# Evidence: lever rule

Parent: — · class: phase behaviour · names merged here: lever rule

4 papers measured or used it, 0 only mentioned it (of 207 kept papers). Papers in year order; each section heading ends with the paper's category / subcategory. Generated by tools/build_evidence.py from registry/concepts.csv and the cards; do not edit.

## 2022 Yang — Phase separation in surfactant-containing amorphous solid dispersions: Orthogonal analytical methods to probe the effects of surfactants on morphology and phase composition · Solid state stability / Physical stability

[2022-yang-surfactant-containing-rtv-pvpva-asd-phase-separation](../../../cards/2022-yang-surfactant-containing-rtv-pvpva-asd-phase-separation/paper.html) · Solid state stability / Physical stability · used · as: lever rule

| id | kind | content | locator |
|---|---|---|---|
| E1 | equation | lever rule: ratio of the amount of phase A to phase B equals the ratio of the length BX to AX | §5.3, p.13; Fig. 11, p.14 |
| C50 | claim, mechanism, authors: "could occur"; "would occur"; "likely" | In a schematic RTV-PVPVA-water ternary diagram, hydration paths from different DLs enter the two-phase region; path a crosses the vitrification line in the metastable region (nucleation and growth of a drug-rich phase), paths b and c in the unstable region (spinodal decomposition), path d gives nucleation of a polymer-rich phase; relative phase amounts set bicontinuous versus discrete morphology. [rests on: argument only; cited: Stropnik et al., 2000; Li et al., 2012] | §5.3, p.13; Fig. 11, p.14 |

## 2023 Deac — Dissolution Mechanisms of Amorphous Solid Dispersions: Role of Drug Load and Molecular Interactions · Dissolution / A. Release mechanism and LoC

[2023-deac-asd-drug-load-molecular-interactions-loc](../../../cards/2023-deac-asd-drug-load-molecular-interactions-loc/paper.html) · Dissolution / A. Release mechanism and LoC · used · as: lever rule

| id | kind | content | locator |
|---|---|---|---|
| E5 | equation | lever rule:  | p.730, p.731, p.733 |
| C34 | claim, mechanism, authors: asserted | By the lever rule, the majority phase after separation is the binode closer to the initial composition on its tie line: an ASD with polymer/drug ratio above the plait point gives a majority hydrophilic phase (discrete hydrophobic domains), one below gives a majority hydrophobic phase (continuous); near the plait point a small shift of the entry point changes the hydrophobic-phase volume strongly, far from it only weakly [rests on: argument only (Fig. 8)] | p.730-731 |
| C36 | claim, generalisation, authors: "approximately"; "is expected" | The hydrophobic-phase volume at initial separation versus drug load is approximately a step function with the step at the plait point, so significant or full continuity of the hydrophobic phase is expected near the plait point [rests on: argument only (Fig. 8d)] | p.731 |

## 2023 Yang — Drug Release from Surfactant-Containing Amorphous Solid Dispersions: Mechanism and Role of Surfactant in Release Enhancement · Dissolution / A. Release mechanism and LoC

[2023-yang-surfactant-containing-asd-release-enhancement](../../../cards/2023-yang-surfactant-containing-asd-release-enhancement/paper.html) · Dissolution / A. Release mechanism and LoC · used · as: lever rule

| id | kind | content | locator |
|---|---|---|---|
| E2 | equation | lever rule: (amount of drug-rich phase) / (amount of polymer/water-rich phase) = (length P1X1) / (length D1X1) | Discussion, p.2839; Fig. 15, p.2841 |
| C41 | claim, mechanism, authors: is expected | On a ternary diagram, a low-DL ASD entering the two-phase region below the vitrification line yields little drug-rich phase (lever rule), hence discrete domains; a high-DL ASD yields more drug-rich phase, a continuous morphology and, if mechanically strong enough, a growing barrier. [rests on: E2; cited: R25] | Discussion, p.2837–2840; Fig. 15a, p.2841 |

## 2024 Deac — Dissolution Mechanisms of Amorphous Solid Dispersions: Application of Ternary Phase Diagrams To Explain Release Behavior · Dissolution / A. Release mechanism and LoC

[2024-deac-asd-ternary-phase-diagrams-release](../../../cards/2024-deac-asd-ternary-phase-diagrams-release/paper.html) · Dissolution / A. Release mechanism and LoC · used · as: lever rule

| id | kind | content | locator |
|---|---|---|---|
| E12 | equation | lever rule: W^α = m^α/m^T = (W_i^T − W_i^β)/(W_i^α − W_i^β) | p.1914 |
| P20 | method | lever-rule phase fraction | p.1913-1914 |
| R35 | record, derived (E12, P20) | Wα at onset of water-induced phase separation versus DL — PC-SAFT diagrams, hydration path to spinodal, local equilibrium; (a) MePHPH-PVPVA, (b) PHPH-PVPVA — (a) Wα ≈0.02 at ≈5% DL rising to ≈0.15 at ≈27% DL; dry critical point (Wα 0.5) at ≈33% DL; ≈0.82 at ≈39.5% DL rising to ≈0.85 at ≈67% DL; no computed point between ≈27 and ≈39.5% DL other than the critical point. (b) ≈0.02 at ≈0.9% DL to ≈0.16 at ≈3.0% DL; critical point ≈3.7% DL; ≈0.82 at ≈4.5% DL, ≈0.80-0.86 up to ≈29% DL (all read from Fig. 16); overlaid micrographs: the persistent-morphology images of R18 (10-60% DL) and R19 (5-20% DL) | Fig. 16, p.1915 |
| C51 | claim, assumption, authors: asserted ("we will show later") | The persistent morphology near onset can be inferred by assuming phase inversion at Wα = 0.5 with the majority phase continuous (lever rule); small deviations from 0.5 do not significantly alter the predicted morphology versus DL [rests on: R35; cited: refs 48-51] | p.1914 |