MOLECULAR STRUCTURE AND MECHANICAL PROPERTIES OF HIGH POLYMERS *)

H. Mark

For many centuries man has used natural materials—wood, stone, cotton, wool, etc.—and factory-produced inorganic products—ceramics, glass, and metals—for the construction of dwellings, the making of clothing, machines, and most other necessities and luxury articles. In recent decades a new type of material for the production of various objects has been discovered and developed, namely synthetic organic polymers. They have acquired great and ever-increasing importance for many important branches of industry and, owing to their specific properties, make it possible to introduce substantial improvements in the manufacture of a great many objects: buildings, steamships, automobiles, airplanes, electric motors, scientific instruments, automobile tires, footwear, clothing, and so forth. Some of the polymers, for example nylon, cellophane, bakelite, Buna rubber, viscose, and celluloid, are well known to the general public because of their outstanding qualities; many others are being developed in industrial research laboratories and will soon be released to the market. A common property of all these substances is that they are organic in nature, i.e., consist chiefly of carbon, hydrogen, oxygen, and nitrogen. Some of them, however, for example vinylite, pliofilm, and Saran, also contain chlorine, while others, for example silicones, contain a certain amount of silicon. Another important circumstance is that the majority of these organic polymeric, or high-polymeric, substances can be made from such simple and abundantly available starting materials as air, water, coal, petroleum, limestone, rock salt, and sand by means of chemical operations carried out on a large scale, which makes it possible to produce polymers at accessible prices.

The term “high polymers” applies to an entire class of compounds whose molecules have a specific structure. Above all, this name indicates the very high molecular weight of the compounds. Let us recall that the molecular weight of hydrogen is 2, of oxygen—32,

) American Journal of Physics 13*, 207 (1945). Translated by N. Fuchs.

sugar—342. At the same time, the molecular weight of organic high polymers (synthetic or natural) has an order of magnitude from tens of thousands to several millions. Table 1 gives several typical figures for illustration.

Table 1

Molecular weight and degree of polymerization of some typical polymers

As is evident from the table, all the substances listed in it, both natural—cotton cellulose, silk protein, and rubber from the latex of rubber-bearing plants—and synthetic—nylon, vinylite, saran, and vistanex—have molecular weights on the order of tens and hundreds of thousands.

The word “polymer” is composed of two Greek words: “polys,” meaning “many,” and “meros,” i.e., “part.” It means that the molecules of all these substances are built of many identical parts, or structural units, called monomers. In rubber such a unit is the isoprene residue, in cellulose—the glucose residue, in vistanex—isobutylene, in bakelite—phenol and formaldehyde, and so on. High polymers are thus compounds with very large molecules, built from repeating structural units—monomers (of one or several kinds). Dividing the molecular weight of a polymer by the molecular weight of the corresponding monomer gives the number of repeating structural units contained in the polymer molecule, called the degree of polymerization (d.p.) of the substance. Table I contains the values

for the polymers listed in the table: they have a value of about 1000.

The third characteristic property of synthetic organic polymers is that those structural units—monomers—from which the gigantic molecules of polymers are built are connected with one another by chemical forces. These forces are rather large, and to break the corresponding homopolar bonds requires from 70 to 100 kilocalories per mole. Such bonds can be broken only under the action of very active chemical reagents or upon heating to temperatures above 250–300°; they change little during the dissolution and melting of polymers, and also during such thermomechanical operations as spinning, casting, injection molding, and pressing. Finally, let us add that in many, although not all, synthetic

Fig. 1.

organic polymers the structural units—monomers—are connected with one another in such a way that they form long molecules in the form of chains, possessing, owing to a certain freedom of rotation about homopolar bonds, a certain flexibility.

Summarizing, one may say that organic high polymers consist for the most part of long flexible chain molecules with a large molecular weight, in which the monomers are connected by strong chemical bonds. In Fig. 1 several examples of such chain molecules are given, the structure of which has been established by means of X-ray analysis of certain polymers in the crystalline state.

After these brief remarks on the general structural features of organic polymers, it is natural to pose the question: is there a known dependence between the structure of a given polymer and the mechanical properties of a specimen made from it? Knowledge of this dependence would be of great benefit in the development of new polymers intended for a definite purpose, and would help to improve the quality of already known polymers. To this question one must answer that we still do not have a well-developed mathematical theory quantitatively relating the structure of a polymer to its properties, but at the same time a number of rules and regularities are known concerning

dependences between structure and properties and, in a number of cases, made possible the production of products with higher qualities.

