Adsorption of uniform lattice animals with specified topology

Soteros, C E

doi:10.1088/0305-4470/25/11/023

Cited by 22 publications

(31 citation statements)

References 15 publications

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“…Zhao and Lookman (1992b) show that for trails in a hypercubic lattice with c cycles (a c trial), y, =y+c and v, = v. topologies with cut edges, the free energy is not the same as for SAWs (Whittington and Soteros, 1992;Soteros, 1992). However, it can be shown that the transition point and crossover behavior are the same (Zhao, 1992).…”

Section: Critical Exponentsmentioning

confidence: 99%

“…, n2d ). Using Euler's law of edges, we haveZhao and Lookman (1991b) andSoteros (1992) have shown that for d )2 1 hm lnG"(c, n3 n2d co)= A (co), n Kn (86) E. Lattice animals Lattice animals and trees have been considered as models of branched polymers with excluded volume, and where A (co) is the reduced free energy of SAWs in terms of the number of edges in the surface. For d =2 and for…”

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confidence: 99%

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Surface phase transitions in polymer systems

1993

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Self-avoiding walks, lattice trees, and related geometrical models provide a link between the physics of polymers and the study of critical phenomena. In particular, these models in the presence of a surface provide insight into surface adsorption in dilute polymer systems in a good solvent. The theme of this review is the influence of polymer structure (topology) on the critical properties of these models. Emphasis is placed on recent results by rigorous methods, scaling theory, and conformal covariance theory. Numerical results that may be used to test the predictions of scaling and conformal covariance theories are also summarized. Related topics such as the adsorption of directed polymers, the semidilute regime, the theta point and theta solvents, and percolation (polymer gels) are briefly discussed in the final section.

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Section: Critical Exponentsmentioning

confidence: 99%

mentioning

confidence: 99%

Surface phase transitions in polymer systems

1993

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“…The proof of this theorem follows from results in [42], in Sections 3 and 4. When d ≥ 3 it is relatively straightforward to show that κ 0 (a) = κ(a) so the location of the adsorption transition is the same as that of walks.…”

Section: Polygons Adsorbing At a Surfacementioning

confidence: 90%

“…We have the following theorem. A proof is given in Section 4 of [42]. This theorem implies that there is an adsorption transition at a = a and, with a little more effort, the upper bound can be made strict.…”

Section: Polygons Adsorbing At a Surfacementioning

confidence: 98%

“…When d ≥ 3 it is relatively straightforward to show that κ 0 (a) = κ(a) so the location of the adsorption transition is the same as that of walks. See Section 3 of [42] for a proof when d = 3 that can be extended to d > 3 without much difficulty. When d = 2 the situation is slightly different because a polygon cannot lie entirely in the confining line.…”

Section: Polygons Adsorbing At a Surfacementioning

confidence: 99%

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Polygons pulled from an adsorbing surface

Guttmann¹,

Rensburg²,

Jensen³

et al. 2018

J. Phys. A: Math. Theor.

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Abstract. We consider self-avoiding lattice polygons, in the hypercubic lattice, as a model of a ring polymer adsorbed at a surface and either being desorbed by the action of a force, or pushed towards the surface. We show that, when there is no interaction with the surface, then the response of the polygon to the applied force is identical (in the thermodynamic limit) for two ways in which we apply the force. When the polygon is attracted to the surface then, when the dimension is at least 3, we have a complete characterization of the critical force-temperature curve in terms of the behaviour, (a) when there is no force, and, (b) when there is no surface interaction. For the 2-dimensional case we have upper and lower bounds on the free energy. We use both Monte Carlo and exact enumeration and series analysis methods to investigate the form of the phase diagram in two dimensions. We find evidence for the existence of a mixed phase where the free energy depends on the strength of the interaction with the adsorbing line and on the applied force.

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Comparison of Linear and Ring Polymers Partitioning into Pores Using Random Walks and Self‐Avoiding Walks Models

Litle,

Wang

2023

Macro Theory & Simulations

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We present Monte Carlo simulations that examine the partitioning of dilute solutions of ring or linear chains into a slit pore using two chain models, the random‐walk (RW) model and the self‐avoiding walk (SAW) model. We compared the partitioning coefficients K of the ring against the linear chains at the surface interaction that are both under the critical adsorption point (CAP), the exclusion regime, and above the CAP, the adsorptive regime. In both chain models, K for the ring remain larger than K for the linear chains at both regimes. The ring chain crosses over the point K = 1 at a weaker surface interaction than the linear chain. When extrapolated to infinite chain length, the cross‐over point for the ring and linear chain becomes the same (within statistical errors) for the RW model but remains different for the SAW model. The density profiles of the ring chain within the pore reveal the development of humps near the wall as the surface interaction crosses over the CAP. The excluded volume interaction in the SAW model additionally impacts the partitioning of chains in a solution consisting of a binary mixture of ring and linear chains and makes the K values in a binary mixture differ from the monodispersed solution.This article is protected by copyright. All rights reserved

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Adsorption of uniform lattice animals with specified topology

Cited by 22 publications

References 15 publications

Surface phase transitions in polymer systems

Surface phase transitions in polymer systems

Polygons pulled from an adsorbing surface

Comparison of Linear and Ring Polymers Partitioning into Pores Using Random Walks and Self‐Avoiding Walks Models

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