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Polymer Science and Engineering: The Shifting Research Frontiers 4 Enabling Science Enabling science describes the fundamental work that makes possible the development of technological applications. This work includes synthesis, characterization, and theory. POLYMER SYNTHESIS Synthesis provides the underpinnings for all advances in the science and engineering of polymeric materials. The past decade has produced many notable synthetic advances: the extension of living polymerization methods to new classes of reactive intermediates and new classes of monomers, the appearance of hyperbranched polymers, the controlled preparation of inorganic polymers and organic-inorganic hybrids, the development of efficient biological polymerization strategies, and many others. This section considers the objectives of synthetic polymer chemistry, both fundamental and practical. The most important issues examined below include: Control of chain architecture, Synthesis of polymers of controlled end-group structure, Design and synthesis of polymers with outstanding thermal stability or useful electronic properties, Modification of polymer surfaces, Development of new polymerization methods, Challenges in reactive processing, and Interplay of organic, inorganic, and biological chemistry in producing novel macromolecular materials.
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Polymer Science and Engineering: The Shifting Research Frontiers Some of the key synthetic advances of the last 10 years are noted, and unsolved problems and important research directions are identified. Control of Chain Architecture Topology Chain topology controls many critical properties (e.g., crystallization, solubility, and rheological behavior) of polymeric systems. The development of linear polyethylene via the Ziegler and Phillips processes in the 1950s provides the most important example, wherein "straightening of the chain" resulted in a rise in Tm of ~30°C and significant improvements in strength and toughness. Control of topology in this case led directly to a new class of materials now sold in quantities of millions of tons per year. Current synthetic methodology affords a high level of control of chain structure, and syntheses of linear and branched chains, stars, rings, and combs have been achieved. A striking recent advance has been the preparation of hyperbranched—or dendritic—macromolecules, in which iterative branching steps lead to structures in which segment density grows rapidly as one proceeds radially from the molecular "core" (Figure 4.1). Dendritic polymers of narrow molecular weight distribution have been prepared by laborious stepwise synthesis, while "one-pot" methods have been developed for polydisperse samples. In some instances, remarkable improvements in solubility (in comparison with linear analogues) have been reported for hyperbranched chains, and there has been plausible speculation that dendritic polymers may have useful sequestration and reactivity properties. Commercial applications for these materials have not emerged as of this writing. Polymeric rotaxanes, in which the chain backbone is threaded through a series of macrocycles, have also been reported recently. In this arrangement, the macrocyclic "rotors" are not covalently attached to the "axle" but instead are constrained by bulky end groups from topological dethreading. It has been suggested that controlled, reversible switching of rotor positions on the axle might provide a basis for functional molecular devices (Figure 4.2). Even given these advances, there is no shortage of intriguing and important topological issues yet to be addressed, and it appears likely that attention will shift to molecules of even greater complexity. Preliminary reports of two-dimensional ribbonlike polymers have appeared, as have descriptions of synthetic DNAs with the topological character of a cube. Particularly intriguing is the prospect of exploiting both covalent and non-covalent interactions, to provide control not only of topology, but also of the molecular geometry over large length scales in real space.
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Polymer Science and Engineering: The Shifting Research Frontiers FIGURE 4.1 A schematic illustration of the divergent synthesis of dendritic polymers. Segment density grows rapidly as one proceeds radially from the molecular "core." SOURCE: Reprinted with permission from Tomalia et al. (1992). Copyright© 1992 by the American Chemical Society.
