Self-avoiding walks adsorbed at a surface and pulled at their mid-point

Self Cite

We consider self-avoiding walks terminally attached to a surface at which they can adsorb. A force is applied, normal to the surface, to desorb the walk and we investigate how the behaviour depends on the vertex of the walk at which the force is applied. We use rigorous arguments to map out some features of the phase diagram, including bounds on the locations of some phase boundaries, and we use Monte Carlo methods to make quantitative predictions about the locations of these boundaries and the nature of the various phase transitions.

“…First we prove a result about the free energy when 0 < t < 1, y > 1 and a ≤ a c . This extends a result in [16] when y > 1 and a ≤ 1.…”

Section: Rigorous Resultssupporting

confidence: 87%

“…Proof: We know from [16] that ω t (a, y) = tλ(y)+(1−t) log µ d = ω t (1, y) when a ≤ 1 and y > 1. For a ≤ a c and y > 1 monotonicity implies that the free energy is bounded below by ω t (1, y).…”

Section: Rigorous Resultsmentioning

confidence: 99%

Adsorbed self-avoiding walks pulled at an interior vertex

Bradly¹,

Rensburg²,

Owczarek³

et al. 2019

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“…Mixed phases have been seen in a two dimensional directed model of adsorbing polygons subject to a force [2] and have been predicted numerically for a similar model for self-avoiding polygons in two dimensions [4]. They can also occur when an adsorbed self-avoiding walk is pulled at an interior vertex [20].…”

Section: Discussionmentioning

confidence: 99%

“…It is known that lim n→∞ 1 n log B † n (1, y) = λ(y) (see equation (22) in reference [20]). Since B † n (0, y) = B † n−1 (1, y), it follows that lim…”

Section: Stars When D ≥mentioning

confidence: 99%

Force-induced desorption of 3-star polymers: a self-avoiding walk model

Rensburg¹,

Whittington²

2018

Self Cite

We consider a simple cubic lattice self-avoiding walk model of 3-star polymers adsorbed at a surface and then desorbed by pulling with an externally applied force. We determine rigorously the free energy of the model in terms of properties of a self-avoiding walk, and show that the phase diagram includes 4 phases, namely a ballistic phase where the extension normal to the surface is linear in the length, an adsorbed phase and a mixed phase, in addition to the free phase where the model is neither adsorbed nor ballistic. In the adsorbed phase all three branches or arms of the star are adsorbed at the surface. In the ballistic phase two arms of the star are pulled into a ballistic phase, while the remaining arm is in a free phase. In the mixed phase two arms in the star are adsorbed while the third arm is ballistic. The phase boundaries separating the ballistic and mixed phases, and the adsorbed and mixed phases, are both first order phase transitions. The presence of the mixed phase is interesting because it doesn't occur for pulled, adsorbed self-avoiding walks. In an atomic force microscopy experiment it would appear as an additional phase transition as a function of force. PACS numbers: 82.35.Lr,82.35.Gh,61.25.Hq AMS classification scheme numbers: 82B41, 82B80, 65C05Force-induced desorption of 3-star polymers: a self-avoiding walk model

“…We already have a number of rigorous results available for the self-avoiding walk model of a linear polymer [30,32,33]. The behaviour might depend on polymer architecture and we begin to investigate this issue in this paper by considering a self-avoiding polygon model of a ring polymer.…”

Section: Discussionmentioning

confidence: 99%

Polygons pulled from an adsorbing surface

Guttmann¹,

Rensburg²,

Jensen³

et al. 2018

Self Cite

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.