Self-consistent variational theory for globules

• Published in: Europhysics letters Vol. 71; no. 1; pp. 49 - 55
• Main Authors: Dua, A, Vilgis, T. A
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01-07-2005; EDP Sciences
• Subjects: 36.20.-r; 61.25.Hq; 82.35.Rs
• ISSN: 0295-5075; 1286-4854
• DOI: 10.1209/epl/i2005-10062-x

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 $\xi_{T}$. Since these two length scales follow very different statistics —Gaussian on length scales $\xi_{T}$, 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.