwhelming majority (about 80) of the elements account, in all, for no more than 2%. In the seas, which, as is known, cover the greater part of the earth’s surface, an enormous predominance is of course held by the molecule of water, H₂O. In minerals the basis of the structure is the oxygen atom: the recent work of W. L. Bragg and his collaborators has shown that almost the entire earth’s crust is built of oxygen atoms bound to one another by atoms of other elements: silicon, aluminum, iron, and magnesium. In some cases the arrangement of the oxygen atoms has an exceedingly simple character and is apparently determined exclusively by the dimensions of the space they occupy. In other substances, for example in quartz, a considerably

a more complex structure, formed under the influence of the mutual attraction of silicon and oxygen atoms.

Among the elements that form living matter, the carbon atom has the most essential significance. Although the total mass of carbon amounts to only about \(1/40\%\) of the total mass of matter in the universe, its significance for life is truly enormous. In living matter two types of molecular structure are most often encountered: a long chain of carbon atoms, which is the basis of the structure of most fats, oils, paraffins, etc., and the benzene ring, consisting of six carbon atoms closely bound to one another in the form of a hexagon.

A large part of organic chemistry deals precisely with these two types of molecules and their derivatives; moreover, they are extremely important for biochemistry and for industrial chemistry.

Cellulose and the Fibrous Structure of Tissues

The principal role in the process of plant growth is played by the cellulose molecule. In order to grasp its whole significance, incomprehensible at first sight, it is enough to recall that forests, shrubs, cereals, and in general all kinds of plants consist mainly of cellulose. What properties of the cellulose molecule account for its exceptional role?

Through cellulose the growth of plants takes place. It is also found in the animal world. In other words, with the aid of the cellulose molecule a “directionality” is established in the development of living matter. Since the process of growth proceeds along definite lines, it is clear that cellulose, which forms part of plants, cannot possess identical properties in all directions. With one or two exceptions (such as, for example, asbestos), none of the inorganic substances possesses that curious property which is denoted by the word “fibrousness.”

Cellulose is a fibrous substance. This fact is evidently rooted in the very structure of its molecule (or combination of molecules). The fibrous character

plant stems and leaves is their most characteristic feature. At the basis of the whole process of their growth and of all their constructive capacities lies the above-mentioned property of “directionality.” We make use of this property for technical purposes as well. From the natural fibers of cotton, hemp, jute, etc., we spin threads and ropes, whose special purpose is to withstand tension in one definite direction. From cotton fibers we weave clothing for ourselves; from comminuted cellulose we make paper. In these cases the fibers are distributed in one plane in various directions and thus form layers that withstand two-dimensional stresses. In recent years, from specially prepared cellulose, threads of artificial silk have begun to be manufactured. Thus, the fibrous structure of cellulose is of essential importance not only for its natural qualities, but also for technical applications. What, then, is this cellulose, and in what do the peculiarities of its structure consist?

Chemical composition of cellulose

This question has been dealt with chiefly by chemists, who have succeeded in decomposing cellulose into the atoms composing it; and it has turned out that it represents a multiple of the group C₆H₁₀O₅. This fact by itself is, of course, insufficient for explaining the properties of cellulose, since a number of other substances (starch, glycogen, dextrin, etc.) possess the same composition. The characteristic features of cellulose must evidently be determined by the mutual arrangement of the 21 atoms forming it. The task consists in finding this arrangement. It would be inappropriate to set forth here in detail the attempts that chemists have made in this direction. We recently heard, in the Royal Society, a report by Sir James Irvine, a pioneer in this field of research, on the arrangement of atoms in the sugar molecule (in its structure cellulose is extremely close to sugar). For us it will be sufficient briefly to indicate some of the results obtained by chemists.

It may be regarded as proven that in the compounds of interest to us the six carbon atoms are arranged in chain order. This chain, however, need not be imagined as a straight line. When a chemist writes a formula of rectilinear character, he means thereby to indicate only the order of arrangement of the atoms, and nothing more. Figure 1 shows the usual way of writing the formula for glucose, in which the group $C_6H_{10}O_5$ is in the anhydride form.

