Supersaturated danazol: droplets before crystals, and what small amounts of polymer change

Background and motivation

Many new drug candidates are so poorly soluble in water that their absorption is limited. One way around this is the amorphous solid dispersion (ASD): the drug is dispersed, ideally molecularly, in a hydrophilic polymer, and on dissolution it reaches concentrations far above the solubility of its crystal. The price is instability. The amorphous drug has a higher free energy than the crystal and tends to crystallize, both in storage and in the supersaturated solution that forms when the ASD dissolves; additives, usually polymers, are included to slow nucleation and crystal growth. C6·C9

The authors frame the problem around a ceiling. The largest concentration an amorphous solid can produce is its amorphous solubility, which can be estimated from thermodynamic data (Murdande et al. 2010, ref 24; Hancock and Parks 2000, ref 5) and in some cases measured. C8·C10 Earlier work from the same group had shown that highly supersaturated drug solutions, such as those formed from ASDs, can undergo liquid–liquid phase separation (LLPS) before they crystallize, and that for several compounds the concentration at which they spontaneously precipitate lies very close to the estimated amorphous solubility (Ilevbare and Taylor 2013, ref 16). C9·R29 LLPS is familiar to process chemists as "oiling out", but its mechanisms and the variables that control it were not understood in drug delivery. C9 Another strand of earlier work showed that precipitation to an amorphous form keeps a solution supersaturated, while precipitation to crystals rapidly removes the supersaturation (Hsieh et al. 2012, ref 42). R30

For ritonavir, a slowly crystallizing drug, the group had found that induction times were shorter when drug-rich droplets were present, that additives could either shorten or lengthen induction times depending on their structure, and that polymers did not move the LLPS concentration. R28 (The text cites the additive study as ref 12; the matching paper, Ilevbare et al. 2013 on ritonavir nanodroplets, is printed as ref 11 in the reference list, while ref 12 is a study of α-mangostin nanomicelles. X10)

Danazol is a contrasting case. It is a relatively hydrophobic drug that has been studied extensively for amorphous dissolution, precipitation and bioavailability (Warren et al. 2010, ref 18), and when amorphous danazol was dissolved in earlier studies the highest concentration reached was less than a quarter of the expected value, because the solid crystallized before it had dissolved (refs 3 and 35). R27 This paper asks whether danazol, a fast crystallizer, also passes through a liquid drug-rich phase, and how small amounts of three common ASD polymers change where that phase forms and how long supersaturation lasts. To tell a noncrystalline precipitate from a crystalline one at concentrations of a few µg/mL, the authors combine UV spectroscopy, an environmentally sensitive fluorescent probe (pyrene) and second harmonic generation imaging.

Background concepts

Supersaturation, solubilization and the amorphous ceiling. The authors stress a distinction that is easy to blur. In a supersaturated solution the drug concentration, and with it the chemical potential, is higher than in a solution saturated with crystals; there is a driving force for crystallization, and the raised chemical potential can increase flux across a membrane. In a solubilized solution (for example with micelles) the equilibrium crystalline solubility itself is raised, so concentration rises without any rise in chemical potential and without any risk of crystallization, and membrane flux does not increase unless dissolution was the slow step (refs 44, 45). C42 An additive can therefore reduce precipitation in two ways: by raising the crystalline solubility, which lowers supersaturation, or by slowing nucleation or growth of the crystals. C43

Estimating the amorphous solubility. The ratio of amorphous to crystalline solubility is estimated with Equation 1 of the paper:

Here ${\sigma }^{\mathrm{a}\mathrm{m}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{h}}$ and ${\sigma }^{\mathrm{c}\mathrm{r}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{l}}$ are the amorphous and crystalline solubilities, $\Delta G$ is the free energy difference between the amorphous and the crystalline drug, $R$ is the gas constant and $T$ the operating temperature. The factor $e^{-I(a_2)}$, derived by Murdande et al., is the activity of the amorphous drug once it has taken up water; it corrects for the water that dissolves in the amorphous phase and lowers its activity. In plain terms: the amorphous form can reach a higher concentration than the crystal by the exponential of their free energy difference, slightly reduced because wet amorphous drug is not pure drug. E1·C10 The free energy difference is approximated with the Hoffman equation (Equation 2):

