Polymers in Confined Geometry.pdf

(a) λ-DNA (b) T2-DNA
Figure 1.2: Average intensity of fluorescently dyed DNA (persistence length of undyed DNA
lp ≈ 52 nm and contour-length of λ-DNA L ≈ 16.5 µm and T2-DNA L ≈ 55.8 µm) in nanochannels
of decreasing size (aspect ratio near one, width 440 nm down to 30 nm). The DNA stretches
to near full its length upon confinement to sizes around its persistence length. Courtesy of W.
Reisner et al. [38].
nanopore (cf. [38]).
To turn this idea into a useful device a quantitative theoretical understanding
of polymer conformations in confined geometry is needed. Previous models (discussed
in more detail in chapter 2 and section 3.2) were unable to account for the
effect of varying confinement over the entire range of scales used in nano-devices.
Only asymptotic results valid in special limits were available. In this thesis we
try to close this gap.
We will proceed as follows:
• A general introduction to specific models and universal behavior of unconfined
polymers is given in chapter 2. We present a derivation of exactly
known results as well as some scaling arguments. This chapter also serves
as a concise introduction into the field of study and introduces our basic
polymer model, the worm-like chain, used in the subsequent analysis.
• In chapter 3 we begin our discussion of polymer configurations confined to
tubes (represented in terms of a harmonic potential with cylindrical symmetry).
After discussing some scaling arguments we present an analytical
calculation in the limit of strong confinement. This allows us to give explicit
expressions for the correlation function and end-to-end distances.
• Since it is not possible to obtain analytical expressions for all relevant parameter
ranges it becomes necessary to perform Monte-Carlo simulations
in order to arrive at quantitative results. Chapter 4 will give a general introduction
to the basic principles needed for the simulations and a detailed
3