by Alexander VOLYNSKY, Dr. Sc. (Chem.), M. V. Lomonosov Moscow State University
The commonest and best-known form of self-organization of matter is seen in the example of crystalline substances found in great abundance. Crystalline lattices owe their origin to rather strong interatomic or intermolecular interactions (ionic, covalent and others). Such forces operate at very short distances on an angstrom scale, something that determines the structural parameters of the lattices.
Regular periodic structures whose parameters are determined by intermolecular interactions:
a - table salt crystal;
However, we come upon even more surprising and no less orderly forms of self-organized matter. These are above all helical (spiral) structures, an essential part of biological reproductive material, its "building bricks" so to speak. Protein is one such "brick", the main one. Any biological structure is built to "designs" recorded in DNA. Typical of both the protein and the DNA are highly ordered periodic structures in the shape of spirals, or helices (helical structures), endowed with specific characteristics-such as an ability to diffract X-rays. The periods of helical structures have been determined with very high accuracy and, as it is with ordinary crystalline substances, they are constants. Biological helices are stable on account of intermolecular hydrogen bonds whose "radius of action" is quite short, being of the same order as that of other intermolecular forces-just a few angstroms.
The list of such examples of self-organized matter in regular periodic structures could well be continued. But there is one common characteristic proper to them: regularity and specificity due to intermolecular interactions which are responsible for each kind of self-organization of matter mentioned above. As we have said, these interactions operate at ultrashort distances (angstroms and even fractions of this unit) and depend on the structure of individual atoms or molecules.
HARD COATING ON "ELASTIC" BASE
Regular periodic structures are by no means confined to systems characterized by fixed values of their lattice parameters. Recently yet another system was discovered and studied, and this is what we call a "hard coating on elastic base (substrate)". The fundamental structural-and-mechanical properties of these systems can best be demonstrated by such widespread objects as polymer films with a thin and hard coating.
A simple stretching (distension) of such films - so common in our daily life and, as it seems, studied well enough - is accompanied by two processes at least - by a cracking of the coat into many regular "isles" and by a distension of the orderly, axially oriented relief. The structures thus arising are highly ordered, and they dissipate and decompose light like real diffraction lattices. The discreteness of the diffractograms obtained thereby is proof of the high orderliness both in the arrangement of elements of a structure (elements responsible for regular microrelief) and in the dimensions of coat fragments and their arrangement on the surface of an elastic substrate.
The emergence of all these structures is of general nature and does not depend on what kind of material a substrate and coating are made of. However, there is one essential condition accounting for the very possibility of their emergence, and this is the deformation of systems of the "hard-coating-on-elastic-substrate" type; such systems are remarkable for a negligibly small thickness of the coating compared with that of the substrate, and for a significant difference in the elasticity modulus of the coating and the substrate.
To understand the formative mechanism of such type regular structures it is important to know that a polymer film stretched uniaxially is acted upon by two deformations simultaneously: elongation in one direction and compression perpendicular to it. And so the coating of a film surface is compressed and distended at the same time. This phenomenon enables us to examine separately the two processes - microrelief formation and coat fragmentation. It is the coat compression that is responsible for the formation of a microrelief Here we are dealing with an anisodiametric (i.e. not even in diameter) solid body deformed by uniaxial compression on the surface of a distended polymer film.
More than 200 years ago Leonard Euler, an illustrious physicist and mathematician (and honorary member of the St. Petersburg Academy of Sciences), was the first to consider phenomena attending these processes. He demonstrated that uniaxial compression causes an anisodiametric solid body (fiber, film, membrane) to lose stability at critical loads and take the form of a half-wave. We come to deal with such phenomena in our daily life - say, if we press a thin metal ruler or a sheet of paper. But should a thin hard coat be rigidly bound with an elastic substrate (base), the stability loss pattern of the former will change dramatically. Upon reaching a critical compressive load an anisodiametric solid body will not be able to take the form of a half-wave because with the deflection from a rectilinear form it will be acted upon by a rotary force coming from the base, a force proportional to the deflection value. As a result of interac-
How an anisodiametric body changes its form if compressed: when in a free state (a, b) and when on an elastic base (c, d).
tion between the external force and the internal resistance of the substrate, the coating is to fold like a folding rule and take a sinusoidal form with a wave period equal to X (lambda).
