Multiscale Problems in Polymer Science: Simulation Approaches
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Multiscale Problems
in Polymer Science: Simulation Approaches K. Kremer and F. Müller-Plathe
Polymer materials range from industrial commodities, such as plastic bags, to high-tech polymers used for optical applications, and all the way to biological systems, where the most prominent example is DNA. They can be crystalline, amorphous (glasses, melts, gels, rubber), or in solution. Polymers in the glassy state are standard materials for many applications (yogurt cups, compact discs, housings for technical equipment, etc.). They often combine relatively low specific weight with ductility, and they can be processed at moderate temperatures. In the melt state, polymers are viscoelastic liquids. Added to a solvent, polymers can be used as either shearthickening or shear-thinning viscosity modifiers. Polymer networks form gels or rubber. Applications range from gels in (e.g., low-fat) foods, to hydrogels used in modern body care (e.g., diapers), to biological systems (cytoskeletons), and all the way to classical elastomers (e.g., car tires). This range of applications is due to the variability of physical properties, which is based on the many different molecular building blocks, molecular architectures, and molecular weights of polymers. It is the combination and the rather subtle interplay of local chemical and more global architectural and size properties that makes macromolecules so versatile. This means that many different length and time scales are relevant; understanding the properties on one scale is not sufficient.
Chemical Repeat Units: Material-Specific Aspects The simplest polymers are chain molecules with identical segments, repeat units, or monomers. Examples are listed in Table I. These simple examples range from polyethylene (PE) (e.g., plastic bags) to
MRS BULLETIN/MARCH 2001
bisphenol-A polycarbonate (BPA-PC) (e.g., compact discs). There are also many complex cases (e.g., DNA, proteins, copolymers), where several different building blocks are present in one molecule. While most polymers are not water-soluble, poly(ethylene oxide) (PEO) has the exceptional property of being both water- and oil-soluble. Other water-soluble polymers include polyelectrolytes, which dissociate ions into water and stay in solution even if their backbone is hydrophobic. Although polyelectrolytes are beyond the scope of this article, the typical simulation approaches for polyelectrolytes are conceptually very similar to the ones discussed here.1–4
Architecture/Morphology: Universal Structural Aspects The simplest polymers are long linear objects of identical repeat units. Due to their intrinsic flexibility, they can assume distinct spatial conformations of the order of O(q N ), where q represents the number of torsional states of the subsequent bonds, and N is the number of repeat units in a melt or solution. PE, for example, has stiff bond angles between subsequent carbon– carbon bonds. Each added bond is in principle allowed to take one of the three torsional states (trans, gauche, or gauche). Due to excluded volume e
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