The Self-Avoiding Walk

Madras, Neal; Slade, Gordon

doi:10.1007/978-1-4614-6025-1

Cited by 188 publications

(320 citation statements)

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“…This simplification is achieved with a grand-canonical algorithm of the BFACF type, 39,40,52 which has the property of preserving the knot type because it lets the configurations evolve only with local and crankshaft deletion/insertion moves. In our case the simplification is achieved with a bias toward deletion that emerges from choosing a low fugacity K per step.…”

Section: Variable Topologymentioning

confidence: 99%

Knotted Globular Ring Polymers: How Topology Affects Statistics and Thermodynamics

2014

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The statistical mechanics of a long knotted collapsed polymer is determined by a free-energy with a knot-dependent subleading term, which is linked to the length of the shortest polymer that can hold such knot. The only other parameter depending on the knot kind is an amplitude such that relative probabilities of knots do not vary with the temperature T , in the limit of long chains. We arrive at this conclusion by simulating interacting self-avoiding rings at low T on the cubic lattice, both with unrestricted topology and with setups where the globule is divided by a slip link in two loops (preserving their topology) which compete for the chain length, either in contact or separated by a wall as for translocation through a membrane pore. These findings suggest that in macromolecular environments there may be entropic forces with a purely topological origin, whence portions of polymers holding complex knots should tend to expand at the expense of significantly shrinking other topologically simpler portions. 1

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Section: Variable Topologymentioning

confidence: 99%

Knotted Globular Ring Polymers: How Topology Affects Statistics and Thermodynamics

2014

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“…The number of SAWs in three-dimensional space (without obstacles) is governed by the critical exponent γ ≈ 1.158 [33] (corresponding to η ≈ 0.03), while in two dimensions, γ = 43/32 [53] (η = 5/24). (For ideal polymers these exponents do not depend on d: γ 0 = 1 and η 0 = 0.)…”

Section: Self-avoiding Polymers: Simulationsmentioning

confidence: 99%

Polymer-mediated entropic forces between scale-free objects

2012

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The number of configurations of a polymer is reduced in the presence of a barrier or an obstacle. The resulting loss of entropy adds a repulsive component to other forces generated by interaction potentials. When the obstructions are scale invariant shapes (such as cones, wedges, lines or planes) the only relevant length scales are the polymer size R0 and characteristic separations, severely constraining the functional form of entropic forces. Specifically, we consider a polymer (single strand or star) attached to the tip of a cone, at a separation h from a surface (or another cone). At close proximity, such that h ≪ R0, separation is the only remaining relevant scale and the entropic force must take the form F = A kBT /h. The amplitude A is universal, and can be related to exponents η governing the anomalous scaling of polymer correlations in the presence of obstacles. We use analytical, numerical and ǫ-expansion techniques to compute the exponent η for a polymer attached to the tip of the cone (with or without an additional plate or cone) for ideal and selfavoiding polymers. The entropic force is of the order of 0.1pN at 0.1µm for a single polymer, and can be increased for a star polymer.

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“…This may be done as follows. A bridge is a self-avoiding walk from the origin, with first step in the x-direction, never to return to the x = 0 plane, and with last vertex having maximal x-coordinate (see, for example, reference [22] for a definition). If a bridge has x-span equal to w , then it has width w .…”

Section: Discussionmentioning

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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The Self-Avoiding Walk

Cited by 188 publications

References 0 publications

Knotted Globular Ring Polymers: How Topology Affects Statistics and Thermodynamics

Knotted Globular Ring Polymers: How Topology Affects Statistics and Thermodynamics

Polymer-mediated entropic forces between scale-free objects

Forces and pressures in adsorbing partially directed walks

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