Polymers in Confined Geometry.pdf

Chapter 5
Simulation results
In this chapter we are going to explore the scaling behavior of the worm-like chain
upon confinement, using the Monte-Carlo algorithm discussed in the preceding
chapter 4. After validating the simulation with exactly known results in bulk
solution (cf. chapter 2), we turn to the influence of a harmonic potential with
cylindrical symmetry on the polymer configuration. The undulations and the
tangent-tangent correlation function are compared to analytical results (cf. chapter
3). After becoming familiar with the influence of the confining environment,
we explore the scaling behavior of the mean-square end-to-end distance 〈R 2 〉 with
the ratio of the collision parameter to the persistence length c/ɛ.
We also go beyond an analysis of the moments by studying the full probability
distribution function of the end-to-end distance. It turns out that there is a
cross over from the well known unconfined distribution to the confined regime,
strongly peaked towards full stretching, with an intermediate bimodal distribution
function, as one decreases the channel width.
Finally we have also started to explore other types of confining potentials, in
particular hard-wall potentials with square and cylindrical cross section.
Before starting the investigation, some preliminary remarks are in order:
• In this chapter all values are measured in units of the total length L.
• In the plots the statistical error is smaller than the symbols if not stated
otherwise.
• All simulations were performed without using self-avoidance effects. We
have convinced ourselves that such effects are negligible for flexible filaments
up to a length of at least N = 500 segments.
• The simulations were performed on a standard computer desktop system
(Intel Pentium IV processor, various frequencies). A typical simulation for
fixed segment size N, flexibility ɛ and collision parameter c takes about one
hour for N = 50 and up to the order of a week for N = 1000 segments.
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