Deformations caused by the compression of an anisodiametric solid body (coating) will be growing with an increase in the number of perfect bandings (and with a decrease in the period of relief). Yet an elastic (and rather long) base "fixed" to a coat will make certain corrections in the course of this process. Obviously, the larger the relief period, the larger-other things being equal - the relief amplitude will be. Such an increase means a "pull-out" of the part of a polymer "fixed" to the substrate - it will move rather far from the initially smooth surface. Such kind of deformation of the substrate involves certain effort, that is some work should be done.
That is to say, an increase in the relief period, so "good" to the coating, is "no good" at all to the elastic polymer base. Under like conditions, nature always takes the course of minimizing energy expenditures. Research scientists at Moscow State University's Department of Chemistry computed the value of such expenditures for rubber and plastic substrates and then proved it experimentally. This shows the validity of our surmises with respect to the mechanism of this particular kind of self-organization of matter.
Regular fragmentation of a hard coating is also related to the specifics of the transmission of mechanical stress from an elastic base to a hard coating through interface. In particular, the nature of such fragmentation is a function of the substrate deformation mechanism. By our daily experience we know: polymer films are deformed at least in two ways-homogeneously (like rubber) and inhomogeneously (like polyethylene film). In the latter case fragments of the initial polyethylene and those of the oriented film ("neck") coexist.
In the case of the homogeneous deformation of a substrate polymer, the dimensions of coat fragments are not identical at the start of distension. The point is that at this initial stage of destruction (at small elongations of the substrate polymer) it is the inevitable surface microdefects, setting off the destruction process, that make a decisive contribution to the fragmentation of a coating. Such kind of defects, arranged on the coating in a random, chaotic mode, are thus responsible for its irregular and random destruction.
But then comes a unique process when each of the fragments is destroyed. The thing is that the process of substrate distension continues after the breakup of the coating into fragments and, as a consequence, each fragment keeps under load. The stress in each fragment is distributed most unevenly - it is equal to zero at a fragment's ends but grows toward the middle to attain a maximum right in the center. The
stress continues with the further distension of the substrate and reaches the ultimate tensile strength of the fragment - again, in its center. As a result we can see a surprisingly elegant process of coating destruction whereby the coating splits into two equal parts (all this can be observed in direct microscopic experiments). Then the dimensions of the fragments are equalized, and on the surface of the substrate there appears a system having a rather narrow pattern of distribution according to dimensions.
The coating breaks up even more equally in the case of the inhomogeneous deformation of the substrate polymer to give rise to a structure built of well-nigh identical ultrathin coating tapes parallel to one another and spreading from one edge of a deformed sample to the other. The cause of the spontaneous formation of such a unique structure is this: a set of characteristic defects of the coating does not affect fragmentation. As we have already said, in the case of inhomogeneous deformation both kinds of fragments coexist - those of the initial, non-deformed polymer, and those of the deformed polymer converted into an oriented state. This means that two parts of the coat-
ing should be there: one broken into fragments and the other persisting in an integral, intact form. All events related to the fragmentation of the coating occur in a narrow shifting zone between the oriented and the nonoriented parts of the deformed polymer. Always present there is the edge of the destroyed coating where the stress is equal to naught. It increases away from the edge of the coating and attains fast the ultimate strength value. At this very moment yet another tape of the coating is off.
Microdefects in this case do not impact the coating's fragmentation because the surface of a non-oriented polymer is not deformed in practical terms, with the value of elastic deformation being not above a few percent.
"Hard-coating-on-elastic-base" systems give rise to helical periodic structures as well. Such kind of self-organization takes place with the shrinkage of polyamide coated with a thin and hard layer. A helical crack develops in the hard coating, and in the end the layer turns into a marvelously orderly helix. Although the mechanism of this phenomenon is not elucidated yet, there can be no doubt that we are dealing with one instance of self-organization achieved by means of regular periodic structures within "hard-coating-on- elastic-base" systems. The main parameters of the structures thus formed (relief period, average dimensions of coat "isles" and helical lead) may vary in a wide range; they depend on external factors: correlation of elasticity moduli of the coating and base (substrate); level of the stress sustaining deformation; coat thickness.
In a nutshell: besides regular periodic structures whose parameters are determined by interatomic interactions, there are also structures predicated on yet another principle of self- organization of matter in "hard-coating-on-elastic-base" systems which depends on macroscopic characteristics of materials.