Two main factors influence the properties of a polymer: 1) the structural configuration of the chain molecules themselves and 2) the arrangement of these molecules in the polymer specimen, or, using other terminology: 1) the chemical structure of the molecules and 2) the physical texture of the macroscopic specimen. We shall now consider both factors in order.

DETAILS OF THE STRUCTURE OF MOLECULAR CHAINS AND THE MECHANICAL PROPERTIES OF POLYMERS

Let us first enumerate the most important details of the structure of high-polymer molecules and indicate what is at present known about their influence on the mechanical properties of polymers. First of all, let us mention the average molecular weight of the polymer, varying, according to Table 1, from 20,000 to 1,000,000, and the average d.p. (degree of polymerization), whose value is from 100 to 5000. Next comes the distribution of molecular weights, which characterizes the degree of heterogeneity of the material; in some polymers the molecular weights lie within comparatively narrow limits, while in others the distribution curve is quite strongly extended. Finally, a very essential factor is also the flexibility of the individual chains, which depends on the chemical nature of the bonds between the monomers.

The dependence between the mechanical properties of polymers and the average d.p. has been investigated rather thoroughly. The following general conclusion has been obtained: in order for a polymer to possess any mechanical strength at all, a certain minimum d.p. is necessary, lying between 40 and 80. As soon as the d.p. exceeds this critical value, the substance begins to exhibit mechanical strength, which then increases continuously as the average d.p. is further increased. In Fig. 2 it is shown schematically that, up to d.p. values between 40 and 80, the tensile strength of a film made from the polymer is negligible, but then begins to increase approximately in proportion to the chain length. The left edge of the shaded area, marked by circles, refers to polyamides; the right edge (crosses) to polyhydrocarbons. The curves for all other chain polymers, such as cellulose esters, polyvinyl derivatives, etc., lie within the shaded area. Proportionality between mechanical strength and d.p. is maintained up to a d.p. of about 250. Thereafter the curve bends, and, when the d.p. reaches approximately 600, further increase in it has little effect on the mechanical properties.

Whereas the influence of the average d.p. on mechanical strength has been clarified fairly well, the significance of the distribution of molecular weights still represents an unresolved problem. Recently a very promising attempt¹² was made to establish the dependence—

...dependence between the distribution curve and the mechanical properties of high polymers; it turned out that a comparatively small content (10–15% by weight) of components with a degree of polymerization less than 150 has an adverse effect on such mechanical properties as tensile and flexural strength, the ability to withstand prolonged action of a variable load, etc. Removal of low-molecular-weight components considerably improves the quality of the polymer.

Let us now consider the flexibility of individual molecules. It has been firmly established that every atom in a small molecule undergoes rapid

Fig. 2.

vibrations, the energy of which constitutes the main part of the heat content of solid (crystalline) substances. These vibrations can be investigated by means of molecular spectra (ultraviolet, infrared, Raman spectra) and from the dependence of heat capacity on temperature. In large molecules, such as those listed in Table I, in addition to these rapid vibrations of individual atoms, there also occur comparatively slow vibrational and rotational motions of separate parts or links of the molecule. One should not, however, think that they can rotate freely about ordinary bonds between carbon atoms. In reality, as recent investigations have shown, owing to the interaction between substituent radicals, adjacent \(\mathrm{CH}_2\) groups in a long paraffin molecule cannot rotate freely about the bonds connecting them. However, vibrational motions about these bonds with an amplitude not exceeding \(10^\circ\) encounter almost no obstacles, as a result of which a chain consisting, say, of 1000 or more \(\mathrm{CH}_2\) groups will, as a whole, possess a certain flexibility. In a segment consisting of only a few \(\mathrm{CH}_2\) groups, one cannot expect the appearance of sharp bends, but the chain as a whole can assume many different, more or less curved configurations, and the probability that such a long molecule will assume a state extended in one direction is exceedingly small. If the molecule

brought into such a state by external tensile forces, it tends, under the action of disordered thermal motions, to return to the most probable configuration, characterized by a certain curvature and coiling of the chain. This is the reason for the spontaneous contraction of stretched high-polymer molecules.

