The tension of framed membranes from computer simulations (original) (raw)
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Creasing of flexible membranes at vanishing tension
Physical Review E
The properties of freestanding tensionless interfaces and membranes at low bending rigidity κ are dominated by strong fluctuations and self-avoidance and are thus outside the range of standard perturbative analysis. We analyze this regime by a simple discretized, self-avoiding membrane model on a frame subject to periodic boundary conditions by use of Monte Carlo simulation and dynamically triangulated surface techniques. We find that at low bending rigidities, the membrane properties fall into three regimes: Below the collapse transition κ BP it is subject to branched polymer instability where the framed surface is not defined, in a range below a threshold rigidity κ c the conformational correlation function are characterized by power-law behavior with a continuously varying exponent α, 2 < α 4 and above κ c , α = 4 characteristic for linearized bending excitations. Response functions specific heat and area compressibility display pronounced peaks close to κ c. The results may be important for the description of soft interface systems, such as microemulsions and membranes with in-plane cooperative phenomena.
Coarse-grained simulations of membranes under tension
The Journal of Chemical Physics, 2010
We investigate the properties of membranes under tension by Monte-Carlo simulations of a generic coarse-grained model for lipid bilayers. We give a comprising overview of the behavior of several membrane characteristics, such as the area per lipid, the monolayer overlap, the nematic order, and pressure profiles. Both the low-temperature regime, where the membranes are in a gel L β ′ phase, and the high-temperature regime, where they are in the fluid Lα phase, are considered. In the L β ′ state, the membrane is hardly influenced by tension. In the fluid state, high tensions lead to structural changes in the membrane, which result in different compressibility regimes. The ripple state P β ′ , which is found at tension zero in the transition regime between Lα and L β ′ , disappears under tension and gives way to an interdigitated phase. We also study the membrane fluctuations in the fluid phase. In the low tension regime the data can be fitted nicely to a suitably extended elastic theory. At higher tensions the elastic fit consistently underestimates the strength of longwavelength fluctuations. Finally, we investigate the influence of tension on the effective interaction between simple transmembrane inclusions and show that tension can be used to tune the hydrophobic mismatch interaction between membrane proteins.
First-order transition of tethered membranes in three-dimensional space
Physical review. E, Statistical, nonlinear, and soft matter physics, 2002
We study a model of phantom tethered membranes, embedded in three-dimensional space, by extensive Monte Carlo simulations. The membranes have hexagonal lattice structure where each monomer is interacting with six nearest-neighbors (NN). Tethering interaction between NN, as well as curvature penalty between NN triangles are taken into account. This model is new in the sense that NN interactions are taken into account by a truncated Lennard-Jones potential including both repulsive and attractive parts. The main result of our study is that the system undergoes a first-order crumpling transition from low-temperature flat phase to high-temperature crumpled phase, in contrast with early numerical results on models of tethered membranes.
Journal of Mathematical Chemistry, 2015
A Monte Carlo (MC) study is performed to evaluate the surface tension γ of spherical membranes that may be regarded as the models of the lipid layers. We use the canonical surface model defined on the self-avoiding triangulated lattices. The surface tension γ is calculated by keeping the total surface area A constant during the MC simulations. In the evaluation of γ, we use A instead of the projected area A p , which is unknown due to the fluctuation of the spherical surface without boundary. The pressure difference ∆p between the inner and the outer sides of the surface is also calculated by maintaining the enclosed volume constant. Using ∆p and the Laplace formula, we obtain the tension, which is considered to be equal to the frame tension τ conjugate to A p , and check whether or not γ is consistent with τ. We find reasonable consistency between γ and τ in the region of sufficiently large bending rigidity κ or sufficiently large A/N. It is also found that τ becomes constant in the limit of A/N → ∞ both in the tethered and fluid surfaces.
Tethered membranes far from equilibrium: Buckling dynamics
Physical Review E, 1999
We study the dynamics of the classical Euler buckling of compressed solid membranes. We relate the membrane buckling dynamics to phase ordering phenomena. Membranes develop a wavelike pattern whose wavelength grows, via coarsening, as a power of time. We find that evolving membranes are similar to growing surfaces ͑''growing interfaces''͒ whose transverse width grows as a power of time. The morphology of the evolving membranes is characterized by the presence of a network of growing ridges where the elastic energy is mostly localized. We used this fact to develop a scaling theory of the buckling dynamics that gives analytic estimates of the coarsening exponents. Our findings show that the membrane buckling dynamics is characterized by a distinct scaling behavior not found in other coarsening phenomena. ͓S1063-651X͑99͒04510-9͔
Shape Instabilities in the Dynamics of a Two-Component Fluid Membrane
Physical Review Letters, 1998
We study the shape dynamics of a two-component fluid membrane, using a dynamical triangulation monte carlo simulation and a Langevin description. Phase separation induces morphology changes depending on the lateral mobility of the lipids. When the mobility is large, the familiar labyrinthine spinodal pattern is linearly unstable to undulation fluctuations and breaks up into buds, which move towards each other and merge. For low mobilities, the membrane responds elastically at short times, preferring to buckle locally, resulting in a crinkled surface.
Simulation of light-weight membrane structures by wrinkling model
International Journal for Numerical Methods in Engineering, 2005
The computational challenge in dealing with membrane systems is closely connected to the lack of bending stiffness that constitutes the main feature of this category of structures. This manifests numerically in badly conditioned or singular systems requiring the use of stabilized solution procedures, in our case of a 'pseudo-dynamic' approach. The absence of the flexural stiffness makes the membrane very prone to local instabilities which manifest physically in the formation of little 'waves' in 'compressed' areas. Current work presents an efficient, sub-iteration free 'explicit', penalty material based, wrinkling simulation procedure suitable for the solution of 'static' problems. The procedure is stabilized by taking full advantage of the pseudo-dynamic solution strategy, which allows to retain the elemental quadratic convergence properties inside the single solution step. Results are validated by comparison with published results and by setting up 'numerical experiments' based on the solution of test cases using dense meshes.
Topology changes in fluid membranes
Physical Review A, 1992
Shape changes of a fluid membrane with fixed area modeled by a curvature Hamiltonian and a boundary line tension are investigated. The zero-temperature energetics are studied using a variational principle in the space of axisymmetric shapes. For zero spontaneous curvature, the only energy minimizing shapes are the disk and the sphere. The energy barrier heights between these configurations are determined as a function of the Hamiltonian parameters. Thermal fluctuations of the shape are studied by means of a Monte Carlo simulation. The "phase transition" from open to closed topology is determined as a function of the rigidity and line tension at nonzero temperature. The transition is found to persist even at zero membrane rigidity. The energetics of the transition are shown to be related to the branched polymer scaling behavior of the fluid membrane.
The stretching elasticity of biomembranes determines their line tension and bending rigidity
In this work, some implications of a recent model for the mechanical behavior of biological membranes (Deseri et al. in Continuum Mech Thermodyn 20(5):255-273, 2008) are exploited by means of a prototypical one-dimensional problem. We show that the knowledge of the membrane stretching elasticity permits to establish a precise connection among surface tension, bending rigidities and line tension during phase transition phenomena. For a specific choice of the stretching energy density, we evaluate these quantities in a membrane with coexistent fluid phases, showing a satisfactory comparison with the available experimental measurements. Finally, we determine the thickness profile inside the boundary layer where the order-disorder transition is observed.