Knots as a Topological Order Parameter for Semiflexible Polymers

Area of Science:

• Polymer Physics
• Computational Chemistry
• Materials Science

Background:

• Understanding polymer conformations is crucial for predicting material properties.
• Semiflexible polymers exhibit complex behaviors influenced by bending stiffness.
• Previous models often simplify the interplay between flexibility and structural organization.

Purpose of the Study:

• To investigate the impact of bending stiffness on polymer conformations.
• To map the pseudophase diagram for semiflexible polymers.
• To identify novel conformational phases and transitions in a simplified homopolymer model.

Main Methods:

• Utilized a combination of the multicanonical Monte Carlo algorithm and the replica-exchange method.
• Simulated a bead-stick homopolymer model across a range of bending stiffness values.
• Analyzed conformational phases and thermodynamic properties.

Main Results:

• Observed a rich variety of conformational phases, including bent, hairpin, and toroidal structures.
• Identified thermodynamically stable knots within the polymer model.
• Discovered unusual transitions into knotted phases with clear phase coexistence and minimal latent heat.

Conclusions:

• Bending stiffness significantly influences the conformational landscape of semiflexible polymers.
• The bead-stick model effectively captures complex polymer behaviors, including knot formation.
• The findings provide insights into the fundamental physics governing polymer self-assembly and phase transitions.