The tension of framed membranes from computer simulations

Daniel Hamkens, Claus Jeppesen, John H. Ipsen*

*Corresponding author for this work

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Abstract

We have analyzed the behavior of a randomly triangulated, self-avoiding surface model of a flexible, fluid membrane subject to a circular boundary by Wang-Landau Monte Carlo computer simulation techniques. The dependence of the canonical free energy and frame tension on the frame area is obtained for flexible membranes. It is shown that for low bending rigidities the framed membrane is only stable above a threshold tension, suggesting a discontinuous transition from the collapsed (branched polymer) state to a finite tension extended state. In a tension range above this threshold tension the membranes display power-law characteristics for the equation of state, while higher tension levels includes both an extended linear (elastic) as well as a highly non-linear stretching regime. For semi-flexible membranes a transition from extended to buckled conformations takes place at negative frame tensions. Our analysis indicates that at zero frame tension the crumpling transition of fluid membranes show characteristics of both critical behavior and a discontinuous transition at low bending rigidities.

Original languageEnglish
Article number42
JournalEuropean Physical Journal E
Volume41
Issue number3
Number of pages11
ISSN1292-8941
DOIs
Publication statusPublished - Mar 2018

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Computer Simulation
computerized simulation
membranes
Membranes
Computer simulation
Rigidity
rigidity
Fluids
Equations of state
Free energy
Stretching
thresholds
Conformations
fluids
Polymers
equations of state
free energy
polymers

Keywords

  • Soft Matter: Interfacial Phenomena and Nanostructured Surfaces

Cite this

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title = "The tension of framed membranes from computer simulations",
abstract = "We have analyzed the behavior of a randomly triangulated, self-avoiding surface model of a flexible, fluid membrane subject to a circular boundary by Wang-Landau Monte Carlo computer simulation techniques. The dependence of the canonical free energy and frame tension on the frame area is obtained for flexible membranes. It is shown that for low bending rigidities the framed membrane is only stable above a threshold tension, suggesting a discontinuous transition from the collapsed (branched polymer) state to a finite tension extended state. In a tension range above this threshold tension the membranes display power-law characteristics for the equation of state, while higher tension levels includes both an extended linear (elastic) as well as a highly non-linear stretching regime. For semi-flexible membranes a transition from extended to buckled conformations takes place at negative frame tensions. Our analysis indicates that at zero frame tension the crumpling transition of fluid membranes show characteristics of both critical behavior and a discontinuous transition at low bending rigidities.",
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The tension of framed membranes from computer simulations. / Hamkens, Daniel; Jeppesen, Claus; Ipsen, John H.

In: European Physical Journal E, Vol. 41, No. 3, 42, 03.2018.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - The tension of framed membranes from computer simulations

AU - Hamkens, Daniel

AU - Jeppesen, Claus

AU - Ipsen, John H.

PY - 2018/3

Y1 - 2018/3

N2 - We have analyzed the behavior of a randomly triangulated, self-avoiding surface model of a flexible, fluid membrane subject to a circular boundary by Wang-Landau Monte Carlo computer simulation techniques. The dependence of the canonical free energy and frame tension on the frame area is obtained for flexible membranes. It is shown that for low bending rigidities the framed membrane is only stable above a threshold tension, suggesting a discontinuous transition from the collapsed (branched polymer) state to a finite tension extended state. In a tension range above this threshold tension the membranes display power-law characteristics for the equation of state, while higher tension levels includes both an extended linear (elastic) as well as a highly non-linear stretching regime. For semi-flexible membranes a transition from extended to buckled conformations takes place at negative frame tensions. Our analysis indicates that at zero frame tension the crumpling transition of fluid membranes show characteristics of both critical behavior and a discontinuous transition at low bending rigidities.

AB - We have analyzed the behavior of a randomly triangulated, self-avoiding surface model of a flexible, fluid membrane subject to a circular boundary by Wang-Landau Monte Carlo computer simulation techniques. The dependence of the canonical free energy and frame tension on the frame area is obtained for flexible membranes. It is shown that for low bending rigidities the framed membrane is only stable above a threshold tension, suggesting a discontinuous transition from the collapsed (branched polymer) state to a finite tension extended state. In a tension range above this threshold tension the membranes display power-law characteristics for the equation of state, while higher tension levels includes both an extended linear (elastic) as well as a highly non-linear stretching regime. For semi-flexible membranes a transition from extended to buckled conformations takes place at negative frame tensions. Our analysis indicates that at zero frame tension the crumpling transition of fluid membranes show characteristics of both critical behavior and a discontinuous transition at low bending rigidities.

KW - Soft Matter: Interfacial Phenomena and Nanostructured Surfaces

U2 - 10.1140/epje/i2018-11651-6

DO - 10.1140/epje/i2018-11651-6

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JO - The European Physical Journal E: Soft Matter and Biological Physics

JF - The European Physical Journal E: Soft Matter and Biological Physics

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