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Periodic spin unrestricted, gradient corrected DFT calculations joined with atomistic thermodynamic modeling and experiment were used to study the structure and stability of various reactive oxygen species (ROS) and oxygen vacancies produced on the most stable terminations of the cobalt spinel ( 100) surface. The surface state diagram of oxygen in a wide range of pressures and temperatures was constructed for coverage varying from Θ O = 1.51 atom•nm −2 to Θ O = 6.04 atom•nm −2 . A large variety of the unraveled surface ROS includes diatomic superoxo (Co O −O 2 − −Co O ), peroxo (Co T −O 2 2− −Co O ), and spin paired (Co O −O 2 −Co O ) adducts along with monatomic metal-oxo (Co T −O + , Co O −O 2+ ) species, where Co T and Co O stand for the tetrahedral and octahedral cobalt surface centers, respectively. There are also two kinds of peroxo species associated with surface oxygen ions connected with 3Co O or 2Co O and 1Co T cations ((O 2O,1T −O) 2− and (O 3O −O) 2− ), respectively). The results revealed that in the oxygen pressure range of typical catalytic reactions (p O 2 /p°from ∼0.01 to 1), the most stable stoichiometric (100)-S surface accommodates the Co T −O 2 2− −Co O and Co O −O 2 −Co O adducts at temperatures below 250−300 °C. In the temperature from 250 to 300 °C and from 550 to 700 °C, it is covered by the O species associated with the exposed tetrahedral cobalt sites (Co T − O + ) or remains in a bare state. In more reducing conditions (T > 550−700 °C), the (100)-S facet is readily defected due to trigonal oxygen (O 2O,1T ) release and formation of surface oxygen vacancies. The reactivity of surface ROS was tested in 16 O 2 / 18 O 2 isotopic exchange, N 2 O decomposition, and oxidation of CH 4 and CO model reactions, carried over Co 3 O 4 and Co 3 18 O 4 nanocrystalline samples with the predominant (100) faceting revealed by high angle angular dark field STEM examination. The Co O −O 2+ adducts associated with octahedral cobalt sites, as well as the peroxo (O 2O,1T −O) 2− and (O 3O −O) 2− surface species being thermodynamically unstable are involved in surface oxygen recombination processes, probed by 16 O 2 / 18 O 2 exchange and N 2 O decomposition. It was shown that at low temperatures CO is oxidized by the suprafacial Co O −O 2 −Co O and Co T −O 2 −Co O diatomic oxygen, whereas in CH 4 activation, the highly reactive cobalt-oxo species (Co T −O + ) are involved. Above 600 °C at p O 2 /p°= 0.01, due to the onset of oxygen vacancy formation, the suprafacial methane oxidation gradually changes into the intrafacial Mars-van Krevelen scheme. The constructed surface phase diagram was used for rationalization of the obtained catalytic data, allowing delineation of the specific role of the chemical state of the cobalt spinel surface in the investigated processes, as well as the range of the corresponding temperatures and oxygen pressures. It also provides a convenient background for molecular understanding of remarkable activity of Co 3 O 4 in many other catalytic redox reactions.

Plane wave periodic GGA-PBE+U density functional theory calculations were used to study the structure, surface energy, and equilibrium shape of faceted nanocrystals for a series of cubic (Fd3m) 2−3 AB 2 O 4 spinels with the following formula:

A thorough periodic DFT/PW91 study of water sorption (0.1 < Θ < 1) on tetragonal ZrO2 (P42/nmc) nanocrystals was performed by means of the plane-wave periodic DFT calculations complemented by atomistic thermodynamics. All (101), (001), (100), (111), and (110) planes exposed by faceted t-ZrO2 nanocrystals were taken into account, and their atomic structure, surface reconstruction, and stabilization upon water adsorption were systematically investigated and analyzed in detail. Using the calculated surface energies of the reconstructed planes, a doubly truncated tetragonal-bipyramidal shape of the tetragonal zirconia nanocrystallites in dry and wet conditions was predicted by means of the Wulff construction. The results remain in very good agreement with the experimental HR-TEM images. For each of the exposed planes, the computed changes in the free enthalpy of water adsorption under specified hydration conditions were used to construct two-dimensional surface coverage versus temperature and pressure diagrams, θ hkl = f(T, p H2O). The predicted temperature dependence of total adsorption Θ(T) and dΘ/dT patterns compare well with water TPD experiments. It was found that water adsorption/desorption occurs in a tri-(101), bi-(001) and (111), and a monomodal (100) way. To epitomize the overall water adsorption thermodynamics at the macroscopic scale, a multisite Langmuir and Fowler–Guggenheim isotherms were calculated and interpreted in terms of intermolecular and interfacial interactions between the adspecies and the surface.

