Elasticity of polymer vesicles by osmotic pressure: an intermediate theory between fluid membranes and solid shells

TL;DR

This paper develops an intermediate elastic theory for polymer vesicles under osmotic pressure, combining curvature and in-plane strain energies, and analyzes their stability and mechanical properties.

Contribution

It introduces a new elastic free energy model for polymer membranes that bridges fluid membranes and solid shells, including in-plane strains and osmotic effects.

Findings

Polymer vesicles have mechanical properties between fluid membranes and solid shells.

Critical osmotic pressure for stability is derived considering in-plane and out-of-plane modes.

In-plane modes significantly influence the stability of polymer vesicles.

Abstract

The entropy of a polymer confined in a curved surface and the elastic free energy of a membrane consisting of polymers are obtained by scaling analysis. It is found that the elastic free energy of the membrane has the form of the in-plane strain energy plus Helfrich's curvature energy [Z. Naturforsch. C \textbf{28}, 693 (1973)]. The elastic constants in the free energy are obtained by discussing two simplified models: one is the polymer membrane without in-plane strains and asymmetry between its two sides, which is the counterpart of quantum mechanics in curved surface [Jensen and Koppe, Ann. Phys. \textbf{63}, 586 (1971)]; another is the planar rubber membrane with homogeneous in-plane strains. The equations to describe equilibrium shape and in-plane strains of the polymer vesicles by osmotic pressure are derived by taking the first order variation of the total free energy containing the elastic free energy, the surface tension energy and the term induced by osmotic pressure. The critical pressure, above which spherical polymer vesicle will lose its stability, is obtained by taking the second order variation of the total free energy. It is found that the in-plane mode also plays important role in the critical pressure because it couples with the out-of-plane mode. Theoretical results reveal that polymer vesicles possess the mechanical properties intermediate between fluid membranes and solid shells.