# Evidence: Flory-Huggins theory

Parent: — · class: thermodynamics · names merged here: Flory-Huggins free energy of mixing; Flory-Huggins lattice theory; Flory-Huggins theory; Flory-Huggins theory of mixing

14 papers measured or used it, 1 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 Konno — Influence of Different Polymers on the Crystallization Tendency of Molecularly Dispersed Amorphous Felodipine · Solid state stability / Physical stability

[2006-konno-felodipine-polymer-crystallization-nucleation-solid-dispersions](../../../cards/2006-konno-felodipine-polymer-crystallization-nucleation-solid-dispersions/paper.html) · Solid state stability / Physical stability · used · as: Flory-Huggins theory

| id | kind | content | locator |
|---|---|---|---|
| E9 | equation | Flory-Huggins activity of the small molecule: ln a = ln Φ1 + (1 − 1/x12)·Φ2 + χ·Φ2² | p.2702 |
| C35 | claim, mechanism, authors: "would only predict"; "probably" | Flory-Huggins theory with data for comparable systems [R20] predicts little lowering of drug activity at the polymer levels used, so ΔGv is not significantly reduced and probably cannot explain the lower nucleation rate [rests on: R20; E9] | p.2703 |
| R20 | record, cited | Flory-Huggins activity lowering in comparable polymer systems — PVP with sucrose or water (refs 42, 43) — significant lowering of small-molecule activity predicted only when polymer volume fraction approaches a value greater than 0.5 | p.2703 |

## 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 · used · as: Flory-Huggins lattice theory

| id | kind | content | locator |
|---|---|---|---|
| E1 | equation | Flory–Huggins free energy of mixing: ΔG_M/RT = n_drug ln Φ_drug + n_polymer ln Φ_polymer + n_drug Φ_polymer χ | p.2419 |
| E3 | equation | melting point depression (Flory–Huggins, crystalline drug in amorphous polymer): 1/T_M^mix − 1/T_M^pure = (−R/ΔHfus)[ln Φ_drug + (1 − 1/m)Φ_polymer + χΦ_polymer²] | p.2421 |
| E6 | equation | Flory–Huggins activity coefficient of the drug: ln γ_drug = ln(Φ_drug/x_drug) + (1 − 1/m)Φ_polymer + χΦ_polymer² | p.2423-2424 |
| P6 | method | Flory–Huggins lattice modelling | p.2418-2420 |
| C8 | claim, prior hypothesis, authors: "still considered" | Flory–Huggins theory has documented limitations and more advanced models exist, but it is still an excellent starting point for polymer thermodynamics [rests on: cited: refs 18-22] | p.2419 |
| C9 | claim, assumption, authors: "If the amorphous drug is considered to behave similarly to a solvent" | If the amorphous drug behaves similarly to a solvent, Flory–Huggins theory applies to API–polymer systems; the lattice volume is set equal to the drug molecular volume [rests on: argument only] | p.2418, p.2419 |

## 2006 Marsac — A Comparison of the Physical Stability of Amorphous Felodipine and Nifedipine Systems · Solid state stability / Physical stability

[2006-marsac-physical-stability-amorphous-felodipine-nifedipine](../../../cards/2006-marsac-physical-stability-amorphous-felodipine-nifedipine/paper.html) · Solid state stability / Physical stability · used · as: Flory-Huggins lattice theory

| id | kind | content | locator |
|---|---|---|---|
| E10 | equation | Flory-Huggins activity of the solvent (drug): ln a_drug = ln Φ_drug + (1 − 1/m) Φ_PVP + χ Φ_PVP² | p.2314 |
| R19 | record, simulated (E10) | drug activity versus PVP volume fraction — Flory-Huggins with χ of R18 (P11) — sub-table below; nifedipine (solid) and felodipine (dashed) curves almost overlap; text: predicted activity reduction very similar for both drugs and small for the PVP range of the study | Fig. 13, p.2314 |
| C46 | claim, assumption, authors: "can provide a basis for comparison" | Flory-Huggins lattice theory, with the amorphous drug treated as the solvent, can approximate the drug activity versus polymer concentration and give a basis for comparing the two drugs, despite its known limitations and the non-equilibrium state of the glasses [rests on: cited: refs 19, 48] | p.2314 |

## 2009 Marsac — Estimation of Drug–Polymer Miscibility and Solubility in Amorphous Solid Dispersions Using Experimentally Determined Interaction Parameters · Solid state stability / Miscibility and drug-polymer interactions