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Polymer Science and Engineering: The Shifting Research Frontiers FIGURE 4.2 A polymeric rotaxane with an aromatic polyamide "axle" and macrocyclic polyether "rotors." SOURCE: Reprinted with permission from Gibson et al. (1992). Copyright© 1992 by the American Chemical Society. Length Many desirable properties of polymers, such as mechanical strength, thermal behavior, processibility, diffusion, miscibility, and adsorption at interfaces, are dependent to a large extent on the molecular weight. Hence, synthetic polymer chemists have directed attention to development of methods appropriate for molecular weight control. Great strides have been made, especially in the area of living polymerizations. Over the past decade, besides improvement in living anionic techniques, several new methods have been devised and/or improved. Notable among these are group transfer polymerization (GTP) for polymerization of (meth)acrylates (Figure 4.3), ring-opening metathesis polymerization for cyclic hydrocarbons (ROMP), Lewis base-mediated cationic polymerization for vinyl ethers, and immortal (metalloporphyrin-catalyzed) polymerization for heterocyclic monomers. All of these methods are capable of controlling not only the average chain length but also the molecular weight distribution. However, chain length control is still statistical. One can argue that one of the current major challenges facing the polymer chemist is the preparation of polymers of absolutely uniform chain length for a wide range of polymers. There are indications that this may be met through the use of genetic techniques and solid-phase synthesis. How properties will be affected and which properties will be influenced by the truly monodisperse materials are two questions to be explored. Another challenge is in condensation polymerization, where chain length control is not precise. The use of the cyclic oligomer method recently developed shows promise, but there is a need for further studies. A thorough mechanistic
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Polymer Science and Engineering: The Shifting Research Frontiers FIGURE 4.3 Group transfer polymerization (GTP). study to delineate the factors affecting chain termination and chain transfer, events that adversely affect chain length control, is also needed if one is to solve completely the problem of molecular weight control. Sequence Control of monomer unit sequence in copolymers is the most difficult of the fundamental problems facing polymer synthesis. Whereas nature prepares macromolecules of precisely defined length and sequence, synthetic polymers are mixtures of chains characterized by substantial heterogeneity. As described in the preceding section, considerable progress has been made in the development of polymers with narrow distributions of chain length. By comparison, the control of sequence that can be exercised is primitive and is limited essentially to the preparation of statistical, alternating, and block copolymers. Three approaches to the synthesis of copolymers of controlled sequence are available, but all suffer from significant limitations. Solid-phase methods, developed in the 1960s for peptide synthesis, remain slow and costly. Genetic engineering techniques are more rapid and efficient, but are for the foreseeable future restricted to the preparation of polypeptides. The third method, now in its infancy, consists of the controlled, portionwise addition of monomers to living chain ends. While this method is unlikely ever to lead to precise control of sequence at the monomer level, the preparation of complex architectures comprising many short monomer blocks appears to be feasible. One might expect such controlled-sequence copolymers to exhibit unique and interesting behavior in self-assembly, at interfaces, or in optical or electronic applications. Isomerism The geometrical, stereochemical, and regioisomeric structures of the constituent chains have major influences on the transition behavior, morphology,
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Polymer Science and Engineering: The Shifting Research Frontiers thermal stability, and so on, of polymeric materials. Geometrical isomers can be most easily illustrated by pointing out the possible microstructures available in polydienes, such as polyisoprene and polybutadiene. Microstructures of polybutadiene are shown in Figure 4.4. Polybutadiene can exist in the cis or trans arrangements or in vinyl or 1,2-structures. Furthermore, the 1,2-microstructure can exist in highly isotactic or syndiotactic configurations or in a mixture of the two, which one describes normally as atactic. The importance of these various isomers varies widely. The cis structure has a remarkably low glass transition temperature and is widely used in tires and other important elastomeric applications. By contrast, the trans structure is highly crystalline and currently has no important applications, even though various biomedical uses (e.g., casts) have been proposed in the past. Both highly isotactic and syndiotactic semicrystalline 1,2-polybutadiene materials have been prepared by coordination catalysis; however, at this time neither has found significant application. Atactic 1,2-polybutadiene is accessible by anionic polymerization and has been considered as a potential hydrophobic, moderate-cost starting material for low dielectric thermosetting networks. However, significant applications of this material have not been developed. The current state of the art in these areas utilizes principally free radical, anionic, and coordination catalysis. Free radical polymerization of butadiene in emulsion is practiced and produces a mixed cis-trans structure with about 20 percent of the 1,2-microstructure. The ratio of cis to trans units is polymerization temperature dependent. Current practices produce approximately 50 to 60 percent trans, ~20 percent 1,2-microstructure, and the remainder cis 1,4-microstructure. Anionic polymerization in hydrocarbon solvents is industrially important and produces 90 percent 1,4-microstructure with short sequences of cis and trans arrangements predominating. About 10 percent of the chains are atactic 1,2-units. This material is used in a variety of applications and displays a glass transition temperature of about -90°C. Coordination catalysis can generate rather high isomeric purity in all of these systems. Regioisomerism can include variations on the usual head-to-tail enchainment that is observed in most chain polymerization of vinyl monomers. In general, both electronic and steric driving forces produce largely head-to-tail enchainment. However, it is well known that small amounts of the abnormal head-to-head and tail-to-tail structures are found in a variety of materials, including poly(vinylidene fluoride), poly(vinyl chloride), and to some extent, poly(vinyl acetate). Minor imperfections of this type can influence critical performance or processing parameters, such as piezoelectricity or thermal stability in the melt. This has been a problem in poly(vinylidene fluoride), where variation in polymerization conditions can result in a proportion of head-to-head structures as high as 20 to 30 percent. These structures are inevitably less thermally stable and, in general, are undesirable. Exceptions certainly are possible, particularly where controlled instability is desired, as in some resist materials.
