Max Boleininger's visualisation of Solitons
By Max Boleininger
Among their remarkable tensile strength, Aligned polyethylene chains are well known for unusual properties. One of them will be presented here.
Strained polymer chains can be quantitatively modelled in a very minimalistic system. Consider a chain with its endpoints fixed in space and a parallel neighbouring one which is allowed to move freely along its length. By varying the fixed chain's length a strain is applied to the system to which the free chain reacts.
The forces acting on this system can be split up in two contributions. First, each individual chain is assumed to be linearly elastic as we only consider small strains. Secondly, each node of a chain interacts with each node of the other chain with a Lennard-Jones potential, an interaction that is often used to model attraction between neutral molecules.
When the simulation is started (tick 'start') the free chain begins to oscillate and will continue doing so until friction is enabled. Damping causes the free chain to slowly lose its kinetic energy until it reaches a local energy minimum. In the displacement plot a curious phenomenon becomes visible: the mostly smooth, linear curve divides into steps. These are solitons, strongly localised wave packets which preserve their shape over time, their number depending on the fixed chain's length. This suggests that the elastic energy of aligned polymer chains is stored locally in form of solitons.