Effect of reduction potential on particle size of chemically precipitated silver particles
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.