Glucose      Cellobiose

Fig. 1

According to this formula, each carbon atom is bonded to four other atoms. The hydrogen atoms and the OH groups are drawn on different sides of the carbon atom in order to show that a rearrangement of them changes the character of the substance. The most remarkable thing in this diagram is that the first and fifth carbon atoms are linked to one another through an oxygen atom. It is possible, however, that in reality it is not the first and fifth, but the first and fourth atoms that are joined to one another in this way. Most investigators long adhered to precisely this point of view, but recent work (belonging chiefly to Haworth) has made the 1 : 5 linkage more probable, and for the present we shall proceed from it.

The oxygen atom which is placed at the side in the diagram is, in real space, evidently in contact with the two atoms with which, according to the formula, it is bonded. By the expression “is in contact” we mean in the present case that the distance between the centers of the pair of atoms under consideration, other conditions being equal, is practically constant. It is clear that oxy-

STRUCTURE OF CELLULOSE

...rod cannot simultaneously be in contact with the first and fifth carbon atoms while lying with them on the same straight line. In order for such contact to become possible, our chain must be bent. Hence arises the conception of a six-membered ring consisting of 5 carbon atoms and one oxygen atom.

It has been unquestionably proved that this ring is the fundamental structural element of all living plants and of all substances for which they serve as material. This astonishing fact in itself already provides sufficient stimulus for undertaking an investigation of the structure of the ring by all methods at our disposal. Moreover, industrial enterprises in which cellulose is used are directly interested in this kind of research: all kinds of cotton-paper factories, enterprises dealing with celluloid, explosives, certain varnishes, and so on.

Fig. 2. Model of cellulose. The shaded circles represent carbon atoms; oxygen atoms are represented as double circles, in order to show the limits between which their diameters probably lie. This model, due to Mark, represents two glucose rings, deprived of some atoms unessential for showing the mode of combination, and the oxygen atoms connected with one another into the nucleus of the cellulose molecule. In the figure the model is shown as it appears in two perpendicular directions. The dimensions of the nucleus in the direction marked by the arrow \(A\) (the repeat period) \(= 10.3\ \text{Å}\). Cf. Fig. 1.

Chemical methods do not make it possible to proceed further in this direction than the picture indicated. All the results of deeper investigations by chemists are extremely vague and do not lend themselves to unambiguous interpretation. The most important of these results is the establishment of the formula of one of the derivatives of cellulose—the so-called...

of the cellulose under consideration. As we said above, cellulose is a whole that is a multiple of the element \(C_6H_{10}O_5\), i.e., it consists of the above-described rings (glucose rings). Cellobiose contains two such rings, the arrangement of which in ordinary chemical notation is shown in the right-hand part of Fig. 1. As is evident from the figure, in such an arrangement the first carbon atom of the glucose ring is joined to the fourth atom of the second ring. Further, in the process of joining the rings, two hydrogen atoms and one oxygen atom are eliminated, i.e., the constituent parts of one molecule of water. By attaching to the cellobiose molecule, by means of the same linking oxygen atom, a third ring, we obtain a cellotriose molecule consisting of three rings. Proceeding further in this way, we ultimately, after joining a certain number of rings, arrive at the cellulose molecule. The actual arrangement of the atoms in the latter apparently corresponds to Fig. 2, but in order finally to establish the form of this diagram it is necessary to turn to X-ray analysis. Therefore we shall break off our discussion here and proceed to describe the data obtained with the aid of X-rays.

METHODS OF X-RAY ANALYSIS

As is known, the power of the new method of X-ray analysis lies in its ability to detect any regularity in the arrangement of atoms or molecules. This method is so sensitive that with its help one can obtain precise information about the mutual arrangement of several hundred molecules (with a larger number of molecules, inaccuracies already appear).

As we have already said above, if cellulose really plays so essential a role in the process of plant growth as we ascribe to it, then it must possess some special properties in one definite direction. Of course, a priori it is not excluded that this “directionality” is determined by the properties of some other, as yet unknown, constituent part of plants. But

in favor of cellulose is indicated, first, by the fact that it is the most essential constituent part of all plants, and, second, by the fact that, as we shall see below, the anisotropy of its properties is comparatively easy to explain.

