Exchange Symmetries in Motzkin Path and Bargraph Models of Copolymer Adsorption

Rensburg, E J Janse van; Rechnitzer, Andrew

doi:10.37236/1637

Cited by 14 publications

(7 citation statements)

References 26 publications

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“…which simplifies to z 0 z 1 = 3 − z 1 when α = 0; this is the critical curve for adsorbing Motzkin paths; see for example [28].…”

Section: Lifted Motzkin Paths and Statements Of Resultsmentioning

confidence: 98%

Adsorbing Motzkin paths

Rensburg¹

2010

J. Phys. A: Math. Theor.

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The adsorption of a Motzkin path with lifted endpoints onto an adsorbing line is examined as a model of polymer adsorption. The partition function of this model is determined exactly, and the free energy is derived by examining the partition function. The location of the critical point in the model is given exactly in one case, and as the solution of a nonlinear equation in another case. The phase diagram of the model is examined, and I show that the transition is in general a first-order adsorption transition, except in cases where one or both endpoints of the path are restricted to be close to the adsorbing line.

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“…which simplifies to z 0 z 1 = 3 − z 1 when α = 0; this is the critical curve for adsorbing Motzkin paths; see for example [28].…”

Section: Lifted Motzkin Paths and Statements Of Resultsmentioning

confidence: 98%

Adsorbing Motzkin paths

Rensburg¹

2010

J. Phys. A: Math. Theor.

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“…Next, the pressure P w, 0 derived in reference [18], can be used. Substitute these in equation (71), and approximate the summation by an integral (notice that the summation in equation (71) includes values of ℓ close to zero, and again close to n, where the approximations in equations (62) and (74) are poor).…”

Section: The Pressure On the Adsorbing Wallmentioning

confidence: 99%

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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“…derived in reference [18], can be used. Substitute these in equation ( 71), and approximate the summation by an integral (notice that the summation in equation ( 71) includes values of close to zero, and again close to n, where the approximations in equations ( 62) and (74) are poor).…”

Section: (B)mentioning

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.

show abstract

Exchange Symmetries in Motzkin Path and Bargraph Models of Copolymer Adsorption

Cited by 14 publications

References 26 publications

Adsorbing Motzkin paths

Adsorbing Motzkin paths

Forces and pressures in adsorbing partially directed walks

Forces and pressures in adsorbing partially directed walks

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