# Surface tension and Laplace pressure in triangulated surface models for membranes without fixed boundary

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## Abstract

A Monte Carlo (MC) study is performed to evaluate the surface tension \(\gamma \) 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 \(\gamma \) is calculated by keeping the total surface area *A* constant during the MC simulations. In the evaluation of \(\gamma \), 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 \({\varDelta }p \) between the inner and the outer sides of the surface is also calculated by maintaining the enclosed volume constant. Using \({\varDelta }p \) and the Laplace formula, we obtain the tension, which is considered to be equal to the frame tension \(\tau \) conjugate to \(A_p\), and check whether or not \(\gamma \) is consistent with \(\tau \). We find reasonable consistency between \(\gamma \) and \(\tau \) in the region of sufficiently large bending rigidity \(\kappa \) or sufficiently large *A* / *N*. It is also found that \(\tau \) becomes constant in the limit of \(A{/}N\rightarrow \infty \) both in the tethered and fluid surfaces.

## Keywords

Surface tension Frame tension Membranes Laplace formula## Notes

### Acknowledgments

This work is supported in part by the Grant-in-Aid for Scientific Research (C) Number 26390138. We acknowledge the support of the Promotion of Joint Research 2014, Toyohashi University of Technology. We are grateful to K. Osari and S. Usui for the computer analyses.

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