Any anisotropy can exist only in the presence of a certain regularity in the arrangement of the molecules. The latter must form some regularly repeating lattice, the orientation of which, in the present case, is evidently connected with the direction of the line of growth. Therefore, when X-rays pass through a fiber of cotton or of ramie, one should expect the appearance on a photographic plate of the same effect as when they pass through a crystal. In fact, a crystal is nothing other than a regularly arranged aggregate of atoms.

Experiment shows that such an effect is indeed observed. Moreover, its presence may be regarded as proof of the fibrous structure of the substance in question. Let us dwell on this point in greater detail.

When a monochromatic beam of X-rays passes through a crystal rotating about some axis, the planes of the crystal one after another acquire the angle of reflection characteristic of them; moreover, from the crystal there emerges a reflected ray which makes with the original beam an angle equal to twice the angle of reflection. Let us recall that through the nodes of a crystal lattice one may mentally draw an innumerable multitude of systems of parallel, equally spaced planes. For each such system there exists a characteristic angle of reflection, connected with the length of the incident wave \(\lambda\) and the distance between the planes \(d\) by the formula \(n\lambda = 2d \sin\theta\), where \(n\) is an integer.

The photographic plate may be arranged so as to give images of the various reflected rays. If both the axis of rotation and the plate are perpendicular to the original beam, then symmetrically arranged spots appear on the plate. As an example one may take, for instance, Fig. 3. It shows a roentgenogram

crystal of asparagine—a derivative of one of the constituent parts of wool—of the order of one milligram in weight.

The methods of X-ray analysis make it possible, on the basis of data on the positions and intensities of the spots, to obtain information about the structure of the crystal. The calculations used in this are partly geometrical and partly physical in character. We shall not dwell here on these details.

Fig. 3. Asparagine. X-ray diagram, obtained by W. H. George by means of the rotating-crystal method. X-rays are monochromatic; the crystal rotated during the exposure. The grid, against whose background the diagram was obtained, has been added for convenience of interpretation.

Let us merely note that the interpretation of X-ray photographs is by no means easy: some results can be obtained quickly and accurately, but others require more complex analysis.

The sharp separation of the spots in the photograph of asparagine, and the fact that they are arranged on several sharply outlined lines, show that the axis of rotation coincides with some exceptional direction in the crystal.

More precisely, it passes through a large number of lattice nodes and serves as the intersection of several principal systems of planes. According to the laws of the crystal lattice, the distance between any two neighboring nodes lying on the axis of rotation must be the same. The magnitude of this distance is easy to determine from the photograph. All the spots are arranged on a system of hyperbolas. If \(v_n\) is the distance from the focus of the \(n\)-th hyperbola to the horizontal line called the equator, and \(D\) is the distance from the crystal to the photographic plate, then the required distance between the nodes is given by the formula \(\frac{1}{n}\lambda \operatorname{cosec}\theta\), where \(\operatorname{tg}\theta=\frac{v_n}{D}\). A proof of this formula may be found in special courses.

If the spots are not very blurred, then by this formula one can obtain results with an accuracy of at least 1–2%.

It is clear that, by making the crystal rotate successively about three different (non-coplanar) axes, one can in this way determine the character of its periodicity in three directions, i.e., find the form of the crystal lattice.

X-ray diagram of cellulose

If a monochromatic beam of X-rays is passed in the above-described manner through some cellulose fiber, for example ramie, then on the photographic plate there is obtained a system of spots of exactly the same character as in the case of an asparagine crystal. Hence it is clear that, in its structure, the fiber is in a certain sense analogous to a crystal. In obtaining an X-ray photograph of ramie, however, we encounter the essential peculiarity that in the present case it is not at all necessary to rotate the substance being photographed, as we do with asparagine. This peculiarity is explained by the fact that ramie contains not one crystal, but a whole series of crystals, which have one common characteristic direction (the existence of it

and determines the sharpness of the lines in the photograph. Around this direction the crystals may be oriented in any way whatever, so that the diagram is quite analogous to that which would have been obtained in the case of a single rotating crystal.

Let us note that the photograph of ramie (Fig. 4) is somewhat more diffuse than the others. This is explained, chiefly, by imperfections in the regularity of the mutual arrangement of the crystals.

Fig. 4. X-ray photograph of ramie fibers.

