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10 Polymers INTRODUCTION Polymers are macromolecules made up of long sequences (thou- sands) of small chemical units repetitively attached by strong chemical bonds to form chains or other structures. Differences from one type of polymer to another are due not only to the chemical nature of their constituents but also to their physical arrangement. Small structural differences, such as branching or cross-linking, can produce profound differences in properties. Research in the field of polymer science is a massive endeavor in the United States and abroad. Polymers possess a range of properties, often unique, that have proved to be adaptable to a wide variety of uses. The production of polymers in this country as measured by volume exceeds that of steel. The investigation of polymers is diverse, requiring interdisciplinary efforts of physicists, chemists, materials scientists, biochemists and biophysicists, and chemical and mechanical engineers. Research in the field is currently vigorous. In the past 10 or 15 years new instrumental developments, e.g., small-angle neutron scattering; Fourier transform infrared spectroscopy; solid-state nuclear magnetic resonance (NMR); light, x-ray, and electron scattering; electron microscopy; new surface probes; computerized instrumentation; and computer simulation, have had a large impact. Paralleling this have been theoretical breakthroughs 206

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POL YMERS 207 in problem areas central to the field, e.g., polymer disentanglement, the excluded volume problem, "elation, and nonlinear mechanics. Another factor enlivening the field is the uncovering of new materials and properties. Examples are semiconducting and conducting polymers, piezoelectrics, liquid crystals, block copolymers, high-strength ex- truded materials, immobilized enzymes, and polymeric membranes. RESEARCH PROBLEMS Amorphous State Solutions and Melts The dilute-solution state is one in which attention can be focused on the behavior of individual macromolecules. For the most part polymer chains form loose coils, and it has been useful to draw an analogy between the path of such a chain and the path a walker might follow wandering randomly through space. However, there is an important difference. The walker can freely recross his path, but the polymer chain cannot cross parts of its path already occupied. This is referred to as the excluded volume, or self-avoiding walk, problem. A coiled molecule expands, on average, to decrease regions of overlap. Whereas the average end-to-end distance of a random walk of N steps goes like N'/9, that of a self-avoiding walk goes like No with v ~ 0.6. The appearance of a characteristic exponent is reminiscent of critical phenomena, reviewed elsewhere in this report (see Chapter 31. In that chapter there is a discussion of magnetic models and their differences according to the dimensionality of the spin. Formally it is found that the polymer problem is in the same universality class as a magnet of zero-spin dimensionality This may make no physical sense for mag- nets, but it illustrates the importance in modern theory of limits defined only mathematically. Once the theory of critical phenomena was applied to polymer problems it proved capable of describing a vast array of observations, both static and dynamic. This includes the description of a state unique to polymers, semidilute solutions. Dilute solutions are those in which the units are widely separated. For polystyrene of molecular weight 106 g/mol (about 10,000 styrene monomers per molecule) a solution of about 0.1 percent polymer has monomer units widely separated, but the polymer molecules as a whole are beginning to overlap each other, i.e., are not dilute. In this semidilute condition, a screening of the excluded volume interactions between monomers on the same chain develops. Screening is another critical phenomena concept (cf. Chap- ter 31. From an experimental point of view, common polymers may not

