The Monte Carlo Method in

Statistical Physics

D. W. Heermann


The lectures are centred around three main themes:

1. Modelling of Polymer Systems:

I present and give results for model for polymers with flexible one-dimensional rod chains as backbone. This model is able to simulate polymers consisting of large monomer units which cannot be described by a bead spring model with satisfying results. In spite of using large coarse grained units no bond crossing can occur because of a continuous excluded volume along the backbone. The rods interact with con-focal force fields. The geometric shape of the chemically realistic monomers is conserved by using ellipsoids which represents the interaction volume as building units for the coarse grained model of the monomers. We give evidence that the model is able to reproduce the expected scaling behaviour of static and dynamic properties of polymer melts. Furthermore I compare the results to those obtained using the bond-fluctuation-model.



2. Simulation of Mechanical Properties of Polymer Surfaces

I report on dynamic surface properties, sound velocity and diffusion of surface monomers, and computer experiments of nano-indentation into amorphous polymer material. The bulk polymer is described by a united atom model in connection with molecular dynamics methods. Measured were the compressibility of the polymer material for different chain lengths and the sound velocities. The dynamics of the tool is modelled as over-damped, such that the indentation velocity is proportional to the difference between the external force acting onto the tool and the resistance force built up in the polymer material. I will concentrate on the initial, kinetic stage of the indentation process and give results for the motion of the indenting tool, or indentation depth dependent on external force and chain length, the deformation field of the polymer material and the density profile of monomers around the tool.

I further present studies the deformation of nano-scale polymer films which are subject to external bending forces by means of computer simulation. The film is loaded by the action of a prismatic blade which is pressed into the polymer bulk from above and a pair of columns which support the film from below. The interaction between blade and support columns and the polymer is modelled by the repulsive part of a Lennard-Jones potential. The results
allow to give a characterisation of deformed states for such films.



3. Diffusion and Nucleation in Polymer Systems

The last theme covers the simulation of the diffusion of gas molecules with different size inside amorphous polystyrene and the clustering in the nucleation process. Of interest will be the relationship between the diffusion constant and gas as well as the dynamical behaviour of gas
molecules at the small time scale, the so-called ``hopping-process''.