Stiffness induced structures and morphological transitions in semiflexible polymers

TL;DR

This work develops a coarse-grained, field-theoretic free-energy framework that unifies coil, globule, toroid, and rod morphologies of semiflexible polymers in poor solvents. By introducing density $\phi$ and nematic order $\mathbf{Q}$ fields and incorporating bending rigidity, surface tension, and density–nematic coupling, the authors derive analytic scaling relations for the free energies of competing morphologies and map a phase diagram in reduced attraction $\epsilon^*$ and reduced stiffness $L_p^*$. Fluctuation effects, especially density fluctuations, shift morphology boundaries by promoting orientational order and renormalizing interfacial penalties, notably moving the globule–toroid boundary toward toroids. The results reproduce qualitative features observed in simulations (e.g., Srinivas–Bagchi) and DNA condensation phenomena, and they offer a transparent, extensible framework to interpret and predict morphology changes in semiflexible polymers. The theory sets the stage for incorporating additional ingredients (electrostatics, sequence effects, torsion) to further align with experiments and complex biopolymer systems.

Abstract

Semiflexible polymers in poor solvents exhibit a rich variety of collapsed morphologies, including globules, toroids, and rodlike bundles, arising from the competition between attractive interactions and chain stiffness. Computer simulations and experiments on stiff and conjugated polymers have revealed complex morphological crossovers, yet a unified theoretical description remains incomplete. Here we develop a coarse-grained, field-theoretic free-energy framework for linear polymers with variable stiffness that captures these morphologies and their transitions within a common description. The theory is built on three key ingredients: a density field describing monomer attraction and excluded-volume effects, a nematic order parameter accounting for orientational ordering in dense regions, and the bending rigidity of a worm-like chain. Using simple variational ansatzes for competing morphologies, we derive analytic expressions for their free energies and identify the boundaries separating coil, globule, toroidal, and rodlike conformational regimes as functions of the reduced attraction strength and the effective persistence length. The resulting phase-diagram topology provides a transparent free-energy-based framework for interpreting morphology diagrams observed in simulations and experiments on semiflexible polymers in poor solvents. We find the possibility of the existence of a triple point involving globules, rods and toroids.

Figures (1)

• Figure 1: Schematic P--T--type phase diagram of a semiflexible polymer in the plane of reduced attraction strength $\epsilon^{*}=\epsilon/k_BT$ and reduced stiffness $L_p^{*}=L/b$. The solid boundary between globule and toroid bends toward higher $\epsilon^{*}$ at low stiffness, reflecting the persistence of isotropic globules at strong attraction and weak bending rigidity.