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208 A DECADE OF CONDENSED-MATTER PHYSICS be long enough for the semidilute theory to apply fully over a large range of concentrations; i.e., they may always be in what is termed a crossover region between dilute and semidilute. It is hoped that progress in handling such crossover effects will soon be made. Poly- mers provide many other manifestations of crossovers that may help to delineate the effects. An extremely valuable advance in investigating polymers occurred some 10 years ago with the development of small-angle neutron scattering. It opened up the possibility for studying the properties of single-polymer molecules in condensed states, when they are perme- ated by other molecules of the same kind. This is done by labeling some of the molecules through replacement of hydrogen atoms with deute- rium. It was quickly confirmed that, in the melt, random-walk statistics apply to single-polymer chains. Since then many other results, some quite surprising, have been obtained (see below). The flow properties (rheology) of polymers are rather unusual, exhibiting long-term memory, viscoelastic effects, and nonlinearities. These are due to the fact that polymer systems, melt or semidilute, are entangled masses. When a strain is induced in a polymer melt the individual molecules are distorted and continue to exert a force (stress) resisting that strain, until the molecules have moved out of the strained, entangled mass and have relaxed to an equilibrium entangled condition. The quantitative description of the dynamic entanglement problem has recently been achieved in a marvelously simple way. Consider a single, long-chain molecule. The molecules surrounding it can be considered, effectively, to form a tube. Think of a snake in a tube as long as itself. If the tube is distorted these distortions are transferred to the snake. That distortion is experienced on some part of the snake as it moves out of the tube until it has fully escaped. Of course, escape is only possible by moving along the tube, lateral motions being prevented. Because of this analogy the proposal is called the reptation theory. It has been successfully applied to describe diffusion, rheology, relaxation of rubbers, healing of cracks, crystalli- zation from the melt, and phase-separation dynamics. There is much experimental activity aimed at testing the applicability and limits of the theory and at developing new refinements, extensions, and uses. To this point we have discussed problems involving properties of systems where the most important aspect is the chain character of the molecule, and the detailed structure and motions on the atomic scale (nanometers) are of peripheral importance. There are many character- istics of structure, packing, and dynamics on the smaller scale that affect polymer properties. Modern tools have advanced the science

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POL YMER5 209 enormously in a decade. These include NMR, fluorescence spectros- copy, Raman and infrared spectroscopy (especially Fourier transform infrared spectroscopy, or FTIR), wide-angle neutron scattering, neu- tron spin-echo spectroscopy, and computer simulation. Traditional methods have been important, too. Light has been shed on how the small units of the molecule pack and manage to move, given that they are restricted by being only pieces of a larger molecule. Structure and properties have been correlated as a step toward a fuller understanding of their relationship. An aim, actually achieved to some extent' is to tailor-make materials with desired physical properties by controlling the molecular or physical structure. Glass The glassy state is extremely common in polymeric materials. The usual glassy brittleness has been circumvented by blending and grafting glassy polymers with rubbery particles in complex ways that are not fully understood. Let us concentrate here on the pure glasses. In general one can say that the theoretical foundations for describing the glass are primitive compared with other physical states of matter. There is substantial, but indirect, evidence that the explanation for some properties involves atom-sized bits of free volume in the glass and that motion is only possible in association with this free volume. What is a glass? It is a disordered material in which the times are long for relaxation back to equilibrium following a change of physical conditions (e.g., temperature or stress). These times may be seconds or centuries. It was once hoped that a description could be achieved in terms of only one extra fundamental parameter that had not relaxed. Recent evidence is that this is not so. However, there seems to be a universal function that the slow relaxations obey. If the system is driven (or normally fluctuates) out of equilibrium, it returns according to the formula expE-(t/~l, where t is the time and ~ and ,8 are parameters. Unfortunately this is not a mathematical expression that is frequently encountered in physics, so little idea exists of what the underlying mechanisms are. Elastomers, Gels, Cross-linked Networks One of the outstanding, early achievements of polymer physics was the development of a working picture for rubber elasticity. A rubber (gel, elastomer) is formed from a nonglassy, amorphous polymer when the molecules are tied together by a few cross-links per molecule.

