Force-induced desorption of uniform branched polymers

Rensburg, E J Janse van; Whittington, S G

doi:10.1088/1751-8121/aafeb5

Cited by 7 publications

(14 citation statements)

References 39 publications

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“…By equation (21), the above simplifies to * (y) = y d dy λ(y) = β * (y) (for every y where equation (20) has a solution).…”

Section: The Density Function Of Pulled Walksmentioning

confidence: 99%

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Force-induced desorption of uniform block copolymers

Rensburg¹,

Soteros²,

Whittington³

2020

J. Phys. A: Math. Theor.

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We investigate self-avoiding walk models of linear block copolymers adsorbed at a surface and desorbed by the action of a force. We rigorously establish the dependence of the free energy on the adsorption and force parameters, and the form of the phase diagram for several cases, including AB-diblock copolymers and ABA-triblock copolymers, pulled from an end vertex and from the central vertex. Our interest in block copolymers is partly motivated by the occurrence of a novel mixed phase in a directed walk model of diblock copolymers Iliev and Janse van Rensburg (2012 J. Stat. Mech. P01019) and we believe that this paper is the first rigorous treatment of a self-avoiding walk model of the situation.

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“…By equation (21), the above simplifies to * (y) = y d dy λ(y) = β * (y) (for every y where equation (20) has a solution).…”

Section: The Density Function Of Pulled Walksmentioning

confidence: 99%

“…In other words, β * (y) = y d dy λ(y) = * (y) except for y equal to a critical point-that is y d dy λ(y) = * (y) for almost all y ∈ [y a , y b ]. By equation (21), the above simplifies to…”

Section: The Density Function Of Pulled Walksmentioning

confidence: 99%

Force-induced desorption of uniform block copolymers

Rensburg¹,

Soteros²,

Whittington³

2020

J. Phys. A: Math. Theor.

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“…Several homeomorphism types (corresponding to different polymer architectures) have been investigated including polygons (as a model of ring polymers) [5] and various types of branched polymers [4,16,17]. In particular, consider 3-star polymers modelled as 3-stars on the simple cubic lattice [16].…”

Section: A Brief Reviewmentioning

confidence: 99%

“…In two dimensions the situation is more difficult but Beaton [3] has given an essentially complete solution for staircase polygons in two dimensions. Various models of branched polymers have also been investigated [4,16,17].…”

Section: Introductionmentioning

confidence: 99%

Force-induced desorption of 3-star polymers in two dimensions

Bradly¹,

Rensburg²,

Owczarek³

et al. 2019

J. Phys. A: Math. Theor.

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We investigate the phase diagram of a self-avoiding walk model of a 3-star polymer in two dimensions, adsorbing at a surface and being desorbed by the action of a force. We show rigorously that there are four phases: a free phase, a ballistic phase, an adsorbed phase and a mixed phase where part of the 3-star is adsorbed and part is ballistic. We use both rigorous arguments and Monte Carlo methods to map out the phase diagram, and investigate the location and nature of the phase transition boundaries. In two dimensions, only two of the arms can be fully adsorbed in the surface and this alters the phase diagram when compared to 3-stars in three dimensions.

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“…These problems have also been investigated numerically by exact enumeration methods [9,32] and using Monte Carlo techniques [5,27,28]. Other polymer architectures have been considered, including star polymers [4,6,25,26], and other branched polymers such as combs [26].…”

Section: Introductionmentioning

confidence: 99%

Copolymeric stars adsorbed at a surface and subject to a force: a self-avoiding walk model

van Rensburg,

Whittington

2022

Preprint

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We consider a model of star copolymers, based on self-avoiding walks, where the arms of the star can be chemically distinct. The copolymeric star is attached to an impenetrable surface at a vertex of unit degree and the different monomers constituting the star have different interaction strengths with the surface. When the star is adsorbed at the surface it can be desorbed by applying a force, either at a vertex of degree 1 or at the central vertex of the star. We give some rigorous results about the free energy of the system and use these to establish the general form of the phase diagrams, and the orders of certain phase transitions in the system. We also consider the special case of spiders, ie stars constrained to have all degree 1 vertices in the surface.

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Force-induced desorption of uniform branched polymers

Cited by 7 publications

References 39 publications

Force-induced desorption of uniform block copolymers

Force-induced desorption of uniform block copolymers

Force-induced desorption of 3-star polymers in two dimensions

Copolymeric stars adsorbed at a surface and subject to a force: a self-avoiding walk model

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