Correlation of Enhanced Strength and Internal Structure for Heat‐Treated Submicron Stöber Silica Particles

The Stöber–Fink–Bohn (SFB) method allows the synthesis of spherical silica particles over a wide size range. Owing to the complex formation mechanism, the internal structure and related mechanical properties are not well understood. Within this account, the internal structure of synthesized SFB particles is changed systematically by heat treatments. Characterization by colloid titration, infrared spectroscopy, and solid‐state nuclear magnetic resonance spectroscopy and the assessment of mechanical properties for single particles by in situ micromanipulation shed light on structure–property relations. Over the course of heat treatment, SFB particles become denser and owing to condensation of internal hydroxyl groups, the cross‐linking of the silica network is enhanced. The observed chemical and structural changes are reflected by the mechanical properties of the particles: starting from a low Young's modulus and hardness, clearly below the bulk properties of fused silica, both values are increasing over the course of the thermal treatment. Hardness for fused silica is approached after a treatment at 800 °C and exceeded after a treatment at 1000 °C. Young's modulus approaches the bulk value. Furthermore, a significant plasticity is found: the sustained deformations are extremely high, and thus silica spheres with enhanced strength have been obtained by the thermal treatment.     

On subextension of pluriharmonic and plurisubharmonic functions

The problem of subextension of plurisubharmonic functions is considered. Recently it was shown by Cegrell–Zeriahi, that subextension is always possible for negative plurisubharmonic functions in the energy class ℱ. In this paper we construct, for every hyperconvex domain Ω, a negative plurisubharmonic function in the class ℰ which cannot be subextended. Given any pseudoconvex domain we construct a pluriharmonic function that cannot be subextended.