The tension of framed membranes from computer simulations

Abstract

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.

Creasing of flexible membranes at vanishing tension

“…The obtained A p is in overall agreement with the thermodynamic analysis in Ref. [27]. For for κ > 3 A p varies weakly as expected for locally smooth surface configurations [Fig.…”

“…However, it remains unclear to which extent the rigid membrane analysis can be extended to low κ with some corrections to ξ [24] or if new physical phenomena will emerge in this regime for self-avoiding surfaces [26]. A recent numerical analysis of the thermodynamics of a framed, semiflexible membrane at fixed A showed that even such surfaces cease to exist for membranes below a threshold bending rigidity κ BP ∼ k B T at vanishing tension [27]. We have in this work analyzed response functions and the two-point correlation function z( x)z( x ) in the regime κ κ BP for framed, tensionless self-avoiding surfaces.…”

Fluctuations and conformational stability of a membrane patch with curvature inducing inclusions

“…Furthermore, instead of the strings of Helfrich vesicles found at high coverage the irregular tubes with elevated concentrations of inclusions are formed at low coverage θ > θ * (C 0 ). The instability point θ * (C 0 ) correlates well with the significant softening of the membrane as shown in Figure 3-B-ii, but it takes place for κ e f f well above the instability criterion of Leibler (κ e f f = 0) and apparently also above the crumpling transition point κ c k B T of a simple framed, fluid membrane 43 . However, the instability at θ * (C 0 ) is accompanied by strong fluctuations as suggested by Eq.…”

“…At θ = 0 the framed membrane patch can sustain semi-flat equilibrium configurations at vanishing tension and a range of negative tensions 42,43 . At low inclusion coverage this is still the case, which makes it possible to perform the fluctuation analysis as above at τ = 0.…”