High-performance functional materials – in particular, nanostructured metal oxides – are regarded as highly promising for sophisticated applications in the fields of ceramics, catalysis or electronics. To cover the increasing demand for these materials, advanced processes such as nonaqueous synthesis are required that yield nanoparticles with defined sizes and morphologies and are suitable for large-scale production. In contrast to aqueous sol-gel methods, chemical reactions and particle formation occur rather slowly, which leads directly to the development of a highly crystalline structure and spares the effort of a further thermal treatment. The particles can be easily dispersed and used for subsequent processing such as stabilization or functionalization. Nevertheless, one has to study the characteristics and kinetics of the chemical reactions that induce particle formation in order to allow for precise control of particle properties. Here, we present a first approach to elucidate the process technology of the nonaqueous synthesis and unravel the underlying mechanisms that lead to nucleation and growth of zirconia as well as titania nanoparticles. For the first time, the population balance equation method was implemented to simulate nanoparticle formation. The nonaqueous sol-gel synthesis involves the reaction of a metal alkoxide, as the precursor, with the solvent benzyl alcohol. The reaction is carried out at temperatures above 180 °C in a closed and agitated vessel. In consecutive chemical reaction steps, intermediate cluster species are formed that consist of benzyloxy groups linked to the metal atom. These intermediate clusters grow to bigger clusters and particle formation occurs when the cluster exceeds a stable (critical) cluster size, which is in good accordance with classical nucleation theory. In fact, we were able to show that during the titania synthesis, oligomer clusters grow most probably to a size of [Ti
16O
16](OBn)
32[1] that serve as nuclei, triggering the nucleation. In addition, a specially designed reaction vessel was used to perform in situ laser light transmission measurements in combination with small-angle X-ray scattering analysis to detect and investigate the nucleation event. For the zirconia system, we found that oligomeric cluster species might also be involved before nanoparticles nucleate with a size of 2 nm. However, the rate-determining step is the chemical reaction that leads to these intermediate cluster species, thus the process is controlled by chemical reaction kinetics rather than by nucleation and growth mechanisms. Due to the small particle size, these reactions yield the anatase polymorph of titania and the tetragonal modification of zirconia that are thermodynamically unstable in bigger size regimes. A thorough process study was conducted to elucidate the interdependence between process parameters, chemical reaction kinetics and resulting nanoparticle properties. We found that autocatalytic reaction kinetics for the titania system and pseudo zero-order kinetics for the zirconia system best describe the respective reaction mechanisms. Both reactions follow the law of Arrhenius and the activation energies were calculated to gain a process function that correlates the yield over time for different initial precursor concentrations and temperatures. Our study revealed that one can tune the crystallite size of TiO
2 in the range of 5 to 15 nm,
[2] and for ZrO
2 in the range of 3 to 7 nm,
[3] by adjusting the process parameters. Syntheses conducted at lower temperatures lead to slow kinetics and yield larger particles with pronounced shapes, whereas elevated temperatures, additional overpressure or seeding lead to fast reaction kinetics, which results in smaller roundish nanoparticles. The zirconia particles undergo a tetragonal-to-monoclinic phase transformation accompanied by a characteristic change in morphology to fractal particles. This can be explained by the crystallite size effect and occurs when particles exceed the size of 4 nm. We propose that this solid–solid phase transformation is induced by heterogeneous nucleation and rather controlled by kinetics, which is ideally in good accordance with the Ostwald rule of stages. For the first time, we propose a model equation that describes the probability of tetragonal particles transforming into monoclinic particles as a function of the crystallite size.
All these findings serve as a framework for a comprehensive population balance equation (PBE) model that simulates nanoparticle formation and is able to predict the final nanoparticle size and phase composition.[4] With our derived kinetic model for the chemical reactions, we compute a theoretical (monomer) cluster concentration that links the mass balances to the population balance and couples the influence of the process parameters to our model. Thus, the monomer concentration is the driving force of particle formation and is incorporated in the respective nucleation and growth terms within the PBE model. We simulate the tetragonal-to-monoclinic phase transition and show how tetragonal crystals nucleate, grow and transit upon a certain size into the monoclinic phase. Hence, we are able to explain why tetragonal particles are larger than monoclinic particles, which initially seems to be in direct conflict with thermodynamics. The simulation was applied only with minor adjustments to the titania system and reflects the spontaneous burst of particles through the autocatalytic reaction kinetics. Furthermore, we extended the PBE model to simulate secondary particle formation, which allowed us to develop a qualitative and quantitative understanding of the agglomeration behavior.
[1] M. Zimmermann, K. Ibrom, P. G. Jones, G. Garnweitner, ChemNanoMat 2016, 2, 1073–1076.
[2] M. Zimmermann, B. Temel, G. Garnweitner, Chemical Engineering and Processing: Process Intensification 2013, 74, 83–89.
[3] P. Stolzenburg, A. Freytag, N. C. Bigall, G. Garnweitner, CrystEngComm 2016, 18, 8396–8405.
[4] P. Stolzenburg, G. Garnweitner, Reaction Chemistry & Engineering 2017, 2, 337–348.