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Polymer Science and Engineering: The Shifting Research Frontiers FIGURE 4.4 Microstructures of polybutadiene. The tacticity of vinyl polymers is critical to the control of the crystallinity and thermal transition behavior of these materials. Free radical polymerization produces mostly atactic structures, with the temperature being one important parameter, which can modestly control placement. In general, ionic polymerization, and especially coordination catalysis, is required to produce either highly isotactic or highly syndiotactic materials. A limited number of possibilities exist with anionic polymerization, for example, with certain methacrylates and with cationic polymerization in, for example, vinyl alkyl ethers. Recent advances in this area concern the preparation of syndiotactic polystyrene with titanium-aluminum
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Polymer Science and Engineering: The Shifting Research Frontiers FIGURE 4.5 Chiral complex for the control of tacticity of polypropylene. catalysts and the production of stereoblock polypropylenes with soluble metallocene catalysts (Figure 4.5). Control of macromolecular asymmetry has also been achieved within the last decade, such that optically active materials can now be prepared on the basis of a controlled helix sense, that is, a predominance of left-or right-handed helices in the solid polymer. Such materials have found application as media for chromatographic resolution of enantiomers. Advances in catalysis that could produce better understanding of polymerization mechanisms are needed to further refine the microstructure and to produce improved materials. Synthesis of Polymers of Controlled End-Group Structure An increasingly important class of polymers are telechelic polymers, which contain reactive end groups that can be used to further increase the molecular weight of a polymer during processing or to generate block copolymers. Perhaps the most widely used materials of this type are the polyols or polyglycols.
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Polymer Science and Engineering: The Shifting Research Frontiers These nominally difunctional materials are used in a wide variety of applications in which they are reacted with isocyanates to prepare segmented polyurethanes and polyureas (Figure 4.6). Polyols can be prepared by either ring-opening or step-growth polymerization. In the latter case, the end-group functionality will be defined by the component that is present in molar excess, and the molecular FIGURE 4.6 Reactive end groups in the synthesis of segmented polyurethanes.
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Polymer Science and Engineering: The Shifting Research Frontiers weight can be controlled by the stoichiometry. Thus, the same chemistry that allows end-group control also can produce other, more sophisticated block or segmented copolymers. The success of the polyglycols, such as polypropylene glycol and polytetramethylene glycol and their copolymers, demonstrates the value of this approach. For example, urethane foams for automobile seats are generated from the polypropylene glycols. Thermoplastic polyurethanes, which are important in a variety of applications, are synthesized from the polyether systems, as well as polyester polyols. Telechelic polymers can also be produced by living polymerization, and either a functionalized initiator or a terminator can be used to introduce the reactive groups of interest (Figure 4.7). Alternatively, a difunctional initiator can be used, and the reactive ends can be functionalized. Both approaches have been demonstrated for anionic and group transfer polymerization, and an analogous technology for cationic polymerizations is beginning to emerge. In cases in which the reaction is not living and cannot be controlled to be living, chain transfer with a functionalized agent is the only solution for the preparation of telechelic polymers. Some success has been realized using this technique for radical polymerizations, and recent advances have been made in the preparation of telechelic polymers using difunctional acyclic olefins as chain transfer agents in ring-opening metathesis polymerization. This system is particularly suited to this approach owing to the near identity of the reactivity of the acyclic chain transfer agent and the cyclic olefin monomer. In spite of this progress, telechelic polymers synthesized by chain processes remain difficult to prepare on a large scale and with a high degree of end-group functionality. New techniques and methods are essential to prepare such materials. For example, there are no straightforward routes for the preparation of telechelic polyethylene and polypropylene. Major advances will come from the development of new techniques to control the molecular weight and molecular weight distribution of step growth polymers and the synthesis of chain growth polymers that have precise end-group structures. Design and Synthesis of Thermally Stable Polymers Thermal stability has been defined as the capacity of a material to retain useful properties for a required period of time under well-defined environmental conditions. Many factors contribute to heat resistance, including primary bond strength, secondary bonding forces (hydrogen bonding, dipolar interactions), and resonance stabilization (in aromatic structures). The mechanism of bond cleavage (particularly with respect to whether the broken chains can be combined or further unzipped) must also be considered. For example, α–methyl-substituted macromolecular materials often will regenerate sizable amounts of monomer, whereas highly aromatic condensation polymers and even vinyl polymers with
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Polymer Science and Engineering: The Shifting Research Frontiers FIGURE 4.7 Introduction of reactive end groups by use of a functional terminator.
