D. Crystallization from solution

How it was shown

Hsieh and co-workers (2012) dissolved each base at low pH in a Sirius GLpKa titrator (37 °C, 0.15 M KCl, nitrogen) and added 0.5 N KOH until a UV/Vis probe detected turbidity; small acid and base aliquots then moved the solution slightly sub- or supersaturated (the CheqSol method), and the neutral-species concentration was calculated from mass and charge balances. The kinetic solubility is the concentration where precipitation first appears, the equilibrium solubility the concentration at zero pH gradient hsieh2012 P4, C6. Precipitates were checked for birefringence, vacuum-dried for 24 h and run in DSC from −50 °C at 5 °C/min, and scaled-up (6- to 40-fold) precipitations were measured by PXRD within 1 h; crystalline solubility came from 72 h shake-flask runs at 37 °C and HPLC hsieh2012 P5, P6, P9, P10, P11. Hsieh, Box and Taylor (2014) ran the same titration without polymer for papaverine, dipyridamole, glyburide and warfarin at 25 °C (1 mg/mL drug in 0.15 M KCl, about 15 mg per run, replicate number not stated), then polarized light microscopy and synchrotron WAXS of the precipitate hsieh2014 P1, P3, P4.

What the data show

Type 1 example. Dipyridamole's neutral concentration climbed to 71.3 µg/mL at about 24–25 min, where turbidity appeared, fell to about 31 µg/mL within a minute and to 4.8–6.5 µg/mL from about 38 min; the peak was 12.5 times the titration equilibrium solubility of 5.7 µg/mL, the supersaturation lasted 14.7 min and the supersaturation factor was 4.6 hsieh2012 R2, R3, R5.b. The precipitate was birefringent needles melting at 165.92 °C onset (53.72 J/g) with PXRD peaks at the reference positions hsieh2012 R11. Type 2 example. Loratadine's concentration rose to 10.7 µg/mL at about 19 min, then stayed at about 9.6–10.3 µg/mL to about 91 min against a crystalline solubility of 1.6 µg/mL; its Bjerrum data followed the curve for 11.3 µg/mL, the HPLC supernatant, from the first point after precipitation hsieh2012 R8, R9, R10.e. The precipitate was non-birefringent with a Tg step from 24.28 to 32.51 °C, a crystallization exotherm near 93 °C on heating and an X-ray halo hsieh2012 R12. After a small KOH aliquot dipyridamole's pH was still falling 150 s later, whereas loratadine's settled at once hsieh2012 R6, R7. Without polymer at 25 °C, dipyridamole peaked at about 84 µg/mL near 15 min and was down to about 5 µg/mL by about 25 min, papaverine peaked at about 240 µg/mL near 16 min and remained near 15 µg/mL from about 18 min, and warfarin peaked at about 165 µg/mL at 19–20 min, fell to about 12 µg/mL at 22 min and stayed near 8 µg/mL thereafter hsieh2014 R1.a–c. Glyburide behaved differently: it peaked at only about 6.5 µg/mL at about 30 min, held 4.5–5.3 µg/mL for about 18 min, fell to about 0.6 µg/mL at about 48 min and 0.2–0.3 µg/mL afterwards; its precipitate was round, non-birefringent aggregates at 15 min and birefringent from 30 min hsieh2014 R1.d, R2, R3. Concentrations measured about 1 h after precipitation were at or below crystalline solubility for all four drugs without polymer (papaverine 9.5 against 12.2, dipyridamole 3.4 against 5.4, glyburide 0.2 against 0.2, warfarin 3.7 against 3.7 µg/mL) hsieh2014 R4.a, R4.k, R4.u, R4.ae.

Figure

Panel (a) shows the neutral concentration peaking near 71 µg/mL and falling to the crystal level within about 15 min; panel (c) shows the Bjerrum data leaving the ionization curve and moving to the crystal-solubility curve hsieh2012 R2, R4.

Panel (a) shows the concentration jumping to about 10.7 µg/mL and staying near 10 µg/mL; panel (b) shows the data lying on the curve for 11.3 µg/mL, far from the crystal-solubility curve hsieh2012 R8, R9.

Why

Hsieh and co-workers explain type 1 behaviour with classical nucleation: crystals need a certain supersaturation before they form, and the concentration then falls to the crystal solubility (J \propto \exp(-\Delta G^{*}/k_B T) with \Delta G^{*} \propto 1/(\ln S)^{2}) hsieh2012 C3, E7, E8, C21. For type 2 they "believe" liquid–liquid phase separation is the best explanation: the separating phase is a supercooled liquid or a glass below the crystal melting point, the solution reaches the amorphous solubility and sits in metastable equilibrium with it hsieh2012 C34, C29. Their support is that turbidity appeared close to the final concentration, the very small metastable zone expected of liquid–liquid separation, that the pH responds instantly, which they read as a very low barrier for exchange between the phases, and that bases which are oils at room temperature (amitriptyline, chlorpromazine, desipramine, fluoxetine, pramoxine) behave as type 2 hsieh2012 R13, C36, C37, R17, C38. The phase itself was not observed, sized or analysed for water hsieh2012 C34, X20. Hsieh and co-workers (2014) read the glyburide plateau as an amorphous stage that lasted about 20 min before crystallization brought the concentration to equilibrium, and found the other three drugs crystallizing within about 15 min hsieh2014 C6, C7, C14. (synthesis: the 2012 and 2014 papers use the same titration, so the glyburide plateau is a fifth, shorter-lived example of the amorphous branch; its 18 min is close to the 14.7 min upper end of the type 1 supersaturation, which shows that duration alone does not separate the branches, whereas precipitate form does.)

Conditions and limits

Both studies used 0.15 M KCl without polymer, at 37 °C (2012) or 25 °C (2014); titration amounts and replicate numbers are not printed, and the duration of supersaturation has no stated start and end criterion hsieh2012 P4, X13, X5; hsieh2014 P1. Solid-state data (PLM, DSC, PXRD with references) are shown for dipyridamole and loratadine only; for the other eight precipitates Table I gives "crystalline" or "amorphous" and birefringence hsieh2012 X7, R1. The degree of supersaturation is defined differently for the two types (peak over titration solubility for type 1; supernatant over HPLC crystalline solubility for type 2), so the two ranges are not on one scale hsieh2012 X3. The 2014 birefringence column has no stated observation time, and WAXS patterns are shown for 8 of the 40 systems of that paper hsieh2014 X3, X14. Precipitate Tg values were measured on vacuum-dried precipitates of unstated water content, so they are not dry-glass values hsieh2012 X20.

Counterexamples and conflicts

No base in the 2012 set broke the match between solution type and precipitate form. The 2014 paper's conclusion that crystals formed within about 15 min "in all cases" does not hold for glyburide, which was non-birefringent at 15 min and had a titration plateau of about 18 min hsieh2014 X2, R3. Some concentrations after precipitation lie below the crystalline solubility (dipyridamole 3.4 against 5.4 µg/mL), which the paper does not discuss; solubility was measured in other buffers over 72 h hsieh2014 X8. The type labels are not tied to crystallization class from the melt: class III covers all five type 2 bases and also three of the four classifiable type 1 bases hsieh2012 X1 (see Crystallization tendency F18).

Transfer check

For a new weak drug, run a pH-shift titration or a rapid pH jump at the intended temperature, record the peak and the concentration after 15, 30 and 60 min, and examine the solid by polarized light and, if possible, PXRD or WAXS within the hour hsieh2012 P4, P5, P10; hsieh2014 P4. Behaviour like type 1 is a fast fall to the crystalline solubility within about 15 min with a birefringent solid; behaviour like type 2 is a concentration that stays at several times the crystalline solubility for an hour or more with a non-birefringent solid hsieh2012 R5, R10. A drug whose solid is amorphous but whose concentration falls within 20–30 min, as glyburide did, is in between and needs a time-resolved solid-state read-out hsieh2014 R1.d, R3.

History

Hsieh and co-workers (2012) first linked CheqSol "chaser" and "non-chaser" behaviour (Box 2006, outside the library) to the form of the precipitate for ten bases hsieh2012 C4, C7, C20. Hsieh, Box and Taylor (2014) extended the titration to two acids and two more bases with synchrotron WAXS and added the question of polymers (F16) hsieh2014 C1. The chapter on amorphous solubility and LLPS continues from here: it follows the LLPS concentration of weak bases against pH (see Amorphous solubility and LLPS F10) and a weak-base salt shifted from gastric to intestinal pH (see F23).