Let us suppose that this arrangement is of an entirely chaotic character, i.e., that in our fiber there are crystals oriented in an arbitrary manner. In that case there can be no preferential direction whatever in the photograph, in particular neither a vertical nor a horizontal axis of symmetry. It must represent simply a series of rings, as in an ordinary photograph of a powder subjected to rapid rotation in its own plane about its center. An example of such a photograph is Fig. 5; cystine—one of the constituents of wool—has been taken here as the material. This photograph was obtained by W. T. Astbury of the Department of Textile Research of the University of Leeds.

When the crystals are properly oriented with respect to one definite direction—the direction of the fiber—the spots in the photograph have a sharply delineated character. When such orientation is completely absent, we have a photograph of the type of Fig. 5. Between these two extreme cases any intermediate states are possible.

...diffraction spots: with any disturbance of the regularity of orientation, the spots simply begin to blur along the circles on which they lie.

To a certain extent this blurring is also explained by the small size of the crystallites. The action of X-rays has the character of diffraction, and, as is known, sharply defined images are obtained through the combined action of a large number of regularly arranged objects. Therefore, from the degree of blurring of a spot one can roughly estimate the number of diffracting centers in the crystal. Such an estimate was given in the extremely important work of G. Mark.

Fig. 5. Chitin. This diagram, belonging to $\Theta$-fibers, is characteristic of a substance consisting of very small crystallites arranged completely at random.

By measuring on a photograph of ramie the distances from the foci of the hyperbolas to the equator, one can, as was already indicated above, find the distance between the lattice nodes on the axis of rotation. The value obtained is close to \(10.3\ \text{Å}\).

Summarizing all that has been said above, one may say that:
1) cellulose contains crystals which may be invisible under the microscope, but are clearly revealed by X-ray analysis; they are usually called crystallites;
2) these crystals are more or less correctly oriented about one direction common to them all; 3) each crystallite has, along this direction, a definite periodicity, which is characterized by a length of 10.3 Å (the so-called “repeat period”).

It would be imprudent to say that all cellulose consists entirely of these crystals, although such an assertion very strongly suggests itself. In its chemical composition cellulose is a multiple of the group C₆H₁₀O₅, and (as has already been indicated above) there is reason to suppose that this group forms a ring which serves as the basis of some definite structure. X-ray analysis does not indicate the presence of any other structure distinct from the ring structure. It is therefore natural to suppose that the whole mass of cellulose consists of this latter structure. This question can be finally clarified only when the methods of X-ray analysis provide more precise data on the intensities of the rays reflected from a given mass of substance, in comparison with other substances of analogous structure.

Comparison of the Results of Chemical and X-ray Analyses

Let us now return to the results of the chemical investigation of cellulose and compare them with the above-stated results of X-ray analysis. As for the first two of the conclusions indicated, they, of course, cannot in any way contradict the conclusions of chemistry: we have simply obtained certain additional information about the structure under investigation. But the third conclusion is of a somewhat different character. Since chemistry has given us the possibility of establishing the arrangement of the atoms, it must also explain the reason for the periodicity we have discovered.

X-ray experiments have shown that when oxygen and carbon atoms are arranged in the form of a regular crystalline lattice, they behave not simply as hard spheres, but in a more complex way. But when the manner of combination of these two atoms is known, the distance between their centers can be determined fairly accurately. In particular, we know that the distance between the centers of two carbon atoms connected with one another by their so-called primary valences (as occurs, for example, in diamond, graphite, benzene, hydrocarbons, etc.) is close to 1.5 Å. The distance between oxygen and carbon atoms is known less accurately, but from data obtained on calcite and other substances one may conclude that it is approximately equal to 1.2 Å. In Fig. 2 is shown Mark’s attempt to use these data to determine the dimensions of the double ring of cellulose. With such a determination, some inaccuracy must inevitably enter, of course, since the form of the ring has not yet been definitively established. Moreover, the very arrangement of the oxygen “bridge” can be judged only by analogy with certain other crystals.

The length of the double ring proves to be equal to 10.3 Å, in complete agreement with the data of the X-ray diffraction photograph. Despite all the possible inaccuracy of this figure, the agreement must be regarded as extremely significant. It is a splendid confirmation of the idea that cellulose is a long chain, the links of which are glucose rings joined to one another by oxygen “bridges,” as shown in Fig. 2.

