2003/12/31 by Z. C. Tu, L. Q. Ge, Liqin Ge +3
Biochemistry, Genetics and Molecular Biology · Materials Science · Physics and Astronomy · #Force Microscopy Techniques and Applications #Lipid Membrane Structure and Behavior #Polymer Surface Interaction Studies #cond-mat.soft
paper · pdf · doi:10.1103/physreve.72.021806
published as Phys. Rev. E 72, 021806 (2005) · 17 pages, 1 figure, 1 table
openalex publication_date 2005/08/17 · arxiv created 2005/08/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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 a curved surface [H. Jensen and H. Koppe, Ann. Phys. (N.Y) 63, 586 (1971)]; the other 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 a 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 an important role in the critical pressure because it couples with the out-of-plane mode. Theoretical results reveal that polymer vesicles possess mechanical properties intermediate between those of fluid membranes and solid shells.