Eur. Phys. J. E 5, 359-375
Renormalization group analysis of weakly charged polyelectrolytes
T.B. Liverpool1, 2, 3 and M. Stapper31 Condensed Matter Theory Group, Blackett Laboratory, Imperial College, London SW7 2BZ, UK
2 Physico-Chimie Théorique, ESA CNRS 7083, E.S.P.C.I., 75231 Paris Cedex 05, France
3 Max-Planck-Institut für Polymerforschung, Postfach 3148, D-55021 Mainz, Germany
t.liverpool@ic.ac.uk
(Received 16 December 1999 and Received in final form 13 December 2000)
Abstract
We present a field-theoretic Renormalization Group (RG)
analysis of the statistical mechanics of long flexible, screened
polyelectrolyte chains (Debye-Hückel chains) in polar solvents
where the screening length is of the order of the chain size. A
systematic analysis of the resulting field theory shows that the
system is one with two length-scales requiring the calculation
of scaling functions as well as exponents to fully describe its
physical behaviour. This means that care must be taken to understand
the interplay of the length-scales. Using the RG we identify the
relevant scaling variables and explicitly calculate the scaling
behaviour of the end-to-end distance for single chains. In addition
we consider the many-chain system and calculate the scaling
behaviour of the osmotic pressure of a dilute solution of chains.
05.20.-y - Classical statistical mechanics.
36.20.-r - Macromolecules and polymer molecules.
64.60.-i - General studies of phase transitions.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001
