On the surface tension of fluctuating quasi-spherical vesicles

TL;DR

This paper derives the mechanical surface tension of fluctuating quasi-spherical vesicles by calculating the stress tensor and analyzing thermal averages, revealing conditions under which tension becomes negative, affecting vesicle pressure dynamics.

Contribution

It introduces a method to compute the surface tension of fluctuating vesicles by stress tensor analysis and explores the implications of negative tension states.

Findings

Surface tension can become negative before shape transitions.

Negative tension can reach large magnitudes in small vesicles.

Negative tension implies inner pressure may be lower than outer pressure.

Abstract

We calculate the stress tensor for a quasi-spherical vesicle and we thermally average it in order to obtain the actual, mechanical, surface tension $\tau$ of the vesicle. Both closed and poked vesicles are considered. We recover our results for $\tau$ by differentiating the free-energy with respect to the proper projected area. We show that $\tau$ may become negative well before the transition to oblate shapes and that it may reach quite large negative values in the case of small vesicles. This implies that spherical vesicles may have an inner pressure lower than the outer one.