The rate of this contraction, however, depends not on how much more probable the final (contracted) configuration is than the initial (stretched) one, but on how rapidly the molecular chain can pass from the stretched to the coiled state; and this, in turn, depends on how rapidly the units of the molecule can pass from one geometrical position to another, separated from the first by a certain energy barrier. Thus the rate of contraction of a polymer is determined by the rate of diffusion of chain units through energy barriers that separate the possible mutual positions of neighboring units. In an isolated long chain molecule the height of these barriers depends on how hindered rotation is about successive bonds in the chain, owing to the rigidity of the bond itself or to the mutual attraction of substituent groups. It must be added that rubber in fact contains not isolated chains, but a dense mass of randomly intertwined chain molecules, attracting one another by intermolecular (van der Waals) forces. Such interaction between molecules also hinders the freedom of motion of individual molecules and their units, and thus affects the rate of contraction of stretched rubber.

Let us now consider the question of the temperature dependence of the flexibility of individual molecules. The factors opposing this flexibility are the energy barriers that the units of the molecule must overcome in their mutual displacements. Each elementary step, when a specimen of material returns to the unstressed state, thus requires a certain activation energy. The latter determines the influence of temperature on the rate of diffusion of the units, and consequently also on the rate of return to the unstressed state. If the energy barriers are high, then as the temperature is lowered it will become increasingly difficult for individual units to acquire the energy needed to overcome the barrier, and the rate of return to the unstressed state will become very small. This means that the material will yield too slowly under the action of an external load and will thereby prove brittle.

It follows from this that the flexibility of individual chains exerts a great influence on the mechanical characteristics of elastomers, chiefly on the rate at which they return from the stretched state and on its dependence on temperature and, in particular, on the temperature at which brittle properties begin to appear in the material.

Let us add that the chemical nature of a polymer is strongly reflected in its reactivity, swelling, and solubility. Thus, polyhydrocarbons, for example natural rubber, polystyrene, polyisobu-

tylene, etc., are very resistant to acids and alkalis and do not absorb water, but they swell and dissolve in liquid hydrocarbons and some other organic solvents. Polymers, on the other hand, that contain a large number of hydroxyl groups, such as cellulose or polyvinyl alcohols, are, conversely, very resistant to the action of organic solvents, but absorb moisture and even gradually dissolve in water and in weak alkali solutions. At the same time, the mechanical properties of polymers apparently depend not so much on whether the corresponding monomer is a hydrocarbon, an ether, a carbohydrate, or an alcohol, as on the molecular structure of the chains, determined by the average degree of polymerization, the distribution of the degree of polymerization, and the flexibility of the chain molecules. Indeed, as Table II shows, sufficiently strong fibers can be obtained from substances of the most diverse chemical nature.

Table II

Tensile strength of some typical fibers of different chemical type

After these brief data on the influence of the details of the structure of individual chains on the mechanical properties of polymers, let us turn to the question of the significance of the mutual arrangement of chain molecules in the latter.

ARRANGEMENT OF CHAIN MOLECULES AND MECHANICAL PROPERTIES OF POLYMERS

Let us briefly consider the properties of ordinary organic substances. At the freezing temperature of liquids with low molecular weight—benzene, toluene, isoprene, etc.—their mechanical properties undergo a sharp change within a narrow temperature interval. Below the freezing temperature, ordinary substances are crystalline solids. Under the action of a shearing force they undergo a small (1% or less), mainly reversible deformation and possess a three-dimensional crystalline lattice with a struc-

structures of long-range order (100 Å or more). Each molecule is held by the attractive and repulsive forces from all the surrounding molecules in a certain equilibrium position, about which it executes rapid, quasi-harmonic vibrations. The transition of an individual molecule from one equilibrium state to another (self-diffusion) occurs extremely rarely, since the average magnitude of the amplitude of the vibrations is only about 5% of the distance between neighboring equilibrium states. Such systems appear to us as rigid, solid substances, possessing a definite shape and all the other characteristics of a solid body.

As the temperature is raised, the vibrations of individual molecules continuously increase; finally, at the melting temperature of the substance, the forces acting between the elements of the crystal lattice prove unable to maintain long-range order in the crystal, and the structure of the latter is destroyed. The result is a liquid, whose characteristic property is the absence of long-range geometrical order. Although the nearest neighbors of a given molecule are arranged with respect to it approximately as in the crystalline state of the substance, molecules a few angstroms away already have a practically disordered arrangement. Each molecule does, it is true, execute quasi-elastic vibrations about an equilibrium position, but the latter (being a position with a minimum value of the potential energy) is in this case not fixed at a definite place, since the molecule, in addition to vibrations, also performs a disordered translational Brownian motion and frequently changes its location—self-diffusion proceeds rather rapidly. The absence of long-range order in the arrangement of molecules deprives the liquid of the ability to resist shearing or tensile stresses and to preserve its shape: a liquid is fluid. Eyring, Lennard-Jones, and their collaborators have successfully applied these considerations to the explanation of many fundamental properties of liquids[^3].