According to Haworth (Sugars, p. 84), the elementary parallelepiped of a lattice constructed in this way is not one ring, but a pair of rings (or links), since the structure of the links changes alternately. This is evident if only from Mark’s drawing. As shown in this drawing, the oxygen bridge is located alternately on one side and then on the other side of the principal plane of the molecule. Thus, periodically repeated, strictly

speaking, not one ring, but a pair of rings. As is known, this circumstance should be manifested on the radiograph in the fact that the spots on the first, third, fifth, etc.—in general on the odd hyperbolas—must be weaker than the corresponding spots on the even hyperbolas (as one passes to hyperbolas of higher order, this effect gradually disappears). And, indeed, the weakness of the spots on the first hyperbola in comparison with the second immediately catches the eye.

Thus, the X-ray-analysis data at our disposal speak in favor of the conception of cellulose as a chain composed of glucose rings. The interatomic bonds along this chain are of the same strong character as in diamond. Such a conception had been advanced earlier as well (Herzog. Zeitschr. anorg. Chem. 34, 385, 1921; Polanyi. Naturwiss. 288, 1921), but it was by no means generally accepted. It is set forth, for example, in Haworth’s “Saccharides.” It was also adhered to by the American botanist Sponsler, who made use of X-ray methods. Particularly strong arguments in favor of this point of view were adduced by H. Mark, who supported his arguments with a large number of experimental investigations. But alongside them there were also other chemists who objected to the conception set out above, as, for example, Trogus and Hess did quite recently.

The results of the experiments described above—and also of those that will be discussed below—cannot, however, be regarded as decisive. On the one hand, a whole series of phenomena has not yet been definitively explained; on the other hand, X-ray analysis has not yet reached its full development, and therefore it cannot be used with the confidence that only long application provides. But even now the data of this analysis have great significance and promise even more in the future. In the case that interests us they serve as confirmation of that periodicity of structure which could have been expected on the basis of a very interesting and highly promising theory of cellulose.

ELEMENTARY PARALLELEPIPED OF CELLULOSE

The X-ray photograph gives us, of course, not only the value of the period in one direction, which was discussed above. From the positions of the various spots one can determine the shape and dimensions of the elementary parallelepiped of the lattice. Let us represent this elementary parallelepiped in the form of a rhomboidal cell, shown in Fig. 6. The word “cell” means that if, from the point \(O\), we pass to \(A\), \(B\), or \(C\), we shall notice no change in the crystal. Let, then, \(OB\) be the period found by us, which we shall denote by writing \(10.3\) beside it. The remaining dimensions of the cell are unknown to us and must be found.

Each spot on the equator corresponds to a series of planes parallel to \(OB\). Thus, for example, the series of planes whose successive members are the planes \(OBDA\) and \(CGFE\) gives on the equator a single spot, from the position of which one can determine the distance between the two planes mentioned. The same applies also to the planes \(OBGC\) and \(ABFE\). By choosing two spots on the equator, we can—with certain limitations, of which we shall not speak here—assume that the planes corresponding to them serve as faces of the elementary cell of the lattice. But the diagram gives no direct data whatever concerning the angle which these faces form with one another. If we were dealing with a single crystal, this difficulty would be easily removed, since then we could obtain several additional diagrams by rotating the crystal with respect to at least two other directions, for example \(OA\) and \(OC\). But in the present case we have not one crystal, but an entire multitude of crystals, and this greatly complicates the solution of the problem.

Fig. 6

However, even here it is possible, by a certain indirect though less reliable method, to obtain a definite result. First of all, the general appearance of the diagram under consideration

and comparison of it with other diagrams of an analogous character shows that our crystal is very close to the monoclinic type, i.e. that the straight lines \(OA\) and \(OC\) are almost (if not entirely exactly) perpendicular to \(OB\). Without risk of falling into error, we may regard them as exactly perpendicular (for brevity I do not give here the justification of this assumption). Under this supposition we have only one unknown quantity left, namely—the angle between \(OA\) and \(OC\). To determine it, it is sufficient to know the lengths of the perpendiculars dropped from \(A\) onto \(OC\) and from \(C\) onto \(OA\). Thus, a single assumption is sufficient in order, on its basis, to determine the origin of all the spots on the diagram. In practice, when computing the angle, one has to choose between only one or two possibilities.