Even though this principle of self-organization of matter is not directly related to intermolecular interactions, one thing is obvious, however: such characteristics of solid bodies as elasticity modulus, strength or yield point are ultimately "assigned" by these interactions, by these forces. It is not the absolute values of the above three characteristics that are a decisive factor for the relief structure of "hard-coating-on-elastic-base" systems but rather the ability of a coating to transmit mechanical stresses from an elastic base to any distance. In our case, the absence of a direct connection between the conditions of self-organization of matter and its molecular structure also proves that one of the main factors determining the parameters of new structures is the thickness of a hard overlayer which is in no way connected with intermolecular interactions.
An identity period of such structures is not their constant. This is a conspicuous feature of the given kind of self-organization of matter. Actually, this period has no limitations in size and may vary in a very wide range-from nanometers to thousands of kilometers.
REGULAR PERIODIC STRUCTURES IN THE WORLD WE LIVE IN
As shown by our studies, there are at least two kinds of self- organizing structures in the world we live in. The first, determined by intermolecular interactions, encompasses an immense number of crystalline substances (such type structures make up no less than half of the solid matter both here on earth and in other bodies of the solar system). Also, huge masses of matter organized into regular periodic structures come into being. The terrestrial biosphere is virtually saturated with them: by Academician Vladimir Vernadsky's estimates, the mass of our planet's animate matter must be equal to 10 14 -10 15 tons.
Just as common in our world are "hard-coating-on-elastic-base" systems. All the various fruits (tomatoes, apples and so on), the bodies of animals and man, the earth and other planets belong to this category.
Such type systems are subject to various deformations under natural conditions. And as a consequence, numerous regular structures come to be. Like, say, wrinkles on human faces. The cause of this sad phenomenon is this: with years the soft tissue under the relatively hard skin tends to shrink (it contracts). And so the skin loses its mechanical stability and develops folds (folded relief). Cosmetic problems aside, a loss of stability conditioned by planar compression produces beautiful reliefs similar in their organization to the surface of the brain with all its convolutions. It might well be that during evolution the cerebral cortex of animals lost its stability in the course of growth. Like structures often appear in many other cases, for instance, when a dab of paint dries up, or when a colony of corals grows.
"Hard-coating-on-elastic-base" systems are often deformed by forces of planar tension. For example, as moist soil dries up, a hard crust formed on its surface "will" contract. But such contraction does not really take place because the soil surface is tied up with an underlying soft base incompressible in practical terms. And thus the hard crust is subjected to planar tension. The ever increasing stresses during soil moisture evaporation produce a grid of cracks in the coating crust; these cracks appear and spread in keeping with rigorous laws which are likewise determined by the properties of "hard-coating-on-elastic-base" systems.
Similar pictures are observed in cooling magmatic melts too where a surface crust is also formed and breaks up into fragments for reasons described above. A slow cooling of the melt causes the interface between the hard upper layer and the still hot liquid phase beneath to move deep into the melt. The solid phase, coexisting with the liquid one, is always acted upon by planar tension forces that deform it. If this is a slow process, the pattern of fragmentation is so much regular and orderly as if it were man's handiwork. This particular mechanism accounts for an amazing natural phenomenon, the "basaltic fingers". One such well-known object, described as "giant's causeway", is found in Northern Ireland.
Relief formation of the earth is perhaps the most spectacular example of this type of self-organization of matter. Yes, our planet is a typical system of this kind - "hard-coating-on-elastic-base". Tectonic stresses in its subcrustal strata produce reliefs just like those we see when polymer films with hard coating are deformed. But terrestrial reliefs occupy vast expanses over thousands and thousands of kilometers (at least a third of the entire area of the ocean floor).
Studying these phenomena, we can obtain important quantitative information on the earth's crust as an independent physical object - in spite of the many compounding factors like a spherical form, variable chemical composition and temperature gradients, presence of defects, and so forth. If we consider the earth's crust as one solid body capable of receiving and transmitting mechanical stresses over huge distances (on the scale of oceans and perhaps even on the global scale), we can estimate the value and vector of compressive and tensile stresses as well as such parameters as modulus of elasticity, strength, yield point-all that for the earth shell.
Now, to sum up. There are at least two essentially different kinds of self-organization of matter in the shape of regular periodic structures. The first type is determined by short-term intermolecular forces that account for the periodicity scale (one and two-digit figures on the angstrom scale). The other type is conditioned by macroscopic characteristics of substances, such as modulus of elasticity, strength, yield point, thickness of a hard coat, and so on. The periodicity of such systems is actually open-ended both on the micro- and on the macrolevel.
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