Grambow Rate Law 2 Predicts Competitive Passivation-Erosion Kinetics and Regime Switching in ASD Dissolution

Two seemingly unrelated fields turn out to share a surprisingly deep connection. Geochemists have spent decades developing precise mathematical laws to describe how volcanic glass and nuclear waste glass slowly dissolve in water — work that matters for understanding ocean chemistry and safely storing radioactive materials. Meanwhile, pharmaceutical scientists struggle with a persistent problem: many promising drug compounds barely dissolve in the gut, making them hard for the body to absorb. A clever engineering trick called 'amorphous solid dispersion' (ASD) — essentially trapping the drug in a glassy polymer matrix to keep it in a more dissolve-able form — helps, but predicting *how fast* the drug releases remains surprisingly difficult. This hypothesis proposes borrowing a rate equation originally developed for volcanic glass dissolution — rooted in a branch of chemistry called Transition State Theory — and applying it to predict how ASD drugs dissolve. The key insight is that at the molecular level, both systems involve breaking apart a network of chemical bonds at a solid surface exposed to water. In volcanic glass, silicon-oxygen bonds hydrolyze; in an ASD, the drug molecules are held in a polymer web by hydrogen bonds that water must disrupt. The hypothesis also introduces a practical rule of thumb — a 'Damköhler number' — that tells formulators when the volcanic-glass-style equation applies (low drug loading, below ~20%) versus when simpler diffusion-based models suffice (high drug loading, above ~30%). The cool part is that this isn't just a poetic analogy — the numbers actually line up. The activation energies estimated for drug-polymer bond disruption (65–85 kJ/mol at low loading) fall in the same ballpark as silicon-oxygen hydrolysis energies from geochemistry, suggesting the underlying physics genuinely rhymes across these very different materials.

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