This final choice gave rise to a whole series of disputes. In the end it turned out that all the details of the diagram can be explained in the best way if one takes \(OA = 8.35\ \text{Å}\), \(OC = 7.9\ \text{Å}\), and the angle \(COA = 84^\circ\). The edge \(OB\), as we have already said above, is equal to \(10.3\ \text{Å}\). (Mark and Meyer. Zeitschr. Phys. Chem. Abt. B., 2, 115; Andress. Zeitschr. Phys. Chem. Abt. B., 2, 380).

The approximate data at our disposal on the specific gravity of cellulose show that the cell described above contains four groups \(C_6H_{10}O_5\).

Our picture is thus made more definite. The long chain spoken of above is arranged parallel to \(OB\) (Fig. 6). If the axis of one chain coincides with \(OB\), then completely analogous chains are also present along \(AD\), \(EF\), and \(C(G)\). With such an arrangement within the cell, however, there turn out to be only two glucose rings in all, not four. Here we are aided by certain calculations based on data on the relative intensities of the various spots (the methods of such calculations are set forth in special works on X-ray analysis), which show that in the middle of the cell there is one more chain, passing approximately through the centers of the faces \(OAEI\) and \(BDFG\). This also explains the presence of two additional rings.

Crystallites

Each crystallite is a collection of these long chains arranged side by side. The question arises as to what forces bring about the connection of these chains with one another.

Between the forces that bind together the links of each chain and those that bind one chain to another, there is an essential difference. The former are enormous in magnitude and are quite analogous to the forces that maintain the strength of diamond. The latter, however, are due to the interaction of carbon atoms whose primary valences are already “occupied” by hydrogen atoms or by the hydroxyl group. In their nature they are probably similar to the forces of interaction of molecules in crystals of organic substances, for example, naphthalene. When naphthalene melts or dissolves, its molecules separate from one another, and the work expended in overcoming these secondary valences is negligibly small in comparison with the work that would have to be expended to overcome the forces of primary valences in the molecule itself. True, naphthalene has no hydroxyl group, so that the secondary forces there are not as great as apparently occurs in our case. Nevertheless, the forces acting between the chains must be considerably smaller than those acting within each chain.

Fig. 7. Diagram showing the relative position of the chains.

Confirmation of this view is provided by the very internal structure of our model. Whereas the distance between the centers of two carbon atoms connected with one another by primary valences is 1.5 Å, the smallest ...

the possible distance between carbon atoms belonging to different molecules, close to 3.5 Å. Thus, for example, in graphite the different layers are separated from one another by a distance of 3.41 Å; in naphthalene and in fatty acids the corresponding distance is close to 3.5 Å. An analogous gap must also exist in the cellulose model, since otherwise the chains could not fill the whole volume occupied by it. As shown in Fig. 7, belonging to Mark and Meyer (Zeitschr. Phys. Chem. 122, 1929), the planes of the rings lie for the most part parallel to \(ab\). Reflection from this series of planes gives the strongest spots in the whole diagram (which serves as a very substantial support in constructing the model). The distance between neighboring planes belonging to it proves to be equal to 3.95 Å, which agrees very well with our hypothesis.

Influence of Temperature

Indirect confirmation of the latter can also be obtained from another field. The temperature coefficient of expansion of diamond is extremely small. In graphite, however, it is extremely small in the plane of the layers, but many times greater in the direction perpendicular to this plane (Backhurst, Proc. Roy. Soc. 102, 340, 1922). In other words, when the temperature is raised the layers do not stretch, but move away from one another.

Let us recall that, by comparing the appearance of X-ray diagrams at different temperatures, one can determine the coefficient of expansion of a crystal in any direction. This possibility is preserved also when the crystals are microscopically invisible, although in this case the accuracy of the results is not so great as when we are dealing with a single ideal crystal that can be rotated at will.

Observations on diamond and graphite make it very likely that, with changes of temperature, the distance

between carbon atoms strongly bound to one another changes very little, while between weakly bound atoms (as, for example, in graphite) it undergoes a noticeable change.

