A Symmetry‐Based Kinematic Theory for Nanocrystal Morphology Design

Abstract

The growth of crystalline nanoparticles (NPs) generally involves three processes: nucleation, growth, and shape evolution. Among them, the shape evolution is less understood, despite the importance of morphology for NP properties. Here, we propose a symmetrybased kinematic theory (SBKT) based on classical growth theories to illustrate the process. Based on the crystal lattice, nucleus (or seed) symmetry, and the preferential growth directions under the experimental conditions, the SBKT can illustrate the growth trajectories. The theory accommodates the conventional criteria of the major existing theories for crystal growth and provides tools to better understand the symmetry-breaking process during the growth of anisotropic structures. Furthermore, complex dendritic growth is theoretically and experimentally demonstrated. Thus, it provides a framework to explain the shape evolution, and extends the morphogenesis prediction to cases, which cannot be treated by other theories.

Pursuing unprecedented anisotropic morphologies of halide-free Pd nanoparticles by tuning their nucleation and growth

“…66 A recently developed symmetry-based kinematic theory proposed by Ni et al explains well the shape evolution of nanocrystal growth via a surface nucleation process and layer advancement. 67 This theory, reconciling the gap between thermodynamic and kinetic controlled growth, explains well the observed shape evolutions. 67…”

“…67 This theory, reconciling the gap between thermodynamic and kinetic controlled growth, explains well the observed shape evolutions. 67…”

“…66 A recently developed symmetry-based kinematic theory proposed by Ni et al explains well the shape evolution of nanocrystal growth via a surface nucleation process and layer advancement. 67 This theory, reconciling the gap between thermodynamic and kinetic controlled growth, explains well the observed shape evolutions. 67 The starting apparent pH of the reaction mixture might affect different factors determining the resulting reduction mechanism: (i) the reducing ability of EG might be modified by the introduction of H + in the suspension (i.e., lowering the apparent pH), resulting in an increase in the redox potential of EG, as described by the Nernst law (EG is oxidised to a series of compounds losing H + ); (ii) the apparent pH might interfere with the structure-directing properties of ions and capping polymers, modifying their conformation and/or charge; and (iii) the Pd metal complex might undergo ligand exchange generating aquo-hydroxo and/or nitrate complexes as described by Vasilchenko et al 68 In particular, the presence of nitrates in a basic environment could not be strong enough to substitute the hydroxide ions of [Pd(OH) 4 ] 2− .…”

“…67 This theory, reconciling the gap between thermodynamic and kinetic controlled growth, explains well the observed shape evolutions. 67 The starting apparent pH of the reaction mixture might affect different factors determining the resulting reduction mechanism: (i) the reducing ability of EG might be modified by the introduction of H + in the suspension (i.e., lowering the apparent pH), resulting in an increase in the redox potential of EG, as described by the Nernst law (EG is oxidised to a series of compounds losing H + ); (ii) the apparent pH might interfere with the structure-directing properties of ions and capping polymers, modifying their conformation and/or charge; and (iii) the Pd metal complex might undergo ligand exchange generating aquo-hydroxo and/or nitrate complexes as described by Vasilchenko et al 68 In particular, the presence of nitrates in a basic environment could not be strong enough to substitute the hydroxide ions of [Pd(OH) 4 ] 2− . In contrast, at more neutral (and acidic) pH values, reached with the addition of HNO Otherwise, if one of the above-mentioned factors had caused a kinetic modification only, it would have been unlikely that we would have observed two distinct geometries, as a structural average of the two geometries would have been more likely to occur.…”

Isolating Single Sn Atoms in CuO Mesocrystal to Form Ordered Atomic Interfaces: An Effective Strategy for Designing Highly Efficient Mesocrystal Catalysts

“…Moreover, variation of the ratio between DMF and H 2 O led to a change in the final product morphology (Table S4 and Figure S14, Supporting Information), attributed to the changes in solution viscosity, thereby affecting the formation rate of the primary NPs. [12,43,44] The observed changes in the product morphology when using different precursor salts (Table S5 and Figure S15, Supporting Information) mainly result from the different assembly behaviors of the generated NPs due to the distinct reduction property of the precursor. [45,46] In addition, it was found that in the above cases, once there was the presence of CH 3 COOH, the obtained product was a regular assembly structure, proving that CH 3 COOH plays a pivotal role in directional assembly, consistent with the previous report.…”