How it was shown

Hsieh and co-workers (2012) compared the HPLC supernatant of each type 2 precipitate (ultracentrifuged after titration to at least two pH units above the pKa) with two estimates: the Hoffman free-energy difference from the heat of fusion and melting point, and the same corrected for water sorbed by the amorphous solid (dynamic vapour sorption at 37 °C, Gibbs–Duhem integral, Murdande method) hsieh2012 P11, P13, P8. Jackson and co-workers (2014) detected the onset of a drug-rich phase in danazol by two independent methods, UV extinction at 350 nm while the drug was pumped in, and the pyrene I1/I3 ratio after a solvent shift, and compared it with the same two-factor estimate, \sigma^{amorph}/\sigma^{crystal} = e^{-I(a_2)}\,e^{\Delta G/RT} jackson2014 P6, P7, E1. Hsieh, Box and Taylor (2014) compared the warfarin and glyburide concentrations about 1 h after precipitation with the Hoffman estimate from DSC melting data hsieh2014 P6, P8, E2, E3. Ilevbare and co-workers dissolved amorphous ritonavir (a spin-coated film), efavirenz and celecoxib (solvent-evaporated solid) in pH 6.8 buffer at 37 °C with in-situ UV and compared the maximum with the calculated value ilevbare2012b P5, P6; ilevbare2013c P7, R2. Raina and co-workers (2015) precipitated six dihydropyridines by a solvent shift to a nominal 10 mg/mL in pH 6.8 buffer with 10% DMSO and compared the supernatant at 3 h (ultracentrifugation, UV, n = 3) with a Hoffman estimate with a water-sorption correction (see F21) raina2015b P1, P3, P7, E2. Duong, Ni and Taylor (2022) measured the onset of light scattering of posaconazole pumped from a DMSO stock into phosphate buffers of pH 1.0–7.0 (37 °C, 350 rpm) and estimated the amorphous solubility at pH 7.0 from DSC melting data with the Hoffman approximation and a water-sorption activity factor of 0.33 duong2022b P5, P6, R7. Shah and Taylor (2025) took the drug left in the supernatant after ultracentrifuging 100 µg/mL posaconazole in 900 µg/mL HPMCAS as the LLPS concentration shah2025 P3.

What the data show

Table V of the 2012 paper: carvedilol, crystalline 1.1 µg/mL, supernatant 8.68, estimates 24.4 (ratio 22.2) and 13.53 (12.3), titration equilibrium and kinetic values 19.4 and 21.8; clotrimazole 0.4, 5.09, 5.0 (11.9) and 4.00 (9.8), titration 5.7 and 6.8; clozapine 8.8, 157, 179.5 (20.4) and 147 (16.7), titration 170 and 180; ketoconazole 3.7, 76.5, 202 (54.6) and 56.6 (15.3), titration 84.9 and 91.7; loratadine 1.6, 11.3, 11.0 (7.0) and 6.8 (4.3), titration 9.9 and 10.7 hsieh2012 R10. The uncorrected value fits clotrimazole and loratadine, the corrected value fits clozapine, and ketoconazole's supernatant lies between an estimate 2.6 times higher and one 0.74 times as high (synthesis: 202/76.5 = 2.6 and 56.6/76.5 = 0.74) hsieh2012 X2. The correction lowered every estimate, for ketoconazole from 202 to 56.6 µg/mL hsieh2012 R10.d. For danazol the onset was 13 µg/mL by the probe and by UV extinction, with the crystalline solubility 0.9 ± 0.2 µg/mL and the estimate 16 ± 4 µg/mL from a ratio of 19.6; the printed heat of fusion (28.9 kJ/mol), melting point (225.4 °C), 25 °C and water factor 0.935 give 15.4, so about 14 µg/mL (synthesis: 0.9 × 15.4 = 13.9) jackson2014 R5.a, R1.a, R2, X1. Two earlier estimates of the ratio were 13.7 and 26.5 jackson2014 R3. For warfarin and glyburide the Hoffman equation gave about 48-fold and 60-fold (recomputed 47.7 and 59.9), with up to 2-fold less expected from water; warfarin held 103–224 µg/mL, the ratios to the polymer-specific solubility being 23.8, 14.1, 18.7, 13.1, 21.0 and 24.9 (PVP, PVPVA, HPMC, HPMCAS-LF, HPMCAS-HF, Eudragit E100), but 27.8–60.5 against the 3.7 µg/mL of the polymer-free solution, the last exceeding the 48-fold ceiling hsieh2014 R15, R16, R17, E3, X4. When amorphous solid was dissolved, ritonavir reached 19.8 µg/mL against 20.6 calculated and held it for about 2 h before rapid desupersaturation, efavirenz reached 12.3 against 19.8, and celecoxib reached 2.5 against 22.6 µg/mL, a peak supersaturation of 1.7 ilevbare2012b R1, R2; ilevbare2013c R2, R3. Amorphous celecoxib particles turned birefringent within about 1 min in buffer, whereas amorphous efavirenz particles shrank over 3 h with no birefringence ilevbare2013c R4, R5. In the dihydropyridine set the 3-h supernatant without polymer was 1.9, 30.3 and 51.7 µg/mL for cilnidipine, felodipine and nisoldipine against estimates of 0.5, 6.68 and 6.3 µg/mL, but 21.8, 17.3 and 8.7 µg/mL for nifedipine, nimodipine and nitrendipine against 48, 20 and 19.0 µg/mL raina2015b R10.a–f. The authors read the felodipine value as "consistent with" an amorphous precipitate and the nifedipine value as close to its crystalline solubility in 10% DMSO with HPMCAS (28.2 µg/mL) raina2015b C18, R10.c. The printed estimates cannot be reproduced (felodipine 5.93 recomputed against 6.68 µg/mL), the supernatants were measured in 10% DMSO and the estimates refer to buffer, and the felodipine and nifedipine bars of Fig. 9 differ from Table 3 (about 7.9 and 65 against 6.68 and 48 µg/mL) raina2015b X1, X2, X3. A later danazol paper from the same group recalculated the amorphous solubility with heat-capacity data and the water correction as 7.8 µg/mL (the earlier estimate was 16) and found the onset of phase separation at about 8 µg/mL by UV extinction, the pyrene probe read after 1–5 min, NTA and the flux plateau, so the 13 against 16 µg/mL of the first danazol paper does not stand; the ratio of 7.8 to the crystalline solubility of 0.9 ± 0.1 µg/mL is 8.7 (synthesis: 7.8/0.9), where the earlier ratio was 19.6 jackson2016 R3, R4, R8, R10, R13; jackson2014 R2. The thermal inputs of the new estimate are not printed jackson2016 E3.

In the posaconazole paper the measured amorphous solubility was 9.08 ± 0.07 µg/mL at pH 7.0 against an estimated 10.22 ± 0.37 µg/mL (Tm 169.1 °C, ΔHf 76.95 J/g, water uptake 4.6%), which the authors call "reasonable agreement"; the printed ratio of 37.9 cannot be recomputed from these inputs (the extractor obtains about 26.5 with a molar mass of 700.8 g/mol), and the exponent of the printed equation has the wrong sign duong2022b R6, R7, C17, X2. The ratio of amorphous to crystalline solubility stayed at 32.4–37.3 from pH 2.0 to 7.0, as the chapter on amorphous solubility and LLPS found for other weak bases, and fell to 22.4–28.3 at pH 1.0–1.6 duong2022b R1, X5. With 900 µg/mL HPMCAS the posaconazole LLPS concentration was 10.1–12.5 µg/mL at pH 6.5, about 30–40 times its crystalline solubility of 0.31–0.34 µg/mL shah2025 R1, R2, C10.

Figure

Compare the supernatant column with the two estimated amorphous solubilities, and note the one drug (carvedilol) below both hsieh2012 R10.

Why

Hsieh and co-workers give two grounds that the type 2 plateau is the amorphous solubility: the precipitate in contact with the solution is amorphous, and the supernatant "corresponds well" with the estimates; they read the low carvedilol value as conversion to a less soluble form, "possibly" liquid crystalline, during ultracentrifugation, since its titration values agree with the estimates hsieh2012 C30, C31. They also present the titration as "a new avenue" to measure amorphous solubility without a reference amorphous solid and without filtration or centrifugation, which can trigger crystallization hsieh2012 C32, C33. Jackson and co-workers call the agreement between 13 and 16 µg/mL "excellent" and a validation of the estimation approach jackson2014 C22. Hsieh, Box and Taylor read the warfarin supersaturation as "consistent with" an amorphous phase that contains some water, and call glyburide "harder to interpret" because its crystalline solubility is very low and uncertain with polymer and some filtrates stayed turbid hsieh2014 C40, C41, R21. Ilevbare and co-workers read the closeness of the measured and calculated ritonavir values as slow crystallization of both the dissolving solid and the solution, and the low celecoxib value as rapid crystallization ilevbare2013c C21, C22. (synthesis: the three routes, pH jump, solvent shift and dissolution of solid, reach the same ceiling when the drug is slow to crystallize and fall short of it when it is not; the pH-jump and solvent-shift routes avoid the competing crystallization of the dissolving solid.)

Conditions and limits

None of the estimates can be recomputed from the papers: heats of fusion and sorption isotherms are not printed in the 2012 paper, the amorphous samples for sorption are not described, and the danazol ratio does not follow from its inputs hsieh2012 X14; jackson2014 X1. The 2012 supernatants are single time points after ultracentrifugation of unknown delay hsieh2012 X17. The 2014 glyburide reference solubility is a titration value assumed for all polymers because shake-flask values were below the HPLC limit of about 1 µg/mL hsieh2014 R23, X9, X10. "Amorphous solubility" in the 2013 papers means the calculated value, and the celecoxib gap is not discussed ilevbare2013b X9. All measurements are at 25 or 37 °C in simple buffers without surfactant.