The experiments carried out by Dr. Müller on cellulose may be regarded as an illustration of this assertion. A comparison of the two photographs obtained by him (Fig. 8) shows that an increase in temperature has a far greater effect on increasing the distance between the chains than on the length of each chain.

The changes of form which a crystal undergoes under the influence of temperature are usually very complex and difficult

Fig. 8. X-ray photograph of paraffin \(C_{19}H_{40}\) at ordinary temperature \((A)\) and at the temperature of liquid air \((B)\) (after A. Müller). The lines in the center represent different orders of reflection from planes separated by large distances, which in fact are the lengths of the carbon chains. The position of the central lines in the two photographs is the same. But certain lines along the edges, caused by reflections from different chains, are considerably shifted under the influence of the change in temperature.

to interpret. But in the present simple case it is clear that they are explained by the difference in the behavior of the primary and secondary valences.

With a strong lowering of temperature (down to the temperature of liquid air), the change in the length of the cellulose chain must also, evidently, be small. This was demonstrated by the experiments of Mark and Meyer (Zeitschr. phys. Chem., 2, 127), who at the same time found large changes of length in other directions.

Mercerization

So-called mercerization, so interesting from the scientific point of view and so important technically, has a strong effect on the appearance of the X-ray photograph. However, in the latter case ...

so many of the old characteristic features remain that the new structure may certainly be regarded as a modification of the old one. In this, the most essential point is that the distance between the separate links of the chain does not change. Andress (Zeitschr. phys. Chem. Abt. B. 4,190) showed that all the details of the new diagram can be explained by a slight change in the mutual arrangement of the chains, of the kind shown in Figs. 9 and 10. The new arrangement must

Fig. 9. General arrangement of the glucose chains, when viewed along the \(c\)-axis.

Fig. 10. General arrangement of the chains in mercerized glucose, when viewed along the \(c\)-axis.

be regarded as the stable form of the crystal, and the old one as metastable.

The magnitude of the repeat period along the chain remains unchanged not only in various physical processes, such as mercerization, but also in chemical reactions. Thus, for example, there exists a series of forms of trimethylcellulose, acetylcellulose, and nitrocellulose which have a crystalline character, coincide in their general structure with cellulose itself, and possess the same periodicity of 10.3 Å in the direction of the fiber. In the other directions, however, they have entirely different properties. Thus, the appearance of new atomic groups causes only an increase in the distance between the chains and often changes nothing in the chains themselves. When these new atoms are removed by ordinary chemical methods, the X-ray photograph of cellulose for the most part assumes its former appearance and only in some cases (under special modes of action) passes into the X-ray photograph of mercerized cellulose.

Alongside those mentioned, there also exist other cellulose derivatives in which chemical reactions produce more radical changes. For example, in another form of nitrocellulose the period of repeat, according to Mark, is equal to 25 Å; in cellulose acetate and cuprammonium cellulose a period of 15 Å is found.

Thus the chain, generally speaking, preserves its nature over a wide range of temperature changes and in a number of chemical processes. This circumstance is in complete agreement with the conception—advanced by chemists who studied the structure of sugar, and now confirmed by the data of X-ray analysis—according to which it consists of glucose rings closely linked with one another in the manner of diamond molecules. All the chains are connected with one another into “bundles” of their own kind, and, when the length of the chains is great, these lateral bonds—although each of them individually is comparatively weak and easily yields to physical and chemical influences—prove sufficiently strong to make each bundle a definite element in the structure of cellulose. The variety of tensile and contraction properties possessed to differing degrees by all fibrous substances is explained by the different possibilities in the mutual arrangement of the chains, by their sliding along one another, by their partial return to the original state, and finally by their flow under excessively great tension. All these properties of the fiber are set forth in detail elsewhere.

Thus we have obtained a remarkable and, in certain respects, very simple picture. As the basis for the structure of all plants, nature has chosen a special kind of combination of atoms, at the very foundation of which lies a fibrous structure. X-ray analysis confirms and refines the previously proposed models of this structure. It is not impossible that in the near future the methods of this analysis will be significantly improved, so that it will begin to yield still more precise and definite results.

1. Lecture delivered at the Royal Institution in London on January 24, 1930. Printed in Suppl. to Nature, No. 3148, March 1, 1930, p. 315. Translated by S. Shubin. ↩