Issue |
Europhys. Lett.
Volume 71, Number 1, July 2005
|
|
---|---|---|
Page(s) | 49 - 55 | |
Section | Atomic and molecular physics | |
DOI | https://doi.org/10.1209/epl/i2005-10062-x | |
Published online | 27 May 2005 |
Self-consistent variational theory for globules
Max-Planck-Institute for Polymer Research - Ackermannweg 10, 55128 Mainz, Germany
Received:
17
March
2005
Accepted:
4
May
2005
A self-consistent variational theory for globules based on the
uniform expansion method is presented. This method, first
introduced by Edwards and Singh to estimate the size of a
self-avoinding chain, is restricted to a good-solvent regime,
where two-body repulsion leads to chain swelling. We extend the
variational method to a poor-solvent regime where the balance
between the two-body attractive and the three-body repulsive
interactions leads to contraction of the chain to form a globule.
By employing the Ginzburg criterion, we recover the correct
scaling for the θ-temperature. The introduction of the
three-body interaction term in the variational scheme recovers the
correct scaling for the two important length scales in the
globule —its overall size R, and the thermal blob size
. Since these two length scales follow very different
statistics —Gaussian on length scales
, and space
filling on length scale R— our approach extends the validity
of the uniform expansion method to non-uniform contraction
rendering it applicable to polymeric systems with attractive
interactions. We present one such application by studying the
Rayleigh instability of polyelectrolyte globules in poor
solvents. At a critical fraction of charged monomers, fc,
along the chain backbone, we observe a clear indication of a
first-order transition from a globular state at small f to a
stretched state at large f; in the intermediate regime the
bistable equilibrium between these two states shows the existence
of a pearl-necklace structure.
PACS: 36.20.-r – Macromolecules and polymer molecules / 61.25.Hq – Macromolecular and polymer solutions; polymer melts; swelling / 82.35.Rs – Polyelectrolytes
© EDP Sciences, 2005
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