A note on the nucleation with multiple steps: Parallel and series nucleation

TL;DR

This paper explores complex nucleation processes involving multiple steps, demonstrating that nucleation rates in parallel and series configurations follow formulas analogous to electrical circuits, and provides methods to calculate these rates.

Contribution

It introduces formulas for calculating nucleation rates in systems with multiple saddle points and extends the analogy to electrical circuits for complex nucleation processes.

Findings

Nucleation rates follow resistor-like formulas in parallel and series configurations.

Formulas for individual and total nucleation rates are summarized.

Extension to more complex nucleation processes is proposed.

Abstract

Parallel and series nucleation are the basic elements of the complex nucleation process when two saddle points exist on the free-energy landscape. It is pointed out that the nucleation rates follow formulas similar to those of parallel and series connection of resistors or conductors in an electric circuit. Necessary formulas to calculate individual nucleation rates at the saddle points and the total nucleation rate are summarized and the extension to the more complex nucleation process is suggested.