Abstract

Aqueous precipitation of transition metal oxides often proceeds through non-equilibrium phases, whose appearance cannot be anticipated from traditional phase diagrams. Without a precise understanding of which metastable phases form, or their lifetimes, targeted synthesis of specific metal oxides can become a trial-and-error process. Here, we construct a theoretical framework to reveal the nanoscale and metastable energy landscapes of Pourbaix (E-pH) diagrams, providing quantitative insights into the size–dependent thermodynamics of metastable oxide nucleation and growth in water. By combining this framework with classical nucleation theory, we interrogate how solution conditions influence the multistage oxidation pathways of manganese oxides. We calculate that even within the same stability region of a Pourbaix diagram, subtle variations in pH and redox potential can redirect a non-equilibrium crystallization pathway through different metastable intermediates. Our theoretical framework offers a predictive platform to navigate through the thermodynamic and kinetic energy landscape towards the rational synthesis of target materials.

Highlights

  • Aqueous precipitation of transition metal oxides often proceeds through non-equilibrium phases, whose appearance cannot be anticipated from traditional phase diagrams

  • Adding a free-energy axis for Pourbaix diagrams can facilitate the evaluation of thermodynamic driving forces between precursors and crystallization products[32], for example, when a Mn2+(aq) precursor is under E-pH conditions where it is metastable with respect to the nucleation of solid MnO2

  • Because these are the natural variables of the Pourbaix diagram, we refer to this thermodynamic grand potential as the Pourbaix potential

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Summary

Introduction

Aqueous precipitation of transition metal oxides often proceeds through non-equilibrium phases, whose appearance cannot be anticipated from traditional phase diagrams. We construct a theoretical framework to reveal the nanoscale and metastable energy landscapes of Pourbaix (EpH) diagrams, providing quantitative insights into the size–dependent thermodynamics of metastable oxide nucleation and growth in water By combining this framework with classical nucleation theory, we interrogate how solution conditions influence the multistage oxidation pathways of manganese oxides. Precipitation of manganese oxides often proceeds by Ostwald’s ‘Rule of Stages’[14], where a variety of metastable manganese oxides and oxyhydroxides nucleate and grow prior to the formation of the equilibrium phase[15,16] These non-equilibrium crystallization pathways can occur both with[17,18], and without[19] impurity ions in solution. Understanding how solution chemistry influences structure-selection along a nonequilibrium crystallization pathway would enable the rational design of aqueous synthesis routes; either towards desirable metastable phases, or away from long-lived metastable byproducts and towards the synthesis of a desired equilibrium phase[21,22]

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