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Polymer Science and Engineering: The Shifting Research Frontiers consequent properties depend critically on thermal history. Similar problems exist to formulate molecular-level composites as mixtures of stiff and flexible chains. Very little theoretical work is available for addressing these problems and guiding critical experimental work. Block Copolymers To achieve a well-defined phase-separated morphology, in the process of designing materials with optimal properties, an important approach is to connect the two polymers of different chemical structures by covalent bonds, thereby producing block copolymers. Many prominent examples include thermoplastic elastomers used in commerce and biomedical technology. Block copolymers also have other uses, such as compatibilizing immiscible polymers, which arise from their ability to form micelles and self-assembled structures. Theories have begun to describe the morphologies of the self-assembled structures but are still unable to explain some observed structures. Further theoretical advances are needed to understand the features of their complex phase diagrams, such as the influence of chain architecture. Improved processing of materials containing block copolymers would benefit from theoretical guidance on the behavior of these systems in shear flows, in external fields, and under pressure, all of which are used as means for controlling morphology. Polymer Interfaces An increasing number of new composite materials are materials that have different phases dispersed throughout. The strengths of such materials are often determined by the strengths and morphologies of the interfaces between the phases. Adhesion is of intense interest: in some cases, such as for paints and bonding agents, adhesion should be high; in other cases, such as for lubricants, it should be low. Hence the need arises to understand the interfacial characteristics between different polymers and to understand the morphologies of compatibilizing agents, typically block or graft copolymers, that join two or more dissimilar components. Only recently have investigations considered the behavior of homopolymers and copolymers at interfaces and the nature of interfacial energies between polymers. There has been much progress in understanding properties of polymer interfaces, but we do not yet have a satisfactory understanding, at the molecular level, of the factors involved in strength and failure. In addition, the viability of certain polymeric materials is affected by the segregation of their components at the interfaces, so the properties of these interfaces are likewise of interest, especially in systems containing block copolymers. Theoretical and computational work will aid greatly in developing novel multicomponent polymer systems, where progress, although remarkable so far, still has a long way to go.
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Polymer Science and Engineering: The Shifting Research Frontiers Polymer Surfaces and Thin Films A number of surface properties of polymers, such as friction, wear, lubrication, adhesion, and sorption of surface species, have been investigated for many years because of their technological importance. But these studies have tended to be macroscopic and empirical, and thus little is known at the molecular level. It is observed that surface enrichment occurs where species preferentially concentrate at the surface according to composition and molecular weight. Surface segregation and phase separations near surfaces are not well understood. Nor is much known about the interactions between polymer surfaces and other materials such as liquid crystals, for example, in flat panel displays. Experimental methods to study the structures and properties of polymers on the 10- to 100-Å thickness scales are limited. Theoretical and computational efforts are critically needed to fill in details from the limited available experiments, which are often difficult and costly to perform. Biopolymers Biopolymers are another important class among polymeric states of matter. Biomolecules adopt an extremely wide variety of structures, spanning a large range of different types of organization and hierarchical complexity. Biology has control over specific monomer sequences, a power that is not yet available in synthetic polymer chemistry. It is the sequences, for example of proteins, RNA, and DNA, that control molecular architectures, and they do so with a high degree of precision. Force-field simulations for polymers were mainly developed first in the biomolecules area, and they continue to be of major importance in understanding biomolecule properties. More synergy is desirable between the polymer and biopolymer communities, because many of the needs and problems for theories and simulations are the same. Major needs in this area are for (1) theories and simulations that can couple and bridge a wide range of time and spatial scales and (2) better understanding of the complex interactions, such as electrostatic, hydrophobic, and hydrogen bond forces, that are important for biomolecules and other polymers in water. Dynamics and Properties Local Motions in Polymers Localized motions in polymers include the same vibrational and torsional movements that are characteristic of motions in small molecules. However, the connectivity of a polymer chain introduces additional scales of "local motion," which can range from side-group rotations to cooperative movements involving segment sizes with tens of repeat units. It is these localized segmental motions
