Search for: All records

Schwarzites are hypothetical carbon allotropes in the form of a continuous negatively curved surface with three-dimensional periodicity. These materials of the future attract interest because of their anticipated large surface area per volume, high porosity, tunable electric conductivity, and excellent mechanical strength combined with light weight. A three-decade-long history attempting schwarzite synthesis from gas-phase carbon atoms went without success. Design of schwarzites is both a digital art and the science of placing tiles of sp2-carbon polygons on mathematically defined triply periodic minimal surfaces. The knowledge of how to connect polygons in sequence using the rules of symmetry unlocks paths for the bottom-up synthesis of schwarzites by organic chemistry methods. Schwarzite tiling by heptagons is systematically analyzed and classified by symmetry and topology. For the first time, complete plans for the bottom-up synthesis of many schwarzites are demonstrated. A trimer of heptagons is suggested as the key building block for most synthetic schemes. 

The acidity of anatase titania before and after KOH doping was probed by pyridine adsorption in a pulse microreactor and modeled by DFT optimization of the geometry of CO and pyridine adsorption on a periodic slab of (101) and (100) surfaces using a GGA/PBE functional and verified by an example of a single-point calculation of the optimized geometry using an HSE-06 hybrid functional. The anatase (101) surface was slightly more acidic compared to the (100) surface. Both experimental and computational methods show that the acidity of anatase surfaces decreased after KOH doping and increased after the dissociative adsorption of water. Higher acidity of Ti metal centers was indicated by the shortening of the Ti-N, Ti-C, and C-O bond lengths, increasing the IR frequency of CO and pyridine ring vibrations and energy of adsorption. The DFT calculated energy of pyridine adsorption was analyzed in terms of binding energy and the energy of lattice distortion. The latter was used to construct Hammett plots for the adsorption of 4-substituted pyridines with electron-donating and -withdrawing substituents. The Hammett rho constant was obtained and used to characterize the acidity of various metal centers of −1.51 vs. −1.46 on pristine (101) and (100) surfaces, which were lowered to −1.07 and −1.19 values on KOH-doped (101) and (100) surfaces, respectively. The mechanism of lowering surface acidity via KOH doping proceeds through the stabilization of the atomic structure of Lewis acid centers. When an alkaline metal cation binds to several lattice oxygen atoms, the surface structure becomes more rigid. The ability of Ti atoms to move toward the adsorbate is restricted. Consequently, the lattice distortion energy and binding energy are decreased. In contrast, higher flexibility of the outermost layer of Ti atoms as a result of electron density redistribution, for example, in the presence of water on the surface, allows them to move farther outward, make shorter contacts with the adsorbate, and attain higher energies of binding and lattice distortion.