Stable knotted phases in semiflexible polymers

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In this project, we plan to perform computer simulations to study the occurrence of knots in linear polymer chains. For flexible polymers it is well known that knots of various types form with a certain probability. Recently, we found in the phase diagram of semiflexible theta polymers well-defined regions, where knots of a specific type exist not only by chance but are thermodynamically stable. This means that almost every conformation is characterized by the same knot type. By combining the multicanoncial algorithm and the replica-exchange Monte Carlo simulation method, we want to understand the properties of these "knotted" phases in more detail. For example, we want to elucidate why there is a clear phase coexistence at the transition into the knotted phases, although no latent heat is observable.To this end we shall employ analyses of the free-energy landscape. In particular, we plan to calculate the free-energy barriers and the transition pathways into the knotted conformations. From preliminary simulations, we suspect that knotted conformations are suppressed in the case that the bond length is identical to the equilibrium distance of the interaction between non-adjacent monomers. For a better understanding of this observation, we will systematically vary the bond length and investigate its influence on the occurrence of stable knotted phases.Next we shall conduct computer simulations to investigate how an adsorbing surface influences the knotted polymers. In a first step, we plan to simulate a semiflexible coarse-grained polymer and investigate which thermodynamically stable knots survive the adsorption process. Besides that we want to get a deeper understanding of the generic aspects of adsorption of semiflexible polymers. This study of a coarse-grained model also serves as a preparation for more demanding simulations of chemically realistic polymers interacting with a surface. In the past few years quite impressive progress has been made in preparation and detection of single polymers adsorbed on surfaces, so that it is now possible to detect polymers consisting of down to 20 monomers. Therefore, we aim to design the simulations in this work such that they can be extended to more realistic models.