Here $\Delta H_f$ is the heat of fusion, $T_m$ the melting temperature and $\Delta T=T_m-T$ the undercooling. In plain terms: the further below its melting point the drug is used, and the larger its heat of fusion, the larger the free energy gap between glass and crystal, assuming that the enthalpies of crystal and supercooled liquid change linearly with temperature. E2·C10 For danazol the paper uses $T_m$ = 225.4 °C, $\Delta H_f$ = 28.9 kJ/mol and a water-activity factor of 0.935, the last obtained by applying the Gibbs–Duhem equation to the water sorption isotherm of quench-cooled amorphous danazol. M1·P4·E3

Liquid–liquid phase separation. Above the amorphous solubility a drug solution cannot stay homogeneous. It separates into a drug-rich phase, present as small droplets, and a drug-lean aqueous phase. The authors argue that once this has happened the concentration in the aqueous phase stays at the LLPS concentration, because the two phases are in equilibrium, so adding more drug produces more droplets but no further rise in supersaturation; they also note that the change from a one-phase to a two-phase solution can itself change nucleation. C28 In the discussion they connect this ceiling to the spinodal: there "appears" to be an upper limit to supersaturation for hydrophobic drugs, beyond which phase separation is spontaneous. C44

Three ways to see what has precipitated.

• UV extinction. Danazol absorbs at 288 nm but not at 350 nm. Any loss of light at 350 nm is therefore scattering by particles or droplets, so a rise in extinction there marks the appearance of a new phase, crystalline or not. C13
• Pyrene I1/I3. Pyrene is a hydrophobic fluorescent molecule whose emission spectrum depends on the polarity of its surroundings. The ratio of its first (373 nm) and third (383 nm) vibronic peaks, I1/I3, is about 1.97 in water and falls in less polar media, to 0.66 in cyclohexane. If a noncrystalline drug-rich phase forms, pyrene partitions into it and the ratio drops; a crystal cannot dissolve pyrene, so when the drug crystallizes the ratio should return to the water value. C11·R6
• Second harmonic generation (SHG). Crystals of a chiral compound such as danazol double the frequency of intense laser light, while solutions and disordered material do not, so SHG imaging (here, SONICC) sees crystals only, with high sensitivity. C12

Methods in detail

All experiments used 10 mM phosphate buffer at pH 6.8 and 25 °C. The polymers were PVP K29/32 (neutral), HPMC 606 grade (neutral cellulosic) and HPMC-AS MF grade (negatively charged cellulosic), each at 10 µg/mL (0.001% w/v) in every experiment. M2·M3·M4·M7 Supersaturation was created by the solvent-shift method: a small volume of a methanolic danazol stock (2 or 4 mg/mL) was added to stirred buffer. P6·P7·P8 The work has four parts that run in parallel and are then compared.

Part 1: the solubility levels

Problem. To interpret any precipitation, the authors need two reference concentrations for each medium: the crystalline solubility (the floor) and the amorphous solubility (the ceiling). What they did. Excess crystalline danazol was agitated in buffer for 48 h at 25 °C, with or without 10 µg/mL polymer, the solid was removed by ultracentrifugation (40,000 rpm, 15 min), and the supernatant was assayed by HPLC (C18 column, detection at 288 nm, triplicate). P1·P2 The melting temperature and heat of fusion came from DSC; amorphous danazol made by quench-cooling 15–20 mg of melt in liquid nitrogen was run through a water sorption isotherm from 5 to 95% RH at 25 °C, which gave the activity factor 0.935. P3·P4·M1 Equations 1 and 2 then gave the ratio of amorphous to crystalline solubility, and the amorphous solubility in each medium was taken as its crystalline solubility multiplied by this ratio. P5·R1·R2

Part 2: when does a new phase appear, and is it crystalline?

