# Evidence: entropy of mixing

Parent: — · class: thermodynamics · names merged here: entropy of mixing; mixing entropy

6 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.

## 2006 Marsac — Theoretical and Practical Approaches for Prediction of Drug–Polymer Miscibility and Solubility · Solid state stability / Miscibility and drug-polymer interactions

[2006-marsac-drug-polymer-miscibility-solubility](../../../cards/2006-marsac-drug-polymer-miscibility-solubility/paper.html) · Solid state stability / Miscibility and drug-polymer interactions · measured · as: entropy of mixing

| id | kind | content | locator |
|---|---|---|---|
| R1 | record, simulated (E1, χ = 0) | entropy of mixing versus volume fraction of polymer or monomer; ordinate labelled ΔS/RT, no scale — nifedipine with methyl pyrrolidone (a), PVP K12 (b), PVP K29/32 (c), PVP K90 (d); lattice site = nifedipine molecular volume (P6) — curve (a) has a far deeper minimum (near Φ ≈0.44) than (b) and (c-d) (minima near Φ ≈0.6); (b) lies slightly below (c-d); (c) and (d) coincide at every composition (caption: "virtually identical") (read from Fig. 1) | Fig. 1, p.2420; text p.2419 |
| C10 | claim, conclusion, authors: "It is clear" | The entropy of mixing for nifedipine with polymer is much less favourable than with methyl pyrrolidone, and the effect of PVP molecular weight grade is much less marked [rests on: R1] | p.2419 |
| C11 | claim, mechanism, authors: asserted | The small entropy of mixing with a polymer arises from the reduced configurational entropy of the polymer caused by the connectivity of its repeat units [rests on: R1; argument only] | p.2419 |
| C12 | claim, generalisation, authors: abstract: "should be relatively constant"; text: "is predicted to be relatively constant" | For typical APIs (MW 200-600) and typical polymers (MW 10,000-1,500,000) the entropy contribution to the free energy of mixing is relatively constant (abstract: always favourable and relatively constant for typical API–polymer systems) [rests on: R1] | p.2417, p.2419 |

## 2008 Marsac — Spontaneous Crystallinity Loss of Drugs in the Disordered Regions of Poly(Ethylene Oxide) in the Presence of Water · Solid state stability / PEG dispersions

[2008-marsac-peo-water-spontaneous-drug-crystallinity-loss](../../../cards/2008-marsac-peo-water-spontaneous-drug-crystallinity-loss/paper.html) · Solid state stability / PEG dispersions · used · as: entropy of mixing

| id | kind | content | locator |
|---|---|---|---|
| C14 | claim, conclusion, authors: PEG 400: "would suggest"; water: asserted | If mixing entropy is close to ideal, all drugs mix exothermically with PEG 400 (activity coefficients below 1) and endothermically with water (activity coefficients much greater than in PEG): acetaminophen of order 10¹, ketoprofen, naproxen and ibuprofen 10³-10⁴, felodipine and ketoconazole 10⁵ [rests on: R14] | p.3188 |
| C19 | claim, generalisation, authors: "might anticipate"; "it generally appears"; "remains elusive" | PEG 400 and PEO differ: end-group effects predict higher solubility of these relatively nonpolar drugs (except acetaminophen) in PEO than in PEG 400, entropy effects predict lower; relatively nonpolar drugs generally appear more soluble as PEG molecular weight increases [rests on: R18, R20, R21] | p.3189 |

## 2010 Rumondor — Effect of Polymer Hygroscopicity on the Phase Behavior of Amorphous Solid Dispersions in the Presence of Moisture · Solid state stability / Physical stability

[2010-rumondor-polymer-hygroscopicity-moisture-phase-separation-asd](../../../cards/2010-rumondor-polymer-hygroscopicity-moisture-phase-separation-asd/paper.html) · Solid state stability / Physical stability · used · as: entropy of mixing

