pith. sign in
def

isFragileGlass

definition
show as:
module
IndisputableMonolith.Chemistry.GlassTransition
domain
Chemistry
line
104 · github
papers citing
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plain-language theorem explainer

The definition classifies a glass as fragile when its fragility index m satisfies 100 ≤ m ≤ 200. Physical chemists modeling supercooled liquids cite this range to separate polymer-like fragile glasses from strong glasses such as SiO2. The classification is a direct definition that applies the upper bound fragilityMax set to 200.

Claim. A glass with fragility index $m$ is fragile when $100 ≤ m ≤ 200$.

background

The module sets glass transition within Recognition Science via 8-tick relaxation dynamics. Fragility quantifies the rapid rise in viscosity near Tg, with strong glasses (SiO2, GeO2) at low values and fragile glasses (o-terphenyl, polymers) at high values. The RS mechanism ties fragility to deviation from Arrhenius behavior through the eight-tick period and φ-scaling of relaxation time τ = τ₀ × φ^n.

proof idea

This is a direct definition that applies the conjunction 100 ≤ m ∧ m ≤ fragilityMax, where fragilityMax is the constant 200 supplied by the sibling declaration.

why it matters

The definition supports fragility classification inside the glass transition model, which predicts a universal Kauzmann ratio ≈ 2/3 and links fragility to molecular complexity. It rests on the eight-tick octave (T7) from the forcing chain and the φ-scaling of relaxation times. No downstream theorems are recorded.

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