Counterexamples and conflicts

Carvedilol (8.68 against 13.53–24.4 µg/mL) does not match, and celecoxib and efavirenz reach only 11% and 62% of the calculated value when the solid is dissolved (synthesis: 2.5/22.6 = 0.11 and 12.3/19.8 = 0.62) hsieh2012 R10.a; ilevbare2013c R2. The warfarin ratio against the polymer-free solubility exceeds the Hoffman ceiling for Eudragit E100 (60.5 against about 48) hsieh2014 X4. With polymer, the measured danazol onsets (8–11 µg/mL) lie far below the same ratio applied to the solubility with polymer (22–43 µg/mL), see F15 and F19 jackson2014 R5, R1. In the dihydropyridine set the 3-h supernatants of nifedipine, nimodipine and nitrendipine lay at 0.45, 0.87 and 0.46 of their estimates, the crystal-limited side of the celecoxib and efavirenz pattern, while felodipine and nisoldipine lay at 4.5 and 8.2 times theirs, a ratio that mixes a 10% DMSO medium with a buffer estimate (synthesis: 21.8/48, 17.3/20, 8.7/19.0, 30.3/6.68, 51.7/6.3) raina2015b R10, X3, X4. For posaconazole the printed estimate (10.22 µg/mL) agrees with the onset, but the extractor's recalculation from the printed melting data gives a ratio of about 26.5 instead of 37.9, so the agreement cannot be checked from the paper duong2022b X2.

Transfer check

Measure the crystalline solubility under the test conditions (same buffer, temperature and polymer), calculate the Hoffman estimate with and without a water-sorption correction from DSC data and the sorption isotherm of the amorphous drug, and compare both with the onset of a drug-rich phase (UV extinction at a non-absorbing wavelength and a polarity probe) and with the plateau after a pH jump jackson2014 P6, P7; hsieh2012 P13. A drug within a factor of about 1.5 of one of the two estimates is inside the evidence; a drug whose dissolving solid crystallizes first (celecoxib) will not reach the calculated value by dissolution and needs the solvent-shift or pH-jump route ilevbare2013c R2, R4.

History

Hsieh and co-workers (2012) first proposed in the library that a pH-induced plateau is the amorphous solubility and presented the titration as a way to measure it hsieh2012 C30, C32. Ilevbare and co-workers (2012, 2013) used the calculated value as the top supersaturation of their growth and nucleation tests and found it reached by slow crystallizers only ilevbare2012b R3; ilevbare2013c R2. Jackson and co-workers (2014) added the independent detection of the onset by scattering and a probe, and Hsieh, Box and Taylor (2014) compared a stable amorphous precipitate of warfarin with the Hoffman limit jackson2014 C22; hsieh2014 C40. The chapter on amorphous solubility and LLPS then built the systematic comparison of onsets with the calculation (see Amorphous solubility and LLPS F5 and F6). Raina and co-workers (2015) added six dihydropyridines at a nominal 10 mg/mL by solvent shift, with the 3-h supernatant of each compared with its estimate raina2015b R10. Jackson and co-workers (2016) re-measured the danazol onset with four methods and recalculated the estimate, moving both to about 8 µg/mL (see F22) jackson2016 R3, R8. Duong, Ni and Taylor (2022) added posaconazole across pH, with an onset near the estimate and a constant ratio of about 34 from pH 2 to 7 (see Amorphous solubility and LLPS F10) duong2022b C17, C19.

How it was shown

Ilevbare and co-workers (2013) pumped a 4 mg/mL methanol solution of drug into 50–80 mL of stirred buffer (pH 6.8, 37 °C, 300 rpm) to reach 20 µg/mL ritonavir, 19 µg/mL efavirenz or 22 µg/mL celecoxib, said to match their calculated amorphous solubility, and followed extinction at 280 or 350 nm every 30 s; the induction time is the intersection of regression lines through the flat and rising parts, in triplicate ilevbare2013c P9, P10, R6. Alonzo and co-workers (2012) used the same fibre-optic UV approach for felodipine at S 10 (5 µg/mL, 25 °C, 50 mM phosphate, pH 6.8, n = 3) and took the intersection of a line through the flat start with a line through the falling part alonzo2012 P5, R16. Jackson and co-workers (2014) followed danazol at 10, 15 and 20 µg/mL by UV absorbance, UV extinction and pyrene fluorescence jackson2014 P8, R17. The growth side comes from seeded desupersaturation: 0.010 g seeds in 50 mL at 37 °C, slope over the first 2 min, divided by seed mass and BET area ilevbare2013b P10, P15, E6. From 2018 the polymer-free controls of the inhibitor papers add further drugs: nine drugs from methanol, DMSO or DMF stocks into 47 mL of 100 mM phosphate buffer pH 6.8 at 37 °C, 300 rpm, at 4 to 58 times their cited crystalline solubility (UV at two wavelengths, n = 3) mosqueragiraldo2018a P4, X11; four drugs at each medium's amorphous solubility in 20 mL of pH 6.5 phosphate buffer at 37 °C by light scattering indulkar2018 P9; enzalutamide at 30–120 µg/mL in 35 mL of 50 mM phosphate pH 6.5 by UV at 237 and 446 nm wilson2021 P3; atazanavir in 15 mL of FaSSIF buffer pH 6.5 at its amorphous solubility enright2020 P14; atazanavir and posaconazole in 4 mL of two blank FaSSIF buffers elkhabaz2021 P7; and posaconazole in PBS pH 6.5 from S 5 to 33.6 and in maleate buffer at 10 µg/mL duong2022b P7; shah2025 P4.

What the data show

Without polymer the mean induction times were about 2.4 (celecoxib), 5.1 (efavirenz) and 120 min (ritonavir); the starting supersaturation was about 14.7 and 15.4 for celecoxib and ritonavir but only about 2.3 for efavirenz (19/8.2, where the paper's 2.4 is the ratio of the calculated amorphous solubility 19.8 to 8.2) ilevbare2013c R8, R9.a, R1.a, X4. Celecoxib started at 11 µg/mL (S 7.3) crystallized after 27.5 ± 0.7 min ilevbare2013c R15. Ritonavir in the binary-additive study did not desupersaturate for 8 h at 10 µg/mL and nucleated after about 2 h at 20 µg/mL ilevbare2012a R9. Felodipine at S 10 began to lose drug after about 10–15 min and its induction time was 15.3 min alonzo2012 R15, R16. Danazol's induction times were 10 ± 6, 6 ± 1 and 7 ± 3 min at 10, 15 and 20 µg/mL by UV absorbance jackson2014 R17.a–c. For growth, the normalized rates at S 1.2–1.3 were 0.20 (ritonavir), 0.91 (celecoxib) and 2.97 mg min⁻¹ m⁻² (efavirenz), about 15-fold between the extremes (synthesis: 2.97/0.20 = 14.9); at S of 6.6 and 7.6 celecoxib and ritonavir were nearly equal at 6.23 and 6.14, and at the amorphous-level S of 14.7 and 15.4 they were 19.08 and 14.32 ilevbare2013b R7.a–g. Efavirenz was the only drug with detectable secondary nucleation above 10 µg/mL (S 1.2), so its growth with polymers was tested at one supersaturation only ilevbare2013b R5. Amorphous celecoxib particles showed birefringence within about 1 min in buffer, amorphous efavirenz particles none in 3 h ilevbare2013c R4, R5. Chen and co-workers (2015) chose the supersaturation of each of 11 drugs in buffer (ratio of concentration to crystalline solubility 1.5–15, at 25 °C, telaprevir at 37 °C) so that the induction time would be under 100 min, and found about 7 min for bifonazole, 8 for felodipine, tadalafil and naproxen, 20 for nevirapine, 28 for compound 1, 30 for indomethacin, 34 for telaprevir, 76 for warfarin, 78 for griseofulvin and 87 min for celecoxib (see F28) chen2015 R3, P2. In the solvent-shift study of six dihydropyridines at a nominal 10 mg/mL the first crystalline sampling time without polymer was 0.25 h for nifedipine, 3 h for nimodipine and nitrendipine, 6 h for felodipine and nisoldipine and 12 h for cilnidipine (details in F21) raina2015b R6. For acetaminophen at S 1.5 (pH 6.8, 20 °C) without polymer, 95% of 1.2 mL vials had crystallized within 26 min and the first crystals in a 4 mL vessel were counted after 150–785 s (see F27) trasi2015 R1, R10. Li and co-workers (2016) found 5 ± 2 min for celecoxib at 20 µg/mL, 2 ± 1 min for nevirapine at 800 µg/mL and 5.4 ± 0.4 min for flibanserin at 45 µg/mL in pH 6.5 buffer at 37 °C (see F29); the same two drugs, nevirapine and celecoxib, crystallized after about 20 and 87 min in the earlier study at lower relative supersaturation (C/Ceq 4 and 5; the later study's ratios are about 7.6 and 17, synthesis: 800/105.3, 20/1.2) li2016a R6.a, R1.a, M2; chen2015 R3.j, R3.a. For telaprevir (pH 6.5, 50 mM phosphate, 37 °C) the unseeded induction time without additive was about 30 min at an activity-based supersaturation δ of 11.5 (about 60 µg/mL) and immediate at δ 28.8 (about 150 µg/mL, just above the amorphous solubility), against about 14–15 min at 150 µg/mL in 100 mM phosphate at pH 6.8 in another study (see F32) lu2017 R3.a, R4.a; mosqueragiraldo2016 R4.a.

