Simplified model describes higher order clustering

CMI researchers at Idaho National Laboratory conducted the activity for this highlight

Innovation
Expanded the stepwise hydration solution model from simple 1:1 salts (e.g., NaCl) to more complex 2:2 (e.g., MnSO₄) and 3:2 salts (e.g., Nd₂(SO₄)₃), with direct relevance to critical material production.

Achievements

Developed an equilibrium cluster model that separates solute concentration function (e.g. reaction order) from final cluster size, making calculations more straightforward.
Demonstrated that Debye–Hückel long-range interactions and mass action ion pairing, though mechanistically different, are mathematically similar.

Significance and Impact
Advancing mechanistic models of solutions at high concentration/saturated conditions will facilitate development of approaches for crystallization and precipitation (e.g., dimethyl ether fractional crystallization) as well as other separations.

Hub Target Addressed

Minimizing hazardous chemical use and waste generation
Efficient co-recovery of materials

Aaron D. Wilson, Mouad Arrad, Anthony S. Wexler, "Step-wise Hydration: Comparison of Debye-Hückel Long-Range interactions and ion pairing," Journal of Molecular Liquids (2025) 127805. https://doi.org/10.1016/j.molliq.2025.127805.

two sets of data plots represent modeled ion speciation for MnSO₄, shown as (A) free ion concentration relative to total ion concentration and (B) total unnormalized clustered species relative to total ion concentration. In panel (B) the mathematically simple and flexible uncoupled (4,2) expression models similarly to the mathematically complex and rigid tetramer (4,4) expression. — Modeled ion speciation for MnSO₄, shown as (A) free ion concentration relative to total ion concentration and (B) total unnormalized clustered species relative to total ion concentration. In panel (B) the mathematically simple and flexible uncoupled (4,2) expression models similarly to the mathematically complex and rigid tetramer (4,4) expression.