Polymers in Confined Geometry.pdf

76 CHAPTER 6. CONCLUSION
strong confining limit for semi-flexible to flexible polymers. In particular we could
derive an explicit expression for the mean-square end-to-end distance 〈R 2 〉. It
shows that instead of depending on both the persistence length and the Odijk
length (or tube diameter), it depends on a single scaling parameter c/ɛ, the ratio
of the confinement strength to the flexibility of the polymer, only.
By off-lattice Monte-Carlo simulations we were able to verify this scaling
behavior over a broad parameter range. This allowed us to verify the validity of
the weakly-bending rod approximation in the strong confinement limit. It is found
that polymers (for all flexibilities) stretch out to nearly their full contour length
upon confinement to lateral dimensions smaller than their persistence length.
These results obtained for the cylindrical harmonic potential were compared
to experimental data obtained for λ-DNA confined in channels with a square
cross section. The overall trend of the data for the apparent end-to-end distance
is well described by the Monte-Carlo data. There are some systematic deviations
hinting at additional effects not accounted for by a worm-like chain model.
Further preliminary simulation for different geometries with hard-walls were
performed as well. The results show a similar behavior as those for the harmonic
potential. This implies that the universal behavior of the end-to-end distance is
not sensitive to the specific details (e.g. channel shape) of the confining geometry
used. As the key features of the confining potentials we have identified the collision
parameter characterizing the lateral extension of the channel and, of course,
the overall symmetry of the channel.
There are also some limits of our investigations, clearly seen in the deviations
of the simulation data from the experimental results in the weak to intermediate
confinement regime for long semi-flexible polymers. This hints towards
additional physical effects not contained in the worm-like chain model, e.g. the
polyelectrolyte nature of DNA and resulting self-avoidance effects along the backbone.
We were able to rule out that effects of simple excluded volume could
explain the deviations. Modeling electrostatic effects leads to the theory of polyelectrolytes,
which ask for special sophisticated simulation techniques not easily
implemented. The development of an effective algorithm to simulate polyelectrolytes
in nanochannels is an interesting task for future projects.
In addition, there is room for improving the algorithm by introducing more
complex Monte-Carlo moves. This would enable us to explore the behavior of
chains with a larger number of segments or even different topologies of the confining
environment.