[2009-marsac-drug-polymer-miscibility-solubility-asd-interaction-parameters](../../../cards/2009-marsac-drug-polymer-miscibility-solubility-asd-interaction-parameters/paper.html) · Solid state stability / Miscibility and drug-polymer interactions · used · as: Flory-Huggins lattice theory

| id | kind | content | locator |
|---|---|---|---|
| E2 | equation | Flory–Huggins melting point depression: (1/T_M^mix − 1/T_M^pure) = (−R/ΔH_fus)(MV_drug/MV_lattice)[(ln Φ_drug)/m_drug + (1/m_drug − 1/m_polymer)Φ_polymer + χΦ_polymer²] | p.142 |
| E8 | equation | Flory–Huggins scaling of an activity coefficient from a liquid analogue to the polymer: ln γ_drug^PVP = (MV_drug/MV_lattice)[(1/m_drug) ln(Φ_drug/x_drug) + (1/m_drug − 1/m_PVP)Φ_PVP] + ln γ_drug^EP | p.143 |
| E10 | equation | Flory–Huggins free energy of mixing: ΔG/RT = (Φ_drug/m_drug) ln Φ_drug + (Φ_polymer/m_polymer) ln Φ_polymer + χΦ_drug Φ_polymer | p.146 |
| C25 | claim, prior hypothesis, authors: asserted | Amorphous molecular level dispersions are ideally single-phase, needing thermodynamic miscibility during processing and ideally at storage; Flory–Huggins theory is a useful tool because it accounts for the large size difference of drug and polymer [rests on: cited: refs 39, 54, 57] | p.145-146 |

## 2009 Rumondor — Phase Behavior of Poly(vinylpyrrolidone) Containing Amorphous Solid Dispersions in the Presence of Moisture · Solid state stability / Physical stability

[2009-rumondor-pvp-asd-moisture-induced-immiscibility](../../../cards/2009-rumondor-pvp-asd-moisture-induced-immiscibility/paper.html) · Solid state stability / Physical stability · used · as: Flory-Huggins theory of mixing

| id | kind | content | locator |
|---|---|---|---|
| E4 | 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.1503 |
| C42 | claim, mechanism, authors: asserted ("must therefore") | Water uptake forms a one-phase ternary system; the entropy of mixing is favourable, so phase separation in the ternary system must be caused by a positive ΔHmix (eq 4) [rests on: E4] | p.1503 |
| C43 | claim, mechanism, authors: "is expected" | Complete miscibility is expected when ΔHmix is negative or not substantially positive owing to the balance of W-D, W-P and D-P interactions, giving a negative ΔGmix and a single minimum of ΔGmix versus composition [rests on: E4] | p.1504 |

## 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: Flory-Huggins theory

| 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 |
| C26 | claim, assumption, authors: "can be used to help qualitatively understand" | The ternary Flory-Huggins model (E1) can help understand qualitatively how the thermodynamics change when water is absorbed; its first three terms are the combinatorial entropy of mixing, the last three the enthalpy of mixing [rests on: E1] | 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 |

## 2011 Baird — Evaluation and modeling of the eutectic composition of various drug-polyethylene glycol solid dispersions · Solid state stability / PEG dispersions

[2011-baird-drug-peg-eutectic-composition-modeling-solid-dispersions](../../../cards/2011-baird-drug-peg-eutectic-composition-modeling-solid-dispersions/paper.html) · Solid state stability / PEG dispersions · used · as: Flory-Huggins lattice theory

| id | kind | content | locator |
|---|---|---|---|
| E1 | equation | Flory–Huggins melting point depression, drug liquidus (Lacoulonche model): T_liquidus = (ΔH_fus,d + ΔW_d,p (1 − φ_d)²) / (ΔH_fus,d / T_melt,d − R [ln(φ_d) + (1 − φ_d)(1 − V_mol,d / V_mol,p)]) | p.203 |
| E2 | equation | Flory–Huggins melting point depression, polymer liquidus (Lacoulonche model): T_liquidus = (ΔH_fus,p + ΔW_d,p (φ_d)²) / (ΔH_fus,p / T_melt,p − R [ln(1 − φ_d) + (φ_d)(1 − V_mol,p / V_mol,d)]) | p.203 |
| C5 | claim, prior hypothesis, authors: "still debatable"; "potentially" | The Lacoulonche model applies Flory–Huggins lattice theory to drug-PEG eutectics (flurbiprofen-PEG 6000) and has been evaluated for flurbiprofen and other organic compounds in PEG; which drug or polymer properties cause its inaccuracies is still debatable; both physical properties and specific-interaction strength potentially affect the predicted eutectic [rests on: cited: refs 25-27] | p.202 |
| C26 | claim, assumption, authors: asserted | Mixing theories that assume components of similar volume do not suit polymer-small molecule mixtures; Flory–Huggins theory treats the polymer as segments the size of a solvent molecule, and χdp > 0, = 0 and < 0 mean endothermic, athermal and exothermic mixing [rests on: cited: refs 33-35] | p.208 |

