Elasticity of spheres with buckled surfaces

The buckling instabilities of core-shell systems, comprising an interior elastic sphere, attached to an exterior shell, have been proposed to underlie myriad biological morphologies. To fully discuss such systems, however, it is important to properly understand the elasticity of the spherical core. Here, by exploiting well-known properties of the solid harmonics, we present a simple, direct method for solving the linear elastic problem of spheres and spherical voids with surface deformations, described by a real spherical harmonic. We calculate the corresponding bulk elastic energies, providing closed-form expressions for any values of the spherical harmonic degree (l), Poisson ratio, and shear modulus. We find that the elastic energies are independent of the spherical harmonic index (m). Using these results, we revisit the buckling instability experienced by a core-shell system comprising an elastic sphere, attached within a membrane of fixed area, that occurs when the area of the membrane sufficiently exceeds the area of the unstrained sphere [C. Fogle, A. C. Rowat, A. J. Levine and J. Rudnick, Phys. Rev. E 88, 052404 (2013)]. We determine the phase diagram of the core-shell sphere's shape, specifying what value of l is realized as a function of the area mismatch and the core-shell elasticity. We also determine the shape phase diagram for a spherical void bounded by a fixed-area membrane.Comment: 18 pages, 10 figures, submitted to Physical Review

Biofunctionalization of Microgroove Surfaces with Antibacterial Nanocoatings

Objectives. To investigate the physical properties of the modified microgroove (MG) and antibacterial nanocoated surfaces. In addition, the biological interactions of the modified surfaces with human gingival fibroblasts (HGFs) and the antibacterial activity of the surfaces against Porphyromonas gingivalis were studied. Methods. The titanium nitride (TiN) and silver (Ag) coatings were deposited onto the smooth and MG surfaces using magnetron sputtering. A smooth titanium surface (Ti-S) was used as the control. The physicochemical properties including surface morphology, roughness, and hydrophilicity were characterized using scanning electron microscopy, atomic force microscopy, and an optical contact angle analyzer. The “contact guidance” morphology was assessed using confocal laser scanning microscopy. Cell proliferation was analyzed using the Cell Counting Kit-8 assay. The expression level of the main focal adhesion-related structural protein vinculin was compared using quantitative reverse transcription PCR and Western blotting. The antibacterial activity against P. gingivalis was evaluated using the LIVE/DEAD BacLight™ Bacterial Viability Kit. Results. The Ag and TiN antibacterial nanocoatings were successfully deposited onto the smooth and MG surfaces using magnetron sputtering technology. TiN coating on a grooved surface (TiN-MG) resulted in less nanoroughness and greater surface hydrophilicity than Ag coating on a smooth surface (Ag-S), which was more hydrophobic. Cell proliferation and expression of vinculin were higher on the TiN-MG surface than on the Ag-coated surfaces. Ag-coated surfaces showed the strongest antibacterial activity, followed by TiN-coated surfaces. Conclusion. Nano-Ag coating resulted in good antimicrobial activity; however, the biocompatibility was questionable. TiN nanocoating on an MG surface showed antibacterial properties with an optimal biocompatibility and maintained the “contact guidance” effects for HGFs