Osmotic pressure of compressed lattice knots

Abstract

A numerical simulation shows that the osmotic pressure of compressed lattice knots is a function of knot type, and so of entanglements. The osmotic pressure for the unknot goes through a negative minimum at low concentrations, but in the case of non-trivial knot types $3_1$ and $4_1$ it is negative for low concentrations. At high concentrations the osmotic pressure is divergent, as predicted by Flory-Huggins theory. The numerical results show that each knot type has an equilibrium length where the osmotic pressure for monomers to migrate into or our of the lattice knot is zero. Moreover, the lattice unknot is found to have two equilibria, one unstable, and one stable, whereas the lattice knots of type $3_1$ and $4_1$ have one stable equilibrium each.

References in corpus (8)

• Accurate estimate of the critical exponent $\nu$ for self-avoiding walks via a fast implementation of the pivot algorithm
• Fractal Dimension and Localization of DNA Knots
• Equilibrium shapes of flat knots
• Gel Electrophoresis of DNA Knots in Weak and Strong Electric Fields
• Minimal knotted polygons in cubic lattices
• Lattice Knots in a Slab
• The Compressibility of Minimal Lattice Knots
• The entropic pressure of lattice knots

Cited by in corpus (1)

• Phase diagrams of confined square lattice links