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      Non-spherical shapes of capsules within a fourth-order curvature model

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          Abstract

          We minimize a discrete version of the fourth-order curvature based Landau free energy by extending Brakke's Surface Evolver. This model predicts spherical as well as non-spherical shapes with dimples, bumps and ridges to be the energy minimizers. Our results suggest that the buckling and faceting transitions, usually associated with crystalline matter, can also be an intrinsic property of non-crystalline membranes.

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          Bond-orientational order in liquids and glasses

          Paul J. Steinhardt, David R. Nelson, Marco Ronchetti (1983)
          Article 0 comments Cited 941 times – based on 0 reviews     Review now
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            Virus shapes and buckling transitions in spherical shells

            Jack Lidmar, David R. Nelson, Leonid A. Mirny (2003)
            We show that the icosahedral packings of protein capsomeres proposed by Caspar and Klug for spherical viruses become unstable to faceting for sufficiently large virus size, in analogy with the buckling instability of disclinations in two-dimensional crystals. Our model, based on the nonlinear physics of thin elastic shells, produces excellent one parameter fits in real space to the full three-dimensional shape of large spherical viruses. The faceted shape depends only on the dimensionless Foppl-von Karman number \gamma=YR^2/\kappa, where Y is the two-dimensional Young's modulus of the protein shell, \kappa is its bending rigidity and R is the mean virus radius. The shape can be parameterized more quantitatively in terms of a spherical harmonic expansion. We also investigate elastic shell theory for extremely large \gamma, 10^3 < \gamma < 10^8, and find results applicable to icosahedral shapes of large vesicles studied with freeze fracture and electron microscopy.
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              Anharmonic magnetic deformation of self-assembled molecular nanocapsules

              W Feast, J. C. Maan, A F M Kilbinger … (2007)
              High magnetic fields were used to deform spherical nanocapsules, self-assembled from bola-amphiphilic sexithiophene molecules. At low fields the deformation -- measured through linear birefringence -- scales quadratically with the capsule radius and with the magnetic field strength. These data confirm a long standing theoretical prediction (W. Helfrich, Phys. Lett. {\bf 43A}, 409 (1973)), and permits the determination of the bending rigidity of the capsules as (2.6\(\pm\)0.8)\(\times 10^{-21}\) J. At high fields, an enhanced rigidity is found which cannot be explained within the Helfrich model. We propose a complete form of the free energy functional that accounts for this behaviour, and allows discussion of the formation and stability of nanocapsules in solution.
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                Author and article information

                Journal
                Publication date Created: 07 June 2010
                Article
                DOI: 10.1140/epje/i2010-10631-2
                ArXiV ID: 1006.1292
                SO-VID: f50be66a-dd65-4df9-82f5-da396678170e
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                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
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                Journal reference Eur. Phys. J. E032: 223-228,2010
                Comments 6 pages, 4 figures (LaTeX macros EPJ), accepted for publication in EPJ E
                Categories cond-mat.soft

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