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

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 ${\itΔ}p$ between the inner and the outer sides of the surface is also calculated by maintaining the enclosed volume constant. Using ${\itΔ}p$ 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 $A/N\to \infty$ both in the tethered and fluid surfaces.

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