## 2012 Eerdenbrugh — Molecular Weight Effects on the Miscibility Behavior of Dextran and Maltodextrin with Poly(vinylpyrrolidone) · Solid state stability / Miscibility and drug-polymer interactions

[2012-van-eerdenbrugh-dextran-maltodextrin-pvp-molecular-weight-miscibility](../../../cards/2012-van-eerdenbrugh-dextran-maltodextrin-pvp-molecular-weight-miscibility/paper.html) · Solid state stability / Miscibility and drug-polymer interactions · used · as: Flory-Huggins theory

| id | kind | content | locator |
|---|---|---|---|
| E4 | equation | Flory-Huggins enthalpy of mixing per lattice site: ΔH_mix = kTχφ1φ2 | p.2762 |
| E5 | equation | Flory-Huggins combinatorial entropy of mixing per lattice site: −TΔS_mix = kT[(φ1/N1) ln φ1 + (φ2/N2) ln φ2] | p.2762-2763 |
| C31 | claim, assumption, authors: "serves as a good starting point"; "we anticipate" | The Flory-Huggins equation is a good starting point to rationalise MW effects despite its limitations, and the combinatorial entropy is expected to vary widely among the 20 combinations [rests on: cited: refs 35-37; E5] | p.2762 |

## 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: Flory-Huggins theory

| 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 |

## 2017 Tian — Impact of Polymers on the Melt Crystal Growth Rate of Indomethacin Polymorphs · Solid state stability / Physical stability

[2017-tian-polymers-melt-crystal-growth-indomethacin-polymorphs](../../../cards/2017-tian-polymers-melt-crystal-growth-indomethacin-polymorphs/paper.html) · Solid state stability / Physical stability · used · as: Flory-Huggins free energy of mixing

| id | kind | content | locator |
|---|---|---|---|
| E2 | equation | Flory-Huggins free energy of mixing: ΔG_mix = RT[Φ ln Φ + ((1 − Φ)/m) ln(1 − Φ) + χΦ(1 − Φ)] | Eq. 2, p.17 |
| C30 | claim, mechanism, authors: "is also expected"; "would have" | Adding polymer is expected to change the thermodynamic driving force for growth through the free energy of mixing (Eq. 2); systems with stronger drug-polymer interactions would have lower free energy and hence a smaller driving force for crystal growth [rests on: cited: ref 42; argument only] | p.17 |

## 2018 Li — Tailoring supersaturation from amorphous solid dispersions · Dissolution / B. Supersaturation from ASD dissolution

[2018-li-tailoring-supersaturation-lopinavir-insoluble-polymer-asd](../../../cards/2018-li-tailoring-supersaturation-lopinavir-insoluble-polymer-asd/paper.html) · Dissolution / B. Supersaturation from ASD dissolution · used · as: Flory-Huggins theory

| id | kind | content | locator |
|---|---|---|---|
| E4 | equation | Flory-Huggins drug chemical potential: Δμ_drug/RT = ln Φ_drug + (1 − 1/r) Φ_poly + χ Φ_poly² | p.122 |
| C43 | claim, prior hypothesis, authors: asserted | Mixing with a polymer lowers the drug chemical potential relative to the pure amorphous phase; Flory-Huggins theory models this, and the Huang model combines FH for the polymer with the Gibbs-Duhem equation for absorbed water for a drug molecularly mixed with a poorly soluble polymer [rests on: E3-E6; cited: refs 30, 44, 45] | p.120-122 |
| C44 | claim, generalisation, authors: "it is clear"; "it is apparent" | From FH, low DL and a more negative χ reduce drug solubility relative to the pure amorphous form; from GD, more water absorbed by the ASD lowers drug chemical potential and solubility, more so with favourable drug-water interactions [rests on: E4, E5, E6] | p.122 |

## 2018 Moseson — The application of temperature-composition phase diagrams for hot melt extrusion processing of amorphous solid dispersions to prevent residual crystallinity · ASD process / ASD process

[2018-moseson-temperature-composition-phase-diagrams-hme-asd-residual-crystallinity](../../../cards/2018-moseson-temperature-composition-phase-diagrams-hme-asd-residual-crystallinity/paper.html) · ASD process / ASD process · used · as: Flory-Huggins theory

| id | kind | content | locator |
|---|---|---|---|
| E1 | equation | Flory-Huggins free energy of mixing: ΔG = RT[φ ln φ + ((1 − φ)/m) ln(1 − φ) + χφ(1 − φ)] | p.7 |
| E2 | equation | Flory-Huggins melting point depression: 1/Tc − 1/Tm = −(R/ΔH)[ln φ + (1 − 1/m)(1 − φ) + χ(1 − φ)²] | p.8 |
| C8 | claim, prior hypothesis, authors: asserted | Miscible drug-polymer systems show melting point depression because exothermic mixing plus favourable mixing entropy lowers the drug's chemical potential; immiscible systems show none [rests on: cited: refs 41, 42] | p.7-8 |
| C9 | claim, prior hypothesis, authors: asserted; "can display" | A negative χ indicates a favourable enthalpy of mixing and adds melting point depression beyond that from combinatorial entropy; χ can depend on temperature, chain length and composition [rests on: cited: refs 3, 78] | p.8 |

