---
review: 2024-ueda-amorphous-solubility-advantage
title: "Amorphous Solubility Advantage: Theoretical Considerations, Experimental Methods, and Contemporary Relevance"
authors: "Keisuke Ueda, Dana E. Moseson, Lynne S. Taylor"
year: 2024
journal: "Journal of Pharmaceutical Sciences"
doi: "10.1016/j.xphs.2024.08.029"
pages: 71
---
# Amorphous Solubility Advantage: Theoretical Considerations, Experimental Methods, and Contemporary Relevance

**Scope.** This journal pre-proof (received 12 July 2024, accepted 26 August 2024) reviews the history, theory, measurement and practical use of the amorphous solubility, with free-energy and water-sorption equations for the additive-free drug and methods for measuring amorphous solubility and maximum activity. Its organising idea is the difference between a measured concentration and its thermodynamic consequence, set out as three cases of additive action (complex formation in water, distribution into the drug-rich phase, or both). Page numbers below are PDF pages, one above the printed "Page N of 70".

**Summary of the check.** The wiki matches the review on most individual facts: the amorphous solubility as the ceiling, the water correction, the fall of the concentration ratio against a constant flux ratio in micellar media, and polymer mixing lowering the ceiling. It holds later and more specific evidence on 23 points, notably boundary-layer-limited transfer above the amorphous solubility and row-by-row prediction tables. Four claims differ: the size of amorphous precipitates (R12), the ionization correction under buffer (R35), taurocholate as purely Case I (R49) and the crystalline solubility of tacrolimus behind the dose number (R69); all four need a research paper to settle. The main gap is structural: the wiki does not have the Case I/II/III classification with its equations, so its statements about $S_c$, $S_a$, the ratio and SRmax are given system by system, and some general sentences hold for Case I only. Further gaps are dose number, PGSE-NMR, cyclodextrins, ketoprofen, the Fig. 5c construction and PBBM use of amorphous solubility.

**Counts.** agrees 22 · wiki narrower 12 · wiki extends 23 · differs 4 · wiki silent 9

## 1. Introduction

### R1. Many routes create supersaturation, and the amorphous solubility limits all of them
- **Review** [pp. 8–9, Fig. 1]: Supersaturation can arise during gastrointestinal transit from salts, cocrystals, polymorphs and prodrugs, from formulations solubilized with cosolvents, surfactants, lipids or cyclodextrins, from amorphous content formed by process-induced disorder, moisture or salt disproportionation, and from hydration-induced disorder or a pH or solvent shift. The maximum extent of supersaturation (maximum thermodynamic activity) is limited by the amorphous solubility.
- **Kind**: framework
- **Wiki**: [Overview F1](../../overview/findings.md#f1) "The amorphous solubility is the reference of every category"; [Bioperformance F29](../../bioperformance/bioperformance/findings.md#f29) "Absorption is proportional to supersaturation"
- **Verdict**: wiki narrower
- **Note**: The wiki states the ceiling for solvent shift, pH shift and dissolving dispersions. Prodrug conversion, cosolvent and lipid formulations and hydration-induced disorder are not treated as routes to the same limit.

### R2. Early solubility screening by anti-solvent addition may measure the amorphous form
- **Review** [p. 9]: Adding dissolved drug to water or solvent during early solubility screening may give an amorphous rather than a crystalline precipitate, and the value measured may then be the solubility of the amorphous form.
- **Kind**: cited (Alsenz and Kansy)
- **Wiki**: none
- **Verdict**: wiki silent
- **Note**: No wiki statement warns that a discovery kinetic solubility may be an amorphous solubility. This affects how discovery solubility data are read when choosing an enabling formulation.

### R3. Predicted advantages of amorphous forms and of polymorphs have different magnitudes
- **Review** [p. 8]: From the thermal properties of several compounds, Hancock and Parks estimated an amorphous solubility advantage of 12–1652 fold and a predicted advantage for crystalline polymorphs of 1.1–3.6 fold. Experimental indomethacin values under-estimated the advantage because of recrystallization.
- **Kind**: cited (Hancock and Parks 2000)
- **Wiki**: none for these ranges
- **Verdict**: wiki silent
- **Note**: The wiki gives measured ratios only, and neither predicted range is present. The 1652-fold upper value is from the free-energy calculation without the water correction and exceeds the "most drugs less than 100-fold" of p. 27 (R34).

## 2.1 Milestones toward characterization and prediction of amorphous solubility

### R4. Early amorphous/crystalline ratios agreed with dissolution rate and absorption ratios
- **Review** [pp. 11–13]: Novobiocin amorphous solubility was about ten-fold above the crystalline free acid, the crystalline form was not absorbed and the amorphous form was, and the amorphous solid probably formed by pH-induced LLPS; methylcellulose delayed and surfactants increased crystallization. Sulfathiazole gave a ratio of 3.8 at 37°C against an initial dissolution-rate ratio of 3.7. For 1:5 reserpine–PVP the rate ratio was ~2.5, the solubility ratio ~3, and in rats the rate and extent of absorption ~2.7 and ~3.2 fold. β-Carotene–PVP gave spherical colloids of approximately 100 nm.
- **Kind**: cited (Mullins and Macek 1960; Tachibana and Nakamura 1965; Simonelli 1969, 1976; Stupak 1974)
- **Wiki**: [Release mechanism F2](../../dissolution/a-release-mechanism-and-loc/findings.md#f2) "Simonelli and co-workers (1969, cited) described polymer-controlled release of sulfathiazole–PVP at very low loading"
- **Verdict**: wiki silent
- **Note**: The wiki cites Simonelli for a different point, polymer control at low loading. The review uses high-loading coprecipitates to infer that amorphous drug controlled release; the historical ratios are not in the wiki.

### R5. Predictions need water and ionization corrections, and kinetic values fall below them through recrystallization
- **Review** [p. 13]: Murdande and coworkers added water absorption by the amorphous solid, a possible correction for different extents of ionization, and better heat capacity measurements. Predictions largely exceeded kinetic solubility values because the dissolving solid recrystallized, and the match improved when dissolved polymer delayed crystallization.
- **Kind**: cited (Murdande 2010)
- **Wiki**: [amorphous solubility advantage](../../concepts/amorphous-solubility-advantage.md) "because the solid or the solution crystallizes"; [water sorption correction](../../concepts/water-sorption-correction-of-amorphous-solubility.md) "water dilutes the amorphous drug, and lowers the predicted amorphous solubility"
- **Verdict**: agrees
- **Note**: The same explanation is given for the same observation. The ionization term is taken up separately in R35.

### R6. Onset of scattering locates the amorphous solubility
- **Review** [pp. 13–14]: Lindfors 2006 added stabilized amorphous nanoparticle suspension to water and took the concentration at which scattering disappeared as the amorphous solubility, in good agreement with theory. This is the basis of the UV and fluorescence onset methods.
- **Kind**: cited (Lindfors 2006)
- **Wiki**: [Amorphous solubility F4](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f4) "locate the same onset within a few µg/mL, but absorbance alone and scattering alone can mislead"
- **Verdict**: wiki extends
- **Note**: The wiki compares several onset methods on the same solutions (Ilevbare 2013, Trasi 2015, Almeida e Sousa 2015 and later) and adds how each one fails. It does not cite the 2006 method, which approached the boundary from the dissolving side.

### R7. PC-SAFT has been applied to calculate the advantage
- **Review** [p. 14]: Paus and coworkers (2015) applied PC-SAFT to calculate the amorphous solubility advantage; modelling matters because the measurement is difficult for some compounds.
- **Kind**: cited (Paus 2015)
- **Wiki**: [Release mechanism F30](../../dissolution/a-release-mechanism-and-loc/findings.md#f30) "Measured drug–PVPVA–water phase diagrams placed the limit of congruency near the critical point"
- **Verdict**: wiki silent
- **Note**: PC-SAFT appears in the wiki only behind drug–polymer–water phase diagrams for release, not as a route to the advantage.

## 2.2 Discovery and significance of liquid-liquid phase separation

### R8. LLPS gives two metastable phases in equilibrium with each other
- **Review** [p. 14]: LLPS produces solute-rich and solvent-rich phases; below the melting point it does not give the most stable form, the solute has the same chemical potential in both phases, and because both are metastable crystallization will eventually occur if a crystalline form exists. Precipitation should be defined by the structure of the precipitate.
- **Kind**: cited (Bonnett 2003) and framework
- **Wiki**: [thermodynamic activity](../../concepts/thermodynamic-activity.md) "at phase equilibrium it is equal in all phases"; [Amorphous solubility F3](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f3) "The drug-rich phase is a transient precursor of crystals"
- **Verdict**: agrees
- **Note**: Same statement under the same conditions.

### R9. The onset does not depend on the route and is the highest attainable concentration
- **Review** [p. 15]: For ritonavir, cooling, antisolvent addition and ASD dissolution gave LLPS at the same concentration, which matched the predicted amorphous solubility and the maximum from dissolving the neat amorphous drug. Phase separation was inevitable when this supersaturation was exceeded.
- **Kind**: cited (Ilevbare and Taylor 2013)
- **Wiki**: [Amorphous solubility F13](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f13) "reaches, but does not exceed, the same limit when crystallization is slow enough"
- **Verdict**: agrees
- **Note**: Same finding and same reading.

### R10. LLPS may explain promiscuous aggregation, and small aggregates were linked to good absorption
- **Review** [p. 15]: LLPS was identified as likely responsible for promiscuous aggregation in high-throughput screening. In a survey of non-nucleoside reverse transcriptase inhibitors, good absorption depended on aggregate size (<100 nm), which the review calls speculation.
- **Kind**: cited (Ilevbare and Taylor 2013; Shoichet; Frankel 2005, as printed)
- **Wiki**: [Amorphous solubility F1](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f1) "close to 20% of nearly 300 screened compounds formed aggregates"
- **Verdict**: wiki narrower
- **Note**: The link to aggregation is present, whereas the <100 nm absorption correlation is not.

### R11. Drug-rich species raise boundary-layer permeability by particle drifting
- **Review** [pp. 15–16]: It has been suggested that drug-rich species improve aqueous boundary layer permeability of highly membrane-permeable drugs through a particle drifting effect, reducing the concentration gradient across the layer so that the concentration at the membrane surface approaches the maximum set by the amorphous solubility.
- **Kind**: interpretation (cited: refs 45–49)
- **Wiki**: [Bioperformance F15](../../bioperformance/bioperformance/findings.md#f15) "Brownian-motion-induced nanoscale convection in the laminar boundary layer"; [Bioperformance F22](../../bioperformance/bioperformance/findings.md#f22) "the mass flow keeps rising with the number of nanodroplets"
- **Verdict**: wiki narrower
- **Note**: The wiki reports the rise in transfer (Hate 2018, 2022) and lists untested mechanisms, without naming particle drifting. The review cites Hate 2022 (ref 46) for the effect beside Narula, Stewart and Yoshikawa (refs 45, 47, 48), so the mechanism can be added once those papers are read.

### R12. The size of amorphous precipitates is called of paramount importance
- **Review** [p. 17; repeated p. 53]: For amorphous precipitates, size is of paramount importance because it influences redissolution kinetics and particle drifting, which may in turn affect boundary layer permeability.
- **Kind**: interpretation
- **Wiki**: [Bioperformance F22](../../bioperformance/bioperformance/findings.md#f22) "droplets of about 1000 nm gave the same as droplets of about 280 nm"
- **Verdict**: differs
- **Note**: In the wiki PAMPA sink result droplet size between about 280 and 1000 nm did not change transfer, whereas the review makes size decisive. The review's size statement cites refs 42, 43 and 45, and Hate 2022 is in its particle drifting list (ref 46), so the two are from different systems and setups. Settle by reading the size claim of Hate 2022 against refs 42, 43 and 45; the wiki result is the only direct size comparison available here.

### R13. In situ generation gives good agreement between predicted and measured amorphous solubility
- **Review** [p. 16, Fig. 3]: Generating hydrated amorphous material in situ via LLPS avoids many crystallization problems; predicted and measured values agree well for many drugs (Fig. 3, 23 compounds, axes to 400 µg/mL, reference line of slope 1).
- **Kind**: direct claim (figure reproduced from Taylor and Zhang 2016)
- **Wiki**: [Amorphous solubility 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"
- **Verdict**: wiki extends
- **Note**: The wiki (Ilevbare 2013 to Ueda 2022) tabulates the agreement row by row and notes that some 2013 predictions cannot be recomputed from the printed inputs. It adds outliers that the plot does not resolve, such as telaprevir with the Hoffman free energy.

### R14. LLPS keeps the system supersaturated, crystallization depletes it, and the attributes of each precipitate matter
- **Review** [pp. 16–17]: After LLPS the system remains highly supersaturated, whereas crystallization depletes supersaturation, so the phase transition should be characterized. For crystalline precipitates, crystallite size, surface area, disorder, polymorphic form and residual supersaturation affect crystal growth, consumption of supersaturation and subsequent absorption.
- **Kind**: framework
- **Wiki**: [Solution methods F3](../../characterization-methods/solution-methods/findings.md#f3) "The same measurement cannot tell liquid from crystal"; [Supersaturation from ASD F22](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f22) "a reason to revise PBPK models that assume a return to the crystalline solubility"
- **Verdict**: wiki extends
- **Note**: The wiki adds Que 2018 (crystalline seeds and residual supersaturation) and a tacrolimus capsule that crystallized in storage yet still gave higher exposure than reference crystals (Purohit 2019, Bioperformance F30).

### R15. Maximum membrane flux coincides with the amorphous solubility
- **Review** [p. 17]: Maximum achievable flux across a cellulose acetate membrane coincided with supersaturated solution concentrations at or above the amorphous solubility, confirming that maximum thermodynamic activity corresponds to the amorphous solubility concentration.
- **Kind**: cited (Raina 2014)
- **Wiki**: [Bioperformance F2](../../bioperformance/bioperformance/findings.md#f2) "flux rises with donor concentration up to about the concentration of the second phase and then stays at a plateau"; [Bioperformance F15](../../bioperformance/bioperformance/findings.md#f15) "keeps rising above the amorphous solubility, at a lower slope"
- **Verdict**: wiki extends
- **Note**: The wiki keeps the plateau for membrane-limited cells and adds that with a boundary-layer-limited module (hollow fibre, Hate 2018) transfer keeps rising. The review's sentence holds for membrane-limited transport only, which it states later at p. 51.

## 2.3 Investigations of media and formulation impact on amorphous solubility

### R16. Amorphous solubility of weak bases follows Henderson–Hasselbalch in simple buffer
- **Review** [p. 17]: Amorphous solubility concentrations appear to follow the Henderson–Hasselbalch equation for weakly basic drugs in a simple buffered solution, provided the amorphous solubility of the free form is known.
- **Kind**: cited (Indulkar 2015)
- **Wiki**: [Amorphous solubility F10](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f10) "amorphous values at pH 5 and 5.5 lay below the Henderson–Hasselbalch curve"
- **Verdict**: wiki extends
- **Note**: The wiki confirms the rule and adds deviations in later work on pazopanib (Sugihara 2018: 60 against about 250 µg/mL at pH 5, 40 against about 80 at pH 5.5). It should be read with the qualification on "simple buffered solution".

### R17. Membrane transport follows activity at the membrane, not total concentration
- **Review** [pp. 17–18]: Solubilizing additives altered amorphous solubility and hence transport, showing that membrane transport is driven by solute activity at the membrane surface and not by total concentration (also Higuchi, and the transdermal literature).
- **Kind**: cited (Raina 2015; Higuchi)
- **Wiki**: [Bioperformance F3](../../bioperformance/bioperformance/findings.md#f3) "the concentration ratio does not track the driving force"
- **Verdict**: agrees
- **Note**: Same statement. The review calls this difference between concentration and its thermodynamic consequence a central theme.

### R18. Solubilization at the amorphous solubility depends on the bile salt and on supersaturation
- **Review** [p. 18]: Dihydroxy bile salts modulate amorphous solubility and transport of telaprevir through solubilization, whereas trihydroxy salts (sodium taurocholate, sodium glycocholate) had minimal impact. With SDS the extent of solubilization depended on the degree of supersaturation, so that the amorphous solubility changed in a complex way.
- **Kind**: cited (Lu 2017; Indulkar 2017)
- **Wiki**: [Amorphous solubility F17](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f17) "trihydroxy salts do little"; [Amorphous solubility F18](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f18) "because the micelle/water partition coefficient falls with drug concentration"
- **Verdict**: agrees
- **Note**: Same systems and same reading in both cases.

### R19. Concentration ratios under-report the advantage in complex media, whereas flux ratios stay constant
- **Review** [pp. 18–19, Fig. 4]: Concentration-based and activity-based ratios were compared in biorelevant media and human intestinal fluid. In Fig. 4 the membrane flux ratio is about 50–56 throughout, whereas the concentration ratio is about 14 in FaHIF, 32 in Composite FaSSIF, 38–39 in FaSSIF V1 and V2 and 55–57 in buffers.
- **Kind**: cited (Elkhabaz 2019)
- **Wiki**: [Bioperformance F18](../../bioperformance/bioperformance/findings.md#f18) "about 50–56 in all six media"
- **Verdict**: agrees
- **Note**: The values match for atazanavir. The wiki also gives posaconazole, which the figure in the review does not show. Values read from the figure are approximate.

### R20. A second component can lower or raise the apparent amorphous solubility
- **Review** [p. 19]: Increasing miglyol decreased amorphous solubility, and a second poorly water-soluble drug lowered the maximum supersaturation of the first and vice versa. For ibuprofen, an ASD polymer that mixed with the colloidal phase decreased amorphous solubility, and one that solubilized the bulk phase increased it.
- **Kind**: cited (Lindfors 2006; Trasi 2015; Ueda 2020)
- **Wiki**: [Overview F2](../../overview/findings.md#f2) "A component that mixes into the drug-rich phase lowers the ceiling in every system tested"; [Amorphous solubility F19](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f19) "without changing its crystalline solubility"
- **Verdict**: agrees
- **Note**: Same mechanisms. Miglyol is not named in the wiki, but the mixing statement covers it.

### R21. HPMCAS grade decides whether the amorphous solubility falls
- **Review** [pp. 19–20]: With four model drugs, HPMCAS-HF substantially reduced amorphous solubility by distributing into the drug-rich colloidal phase, while HPMCAS-LF had limited impact.
- **Kind**: cited (Ueda 2020)
- **Wiki**: [Bioperformance F19](../../bioperformance/bioperformance/findings.md#f19) "whereas AS-LF changes it by under a tenth"
- **Verdict**: agrees
- **Note**: The wiki gives numbers, which the review omits in the text; the statement is the same.

### R22. Reductions in amorphous solubility change in vivo performance
- **Review** [pp. 20, 55]: Reductions in amorphous solubility attributed to polymer interactions have been shown to affect in vivo performance. For belinostat with three polymers (likely Case II), each amorphous solubility value in an in silico model predicted the absorption in dogs, and different dissolution rates were also considered likely to be critical.
- **Kind**: cited (Stewart 2019)
- **Wiki**: [Bioperformance F19](../../bioperformance/bioperformance/findings.md#f19) "with AS-HF there is less of it to cross the membrane"
- **Verdict**: wiki narrower
- **Note**: The wiki shows the fall in flux in vitro (Ueda 2020) but has no in vivo example that isolates a lower amorphous solubility, and belinostat is absent.

### R23. Surfactants can partition into the droplets, act at their surface or solubilize drug in the bulk
- **Review** [p. 20]: Surfactants can partition into the drug-rich colloidal phase, interact with the nanodroplet surface and/or solubilize drug in the bulk phase, increasing or decreasing amorphous solubility or changing colloidal stability.
- **Kind**: cited (Ueda surfactant papers, refs 66, 67)
- **Wiki**: [surfactant partitioning](../../concepts/surfactant-partitioning-into-the-drug-rich-phase.md) "non-ionic surfactants partition into the clopidogrel-rich phase while ionic ones act at the nanodroplet–water interface"
- **Verdict**: wiki extends
- **Note**: The wiki adds Correa-Soto 2022 for clopidogrel and the atazanavir–Span values (64 to 46 µg/mL). Ketoprofen, the review's main surfactant example, is absent (R46).

### R24. Cyclodextrins change the apparent amorphous and crystalline solubility differently
- **Review** [pp. 20, 33]: Cyclodextrin type had complex effects on apparent amorphous solubility, most notably with dimethyl-β-CD. Ibuprofen/β-CD shows a BS-type diagram: the apparent crystalline solubility plateaus at higher β-CD through the limited solubility of the complex crystal, the apparent amorphous solubility rises linearly, so the ratio becomes much larger, whereas SRmax stays constant.
- **Kind**: cited (Ueda CD paper, ref 68)
- **Wiki**: none on these solubilities
- **Verdict**: wiki silent
- **Note**: The wiki mentions cyclodextrin only in flux data from Raina 2015. A cyclodextrin can thus give a large concentration ratio without any gain in activity, which matters where a cyclodextrin is a formulation candidate.

### R25. A dispersion does not necessarily deliver the full advantage
- **Review** [pp. 20, 48]: In ASDs drug–polymer interactions and drug loading may lower the drug chemical potential and suppress amorphous solubility, and in one ASD the amorphous drug solubility fell below the crystalline value. Amorphous–amorphous phase separation, slow dissolution, crystallization from the solid or insoluble drug–polymer complexes may prevent complete release.
- **Kind**: cited (Huang 2016; Li 2018)
- **Wiki**: [Supersaturation from ASD F18](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f18) "lowered the maximum lopinavir concentration below the amorphous solubility, most at low drug loading and with HPMCP and EC"; [Supersaturation from ASD F11](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f11) "mixing with it lowers the chemical potential of the drug"
- **Verdict**: wiki extends
- **Note**: The wiki gives the conditions from Li 2018 and adds the polymer-dissolution dependence. Huang 2016 is not in the library, and the wiki's Li and Taylor passage is the matching evidence.

## 3.1 What is amorphous solubility?

### R26. Amorphous solubility is a metastable equilibrium with water-saturated amorphous drug
- **Review** [pp. 4, 21]: Crystal solubility requires equilibrium and confirmation that the residual solid is the stable crystal. If the transformation is slow or inhibited and the residual drug is still amorphous at metastable equilibrium, the value measured is the amorphous solubility. The free energy difference between anhydrous forms does not translate directly into the solubility difference, because amorphous drug takes up water and its chemical potential falls, whereas sorption by the crystal is typically negligible.
- **Kind**: framework
- **Wiki**: [amorphous solubility](../../concepts/amorphous-solubility.md) "more rigorously with the water-saturated supercooled liquid or glass"; [water sorption correction](../../concepts/water-sorption-correction-of-amorphous-solubility.md) "water dilutes the amorphous drug"
- **Verdict**: agrees
- **Note**: Same definition.

### R27. Both solubilities generally rise with temperature and their ratio falls
- **Review** [p. 22, Fig. 5b]: Crystal and amorphous solubility generally both increase with temperature, and the ratio is typically reduced, because the free energy difference between crystal and water-saturated amorphous form decreases and disappears at the melting point.
- **Kind**: framework
- **Wiki**: [Amorphous solubility F9](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f9) "the ritonavir limit fell from about 58 µg/mL at 10 °C to a minimum of about 37 near 35 °C and rose to about 53 at 65 °C"; [Amorphous solubility F6](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f6) "falling from 5.8 to 2.5 between 25 and 60 °C"
- **Verdict**: wiki extends
- **Note**: The wiki confirms the falling ratio with ibuprofen data and adds an exception to the "generally": the ritonavir amorphous limit is not monotonic with temperature (Ilevbare 2013, as carried in F9).

### R28. Water depresses the melting point, and the two solubility curves meet there
- **Review** [pp. 22, 24, Fig. 5c]: Water lowers the melting point of the crystal. The crystalline and amorphous solubilities converge at this depressed Tm; above it the crystal cannot exist and any measured solubility follows the LLPS boundary between liquid drug and water, and extending that boundary below Tm gives the amorphous solubility curve in the supercooled, metastable region.
- **Kind**: framework
- **Wiki**: none
- **Verdict**: wiki silent
- **Note**: The wiki has a ritonavir binodal in Amorphous solubility F3 but not this construction. It is needed to read measurements on low-melting drugs (R58).

### R29. Water-saturated supercooled liquid above wet-Tg, and an open question below it
- **Review** [pp. 22–23]: Above the wet-Tg the amorphous solubility is the concentration in the drug-lean phase in equilibrium with the water-saturated supercooled liquid. Below the wet-Tg the glass has a higher free energy and hence a higher expected solubility. It remains controversial which state the solubility reflects, and it is unclear whether the water-saturated glass stays glassy, in particular at the surface in contact with water. Extrapolating supercooled liquid properties works reasonably for some small molecules.
- **Kind**: framework and cited (Almeida e Sousa 2015, ref 31)
- **Wiki**: [Amorphous solubility F2](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f2) "the onset matched the supercooled-liquid prediction, not the glass prediction"
- **Verdict**: wiki extends
- **Note**: The wiki (Almeida e Sousa 2015, Ueda 2020, Yang 2021) adds drug-specific comparison and states when the separated phase is liquid or glassy from its water-plasticized Tg. The review keeps the question open, and the wiki's evidence favours the supercooled liquid in the systems tested.

## 3.2 Amorphous solubility in the absence of additives

### R30. The calculated ratio serves as a check on measurements and a benchmark in release testing
- **Review** [pp. 25, 27]: The theoretical value shows whether a supersaturating strategy can give a high gain, which matters when absorption is solubility limited and a faster dissolution rate alone does not help; comparison with it confirms that an experiment is not confounded by other components or crystallization. The ratio benchmarks formulation performance and helps to detect LLPS or crystallization during release testing.
- **Kind**: framework
- **Wiki**: [amorphous solubility advantage](../../concepts/amorphous-solubility-advantage.md) "the yardstick for what a dissolving amorphous solid or dispersion should reach"
- **Verdict**: agrees
- **Note**: Same use of the ratio. The check against confounding in an experiment is implicit in the wiki's predicted/measured table.

### R31. The additive-free ratio follows from the free energy difference
- **Review** [pp. 25–26]: Eq. 1, $S_a^0/S_c^0=e^{\Delta G_{c\to a}/RT}$, also applies to metastable polymorphs. $\Delta G_{c\to a}$ comes from the melting temperature and melting enthalpy, with the heat capacity difference assumed zero, assumed constant at its Tm value, or measured against temperature for improved predictions. The heat capacity method can also be used if the solubility follows the GLPS boundary.
- **Kind**: framework
- **Wiki**: [advantage from free energy difference](../../formulas/amorphous-solubility-advantage-from-free-energy-difference.md) "$\frac{S_A}{S_C} = \exp\left(\frac{\mu_A - \mu_C}{RT}\right)$"; [Amorphous solubility F7](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f7) "the Hoffman free energy overshoots the onset"
- **Verdict**: wiki extends
- **Note**: The wiki writes the same relationship in chemical potentials and adds drug-level comparison of the free energy estimates (Almeida e Sousa 2015, 2016; Indulkar 2017 for telaprevir and atazanavir). The polymorph use of Eq. 1 is not stated in the formula page.

### R32. Water absorption is corrected with the Gibbs–Duhem activity term
- **Review** [p. 26]: Eq. 2, $S_a^0/S_c^0=e^{-I(a_2)}\cdot e^{\Delta G_{c\to a}/RT}$, where $e^{-I(a_2)}$ is the activity of the water-saturated amorphous drug, estimated by applying Gibbs–Duhem to the water sorption isotherm.
- **Kind**: framework
- **Wiki**: [advantage with water sorption correction](../../formulas/amorphous-solubility-advantage-with-water-sorption-correction.md) "$\frac{S_a^{0}}{S_c^{0}} = e^{-I(a_2)}\,e^{\Delta G_{c\to a}/RT}$"
- **Verdict**: agrees
- **Note**: The same equation appears in the wiki as written by Ueda 2022. Two other wiki forms use a negative $\Delta G$ (see the last section).

### R33. The size of the water correction depends on the drug
- **Review** [pp. 26–27]: Eq. 1 and Eq. 2 give almost the same value for ibuprofen and tolnaftate, which absorb minimal water, whereas Eq. 2 reduces the value by 30–70% for telaprevir and griseofulvin.
- **Kind**: cited (Murdande; Almeida e Sousa)
- **Wiki**: [water sorption correction](../../concepts/water-sorption-correction-of-amorphous-solubility.md) "ibuprofen to griseofulvin | 0.999, 0.997, 0.985, 0.932, 0.750, 0.699"
- **Verdict**: wiki extends
- **Note**: The wiki has per-drug activity values in a table from Almeida e Sousa 2015 (ibuprofen 0.999 down to griseofulvin 0.699), and telaprevir, atazanavir and ritonavir at about 0.22–0.30 from other papers. Its griseofulvin value of 0.699 is a reduction of about 30%, at the low end of the review's range.

### R34. Free energy differences constrain most ratios to below 100-fold
- **Review** [p. 27]: $\Delta G_{c\to a}$ of most drugs is typically less than ~10 kJ/mol at ambient conditions; experimentally determined ratios of most drugs are less than 100-fold.
- **Kind**: direct claim
- **Wiki**: [Amorphous solubility F6](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f6) "the highest the authors' group had measured"
- **Verdict**: wiki extends
- **Note**: The wiki range runs from about 2 to about 600, the top value for pazopanib (Sugihara 2018), and its concept pages give Hoffman values above 10 kJ/mol for telaprevir (13.31) and atazanavir (14.55). These do not contradict "most" but mark the exceptions.

### R35. The ionization correction applies only without a buffer
- **Review** [pp. 27, 29]: Eq. 3, $S_a^0/S_c^0=\frac{(1-\bar\alpha^c)}{(1-\bar\alpha^a)}\cdot e^{-I(a_2)}\cdot e^{\Delta G_{c\to a}/RT}$, applies to ionizing drugs because the ionized fraction falls at the higher concentration of the amorphous form, which lowers the ratio. Eq. 3 is only relevant for unbuffered conditions; the additive sections assume unionized drug or a constant ionized fraction under buffer.
- **Kind**: framework (Murdande 2010)
- **Wiki**: [supersaturation ratio](../../concepts/supersaturation-ratio.md) "from 500–600 at pH 6.4–8.4 to about 103 at pH 5.0"; [supersaturation ratio](../../concepts/supersaturation-ratio.md) "The clotrimazole ratio is about 8 at pH 4–4.5"; [supersaturation ratio](../../concepts/supersaturation-ratio.md) "not affected by degree of ionization"
- **Verdict**: differs
- **Note**: A form with ionization terms is on the [water-sorption formula page](../../formulas/amorphous-solubility-advantage-with-water-sorption-correction.md) [raina2014a E4], so Eq. 3 is not absent from the wiki. The review's constant ionized fraction under buffer implies a ratio independent of pH, as does the Indulkar 2015 sentence quoted on the wiki page, whereas the same page reports buffered ratios that change with pH for pazopanib and clotrimazole. The measured ratios are the direct evidence; settle from Sugihara 2018 (pazopanib, amorphous values below the Henderson–Hasselbalch curve) and Indulkar 2015 (clotrimazole).

### R36. Supersaturation is an activity ratio and sets the expected absorption gain
- **Review** [pp. 27–28]: Eq. 4, $SR=a/a^*=\gamma c/(\gamma^* c^*)$. In dilute additive-free solution γ/γ* ~ 1, and the concentration ratio then gives SRmax; in media with micelles the assumption may fail. For solubility-limited absorption, supersaturation is directly related to the expected improvement through passive diffusion.
- **Kind**: framework
- **Wiki**: [activity-based supersaturation ratio](../../formulas/activity-based-supersaturation-ratio.md) "$SR = \frac{a}{a^{*}} = \frac{\gamma\,c}{\gamma^{*}\,c^{*}}$"; [Bioperformance F29](../../bioperformance/bioperformance/findings.md#f29) "Absorption is proportional to supersaturation"
- **Verdict**: agrees
- **Note**: The equation and its assumption are the same. Wiki F29 rests on one model, while the review states the relation generally.

## 3.3 Amorphous solubility in the presence of an additive (or second drug)

### R37. The effect of an additive falls into three cases
- **Review** [pp. 28–30, Table 1, Fig. 6]: Case I is formation of a drug/additive complex in the aqueous phase; Case II is distribution of a large amount of additive into the drug-rich phase; Case III is both. Table 1 lists the reported systems, including ATZ/SDS and IBP/EUD-E (I), LPV/RTV and ATZ/HPMCAS-HF (II), and KTP/CTAB and TPV/STCDC (III).
- **Kind**: framework
- **Wiki**: [Dissolution F12](../../dissolution/findings.md#f12) "Intestinal media act at three points with different signs"; [Overview F2](../../overview/findings.md#f2) "A component that mixes into the drug-rich phase lowers the ceiling in every system tested"
- **Verdict**: wiki narrower
- **Note**: The wiki holds the components of the scheme system by system, but it has no classification that predicts how $S_c$, $S_a$, the ratio and SRmax move together. This is the largest structural difference from the review.

### R38. Solubilization adds complexed drug to the free drug at the same activity
- **Review** [pp. 31–32]: With "complex" as an umbrella term for species formed by additive–drug interaction, Eq. 5 $S_a=S_a^0+S_af^a_{com}$, Eq. 6 $S_a=S_a^0/(1-f^a_{com})$, Eq. 7 $S_a/S_c=\frac{(1-f^c_{com})}{(1-f^a_{com})}\cdot e^{-I(a_2)}\cdot e^{\Delta G_{c\to a}/RT}$. Because $f_{com}$ generally falls as drug concentration rises, $S_a/S_c$ generally becomes smaller than $S_a^0/S_c^0$; if $f_{com}$ is constant, Eq. 7 becomes Eq. 2 (ibuprofen or ketoprofen in Eudragit E PO).
- **Kind**: framework
- **Wiki**: [thermodynamic activity](../../concepts/thermodynamic-activity.md) "the free atazanavir at the amorphous solubility was 65–70 µg/mL, the same as in buffer"; [Amorphous solubility F12](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f12) "the concentration ratio fell from about 65 to about 33"; [Amorphous solubility F19](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f19) "kept the ratio at 6.09"
- **Verdict**: wiki narrower
- **Note**: All the outcomes are present as examples, including both the falling and the constant ratio, but the equations with $f_{com}$ that join them are not.

### R39. In Case I SRmax is unchanged and larger than the apparent ratio
- **Review** [pp. 32–33]: Sc and Sa rise with additive concentration, while free drug at each limit is unchanged. Thus SRmax stays at the additive-free value and is generally larger than the apparent $S_a/S_c$, γ/γ* ~ 1 is not correct with a complexing agent, and the ratio does not reflect the driving force for crystallization or membrane transport.
- **Kind**: framework
- **Wiki**: [Amorphous solubility F16](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f16) "the flux-based activity ratio at the amorphous solubility is the same as without micelles"
- **Verdict**: agrees
- **Note**: The same statement for micellar media.

### R40. Additive distribution depends on chemical affinity and the entropy of mixing
- **Review** [p. 35]: Distribution of an additive depends on its relative affinity for each phase and on the entropy of mixing. Hydrophobic additives are more likely to distribute into the drug-rich phase, and hydrophilic additives with strong specific interactions may also be present in large amounts (HPMC, PVPVA, as well as HPMCAS).
- **Kind**: framework
- **Wiki**: [Amorphous solubility F21](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f21) "endothermic over most of the range and entropy-driven"; [Release mechanism F27](../../dissolution/a-release-mechanism-and-loc/findings.md#f27) "Drugs that hydrogen-bond to PVPVA carried it into their insoluble drug-rich phase"
- **Verdict**: wiki extends
- **Note**: The wiki supplies calorimetry on drug–polymer mixing (Ueda 2022) and an analogue series for PVPVA (Deac 2023, 2024).

### R41. Mixing lowers amorphous solubility by mole fraction, regular solution or Flory–Huggins terms
- **Review** [pp. 35–36]: Eq. 8 $S_a=S_a^0\cdot x_{drug}$ for ideal mixing. Eq. 9 $S_a=S_a^0 x_{drug} e^{\{\chi(1-x_{drug})^2\}}$ from Bragg–Williams, where a more negative χ gives a greater reduction, applicable to similar molecular volumes. Eq. 10 $S_a=S_a^0\Phi_{drug}e^{\{(1-1/r)(1-\Phi_{drug})+\chi(1-\Phi_{drug})^2\}}$ from Flory–Huggins for polymers.
- **Kind**: framework
- **Wiki**: [ideal mixing reduction](../../formulas/ideal-mixing-reduction-of-amorphous-solubility.md) "$S_a = S_a^{0}\,x_{drug}$"; [Flory–Huggins activity](../../formulas/flory-huggins-activity-equation.md) "$\ln a = \ln\Phi_1 + \left(1-\frac{1}{x_{12}}\right)\Phi_2 + \chi\,\Phi_2^{2}$"; [Amorphous solubility F20](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f20) "a literature χ of about −1 brought the PVP-VA prediction to about 100 against about 90 µg/mL measured"
- **Verdict**: agrees
- **Note**: Eq. 8 and Eq. 10 are present in equivalent form and F20 applies the χ term. Eq. 9 is not written out in the wiki.

### R42. The mixing equations assume unchanged water content
- **Review** [p. 36]: Eq. 11 and Eq. 12 give $S_a/S_c$ as $e^{-I(a_2)}e^{\Delta G_{c\to a}/RT}$ times the mixing terms of Eq. 9 and 10, since Sc is minimally changed. Eq. 9–12 assume that the additive does not change the water in the drug-rich phase; a corrected form using water activity in the drug/additive mixture has been proposed.
- **Kind**: framework (correction cited: Huang 2016)
- **Wiki**: [water sorption correction](../../concepts/water-sorption-correction-of-amorphous-solubility.md) "water content of the ibuprofen-rich phase without polymer is negligible"
- **Verdict**: wiki narrower
- **Note**: Amorphous solubility F20 cautions that water content was not measured in the hydrated drug-rich phase, but the wiki does not state that the mixing equations assume unchanged water or give the corrected form.

### R43. In Case II the crystalline solubility stays, and amorphous solubility, SRmax and flux fall
- **Review** [pp. 36–37]: In Case II Sc is unchanged, Sa falls with additive concentration, free drug at the amorphous limit falls, and SRmax decreases, with lower maximum membrane flux. $S_a/S_c$ directly reflects SRmax.
- **Kind**: framework
- **Wiki**: [Amorphous solubility F19](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f19) "without changing its crystalline solubility"; [Bioperformance F19](../../bioperformance/bioperformance/findings.md#f19) "whereas AS-LF changes it by under a tenth"
- **Verdict**: agrees
- **Note**: Same behaviour in the same class of system.

### R44. In Case II the amorphous solubility rises with the amount of drug-rich phase
- **Review** [p. 37, Fig. 8]: In additive-free solution or Case I the measured Sa does not depend on the amount of drug-rich phase. In Case II, the additive/drug ratio falls as the drug-rich phase grows at fixed additive concentration, so that the activity recovers and apparent Sa may rise with total drug concentration.
- **Kind**: framework (Ueda 2021, ref 93)
- **Wiki**: [Amorphous solubility F20](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f20) "PVP K25 and PVP-VA reach a ceiling, HPMC 603 does not"
- **Verdict**: wiki extends
- **Note**: The wiki (Ueda 2021) shows that the behaviour differs among polymers, which the schematic does not.

### R45. In Case III activity falls continuously and Sa is not a simple function of the additive
- **Review** [pp. 38–40, Figs. 7c, 8, 9]: Eq. 13 $S_a=\frac{S_a^0}{(1-f^a_{com})}x_{drug}e^{\{\chi(1-x_{drug})^2\}}$; Eq. 14 $S_a/S_c=\frac{(1-f^c_{com})}{(1-f^a_{com})}e^{-I(a_2)}e^{\Delta G_{c\to a}/RT}x_{drug}e^{\{\chi(1-x_{drug})^2\}}$. Sc rises with additive; Sa may rise as in Case I or first fall at low additive concentration and then rise; SRmax falls continuously, and the ratio does not reflect it. Once a drug-rich phase forms, Sa falls as the amount of that phase increases.
- **Kind**: framework
- **Wiki**: [Amorphous solubility F17](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f17) "STCDC and SGCDC lower the maximum supersaturation"; [Bioperformance F7](../../bioperformance/bioperformance/findings.md#f7) "the crystalline solubility rose to 25"
- **Verdict**: wiki narrower
- **Note**: The wiki reports individual Case III results, telaprevir with STCDC/SGCDC and with cellulose acetate suberate, but does not group them. It lacks the Sa curve that first falls and then rises, the fall of Sa with drug-rich phase amount, and Eq. 13–14.

## 3.4 Case studies illustrating the impact of additives on amorphous solubility

### R46. Ketoprofen shows all three cases
- **Review** [pp. 40–43, Fig. 10]: With Eudragit E PO (Case I), micelles raise both solubilities with SRmax unchanged since the polymer minimally enters the KTP-rich phase. With PVP (Case II), mixing reduces activity with no effect on dissolved drug. With CTAB (Case III), apparent amorphous solubility rises while the maximum activity falls.
- **Kind**: cited (Ueda ketoprofen papers; refs 66, 67, 95, 96)
- **Wiki**: none
- **Verdict**: wiki silent
- **Note**: Ketoprofen appears only in the solid-state chapters of the wiki. These papers are not in the library.

### R47. Crystallization inhibition may be traded against SRmax
- **Review** [p. 41]: Polymers that inhibit crystallization may reduce maximum activity. Relatively hydrophobic polymers that mix more extensively with the drug-rich phase inhibit crystallization from that phase more effectively, while reducing the maximum supersaturation.
- **Kind**: interpretation
- **Wiki**: [Amorphous solubility F22](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f22) "better size stability against a lower maximum supersaturation"; [Crystallization from solution F37](../../dissolution/d-crystallization-from-solution/findings.md#f37) "Eudragit E PO loaded enzalutamide droplets most and inhibited worst"
- **Verdict**: wiki extends
- **Note**: The wiki confirms the trade-off (Ueda 2020, Wilson 2021) and adds a counterexample from Shah 2025: polymer uptake does not by itself rank inhibitors.

### R48. Co-formulated or co-dosed drugs lower each other's amorphous solubility
- **Review** [pp. 41–42]: Ritonavir and lopinavir reduce each other's amorphous solubility in a ratio-dependent way (Case II); supersaturating regimens with several drugs, in discrete dosage forms or fixed dose combinations, carry the same risk.
- **Kind**: cited (Trasi 2015; Ueda)
- **Wiki**: [Bioperformance F6](../../bioperformance/bioperformance/findings.md#f6) "lowers each drug's free-concentration ceiling in proportion to its mole fraction"
- **Verdict**: wiki extends
- **Note**: The wiki adds product-level data (ritonavir about 4 µg/mL at pH 6.8 against about 30 in Overview F2) and later co-dosing work (Alkalla 2026).

### R49. Sodium taurocholate as a Case I additive
- **Review** [pp. 29, 42]: STC, STCDC and SGCDC enhanced the apparent amorphous solubility of atazanavir and posaconazole by micellar solubilization; with biorelevant media containing STC the SRmax remained unchanged (Case I). Table 1 lists ATZ/STC, FEL/STC and PCZ/STC under Case I.
- **Kind**: cited (Elkhabaz 2019)
- **Wiki**: [Crystallization from solution F19](../../dissolution/d-crystallization-from-solution/findings.md#f19) "3 mM STC alone cut atazanavir's from 65 to 38 µg/mL"
- **Verdict**: differs
- **Note**: The wiki reports the mixing (Case II) effect with STC alone at 3 mM, where the review reports only solubilization and no change of activity in STC-containing media. Both could hold if the effect depends on bile salt concentration or lecithin, but the review gives no concentration limit; settle from Indulkar 2018 and Elkhabaz 2019 (atazanavir at the amorphous solubility in STC).

### R50. STCDC and SGCDC mixing explains the posaconazole decrease, and Km/w differs at the two solubilities
- **Review** [p. 42]: SRmax of posaconazole fell with STCDC and SGCDC, but that of atazanavir did not; these salts likely mixed with the posaconazole-rich phase (Case III). Km/w for posaconazole differs at crystalline and amorphous solubility in biorelevant media.
- **Kind**: cited (Elkhabaz 2019; Van Duong 2022)
- **Wiki**: [Amorphous solubility F18](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f18) "almost halved for posaconazole in four intestinal media"; [free drug concentration](../../concepts/free-drug-concentration.md) "which the small fall of the posaconazole flux ratio questions"
- **Verdict**: agrees
- **Note**: Same statement. Both sources mark the mixing as an inference.

## 4. Experimental methods for determination of amorphous solubility and maximum thermodynamic activity of drug

### R51. Measure amorphous solubility in the medium of interest, and do not take the ratio as SRmax with solubilization
- **Review** [pp. 44, 51]: Measuring in the media or formulation conditions of interest is often easier than obtaining the inputs for calculation. The ratio may not reflect the thermodynamic maximum supersaturation, especially in Case I and III. Activity can be deduced from Sa without additive or in Case II, but is difficult to infer from Sa alone in Case I and III.
- **Kind**: direct claim
- **Wiki**: [Crystallization from solution F19](../../dissolution/d-crystallization-from-solution/findings.md#f19) "supersaturation has to be referred to values measured in the same medium"; [Bioperformance F3](../../bioperformance/bioperformance/findings.md#f3) "the concentration ratio does not track the driving force"
- **Verdict**: agrees
- **Note**: Same recommendation, although the wiki does not state the exempt case (additive-free or Case II) as a rule.

### R52. Intrinsic dissolution rate does not provide the amorphous solubility advantage
- **Review** [p. 44]: Neat-solid and dissolution-rate methods (intrinsic dissolution rate, single-particle analysis) are excluded because of crystallization and because media and formulation effects matter. For poorly water-soluble drugs the crystalline intrinsic dissolution rate is typically inaccessible, and for multicomponent systems it does not reflect the amorphous solubility because phase separation at the solid–solution interface occurs during release.
- **Kind**: direct claim
- **Wiki**: [intrinsic dissolution rate](../../concepts/intrinsic-dissolution-rate.md) "Bhardwaj and co-workers equate the ratio of the intrinsic dissolution rates of two solid forms with the ratio of their solubilities"
- **Verdict**: wiki narrower
- **Note**: The wiki reports the Bhardwaj equality without this limit. It holds at most for a neat form that stays unchanged during measurement.

## 4.1 Kinetic methods for amorphous solubility

### R53. More drug-rich phase increases the crystallization risk
- **Review** [p. 45]: Solutions created at higher initial supersaturation, holding more drug-rich phase, are at higher risk of crystallization, and hence rapid kinetic methods are preferred.
- **Kind**: direct claim (ref 108)
- **Wiki**: [Dissolution F5](../../dissolution/findings.md#f5) "crossing enzalutamide's amorphous solubility cut the induction time with 2.5 µg/mL HPMCAS from about 129 to 43 min"
- **Verdict**: wiki extends
- **Note**: The wiki gives induction times (Wilson 2021) for the same statement.

### R54. Onset can be found by changing concentration, temperature or pH
- **Review** [pp. 45, 47, Fig. 11]: The three kinetic designs are titration of a stock solution into the medium (total organic solvent ideally less than 1%), lowering the temperature at a given concentration, and changing pH for ionizable drugs at a given concentration.
- **Kind**: direct claim
- **Wiki**: [amorphous solubility](../../concepts/amorphous-solubility.md) "onset of scattering during slow addition of a drug stock"; [Amorphous solubility F10](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f10) "the total LLPS concentration rises with ionization as Henderson–Hasselbalch predicts"
- **Verdict**: agrees
- **Note**: The designs are the same, and the wiki has the temperature route for ritonavir in F3. The limit of less than 1% organic solvent is not stated in the wiki.

### R55. Turbidity cannot tell LLPS from crystallization, and UV concentrations need caution
- **Review** [p. 46]: Scattering arises from either a drug-rich phase or crystals. Measuring at an absorbing and a nonabsorbing wavelength helps, and polarized light microscopy can examine the precipitate afterwards. The UV extinction coefficient may change in the presence of the LLPS phase.
- **Kind**: direct claim
- **Wiki**: [Solution methods F3](../../characterization-methods/solution-methods/findings.md#f3) "The same measurement cannot tell liquid from crystal"; [Supersaturation from ASD F8](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f8) "which the authors attribute to a changed extinction coefficient with nanodroplets"
- **Verdict**: agrees
- **Note**: Same cautions.

### R56. Predissolved polymer can change the value it is meant to protect
- **Review** [p. 46]: A polymer predissolved to inhibit crystallization may itself change amorphous solubility by distribution into the drug-rich phase (Case II and III), although that value may be relevant to a comparably formulated system.
- **Kind**: direct claim
- **Wiki**: [Solution methods F7](../../characterization-methods/solution-methods/findings.md#f7) "but it lowered it for danazol and ibuprofen"
- **Verdict**: wiki extends
- **Note**: The wiki (Raina 2015, Tres 2018, Ueda 2020, 2021) names the systems in which the polymer did and did not move the onset. It does not state the review's practical point that the value may be the relevant one for the formulation.

### R57. Fluorescent probes select the drug-rich phase and autofluorescent drugs need none
- **Review** [p. 47]: Probes such as pyrene and PRODAN detect the drug-rich phase selectively because they generally do not distribute into crystallized solids. For autofluorescent compounds such as felodipine, fluorescence intensity or lifetime of the drug can be used directly.
- **Kind**: direct claim
- **Wiki**: [Solution methods F6](../../characterization-methods/solution-methods/findings.md#f6) "The drug's own fluorescence determines how phase separation is monitored"; [Amorphous solubility F4](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f4) "one probe moved in opposite directions for two drugs"
- **Verdict**: wiki extends
- **Note**: The wiki (Raina 2015, Tres 2017, 2018, Elkhabaz 2019) adds the failure cases, including masking of the probe by the drug's own emission.

## 4.2 Static measurements for amorphous solubility

### R58. Shake-flask measurement works only for slow crystallizers and low-melting drugs
- **Review** [pp. 48, 50–51, Fig. 12a]: Shake-flask with amorphous powder is easy for slow crystallizers such as cyclosporine A. If the melting point in water is below the test temperature, the crystal melts, crystalline solubility cannot be obtained and the method yields the amorphous solubility. For most drugs, grinding favours crystallization before metastable equilibrium; static methods allow more time for crystallization, particularly with excess drug-rich phase.
- **Kind**: direct claim
- **Wiki**: none
- **Verdict**: wiki silent
- **Note**: The wiki has no statement on when a shake-flask measurement of amorphous solubility is valid, nor on melting in water.

### R59. Centrifugation may not separate small droplets
- **Review** [p. 49, Fig. 12b]: Droplets of less than several tens of nanometers may not separate fully, even by ultracentrifugation, and the measured value may be too high. A drug-rich phase of lower density than water forms the upper layer rather than a pellet.
- **Kind**: direct claim
- **Wiki**: [Amorphous solubility F3](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f3) "the vial ended clear with a floating drug-rich droplet"; [Solution methods F11](../../characterization-methods/solution-methods/findings.md#f11) "a 0.22 µm filter retained phase-separated particles that a 0.7 µm filter passed"
- **Verdict**: wiki narrower
- **Note**: The wiki has the floating droplet and filter behaviour, but it does not give the size limit for ultracentrifugation.

### R60. Solution NMR reads the dissolved drug directly and shows the case
- **Review** [p. 49, Fig. 12c]: The dissolved peak area rises linearly up to Sa, and then stays constant in an additive-free solution (Case I), rises more slowly in Case II or falls in Case III. The drug-rich phase signal is usually lost to broadening, but for drugs with a low melting point or Tg (ibuprofen, ketoprofen, fenofibrate, even at 37°C) separated-phase peaks are seen at higher field.
- **Kind**: direct claim
- **Wiki**: [Amorphous solubility F15](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f15) "at higher field for drug in the drug-rich phase"
- **Verdict**: agrees
- **Note**: Same peak assignment and the same dependence on Tg. Using the slope above Sa to assign the case is not in the wiki.

## 4.3 Approaches to determine the maximum drug thermodynamic activity

### R61. Membrane diffusion measures activity under stated conditions
- **Review** [p. 51, Fig. 13a]: When the membrane limits permeation of droplets and complex and is poorly permeable to the drug, the permeation rate is proportional to the thermodynamic activity in the donor. Solutions of known supersaturation or at the crystalline solubility serve as controls.
- **Kind**: direct claim
- **Wiki**: [thermodynamic activity](../../concepts/thermodynamic-activity.md) "assume that only dissolved drug crosses the membrane and that the additive does not change it"; [Bioperformance F21](../../bioperformance/bioperformance/findings.md#f21) "the unstirred water layer, not the membrane, limits the transport of lipophilic drugs"
- **Verdict**: wiki extends
- **Note**: The wiki (Hate 2022) adds that the boundary layer limits flux in other membrane setups. Together the two state when the flux read-out fails as an activity measurement.

### R62. PGSE-NMR gives the free drug fraction
- **Review** [pp. 51–52, Fig. 13b]: PGSE-NMR gives the diffusion coefficient of the drug; with fast exchange the dissolved drug peak averages the free and complexed environments, $D_{obs}=f_{free}D_{free}+f_{complex}D_{complex}$, which gives the distribution ratio and hence the maximum activity even in the presence of drug-rich phase and complex.
- **Kind**: direct claim (ref 68, 118)
- **Wiki**: none
- **Verdict**: wiki silent
- **Note**: The wiki has no PGSE or diffusometry method for free drug. It is the only method in the review that gives free drug without a membrane.

## 5. Practical applications of amorphous solubility to formulation development and bioavailability enhancement

### R63. Colloids are released at low loading and common analytics do not separate them
- **Review** [p. 53]: ASDs can release a colloidal drug-rich phase under nonsink conditions, particularly at low drug loading, and not all do at higher loading. Centrifugation, filtration or in situ UV may not distinguish these states, so the amount of dissolved drug and the amount available to permeate stay ambiguous.
- **Kind**: direct claim
- **Wiki**: [Release mechanism F4](../../dissolution/a-release-mechanism-and-loc/findings.md#f4) "only release that stayed under polymer control passed the amorphous solubility and formed drug-rich nanodroplets"; [Supersaturation from ASD F8](../../dissolution/b-supersaturation-from-asd-dissolution/findings.md#f8) "In situ UV overreads the dissolved drug once submicron particles form"
- **Verdict**: agrees
- **Note**: Same statement, with the wiki giving a more detailed loading and congruency frame.

### R64. Dissolution profile differences do not necessarily predict absorption
- **Review** [p. 54]: Because precipitation is poorly characterized, differences in dissolution profiles between formulations do not necessarily correlate with in vivo absorption; knowing amorphous solubility and nanoparticle size and composition and the time of phase transformations improves prediction.
- **Kind**: direct claim (Qian 2012 cited)
- **Wiki**: [Bioperformance F25](../../bioperformance/bioperformance/findings.md#f25) "while closed non-sink dissolution and induction time did not"
- **Verdict**: wiki extends
- **Note**: The wiki gives rat studies with enzalutamide (Wilson 2018, 2020) in which mass flow across a dialysis membrane ranked the formulations and closed dissolution did not.

### R65. The sink index is defined for both solid forms
- **Review** [p. 54]: Eq. 15 $SI_{cr}=S_c/(Dose/V)$, Eq. 16 $SI_{am}=S_a/(Dose/V)$. $SI_{cr}\geq 3$ is taken as sink and $SI_{cr}<3$ as nonsink.
- **Kind**: framework
- **Wiki**: [sink index](../../formulas/sink-index.md) "three times the solubility needed"
- **Verdict**: agrees
- **Note**: The definition and threshold are the same. The wiki formula page has one index; the separate amorphous index appears in findings.

### R66. An amorphous sink index of 1 gives maximum activity with all drug dissolved
- **Review** [pp. 54–55]: At $SI_{am}=1$ the dose confers the maximum activity, and all amorphous material can in theory dissolve molecularly. At $SI_{am}<1$ a colloidal phase can form, with risk of crystallization and coarsening, so that analytical methods separating dissolved drug from colloid are desirable.
- **Kind**: direct claim
- **Wiki**: [Bioperformance F16](../../bioperformance/bioperformance/findings.md#f16) "tests in 100 and 40 mL of medium separate them"; [Bioperformance F15](../../bioperformance/bioperformance/findings.md#f15) "keeps rising above the amorphous solubility, at a lower slope"
- **Verdict**: wiki extends
- **Note**: The wiki supplies data (Purohit 2018, Hate 2019, Purohit 2019), and in systems limited by the boundary layer mass flow continues to rise above $SI_{am}=1$ (Hate 2018, 2022), which qualifies "highest driving force" in the review as a statement about activity rather than transfer.