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Polymer Science and Engineering: The Shifting Research Frontiers that underlie variations in physical properties of polymers as a function of temperature and that influence mechanical and other properties of polymer materials. Theoretical descriptions of local motions lag far behind the experimental advances made in the last decade. Experimental advances have derived from tools such as NMR, fluorescence, electron spin resonance (ESR), and dielectric, rheo-optical, and dynamic mechanical instruments. Theoretical and simulation efforts are badly needed to provide a focus for producing a unified picture of chain dynamics with predictive capabilities based on fundamental principles. Also, currently available theoretical techniques have not yet linked the microscopic details of local motions to the long time relaxation behavior that is central to understanding mechanical, viscoelastic, and aging properties of materials. It is thus necessary to develop more molecular treatments of long time dynamics. Nowhere is this problem more apparent than in work on protein dynamics and folding, the separations of biomolecules according to their mobility under electric fields in polymer gels, and the rheology of entangled polymers. Important steps are being made in understanding how small molecules, such as gases and diffusants, affect local motions of polymeric chains, in order to diffuse through them. Such studies are necessary for developing better polymeric membranes for gas separations technology and better polymeric packaging materials for electronic circuitry, soft drink containers, and so on. Rheology of Liquid Polymers Molecular rheology has received considerable attention in the last 15 years. Substantial advances have been made by using the simple idea that the transport kinetics of polymers in dense media can be described in terms of the "reptating" motion of one chain within a medium of other chains by snakelike motions of the chain through a "tube" created by entangled neighboring chains. Much work remains to be done because current theories are still mainly of the single-chain type. New insights are required to better describe the nature of entanglement phenomena of the surrounding chains and to incorporate the relaxation of the surroundings and other motions on the rheological properties. Advances in this area will also benefit from increased studies on copolymers in solvents, and on systems with complex topologies, such as stars and rings, and well-defined molecular weight distributions. We do not yet have a good theoretical understanding of the influence of chemical structure on rheology, because these effects are currently described by simple empirical monomer friction coefficients. Advances are likewise desirable in treating thermodynamics and phase behavior of polymers under the strong flows typical of processing conditions used to fabricate commercial materials. The molecular rheology of stiff chains, with its relationship to the nature of liquid crystalline order and their domain boundaries or disclinations, is another area that requires much more effort. An increased use of continuum rheological models to solve realistic polymer-processing
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Polymer Science and Engineering: The Shifting Research Frontiers flow problems has been spurred by the recent expansion in computing power. Further increases in computing power will enable workers to tackle more complex flows and to use the more sophisticated nonlinear models available. Instabilities in fibers, jets, wakes, and inlets will need continuing attention in this regard. Furthermore, a better connection between continuum and molecular rheology is necessary. Continuum rheology describes phenomena in terms of coefficients whose molecular significance is not clear. The rheology of multiphase systems is currently an active research area. This work considers the rheology due to assemblies of continuum phases with small dimensions. Examples are rigid fibers or more symmetrical ones in polymer fluids, phase-separated block or graft copolymers, and phase-separated polymer liquid crystals. Questions associated with polymer interfaces will be prominent in this area, because the wetting and bonding of the heterophases are important in these systems. Mechanical Properties There has recently been considerable improvement in molecular descriptions for the crazing and failure mechanisms of single-phase glassy polymers in terms of entanglements and chain breakage. The use of multiphase polymers, particularly block copolymers and polymer blends, has increased substantially in the last 10 years, but the deformation and toughening mechanisms of these systems are little understood. In general, a molecular-level description for mechanical properties of glassy polymers, such as toughness and fatigue, is still at a primitive stage, although computer simulation studies have recently shown promising results in understanding mechanical modulus and certain plastic flow processes. Mechanical properties, such as adhesion, at polymer interfaces have recently received considerable theoretical attention, because they are critical to many technological problems. Present theoretical models that are based on simple single-chain-level pull-out and breakage need improvements in view of recent carefully designed experimental tests. All the highly oriented polymer fibers, such as Kevlar®, that exhibit outstanding tensile moduli and strength unfortunately show poor compressive strength, thus complicating their applications. Molecular-level description of compressive properties of oriented polymers is sorely needed in order to overcome this fundamental weakness in understanding high-strength polymers. There is a continuing use of macroscopic nonlinear viscoelasticity models to describe polymer deformations, but the problems of uniqueness and physical significance of the representations are by no means solved. Fracture mechanics has proved useful in describing the failure of brittle materials and is now being extended to tougher materials. More work is required for the description of the failure process and its relation to other mechanical properties, especially for polymer matrix composites. Again, it is important to establish bridges between