The 2018–2025 controls (min; read from bars unless stated): with one protocol the nine drugs crystallized after about 1 (griseofulvin, danazol), 2–3 (ezetimibe), 4 (celecoxib), 6 (nifedipine), 8 (nevirapine), 15–16 (telaprevir), 40 (atazanavir) and 66 ± 18 min (ritonavir), the order of the authors' fast, intermediate and slow classes but at supersaturations from about 4 to 58 mosqueragiraldo2018a R1, R2, X11. At each one's amorphous solubility in pH 6.5 buffer, atazanavir took 170, cilnidipine 210 ± 90, ritonavir 320 ± 150 and tacrolimus 340 ± 100 min indulkar2018 R19. Enzalutamide crystallized within about 5–15 min at 30–120 µg/mL, with no difference between solutions below and above its amorphous solubility of 42 µg/mL (Kruskal–Wallis p = 0.51) wilson2021 R1, R5. Atazanavir took 253 ± 65 min in FaSSIF buffer and about 92–102 min in two blank buffers of another paper, and posaconazole about 5–8 min in those buffers, 8.4 min at S 33.6 in PBS and 29 ± 5 min at 10 µg/mL in maleate buffer pH 6.5 enright2020 R2; elkhabaz2021 R6, R7; duong2022b R10; shah2025 R3. Telaprevir in 50 mM phosphate at δ 11.5 took about 27–30 min in three figures of the 2018 media paper, as in the 2017 paper lu2018 R3.a, R4.a, R6.a; lu2017 R3.a.

Figure

Panels (a), (c) and (e) are the polymer-free runs; the induction time is where the two fitted lines cross, at about 2.3, 5.8 and 106 min in these single runs ilevbare2013c R6.

Why

Ilevbare and co-workers attribute ritonavir's slow nucleation "most likely" to its higher molecular weight and greater conformational flexibility, and read the fast crystallization of celecoxib and efavirenz from amorphous dissolution as faster nucleation ("suggests"); neither explanation was tested ilevbare2013c C24, C25. Hsieh, Box and Taylor add that molecules with several low-energy forms, such as the tautomers of glyburide and warfarin, may crystallize more slowly, because only the form that crystallizes is incorporated into a nucleus hsieh2014 C31. Classical nucleation theory predicts the supersaturation dependence seen for celecoxib, a longer induction time at 11 than at 22 µg/mL xie2016a C13. (synthesis: because celecoxib and ritonavir grew at almost equal rates per seed area at S of about 7 but their induction times at S of about 15 differ about fifty-fold (120/2.4 = 50), ritonavir's persistence in solution is a nucleation property; this comparison mixes two supersaturations and two kinds of experiment, and efavirenz, with the highest growth rate and a 5 min induction time at S 2.3, is fast in both.)

Conditions and limits

The starting supersaturation of efavirenz (about 2.3) differs from that of the other two (about 15), the methanol fraction (about 0.5% v/v) is not stated and the solubility used for S was measured without methanol ilevbare2013c X4, X16. Induction times include the time to grow nuclei to a detectable size, so slow-growing systems read longer (see F5) ilevbare2013c E2, X14. The felodipine and danazol runs are at 25 °C and in different buffers (50 mM and 10 mM phosphate), the others at 37 °C in 100 mM phosphate alonzo2012 P5; jackson2014 P8; ilevbare2013c P9. Only three drugs have both a growth and a nucleation measurement.

Counterexamples and conflicts

The melt-quench class does not explain the order: ritonavir and efavirenz are both class III but differ 24-fold in induction time (120/5.1 = 24, synthesis), see Crystallization tendency F18 ilevbare2013c R8. Efavirenz crystallizes in minutes at S 2.3 while ritonavir takes 2 h at S 15.4, so supersaturation alone does not set the time ilevbare2013c R9.a, X4. Nitrendipine, Class III from the melt, was crystalline by 3 h in solution, as early as the Class II nimodipine raina2015b R1.f, R1.d, R6.f, R6.d. The same drug can differ many-fold between studies when the supersaturation differs: nevirapine crystallized after about 20 min at C/Ceq 4 and about 2 min at about 7.6, and celecoxib after about 87 min at C/Ceq 5 and about 5 min at about 17 (synthesis: 800/105.3, 20/1.2), which is the supersaturation dependence of F14 seen across two papers, with pH and temperature also different chen2015 R3.j, R3.a; li2016a R6.a, R1.a. For telaprevir the 2018 media paper and the 2017 bile-salt paper, with one protocol, gave the same control (about 27–30 min at δ 11.5), and the cellulose-ester paper of 2018 gave about 15–16 min at 150 µg/mL as the 2016 polymer paper did (about 14–15 min), whereas atazanavir and posaconazole controls differ up to about sixfold between protocols (see F35) lu2018 R6.a; lu2017 R3.a; mosqueragiraldo2018a R1.c; mosqueragiraldo2016 R4.a.

Transfer check

For a new drug measure the unseeded induction time at the supersaturation the formulation will create, in the intended medium and at 37 °C, in triplicate, with detection by light scattering at a wavelength the drug does not absorb; add a seeded growth rate at the same supersaturation if nucleation and growth are to be separated ilevbare2013c P9, P10; ilevbare2013b P10. A drug whose induction time is under 10 min at its amorphous solubility is inside the fast group (celecoxib, efavirenz, danazol, felodipine); one above 1 h is in the ritonavir group ilevbare2013c R8; jackson2014 R17.

History

Alonzo and co-workers (2012) gave the first induction time of the chapter (felodipine, 15.3 min at S 10) alonzo2012 R16. Ilevbare and co-workers (2012, 2013) added the 8 h and 2 h values for ritonavir and the three-drug comparison ilevbare2012a R9; ilevbare2013c R8. Jackson and co-workers (2014) showed that three read-outs place danazol crystallization at 5–15 min jackson2014 R13, R17. Xie and co-workers (2016, in the ASD dissolution chapter) confirmed the celecoxib times at 22 and 11 µg/mL xie2016a R2. Raina and co-workers (2015) added a six-analogue series by solvent shift at 10 mg/mL and showed melt classes and solution times diverging for close analogues raina2015b C28, C29. The title was widened from "about 2 min to 2 h" to "about 1 min to 6 h" after the papers of 2018–2025: the cellulose-ester paper of 2018 added nine drugs in one protocol, the media papers of 2018–2021 added atazanavir, ritonavir, cilnidipine and tacrolimus at their amorphous solubility, and the enzalutamide and posaconazole papers of 2021–2025 added two more drugs mosqueragiraldo2018a R1; indulkar2018 R19; enright2020 R2; wilson2021 R1; duong2022b R10; shah2025 R3.

How it was shown

Jackson and co-workers (2014) used four read-outs on 10 mM phosphate buffer (pH 6.8) at 25 °C: UV extinction at 350 nm while a 4 mg/mL methanol stock was pumped in at 5 µg/mL/min and the onset taken at the crossing of two fitted lines; the pyrene I1/I3 ratio of 2 µM pyrene after a solvent shift, read after 30 s and 15 min (excitation 332 nm); SHG imaging (SONICC) of 10 and 50 µg/mL solutions in 96-well plates, from 30–60 s after mixing; and DLS for droplet size jackson2014 P6, P7, P10, P9. The induction time was taken at the change of slope of the UV signal together with the rise of I1/I3, on 200 mL at 200 rpm with a dip probe at 288 and 350 nm jackson2014 P8, C30. Controls were pyrene in solvents and in a dry amorphous danazol film jackson2014 P7, R6, R9. Jackson and co-workers (2016) added nanoparticle tracking (NTA) of the scattering particles against added drug, ultracentrifugation with HPLC of the continuous phase, a diffusion-cell flux curve and pyrene readings at 15 s, 1 min and 5 min after each addition, in 10 mM phosphate (pH 6.8) at 25 °C (see F22) jackson2016 P5, P6, P7, P8, P9.

