Verlag des Forschungszentrums Jülich
JUEL-3040
Everaers, Ralf
Elastische Eigenschaften von Polymernetzwerken
177 S., 1995
Summary
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 from 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 part,
i•cui, arr" y strong t,o.r.,tWO n,.imensi•onai1 netj work1 s ac1soro1 eo1 on a surrface.
Motivation for the third part were some recent observations on multiple
stranded marcromolecules. Generally such molecules have a very high bending
stiffness. 'Ale 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 the 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 YIMP proved to be significantly faster than older programs.
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