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Polymer Science and Engineering: The Shifting Research Frontiers these continuum descriptions of fracture processes and molecular mechanisms involving stress concentrations on chemical bonds and the relationship to molecular topology. Electro-active Properties Conducting polymers have been an active research area during the last 15 years, but there are still fundamental problems in understanding the conduction processes. This understanding is critical to decreasing the bandgap of a conducting polymer to find an intrinsic conductor without any stability problems, to shifting the optical transitions out of the visible region in order to produce a transparent conductor, and to boosting the conductivity to obtain a truly metal-like conductor. Relatively little is known about the nature of conduction carriers for many of the polymers that are being investigated for this purpose. The mechanism of charge transport needs greater study, particularly with regard to the jumping of charge carriers between chains. Many unsolved problems persist concerning fabrication and stability of these materials, and theory could be very helpful in this regard. Nonlinear optical properties of polymers, both second-and third-order non-linearities, present enormous potential applications for future electro-optic devices, such as high-speed communications, data storage, and optical computing. Hence, the nonlinear optical properties exhibited by a large number of chromophore structures and polymer architectures have been investigated in the last several years. Despite the impressive amount of experimental work so far, advances in device applications are hampered by the lack of predictive capabilities for the optical absorption, linear optical, and nonlinear optical characteristics of chromophore structures, and chromophore-polymer interactions. Semiempirical computational methods, with the parameters optimized by using available experimental data, do provide reasonable trends within a given class of materials, but they are not reliably transferable to different types of chromophores. More theory is needed to relate these semiempirical methods to first-principle ab initio approaches to guide the improvement of the former methods. We need new theory dealing with methods for correlating many electrons. Polymers have become an integral part of the current flat panel liquid crystal display technologies, where polymers form the aligning layers to give the liquid crystals the desired tilt angles. Moreover, polymer-dispersed liquid crystal systems show great promise for improved display applications. There is not yet theory for polymer-liquid crystal systems and their dynamics under electric fields. This is required to understand their display characteristics. Computational Methods As noted above, the growth in computing capabilities has enabled the modeling of polymer properties through computer simulations, often called computer
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Polymer Science and Engineering: The Shifting Research Frontiers experiments. Computer experiments are useful to address a wide range of questions and to model systems at the level of atomic interactions and in other situations at the macroscopic level. However, the simulation of equilibrium and dynamical polymer properties is complicated by the huge variations in processes that occur on disparate time and length scales. Local small motions and small deformations occur on short time scales of picoseconds to nanoseconds while diffusion of entangled polymers and protein folding occur on time scales of milliseconds to seconds. Many other polymer processes occur on intermediate scales or over wide ranges of scales from the microscopic to the macroscopic. Different simulation methods (and theories) are needed for the different time and length scales. Force-Field Simulation One important computational tool is high-resolution force-field computer simulation. It is based on the interatomic forces, appropriately parameterized from either experiments on simple systems or ab initio quantum mechanical methods. Molecular dynamics (MD) methods, for example, use these forces to continually solve Newton's laws of motions for successive steps in time. A typical time step is about 1 femtosecond, at which the positions and velocities of the particles are recomputed. As the system evolves in time, the computer monitors the internal structures, the motions of molecules, and related properties. Given current capabilities, it is now possible to simulate systems having about 10,000 atoms to hundreds of picoseconds. These simulations are instructive for learning about the behavior of polymers and biopolymers and for capturing our understanding of them in underlying physical force laws on atomistic scales and in terms of the repeat chemical structure of polymers. However, the power of MD simulations is currently limited by the practically achievable time scales and physical sizes and the uncertainties in the force-field parameterization. Figure 4.11 shows the power and limitations of force-field methods. The second line of the figure shows many processes of biopolymers, and the first line gives the time scale on which they occur. The third line shows processes of synthetic polymers. The power of force-field methods is the wide range of phenomena to which they can be applied, because all physical processes are ultimately derivable from the underlying forces. The main limitation of the method is that computer power is not currently great enough to explore many properties. The fourth line shows projections for the year in which various properties are expected to be accessible by simulations. This time line is based on estimated developments in parallel-processing computing. The maximum run length for a small protein in water in 1992 was about 500 picoseconds (ps), which requires a few hundred hours on a supercomputer. But a single run does not yield an understanding of a process. In 500 ps, we can observe about 10 occurrences of a process that has a 50-ps relaxation time. If we need 10 different samples of the computer experiment in order to understand the statistical errors,
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Polymer Science and Engineering: The Shifting Research Frontiers FIGURE 4.11 Time scales for various motions within biopolymers and nonbiological polymers. The year scale at the bottom shows estimates of when each such process might be accessible to force-field simulation on supercomputers, assuming that parallel processing capability on supercomputers increases at about the rate of 103 every 10 years and neglecting new approaches or breakthroughs. At current capabilities, a given allotment of computer time can be used for one run performed over a few hundred picoseconds for a small protein in a few thousand water molecules, or for 1,000 runs to explore 1,000 processes that have relaxation times of hundreds of femtoseconds; this range is indicated by the error bar below the year scale. SOURCE: Reprinted with permission from Chan and Dill (1993), p. 29. Copyright © 1993 by the American Physical Society.
