Relative knot probabilities in confined lattice polygons

Area of Science:

• Polymer Physics
• Computational Chemistry
• Statistical Mechanics

Background:

• Ring polymers exhibit complex topological states.
• Confining polymers influences their conformational properties and knotting behavior.

Purpose of the Study:

• To investigate the relative knotting probabilities of ring polymers in a cubic lattice confinement.
• To determine how polymer concentration affects knot formation in confined systems.

Main Methods:

• Utilized a lattice model of ring polymers within a cubic cavity.
• Employed Monte Carlo simulations to estimate conformation counts.
• Calculated relative knotting probabilities (ρ_{n,L}(K/0₁)) for various knot types.

Main Results:

• Relative knotting probabilities remain low for a wide range of monomer concentrations (φ=n/V) within the studied confinement sizes (L≤12).
• The model is predominantly characterized by unknotted lattice polygons.
• Knotting probability increases with concentration, eventually plateauing as the Hamiltonian state is approached.

Conclusions:

• Confinement significantly suppresses knot formation in ring polymers.
• The concentration-dependent knotting behavior follows a predictable trend, saturating at high densities.