UV extinction. Danazol stock was pumped into 50 mL of stirred buffer at 5 µg/mL/min without polymer (fast, to reach the LLPS concentration before crystals form) and at 1 µg/mL/min with polymer. Extinction at 350 nm was plotted against the concentration measured by UV absorbance, and the onset was taken where straight lines fitted to the low- and the high-extinction regions crossed. P6

Pyrene. Separate solutions of 0 to 30 µg/mL danazol were made by a single solvent shift into about 10 mL buffer containing 2 µM pyrene, with or without polymer, and sampled after 30 s and again after 15 min (excitation 332 nm, emission 350–420 nm, triplicate). Controls were crystalline danazol (about 1 mg/mL) stirred in buffer with pyrene, with and without polymer, and a dry amorphous danazol film containing pyrene, spin-coated on quartz. Reference spectra of pyrene in water, acetonitrile, methanol, isopropanol and cyclohexane calibrated the ratio. P7·P11

SHG. Solutions of 10 µg/mL (below the drug-alone LLPS concentration) and 50 µg/mL (above it) were dispensed into a 96-well plate and imaged by SONICC from 30–60 s after mixing, scanning the well from the bottom to the meniscus in steps of about 40 µm. P10

Part 3: how long does supersaturation last?

Problem. Once droplets are present, UV absorbance no longer reports dissolved drug cleanly, because droplets also absorb and scatter, and their contribution changes as they grow. What they did. Solutions of 10, 15 and 20 µg/mL (200 mL, 25 °C, 200 rpm) were followed with a fiber-optic UV dip probe every 30 s at 288 nm (absorbance) and 350 nm (extinction), while 2 mL aliquots were taken for pyrene fluorescence at intervals. The three concentrations were chosen relative to the drug-alone LLPS concentration: below (10 µg/mL), just above (15 µg/mL) and above (20 µg/mL). P8 The crystallization induction time was taken as the time at which the UV signal changed slope, simultaneous with the rise in I1/I3; at 10 µg/mL without polymer, where there is no drug-rich phase for pyrene to report, it was read from the sudden drop in UV absorbance alone. C30 Why it works. Three signals with different weaknesses are read on the same solution: absorbance tracks dissolved drug but is distorted by droplets, extinction tracks scattering, and pyrene tracks whether a hydrophobic noncrystalline phase is still present. Where they change together, the change is assigned to crystallization.

Part 4: droplet size and charge

Supersaturated solutions above the LLPS concentration (the exact danazol concentration is not printed) were sampled over 12 h for dynamic light scattering (Z-average diameter, backscatter at 173°) and for zeta potential, with and without polymer. P9·X11

Experimental analysis

The solubility levels

The crystalline solubility of danazol was 0.9 ± 0.2 µg/mL. With 10 µg/mL polymer it was 1.3 ± 0.4 (PVP), 2.2 ± 0.5 (HPMC) and 1.1 ± 0.4 µg/mL (HPMC-AS); the authors conclude that within error PVP and HPMC-AS have negligible impact, while HPMC raises the solubility appreciably. R1·C16 The paper gives the amorphous:crystalline ratio as 19.6 and the amorphous solubility of danazol as 16 µg/mL, and considers this in "reasonable agreement" with earlier estimates of the ratio, 13.7 (Ozaki et al.) and 26.5 (Murdande et al.), while noting errors from the Hoffman assumptions and the solubility measurement. R2·R3·C14·C15

Note by the AI writer (not discussed in the paper): the printed inputs do not reproduce these two numbers. With $T_m$ = 498.55 K, $T$ = 298.15 K, $\Delta H_f$ = 28.9 kJ/mol and the factor 0.935, Equations 1 and 2 give $\Delta G$ ≈ 6.95 kJ/mol and a ratio of 15.4, not 19.6. The danazol row of Table 2 also does not follow its own footnote: 0.9 × 19.6 = 17.6, not 16, whereas the three polymer rows do follow it (25, 43 and 22 µg/mL). With the recomputed ratio the estimate would be about 14 µg/mL. The paper does not say whether unrounded inputs or a different convention were used. E1·X1