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Polymer Science and Engineering: The Shifting Research Frontiers then our ''understanding" of processes could be said to be only in the tens of picoseconds range at the present time. By these estimates, it will be tens of years until many processes such as protein folding, glass transition, shear thinning, and creep and aging in polymers will be fully understood by force-field simulation. Nevertheless, important steps are already being made. For example, it is expected that advances in algorithms that exploit newer techniques to integrate Newton's equations of motion for the system will be developed to effectively increase the size of the time step. Among these methods are united-atom algorithms, Monte Carlo sampling of configuration space coupled with MD, Brownian dynamics, and the stiff-equation methods. By these means, times into the nanosecond real-time domain will become accessible. One of the most important aspects of MD simulation is the fact that the algorithms are well suited to vectorization and parallelization. With the development of teraflop machines, MD codes will be among the first to be developed for massively parallel computers. The machines will be approximately 1,000 times faster than the current fast single processors, and the time domains that can be reached will then be on the order of microseconds of real time. While this is not yet into the very long times of seconds to years that characterize the longer relaxation times in polymers, the dynamical range that will be covered with the new technology could span 9 orders of magnitude (from femtoseconds to microseconds). Continued progress will also require improvements and stringent testing in force-field potentials and parameters. Advances in computational capabilities will allow the ab initio quantum mechanical calculations of geometries and force-field energies to be carried out on appropriate chain segment scales with adequate basis functions and rudimentary electron correlation effects. However, limitations on treating electron correlation put the reliable accuracy in these potentials as optimistically no better than about 0.3 kilocalories per mole, nearly comparable to RT (where R is the gas constant and T is the temperature). Hence, the results of quantum mechanical calculations will provide a good guide to force-field parameterization, but the parameters must be adjusted further and tested against experiments. Coarse-grained Simulations An alternative to solving Newton's laws for the dynamics of molecules is the use of statistical sampling methods, referred to as Monte Carlo, or complete enumeration of polymer or biopolymer conformations. These approaches are often used with lower-resolution representations of chain molecules (e.g., where chains are represented as strings of "beads," rather than in atomic detail). The advantage over high-resolution simulations is the ability to explore more conformations and thereby represent more accurately some physical properties. Exhaustive simulations are the most complete in this regard, but they suffer either a power-law or exponential dependence of computer time on chain length and are
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Polymer Science and Engineering: The Shifting Research Frontiers therefore not practical for long chains. Nevertheless, exhaustive simulations and Monte Carlo methods have been important for testing physical principles, for testing underlying assumptions in other simple models of polymer behavior, and for motivating some of the theoretical developments described below. Among the most exciting new developments are the Gibbs ensemble Monte Carlo and configurational bias Monte Carlo techniques. They permit computation of phase diagrams from force-field simulations, and chemical potentials for insertion of polymer chains, even into high-density media. More advances in sampling methods and in algorithms are needed, especially to take advantage of massively parallel computer architectures. Such advances would be particularly valuable for improving our abilities to simulate dense polymer systems and thereby guide further experiments and theoretical developments. A lower-resolution alternative to force-field simulation for dynamic properties is known as the Brownian dynamics simulation. This method usually models the polymer chain as beads interconnected by elastic springs and moving in a viscous medium. While this method allows the probing of much longer time scales, the spring and viscous damping constants are not directly derivable from atomic quantities, and the model itself becomes problematic for dense polymer systems. Better algorithms and models are required, as well as statistical mechanical methods that will link the parameters in the Brownian dynamics method to molecular-level potentials available in the force-field simulations. Impressive advances are also being made in the atomistic modeling of glassy polymers. In this approach, the model system is a cube with periodic boundaries, filled with polymer segments. An initial configuration is generated and then relaxed by potential energy minimization. The resulting "equilibrium" structure is examined for predictive and interpretive information. In this way, it is possible to obtain estimates of cohesive energy densities, Hildebrand solubility parameters, degree of randomization of the "amorphous" chains, elastic constants, thermal expansion coefficients, and structural changes brought about by shear and tension