What the data show

Below about 13 µg/mL the solutions scattered almost nothing at 350 nm; above it extinction rose to about 0.026 at 15 µg/mL and about 0.068 at about 20 µg/mL jackson2014 R4. Pyrene read 1.95 ± 0.03 in buffer, stayed at about 1.92–1.94 up to 13 µg/mL, dropped to about 1.77 at 14 µg/mL and reached about 1.53 at 24 µg/mL and about 1.52 at 30 µg/mL; 50 and 100 µg/mL went no lower jackson2014 R7, R8, R10. Reference values were 1.97 in water, 1.55 in methanol, 0.66 in cyclohexane and 1.4 in dry amorphous danazol jackson2014 R6, R9. After 15 min the ratio of every solution above the onset was back at about 1.92–1.945 jackson2014 R11. At 20 µg/mL the apparent UV concentration fell from about 19.2 µg/mL at 1 min to about 14.4 at 5, 11.8 at 10, 2.1 at 30 and 1.4 µg/mL at 60 min, while 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 1.93 at 30 min jackson2014 R15. The first SHG spots appeared at 5 min in both the 10 and the 50 µg/mL solutions, and the signal was widespread at 12 and 10 min jackson2014 R13. The droplet size by DLS was about 490 nm at once and about 9800 nm after 1 h jackson2014 R22. Induction times (UV absorbance, UV extinction, fluorescence, min) were 10 ± 6 at 10 µg/mL, 6 ± 1, 7 ± 1, 10 ± 2 at 15 µg/mL and 7 ± 3, 10 ± 7, 9 ± 3 at 20 µg/mL jackson2014 R17.a–c. At 10 µg/mL, below the onset, the absorbance fell suddenly at about 5 min jackson2014 R16. In the later paper the onset without polymer was 8.3 ± 1.0 µg/mL by UV extinction at 450 nm (slow addition), 8 µg/mL by the probe read after 1 or 5 min and 8 µg/mL by NTA, where the count rose from about 2 × 10⁷ per mL below 7 µg/mL to about 1.8 × 10⁸ at 8 and about 3.2 × 10⁹ at 15 µg/mL; the flux rose linearly to 8 µg/mL and then levelled off; read 15 s after the addition the probe ratio fell only between 10 and 14 µg/mL (about 1.90 at 10 µg/mL and 1.75 at 14 µg/mL, against about 1.80 and 1.57 at 1 min) jackson2016 R7, R8.a, R10, R13. The 13 µg/mL of the first paper is therefore a 15 s reading, and the onset is about 8 µg/mL (see F22). Without polymer the induction time at 15 µg/mL is about 5 min in the bar chart and 10–15 min in the text jackson2016 R17.a, X2.

Figure

The black series (danazol alone) falls from about 1.95 to about 1.5 above 13 µg/mL; a lower ratio means pyrene sits in a hydrophobic, noncrystalline drug-rich phase jackson2014 R8.

Why

The authors read the abrupt fall of the pyrene ratio as pyrene partitioning into a new, noncrystalline danazol phase ("consistent with"), the plateau near 24 µg/mL as most pyrene now sitting in it, and the gap between 1.5 and the dry-film value of 1.4 as some water in the droplets ("can be attributed") jackson2014 C19, C20, C21. They argue that once the concentration exceeds the amorphous solubility, phase separation is unavoidable because supersaturation of a hydrophobic drug is capped by the spinodal ("it appears"), after which the surrounding solution stays at the separation concentration; crystals could form from the drug-rich or the drug-lean phase, and how LLPS affects crystallization is "not well understood" jackson2014 C44, C28, C45. They attribute the early fall of the UV signal at 20 µg/mL to coalescence of the droplets, which changes how they absorb and scatter light, not to crystallization ("is attributed") jackson2014 C29. The return of pyrene to the water value is read as crystallization excluding pyrene from the solid ("strongly suggesting") jackson2014 C25. (synthesis: for danazol without polymer the drug-rich phase is a short-lived precursor, as telaprevir and ritonavir are in the chapter on amorphous solubility and LLPS; here its lifetime of 6–10 min is of the same order as the nucleation time of the fastest crystallizers in F3.)

Conditions and limits

One drug, one buffer, one temperature and no replicate number for the onsets, Table 4, DLS or zeta potential jackson2014 X11. The methanol fraction rises with the danazol concentration (about 0.5% at 20 µg/mL, about 1.5% at 30 µg/mL from the 2 mg/mL stock, extractor calculation) jackson2014 X12. The coalescence explanation has no droplet size in the first minutes: the DLS data for the drug alone are two points, 0 and 1 h, the second after crystallization jackson2014 X6. SHG sees only crystals, not solutions or disordered material, and the frames at 20 µg/mL used for the time overlay are not described in the methods jackson2014 C13, X8.

Counterexamples and conflicts

The 10 µg/mL solution, below the 13 µg/mL onset read at 15 s, crystallized in about the same time (10 ± 6 min against 6 ± 1 and 7 ± 3 min) jackson2014 R17.a–c. (synthesis: read against the first paper's onset this suggested that droplets do not shorten the induction time of danazol, whereas the ritonavir study cited by the authors found it shorter with droplets present jackson2014 R28; the later onset of about 8 µg/mL puts all three concentrations in the two-phase region, so the series does not test that question.) The estimate used for comparison, 16 µg/mL, comes from a ratio of 19.6 that the printed inputs reproduce as 15.4 (F2) jackson2014 X1. With the onset at about 8 µg/mL, the 10 µg/mL solution that crystallized as fast as the 15 and 20 µg/mL ones already contained droplets, so its crystallization time says nothing about solutions below the onset, and the contrast with the ritonavir study is not a contrast of one-phase and two-phase solutions jackson2016 R8, R17.a.

Transfer check

To test whether a drug passes through a drug-rich phase, add the drug stepwise to the intended medium with a scattering read-out at a non-absorbing wavelength and a polarity probe such as pyrene, then repeat after 15 min; a probe ratio that drops and then returns to the water value while particles appear marks a transient noncrystalline phase that crystallizes jackson2014 P6, P7, R11. Confirm crystals with SHG or polarized light, because turbidity alone cannot tell droplets from crystals jackson2014 C55, C56.

History

The title was changed after the later danazol paper moved the onset from 13 to about 8 µg/mL. Ilevbare and co-workers (2013) had shown the drug-rich phase for ritonavir and the closeness of its onset to the amorphous solubility (see Amorphous solubility and LLPS F1) jackson2014 R29. Jackson and co-workers (2014) added danazol, a faster crystallizer, with three independent read-outs and polymer series (F15) jackson2014 C1, C22. Jackson and co-workers (2016) moved the onset from 13 to about 8 µg/mL by reading later than 15 s and by four further methods, and counted more than 3 × 10⁹ droplets per mL at 15 µg/mL jackson2016 R13, R7, C20.

How it was shown

Raina and co-workers (2015) diluted a 100 mg/mL DMSO stock 1:9 into 50 mM phosphate buffer, pH 6.8 (ionic strength 0.155 M), to a nominal 10 mg/mL in 10% DMSO in a polypropylene tube; the drug precipitated at once, and the temperature of this step is not stated raina2015b P1, R4, X16. The suspension was loaded into capillaries and measured at beamline 12-ID-B of the Advanced Photon Source (12 keV, wavelength 1.033 Å, WAXS q 0.88–2.33 Å⁻¹, 1 s exposures) at 15 and 30 min and 1, 3, 6, 12 and 24 h, a precipitate counting as crystalline once sharp Bragg peaks stood on its broad halo; the earliest possible point was 15 min raina2015b P4, R5. Drops of the same suspensions were viewed between crossed polarizers (10×; 15 min and 6 h shown) raina2015b P5. For the melt screen, crystals were heated at 10 °C/min, cooled at 20 °C/min and reheated at 20 °C/min in pinholed pans, and a drug that recrystallized on cooling was Class I, on reheating Class II and not at all Class III raina2015b P6. The 3-h supernatant of the suspensions was measured by UV after ultracentrifugation (n = 3) and compared with the crystalline solubility at 25 °C and an amorphous solubility estimated from the Hoffman free-energy difference with a water-sorption correction raina2015b P2, P3, P7, E1, E2.

What the data show

Every sample turned turbid at once, and all WAXS patterns carried a broad halo with its maximum near q 1.7–1.8 Å⁻¹ raina2015b R4, R5. Sharp peaks were present for nifedipine at 15 min, 30 min and 1 h, for nifedipine, nimodipine and nitrendipine at 3 h, for all but cilnidipine at 6 h and for all six at 12 h, which gives the first crystalline sampling times 0.25, 3, 3, 6, 6 and 12 h for nifedipine, nimodipine, nitrendipine, felodipine, nisoldipine and cilnidipine raina2015b R5, R6. Only nifedipine was birefringent at 15 min and all but cilnidipine at 6 h raina2015b R7, R8. The authors rank them cilnidipine < felodipine = nisoldipine < nitrendipine = nimodipine < nifedipine, where "=" means the same sampling interval raina2015b C13, X18. Molecular weight (346.33–492.52), log P (1.82–4.10), hydrogen-bond counts, rotatable bonds (6–11) and polar surface area did not track the order, and only cilnidipine stands out as structurally more complex raina2015b M1–M6, C31. In the melt screen nifedipine showed a Tg at 47 °C, a crystallization exotherm near 115 °C on reheating and endotherms at 162 and 173 °C, nimodipine recrystallized with polymorphic transitions (Tm2 116 °C), and felodipine, cilnidipine, nisoldipine and nitrendipine showed no recrystallization on cooling or reheating raina2015b R1–R3. Drugs of one melt class therefore spread over 3–12 h in solution: nitrendipine, Class III, crystallized by 3 h, as early as the Class II nimodipine raina2015b R1.f, R1.d, R6.f, R6.d. Without polymer the 3-h supernatant was 1.9, 30.3 and 51.7 µg/mL for cilnidipine, felodipine and nisoldipine against estimated amorphous solubilities of 0.5, 6.68 and 6.3 µg/mL (ratios 3.8, 4.5 and 8.2; synthesis: 1.9/0.5, 30.3/6.68, 51.7/6.3), but 21.8, 17.3 and 8.7 µg/mL for nifedipine, nimodipine and nitrendipine against 48, 20 and 19.0 µg/mL (ratios 0.45, 0.87 and 0.46; synthesis) raina2015b R10.a–f, X4. The supernatant was measured in 10% DMSO and the estimate refers to buffer, so the ratios mix media raina2015b X3.

Figure

Grey cells are amorphous and black cells crystalline at each sampling time; the first black cell is the first time with Bragg peaks raina2015b R6.

Four drugs that are "slow" from the melt spread over four classes in solution raina2015b C28.

Why

Raina and co-workers argue from free energy that the nominal 10 mg/mL lies far above every amorphous solubility, so the drug separates at once, and that a fast crystallizer lowers its free energy by a liquid-to-solid step straight to crystals (nifedipine), whereas a slower one first separates an amorphous drug-rich phase by liquid–liquid phase separation and crystallizes later, from the precipitate or from the solution ("likely") raina2015b C22, C23, C39. From the dry Tg values and an estimated water content they think most of the precipitates are "likely" viscous supercooled liquids above their Tg in metastable equilibrium with a supersaturated water-rich phase; the water contents and wet Tg values are not printed raina2015b C24, X17. They attribute the poorer discrimination of the melt screen to the different crystallization environment, with temperature, solvent effects and viscosity "likely" playing important roles raina2015b C30. They find no structural predictor and conclude that sustained supersaturation cannot be predicted a priori raina2015b C31, C32. (synthesis: the 3-h supernatants of felodipine and nisoldipine above their estimated amorphous solubility and of the three faster drugs below it are what a drug-rich phase that persists for hours, against crystals that remove it, would give; this is the pattern of the transient drug-rich phase in F4 and in Amorphous solubility and LLPS F3, but no droplet, size or composition was measured here.)

Conditions and limits

One scaffold, one solvent-shift route to an extreme supersaturation (nominal 10 mg/mL, two to four orders of magnitude above the estimated amorphous solubilities of 0.5–48 µg/mL), pH 6.8 and 10% DMSO raina2015b C23, R10. The temperature of the precipitation, WAXS, polarized-light and 3-h experiments is not stated, the number of capillaries per condition is not stated, and the onset times are bounded by the sampling grid, so "6 h" means between 3 and 6 h raina2015b X16, X18. The estimated amorphous solubilities cannot be reproduced from the printed inputs (felodipine 5.93 recomputed against 6.68 µg/mL), differ between media in ways the equation does not allow, and the felodipine and nifedipine bars of Fig. 9 differ from Table 3 (about 7.9 and 65 against 6.68 and 48 µg/mL) raina2015b X1, X2. "Slower crystallizers exhibited higher solution concentrations" holds relative to each drug's estimate but not in absolute terms: cilnidipine, the slowest, had the lowest 3-h concentration, 1.9 µg/mL raina2015b C49, X4. The Fig. 10 class of cilnidipine is "Slow" in the figure and "very slow" in the text raina2015b X15.

Counterexamples and conflicts

The claim that failure to crystallize in the DSC screen does not guarantee slow crystallization is the finding itself: four Class III drugs crystallized between 3 and 12 h raina2015b C29, R6. Nifedipine and nimodipine, the two Class II drugs, are at the fast end, so the screen caught the fastest crystallizers but did not rank the rest raina2015b R1, R6. In the same group's titration work, Class III covered all five type 2 (amorphous-branch) bases and also three of the four classifiable type 1 (crystal-branch) bases, so the melt class did not separate the solution behaviours there either (F1) hsieh2012 X1. The only direct evidence for a liquid precipitate is the absence of Bragg peaks; no polarized-light or droplet observation with polymer present exists for nifedipine raina2015b X19.

Transfer check

For a new compound, precipitate it from a concentrated stock to a concentration far above its estimated amorphous solubility, record the first time at which WAXS or PXRD shows Bragg peaks at a fixed grid of times (for example 15 min to 24 h) at a stated temperature, and look at the sample between crossed polarizers at two times raina2015b P1, P4, P5. Do not take a Class III result from the melt as evidence of a slow solution crystallizer: the six drugs here show that it can be as fast as 3 h raina2015b C29, R6.f. A compound that is amorphous for under 15 min is inside the nifedipine group; one that is still amorphous at 6 h is inside the felodipine and cilnidipine group raina2015b R6.

History

Hsieh and co-workers (2012, 2014) had tied the form and duration of a pH-shift precipitate to the drug (F1, F16) and compared melt classes with solution behaviour hsieh2012 X1; hsieh2014 R18. Raina and co-workers (2015) applied the synchrotron ranking of precipitates (method of Van Eerdenbrugh and co-workers 2014, outside the library) to six close analogues and found the order in solution wider than the melt classes, for a scaffold not tested in the melt-quench classification of Crystallization tendency raina2015b C13, C28, C46.

How it was shown

Jackson and co-workers (2016) worked in 10 mM phosphate buffer (pH 6.8, sodium chloride for constant ionic strength) at 25 °C, creating supersaturation by adding a 5 mg/mL methanol stock of danazol to buffer that already held the polymer jackson2016 M9, P4, P5. UV extinction at 450 nm was followed while a syringe pump added drug at 1 µg/mL/min (without polymer the run started from an aliquot giving 5 µg/mL, to outpace crystallization), n = 3; the pyrene I1/I3 ratio (2 µM pyrene, excitation 332 nm) was read after solvent-shift additions, at 15 s, 1 min and 5 min in the time-resolved series; ultracentrifugation of 15 µg/mL solutions (35,000 rpm, 30 or 60 min) and HPLC of the supernatant gave the concentration of the continuous phase; and nanoparticle tracking (NTA) counted scattering particles against added drug jackson2016 P4, P5, P6, P7, P8. The flux was measured in a side-by-side diffusion cell (regenerated cellulose, 6–8 kDa, orifice 7.065 cm²) with the same polymer in both chambers, donor 0–15 µg/mL and the receiver kept below 0.3 µg/mL; flux is proportional to the drug's activity, so a plateau marks the maximum free-drug concentration jackson2016 P9, E1, E2, C9. The amorphous solubility was calculated from the crystalline solubility in buffer, the melting temperature, heat of fusion, glass transition temperature and heat capacity by DSC (no degradation after heating) and a correction for the water sorbed by the amorphous drug jackson2016 P3, R5. Crystalline solubility was a 48 h shake-flask with polymer, n = 3 jackson2016 P1.

What the data show

Onset. NTA saw no scattering at 3 µg/mL, a few droplets at 8 and many at 11; the count was about 2 × 10⁷ per mL up to 3 µg/mL, about 6 × 10⁷ at 7, about 1.8 × 10⁸ at 8, about 6.3 × 10⁸ at 9 and about 3.2 × 10⁹ per mL at 15 µg/mL jackson2016 R6, R7. For danazol alone, UV extinction gave 8.3 ± 1.0 µg/mL (read from a misaligned row, X1), the probe 8 and NTA 8; the HPLC value could not be obtained because the drug crystallized during the spin jackson2016 R8.a, X1, C56. With polymer (Table II, 15 conditions) the values were 7.6–8.7 (UV extinction), 7–9 (probe), 8.0–9.1 (HPLC) and 7–8 µg/mL (NTA), with no trend with polymer or level jackson2016 R8, C14. The amorphous solubility calculated here is 7.8 µg/mL, half the earlier 16 µg/mL of the same group, which the authors attribute to the more rigorous calculation with heat-capacity data; the thermal inputs are not printed jackson2016 R3, R4, C11. Against the crystalline solubility of 0.9 ± 0.1 µg/mL the ratio is 8.7 (synthesis: 7.8/0.9) jackson2016 R1.a, R3. Crystalline solubility. 0.8–1.3 µg/mL with PVP, 0.9–2.2 with HPMC and 1.0–1.4 µg/mL with HPMC-AS at 1–1000 µg/mL, identical at 10 µg/mL to the earlier paper's 1.3, 2.2 and 1.1; HPMC about doubles it, which the authors call "relatively minor" and "no significant changes", untested jackson2016 R1, C10, C39, X5. Flux. Without polymer the flux rose linearly from about 0.0034 at 2 µg/mL to about 0.0152 at 8 µg/mL and stayed at about 0.0156–0.0159 to 12 µg/mL; at 15 µg/mL with 10 µg/mL polymer it was about 0.0149 (PVP), 0.0156 (HPMC) and 0.0165 (HPMC-AS), and across 1–1000 µg/mL the maximum flux ranged from about 0.0126 (10 µg/mL PVP) to 0.0175 (500 µg/mL HPMC) against about 0.0153 jackson2016 R10, R11. The axis lacks a time unit, replicates and any test are not stated, and a crystalline suspension gave about 0.0011 in one figure and 0.0008 in the other; the plateau-to-crystal flux ratio (about 14 and 19) exceeds the concentration ratio 8/0.9 of about 9, which is not discussed jackson2016 X9, X10, X11. Time of reading. Without polymer the pyrene ratio stayed near the buffer value (about 1.93) to 6 µg/mL at all three times; at 8 µg/mL it was about 1.91 at 15 s and 1.87–1.88 at 1 and 5 min; at 10 µg/mL about 1.90, 1.80 and 1.78; at 12 µg/mL about 1.88, 1.65 and 1.64; at 14 µg/mL about 1.75, 1.57 and 1.60 jackson2016 R13. With HPMC and HPMC-AS the ratio changed at 7–8 µg/mL at every reading time and with PVP the time dependence of danazol alone remained, from data that are not shown and for an unstated polymer level; the group had not seen such an effect in more than 20 other compounds jackson2016 R14, R15. The earlier paper had read 13 µg/mL by probe at 15 s and 8–11 µg/mL with 10 µg/mL polymer jackson2016 R12.