| id | kind | content | locator |
|---|---|---|---|
| E1 | equation | Flory-Huggins free energy of mixing, ternary (water-drug-polymer): ΔG_mix/RT = n_W ln φ_W + n_D ln φ_D + n_P ln φ_P + n_W φ_D χ_WD + n_W φ_P χ_WP + n_D φ_P χ_DP | p.488 |
| C27 | claim, assumption, authors: "expected"; "Assuming" | Complete miscibility is expected where ΔGmix is negative with a single minimum versus composition; assuming a new component favours mixing entropy, amorphous-amorphous separation is expected only when ΔHmix is positive enough to counteract it; ΔHmix is set by χDP, χWD and χWP and can be negative or positive [rests on: cited: ref 32; E1] | p.488 |
| C39 | claim, generalisation, authors: abstract: "It is concluded"; conclusions: "It is suggested" | The balance between the enthalpy and entropy of mixing in the ternary water-drug-polymer system is the important factor deciding which dispersions are susceptible to moisture-induced demixing [rests on: argument only; E1] | p.477, p.490 |

## 2015 Purohit — Miscibility of Itraconazole-Hydroxypropyl Methylcellulose Blends- Insights with High Resolution Analytical Methodologies · Solid state stability / Miscibility and drug-polymer interactions

[2015-purohit-itraconazole-hpmc-miscibility-high-resolution-methods](../../../cards/2015-purohit-itraconazole-hpmc-miscibility-high-resolution-methods/paper.html) · Solid state stability / Miscibility and drug-polymer interactions · used · as: entropy of mixing

| id | kind | content | locator |
|---|---|---|---|
| E1 | equation | Flory-Huggins free energy of mixing: ΔG_mix/(RT) = n_D ln φ_D + n_P ln φ_P + n_D φ_P χ | p.15 |
| C41 | claim, prior hypothesis, authors: asserted | In Flory-Huggins theory the first two terms (entropy) always favour mixing and the third (χ) term carries the non-ideal, enthalpic part; negative χ means adhesive drug-polymer interactions stronger than cohesive ones, positive χ means mixing needs enough entropy to overcome unfavourable enthalpy [rests on: cited: refs 75-77; E1] | p.15-16 |
| C42 | claim, mechanism, authors: "likely" | HPMC substitution reduces the hydroxyl donors available to ITZ's carbonyl acceptor and ITZ has no donor groups, so any ITZ-HPMC miscibility is likely entropy-driven with little contribution from favourable interactions [rests on: argument only (Fig. 1 structures); M1, M2; cited: ref 20] | p.16 |
| C47 | claim, mechanism, authors: "An alternative explanation"; "very likely trap" | Alternatively ITZ and HPMC have limited miscibility at room temperature that increases with temperature (UCST behaviour): near the drug melting point mixing is favoured by entropy and mobility, and on cooling the glassy blend is trapped in a miscible state [rests on: argument only; cited: ref 77] | p.17 |

## 2024 Shah — Orthogonal Analytical Methods to Elucidate How Low Levels of Residual Crystallinity in Posaconazole Amorphous Solid Dispersions Impact Phase Behavior during Release · ASD process / ASD process

[2024-shah-posaconazole-asd-residual-crystallinity-release-phase-behavior](../../../cards/2024-shah-posaconazole-asd-residual-crystallinity-release-phase-behavior/paper.html) · ASD process / ASD process · used · as: mixing entropy

| id | kind | content | locator |
|---|---|---|---|
| C16 | claim, conclusion, authors: results: asserted ("signifies"); discussion: "suggests" | χ = 0.43 signifies weak PCZ-HPMCAS interactions and gives only a minor melting point depression (results); the positive χ suggests moderately unfavourable interactions, with a small depression driven by favourable mixing entropy, smaller than in systems with negative χ (discussion) [rests on: R1, R4, R5, R23] | p.444, p.450 |

## 2026 Alkalla — Coadministration of a crystalline drug compromises supersaturation and membrane transport of an amorphous drug · Bioperformance / Bioperformance

[2026-alkalla-crystalline-darunavir-compromises-amorphous-atazanavir-supersaturation-transport](../../../cards/2026-alkalla-crystalline-darunavir-compromises-amorphous-atazanavir-supersaturation-transport/paper.html) · Bioperformance / Bioperformance · used · as: entropy of mixing

| id | kind | content | locator |
|---|---|---|---|
| C40 | claim, mechanism, authors: "likely" | The water-promoted miscibility of the drugs in the colloidal phase likely comes from a larger entropy contribution when three components (atazanavir, darunavir, water) are present [rests on: argument only] | p.9 |