Polymers in Confined Geometry.pdf

Chapter 2
Polymer models
This chapter introduces some of the basic models used in polymer physics. After
a short motivation of why using a minimal model—only keeping the most important
features—is possible, we turn to a detailed description of specific realizations
of these models. We present both heuristic scaling arguments and analytical calculations
in limiting cases. We conclude by a short discussion of when and how
to include more realistic effects.
2.1 Motivation
Condensed matter physics has a long standing tradition of reductionists approaches.
In order to describe the generic properties of a system one tries to
skip as much details as possible and keep only the essential features. How many
details have to be kept for a specific description depends on the length-scale on
which a problem is investigated and is not always obvious to decide.
Polymer physics is a paradigmatic example for such an approach. A biopolymer
consists of a large number of backbone monomers, i.e. molecules (e.g. DNA
base-pairs) normally consisting of several atoms (e.g. carbon, hydrogen). These
atoms again consist of electrons and nuclei build of quarks and so on. Naively
one might think that an exact model should actually start at the lowest possible
level. But this is neither feasible nor necessary since there is usually a separation
of time- and length scales between a microscopic description and the mesoscopic
level we are interested in.
For many applications it is even possible to disregard all atomistic details and
consider each monomer as a structureless segment of a given length l. This is
motivated by the fact that molecular processes within each monomer relax on
a much shorter time scale than the overall polymer conformations. Interactions
between successive segments are modeled such that its essential properties are
kept, e.g. bending and torsional stiffness of the thread. The basic models used in
polymer physics are distinct at this level, for a thorough discussion we refer to
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