A liquid can be supercooled below the equilibrium melting temperature of the substance, while retaining all the characteristic properties of a disordered (amorphous) geometrical structure. The increase of the viscosity coefficient \(\eta\) with decreasing temperature may be expressed, in rough approximation, by the formula

\[ \eta = A e^{-bT}, \]

where \(A\) and \(b\) are constants, and \(T\) is the absolute temperature. At a sufficiently low temperature the material becomes hard and brittle; it is then called a glass. The transition from a solid glass to a viscous liquid often occurs in a comparatively narrow temperature interval (the softening temperature), without being accompanied by an abrupt change in structure or by a jump in the values of the principal thermodynamic parameters, such as heat content, free energy, and specific volume.

Thus, in the case of ordinary (low-molecular) organic substances, the relationship among the crystalline, glassy, and liquid states may be expressed by the scheme given in Table III.

Table III

Different states in which polymers may exist

The properties of high polymers, consisting of long chain molecules, are more complex. The strong chemical bonds within individual chains are only rarely broken during ordinary mechanical deformations of polymers, for example when rubber is stretched or nylon is drawn, and also during various thermal treatments, for example during annealing or hot forming.

The changes in shape occurring during these operations are caused by the rupture (and restoration) of bonds between neighboring chains, determined not by chemical forces but by various types of intermolecular forces, such as van der Waals forces and hydrogen bonding.

Let us compare from this point of view the crystalline lattice of isoprene with the lattice of stretched and frozen rubber, and see what happens to them when the temperature is raised. In frozen isoprene each individual molecule \((\mathrm{C}_5\mathrm{H}_8)\) is in a definite equilibrium position and executes about it random, quasi-harmonic vibrations. The distance between any molecule and its nearest neighbor is about \(4\text{–}5\) Å, whereas the interatomic distances within the molecule do not exceed \(1.0\text{–}1.5\) Å.

Hence it is clear why the parts of the \(\mathrm{C}_5\mathrm{H}_8\) molecule are connected with one another by strong chemical bonds with a dissociation energy of \(70\ \mathrm{kcal/mol}\) or even more, whereas the forces acting between molecules belong to the considerably weaker van der Waals type (about \(5\text{–}8\ \mathrm{kcal/mol}\)), so that the molecule forms a quite separate structural unit in the lattice. Nevertheless, below the melting temperature the intermolecular bonds are suffi—

...are sufficient to maintain long-range order in the crystalline lattice, and frozen isoprene constitutes a hard, rigid solid. However, above the melting temperature all elements of long-range order in the arrangement of the molecules disappear, and a liquid is formed, with rapid mutual diffusion of the molecules and with a small coefficient of viscosity (about \(10^{-2}\) poise).

In frozen rubber each isoprene residue \((\mathrm{C}_5\mathrm{H}_8)\), and likewise each carbon and hydrogen atom contained in it, performs oscillations about a definite equilibrium position; however, as a detailed investigation of the lattice shows, each isoprene residue is situated especially close to two other residues. Thus the residues form long linear chains, in which all the distances between nearest neighbors correspond to strong chemical bonds. Bound by these large forces, the isoprene chains extend parallel to the direction of the tensile force, have a length corresponding to several thousand monomers, and constitute the main skeleton of the entire structure. In directions perpendicular to the axes of the chains, the distances between neighboring molecules are determined by van der Waals forces. Such a lattice is, understandably, highly anisotropic: along the chains arranged parallel to one another large forces act, while across them the forces are insignificant.

As the temperature is raised, the weak intermolecular bonds are gradually broken, the mutual arrangement of the chains is disturbed and, in the end, becomes completely disordered. The chains also begin to rotate about their axes, to change their distance from neighboring chains and, finally, to coil up into a disordered ball. Although the weak intermolecular bonds are thereby broken, the strong (chemical) intramolecular bonds remain intact. The molecular chains are thus preserved at temperatures that cause the destruction of the lattice structure. From this follows an important consequence: although the long-range geometrical order in the lattice is disturbed when rubber is heated to the softening temperature, the long-range entanglement, due to the existence of long chain molecules, is nevertheless preserved. This long-range entanglement is the reason why, at the softening temperature of the polymer, we obtain not a liquid but a rubber-like solid.