### R67. The sink index describes crystallization driving force rather than release driving force, and has predictive use
- **Review** [p. 55]: For many ASDs the driving force for release relates to the polymer, not to the drug amorphous solubility, so the SI may not represent it, whereas it matters for crystallization. Tests based on SI have begun to predict the impact of formulation design and critical quality attributes on ASD performance.
- **Kind**: interpretation (refs 54, 55, 127–130)
- **Wiki**: [Release mechanism F1](../../dissolution/a-release-mechanism-and-loc/findings.md#f1) "read continued release into a saturated medium as polymer control"; [Bioperformance F16](../../bioperformance/bioperformance/findings.md#f16) "Compendial tests hardly distinguish crystallinity levels"
- **Verdict**: wiki extends
- **Note**: The wiki gives experiments on release into a saturated medium (from Saboo 2019 onward) and tacrolimus capsule data (Purohit 2018, Hate 2019) behind this statement.

### R68. Dose number should be calculated for both forms
- **Review** [p. 55]: Eq. 17, Dose number $=Mo/(Vo\times S)$, ideally with biorelevant solubility and for the crystal and the amorphous form. Solubility-enabling formulations might be needed when the aqueous dose number is >10, and for <10 conventional formulations may suffice (Van den Bergh).
- **Kind**: cited (Van den Bergh; Wuelfing)
- **Wiki**: [dissolution-rate-limited absorption](../../concepts/dissolution-rate-limited-absorption.md) "dose number 36 at 0.025 mg/mL in FaSSIF, about 100 mL"
- **Verdict**: wiki narrower
- **Note**: The wiki uses a dose number for one case only and has no equation, threshold or comparison between solid forms.

### R69. Tacrolimus and ritonavir leave the dose-limited region when amorphous
- **Review** [pp. 55–56]: Tacrolimus at 1.8 µg/mL crystalline and 50 µg/mL amorphous with 5 mg in 250 mL gives dose numbers of 11 and 0.4. Ritonavir at 100 mg gives ~60 and ~7 in fasted-state intestinal fluid. Absorption should then no longer be limited by dose number.
- **Kind**: direct claim (solubility data cited, Trasi 2016 for tacrolimus)
- **Wiki**: [amorphous solubility advantage](../../concepts/amorphous-solubility-advantage.md) "about 35 (49/1.4)"
- **Verdict**: differs
- **Note**: For tacrolimus the wiki holds a crystalline solubility of 1.4 µg/mL (49/1.4) and elsewhere 2.5 µg/mL (ratio about 33), whereas the review uses 1.8 µg/mL. Since 5 mg in 250 mL is 20 µg/mL, the crystalline dose number would be about 14, 11 or 8, on different sides of the threshold of 10. Settle from Trasi 2016 and Purohit 2019 (medium and temperature of the crystalline value).

### R70. PBBM needs amorphous solubility and dissolved rather than total drug
- **Review** [pp. 56–57]: Amorphous solubility as input predicted linear pharmacokinetics (Mitra), whereas crystalline solubility under-predicted AUC and Cmax above 50 mg. Models also worked for venetoclax with slow crystallization (Emami Riedmaier), belinostat (Stewart) and encorafenib with proton-pump inhibitors. Posaconazole was accurate with molecularly dissolved input and over-predicted with total drug (Holzem). Stewart and Grass represented nanoparticles by a modified effective permeability.
- **Kind**: cited (Mitra 2016; Emami Riedmaier; Stewart 2019; Holzem 2024; Stewart and Grass)
- **Wiki**: [Bioperformance F17](../../bioperformance/bioperformance/findings.md#f17) "in a model that assumes no precipitation in the gut"
- **Verdict**: wiki narrower
- **Note**: The wiki holds simulation evidence on tacrolimus only and none of the review's PBBM cases. The review expects the use of amorphous solubility in such models to become routine.

## 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`.

- [supersaturation ratio](../../concepts/supersaturation-ratio.md) — "same quantity as the" amorphous solubility advantage when measured at the ceiling — Per pp. 33, 37, 39, this holds only without an additive or in Case II; in Case I SRmax exceeds $S_a/S_c$ and in Case III the ratio does not reflect SRmax, so the sentence needs this limit.
- [Amorphous solubility F12](../../dissolution/c-amorphous-solubility-and-llps/findings.md#f12) — "so the supersaturation ratio does not rise" — Correct for Case I only; p. 39 has SRmax falling continuously in Case III, so the general form must name the additive class.
- [Bioperformance F4](../../bioperformance/bioperformance/findings.md#f4) — "because the second phase appears at a higher concentration but at the same activity" — This is the Case I result; Table 1 (p. 29) lists KTP/TWN, CPD/TPGS and CPD/TWN under Case III, where a micelle-forming surfactant also lowers activity.
- [free drug concentration](../../concepts/free-drug-concentration.md) — "Equating the buffer solubility with the free drug assumes that bile salts and lecithin do not mix into the drug phases" — The review supplies the general form: buffer value equals free drug only in Case I, and in Case III (p. 39) free drug at the limit falls.
- [intrinsic dissolution rate](../../concepts/intrinsic-dissolution-rate.md) — "Bhardwaj and co-workers equate the ratio of the intrinsic dissolution rates of two solid forms with the ratio of their solubilities" — P. 44 states that intrinsic dissolution rates of multicomponent systems do not reflect the amorphous solubility, and those of crystalline poorly soluble drugs are typically inaccessible.
- [advantage with water sorption correction](../../formulas/amorphous-solubility-advantage-with-water-sorption-correction.md) — "$C_A = \exp\left[-\frac{\Delta G}{RT}\right]\exp\left[-I(a)\right]C_T$" — This form has $\exp[-\Delta G/RT]$ with $\Delta G$ taken as negative, whereas the review (Eq. 2) has a positive exponent with $\Delta G_{c\to a}$; both are right, but the sign convention must be stated on the page where they sit side by side.
- [sink index](../../formulas/sink-index.md) — "three times the solubility needed" — The review (Eq. 15–16, p. 54) separates $SI_{cr}$ from $SI_{am}$ and uses them for different questions, so the page should do the same.

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

- The Case I/II/III classification with its equations (Eqs. 5–7, 9, 13–14) — pp. 28–39 — It predicts from one additive's behaviour how $S_c$, $S_a$, their ratio and SRmax move, and when a measured ratio can be read as driving force.
- Dependence of Sa on the amount of drug-rich phase in Case III — pp. 39–40 — The measured value then depends on dose, which affects any comparison between formulations at different dose.
- Dose number for crystalline against amorphous solubility — pp. 55–56 — It is a simple first test of whether an amorphous formulation is needed.
- PBBM with amorphous solubility and molecularly dissolved input — pp. 56–57 — It links in vitro phase behaviour to dose linearity, drug–drug interaction and exposure predictions.
- PGSE-NMR diffusometry — pp. 51–52 — It measures free drug in media with droplets and complexes without any membrane.
- Cyclodextrin effects on amorphous and crystalline solubility — pp. 20, 33 — A cyclodextrin can raise the concentration ratio with no gain in activity.
- Ketoprofen as one drug in all three cases — pp. 40–43 — It separates the effects of additive type from those of the drug.
- Melting of the crystal in water, and the construction of Fig. 5c — pp. 22, 24, 48 — It decides whether a crystalline solubility exists at the test temperature for low-melting drugs.
- Ionization correction (Eq. 3) — p. 27 — It lowers the predicted ratio for ionizable drugs in unbuffered media.
- Particle drifting as a mechanism across the boundary layer — pp. 15–16, 53 — It is the mechanism proposed for the absorption gain from nanodroplets and thus the basis for caring about droplet size.
- Hancock and Parks ranges and the early ratios — pp. 8, 11–13 — They give the historical limits for how large an advantage can be predicted against how large it is measured.
- Anti-solvent screening as an accidental amorphous solubility measurement — p. 9 — Discovery solubility values may overstate the crystalline solubility.