* To whom correspondence should be addressed © Springer-Verlag 1996 J. Mol. Model. 1996, 2, 293 – 299 Elastic Properties of Polymer Networks Ralf Everaers* and Kurt Kremer † Institut für Festkörperforschung, Forschungszentrum Jülich, Postfach 1913, D-52425 Jülich, Germany present address: Institut Charles Sadron, 6, rue Boussingault, F-67083 Strasbourg, France (ever@ics.crm.u-strasbg.fr) † Max-Planck Institut für Polymerforschung, Postfach 3148, D-55021 Mainz, Germany Received: 15 May 1996 / Accepted: 6 August 1996 / Published: 27 September 1996 Abstract Many fundamental questions for the understanding of polymer melts and networks are more suitably addressed by current computer simulations than by experiments. The reason is that simulations have simultaneous access to the microscopic structure and the macroscopic behavior of well-defined model systems. The coarse-grained models used often bear little relation to actual chemical species. This is justified by the experimentally estab- lished universality of polymer dynamics and no limitation for the test and development of theories which are directed at these universal aspects. The difficulties already encountered on this level will be illustrated for entanglements between polymers which dominate the dynamic in dense systems. For practical purposes it would, of coarse, be desirable to predict the characteristic length and time scales of experimental systems from the chemical structure of the polymer chains. Due to the extremely long relaxation times it is impossible to achieve this in brute-force simulations of truely microscopic models. Systematic coarse- graining combined with a better theoretical understanding seem to offer a practical alternative. Keywords: polymers networks, dynamics, polymer properties, microscopic models Introduction Polymer networks are the basic structural element of sys- tems as different as tire rubber and gels. They are not only technically important but also commonly found in biologi- cal systems such as the cytoskeleton. Networks of flexible macromolecules display an elastic and thermoelastic behav- iour quite different from ordinary solids. [1] Crystals, met- als, ceramics, or glasses can be stretched only minimally. Small deformations of the sample extend down to atomic scales and lead to an increase of the internal energy. Rubber- like materials reversibly sustain elongations of up to 1000% with small strain elastic moduli that are four or five orders of magnitude smaller than for other solids. Most importantly, the tension induced by a deformation is almost exclusively due to a decrease in entropy. As a consequence, the underly- ing mechanism has to be different from the case of conven- tional solids. The key problem in the theory of rubber elasticity is the correct identification of the microscopic sources of this en- tropy change. An at least qualitative explanation was found in the 1930, when it was realized that rubber is the result of cross linking a melt of long flexible chain molecules. Such polymers adopt random coil conformations and behave as entropic springs. The classical theories of rubber elasticity [1] estimate the elastic properties of a polymer network from the elongation of the network strands. This explanation ne-