Polymer diffusion in a gel network
R.C. Hegeman (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Johan Dubbeldam – Mentor
Timon Idema – Mentor
Neil Budko – Graduation committee member
M. Depken – Graduation committee member
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Abstract
In this thesis, we model the diusion of a tracer polymer inside of a gel network and simulate it, hoping to nd a connection between the diusion of the polymer and the strength of the gel network. This model is made by using the Rouse model for the gel network and the tracer polymer.
The overdamped Langevin equation is then used to nd a set of coupled stochastic dierential equations for the motion of a single tracer bead and the Fourier modes of the gel particles. The single particle system is then analyzed using three dierent numerical methods: The Euler forward method, the Metropolis Monte Carlo method and the Gillespie algorithm. The Gillespie algorithm is then used to expand the single particle model to a model which again includes a tracer polymer instead of a single tracer bead. The simulations of the tracer polymer suggest that the motion of the tracer polymer is superdiusive. This contradicts the theory and the measurements of the single
tracer particle, which suggest that the simulation of the polymer should result in subdiusion. This contradiction seems to be caused by an error in the implementation of the interaction between the dierent beads that make up the tracer polymer, as it creates a tendency for the polymer to move away from its original position. This possible error is hinted at by a simulation of the system with the tracer polymer where the gel is considered stationary. The simulation implies superdiusion as well, which means that the superdiusion is not caused by the gel network. In fact, the simulation with the frozen gel network is much further away from subdiusion that the simulation with the gel network intact, which does seem to imply that the motion would be subdiusive if the model
was implemented correctly, but it is not conclusive.