Are stress-free membranes really 'tensionless'?

TL;DR

This paper reevaluates the relationship between tension and fluctuations in stress-free membranes, demonstrating through simulations and theory that fluctuations are driven by frame tension despite differences in intrinsic stress.

Contribution

It shows that the Monge model's nonlinear predictions align with simulation data, clarifying the distinction between intrinsic stress and frame tension in membranes.

Findings

Intrinsic stress differs from frame tension in membranes.

Fluctuations are driven by frame tension despite intrinsic stress differences.

Monge model predictions match simulation results across various parameters.

Abstract

In recent years it has been argued that the tension parameter driving the fluctuations of fluid membranes, differs from the imposed lateral stress, the 'frame tension'. In particular, stress-free membranes were predicted to have a residual fluctuation tension. In the present paper, this argument is reconsidered and shown to be inherently inconsistent -- in the sense that a linearized theory, the Monge model, is used to predict a nonlinear effect. Furthermore, numerical simulations of one-dimensional stiff membranes are presented which clearly demonstrate, first, that the internal 'intrinsic' stress in membranes indeed differs from the frame tension as conjectured, but second, that the fluctuations are nevertheless driven by the frame tension. With this assumption, the predictions of the Monge model agree excellently with the simulation data for stiffness and tension values spanning several orders of magnitude.