Polymers in Confined Geometry.pdf

5.2. THE HARMONIC POTENTIAL 69
R 2 and R 2 ||
1
0.8
0.6
0.4
0.2
0
0.1
R 2
2 R|| 1
Figure 5.9: The ‘dip’-feature in the end-to-end
distance. The mean-square and mean-square
, are shown versus the collision parameter c for the
parallel end-to-end distance, R 2 and R 2 ||
flexible regime ɛ = 10.
10
c
100
1000
• In particular for biopolymers electrostatic effects play an important role.
E.g. DNA is a highly charged polyelectrolyte, where the electrostatic repulsion
will have a stretching effect, leading to a second source of self-avoidance
(cf. [36]), beside the excluded volume effect.
In our simulations electrostatic effects are not taken into account. Therefore
an extra repulsion between the segments is expected, significantly effecting
the flexible regime. This is expected to shift our results in a way, that the
trend of the experimental data in the intermediate regime is fitted better.
Simulations of polyelectrolytes need special complex techniques. Implementation
of these effects is an interesting task for future projects.
It can be noted by investigating figure 5.8, that changing the observable from
the mean-square end-to-end distance to the apparent end-to-end distance does
not change our discussion about the scaling regime leading to eq. (5.4).
The goal of this scaling plot is to use it as a gauge plot for the experiments, to
convert the apparent length measured, into the real contour length of the polymer
strand.
5.2.4 End-to-end distances
In order to understand the conformational changes which take place upon confinement,
we are going to investigate the differences between the full end-to-end
distance and its component along the tube axis. The definition of these observables
was given in section 4.6. The investigation will explain a global feature
qualitatively, only visible for more flexible chains, which is different between these
two observables.