Polymers in Confined Geometry.pdf

74 CHAPTER 5. SIMULATION RESULTS
geometry. The main features of the behavior of the polymer in the confining ‘tube’
are universal. The relevant ingredient is the rotational symmetry around the tube
axis, but the details, continuous symmetry for the circular tube and harmonic
potential or fourfold discrete symmetry for the square tube, are irrelevant. The
only relevant scale is the deflection length ld! The difference in slope between the
data in the harmonic potential scaling plot and the data presented here is only
due to the relation converting the relevant “input parameters” d and ld by eq.
(3.1).
The details in the shape of the scaling function for hard and soft walls are,
however, quite different. For soft walls discussed in section 5.2.3 we were able to
fit the Odijk scaling result to both the experimental data and the Monte-Carlo
results. Here this seems not to be possible. The Odijk curve fits the experimental
data but misses the sharp increase of the Monte-Carlo data for hard walls in the
limit of strong confinement.
This raises the question on the actual form of the interaction potential between
the polymer an the confining walls. Using a hard wall potential one assumes that
there are steric interactions only. This is not necessarily true since we are dealing
with a charged system. DNA is a polyelectrolyte and therefore we can only hope
to describe this problem by an effective potential. If such a construction of an
effective potential is not possible, an explicit simulation of the charged polymer
and the charges in solution must be performed. This is an interesting future
project but beyond the scope of this thesis.
With the simulation program used to obtain all data here, many interesting
properties can be discussed. Here our first task was to have a comparison to the
analytical theory to validate the simulation and then to obtain experimentally
relevant data presented here. It provides a solid basis for future work.