## 2020 Li — Water-induced phase separation of spray dried amorphous solid dispersions · ASD process / ASD process

[2020-li-water-induced-phase-separation-spray-dried-asd-ritonavir-pvpva](../../../cards/2020-li-water-induced-phase-separation-spray-dried-asd-ritonavir-pvpva/paper.html) · ASD process / ASD process · used · as: Flory-Huggins theory

| id | kind | content | locator |
|---|---|---|---|
| E11 | equation | multicomponent Flory-Huggins free energy of mixing: ΔG_mix = RT Σ_{i=1}^{n} (φ_i/N) ln φ_i Σ_{i=1}^{K−1} Σ_{j=i+1}^{K} χ_ij φ_i φ_j (Eq. 12, printed without an operator between the two sums) | SI p.6; named p.13 |
| E12 | equation | Flory-Huggins sorption isotherm (binary): ln(a_1,g) = ln φ_1 + φ_2 (1 − v_1/v_2) + χ_12 φ_2² (SI footnote 3) | SI p.6 |
| P12 | method | four-component Flory-Huggins phase model | p.13, p.27, p.31; SI p.6 |

## 2021 Ueda — Effect of Polymer Species on Maximum Aqueous Phase Supersaturation Revealed by Quantitative Nuclear Magnetic Resonance Spectroscopy · Dissolution / C. Amorphous solubility and LLPS

[2021-ueda-polymer-species-maximum-aqueous-supersaturation-nmr](../../../cards/2021-ueda-polymer-species-maximum-aqueous-supersaturation-nmr/paper.html) · Dissolution / C. Amorphous solubility and LLPS · used · as: Flory-Huggins theory

| id | kind | content | locator |
|---|---|---|---|
| E4 | equation | Flory-Huggins amorphous solubility with polymer, ideal (athermal) mixing: S_a,IBP = S^0_a,IBP · Φ_IBP · exp((1 − 1/x) · Φ_polymer) | p.1352 |
| E5 | equation | Flory-Huggins amorphous solubility with polymer and interaction parameter: S_a,IBP = S^0_a,IBP · Φ_IBP · exp((1 − 1/x) · Φ_polymer + χ · Φ_polymer^2) | p.1352 |
| R12 | record, derived (E4) | calculated Sa,IBP versus polymer weight ratio, ideal Flory-Huggins mixing — PVP-VA and HPMC 603 (P8) — both curves fall from ≈154 µg/mL at ratio 0 to ≈129 (PVP-VA) and ≈127 µg/mL (HPMC 603) at ratio 1.0 and to ≈93 and ≈91 µg/mL at ratio 2.5, the HPMC 603 curve slightly below the PVP-VA curve; all measured points of R11 lie on or below the curves; text: Sa,IBP from eq 4 "much higher" than the measured dissolved IBP for both polymers; curve values in sub-table | Fig. 9, p.1351; text p.1352 |
| R13 | record, derived (E5) | calculated Sa,IBP versus PVP-VA weight ratio for χ = 1, 0.5, 0, −0.5, −1 — IBP/PVP-VA (P8) — all curves start at ≈154 µg/mL at ratio 0; at ratio 2.5 ≈152 (χ = 1), ≈119 (0.5), ≈93 (0), ≈73 µg/mL (−0.5); the χ = −1 curve reaches 60 µg/mL at ratio ≈2.33; the χ = 1 curve passes a maximum of ≈163 µg/mL near ratio 1; text: lower χ gives lower Sa,IBP; χ ≈ −1 at a 1/1 weight ratio gives ∼100 µg/mL, against an experimental ∼90 µg/mL (R11); curve values in sub-table | Fig. 10, p.1352; text p.1352 |
| C33 | claim, conclusion, authors: "suggesting" | The activity reduction of IBP mixed with a polymer is better treated with volume fractions; the ideal Flory-Huggins Sa,IBP (eq 4) was much higher than the measured dissolved IBP for both PVP-VA and HPMC 603, so factors beyond eq 4 must be considered [rests on: R12, R11] | p.1351-1352 |

## Mentioned only

- 2017 Mugheirbi — [2017-mugheirbi-water-induced-phase-separation-itz-hpmc-asd](../../../cards/2017-mugheirbi-water-induced-phase-separation-itz-hpmc-asd/paper.html) · ASD process / ASD process (ref 6)