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

When scientists study how radioactive nuclear waste locked inside glass slowly leaches into groundwater, they develop precise mathematical rules for how glass dissolves layer by layer over time. Meanwhile, pharmaceutical scientists have a completely different puzzle: how to make poorly water-soluble drugs actually dissolve in the gut by embedding them in a glassy polymer matrix — a technology called amorphous solid dispersions, or basically 'drug-in-a-polymer glass.' These two fields have almost nothing to do with each other on the surface. This hypothesis proposes that a mathematical equation originally built to describe nuclear waste glass dissolution — called Grambow Rate Law 2 — can also predict how drug-polymer glasses dissolve in the body. The key insight is that both systems involve the same physical competition: a protective layer forms on the surface (slowing dissolution) while something else erodes that layer away (speeding it up). In the drug world, that 'something else' is the polymer chains untangling and washing away, a process governed by the polymer's molecular weight. The hypothesis borrows a concept from polymer physics — how long chains reptate, or snake through each other like spaghetti — to predict the erosion rate. Depending on the polymer's molecular weight, the math predicts three totally different release behaviors: slow and decelerating, steady and constant, or fast and accelerating. The supporting data is striking: three versions of the same polymer (HPMCAS) at different molecular weights each show exactly the predicted dissolution behavior, and the erosion rates scale with molecular weight almost exactly as the borrowed physics equations would predict. A control polymer that doesn't follow reptation physics shows no such pattern — which is exactly what the theory would expect.

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