Table A. Solubility levels and measured onsets of phase separation at 25 °C, pH 6.8 (from Tables 2 and 3; crystalline solubility n = 3, ± one standard deviation). R1·R5

Danazol alone: a noncrystalline phase first, crystals within minutes

Without polymer, extinction at 350 nm stayed very low below about 13 µg/mL and rose steadily above it, to about 0.026 at 15 µg/mL and about 0.068 at about 20 µg/mL (Figure 2), which the authors read as a new phase ("suggest"). R4·C17 The pyrene ratio, 1.95 ± 0.03 in the buffer, stayed at about 1.92–1.94 up to 13 µg/mL, then dropped abruptly (about 1.77 at 14 µg/mL) and kept falling to about 1.53 at 24 µg/mL; 50 and 100 µg/mL went no lower (Figure 4). R7·R8·R10 Both methods put the onset at 13 µg/mL. R5

The authors read the abrupt drop as a new, noncrystalline danazol phase into which pyrene partitions ("consistent with"), and the plateau near 24 µg/mL as the point where most of the pyrene sits in that phase ("suggests"). C19 The plateau value, about 1.5, matches the polarity of methanol (1.55); in a dry amorphous danazol film the ratio is 1.4, and the authors attribute the slightly higher value in water to some water in the drug-rich phase ("can be attributed"). R6·R9·C20·C21 The onset lies close to the estimated amorphous solubility; the authors call the agreement "excellent" and present it as additional validation of the Murdande approach. C22 DLS gave an initial droplet size of about 490 nm (abstract: around 500 nm). R22

The droplets were short-lived. After 15 min, the pyrene ratio of every solution in the series had returned to about 1.92–1.945 (text: 1.95 ± 0.03), the water value, which the authors take as "strongly suggesting" that the drug had crystallized and pushed pyrene back into water (Figure 5); crystalline danazol itself did not change the ratio over 15 min (Figure S1). R11·R24·C25 SHG showed no signal in the first frames, isolated crystals at 5 min, and widespread signal by 10–12 min, both at 10 µg/mL and at 50 µg/mL (Figure 6); particles were visible by eye within a few minutes. R13·R14·C26

The kinetic run at 20 µg/mL (Figure 7) shows how the signals relate. The apparent UV concentration fell from about 19.2 µg/mL at 1 min to about 14.4 at 5 min and about 11.8 at 10 min, then faster, to about 2.1 at 30 min and about 1.4 µg/mL at 60 min. The pyrene ratio stayed at about 1.52–1.58 for the first 9 min and rose to about 1.80 at 15 min and about 1.93 at 30 min. R15 The authors attribute the early fall of the UV signal to rapid coalescence of the droplets, which changes how they absorb and scatter light, rather than to crystallization ("is attributed"), and place the induction time at the change of slope that coincides with the rise in I1/I3. C29·C30 The overlay of Figure 13 adds the SHG frames: none at about 2 min, two crystals at 5 min, many at about 15 min. R25 Across Table 4, induction times without polymer were 10 ± 6 min at 10 µg/mL, 6–10 min at 15 µg/mL and 7–10 min at 20 µg/mL. R17

Table B. Danazol without polymer: what each read-out shows (pyrene values read from Figures 4 and 5, approximate). R4·R8·R11·R13·R17

The polymers lower the onset of phase separation

The polymers alone did not change the pyrene ratio of the buffer. R7·C18 With 10 µg/mL polymer the ratio began to fall earlier: with HPMC or HPMC-AS it had dropped to about 1.85 at 9 µg/mL, and with PVP it fell between 12 and 13 µg/mL (Figure 4); extinction rose earlier in the same order (Figure 2). R8·R4 The onsets were 11 and 11 µg/mL with PVP, 9 and 8 with HPMC, and 8 and 8 with HPMC-AS, by pyrene and UV extinction respectively, against 13 µg/mL without polymer (Table A). R5 The authors describe the shift as "somewhat decreased" with the cellulosic polymers and contrast it with ritonavir, where polymers did not change the LLPS concentration. C23·R28