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210 A DECADE OF CONDENSED-MATTER PHYSICS Basically, macroscopic deformation of the specimen is reflected in a distortion in the positions of the cross-link points. This, in turn, decreases the number of ways the chains between the cross-links can arrange themselves (technically speaking, decreases the entropy). Decreasing entropy takes work, just as increasing energy does (as in stretching a spring), hence the resisting force of a stretched rubber. It was long ago realized that idealized calculations of the elastic force were imperfect, but difficulties in preparing well-characterized samples inhibited (and still do) the test of refined models, for instance those that attempt to account for entanglement. Neutron scattering provides a powerful tool for probing this problem, but the early results do not agree with any of the theories. Explanations may involve a deeper analysis of the topology of the network and its reaction to strain (e.g., the unfolding of three-dimensional pleats). In the course of the process whereby a collection of single molecules is transformed into a totally connected network by progressive cross- linking, there is one critical amount of cross-linking that leads to the first appearance of a cluster spanning the sample. This is the gel point. The properties of systems near this condition are well described as crit- ical phenomena. Ramifications of this description are being pursued. Polymer Crystals Looked at on the scale of atomic spacings (nanometers), polymer crystals exhibit the regular characteristic of small-molecule crystals. Looked at on larger scales, the differences are legion. Each crystal that forms tends to be surrounded by amorphous material. Fractional crystallinity might typically be in the 20 to 70 percent range. The crystals are commonly lamellar (plateletlike) in shape, with a thickness of lO to 20 nm and much larger in other directions. The molecules stretch back and forth between the lamellar faces. The polymer chains form high-energy folds at each face and usually re-enter the crystal either adjacently or in nearby positions. The crystal would be more stable if it were thicker (fewer folds per molecule), so this is not the equilibrium state. The crystals form this way for kinetic reasons. To form a more stable crystal would take so long that it does not occur ordinarily. Thus one is faced with the challenge of deciphering the details of the nucleation bottlenecks to growth in order to understand and predict properties of the crystal. The number of proposed growth processes applicable under various conditions has recently increased. After a period of quiescence this problem has received considerable attention of late because of unexpected results that emerged when the state of individual molecules was examined with neutron scattering.

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POF YMERS 21 1 Viewed on a still larger scale, the lamellae frequently arrange themselves in a spherulitic pattern of bifurcating, radial fibrils, often twisting as they grow. Note that the presence of a twist implies a handedness, which is not inherent to the symmetry of the molecule. Recently, attention has focused on how that broken symmetry is introduced and propagated. There are other varieties of crystal morphology, such as fibers formed on drawing or the forms observed when growth is in contact with certain surfaces. Also it appears possible to grow extended chain crystals under pressure, which may be related to liquid-crystallike ordering. Electrical Properties Traditionally, attention has focused on many polymers because of their properties as electrical insulators. Recently, however, the atten- tion of numerous physicists, many new to the field, has turned to macromolecules because of the discovery of interesting electrical properties in certain polymers. An example is polyacetylene, which when pure is a semiconductor but can be doped into the range of metallic conduction. The polymer consists of a chain of carbon atoms with hydrogen atoms attached to each. In a small ring of this nature all the carbon-carbon bonds would be equivalent, and a half-filled metallic band would be formed. In a large ring or a long chain, however, the polymer lowers its energy by displacing atoms to create alternating single and double bonds between carbon atoms, which gives rise to insulating electronic bands. There are two degenerate structures formed by this d~mer~zat~on, each formed from the other by the interchange of the double bonds. Thus either bonds 1, 3, 5, . . . or 2, 4, 6, . . . can be double. Occasionally one gets transitions between the odd and the even patterns. The resulting walls that separate domains of the two degenerate structures are mobile, and are associated with excited electronic states that spread over some 15 atoms. They are called topological solitons. The dopant modifies the electronic state of the soliton, creating charge donors and acceptors. One of the most remarkable properties of these solitons is that the relation between their spin and charge is reversed from the usual situation; i.e., a soliton with charge 0 has spin 1/2, while a soliton with charge +e has spin 0. These appear to be the actual stable states for mobile neutral defects and charges in polyacetylene. Extensions of this idea to other cases has shown that the charge partitioning can be even more pathological, yielding net fractional charges on solitons that can be rational or irrational. These electronic states can be investigated by various

