Elastische Eigenschaften von Polymernetzwerken

Abstract

Polymers are long chain molecules with important biological and technical applications. By introducing additional chemical bonds they can be crosslinked into networks. Subject of this thesis is the statistical mechanical treatment of the elastic properties of polymers and polymer networks. In the first part the first computer simulations of strained polymer networks are used to clarify the physical foundations of rubber elasticity. We investigate idealized model networks with a diamond lattice connectivity. By modifying the interaction potentials it is possible to simulate ensembles with and without topology conservation. The key element of the argumentation is the simultaneous measurement of the macroscopic restoring forces due to deformations and of those microscopic quantities from which the elastic properties are deduced in theories of rubber elasticity. It is shown that the classical moduli calculated form the change in the end-to-end distance distributions for the network strands are significantly smaller than the true moduli. To test a topological theory of rubber elasticity we determine the linking state for all pairs of meshes in the system. Using a distance dependent free energy for linked meshes the linking contribution to the modulus can be estimated within an affine approximation. The result is found to be in excellent agreement with the measured topology contribution. The second part deals with the elastic properties of c* gels. The classical theories of rubber elasticity are combined with recent results on the elastic properties of swollen polymers in a good solvent. The resulting stress-strain curves are non-linear. The deviations from the classical predictions are particularly strong for two dimensional networks adsorbed on a surface. Motivation for the third part were some recent observations on multiple stranded macromolecules. Generally such molecules have a very high bending stiffness. We propose a ''railway track'' model for the effects of backbone coupling. The model can be solved in two dimensions and displays an interesting new type of behaviour for a mechanical model without long-range interactions: a stiffness that is larger on small than on large lengthscales. An estimate shows that coupling effect could contribute to the large bending stiffness of double helical molecules. In the appendix a new algorithm for molecular dynamics simulations with short-range interactions is documented. An optimized implementation on the Cray Y/MP proved to be significantly faster than older programs. (orig.)170 refs.Available from TIB Hannover: RA 831(3040) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman