---
review: 2016-taylor-physical-chemistry-supersaturated-solutions
title: "Physical chemistry of supersaturated solutions and implications for oral absorption"
authors: "Lynne S. Taylor, Geoff G.Z. Zhang"
year: 2016
journal: "Advanced Drug Delivery Reviews"
doi: "10.1016/j.addr.2016.03.006"
pages: 21
---
# Physical chemistry of supersaturated solutions and implications for oral absorption

**Scope.** The review (received January 2016, uncorrected proof) treats the solutions that form when amorphous solid dispersions (ASDs) and other enabling formulations dissolve: crystalline and amorphous solubility, supersaturation, liquid–liquid phase separation (LLPS), solubilization by micelles, and membrane flux. Its organising idea is that the thermodynamic activity of free, un-ionized drug in the central aqueous compartment sets passive absorption, that the amorphous solubility caps this activity, and that drug-rich nanodroplets formed by LLPS act as a reservoir. It closes with simple absorption simulations of four dissolution scenarios and proposes "spring and plateau" as the design goal.

**Summary of the check.** The wiki agrees with nearly all of the review's thermodynamic framework (Eqs. 1–14), its LLPS detection methods and its flux arguments, and for many points it adds 2017–2025 evidence: concentration-dependent micelle partitioning (Indulkar 2017), flux-based supersaturation in human intestinal fluid (Elkhabaz 2019), the limit of congruency (2017–2025) and absorptive tests. The three real differences are the review's statement that dissolved ASD polymers do not mix into the drug-rich phase and leave the amorphous solubility unchanged (the wiki has later counterexamples for ibuprofen, HPMCAS-HF and enzalutamide), its treatment of micelles as a reservoir equivalent to nanodroplets, and its reading of the felodipine ASD nanoparticles of Alonzo 2011 as drug-rich droplets where the wiki records the authors' crystalline assignment. The main gaps are the review's whole absorption-simulation section (Cases 1–4, "spring and plateau" against "spring and parachute", residence time), the BCS II/IV argument, lipid digestion and prodrug routes to LLPS, disintegration against erosion, and the use of the amorphous-to-crystalline ratio in candidate selection. The review's Eq. 7 is printed without the factor RT on its left side.

**Counts.** agrees 19 · wiki narrower 5 · wiki extends 23 · differs 3 · wiki silent 6

## 1. Introduction

### R1. Dissolution rate follows the Noyes–Whitney / Nernst–Brunner equation, and formulation acts on surface area and solubility
- **Review** [p. 2]: $\frac{dM}{dt} = \frac{DS}{h}(C_s - C) \approx \frac{DSC_s}{h}$ under sink conditions ($C \approx 0$); $D$ and $h$ are set by the molecule and the gastrointestinal tract, whereas surface area (particle size reduction, nanosizing) and solubility (salts, co-crystals, amorphous forms, ASDs, solubilizers) can be changed by formulation.
- **Kind**: framework (Noyes–Whitney, Nernst–Brunner)
- **Wiki**: [Noyes–Whitney equation](../../formulas/noyes-whitney-equation.md): "$\frac{dM}{dt} = \frac{DA}{h}\left(C_s - C\right)$ [que2019 E1]"; "$C_s$ is the solubility of the solid form at the dissolving surface, and the rate approaches zero as $C$ approaches it".
- **Verdict**: agrees
- **Note**: Same equation and same reading of $C_s$. The wiki adds that the form fails for dispersions whose release exceeds the amorphous solubility [que2019 E1], which the review does not discuss.

## 2. Theoretical considerations

### R2. Crystalline and amorphous solubility follow from the chemical potential difference and a constant aqueous activity coefficient
- **Review** [pp. 2–3]: $\ln(x_D^{W(c)}\gamma_D^{W(c)}) = (\mu_D^{(c)} - \mu_D^{0(a)})/RT$ with the supercooled liquid as standard state (Eq. 2); $\ln x_D^{W(a)} = -\ln\gamma_D^{W(a)}$ (Eq. 5); combined, $\ln x_D^{W(a)} = \ln x_D^{W(c)} - (\mu_D^{(c)} - \mu_D^{0(a)})/RT$ (Eq. 6), assuming $\gamma_D^{W(c)} \cong \gamma_D^{W(a)}$, "reasonable" for poorly soluble drugs at very low concentration.
- **Kind**: framework (Yalkowsky; Sandler)
- **Wiki**: [solid-liquid equilibrium solubility equation](../../formulas/solid-liquid-equilibrium-solubility-equation.md): "$\ln x_{C,L_1} = -\frac{\Delta G_{a\to c}}{RT} - \ln\gamma_{L_1}$ [ilevbare2013a E3]"; "for the supercooled liquid $\ln x_{SL,L_1} = -\ln\gamma_{L_1}$"; "γ is constant over the crystalline and amorphous concentration range [ilevbare2013a C55]".
- **Verdict**: agrees
- **Note**: Same relations and the same assumption. The review writes the difference with an explicit sign ($\mu^{(c)} - \mu^{0(a)} < 0$); the wiki form, copied from Ilevbare 2013, holds only if $\Delta G_{a\to c}$ is read as a positive magnitude (see the last section).

### R3. Supersaturation is a chemical-potential (activity) ratio; the concentration ratio approximates it only when the activity coefficients are equal
- **Review** [p. 3]: $\ln S = (\mu_D^{W(S)} - \mu_D^{(c)})/RT = \ln(\gamma_D^{W(S)}x_D^{W(S)}/\gamma_D^{W(c)}x_D^{W(c)})$ (Eq. 3); in practice $S_C = C/C^{*}$ (Eq. 4), linked to Eq. 3 by $\gamma_D^{W(S)}/\gamma_D^{W(c)}$ and valid when that ratio is close to 1, likely at very low supersaturation and/or very dilute solutions in simple media.
- **Kind**: framework (Mullin)
- **Wiki**: [activity-based supersaturation ratio](../../formulas/activity-based-supersaturation-ratio.md): "$\ln S = \frac{\mu - \mu^{*}}{RT} = \ln\frac{a}{a^{*}} = \ln\frac{\gamma c}{\gamma^{*} c^{*}}$ [raina2015c E5]"; [supersaturation ratio](../../formulas/supersaturation-ratio.md): "valid only if the activity-coefficient ratio $\gamma/\gamma^*$ is 1 (dilute solution, no solubilizer) and below the amorphous solubility".
- **Verdict**: agrees
- **Note**: Identical definitions and the same validity condition. The wiki states the domain as "below the amorphous solubility" where the review says "very low supersaturations"; both rest on a constant activity coefficient up to the amorphous solubility (R2).

### R4. The amorphous solubility is a metastable liquid–liquid equilibrium, and treating the amorphous drug as a supercooled liquid, also for glasses, allows it to be predicted
- **Review** [p. 3]: strictly no equilibrium with amorphous material exists, but with slow crystallization a metastable equilibrium can be reached; it can be treated as an LLE and predicted from the crystalline solubility; for drugs that are glasses at the temperature of interest, extrapolated supercooled-liquid properties give a reasonable estimate [28,29].
- **Kind**: framework, cited (Paus 2015; Almeida e Sousa 2015; Mosquera-Giraldo 2014)
- **Wiki**: [amorphous solubility](../../concepts/amorphous-solubility.md): "apparent, metastable equilibrium with the amorphous drug, more rigorously with the water-saturated supercooled liquid or glass; it is not a true thermodynamic solubility"; [C F7](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f7): "heat-capacity free energies that treat the new phase as a supercooled liquid fit better".
- **Verdict**: wiki extends
- **Note**: The wiki shows the supercooled-liquid route beating the glass route for griseofulvin, sorafenib and telaprevir and the Hoffman estimate overshooting for high-melting drugs (telaprevir 245 against 90–92 µg/mL; atazanavir, Indulkar 2017), and that pazopanib cannot be calculated because it degrades on melting (Sugihara 2018).

### R5. The crystal–amorphous chemical potential difference with constant ΔCp
- **Review** [p. 3]: $\mu_D^{(c)} - \mu_D^{0(a)} = -\frac{\Delta H_f}{R}\left(\frac{T_m - T}{T_m T}\right) + \frac{\Delta C_p}{R}\left(\frac{T_m - T}{T}\right) - \frac{\Delta C_p}{R}\ln\frac{T_m}{T}$ (Eq. 7); all methods need $\Delta H_f$ and $T_m$, more rigorous ones the heat capacities of crystal and supercooled liquid; Eq. 7 assumes pure crystal and pure amorphous drug.
- **Kind**: framework (Sandler)
- **Wiki**: [solid-liquid equilibrium solubility equation](../../formulas/solid-liquid-equilibrium-solubility-equation.md): "$\ln x = -\frac{\Delta H_f}{R}\left(\frac{1}{T}-\frac{1}{T_m}\right) - \frac{\Delta C_p}{R}\left(1-\frac{T_m}{T}+\ln\frac{T_m}{T}\right) - \ln\gamma$ [raina2014a E1]"; [heat-capacity free energy](../../formulas/amorphous-crystalline-free-energy-difference-from-heat-capacity.md) gives the linear-Cp and integral forms.
- **Verdict**: agrees
- **Note**: The raina2014a terms equal the right side of Eq. 7 term by term, which is therefore $(\mu_D^{(c)} - \mu_D^{0(a)})/RT$: as printed (checked on the page image) the review's left side lacks the factor $RT$. The wiki adds the temperature-dependent Cp forms of Almeida e Sousa 2015.

### R6. Water absorbed by the amorphous drug lowers its chemical potential and hence the amorphous solubility (Eqs. 8–11)
- **Review** [pp. 3–4]: $\mu_D^{L(a)} = \mu_D^{0(a)} + RT\ln a_D^{L(a)}$, $a_D^{L(a)} = x_D^{L(a)}\gamma_D^{L(a)}$; $\ln x_D^{W(a)} = \ln x_D^{W(c)} - (\mu_D^{(c)} - \mu_D^{0(a)})/RT + \ln(x_D^{L(a)}\gamma_D^{L(a)})$ (Eq. 10), equivalent to Murdande's $C_{amorphous} = C_{eq}\,e^{-I(a_2)}\,e^{\Delta G_{c\to a}/RT}$ (Eq. 11); $e^{-I(a_2)}$ is obtained by applying Gibbs–Duhem to the water sorption isotherm extrapolated to 100% RH.
- **Kind**: framework, cited (Murdande 2010)
- **Wiki**: [water-sorption correction](../../formulas/amorphous-solubility-advantage-with-water-sorption-correction.md): "$C_{\mathrm{amorphous}} = C_{\mathrm{eq}}\,e^{-I(a_2)}\,e^{\Delta G_{c\to a}/RT}$ [ueda2021 E1]"; "$e^{-I(a_2)}$ | activity of the amorphous drug saturated with water, from the Gibbs–Duhem treatment of the sorption isotherm | dimensionless, 0.22–0.999".
- **Verdict**: agrees
- **Note**: Same equation, including the mole-fraction form [ilevbare2013a E11]. The review once calls $-I(a_2)$ itself the activity; it is $e^{-I(a_2)}$, as its own equivalence with $x_D^{L(a)}\gamma_D^{L(a)}$ shows.

### R7. A miscibility gap between drug and water has binodal (coexistence) and spinodal compositions; between them demixing needs nucleation, inside the spinodal it is spontaneous
- **Review** [p. 4, Fig. 1]: at the binodal compositions $x_{DW}$ and $x_{WD}$ (common tangent) the chemical potentials are equal in both phases; between binodal and spinodal the solution is metastable and separates by nucleation and growth; at the spinodal $\partial^2G/\partial x^2 = 0$, and inside it separation is spinodal decomposition, a diffusion-controlled process; the amorphous solubility is $x_{WD}$.
- **Kind**: framework (Paus 2015; Deneau and Steele)
- **Wiki**: [binodal](../../concepts/binodal.md): "The coexistence curve of the water-rich and the drug-rich liquid phases ... the spinodal lies inside it"; [spinodal decomposition](../../concepts/spinodal-decomposition.md): "Spontaneous demixing ... with no nucleation barrier; between the binodal and the spinodal a new liquid phase must nucleate".
- **Verdict**: agrees
- **Note**: The wiki adds measured binodal and spinodal temperatures for ritonavir, 4.5–7.7 K apart [ilevbare2013a R11].

### R8. When the water-saturated drug-rich phase is below its glass transition the process is glass–liquid phase separation (GLPS), and DSC of the isolated phase tells which
- **Review** [pp. 4, 8]: if the temperature is below the Tg of the water-saturated drug-rich phase the process is termed GLPS [29]; DSC gives the Tg of the water-saturated amorphous material, showing whether the phase is a supercooled liquid or a glass [29,35,43].
- **Kind**: cited (Mosquera-Giraldo 2014; Ilevbare 2013; Indulkar 2015)
- **Wiki**: [glass–liquid phase separation](../../concepts/glass-liquid-phase-separation.md): "a drug-rich phase that is a glass at the test temperature, because its water-plasticized Tg lies above that temperature"; [C F2](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f2): "a glassy phase behaves much like a liquid one in these tests".
- **Verdict**: wiki extends
- **Note**: The wiki gives wet Tg values (ritonavir 0.4 °C, clotrimazole about 14 °C, atazanavir about 51 °C, telaprevir 52 °C) and shows that glassy phases still form at a reproducible onset and redissolve on dilution; it notes that pazopanib (2018) has only a dry Tg, so its glassy state is not settled.

### R9. At liquid–liquid equilibrium the drug activity is equal in both phases, and the amorphous solubility is reached from either direction
- **Review** [p. 5]: $a_D^{W(a)} = a_D^{L(a)}$ (Eqs. 12–13), so the amorphous solubility is set by the activity of drug in the water-saturated drug-rich phase and the aqueous activity coefficient; the composition $x_{WD}$ is approached either by equilibrating amorphous drug with water or by adding drug to water until LLPS, and both give the same two-phase system; the second route is the one relevant to drug delivery.
- **Kind**: framework
- **Wiki**: [C F1](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f1): "the solution and the droplets are in equilibrium, so the drug has the same activity in both [ilevbare2013a C29, C36]"; [C F13](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f13): "a dissolving ritonavir film gave 34.2 µg/mL in water against an onset of 37.2".
- **Verdict**: agrees
- **Note**: The film-dissolution and onset routes give values within about 10% for ritonavir and 69–110% for three weak bases [indulkar2015 R18].

### R10. Slow crystallizers undergo LLPS before crystallizing; the drug-rich phase is a precursor of crystals and lasts minutes to hours
- **Review** [pp. 5–6, Figs. 2–3]: in region 3 either LLPS or crystallization can occur; because crystal nucleation has kinetic barriers, LLPS can be faster for complex molecules ("slow crystallizers"), and the system, still supersaturated, is expected to crystallize later; "oiling out" in process chemistry is followed by crystallization minutes [36] to hours [34] later; LLPS is favoured by very high or rapidly generated supersaturation, inhibitors, impurities and poor mixing [38].
- **Kind**: interpretation, cited (Bonnett 2003; Deneau and Steele 2005; Tung 2008)
- **Wiki**: [C F3](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f3): "The drug-rich phase is a transient precursor of crystals: for ritonavir it forms inside the metastable zone, and it lasts minutes to hours depending on the drug and the inhibitor".
- **Verdict**: agrees
- **Note**: Same picture; the wiki records the authors' "oiling out" reading for ritonavir and times from about 15 min (telaprevir) to more than 2 h. The impurity and mixing conditions from process chemistry are not tested in the wiki's sources.

### R11. The drug-rich species are 100–500 nm when first formed and can grow, unless additives such as polymers inhibit growth
- **Review** [p. 6]: species formed after LLPS typically measure 100–500 nm by DLS immediately after formation [29,39,40,43]; growth can follow or be inhibited by polymers [40,44]; some compounds persist as a two-phase solution supersaturated at the coexistence concentration until crystallization.
- **Kind**: cited (Mosquera-Giraldo 2014; Jackson 2016; Ilevbare 2013; Indulkar 2015; Alonzo 2011)
- **Wiki**: [C F1](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f1): "The ritonavir phase held about 95% drug and 4–5% water and grew from about 345 to about 842 nm in 64 min"; "ibuprofen, whose drug-rich droplets measured 3182–5313 nm in buffer and 268–345 nm with HPMC or PVP-VA".
- **Verdict**: wiki extends
- **Note**: The 100–500 nm range holds for the 2013–2016 drugs (116–387 nm weak bases, about 300 nm telaprevir), but the 2018–2020 papers add pazopanib at 496 nm and ibuprofen at several µm without polymer, so the range depends on drug and additive ([C F22](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f22)).

### R12. About a third of some 50 drugs crystallize within 2.5 min of solvent shift, a third show LLPS without crystals for 1 h; inhibitors make LLPS observable
- **Review** [p. 6]: in a study of about 50 compounds [45], around a third crystallized within 2.5 min of generating high supersaturation by solvent shift, a third did not crystallize within 1 h although a visible precipitate indicated liquid–liquid demixing, and the rest crystallized at intermediate times; polymers or other inhibitors can permit LLPS by slowing crystallization [49].
- **Kind**: cited (Van Eerdenbrugh 2014; Raina 2015)
- **Wiki**: [D F3](../../dissolution/d-crystallization-from-solution/findings.md#f3): "Without polymer, drugs at similar supersaturation form crystals within about 1 min to 6 h"; [Solution methods F8](../../characterization-methods/solution-methods/findings.md#f8): "Fast crystallizers crystallize before they phase separate unless a polymer slows nucleation".
- **Verdict**: wiki narrower
- **Note**: The wiki covers the same fast/slow split for smaller sets (nine drugs in one protocol, six dihydropyridines, griseofulvin) and shows that solid-state classes predict solution behaviour only partly ([Crystallization tendency F18](../../solid-state-stability/crystallization-tendency/findings.md#f18)), but the 50-compound aqueous classification [45] is not in the library.

## 3. Experimental observations

### R13. The amorphous solubility is hard to measure directly, but values from LLPS onsets agree with predictions for 23 compounds
- **Review** [pp. 6, Fig. 4]: dissolving a pure amorphous reference often fails because it crystallizes first, giving large discrepancies [26,27,50,51]; alternatives are the concentration where added amorphous nanoparticles stop dissolving (felodipine, Lindfors) and generating the phase in situ above the amorphous solubility; for 23 compounds predicted and measured amorphous solubilities lie on the line of slope 1.
- **Kind**: cited (Hancock and Parks 2000; Murdande 2010; Lindfors 2006; data of refs. 28, 29, 35, 39, 43, 53)
- **Wiki**: [C F5](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f5): "17 of the 24 rows of the table below lie between 0.91 and 1.15 times the prediction"; [Bioperformance F1](../../bioperformance/bioperformance/findings.md#f1): "The estimate failed in FaSSIF (214.6 measured against 308.0 estimated)".
- **Verdict**: wiki extends
- **Note**: The wiki agrees in general but lists the outliers that a linear 0–400 µg/mL plot hides: clotrimazole 1.30–1.57, tolnaftate 1.72, CRH1 up to 1.57 and ibuprofen 1.57 times the prediction, telaprevir 0.38 with the Hoffman free energy, and predictions that cannot be reproduced from printed inputs.

### R14. Light scattering at a non-absorbing wavelength, DLS, NTA and a pH swing locate the LLPS onset, with known limitations
- **Review** [pp. 6–7, Fig. 5]: the UV signal at a wavelength where the drug does not absorb rises when a new phase forms (nisoldipine, Fig. 5); the method is simple and rapid but can overshoot because of continuous addition, cannot tell crystalline from amorphous phase, and needs enough scattering near the onset; for ionizable drugs a pH swing creates supersaturation without organic solvent [43,58]; DLS and NTA follow droplet size.
- **Kind**: cited (Thomson 1987; Ilevbare 2013; Raina 2015; Indulkar 2015)
- **Wiki**: [Solution methods F3](../../characterization-methods/solution-methods/findings.md#f3): "Extinction at a wavelength where the drug does not absorb marks the appearance of a second light-scattering phase and gives an LLPS onset, but it does not say what the phase is"; [C F1](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f1): "the solvent-free pH titration of the weak bases agreed with the antisolvent runs above the lowest pH".
- **Verdict**: agrees
- **Note**: The wiki gives the same nisoldipine onset (about 7 µg/mL at 25 °C) and cases where the extinction rise marked crystals (nifedipine, nimodipine) [raina2015a R3, R4].

### R15. Freshly formed drug-rich droplets are small and redissolve quickly when the concentration falls below the amorphous solubility
- **Review** [p. 7]: the new amorphous phase is initially 100–500 nm [29,39,40,43], and the small size gives rapid redissolution when the concentration drops below the amorphous solubility [29,40,58].
- **Kind**: cited (Mosquera-Giraldo 2014; Ilevbare 2013; Hsieh 2012)
- **Wiki**: [C F2](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f2): "the telaprevir phase redissolved within about 2 min on dilution"; [B F9](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f9): "≈350 nm droplets ... at 20 µg/mL, and a return to baseline on dilution back to 10 µg/mL".
- **Verdict**: agrees
- **Note**: The wiki adds that indomethacin nanodroplets formed in acid redissolved within about 2 min after a pH rise [xie2017 R10] ([B F21](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f21)).

### R16. Polarity-sensitive fluorescent probes report LLPS and the later crystallization of the drug-rich phase
- **Review** [p. 7, Fig. 6]: a hydrophobic probe such as pyrene partitions into the drug-rich phase, so its I1/I3 ratio falls at the LLPS onset; when the drug crystallizes the probe is expelled and a polar environment is registered again (nifedipine: crystallization near 200 µg/mL); drug autofluorescence must not interfere and the probe must not alter the phase behaviour.
- **Kind**: cited (Raina 2015; Almeida e Sousa 2015; Ilevbare 2013)
- **Wiki**: [Solution methods F9](../../characterization-methods/solution-methods/findings.md#f9): "When the drug-rich phase crystallizes the fluorescence signal changes again, but each paper shows it for one unverified sample"; [Solution methods F6](../../characterization-methods/solution-methods/findings.md#f6): the drug's own fluorescence "can mask the emission of an external probe or serve as the reporter itself".
- **Verdict**: wiki narrower
- **Note**: The wiki has the same nifedipine trace (pyrene ratio about 1.8 to 60 µg/mL, 0.76 at 200, 1.60 at 400 µg/mL) but notes that the crystallization reading was never checked by an independent solid-state method [raina2015a X15], so the review states it more generally than the evidence supports.

### R17. Ultracentrifugation gives the coexistence concentration; different methods agree, so little supersaturation beyond the amorphous solubility occurs before separation, but kinetic effects should be checked
- **Review** [pp. 7–8]: addition-based methods may overshoot; ultracentrifugation of a phase-separated solution gives the binodal points [35]; agreement between methods suggests most systems do not supersaturate much with respect to the amorphous solubility before separating [35,66]; centrifugation of 30–40 min risks crystallization, which a small amount of polymer can prevent.
- **Kind**: cited (Ilevbare 2013; Almeida e Sousa 2016)
- **Wiki**: [C F4](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f4): "for ritonavir, lopinavir and paclitaxel four methods each agreed within about 2–3 µg/mL"; [D F22](../../dissolution/d-crystallization-from-solution/findings.md#f22): "the lower onsets seen earlier came from reading 15 s after the addition".
- **Verdict**: wiki extends
- **Note**: The wiki confirms the agreement (telaprevir 146, 149 and 148 µg/mL by extinction, ultracentrifugation and flux in 2017) and adds a measured kinetic effect: danazol read 15 s after each addition gave 10–14 µg/mL against about 8 µg/mL after 1–5 min [jackson2016 R13, R12].

### R18. NMR measures dissolved drug and the distribution of polymer between the phases, which correlated with polymer effectiveness as crystallization inhibitor
- **Review** [p. 8]: NMR can give the drug concentration in the water-rich phase and insight into the drug-rich phase [29,67]; with polymers it gave the composition of each phase, "correlating the effectiveness of various polymers as crystallization inhibitors based on their distribution between the aqueous and drug-rich phases" [49].
- **Kind**: cited (Mosquera-Giraldo 2014; LaPlante 2013; Raina 2015)
- **Wiki**: [D F26](../../dissolution/d-crystallization-from-solution/findings.md#f26): "PVPVA, HPMC and HPMCAS, which distribute between the drug-rich precipitate and the water, held four of six dihydropyridine precipitates amorphous beyond 24 h"; [D F37](../../dissolution/d-crystallization-from-solution/findings.md#f37): "how much polymer enters the droplets does not by itself rank the inhibitors".
- **Verdict**: wiki extends
- **Note**: The wiki agrees for the 2015 dihydropyridine study and adds 2021–2025 tests: Eudragit E PO made up about 41 w/w% of enzalutamide droplets yet inhibited worst, while the HPMCAS grade richest in the posaconazole droplets inhibited best [wilson2021 R7, R3; shah2025 R17, R3]. Solution NMR sees the drug-rich phase only for low-Tg drugs ([C F15](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f15)).

### R19. The amorphous-to-crystalline solubility ratio rises with melting point and enthalpy of fusion, is lowered by absorbed water, and ranges from about 4 to about 65 in the authors' data
- **Review** [p. 8, Fig. 7]: high $T_m$ and $\Delta H_f$ give larger advantages, but water content may be non-negligible; measured ratios: ibuprofen only 4 ($T_m$ about 77 °C), atazanavir about 65 ($T_m$ about 208 °C), ritonavir about 15 [35], telaprevir about 20 [29]; the scatter of predicted against measured ratios for 23 compounds most likely comes from crystalline solubilities below 100 ng/mL.
- **Kind**: direct claim, cited (Almeida e Sousa 2015; Ilevbare 2013; Mosquera-Giraldo 2014)
- **Wiki**: [C F6](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f6): "The maximum supersaturation, amorphous over crystalline solubility, differs by more than a hundredfold between drugs, from about 2 to about 600"; [C F5](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f5): outliers attributed "to the fluorescence detection limit and the uncertainty of crystalline solubilities in the ng/mL range".
- **Verdict**: wiki extends
- **Note**: The wiki values agree (ibuprofen 4.3, ritonavir 15.5 in water, atazanavir about 63, telaprevir about 18 from the same paper the review gives as 20) and widen the range to efavirenz 2.2 and pazopanib about 500–600 (2018). The wiki does not state the melting-point trend as such; it shows the Hoffman route failing for high-melting drugs (R4).

### R20. The amorphous-to-crystalline ratio indicates the possible bioavailability gain and should be used in candidate selection
- **Review** [pp. 8, 10]: a drug with a low ratio such as ibuprofen would not be expected to gain much bioavailability as an amorphous form; ratios of about 15 (ritonavir) and 20 (telaprevir) "clearly" translate into a bioavailability advantage, given their commercial amorphous products; the ratio "probably should be considered during lead optimization and candidate selection".
- **Kind**: interpretation
- **Wiki**: none
- **Verdict**: wiki silent
- **Note**: The wiki has exposure data for enzalutamide, pretomanid and tacrolimus in animals ([Overview F14](../../overview/findings.md#f14)) but no statement linking the ratio across drugs to bioavailability gain or to candidate selection.

### R21. Higher ionic strength lowers the amorphous solubility substantially
- **Review** [p. 8, Fig. 8]: ionic strength lowers both solubilities; for ritonavir the amorphous solubility falls from about 37 µg/mL in water to about 19, 14 and 5 µg/mL at 100, 200 and 500 mM, so buffer strength must be considered when comparing values [35].
- **Kind**: cited (Ilevbare 2013)
- **Wiki**: [C F9](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f9): "The ritonavir LLPS concentration at 37 °C fell from 37.2 µg/mL in water to 18.8, 14.3 and 4.7 µg/mL in 100, 200 and 500 mM phosphate buffer".
- **Verdict**: agrees
- **Note**: Same data; the wiki adds telaprevir (onset 149/146 µg/mL in 50 mM pH 6.5 against 104/102 µg/mL in 100 mM pH 6.8) [lu2017b R9].

### R22. For ionizable drugs the amorphous solubility follows Henderson–Hasselbalch with the un-ionized amorphous solubility as input, so the amorphous-to-crystalline ratio is constant with pH
- **Review** [pp. 8–9]: for a weak base the total concentration rises as pH falls while the un-ionized concentration stays at the amorphous solubility; the amorphous solubility follows the Henderson–Hasselbalch relation, and the ratio of amorphous to crystalline solubility stays constant with pH [43].
- **Kind**: cited (Indulkar 2015)
- **Wiki**: [C F10](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f10): "For weak bases the limit is set by the un-ionized drug: the total LLPS concentration rises with ionization as Henderson–Hasselbalch predicts".
- **Verdict**: wiki extends
- **Note**: Agrees for clotrimazole, atazanavir, nicardipine and CRH1, but the wiki adds pazopanib (2018), whose amorphous values at pH 5 and 5.5 lay below the Henderson–Hasselbalch curve (60 against about 250 µg/mL, 40 against about 80) [sugihara2018 R1, R2, R3], so the constant ratio is not general.

### R23. A second drug that mixes into the drug-rich phase lowers the amorphous solubility by its mole fraction; an ionized one does not
- **Review** [p. 9, Fig. 9]: ritonavir and lopinavir lower each other's amorphous solubility because they are miscible in the amorphous phase; assuming ideal mixing, at a mole fraction of 0.5 each amorphous solubility is halved; diclofenac anion has no effect on ritonavir [68].
- **Kind**: cited (Trasi and Taylor 2015)
- **Wiki**: [C F11](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f11): "An ideal-mixing relation, $S_a(x_1) = S_a^\circ x_1$, roughly predicted the ritonavir–lopinavir bulk concentrations"; "ionized diclofenac stayed in solution".
- **Verdict**: agrees
- **Note**: The wiki adds that the same relation holds for co-dosed dispersions and Caco-2 flux ([B F11](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f11), [Bioperformance F6](../../bioperformance/bioperformance/findings.md#f6)); Fig. 9 shows ritonavir points mostly above the ideal line, which "roughly" covers.

### R24. Dissolved ASD polymers do not mix substantially with the drug-rich phase and so do not change the amorphous solubility
- **Review** [p. 9]: PVP, HPMC and HPMCAS had no detectable effect on the amorphous solubility of danazol, "suggesting that these polymers do not substantially mix" with the drug-rich phase [69]; by NMR, PVPVA and HPMCAS made up less than 7 wt.% of the drug-rich phase, "confirming that the polymers do not mix substantially with the drug-rich phase, and thus do not have a discernible impact on the amorphous solubility" [49].
- **Kind**: cited (Jackson thesis 2015; Raina 2015)
- **Wiki**: [D F22](../../dissolution/d-crystallization-from-solution/findings.md#f22): danazol's onset stayed "at about 8 µg/mL"; [C F19](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f19): "HPMC and PVP-VA lowered the amorphous solubility of ibuprofen from 177.1 to 96.9 and 90.7 µg/mL"; [Bioperformance F19](../../bioperformance/bioperformance/findings.md#f19): "AS-HF lowered the amorphous solubility of atazanavir from 81.5 to 35.5 µg/mL".
- **Verdict**: differs
- **Note**: For danazol and the felodipine precipitate the wiki agrees, but 2020–2021 papers show the same polymer classes entering the drug-rich phase and lowering the amorphous solubility by a quarter to over half (ibuprofen with HPMC and PVP-VA, four drugs with HPMCAS-HF, enzalutamide 42 to about 20–37 µg/mL); the review's general conclusion holds only for its systems and is not supported as a rule.

### R25. Dissolution-limited and solubility-limited bioavailability differ, and only supersaturation addresses the second
- **Review** [p. 9]: low solubility lowers bioavailability both through slow dissolution and through the low amount of dissolved drug available for transport; dissolution-limited bioavailability is addressed by faster dissolution, solubility-limited bioavailability only by a supersaturated solution.
- **Kind**: framework
- **Wiki**: [dissolution-rate-limited absorption](../../concepts/dissolution-rate-limited-absorption.md): "Absorption limited by slow dissolution of the dose. LLPS is expected to remove such a limit because droplets equilibrate quickly".
- **Verdict**: wiki narrower
- **Note**: The wiki defines the dissolution-limited case only; solubility-limited absorption appears just as a reason for choosing enzalutamide ([Bioperformance F23](../../bioperformance/bioperformance/findings.md#f23)), without the review's distinction between the two.

### R26. Membrane flux follows solute activity, not concentration: $J \propto S \cdot D/(h\gamma_m)$
- **Review** [p. 9]: in transdermal delivery flux is linear in the degree of saturation [70–74]; supersaturated progesterone raised flux in rat jejunal perfusion [75]; solutions of very different concentration at constant activity (crystal-saturated) gave nearly constant flux [70]; solubility and membrane partition coefficient are reciprocal, so solubilizers do not raise flux [71,77]; flux should be considered in terms of activity [78], giving $J \propto S \cdot D/(h\gamma_m)$ (Eq. 14) with $D$, $h$, $\gamma_m$ constant for a given system.
- **Kind**: cited (Twist and Zatz 1986; Yalkowsky; Miller 2012; Higuchi 1960; Raina 2014, 2015)
- **Wiki**: [membrane flux in terms of solute activity](../../formulas/membrane-flux-in-terms-of-solute-activity.md): "$J = S_i\,\frac{D}{h\,\gamma_m}$ [jackson2015 E3]"; "the rate of transport into sink conditions is proportional to the thermodynamic activity of the solute in the donor, not to its concentration [trasi2016 E2]".
- **Verdict**: agrees
- **Note**: The wiki has the direct counterpart of the constant-activity test: felodipine suspensions holding about 1 and about 40 µg/mL dissolved drug gave the same low flux ([Bioperformance F3](../../bioperformance/bioperformance/findings.md#f3)); the progesterone result appears only as a cited statement ([solubility–permeability interplay](../../concepts/solubility-permeability-interplay.md)).

### R27. Danazol flux rises linearly to its amorphous solubility (about 8 µg/mL) and then plateaus, whether the solution came from antisolvent addition or an ASD
- **Review** [pp. 9–10, Fig. 10]: crystalline danazol solubility is about 1 µg/mL; flux rises linearly to about 8 µg/mL and stays constant above; the plateau, about an order of magnitude above crystalline flux, reflects LLPS at the amorphous solubility [80]; ASDs with 90 wt.% PVP, HPMC or HPMCAS gave a flux similar to antisolvent solutions; a plateau has been seen for several compounds [29,68,69,80].
- **Kind**: cited (Jackson thesis 2015; Raina 2014)
- **Wiki**: [B F7](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f7): "Every danazol dispersion that formed a drug-rich phase gave 7.1–9.1 µg/mL free drug by flux, like antisolvent solutions (7.2–8.2), against an amorphous solubility of 8 µg/mL".
- **Verdict**: agrees
- **Note**: The plateau is repeated in the wiki for felodipine, nifedipine, telaprevir, ritonavir, lopinavir, paclitaxel, clotrimazole, atazanavir and enzalutamide ([C F8](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f8), [Bioperformance F2](../../bioperformance/bioperformance/findings.md#f2)).

### R28. The amorphous solubility is the upper limit of supersaturation for any formulation approach, shown by LLPS at the same concentration from different routes
- **Review** [p. 10, Fig. 11]: flux studies show an upper limit of supersaturation set by the amorphous solubility, and the authors extend this to "any" formulation, pending activity-based characterization; temperature change, antisolvent addition, pH swing, ASD dissolution and salt dissolution have all produced an amorphous drug-rich phase [35,39,40,53,58,66], and different routes give LLPS at the same concentration [35,66].
- **Kind**: interpretation, cited (Ilevbare 2013; Jackson 2016; Raina 2015; Hsieh 2012; Almeida e Sousa 2016)
- **Wiki**: [Overview F1](../../overview/findings.md#f1): "The amorphous solubility is the reference of every category: free drug from dispersions and marketed products levels off there, membrane flux plateaus there".
- **Verdict**: wiki extends
- **Note**: The wiki adds six marketed tacrolimus capsules at about 46–50 µg/mL and a pazopanib salt after a pH shift, and adds a route that stays below the limit: ritonavir from SBA-15 silica plateaued at about 85% of its amorphous solubility with no drug-rich phase [dening2018 R22, C32].

### R29. Strictly, the spinodal rather than the amorphous solubility (binodal) is the upper limit of achievable supersaturation
- **Review** [p. 10]: the amorphous solubility "(or strictly speaking, the spinodal decomposition point, see Fig. 1)" is the upper limit of achievable supersaturation.
- **Kind**: framework
- **Wiki**: [supersaturation](../../concepts/supersaturation.md): "the highest supersaturation a solution can hold without crystals is set by the amorphous solubility"; [spinodal decomposition](../../concepts/spinodal-decomposition.md): continual addition "might approach one of the spinodal decomposition points" for telaprevir.
- **Verdict**: wiki narrower
- **Note**: The wiki uses the binodal (onset or ultracentrifuge value) as the ceiling and mentions the spinodal only as a possible overshoot of addition methods; the review's distinction between the transient (spinodal) and the equilibrium (binodal) limit is not stated, though the ritonavir binodal–spinodal gap is small (4.5–7.7 K) ([C F3](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f3)).

### R30. Co-crystal dissolution can generate supersaturation and is an unexplored route to LLPS
- **Review** [p. 10]: prodrug conversion [82] and co-crystal dissolution [83] can generate supersaturated solutions and are "unexplored potential routes that could result in LLPS".
- **Kind**: interpretation, cited (Childs 2013)
- **Wiki**: [C F14](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f14): "Without polymer the co-crystal, glass and the HCl and HBr salts peaked at about 2.9, 3.3, 3.9 and 5.4 µg/mL"; a drug-rich phase "appeared only for the salts and the ASD".
- **Verdict**: wiki extends
- **Note**: The wiki holds a test the review does not mention, although it cites the same paper [66] for salts: the CRH1 co-crystal (Almeida e Sousa 2016) peaked at about 6.2 µg/mL with HPMC against an amorphous solubility of about 12 µg/mL and formed no drug-rich phase, so for that system the co-crystal route did not reach LLPS.

### R31. Lipid formulation digestion and prodrug conversion may also lead to an amorphous drug-rich phase
- **Review** [p. 10]: there is some evidence that lipolysis of a self-microemulsifying drug delivery system gives an amorphous precipitate [81]; prodrug conversion [82] can supersaturate and could lead to LLPS.
- **Kind**: cited (Sassene 2010; Stappaerts 2015)
- **Wiki**: none
- **Verdict**: wiki silent
- **Note**: No lipid-based or prodrug source is in the library; the wiki's lipid-related evidence concerns lecithin and its digestion products shortening induction times ([D F39](../../dissolution/d-crystallization-from-solution/findings.md#f39)), not LLPS from lipid formulations.

### R32. A solubilized solution differs from a supersaturated one by its activity; micellar solubilization is described by $K_m = C_m/C_w$ and $S_{tot} = S_w + K_m S_w$
- **Review** [pp. 10–11]: in a supersaturated solution the activity exceeds that of the crystal, in a solubilized solution it stays at or below it; $K_m = C_m/C_w$ (Eq. 15), commonly determined at the saturation solubility, and $S_{tot} = S_w + K_m S_w$ (Eq. 16), implying free drug set by the crystal solubility plus micelle-associated drug.
- **Kind**: framework (Yalkowsky 1999)
- **Wiki**: [micellar solubilization](../../concepts/micellar-solubilization.md): "uptake of drug into surfactant or bile-salt micelles raises the equilibrium solubility and the total concentration but not the free drug [raina2015c C30]"; [C F18](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f18) uses the "micelle/water partition coefficient Km/w".
- **Verdict**: wiki narrower
- **Note**: The concept and $K_{m/w}$ are in the wiki, but neither Eq. 16 nor a formula page for $K_{m/w}$ exists: the Bioperformance index links a formula page "micelle–water partition coefficient" that is present only as an unmerged draft.

### R33. Only free drug drives absorption; permeability computed from total concentration in micellar solutions is wrong
- **Review** [p. 11]: in the two-population model only free drug molecules provide the driving force for absorption and micellar solubilization lowers absorption kinetics [84]; permeability calculated from total instead of free drug concentration is erroneous [85].
- **Kind**: cited (Poelma 1991; Katneni 2006)
- **Wiki**: [solubility–permeability interplay](../../concepts/solubility-permeability-interplay.md): "Permeability calculated from total concentration is "implausible" because it is a property of the molecule for a given membrane".
- **Verdict**: agrees
- **Note**: The wiki adds atazanavir in 3.6 mg/mL SDS, where apparent permeability equals the buffer value on an activity basis and is about 20-fold lower on a total basis [indulkar2017a R27, E12].

### R34. Solubilizers raise both the crystalline and the amorphous solubility, the crystalline more (felodipine with vitamin E TPGS)
- **Review** [p. 11]: crystalline felodipine rose from around 1 µg/mL in buffer to 40 µg/mL with vitamin E TPGS micelles, the amorphous solubility from around 10 to 177 µg/mL [79]; the crystalline solubility rises more for a given micellar surfactant concentration.
- **Kind**: cited (Raina 2015)
- **Wiki**: [Bioperformance F4](../../bioperformance/bioperformance/findings.md#f4): "The LLPS onset moved from 10.4 µg/mL in buffer to 177.3 and 214.6 µg/mL, while the onset-to-crystalline ratio fell from 9.2 to 4.5 and 5.0".
- **Verdict**: wiki extends
- **Note**: Same felodipine data; the wiki adds posaconazole (crystalline 14-fold, amorphous 5-fold from buffer to FaSSIF-V1) but also cases where both rose in step, ritonavir with Tween 80 (2.7- and 2.6-fold) and telaprevir with dihydroxy bile salts ([C F12](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f12)), so the larger rise of the crystalline solubility depends on drug and solubilizer.

### R35. Solubilizing additives lower flux at a fixed concentration, and the maximum flux returns once the concentration exceeds the new amorphous solubility
- **Review** [p. 11]: for nifedipine and felodipine, surfactants, proteins and cyclodextrins reduced flux at a given concentration above the equilibrium solubility, i.e. reduced the supersaturation; the same maximum flux, set by the LLPS concentration, was reached by raising the total concentration above the amorphous solubility in the additive [79].
- **Kind**: cited (Raina 2015)
- **Wiki**: [Bioperformance F3](../../bioperformance/bioperformance/findings.md#f3): "six solubilizing additives at levels above their critical micelle concentration cut the flux of a 50 µg/mL felodipine solution from about 0.14 to 0.010–0.12 µg/min"; [F4](../../bioperformance/bioperformance/findings.md#f4): "the same maximum flux is reached only at a much higher total concentration".
- **Verdict**: agrees
- **Note**: The wiki adds that additive levels below the CMC did not lower the flux [raina2015c R7].

### R36. The concentration ratio $C/C^*$ underestimates supersaturation in micellar media; the activity-based ceiling is unchanged
- **Review** [p. 11]: Eq. 4 under-predicts the supersaturation in felodipine and nifedipine solutions with micelles, cyclodextrins and proteins; flux-based supersaturation rose more steeply in TPGS and FaSSIF than Eq. 4 predicts; the amorphous-to-crystalline concentration ratio fell from ~9 to ~4.5 with TPGS, yet the maximum flux was the same, so the amorphous solubility advantage is not lowered on an activity basis.
- **Kind**: cited (Raina 2015)
- **Wiki**: [C F16](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f16): "In micellar media, concentration ratios understate the supersaturation, and the flux-based activity ratio at the amorphous solubility is the same as without micelles".
- **Verdict**: wiki extends
- **Note**: The wiki adds atazanavir in SDS (concentration ratio 33–37.5, activity ratio 65–70) and atazanavir and posaconazole in six media up to pooled human intestinal fluid (flux-based maxima about 50–56 and 29–37, concentration-based down to about 14 and 5) [indulkar2017a R13; elkhabaz2019b R8, R9].

### R37. A micelle–water partition coefficient that falls with solute concentration explains why Eq. 4 fails
- **Review** [p. 11]: $K_m$ is measured at the crystalline solubility and assumed constant; there is "ample evidence" that it falls with solute concentration [86–88], which "provides the most plausible explanation" for the breakdown of Eq. 4, as micellar binding sites approach saturation and free drug rises faster than a constant $K_m$ predicts.
- **Kind**: interpretation, cited (Lee 1990; Goto 1978; Croy 2005)
- **Wiki**: [C F18](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f18): "The micelle/water partition coefficient Km/w fell from about 327 to about 99 as total drug rose to 100 µg/mL (Region I) and then stayed at about 90–114 up to 1450 µg/mL".
- **Verdict**: wiki extends
- **Note**: The wiki has the direct test the review proposed (atazanavir in SDS, 2017) and later biorelevant media (Km/w about half at the amorphous solubility for posaconazole); the drop occurred mainly just above the crystalline solubility and was read as a change from adsorption at the micelle surface to the core, not as gradual site saturation.

## 4. Biological absorption of insoluble drugs from the ASD: a mass transport process

### R38. Only un-ionized free drug in the central aqueous compartment permeates, and its activity, not the total solubilized concentration, sets passive absorption
- **Review** [pp. 11–12, Fig. 12]: the gastrointestinal tract is pictured as a central aqueous compartment in contact with the membrane, with peripheral microenvironments (micelles, vesicles, complexes, crystals, LLPS/GLPS phase); only un-ionized drug undergoes passive absorption [89]; the activity of drug in the central compartment, rather than the total concentration in all compartments, dictates the kinetics of passive absorption.
- **Kind**: framework, cited (Shore 1957; Raina 2015)
- **Wiki**: [speciation](../../concepts/speciation.md): "The split of total drug into free, micellar, complexed, droplet and crystalline species; only free unionized drug is thought to cross a membrane [hate2018 C48; raina2015c C49]".
- **Verdict**: agrees
- **Note**: Same picture; the wiki takes its species list from the Bioperformance papers and does not draw the compartment scheme.

### R39. Drug-rich droplets and micelles both act as reservoirs that replenish free drug, and a well-designed formulation relies on transferring drug into them
- **Review** [pp. 12–13]: peripheral compartments act as reservoirs from which drug moves into the central compartment as it is absorbed; "a well-designed formulation will rely on transferring the drug into drug-rich liquid droplets and compartments such as micelles", since these equilibrate rapidly with the central compartment and replenish free drug.
- **Kind**: interpretation
- **Wiki**: [nanodroplet reservoir effect](../../concepts/nanodroplet-reservoir-effect.md): "Micelle-solubilized drug is not an equivalent reservoir [indulkar2016 C26]"; Indulkar and co-workers find "an LLPS system sustains maximum flux while a micellar system at the same total concentration gives lower flux".
- **Verdict**: differs
- **Note**: Micelles can resupply free drug, but at the activity of the micellar solution, which at a given total concentration is lower than with droplets (the review's own Section 3.8); the flux data in the wiki (Indulkar 2016, 2017) support treating only the drug-rich phase as a reservoir at maximum activity. The wiki also records the mesoporous-silica authors calling micellar solubilization "advantageous" with the caveat that micelles "may actually reduce" free drug ([micellar solubilization](../../concepts/micellar-solubilization.md)).

### R40. Whether an ASD dosage form disintegrates or erodes depends on the matrix polymer, disintegrant and surfactant
- **Review** [p. 12]: disintegration increases surface area; copovidone and HPMC matrices tend to erode on contact with water, whereas HPMCAS formulations can be designed to disintegrate.
- **Kind**: direct claim
- **Wiki**: none
- **Verdict**: wiki silent
- **Note**: The wiki studies release from compacts of constant area and powders; the only erosion statements concern PVP and PAA tablets of probucol in the ASD process chapter, not the polymer comparison made here.

### R41. The driving force for dissolution of multicomponent ASDs is poorly understood: some exceed the amorphous solubility and form nanoparticles, others reach it slowly or not at all
- **Review** [pp. 12–13]: some ASDs dissolve past the amorphous solubility and undergo LLPS, others reach much lower maxima [39,90]; felodipine ASDs at low drug:polymer ratio dissolved rapidly with nanoparticles, at high ratio slowly and only up to the amorphous solubility [44]; drug, polymer, surfactant, ratios, interactions and ionization are expected to matter; "clearly an area that warrants more investigation".
- **Kind**: cited (Jackson 2016; Xie and Taylor 2015; Alonzo 2011)
- **Wiki**: [A F4](../../dissolution/a-release-mechanism-and-loc/findings.md#f4): "In 2017–2020 only release that stayed under polymer control passed the amorphous solubility and formed drug-rich nanodroplets"; [A F6](../../dissolution/a-release-mechanism-and-loc/findings.md#f6): "The limit of congruency is a narrow switch".
- **Verdict**: wiki extends
- **Note**: The open question of the review is the subject of the release-mechanism chapter (2017–2025): a drug-specific limit of congruency, one loading step above which release falls by one to three orders of magnitude, set by drug–polymer hydrogen bonding, wet Tg, surfactants and the drug–polymer–water phase diagram ([A F17](../../dissolution/a-release-mechanism-and-loc/findings.md#f17), [A F18](../../dissolution/a-release-mechanism-and-loc/findings.md#f18), [A F30](../../dissolution/a-release-mechanism-and-loc/findings.md#f30)).

### R42. The nanoparticles shed by low-loading felodipine ASDs are drug-rich (amorphous) species that coarsen and are stabilized by polymers
- **Review** [pp. 12–14]: the nanoparticles from low-loading felodipine ASDs indicate that the amorphous solubility was exceeded [44]; the "initially nano-sized drug-rich particles" grow and agglomerate, and polymers and surfactants reduce coalescence of "nanodroplets", citing the ritonavir study [40] together with the felodipine study [44].
- **Kind**: cited (Alonzo 2011; Ilevbare 2013)
- **Wiki**: [B F9](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f9): "90:10 HPMC–felodipine dispersions shed particles of ≈185 nm ... the authors conclude from spectra and birefringence at about 1 µm (not shown) that they "were indeed crystalline"".
- **Verdict**: differs
- **Note**: The wiki records the felodipine particles as crystalline by the authors' own (unshown) evidence, and by flux the 90:10 dispersion gave about the activity of amorphous felodipine (10.5 against 8.5 relative to crystal, [B F7](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f7)); which reading holds can only be settled from Alonzo et al. 2011 (J. Pharm. Sci. 100, 3316), the nature of the 185–300 nm particles.

### R43. Wetting is a prerequisite for ASD dissolution, aided by surfactants and small particle size
- **Review** [p. 13]: wetting of ASD particles precedes dissolution; surfactants improve the wetting of hydrophobic materials [91], and because intestinal surfactants are mainly in the small intestine the formulation's drug loading and excipients still matter; amorphous nanoparticles may dissolve better than larger amorphous particles [92].
- **Kind**: framework, cited (Luner 1996; Morgen 2011)
- **Wiki**: [A F35](../../dissolution/a-release-mechanism-and-loc/findings.md#f35): "On 75% grazoprevir–HPMCAS particles a secondary excipient helped release only when it made the particles wet".
- **Verdict**: wiki extends
- **Note**: The wiki has one direct test (hiew2025: FaSSIF contact angles of 0–52° went with about 37–52% release, 119–137° with about 8–20%). Amorphous polymeric nanoparticles [92] are not in the library.

### R44. Drug loading and the relative dissolution rates of drug and polymer control ASD release; at moderate to high loading release is drug-controlled
- **Review** [p. 13]: high-loading dispersions with hydrophilic polymers dissolve more slowly and are less likely to undergo LLPS [9,39,44]; in sulfathiazole–PVP the polymer dissolved faster than the drug, so the drug rate fell with time, more so at higher drug:polymer ratio [9]; faster polymer dissolution leaves a drug-enriched surface that dissolves slowly and may crystallize [93]; Corrigan proposed drug-controlled release at moderate to high loading and polymer-controlled release at low loading [94].
- **Kind**: cited (Simonelli 1969; Jackson 2016; Alonzo 2011; Qian 2012; Corrigan 1985)
- **Wiki**: [A F3](../../dissolution/a-release-mechanism-and-loc/findings.md#f3): "Above the switch the polymer leaves first and the drug dissolves near the rate of the neat amorphous drug"; [A F7](../../dissolution/a-release-mechanism-and-loc/findings.md#f7): "Above the limit the dissolving surface turned drug-rich and porous within minutes".
- **Verdict**: wiki extends
- **Note**: Same two regimes; the wiki shows the switch to be narrow (one 5% loading step, up to about 360-fold fall in drug rate) and drug-specific (5–30% in PVPVA for six drugs, 2018–2020) and shows crystals forming on such drug-rich surfaces ([Overview F10](../../overview/findings.md#f10)).

### R45. Water lowers the Tg of the wetted ASD; above physiological temperature mobility drives matrix crystallization unless the polymer inhibits it
- **Review** [p. 13]: water plasticizes the ASD; if the wet Tg is below physiological temperature, nucleation and growth in the amorphous phase speed up, and dissolution is greatly reduced unless the polymer inhibits matrix crystallization; amorphous nifedipine without polymer crystallized immediately in water with no supersaturation, whereas an HPMC formulation inhibited matrix crystallization and gave a supersaturated solution [98].
- **Kind**: cited (Hancock and Zografi 1994; Konno 2008; Rumondor 2010; Raina 2014)
- **Wiki**: [B F1](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f1): "Neat amorphous nifedipine crystallized inside the particles within minutes, with or without polymer in the buffer, whereas in 50:50 dispersions the particles stayed non-birefringent".
- **Verdict**: agrees
- **Note**: The wiki adds that polymer dissolved in the medium does not protect the wetted nifedipine or celecoxib solid while the same polymer inside the dispersion does ([B F2](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f2)), and that wetted felodipine at 37 °C was about 54% crystalline within 1 min.

### R46. Water induces amorphous–amorphous phase separation of ASDs, especially with PVP; it precedes crystallization and should be resisted to keep dissolution fast
- **Review** [p. 13]: water-enhanced mobility can split a miscible ASD into drug-rich and drug-lean domains [100]; PVP dispersions are particularly susceptible [100,103]; drug-rich regions crystallize more readily, so the separation is a precursor to crystallization; stronger interactions and less hygroscopic polymers resist it [104], which "is thought to be of importance for maintaining a high dissolution rate".
- **Kind**: cited (Purohit 2015; Rumondor 2009, 2011)
- **Wiki**: [Miscibility F12](../../solid-state-stability/miscibility-and-drug-polymer-interactions/findings.md#f12): "Sorbed water splits many initially mixed drug–PVP and drug–PVPVA dispersions, and occasionally an HPMCAS one, into a drug-rich and a polymer-rich amorphous phase before any crystals appear"; [Overview F9](../../overview/findings.md#f9): "a separation made before dissolution raised release in one system and lowered it in another".
- **Verdict**: wiki extends
- **Note**: The wiki confirms PVP > PVPVA > HPMCAS ([Miscibility F23](../../solid-state-stability/miscibility-and-drug-polymer-interactions/findings.md#f23)) and that humid storage removed nanodroplets and congruent release of PVP and PVPVA films without crystals ([A F12](../../dissolution/a-release-mechanism-and-loc/findings.md#f12)), but it also has a counterexample to the dissolution expectation: water-separated lopinavir–HPMC films released faster than miscible ones [li2019 R2].

### R47. Crystallization from the supersaturated solution removes the ASD benefit unless an inhibitor polymer is present; with an effective inhibitor the concentration rises to LLPS, after which more dissolution adds only drug-rich phase
- **Review** [p. 13]: crystals forming within the absorption time deplete supersaturation, and although small recrystallized particles may still help, the ASD benefit is mostly lost; felodipine–PVP dispersions gave high but short-lived supersaturation [44]; effective crystallization inhibitors are essential [44,105]; with them the concentration rises until spinodal decomposition to two liquid phases, the highest possible activity, and further dissolution increases only the amount of drug-rich phase.
- **Kind**: cited (Alonzo 2010, 2011)
- **Wiki**: [B F4](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f4): amorphous felodipine "peaked at ≈7.3 µg/mL with PVP and lost most of it within an hour, while HPMC and HPMC-AS held it above 7 and 10 µg/mL for 4 h"; [Dissolution F1](../../dissolution/findings.md#f1): "the free drug levels off at the amorphous solubility, and drug beyond it forms a drug-rich colloid".
- **Verdict**: agrees
- **Note**: Same sequence; the wiki adds that which polymer holds supersaturation best depends on the drug (PVP held indomethacin, did nothing for ritonavir) ([B F4](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f4)).

### R48. Transfer of drug from undissolved dosage form or crystals into the central compartment is much slower than from droplets or micelles, making dissolution rate-limiting
- **Review** [p. 13]: only a small fraction of a high-dose-number drug is in the central compartment at any time; transfer from undissolved solid or crystalline drug is expected to be much slower [58], so dissolution becomes rate-limiting and absorption is reduced.
- **Kind**: interpretation, cited (Hsieh 2012)
- **Wiki**: [Bioperformance F5](../../bioperformance/bioperformance/findings.md#f5): "7.5 mg/mL of 150–250 µm amorphous particles gave no plateau"; [dissolution-rate-limited absorption](../../concepts/dissolution-rate-limited-absorption.md): "LLPS is expected to remove such a limit because droplets equilibrate quickly".
- **Verdict**: wiki extends
- **Note**: The wiki holds a direct comparison (Indulkar 2016): coarse amorphous particles at a large excess did not sustain flux, whereas nanodroplets did; the micelle part of the claim is treated in R39.

### R49. Drug-rich nanodroplets coarsen and agglomerate, their interfaces may favour heterogeneous nucleation, and excipients that inhibit crystallization and keep droplets small are critical
- **Review** [pp. 13–14]: nanodroplets formed by spinodal decomposition grow to reduce surface area and may agglomerate, reducing the area for mass transfer; their interfaces provide sites for heterogeneous nucleation; surfactants and polymers reduce coalescence [40,44], certain polymers also stabilize against crystallization [40], surfactants may inhibit or promote crystallization [40,48,106]; excipients that prevent crystallization and maintain nanodroplets are expected to be critical.
- **Kind**: interpretation, cited (Ilevbare 2013; Alonzo 2011; Chen 2015)
- **Wiki**: [B F13](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f13): "Ritonavir crystallization appeared to start in the drug-rich droplets"; [Dissolution F5](../../dissolution/findings.md#f5): "crystallization came sooner with them present, and keeping droplets small did not by itself delay crystallization".
- **Verdict**: wiki extends
- **Note**: The wiki supports each part (ritonavir induction time about 284 min just below against about 120 min just above the LLPS concentration; ibuprofen droplets lost by creaming) and adds that droplet size and inhibition are separate properties: Tween 80 and several cellulose ethers kept ritonavir droplets at 178–395 nm yet shortened the induction time ([B F12](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f12)).

### R50. For low-permeability (BCS IV) drugs membrane diffusion is rate-determining and activity matters less; for high-permeability (BCS II) drugs raising activity by supersaturation is advantageous
- **Review** [p. 14]: flux is set by the donor activity for artificial and intestinal membranes alike; for BCS class IV compounds slow permeation is likely rate-determining, so activity "may not be the most critical parameter"; for BCS class II compounds a higher activity via supersaturation drives transport.
- **Kind**: interpretation
- **Wiki**: none
- **Verdict**: wiki silent
- **Note**: The wiki's flux and absorption evidence concerns high-permeability drugs (enzalutamide is called BCS class II [wilson2018]); no finding states how the activity argument changes for low-permeability drugs.

### R51. When drug is removed by absorption as fast as it enters by dissolution, the activity in the central compartment is markedly lower than in a closed vessel
- **Review** [pp. 14, 16–18, Fig. 18]: the rate of removal may be high relative to the rate of entry, so absorption can be fully dissolution-rate-limited, which a reservoir with a low barrier overcomes; in the Case 3 simulation the activity reached about 0.29 with absorption against near 1 without.
- **Kind**: interpretation (simulation)
- **Wiki**: [Bioperformance F14](../../bioperformance/bioperformance/findings.md#f14): "A closed vessel overstates how much supersaturation persists and, for a slowly crystallizing solution, the risk of crystallization; with an absorptive sink, slow-releasing dispersions also release more".
- **Verdict**: wiki extends
- **Note**: The wiki has measurements in place of the review's simulation: a nevirapine donor at about 525 µg/mL in a closed vessel fell to about 253 µg/mL with absorption, and 50% atazanavir ASDs released more with a sink [hate2017 R15, R7; hate2018 R18].

### R52. Drug-rich nanodroplets keep the activity, and the flux, at their maximum until they are consumed (clotrimazole)
- **Review** [pp. 14–15, Figs. 13–14]: ideally the activity is held at the amorphous solubility until the dose is absorbed; nanodroplets equilibrate fast because they are pre-wetted and have high specific surface; for clotrimazole (amorphous solubility 7.5 µg/mL) the maximum flux was proportional to donor concentration at 0.5–7 µg/mL and declined with time, whereas above 7.5 µg/mL 200–250 nm droplets, increasing in number with concentration, held the flux at its maximum for a time that roughly correlated with the excess [107].
- **Kind**: cited (Indulkar 2016)
- **Wiki**: [Bioperformance F5](../../bioperformance/bioperformance/findings.md#f5): "donors above it held the peak for about 1.5 h (10 µg/mL), 5 h (15 µg/mL) and at least 13 h (20 µg/mL, 16 h run)" (the 1.5 h was corrected to 1 h on 2026-11-04).
- **Verdict**: wiki extends
- **Note**: Same experiment; the wiki adds coarse amorphous particles that gave no plateau, the atazanavir hollow-fibre and PAMPA results, and the rat enzalutamide trend, and grades the evidence moderate because replicates are not stated and the depletion times do not match a mass balance [indulkar2016 K2, K3, X3].

### R53. Absorption simulations: fast LLPS with stable droplets gives near-complete absorption, crystallization or slow dissolution much less, and a 4 h window cuts all cases
- **Review** [pp. 15–18, Figs. 15–19, Table 1]: assuming crystalline and amorphous solubilities of 1 and 10 µg/mL, a 5 mg dose, a 100 mL central compartment [109] and high permeability, the fraction absorbed at 8 h is 100% (Case 1, stable LLPS; 96% at 6 h), 23% (2a, rapid crystallization), 46% (2b, recrystallized solid at 3 µg/mL), 71% (2c, delayed crystallization), 30% (3, slow ASD dissolution without LLPS) and 13% (4, crystalline suspension); at 4 h the values are 65, 17, 27, 52, 11 and 6%.
- **Kind**: direct claim (simulation)
- **Wiki**: none
- **Verdict**: wiki silent
- **Note**: The wiki's only absorption model is a GastroPlus bioequivalence simulation of partly crystalline tacrolimus ([Bioperformance F17](../../bioperformance/bioperformance/findings.md#f17)); no finding compares LLPS, crystallization and dissolution scenarios or the effect of residence time.

### R54. "Spring and plateau", not "spring and parachute", should be the goal of every enabling formulation with a high dose number
- **Review** [pp. 15–16, 18]: "spring" is fast dissolution to the LLPS/GLPS concentration, the thermodynamic limit, and "plateau" its maintenance by replenishment from the drug-rich phase with crystallization inhibited; the authors "believe that this should be the goal of every enabling formulation with high dose number", rather than the "spring and parachute" profile of Case 2c [76].
- **Kind**: interpretation (Brouwers 2009 for "spring and parachute")
- **Wiki**: none
- **Verdict**: wiki silent
- **Note**: Neither term appears in the wiki; the nearest evidence is the rat enzalutamide result in which ASDs that reached the amorphous solubility beat the crystalline control ([Bioperformance F23](../../bioperformance/bioperformance/findings.md#f23)).

### R55. Fasted and fed states, gastric pH and gastric residence change the processes, and enteric and neutral polymers behave differently in the stomach
- **Review** [p. 18]: gastric pH and residence time differ between fasted and fed states; low gastric pH favours dissolution of bases and disfavours acids; enteric polymers (HPMCAS, Eudragit L 100-55) do not dissolve in the stomach, neutral (PVP, HPMC) and cationic (Eudragit E PO) polymers begin to; all dosage forms take up water in the stomach.
- **Kind**: framework
- **Wiki**: [Dissolution F11](../../dissolution/findings.md#f11): "In a gastric-to-intestinal sequence what forms before the pH rise decides the outcome"; "In acid, where the enteric polymer stays undissolved, posaconazole–HPMCAS and delamanid dispersions crystallized while the medium was subsaturated".
- **Verdict**: wiki extends
- **Note**: The wiki adds that crystals formed in an undissolved enteric matrix cut later release, that an enteric coat prevented this, and that a pretomanid HPMCAS-HF ASD lost exposure with food in monkeys (72% of fasted) while the crystalline product rose ([Bioperformance F26](../../bioperformance/bioperformance/findings.md#f26)).

## 5. Concluding remarks

### R56. Future work should assess supersaturation accurately in complex media and connect the in vitro activity and reservoir findings to in vivo performance
- **Review** [p. 19]: efforts should be directed toward accurate assessment of supersaturation in complex media and toward connecting the in vitro observations on solute activity and the reservoir effect to in vivo performance.
- **Kind**: interpretation
- **Wiki**: [Overview F14](../../overview/findings.md#f14): "the library holds exposure data for three drugs in animals and none for a dispersion in humans".
- **Verdict**: wiki extends
- **Note**: The first aim was met in the wiki's later papers (flux-based supersaturation in pooled human intestinal fluid, Elkhabaz 2019); the second remains thin, with animal data for enzalutamide, pretomanid and tacrolimus only.

## Wiki statements the review would correct or qualify

Applied on 2026-11-04 with the user's agreement; the quotes below are the wording before that date. See `review/corrections_review.html`.

- [amorphous solubility advantage](../../concepts/amorphous-solubility-advantage.md) — "It is not retained when additives raise crystalline solubility more than the LLPS concentration [raina2015c C29]." — The review (p. 11) states from the same data that only the concentration ratio falls (~9 to ~4.5 with TPGS) while the maximum flux is unchanged, so the advantage is retained on an activity basis; the sentence should name the concentration-based ratio (the same page says so later for posaconazole).
- [nanodroplet reservoir effect](../../concepts/nanodroplet-reservoir-effect.md) — "In the papers of 2013–2016 it is argued from the flux plateau and from earlier work, not tested: no experiment depleted the dissolved drug and followed resupply" — The review (pp. 14–15) presents the 2016 clotrimazole flow-through study as a direct demonstration of sustained maximum flux, and the same page lists those 2016 data under Bioperformance; the sentence holds only for the papers of the amorphous solubility chapter.
- [solid-liquid equilibrium solubility equation](../../formulas/solid-liquid-equilibrium-solubility-equation.md) and [water-sorption correction](../../formulas/amorphous-solubility-advantage-with-water-sorption-correction.md) — "$\ln x_{C,L_1} = -\frac{\Delta G_{a\to c}}{RT} - \ln\gamma_{L_1}$ [ilevbare2013a E3]" and "$\exp\left(\frac{\Delta G_{a \to c}}{RT}\right)$" — The review writes the same relations with an explicit sign, $\mu_D^{(c)} - \mu_D^{0(a)}$ (negative) in Eqs. 2 and 6 and $\Delta G_{c\to a}$ in Eq. 11; the wiki forms hold only if $\Delta G_{a\to c}$ is read as a positive magnitude, which the pages do not state (they flag an unstated sign only for indulkar2016).
- [supersaturation](../../concepts/supersaturation.md) — "the highest supersaturation a solution can hold without crystals is set by the amorphous solubility" — The review (p. 10) qualifies this: strictly the spinodal point is the upper limit, the amorphous solubility (binodal) being the level after phase separation; the difference is small where binodal and spinodal lie close (ritonavir).

## Topics of the review that the wiki does not cover

- Absorption simulations of LLPS, crystallization and dissolution scenarios and the "spring and plateau" against "spring and parachute" goal — pp. 15–18 — the review's main design recommendation for enabling formulations has no counterpart in the wiki.
- Effect of the absorption window or residence time (8 h against 4 h, Table 1) — pp. 2, 18 — a shorter window cut absorption in every simulated case, which bears on how long supersaturation must be held.
- BCS class II against class IV: when membrane permeability, not activity, limits absorption — p. 14 — sets the drugs for which supersaturating formulations are worth developing.
- Amorphous-to-crystalline solubility ratio as a predictor of bioavailability gain and a lead-optimization parameter — pp. 8, 10 — a decision rule for whether an amorphous formulation is worth pursuing.
- Lipid formulation digestion and prodrug conversion as routes to a drug-rich phase — p. 10 — extends the activity ceiling to formulations other than ASDs and salts.
- Disintegration against erosion of ASD dosage forms by polymer type (copovidone and HPMC erode, HPMCAS can disintegrate) — p. 12 — a tablet-design factor for ASD release.
- A large aqueous crystallization classification of about 50 drugs (Van Eerdenbrugh 2014) — p. 6 — would anchor the fast/slow-crystallizer split in solution.
- The micellar solubilization equations $K_m = C_m/C_w$ and $S_{tot} = S_w + K_m S_w$ as a formula page — p. 11 — the Bioperformance index already links a "micelle–water partition coefficient" formula page that exists only as an unmerged draft.
- Amorphous polymeric nanoparticles for faster dissolution (Morgen 2011) — p. 13 — a particle-size route for amorphous formulations.