The direction matters. Scaling each crystalline solubility by the drug-alone ratio predicts a higher amorphous solubility with every polymer, up to 43 µg/mL with HPMC, yet the measured onsets all fell. R1·R5 The authors' explanation is that the cellulosic polymers mix into the drug-rich phase ("suggests"), lowering the drug's activity there, much as absorbed water does in Murdande's analysis, and so lowering the concentration at which a drug-rich phase can form. C48 Attempts to measure the polymer content of the droplets were "not very successful" because of the small amounts; preliminary NMR (data not shown) suggested around 10–20% polymer in drug-rich phase formed with HPMC and less than the detection limit, about 10%, with PVP, consistent with HPMC's larger effect on the onset. R26·C49 No value is reported for HPMC-AS, the polymer with the lowest onset. X15

Note by the AI writer (not discussed in the paper): two procedural details deserve mention. The UV titrations used a faster addition rate without polymer (5 µg/mL/min) than with polymer (1 µg/mL/min), but the pyrene onsets, made by the same single addition for every system, agree with the UV onsets within 1 µg/mL, so the polymer effect does not rest on the rate difference. X13 And the methanol carried in with the stock is not reported; from the stock concentrations it rises from about 0.65% v/v at 13 µg/mL to about 1.5% v/v at 30 µg/mL in the pyrene series. X12

The polymers delay crystallization from minutes to hours

With polymer present the pyrene ratio stayed low and constant for 15 min, which the authors read as crystallization being inhibited and the probe remaining in the drug-rich phase ("suggesting"). R12·C27 The full kinetic experiments (Table 4, Figure 12) show how large the effect is:

Table C. Crystallization induction times by three methods (from Table 4; ± as printed, n not stated; N/A where the method gives no signal below the LLPS concentration). R17·X11

The ranking HPMC-AS > HPMC > PVP > no polymer holds at every concentration by UV absorbance. R17 Single representative runs at 20 µg/mL (Figures 8–10) show the same thing as curves: the apparent concentration stayed near 20 µg/mL for about 50 min with PVP, near 17–18 µg/mL for about 3 h with HPMC and for about 5 h with HPMC-AS, and then fell over one to two hours; the pyrene ratio stayed at about 1.51–1.58 until the fall and rose with it. R18·R19·R20·C35 The authors summarise the times as around 1.5 h (PVP), about 2.5 h (HPMC) and 4 h or more (HPMC-AS) in one place, and as about 100 min, 150 min and 6 h, against about 5 min without polymer, in another; they attribute the large scatter to the stochastic nature of nucleation and report "good agreement" between the methods. C32·C40 Two observations follow from Table C. First, the methods do not always agree closely: with HPMC at 15 µg/mL, UV extinction gives 111 ± 14 min against 172 ± 4 and 195 ± 21 min by the other two methods. X5 Second, induction times fall as concentration rises with every polymer, for example 516, 365 and 277 min with HPMC-AS, which the authors describe as solutions above the LLPS concentration "in general" crystallizing sooner than one-phase solutions, most clearly with HPMC. C41

Note by the AI writer (not discussed in the paper): the one-phase label for the 10 µg/mL solutions holds for danazol alone and for PVP (onset 11 µg/mL), but with HPMC and HPMC-AS the measured onsets are 8–9 µg/mL, so these 10 µg/mL solutions were already at or above the onset; the authors themselves say they were "either below or just at" the LLPS concentration. The fall of induction time with concentration is clear; its attribution to one-phase versus two-phase solutions is weakest exactly for HPMC, the example the authors cite. C39·X3