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212 A DECADE OF CONDENSED-MATTER PHYSICS spectroscopic.techniques. Recently efforts have been made to look at the properties of polyacetylene in a way that integrates physical, structural, and chemical (bond arrangements and transitions) aspects. Another material with interesting electrical properties is polyvinyli- dene fluoride, which is ferroelectric, piezoelectric, and pyroelectric. Microscopically these important materials properties arise from di- poles (on the monomer unit) that can be oriented by subjecting the polymer films to high electric fields at elevated temperatures (well above the glass transition). The possibility of building regular dipoles into polymer structures and creating a wider class of such materials is certainly an exciting direction for the future. The combination of the mechanical properties of polymers combined with piezoelectric and other physical properties offers the promise of a variety of technolog- ical applications. Other Polymer Properties There are other types of polymers, and properties of polymers, no less interesting and important than those just described, that space does not permit us to discuss in any detail. 1. Some polymers form liquid crystalline phases as an outgrowth of the rigidity of the backbone or substituent groups attached to the chain. This ordering leads to some high-strength materials. 2. Commonly polymers are blended to form useful materials that are either true mixtures or intimately associated microphases. 3. Block copolymers are made up of two or more chains attached in the same molecule. Phase separation may occur, but only microdo- mains can form because of the chemical connection between the separated units. 4. Some polymers contain ionizable groups. Their structure, in solution or bulk, is strongly influenced by Coulomb forces. 5. The surface is the face a polymeric phase presents to the world. This surface may be the natural one or one modified deliberately or through aging. Tremendous progress in surface science has been utilized by polymer researchers. 6. Last, but by no means least, mention should be made of some of the problems associated with bipolymers: organization, kinetics, func- tion, compatibility, mechanical properties, and transitions. The excitement of the polymer field is an outgrowth of the diversity of properties that these materials exhibit, a list of properties that keeps growing by discovery or design.

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POL YMER5 213 OPPORTUNITIES The following list highlights several important areas of polymer physics in which significant progress may be expected (or at least hoped for) in the next few years. It is intended to be representative and not comprehensive: 1. Experimental and theoretical efforts that contribute to a funda- mental understanding and/or phenomenological description of glasses, including polymeric ones. The nature of relaxational motions and how these relate to ultimate strength. 2. Understanding of crazes formed during failure and application of that knowledge to the toughening of glasses. (Crazes are microcracks caused by environment and/or mechanical working.) 3. A broader development of the reptation idea to the description of processes influenced by entanglements. A better connection between a fundamental description of entanglements and the effective tube de- scription. Attack on a few persistent disagreements between theory and experiments. 4. Characterization of polymer properties under conditions corre- sponding to crossovers between asymptotic regimes, such as solution concentrations between dilute and semidilute. 5. Development and utilization of molecular tags that can be attached to macromolecules. These tags should have properties, such as spectra, fluorescence, or scattering cross section, that make them easier to observe than the polymers themselves. They should reflect the polymer's phase structure or dynamics. The question of the de- gree to which these properties are modified by the tags should be clarified. 6. Transport of low-molecular-weight molecules through polymers. Use of low-molecular-weight molecules as probes of polymer proper ties. 7. Various studies of polymer dynamics employing high fluxes of synchrotron radiation or pulsed neutrons. 8. Definitive characterization of the polymer-fold surface of crys- talline lamellae. 9. Description of the various polymer crystal nucleation, growth, and aging processes, to explain such observations as curved crystals, spherulitic growth of twisted fibrils, and thickening of lamellae during annealing. 10. Rheology of liquid crystalline polymers. Ordering effects of flows and electrical fields on these materials. 11. Mechanisms of charge conduction along and between conduct

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214 A DECADE OF CONDENSED-MATTER PHYSICS ing macromolecules of various types. The role of dopants. Control of the nonelectrical properties (e.g., solubility, morphology, strength, degradation) of these materials. 12. Rheology of polymer blends (those that are fine dispersions), composites (polymer matrices with particulate or fibrous inclusions), thin films, and block copolymers. 13. Modification of polymer surfaces so that their chemical and physical properties (e.g., adhesion, biocompatibility, catalysis, reac- tivity) differ from those of the bulk. 14. Kinetics of phase separation. 15. Understanding of the forces and factors governing polymer miscibility. 16. The role of entanglements in rubber elasticity. 17. Development of an understanding of the physical factors gov- erning the three-dimensional ordering of bipolymers, sufficient to make quantitative predictions of that ordering in viva, and disruption of order by solvents, heat, and other agents. Description of how the ordering influences biological function, especially with respect to complex processes such as enzymatic action and membrane transport. Structure and function of membranes and their protein inclusions.