large number of amorphous noble metal particles and amorphous ultrathin two-dimensional materials could be achieved through this method.
1.4 Growth Mechanisms of Amorphous Nanomaterials
1.4.1 Classical Nucleation Theory
In classical nucleation theory, the formation of solid particles in solution underwent two phases: nucleation and growth. In 1950, Lamer proposed a nucleation mechanism in the energy category based on the sulfur colloid synthesis process in solution, which is still one of the most significant self-consistent nucleation mechanisms [24].
At the nucleation stage, the transition from the liquid phase to the solid phase occurs. There are two kinds of energy changes during this transition. One is the volume free energy (ΔGV), which is defined as the decrease of the free energy of atoms during the transition from the free state in the solution to the crystal nuclei. The other is the surface free energy (ΔGγ), which demonstrates the increasing of the system’s free energy from the generated new interfaces. If the newly generated nucleus is regarded as a sphere, the former is a positive correlation function of volume (the cube of the radius r), ΔGV = 4/3πr3·ρRTln(c/c0), where c0 is the concentration of the supersaturated solution. The latter is a positive correlation function of the surface area (the square of r), ΔGγ = 4πr2·γs−l. This makes a critical radius r* in the nucleation process, which exhibit a negative correlation with the concentration of the supersaturated solution. Therefore, a higher concentration supersaturation lead to smaller nucleation radius.
Taking the formation of metal materials as an example. During the nucleation stage, the original precursors are reduced to metal atoms with external stimulation (reductive agent adding, heating, irradiating, etc.). These atoms will be the modular units for the subsequent construction of the crystal structure. With the decomposition of the precursor, the concentration of metal atoms increases. Once the atomic concentration exceeds the minimum supersaturation point, the atoms exhibit a tendency to aggregate spontaneously to reduce surface energy (surface energy is higher than volume energy before the critical radius). In somewhere of the solution, affected by thermodynamic fluctuations, initial nuclei would instantaneously aggregate by atoms and separate from solution. Once the initial clusters are formed, these seeds then accelerate their growth by adsorbing free atoms in the solution, leading to the decrease of the concentration of atoms in the solution. At this time, the decomposition of the precursor is still continuing and the free atom is continuously added. If the atomic concentration drops rapidly below the minimum supersaturation, no additional nucleation will occur and the resulting product will exhibit a monodisperse size. With the continuous supply of atoms through the precursor decomposition, the initial nucleus will grow into nanocrystals with an increasing size, until achieving an equilibrium state between the surface atoms on the nanocrystals and the free atoms in the solution.
Once the seed is formed, its size would increase by continuous addition of free atoms. From the perspective of chemical deposition, when atoms are added to a solid surface, the atoms diffuse on their surface until they encounter a step position where they can be incorporated. At the same time, as particle size increases, the volume free energy reduces (favorable for growth) and surface energy increases (favorable for dissolution). The dynamic interaction of growth and dissolution leads to the formation of anisotropic nanocrystal with specific morphology. With the development of in-situ electron microscopes, the structure and shape of seeds and nanocrystals produced at different stages could be observed. Therefore, a large number of studies have reported to explore the relationship between the initial seed and the final nanocrystal. After the nucleation and growth of the seed, the generated new nanocrystal will still go through complex evolution, such as Ostwald ripening, Kirkendall diffusion, oriented attachment, etc. Finally, nanoparticles with specific structure and morphology are obtained.
A typical synthesis method developed under the guidance of this theory is the hot injection method proposed by A. P. Alivisatos and Peng Xiaogang of the University of California [25]. Cold stock solution is quickly injected into the rapidly stirred, hot solvent, and a large number of crystal nuclei are instantaneously generated. The monomer concentration is rapidly reduced below the supersaturation threshold, and further nucleation is suppressed. This method separates the nucleation from growth, yielding particles of one size. It is a classic method for preparing monodisperse nanoparticles, especially quantum dots.
However, the theory is still an ideal model under extreme conditions, while the actual reactions and processes that occur in solution are far more complicated. Professor David W. Oxtoby of the University of Chicago, author of the famous Chemistry textbook “Principles of Modern Chemistry” in 1998 [26] stated that “Nucleation theory is one of the few areas of science in which agreement of predicted and measured rates to within several orders of magnitude is considered a major success” to comment the deficiencies of the classic nucleation growth theory.
For example, apart from decomposition to metal atoms, the precursors could also firstly assemble to aggregation and directly decompose to clusters. In the growth stage of the nucleus, the atomic adding mode is not the only growth way. The nucleus and nanocrystals can also directly merge into larger particles through attachment.
1.4.2 Multistep Transformation Mechanism with Amorphous Participation
In the traditional growth mechanism, the formation and growth of amorphous structures could not be explained, and a suitable new mechanism is desired. The rapid development of biomineralization research provides a theoretical basis for explaining the formation of amorphous materials in solution.
Biomineralization is a natural synthesis process, which use organic templates to control the growth of the inorganic phase. For example, amorphous calcium carbonate (ACC) have been particularly well studied as precursor in the biomineralization of invertebrates, such as mollusk shells and sea urchin spines (Figure 1.7). The high degree of crystallographic control is achieved from amorphous precursor in the biologically formed crystals. Scientists hope to be able to extrapolate the knowledge gained from such model systems and apply it to other inorganic systems to regulate crystallographic properties for advanced materials applications.
A large number of observations on biomineralization have found that the formation of many biomineral go through an amorphous precursor, which cannot be explained by the classical crystallization theory. Thus, the biomineralization pathway may be inconsistent with the traditional nucleation theory. Laurie B. Gower of the University of Florida and Helmut Cölfen of the University of Constance have proposed a multistep growth mechanism based on biomineralization for this problem.
Figure 1.7 Different organisms likely use the same strategy to generate diverse skeletal parts from crystals that arise from a transient amorphous calcium carbonate phase. Source: Reproduced with permission from Weiner et al. [27]. Copyright 2005, AAAS.
Gower pointed out [28] that the formation of solids in solution requires a multistep process, with multiple metastable states in it. The Ostwald–Lussac rule specifies that if a solution is supersaturated with respect to more than one phase, the more soluble (least stable) phase is often the first phase to form. Therefore, a highly unstable liquid precursor (polymer-induced liquid precursor) is formed first in the solution, and then it transform into an amorphous phase with unstable structure, followed by successively crystalline phases with decreasing
