科研之友
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摘要
A simple methodology is employed to demonstrate the manifestation of energy quantization in classical, steady-state nucleation of small, geometrically precise clusters. With the use of recent dispersive kinetic theory outcomes, fresh insights into nonsteady-state nucleation-and-growth processes are also put forth. The impetus for this work stems from the fact that classical nucleation theory (CNT), which is often a poor predictor of nucleation rates, relies on macroscopic, continuous material properties to describe the physicochemical characteristics of the critical nucleus that, in turn, determines the activation energy barrier for nucleation; those quantities are not physically relevant on the atomic/nanometer scale. While it is shown that the low apparent interfacial tension of the smallest critical clusters likely gives rise to a very diffuse interface, their crystalline core provides a natural high-energy (metastable) state useful in determining the activation energy. For simplicity, it is assumed that the critical nuclei are two-dimensional, (2D) hexagonal close packed (hcp) structures without defects and that they can be adequately represented by an ensemble of simple harmonic oscillators (SHOs). As a first approximation, different energies are assigned to three distinct daises of monomers/SHOs present in each 2D hcp nucleus, based on their spatial location within the cluster. The energy of formation for each cluster size, at a fixed chemical potential, is then determined by summing together the energy contributions from all of the SHOs contained therein; the (steady-state) activation energy can then be determined from the maximum in the resulting energy profile. Consistency of the approach with CNT outcomes is demonstrated for larger (similar to micrometer-sized), spherical clusters by bridging to traditional, macroscopic properties (surface area, volume, and interfacial tension). Furthermore, it is discussed that while the initial critical nucleus formation at the outset of nonsteady-state (dispersive kinetic) nucleation-and-growth conversions can be a rare. event, as the cluster grows into thermodynamic stability, it acquires interfacial tension that serves both to keep it from, dissociating and to facilitate its continued growth by attracting additional monomers to its surface. At the same time, larger clusters exhibit a stronger monomer attraction that gives rise to,acceleration in both the mean duster growth rate and the rate of the overall phase transformation. Simultaneously, the system supersaturation, which provides the driving force behind (the initiation of) nucleation, decreases over the course of the conversion. Thus, an apparent paradox of nucleation-and-growth rate-limited conversions is that while the formation of the smallest critical clusters is most difficult (because they have the highest activation energy), they are formed first, while the larger nuclei that have lower activation energies of formation are produced later during the conversion and at a lower supersaturation. The explanation lies in the fact that the larger critical clusters that form at later times are predominantly, the growth products of the earlier formed, smallest critical nuclei that survived denucleation, hence the terminology "nucleation-and-growth" for this mechanism.
- 出版日期2013-5