Figure

At 15 s the ratio falls only between 10 and 14 µg/mL; at 1 and 5 min it falls at about 8 µg/mL jackson2016 R13.

The maximum flux with polymer scatters around the value without polymer with no consistent direction jackson2016 R11.

Why

The authors argue from activity: a polymer that mixed into the drug-rich phase would lower the drug's activity there, and so the onset and the flux; one that solubilized the drug would raise the crystalline solubility and lower the supersaturation; neither happened, so "significant amounts of polymer do not mix with the danazol-rich phase", the polymers neither solubilize danazol nor spontaneously mix with the droplets, and the maximum transport rate is set by the amorphous solubility alone ("confirm", "Most definitively") jackson2016 C15, C38, C41, C42, C51. They note that the polymer levels are too low to change viscosity or the supersaturation jackson2016 C47. They explain the time dependence without polymer by "speculating" that danazol has an unusually high energy barrier for forming the new phase, so the amorphous solubility can be exceeded for a short time when supersaturation is generated very rapidly, and that polymer "seemingly" lowers this barrier, "most likely" by lowering the surface tension of the new interface, with HPMC and HPMC-AS but not PVP removing the lag jackson2016 C19, C20, C35, C36, X6. The polymers were taken to sit at the droplet surface because of the zeta potential (see F15) jackson2016 C37. (synthesis: the 2014 and 2016 UV-extinction runs also differ in addition rate, wavelength and starting aliquot, so a faster pump rate may have added to the apparent overshoot in 2014; the fact that the 2014 probe onsets with polymer (8–11 µg/mL) match the 2016 values at every reading time is what a lag-free reading would give.)

Conditions and limits

One drug, one buffer, 25 °C, polymers up to 1 mg/mL, no biorelevant medium and no dissolving dispersion jackson2016 A1, A2. Droplet composition was not measured, so the no-mixing conclusion rests on unchanged onset and flux, which resolve about 0.5–1 µg/mL jackson2016 X14. Flux values are plot readings in relative units; the number of replicates and the meaning of the error bars are not given jackson2016 X9. The fluorescence concentration steps differ between the methods text (0.5 µg/mL), Table II (1 µg/mL) and Fig. 5 (2 µg/mL), and the reading time of the Table II probe values is not stated jackson2016 X7. For the 1 µg/mL HPLC values crystallization during the 30 min spin cannot be excluded, since induction times at that level are only 26–48 min jackson2016 X16. The time-resolved data with polymer are described but not shown and the polymer level is not stated jackson2016 R14. The thermal inputs of the 7.8 µg/mL estimate are not printed jackson2016 E3.

Counterexamples and conflicts

The earlier danazol paper reported onsets lowered by 10 µg/mL polymer from 13 to 8–11 µg/mL by two methods; the later paper's reading-time result removes the conflict only for HPMC and HPMC-AS, because PVP kept the lag jackson2014 R5; jackson2016 R14, X6. In the chapter on amorphous solubility and LLPS, polymers that enter the ibuprofen-rich phase lowered its amorphous solubility by up to about 50%, so "polymers do not change the limit" is a result for danazol, not a rule (see Amorphous solubility and LLPS F19 and F20) jackson2016 C43. Resveratrol, in work cited by the authors, was considerably solubilized by cellulose polymers jackson2016 C43.

Transfer check

Measure the onset with at least two methods and read each addition after 1 min or more as well as at once (a probe ratio at 15 s, 1 min and 5 min; extinction at a slow, stated addition rate), add an ultracentrifugation or NTA onset at the polymer level of the product, and compare the maximum flux with and without the polymer at a donor concentration above the onset jackson2016 P4, P6, P7, P9. A polymer that leaves the onset within about 1 µg/mL and the maximum flux within the scatter of the polymer-free value, as the three here did, is inside the evidence; one that lowers either is not, and the amorphous solubility should then be re-measured with the polymer (see F19) jackson2016 R8, R11.

History

Ilevbare and co-workers (2013) had found for ritonavir that polymers did not move the onset jackson2016 R12. Jackson and co-workers (2014) saw lower onsets with 10 µg/mL polymer than without and speculated that droplet formation is slower without polymer, so that a reading right after supersaturation overestimates the limit jackson2016 C19. Jackson and co-workers (2016) tested this with four methods and several reading times: the onset was about 8 µg/mL with and without polymer, matching a recalculated estimate of 7.8 µg/mL, and the 13 µg/mL was a 15 s reading jackson2016 C20, C14, C40. The heat-capacity route behind the lower estimate is the one that fitted better in Amorphous solubility and LLPS F7 jackson2016 C11.

How it was shown

Duong, Ni and Taylor (2022) asked how supersaturation and medium composition set the crystallization kinetics of the weak base posaconazole. Posaconazole from a DMSO stock was added to 50 mL of stirred PBS pH 6.5 or of four intestinal media at 37 °C: FaSSIF V1 (3.0 mM taurocholate, 0.75 mM lecithin, phosphate, pH 6.5), FaSSIF V2 (3.0 mM taurocholate, 0.2 mM lecithin, maleate, pH 6.5), FeSSIF V1 (15.0 mM taurocholate, 3.75 mM lecithin, acetate, pH 5.0) and FeSSIF V2 (10.0 mM taurocholate, 2.0 mM lecithin, 5.0 mM glycerol monooleate, 0.8 mM sodium oleate, maleate, pH 5.8) duong2022b P7, P1. UV scans every 5–60 s gave the induction time where the 252 nm concentration fell while the 350 nm extinction rose, and crystals were checked by microscopy; the number of replicate runs is not printed duong2022b P7. In the media the concentration ratio was converted to a thermodynamic supersaturation by assuming that the micelle–water partition coefficient falls linearly between the crystalline and the amorphous solubility duong2022b P8, C9. For the high-supersaturation points of each medium the nucleation rate was fitted as \ln(J/S) = \ln A - B/\ln^{2}S with a molecular volume of 920 ų and T = 310 K, giving A from the intercept and γ from the slope, and the critical free energy and nucleus radius followed from the printed equations duong2022b P15, E7, E8, E9. Two other papers give posaconazole without polymer at its amorphous solubility: Elkhabaz and co-workers (2021) in two blank FaSSIF buffers and four simulated or human fluids (4 mL, methanol stock, UV or 400 nm scattering), and Shah and Taylor (2025) at 10 µg/mL in FaSSIF-V2 buffer at pH 5.5–7.5 (extinction at 400 nm, n = 3) elkhabaz2021 P7, R7; shah2025 P4, R3.

What the data show

In PBS the induction time was about 54.5 min at S 5, 41.3 at S 10, 14.2 at S 20 and 8.4 min at S 33.6, the amorphous solubility duong2022b R10. Plotted as log t against x = 1/\log^{2}S, the points fall on two lines, \log t = 1.6703x + 0.2048 (R^{2} 0.9847) above S about 12 and \log t = 0.1167x + 1.4992 (R^{2} 0.9986) below it duong2022b R10, E10. In the media near S 34 the times were about 3.0 min (FaSSIF V2), 2.3 min (FaSSIF V1, at S about 35.7), 1.5 min (FeSSIF V1) and 1.5 min (FeSSIF V2), against about 8.4 min in PBS; near S 12–13 they were about 12–14.5 min in the FaSSIF media, 10.5 min in FeSSIF V1 and 5.6 min in FeSSIF V2, against about 36–39.5 min in PBS duong2022b R11, R10. At the lowest supersaturation FeSSIF V1 (about 112 min at S about 4.3) and FaSSIF V1 (about 89 min at S about 4.7) were slower than PBS (about 54.5 min at S 5), while FeSSIF V2 stayed fastest (about 56 min at S about 4.6) duong2022b R11. The authors rank the media above S 11 as PBS > FaSSIF V2 > FaSSIF V1 > FeSSIF V1 > FeSSIF V2 and below it as FeSSIF V1 > FaSSIF V1 > FaSSIF V2 > FeSSIF V2, the order of induction time duong2022b C31. The fits gave slopes of −234.28, −95.38, −109.47 and −183.34 and intercepts of 0.8915, 1.6379, 1.6074 and 2.2895 for PBS, FaSSIF V1, FaSSIF V2 and FeSSIF V1 (R^{2} 0.8374, 0.9742, 0.8992, 0.8577), and FeSSIF V2 could not be fitted (R^{2} 0.0206, positive slope) duong2022b R15, R16. From these, γ was 3.52, 2.61, 2.73 and 3.24 mJ/m² and A 2.44, 5.14, 4.98 and 9.87 duong2022b R16. The critical free energy in PBS fell from about 5.11 × 10⁻²¹ J at S 13 to about 2.72 × 10⁻²¹ J at S 33.6 and the critical radius from about 5.89 to 4.29 × 10⁻¹⁰ m duong2022b R17. In the other two papers posaconazole crystallized after about 8 and 5 min in the two blank buffers and 3 and 4 min in FaSSIF-V1 and V2, and after about 33, 29 ± 5 and 24 min at 10 µg/mL in maleate buffer at pH 5.5, 6.5 and 7.5 elkhabaz2021 R7; shah2025 R3.