An individual isoprene residue oscillates in amorphous unstretched rubber with almost the same intensity as an isoprene molecule in liquid isoprene at the same temperature, and therefore performs almost the same near Brownian motion. However, because such a residue is part of a chain molecule, it cannot move away as a result of diffusion to a large distance from its original position without carrying with it other parts of the chain. This geometrical restriction of the motions of the various links in flexible linear macromolecules, due to the strong bonds between the links, has as its consequence long-range entanglement...

chains, owing to which the polymer acquires the ability to withstand moderate tensile and shearing forces and, consequently, to preserve a definite volume and shape and to offer elastic resistance to deformation. In this sense rubber-like substances occupy an intermediate position between solid and liquid bodies, analogous to glasses; one may say that glasses are liquids with high viscosity, whereas rubber-like substances are liquids with long-range entanglement (see Table III). The diffusion of chain segments is little hindered by long-range entanglement and therefore proceeds at a high rate; at the same time, any displacement of a large linear molecule as a whole meets an obstacle in the mutual attraction of such molecules over a great length and therefore occurs very slowly. The disordered thermal motion of individual chain segments has, at the suggestion of W. Kuhn, been given the name internal or micro-Brownian motion. The motion of a macromolecule as a whole may be called external or macro-Brownian motion.

Using this terminology, one may say that rubber-like substances possess rapid internal and slow external Brownian motion. Such a combination of properties characterizes the rubber-like state.

SIGNIFICANCE OF THE TWO DIFFERENT TYPES OF BROWNIAN MOTION

Let us consider, first of all, which basic properties of rubber are due to both types of Brownian motion. If we stretch rubber, it begins to deform already under comparatively small forces, since it is a soft, extensible material with a small initial value of Young’s modulus. For typical elastomers (soft rubber and caoutchouc) Young’s modulus has a value from \(10^6\) to \(10^7\ \text{dyn}/\text{cm}^2\). In order for a substance to stretch noticeably under the action of such small forces, it must possess a considerable degree of internal mobility, like a liquid. Indeed, rubber-like substances have many properties in common with ordinary liquids. Their compressibility is very close to the compressibility of liquids; Poisson’s ratio in all “soft” elastomers is close to 0.50; the thermal expansion of rubber and of ordinary liquids is of the same order of magnitude; finally, what is most surprising, the solubility of gases (hydrogen, oxygen, etc.) and of solid substances (sulfur, selenium, etc.) in rubber-like substances is rather close to their solubility in ordinary liquids. The “local” fluidity of elastomers, due to rapid internal Brownian motion, is also the cause of the rapid contraction of a stretched specimen. In stretched rubber, individual segments in the chains assume a configuration whose free energy is greater than in the unstretched state. Therefore, as soon as the action of the external force ceases,

these links begin to diffuse back into their equilibrium positions, corresponding to a minimum value of the free energy and representing a stress-free state of the specimen. How rapidly this contraction occurs depends on the rate of diffusion of the links, which determines the “local” fluidity of the material.

Some materials assume their original shape almost instantaneously, owing to the rapid motion of the links; others “creep,” since the local mutual attraction between the links of the chains is great and prevents them from passing into an unstressed state in a short time. Natural rubber, neoprene, butyl rubber, and Buna rubbers serve as examples of the first case; polystyrene at temperatures above 80°, vinylite, and moist polyvinyl alcohol are examples of the second case. To obtain a good, rapidly contracting elastomer, it is necessary that the internal Brownian motion be as rapid as possible; in other words, the locally liquid character of the system must be enhanced.

On the other hand, if we confine ourselves to creating in the elastomer only such a high local fluidity and subject a macroscopic specimen of the substance to prolonged stress, the substance will begin to flow. It will not resist the applied tensile or shearing force, but, owing to rapid internal Brownian motion, will pass into a stress-free state without returning to its original shape. Thus the substance will behave not like rubber, but like a viscous liquid or a plastic mass. In order to avoid this permanent loss of shape, it is necessary to create a sufficiently long-range crosslinking, one that so slows the external Brownian motion (i.e., the sliding of whole chains past one another) that the latter cannot lead to appreciable flow of the substance during the time the specimen is in the stretched state. The van der Waals forces acting between the chains cannot by themselves provide a long-range crosslinking sufficiently stable for practical purposes. For this, a system of randomly arranged junction points, located at fairly large distances from one another, is usually created in the substance, forming throughout the whole volume of the specimen a stable network capable, nevertheless, of very large deformations. It can be stretched several times, after which it will return to its original shape, since the individual junctions are connected with one another by flexible chain molecules. Such junction points may be obtained in various ways. First of all, one may create strictly localized, strong chemical bonds between separate chains by means of sulfur, oxygen, or methylene bridges, which is probably what occurs in various vulcanization processes. Then, atomic groups possessing especially strong molecular interaction (hydrogen bonds, strong dipoles, easily polarizable groups) can be arranged randomly in the chains.

