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The optimal design of nanoparticle synthesis protocols is often achieved via one-at-a-time experimental designs. Aside from covering a limited space for the possible input conditions, these methods neglect possible interaction between different combinations of input factors. This is where mechanistic models embracing various possibilities find importance. By performing global uncertainty/sensitivity analysis (UA/SA), one can map out the various outcomes of the process vs. different combinations of operating conditions. Moreover, UA/SA allows for the assessment of the model behavior, an inevitable step in the theoretical understanding of a process. Recently, we developed a coupled thermodynamic-kinetic framework in the form of population balance modelling in order to describe the precipitation of calcium-silicate-hydrate. Besides its relevance in the construction industry, this inorganic nanomaterial offers potential applications in biomedicine, environmental remediation, and catalysis most notably due to ample specific surface area that can be achieved by carefully tuning the synthesis conditions. Here, we apply a global UA/SA to an improved version of our computational model in order to understand the effect of variations in the model parameters and experimental conditions (induced by either uncertainty or tunability) on the properties of the product. With the specific surface area of particles as an example, we show that UA/SA identifies the factors whose control would allow a fine-tuning of the desired properties. This way, we can rationalize the proper synthesis protocol before any further attempt to optimize the experimental procedure. This approach is general and can be transferred to other nanoparticle synthesis schemes as well.

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, for example, 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., Comment: Main text and supplementary information (accompanying MATLAB codes available on the journal webpage)