After crystallization with polymer, the solution did not fall to the crystalline solubility within the runs: the text gives around 2–3 µg/mL, and the last plotted values are about 2.6 µg/mL (PVP, about 360 min), 3.8 µg/mL (HPMC, about 900 min) and 3.45 µg/mL (HPMC-AS, about 1400 min), all above the 0.9 µg/mL crystalline solubility. R21·C38·X7 Nor did the pyrene ratio return to the water value; it ended at about 1.80–1.85. Since the polymers alone do not change the ratio, the authors suggest an unknown pyrene–drug–polymer complex. R21·C36 In the crystalline controls the ratio was unchanged at 15 min but fell after 24 h with each polymer (to about 1.785 with PVP, 1.72 with HPMC and 1.85 with HPMC-AS, against about 1.92 without polymer), which the authors think "likely" reflects polymer adsorbed on the crystal surface, where pyrene meets both drug and polymer (Figure S1). R24·C37

Droplet size and charge

Without polymer the droplets measured about 490 nm at the start and about 9800 nm after 1 h. With the cellulosic polymers they stayed small for hours: about 305–345 nm up to 2 h with HPMC (about 820 nm at 4 h, about 7300 nm at 6 h) and about 230–250 nm up to 4 h with HPMC-AS (about 1250 nm at 6 h, about 6200 nm at 12 h). With PVP the size was about 240–250 nm at 0 and 1 h and about 2900 nm at 2 h (Figure 11A). R22 The zeta potential was −8.1025 mV without polymer, −5.295 mV with PVP, −2.33333 mV with HPMC and −13.7 mV with HPMC-AS (Figure 11B). R23

The authors infer that the polymers reduce droplet coalescence ("it is inferred"), which also explains why the UV signal is steadier with polymer, and read the zeta potential changes as polymer adsorbed at the droplet interface ("indicating"): the negatively charged HPMC-AS makes the droplets more negative, the neutral polymers less so, as neutral cellulose polymers do on talc. C33·C34·R31 From size and charge together they conclude that some polymer is "clearly" present in the droplet phase, at least at its interface. C50

Note by the AI writer (not discussed in the paper): the drug-alone DLS data have only two points, and the second (1 h) comes long after crystallization (6–10 min), so the size jump may include crystals. No size was measured in the first minutes, when the UV signal is said to reflect coalescence; that step of the argument is inferred, not measured. X6

Discussion

How the authors connect the findings. The argument runs from the amorphous ceiling to the fate of the droplets:

Supersaturation alone does not explain the ranking. The first mechanism the authors propose is simple: a lower LLPS concentration means a lower supersaturation, and nucleation rate depends strongly on supersaturation, which "would explain" longer induction times with HPMC and HPMC-AS than with PVP or without polymer; HPMC lowers supersaturation further by raising crystalline solubility. C51 But they note that this cannot be the whole story, because HPMC-AS gives longer induction times than HPMC even though the HPMC systems have the lower supersaturation. C52 Their second mechanism is that polymer incorporated in the droplets and associated with the droplet–water interface is "also likely" to disrupt nucleation, particularly heterogeneous nucleation at that interface; in their ritonavir work additives with bulky groups inhibited nucleation while those with long hydrocarbon chains promoted it, without changing supersaturation. C53·R28 Neither the site of nucleation nor the amount of interfacial polymer was measured.

A trade-off, not a free gain. The authors' conclusion is that polymers have "both favorable and unfavorable effects": they inhibit crystallization and so prolong supersaturation, but some polymers lower the maximum supersaturation reachable, both by raising crystalline solubility (HPMC) and by lowering the amorphous solubility, that is, the LLPS onset (all three, most the cellulosics). C57·C4 Because the first precipitate can be noncrystalline and the concentration–time profile depends on its structure, they argue that the structure of the precipitating phase needs to be determined ("highlights the need"). C5

A method point. Distinguishing LLPS from crystallization is difficult at a few µg/mL, and the evolving size of the colloid distorts both absorbance and scattering, so quantitative concentrations from UV alone are "extremely challenging". C54 The authors consider it "quite likely" that the first, disordered precipitate would be missed by turbidity-only methods, and recommend an environmentally sensitive fluorescence probe ("appears to be a good complementary method") and SHG alongside UV. C55·C56 Rapidly raising the concentration also gives a practical way to measure the amorphous solubility of a drug like danazol, whose amorphous solid crystallizes before it dissolves. C47·R27

Note by the AI writer (not discussed in the paper): what it suggests for formulation. For danazol, HPMC-AS held supersaturation longest, but every polymer, at only 10 µg/mL, lowered the concentration at which droplets formed. A polymer chosen on induction time alone can therefore cap how high the concentration goes, and the useful ceiling with a polymer present is the onset measured with that polymer, not a value scaled from the drug-alone ratio (for HPMC the scaled 43 µg/mL against a measured 8–9 µg/mL). The polymer concentrations here are far below those released by a dissolving ASD, so whether these effects grow, saturate or change sign at realistic levels is open.

