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Is there no mathematical relationship between redox potential and particle size saying that an $X$ potential should yield a $Y$ particle size? Right now its general that large redox potential results in smaller particles, but I want to know if, for example, for silver particles I use $\ce{AgNO3}$ with glucose reducing agent and say the redox potential is $\pu{0.33V}$, what the ballpark for the particle size should be based on that potential (assuming $\mathrm{pH}$ does not change)?

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  • $\begingroup$ "Is there no mathematical relationship between redox potential and particle size saying that an X potential should yield a Y particle size?" Electrode potential is a thermodynamic property, it can only say "yes, this reduction or oxidation is favorable" but particle size is a kinetic property. I feel it is very difficult to relate the two. $\endgroup$
    – M. Farooq
    Jan 20 '20 at 5:12
  • $\begingroup$ I do see a relation between the size of the attained nanoparticles and their electrochemical potential, of course. Still the main parameter should be the amount of current flown to the cell. A parallel would be precipitation, where fast means small. In case of a chemical reduction like in your case I would think of small particles with high reducer conc, though thinking of concentration suffices in this context.That the redox properties of the final particles are dictated by size should be out of doubt, as I said above, but I am not sure it relates to the question. $\endgroup$
    – Alchimista
    Jan 20 '20 at 8:04
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Here is an example of a study of fish oil nanoemulsions which examines, to quote:

The influence of surfactant-to-oil-ratio on particle size and physical stability was evaluated.

Here is yet another study to quote:

Although the role of surfactant in the synthesis of particles in the nanometer range has frequently been documented...The surface coverage per surfactant molecule could be related to the surface tension of the latex, thus providing a relationship between particle size and stability.

And, another more expansive work to quote:

It was reported that the formation process of these NPs could be divided into three stages: growth, incubation and Oatwald ripening stages. The higher boiling point of 300 °C of paraffin affords a broader range of reaction temperature and makes it possible to effectively control the size of silver NPs by varying the heating temperature alone without changing the solvent. Moreover, the size of the colloidal silver NPs could be regulated not only by changing the heating temperature, or the ripening time, but also by adjusting the ratio of oleylamine to the silver precursor.

While chemical reduction methods are connected to reduction potential, the multi-stage aspect of the creation process for NPs suggests only a partial correlation, so not a 'mathematical relationship', but perhaps a statistical one.

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