Self-consistent variational theory for globules

Abstract

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-avoiding 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 $\theta$-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, $f_c$, 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.

7 pages, 1 figure

References in corpus (1)

• Structure of Polyelectrolytes in Poor Solvent

Cited by in corpus (4)

• Theory of polyzwitterion conformations
• Stretching Homopolymers
• Weak polyelectrolytes in the presence of counterion condensation with ions of variable size and polarizability
• Looping dynamics of flexible chain with internal friction at different degree of compactness