Surface Tension, Pressure Difference and Laplace Formula for Membranes

Abstract

The surface tension γ and the pressure difference Δp for spherical membranes are calculated using Monte Carlo simulation technique. We study the so-called tethered and uid surface discrete models that are defined on the fixed-connectivity (tethered) and dynamically triangulated (uid) lattices respectively. Hamiltonians of the models include a self-avoiding potential, which makes the enclosed volume well defined. We find that there is reasonable accuracy in the technique for the calculation of γ using the real area A if the bending rigidity κ or A/N is sufficiently large. We also find that γ becomes constant in the limit of A/N → ∞ both in the tethered and uid surfaces. The property limA/N→∞ γ = const corresponds to certain experimental results in cell biology.