Conceptual Approaches for Scaling from Molecular to Macroscopic Levels of Nucleation and Precipitation
The Problem Precipitation may be viewed as two sub-processes, nucleation and crystal growth. Both are path-dependent, and affect precipitation rate. Nucleation, in particular, is poorly understood. At low temperatures, aqueous nucleation can be extremely slow, placing practical limitations on the observation time-scale. Heterogeneous nucleation reduces the time-scale, but added complexities arise such as identification of the type and number of active surface sites. A third problem relates to spatial scales. The earliest formed solid phases are nanometer-sized. Their characterization becomes problematic, because most spectroscopic methods yield atomic level information (Å scale), while traditional microscopic methods work, of course, in the micron size-range. Furthermore, reaction mechanisms are chemically complex. The earli- est precipitated phases are often not thermodynamically the most stable (Ostwald Rule of Stages). Worse, thermodynamic stability, itself, is a function of particle size. Precursor phases transform to the most stable form over time. The sequence of aqueous oligomers and solid precursors determines the reaction pathway and, thus, the rate of nucleation and crystal growth. Minor amounts of other dissolved species can also significantly affect the pathway. Finally, even if the chemical complexity is fully appreciated and understood, it is difficult to incorporate the information into a useful form such as a reactive flow model. 1.3 The Approach A two-pronged tack is presented here for further discussion and debate. First, I link results of molecular orbital (MO) calculations of energy and vibrational frequencies, for heteroge- nous apatite nucleation, to vibrational spectroscopy results. I then suggest links between mo- lecular modeling approaches and microscopy methods. Finally, I review phenomenological models (PM) to nucleation. Values of PM parameters estimated by molecular modeling and spectroscopy/microscopy, can ultimately be incorporated into reactive flow models.