LaMer's 1950 Model for Particle Formation of Instantaneous Nucleation and Diffusion-Controlled Growth: A Historical Look at the Model's Origins, Assumptions, Equations, and Underlying Sulfur Sol Formation Kinetics Data

Abstract

A look back at LaMer's 1950 model of particle formation is undertaken (LaMer, V. K.; Dinegar, R. H. Theory, Production and Mechanism of Formation of Monodispersed Hydrosols. J. Am. Chem. Soc. 1950, 72, 4847-4854), a highly cited paper that has more than 1953 citations as of March 2019. The nonmathematical, verbal version of LaMer's model, namely, the concepts of "instantaneous" (or "burst") nucleation and "diffusion-controlled" growth, continues to be heavily cited because, until recently, it was the only known way to try to explain how narrow particle-size distributions might form from self-assembly syntheses. The following specific topics are addressed in separate sections: (i) the chemical origins of the LaMer model, (ii) the original sulfur hydrosol formation system, (iii) the often-cited schematic and then associated words-only descriptions of the LaMer model, (iv) the nine assumptions underlying the LaMer equation and quantitative model, (v) the question of whether LaMer's model is actually primarily a "growth model" if one notes that "instantaneous nucleation" is an initial assumption made for mathematical purposes, and (vi) the actual LaMer equation (and the question of when it has been used to fit particle formation kinetics data). Additional topics discussed are (vii) the disconnect between LaMer's quantitative model and associated differential equation vs any testing against experimental kinetics data, (viii) a look at the kinetics data for, and the current understanding of, the mechanism of sulfur sol formation, (ix) the 1926, first kinetics data for sulfur sol formation, (x) light scattering data for sulfur sol formation, (xi) fitting of the 1926 kinetics data for sulfur sol formation by a minimalistic two-step mechanism, and (xii) the interesting effect of microfiltration and the removal of dust on the size distribution of sulfur sols. Also provided is (xiii) a summary and conclusions section.