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Soft Matter and Biological Physics

Eur. Phys. J. E 5, 359-375

Renormalization group analysis of weakly charged polyelectrolytes

T.B. Liverpool1, 2, 3 and M. Stapper3

1  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


(Received 16 December 1999 and Received in final form 13 December 2000)

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