The compressibility of minimal lattice knots

Rensburg, E J Janse van; Rechnitzer, Andrew

doi:10.1088/1742-5468/2012/05/p05003

Cited by 8 publications

(11 citation statements)

References 27 publications

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“…Tight lattice knots [24] are minimal length lattice knots [28][29][30]. The compressibility of tight lattice knots is known to be a function of knot type [31,32]. In Fig.…”

Section: Compressed Lattice Knotsmentioning

confidence: 99%

Osmotic pressure of compressed lattice knots

Rensburg

2019

Phys. Rev. E

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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 31 and 41 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 and out 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 31 and 41 have one stable equilibrium each.

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“…Tight lattice knots [24] are minimal length lattice knots [28][29][30]. The compressibility of tight lattice knots is known to be a function of knot type [31,32]. In Fig.…”

Section: Compressed Lattice Knotsmentioning

confidence: 99%

Osmotic pressure of compressed lattice knots

Rensburg

2019

Phys. Rev. E

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“…This is the generating function of walks ending in the adsorbing line (or with endpoint at height zero). Substituting this into equation (19) gives a solution for G(µ):…”

Section: In Lmentioning

confidence: 99%

Forces and pressures in adsorbing partially directed walks

van Rensburg,

Prellberg

2015

Preprint

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Polymers in confined spaces lose conformational entropy. This induces a net repulsive entropic force on the walls of the confining space. A model for this phenomenon is a lattice walk between confining walls, and in this paper a model of an adsorbing partially directed walk is used. The walk is placed in a half square lattice L 2 + with boundary ∂L 2 + , and confined between two vertical parallel walls, which are vertical lines in the lattice, a distance w apart. The free energy of the walk is determined, as a function of w , for walks with endpoints in the confining walls and adsorbing in ∂L 2 + . This gives the entropic force on the confining walls as a function of w . It is shown that there are zero force points in this model and the locations of these points are determined, in some cases exactly, and in other cases asymptotically.

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“…The basic approach is to consider each such polygon as being composed of two walks from 0 to r . The number of such pairs of walks will be estimated by using equation (23).…”

Section: The Number Of Polygons Passing Through a Lattice Point Rmentioning

confidence: 99%

“…The summand in equation ( 24) can be estimated by using equation (23). This replaces the functions c k ( r ) and c n−k ( r ) in the summand of equation ( 24) by factors containing c k and c n−k .…”

Section: The Number Of Polygons Passing Through a Lattice Point Rmentioning

confidence: 99%