deformations. One of the current directions in which these simulations are being extended is to predictions of chain dispositions in the vicinity of a bounding surface. Another is the diffusion of small molecules through polymer films, which is relevant to the understanding of gas-separation membranes and the design of materials of improved permeability and selectivity. Calculations such as these are proving to be quite successful in predicting and interpreting polymer properties and should be extended to other applications. Another centerpiece of polymer science is the rotational isomeric state (RIS) theory developed in Russia, Japan, Israel, and the United States in the 1950s. For certain conditions, it predicts a wide range of polymer properties from the known chemical constitution of the monomer units. Its premise is that skeletal bonds are in one or another of a few favored conformations. Its power comes from its separation of the computation of a polymer conformation into local and
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Polymer Science and Engineering: The Shifting Research Frontiers nonlocal aspects. Computer resources can be used efficiently because the main computational effort is directed only toward extracting information about two-bond or three-bond units, rather than being expended inefficiently in exploring conformations of a long chain. The statistical mechanical machinery then uses that information efficiently to predict the properties of long chains. The RIS theory is a paradigm for combining molecular simulations with statistical mechanics in a way that makes most effective use of both methodologies. Applications to date have focused on isolated chains, and most involve the calculation of equilibrium properties such as chain dimensions, but recent work addresses applications to dynamic properties as well. Mathematical Methods With the tremendous increase in computing capability, it will become feasible to solve many fundamental statistical mechanical equations by numerical integrodifferential methods. Recent advances in ab initio quantum mechanical methods, for example, have been made by advanced numerical methodologies that take advantage of the processing power of present supercomputers or advanced workstations. Similar advances in mathematical methodologies will turn out to be as useful for many polymer problems. Conclusions Theoretical and computational methods play a fundamental role in developing new properties and polymeric materials. Explosive developments in computer technology have fueled the growth of computational experiments and simulations. But computational studies should not overshadow the development of deeper and more rigorous theory, because theory is a powerful wellspring of major paradigm changes. Unique insights will come from theorists and physicists, who should be encouraged to explore polymers and biomolecules. Computational and theoretical methods are often limited to treating narrow ranges of time and spatial scales. But polymers and biomolecules have behaviors that can range over tens of orders of magnitude in time and space within a single system. An important area of future development is methods that can bridge broadly from the fast and microscopic scales to the slow and macroscopic scales. We need to relate continuum fracture mechanics models to atomic levels of bonding, semiempirical predictions of optical properties to ab initio quantum mechanics, picosecond atomic motions of proteins to tens-of-seconds folding processes, atomic bond rotations and interactions to macroscopic glass transitions, and so on. Totally new modeling approaches are needed to bridge these gaps. Force-field simulations and experiments have grown enormously. Further developments will rely not only on increasing computer power and increased
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Polymer Science and Engineering: The Shifting Research Frontiers access to supercomputers and to fast networks, but also on improved force fields, deeper connections to quantum mechanics, and better treatments of the environment of surrounding and entangled chains or solvents. Better quantum mechanical methods are needed to treat large numbers of electrons and atoms. Practical challenges include applying theory and computation to polymer behaviors in complex media—polymer blends, liquid crystalline polymers, semicrystalline materials, composites, block copolymers, interfaces, the rheology of mixtures, branched molecules, soft matter, and so on. REFERENCES Butera, R., L.J. Fetters, J.S. Huang, D. Richter, W. Pyckout-Hinzen, A. Zirkel, B. Farago, and B. Ewen. 1991. "Microscopic and Macroscopic Evaluation of Fundamental Facets of the Entanglement Concept." Physical Review Letters 66:2088. Chan, H.S., and K.A. Dill. 1993. "The Protein Folding Problem." Physics Today 46(2):24-32. Gibson, H.W., C. Wu, Y.X. Shen, M. Bheda, A. Prasad, H. Marand, E. Marand, and D. Keith. 1992. "Synthesis, Thermal and Phase-Behavior of Polyester, Polyurethane and Polyamide Rotaxanes." Polymer Preprints 33(1):235. Mesei, F. 1980. Lecture Notes on Physics. Vol. 122. Berlin: Springer Verlag. Richter, D., B. Farago, L.J. Fetters, J.S. Huang, B. Ewen, and C. Lartique . 1990. "Direct Microscopic Observation of the Entanglement Distance in a Polymer Melt." Physical Review Letters 64:1389. Tomalia, D.A., D.R. Swanson, and D.M. Hedstrand. 1992. "Comb-burst Dendrimers—A New Macromolecular Architecture." Polymer Preprints 33(1):180.
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