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

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.