Carbon carriers play a triple role in the ORR, determining nanoparticle dispersion, faceting, and reaction mechanism.

A combination of periodic, spin unrestricted DFT calculations and first principle thermodynamic modeling was used to evaluate the structure and stability of nine different pristine and eight defected terminations of the (111) surface of cobalt spinel under various redox conditions (T, p O2 ). The surface redox state diagram of possible spinel (111) terminations in the wide stoichiometry range from Co2.62O4 to Co3O3.75 was constructed and thoroughly discussed, revealing that three regions of spinel surface redox behavior may be distinguished. The region of temperatures and pressures of typical catalytic processes (T ∼200 to ∼500 °C, p O2 /p° ∼0.001 to ∼1) corresponds to an energetically well separated stoichiometric (111)-S facet exposing both truncated tetrahedral CoT 3c and octahedral CoO 3c cations. They preserve their bulk-like divalent (q B = 1.29 |e|) and trivalent (q B = 1.45 |e|) state, respectively, in contrast to the spin state of CoO 3c (S = 1, μ = 1.9 μB) comparing to diamagnetic bulk CoO 6c. Under more reducing conditions (T > 600 °C and p O2 /p° < 0.0001), several terminations of different stoichiometry induced by the formation of oxygen vacancies may coexist, providing a thermodynamic background for enhanced redox activity. Redox properties are associated with extended electronic and spin relaxations that entail several octahedral surface (CoO 3c, q B = 1.29) and subsurface (CoO 6c, q B = 0.01) cations which are reduced (Δq B = −0.24 |e|, Δμ = 0.87 μB) upon oxygen release (formation of redox active ensemble). Under the oxygen rich conditions (T < 200 °C and p O2 /p° > 10), the oxidized (111)-O termination, exposing the CoT 3c ions only, is the most stable, and with the rising oxygen pressure, it becomes defected due to the presence of the cationic vacancies in the tetrahedral sites. The sub-stoichiometry (Co deficiency) of the (111)-O surface is reflected in the trivalent state of half of the surface CoT 3c cations, which are characterized by larger charge (Δq B = 0.15 |e|) and lower magnetization (Δμ = −0.7 μB) in line with the (d z 2 , d z 2–y 2 )4(d xy )1(d xz )1 configuration. The shape of the Co3O4 nanograins was modeled by means of the Wulff construction for oxidizing, ambient, and reducing redox conditions. It was shown that rhombicubooctahedral morphology is preserved regardless of the oxygen chemical potential and the (111) termination is more abundant in an oxygen rich environment.

Soot particles are recognized as one of the main sources of air pollution; therefore, it is an urgent need to eliminate them from the air effectively. Catalytic combustion is a promising strategy for soot abatement, yet the development of highly efficient catalysts is still an important challenge for practical applications. In this study, novel hierarchical porous K-OMS-2/3DOM-m Ti0.7Si0.3O2 catalysts, in which the Ti0.7Si0.3O2 supports contain ordered macropores and mesopores and the K-OMS-2 active phase contains micropores, were purposefully designed and successfully prepared using a simple method. The macropores and mesopores in the as-prepared catalysts were formed by PMMA and P123 as templates, and the micropores were brought about by K-OMS-2, a specific crystal form of cryptomelane. The K-OMS-2/3DOM-m Ti0.7Si0.3O2 catalysts exhibit high catalytic activity for soot combustion, along with high stability and good resistance to sulfur and water. Among the synthesized catalysts, K-OMS-2/3DOM-m Ti0.7Si0.3O2-450 shows the highest catalytic activity with T 10, T 50, and T 90 values of 288, 333, and 364 °C, respectively. This catalyst also exhibits good stability after five catalytic cycles with T 10, T 50, and T 90 values in the range of 290 ± 4, 335 ± 4, and 368 ± 4 °C, respectively. The excellent catalytic performance in soot combustion associated with high NO oxidation activity is attributed to the hierarchical pore effect, a synergistic effect between K and Mn, as well as to doping with Ti. Molecular density functional theory (DFT) and thermodynamic modeling indicated that both Langmuir–Hinshelwood and Eley–Rideal mechanisms may operate in the NO to NO2 oxidation on the K-OSM-2 surface, yet the former is energetically slightly more preferred. Because of their easy synthesis, low cost, high activity, good stability, and good resistance to sulfur and water, the developed optimal K-OMS-2/3DOM-m Ti0.7Si0.3O2 catalysts are promising for practical applications in soot combustion filters.

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