or a large volume (phenyl, benzyl, and naphthyl groups); in this way an irregular network is obtained, composed of regions with great molecular adhesion. Finally, very small particles with high adsorption capacity (active fillers) can be distributed throughout the polymer, irreversibly adsorbing on their active surface the segments of mobile chains.

In all the cases indicated, localized, sparsely distributed strong bonds between individual flexible chains suppress external Brownian motion sufficiently to prevent permanent flow of the specimen as a whole, and at the same time are reflected so little in the internal Brownian motion that they permit rapid stretching and contraction of the specimen.

The considerations set forth above show that a polymer can exist not in two but in three condensed states: solid, rubber-like, and liquid. In the solid state (crystalline or glassy), both types of Brownian motion are frozen. In the rubber-like state, external Brownian motion is still frozen, but internal motion is no longer constrained; finally, in the liquid state of the polymer (molten or highly swollen), both internal and external Brownian motion take place. Under the action of an external force, in the solid state only near-range elasticity with a large modulus is observed; in the rubber-like state—long-range elasticity with a small modulus; and in the liquid state—the ability to flow. An ordinary organic substance can be found only in two condensed states, solid and liquid; for it there is only one type of Brownian motion, frozen in the first of these states and free in the second. These two phases, solid and liquid, are in equilibrium with one another at the melting (or freezing) temperature. In polymers there are two characteristic temperatures (or temperature ranges): the brittleness temperature, separating the solid state from the rubber-like state, and the flow temperature, separating the latter from the liquid state. In Table IV we have attempted to represent all that has been said above in the form of a scheme.

From the facts set forth above it follows that, in order to obtain a polymer satisfying practical requirements, it is necessary to synthesize chain molecules with a degree of polymerization of the order of 1000, possessing a certain flexibility. The substance must then be brought into the proper physical state, or into a mixture of such states; in doing so it should be borne in mind that we have at our disposal three different phases—solid, rubber-like, and liquid. The problem of bringing a polymer into the best physical state resembles the problem facing the metallurgist, who, with the aid of the phase diagram of his alloy, seeks the conditions for imparting the desired properties to it, with the sole difference that the “metallurgist”-organic chemist has at his disposal one additional state, namely the rubber-like state, due to the presence of long chain molecules.

As is clear from the foregoing, if we wish to make a strong and elastic fiber, we should take as our basis the solid state, in order to impart to the material a certain degree of rigidity and strength; the rubber-like state will be required only in the amount necessary to give the fiber sufficient elasticity. Liquid components in the fiber are undesirable, since they lead to flow of the substance under prolonged load. To obtain

Table IV

Transition temperatures in ordinary substances and in high polymers

a typical rubber it is necessary that the main mass of the material be in the rubber-like state, with separate crystalline inclusions forming a binding network of nodes. Finally, in obtaining plastic substances, one should proceed from a suitably composed mixture of solid and liquid phases with the smallest possible content of the rubber-like phase; such a product will be easily formed, pressed, and extruded, and will not change the shape imparted to it in this way.

In the above sense one may say that fibrous materials, plastic substances, and rubbers are not essentially

by different systems: they are simply different mixtures of the three basic states characteristic of organic high polymers. There is undoubtedly a continuous series of systems, beginning with sharply expressed fibrous materials and ending with typical rubbers; the properties of the materials in this series depend on the ratio among the solid, rubber-like, and liquid states represented in them.

Thus, there are two independent paths to obtaining polymers with new and interesting mechanical properties: 1) new monomers can be synthesized and used to obtain long chain molecules with a high degree of polymerization and a favorable distribution of molecular weights; 2) these substances can be brought to the required physical state by selecting such ratios among the solid, rubber-like, and liquid components that the mixture possesses the desired properties to the maximum degree. At present, a large number of investigators—chemists and physicists—are working in both of these directions, and these studies will undoubtedly lead to the appearance of ever newer materials with valuable and remarkable properties.