https://doi.org/10.1140/epjb/e2004-00223-9
Statistical mechanics of semiflexible polymers
Martin-Luther-Universität Halle, Fachbereich Physik, 06099
Halle, Germany
Corresponding author: a stepanow@physik.uni-halle.de
Received:
6
June
2003
Revised:
23
March
2004
Published online:
23
July
2004
We present the statistical-mechanical theory of semiflexible polymers based
on the connection between the Kratky-Porod model and the quantum rigid
rotator in an external homogeneous field, and treatment of the latter using
the quantum mechanical propagator method. The expressions and relations
existing for flexible polymers can be generalized to semiflexible ones, if
one replaces the Fourier-Laplace transform of the end-to-end polymer
distance, , through the matrix
, where D and M are related to the spectrum of the quantum rigid
rotator, and considers an appropriate matrix element of the expression under
consideration. The present work provides also the framework to study
polymers in external fields, and problems including the tangents of
semiflexible polymers. We study the structure factor of the polymer, the
transversal fluctuations of a free end of the polymer with fixed tangent of
another end, and the localization of a semiflexible polymer onto an
interface. We obtain the partition function of a semiflexible polymer in
half space with Dirichlet boundary condition in terms of the end-to-end
distribution function of the free semiflexible polymer, study the
behaviour of a semiflexible polymer in the vicinity of a surface, and
adsorption onto a surface.
PACS: 36.20.-r – Macromolecules and polymer molecules / 61.41.+e – Polymers, elastomers, and plastics / 82.35.Gh – Polymers on surfaces; adhesion
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004