Limitations

Limitations stated by the authors. The amorphous solubility estimate carries errors from the assumptions of the Hoffman equation and from the crystalline solubility measurement. C14 Attempts to quantify the polymer in the drug-rich phase were "not very successful", and the NMR numbers are preliminary. R26 Induction times vary widely, which they attribute to the stochastic nature of nucleation. C32 The final pyrene ratio after crystallization with polymer points to an "unknown" pyrene–drug–polymer complex. C36 The consequences of LLPS for subsequent crystallization, including the phase in which crystals form, are "not well understood". C45 And UV-based concentrations in colloidal solutions are unreliable without orthogonal methods. C54

The AI writer's own judgement (1): the numbers behind the headline comparison. The comparison of the measured onset (13 µg/mL) with the estimated amorphous solubility (16 µg/mL) is the paper's validation of the thermodynamic estimate, but the printed inputs give a ratio of 15.4 rather than 19.6, and the danazol row of Table 2 does not follow its own footnote. X1 Agreement within a few µg/mL holds either way, so the qualitative conclusion stands; the specific numbers should not be reused without checking.

The AI writer's own judgement (2): what is measured and what is inferred. The onset of phase separation is the best-supported result: two independent methods agree within 1 µg/mL in all four systems. R5 The crystallization of the drug-alone droplets within minutes is supported by three read-outs. R11·R13·R17 The polymer ranking of induction times is consistent across concentrations and methods, although the methods differ by up to about 40% for some single conditions and n is not stated. R17·X5·X11 The mechanism is much less secure: polymer inside the droplets rests on preliminary NMR that is not shown and gives no value for HPMC-AS X15; coalescence without polymer has no early size data X6; the one-phase versus two-phase contrast in induction times uses 10 µg/mL solutions that are above the onset with HPMC and HPMC-AS X3; and the summary times given for each polymer differ between the abstract, the graphical abstract, the text and Table 4. X4

The AI writer's own judgement (3): smaller issues. The captions of Figures 8–10 give the polymer as 0.01% w/v, while the materials section and the methods give 10 µg/mL, which is 0.001% w/v. X2 The final concentration with polymer is stated as about 2–3 µg/mL, while the figures end at about 2.6–3.8 µg/mL at different times. X7 Figure 13 shows SHG images for a 20 µg/mL solution, a condition the methods do not describe. X8 The Figure 2 caption puts the extinction rise ">10 µg/mL" for all polymer solutions, while Table 3 gives 8–11 µg/mL. X14 Several text citations of ref 12 point to work printed as ref 11. X10

Conclusion

The paper shows, for danazol in pH 6.8 buffer at 25 °C, that a supersaturated solution pushed above about 13 µg/mL does not go straight to crystals: it first separates into noncrystalline drug-rich droplets, close to the estimated amorphous solubility, and these crystallize within 6–10 min without polymer. R5·R17·C1·C22 At only 10 µg/mL, PVP, HPMC and HPMC-AS stretch the lifetime of this supersaturated two-phase solution to hours, HPMC-AS the most, but each also lowers the concentration at which droplets form, so the polymers both help and hurt. R17·R5·C2·C57 The authors' explanation, polymer mixing into the droplets and sitting at their surface to slow nucleation, fits the size, charge and onset data but rests on preliminary measurements and was not tested directly. C48·C53·X15 The study also demonstrates a practical toolset, UV extinction, a pyrene polarity probe and SHG, for telling a noncrystalline precipitate from crystals at concentrations of a few µg/mL. C56