Pressure exerted by a grafted polymer on the limiting line of a semi-infinite square lattice

Jensen, Iwan; Dantas, W. G.; Marques, Carlos M.; Stilck, Jürgen F.

doi:10.1088/1751-8113/46/11/115004

Cited by 9 publications

(17 citation statements)

References 28 publications

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“…There are several other recent papers which modelled the entropic pressure due to the conformational entropy of polymer. These include the pressure of a grafted two dimensional self-avoiding walk on a line [21], and the entropic pressure of a two dimensional adsorbing directed path onto the adsorbing line [16].…”

Section: Discussionmentioning

confidence: 99%

The entropic pressure of a lattice polygon

Gassoumov¹,

Rensburg²

2013

J. Stat. Mech.

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Section: Discussionmentioning

confidence: 99%

The entropic pressure of a lattice polygon

Gassoumov¹,

Rensburg²

2013

J. Stat. Mech.

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“…The above approach was used for a square lattice self-avoiding walk model of linear polymers grafted to a hard wall [7]. In this exact enumeration study the data show that pressure decreases with distance from the origin.…”

Section: Introductionmentioning

confidence: 99%

The pressure exerted by adsorbing directed lattice paths and staircase polygons

Rensburg

Prellberg

2013

J. Phys. A: Math. Theor.

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A directed path in the vicinity of a hard wall exerts pressure on the wall because of loss of entropy. The pressure at a particular point may be estimated by estimating the loss of entropy if the point is excluded from the path. In this paper we determine asymptotic expressions for the pressure on the X-axis in models of adsorbing directed paths in the first quadrant. Our models show that the pressure vanishes in the limit of long paths in the desorbed phase, but there is a non-zero pressure in the adsorbed phase. We determine asymptotic approximations of the pressure for finite length Dyck paths and directed paths, as well as for a model of adsorbing staircase polygons with both ends grafted to the X-axis.

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“…The induced force is repulsive, and the polymer exerts an average net pressure on the wall. These entropic pressures have been seen in experiments [2,6,12] and have been modelled numerically (see for example reference [21]). …”

Section: Introductionmentioning

confidence: 67%

Forces and pressures in adsorbing partially directed walks

Rensburg¹,

Prellberg²

2016

J. Phys. A: Math. Theor.

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Abstract. 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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Pressure exerted by a grafted polymer on the limiting line of a semi-infinite square lattice

Cited by 9 publications

References 28 publications

The entropic pressure of a lattice polygon

The entropic pressure of a lattice polygon

The pressure exerted by adsorbing directed lattice paths and staircase polygons

Forces and pressures in adsorbing partially directed walks

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