Computer Simulations for Macromolecular Science

Macromolecules, or in the most simple version chain molecules of a given length posed and still pose a significant challenge to theoretical physics and chemistry. The computational materials science emerging from this is a growing and exciting field of science. Despite remarkable progress over many years, which is well documented in many research papers and several reviews, only (few) rather simple limiting cases are really well understood in (all) detail. E.g. the very basic problem of the chain excluded volume can be solved approximately and it iswell known that the isolated chain in good solvent is expanded, while in a melt of identical other chains the average conformation is that of a randomwalk.While this problemwas and ismostly discussed in terms of simple lattice walks or bead spring chains in simulations, continuous paths in space are used in analytic theory. This leads to the general scaling behavior. However a precise and controllable approach to go beyond that and to deal with specific chemical systems and to describe also the ‘‘prefactors’’ or the local packing as well, is still lacking. This somehow, on a very elementary level, explains the range of questions one faces, when dealing with macromolecular systems. Since most of these current models can only be treated in a rather approximative manner, it is not surprising at all that computer modelling plays an increasingly important role. Since the very early days of computer simulations scientists addressed the by now classical problems of polymer theory by these new methods. The first papers date back about 50 years. Already in 1955, two years after the invention of Monte Carlo Simulations, Rosenbluth and Rosenbluth in a seminal paper recognized and tried to overcome the attrition problem when generating self avoiding walks (SAWs). This problem occurs, when on a lattice with coordination number q randomly walks are grown. For an N-step SAW the number of possible conformations on a lattice is Z/N qeff N , with g being a so called critical exponent and qeff< q 1 an effective coordination number. Since thewalks are generated out of (q 1) randomwalks, the success rate of generating SAWs, O((qeff /(q 1))), vanishes exponentially. Such a difficulty is of such a fundamental nature, that it cannot simply be solved by faster computers. To overcome this problem a number of Review: In the context of a few characteristic examples, the perspectives of computational materials science for polymeric systems are being discussed. The examples chosen cover the range from atomistic/quantum models to coarse grained bead spring polymer models.