Nine accurate experimental data sets on amorphous calcium carbonate (ACC) formation in dilute solution were collected varying temperature and pH. The entire precipitation process is described using a complete thermodynamic-kinetic model. The thermodynamic model includes two new complex chemical interactions whereas the kinetic model is based on the discretized population balance approach. Saturation, primary particles size distribution, average secondary particles size, nucleation, and growth rates, as well as a number of additional parameters on the ACC precipitation reaction, are reported. The excellent agreement among experiments, calculated results, and literature data demonstrates that a complete thermodynamic-kinetic model can significantly contribute toward the understanding of a plausible pathway for precipitating systems. In this case study, the classical nucleation theory, which includes homogeneous nucleation, “true” secondary nucleation, and diffusion limited growth events, is able to completely describe the entire precipitation process. The calculated surface (γ) and cohesion (β) energies range from 28 to 35 and 30 to 42 mJ m–2, respectively, as a function of pH and temperature. Clusters or prenucleation entities act as spectators and are not directly involved in the solid formation pathway. The general methodological approach presented can be readily applied to other solid phase formation processes.

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An overarching computational framework unifying several optical theories to describe the temporal evolution of gold nanoparticles (GNPs) during a seeded growth process is presented. To achieve this, we used the inexpensive and widely available optical extinction spectroscopy, to obtain quantitative kinetic data. In situ spectra collected over a wide set of experimental conditions were regressed using the physical model, calculating light extinction by ensembles of GNPs during the growth process. This model provides temporal information on the size, shape, and concentration of the particles, and any electromagnetic interactions between them. Consequently, we were able to describe the mechanism of GNP growth and divide the process into distinct genesis periods. We provide explanations for several longstanding mysteries, e.g., the phenomena responsible for the purple-greyish hue during the early stages of GNP growth, the complex interactions between nucleation, growth and aggregation events, and a clear distinction between agglomeration and electromagnetic interactions. The presented theoretical formalism has been developed in a generic fashion so that it can readily be adapted to other nanoparticulate formation scenarios such as the genesis of various metal nanoparticles. KeywordsGold nanoparticles, seeded growth, UV-Vis spectroscopy, computational modeling, kinetics and mechanism.reason, there is a great need for a general and easily adaptable theoretical framework that utilizes the practical application of OES in the study of nanomaterial formation.So far, several investigations have addressed the mechanistic aspects during the (seeded) growth of GNPs using various characterization techniques such as atomic force microscopy (AFM), 5,14,18 electrophoretic measurements, 19,20 redox potential/pH measurements, 18-20 dynamic light scattering (DLS), 14,19,21 ex situ TEM, 4,5,7,14,[19][20][21][22][23] in situ TEM, 4,5 , and X-ray scattering. 6,7,13,23,24 Many of these studies follow the process also using ex situ 5,[19][20][21][22] or in situ 14,23,24 UV-vis spectroscopy but the information is treated merely qualitatively.From the plethora of research, some of which was summarized above, we know that the processes of seeded growth is typically accompanied by nucleation of new particles. 5,25 This could either be in a homogeneous fashion, 25 or in the close vicinity of the already present seed surface 5 (so called true catalytic secondary nucleation 26 or, equivalently, near surface nucleation followed by particle mediated growth 5 ). Additional complications arise from the possibility of agglomeration/aggregation invoked in many studies to describe the transient enhanced extinction in the wavelength range 600-800 nm, namely, the temporary purple-greyish colour of the suspension. 7,[18][19][20]27 Biggs et al. 18 and Chow and Zukoski 19 explained this in the light of the reduced colloidal stability in the presence of Au(III) in solution. Later, Rodriguez-Gonzalez and co-workers noticed that a homogeneous Au(III)→Au(I...