Figure

Read the left panel at a fixed supersaturation: above S about 11 every medium lies below the buffer curve, below it FeSSIF V1 and FaSSIF V1 lie above it; the two panels place the media points at somewhat different S duong2022b R11, X6.

γ is lower in the three fitted media than in PBS, and A is two to four times higher duong2022b R16.

Why

The authors use classical nucleation theory in the form J = A\,S\,\exp\left(-\frac{16\pi\gamma^{3}\nu^{2}}{3k^{3}T^{3}\ln^{2}S}\right), in which J rises steeply with S and falls steeply with γ duong2022b E6. They read the steep high-S line as homogeneous and the shallow low-S line as heterogeneous nucleation, an assignment taken from earlier work ("has been attributed") and not tested duong2022b C28, X11. Because PBS and FeSSIF V1 have similar γ but different induction times, they see no trend with γ, contrary to the earlier idea that adsorbed surfactant lowers γ, and they find A rising in every medium, most in FeSSIF V1, in the order of the induction times duong2022b C51, C52. They read A as the rate of forming sub-critical clusters and propose that micelles, which hold many more drug molecules than the water, "may promote" pre-nucleation clusters by raising local concentration and collision frequency, or template nucleation; at low S they propose that surfactants "could potentially" block foreign surfaces, and that glycerol monooleate and oleate "possibly" accelerate nucleation at every S duong2022b C53, C54, C55, C33. The earlier papers of the chapter proposed the opposite route: lecithin "possibly" lowering the interfacial energy of the growing nucleus, SDS hemimicelles lowering the crystal–water interfacial energy ("is hypothesized to play a role"), and phospholipid digests lowering it further ("it is postulated") indulkar2018 C40; indulkar2019b C33; enright2020 C26. The human-fluid paper had noted that surfactants that lower γ should speed nucleation, which human fluid did not do, and offered a lower monomer-attachment rate in A = fZn as a compensating term ("may explain") elkhabaz2021 C20, C22, E3. (synthesis: the fits obtain A and γ from the same few induction times, and the extractor notes that in the FaSSIF media the critical free energy is less than half the PBS value at equal S, so a lower γ is not excluded; the data favour "both terms move" over "only A moves".) duong2022b X12, R17

Conditions and limits

One drug, no polymer, single-phase solutions at 37 °C duong2022b P7. The media differ from PBS in pH (5.0–6.5), buffer species and salt as well as in surfactants, and all are compared with PBS pH 6.5 only duong2022b X16. The supersaturation of the media points rests on the Km/w assumption and differs by up to about 1.5-fold between the two panels of the figure; two FaSSIF V1 points lie above S 34, beyond the stated amorphous limit duong2022b X6, X13. The abstract's "much shorter" induction times in biorelevant media hold above S about 8 duong2022b X7. The value of A depends on how J was derived from induction time, which is not stated, and A should be compared only between media of this paper duong2022b X10.

Counterexamples and conflicts

At the lowest supersaturation the bile-salt- and lecithin-rich media slowed nucleation, so "intestinal media accelerate posaconazole nucleation" holds only above S about 8 duong2022b R11, X7. Without polymer posaconazole took about 29 ± 5 min at 10 µg/mL in maleate buffer pH 6.5 in one paper and about 8.4 min at S 33.6 in PBS pH 6.5 in another, about 3.5 times shorter (synthesis: 29/8.4), a spread between protocols that limits the comparison of absolute times across papers (see F35) shah2025 R3; duong2022b R10. The interfacial-energy explanation of the lecithin and SDS effects proposed in 2018 and 2019 is not supported by these fits, and neither explanation was measured directly in any paper indulkar2018 C40; indulkar2019b C33, X4; duong2022b C51.

Transfer check

For a new drug, measure the induction time at four or more supersaturations from about 5 to the amorphous limit, in buffer and in the intended medium, at an activity-based supersaturation; plot log t against 1/\log^{2}S and read whether the media cross the buffer line, because the ranking of media may reverse with supersaturation duong2022b R10, R11, C31. Fit A and γ only when at least five points lie in the high-S regime and report how J was obtained duong2022b X10, X11.

History

Indulkar and co-workers (2018) and (2019) and Enright and co-workers (2020) explained lecithin, SDS and digest acceleration by a lower interfacial energy without measuring it indulkar2018 C40; indulkar2019b C33; enright2020 C26. Elkhabaz and co-workers (2021) pointed out that human fluid slowed nucleation despite its surfactants and suggested an attachment-rate term elkhabaz2021 C21, C22. Duong, Ni and Taylor (2022) were the first in the library to fit classical nucleation theory to induction times across media and placed the medium effect in the pre-exponential factor; they also confirmed for posaconazole the constant amorphous-to-crystalline ratio of about 34 across pH (see F2) duong2022b C52, C19.

How it was shown

Alonzo and co-workers (2012) added about 2.5 mg felodipine seeds (sieved below 106 µm, specific surface area 0.804 ± 0.3 m²/g by laser diffraction) to 18 mL buffer at 25 °C, equilibrated 40 min, created supersaturation by adding drug in methanol and took the slope of the first 5 min as growth rate; concentration came from a PLS model on second-derivative UV spectra (270–440 nm), which removes scattering baselines, and the 361 nm peak was checked for the red shift that marks nanoparticles alonzo2012 P2, P3, P4, R19, R20. Ilevbare and co-workers used 0.010 g ritonavir seeds (below 250 µm) in 50 mL at 37 °C and 400 rpm, drug added in methanol at 1:200 by volume, spectra every 5 s, the slope of the first 2 min as the initial growth rate and the ratio E_g = R_{g0}/R_{gp} without and with polymer as effectiveness, in triplicate ilevbare2012a P8, E3, E4; ilevbare2013b P10, E5, E8. In 2013 they normalized the rate by seed mass and BET area, and flagged secondary nucleation by turbidity at 280 or 350 nm ilevbare2013b P11, P15, E6. The unseeded run is the same medium without seeds, with the induction time at the crossing of a line through the flat start and a line through the rising extinction or falling concentration alonzo2012 P5; ilevbare2013c P9, P10. Combining the two gives the relative nucleation rate J/J_0 = (t_s/t_{s,0})^{3}\,(t_{u,0}/t_u)^{4}, with the seeded induction-time ratio replaced by the growth-rate ratio R/R_0 alonzo2012 P10, E9, E10. Jackson and co-workers (2014) took the induction time from the UV slope together with pyrene fluorescence and checked it against SHG jackson2014 P8, C30. Schram, Beaudoin and Taylor (2015) used a variant: felodipine seed crystals mounted on a rotating disc at 1000 rpm in 50 mM phosphate buffer at 25 °C, supersaturation S 8 made with a 10 mg/mL methanol stock (4 µg/mL, solubility about 0.5 µg/mL), 5 µg/mL polymer dissolved by mixing for 24 h, and absorbance at 360 nm every 10 s for 1 h, the slope of concentration against time taken as the growth rate in triplicate schram2015 P2, C5, C6, E1, E4. Trasi and co-workers (2015) measured unseeded nucleation of acetaminophen in two instruments: 1.2 mL vials cycled about 80 times with laser transmission and a Poisson fit of the cumulative induction-time distribution, P(t) = 1 - \exp[-J V (t - t_g)], for the nucleation rate J and the growth time t_g, and a 4 mL vessel with images every second and a count of crystals, in triplicate (see F27) trasi2015 P3, P4, E5. Elkhabaz and co-workers (2021) imaged aliquots by second harmonic generation (SONICC, 10× objective, at least three fields) and took the change in particle count per minute as the nucleation rate and the change in size as the growth rate elkhabaz2021 P9, P10, E5, E6. Duong, Ni and Taylor (2022) converted induction times into nucleation rates and fitted \ln(J/S) = \ln A - B/\ln^{2}S to the high-supersaturation points of each medium duong2022b P15, E7.

What the data show

The checks that the 2-min slope is growth: the ritonavir seed size distribution after growth at 10 µg/mL was monomodal, with no second population of small crystals; ritonavir at 10 µg/mL did not desupersaturate in 8 h without seeds and nucleated after about 2 h at 20 µg/mL, both longer than the 30 min growth runs; the volume increase expected from the solute removed (3.17 × 10⁻¹⁷ m³) was 0.44 times that from the measured crystal dimensions (7.19 × 10⁻¹⁷ m³; synthesis: 3.17/7.19 = 0.44, that is a factor of 2.3 apart), which the authors call similar ilevbare2012a R7, R8, R9, X10. For celecoxib and ritonavir the turbidity did not rise between 5 and 22 µg/mL, so the authors judged desupersaturation to be mainly seed growth; efavirenz showed secondary nucleation above 10 µg/mL (S 1.2) once macroscopic crystals formed ilevbare2013b R5, C12, C13. For felodipine the long seeded runs fell below 2.5 µg/mL within 45 min and then levelled above the solubility of 0.5 µg/mL alonzo2012 R3. The nucleation-rate estimate rests on one pair of induction times (15.3 and 136.5 min) entering to the fourth power, so a 10% change in the polymer-case time changes J/J_0 about 1.5-fold (extractor calculation) alonzo2012 R16, R17, X7. Induction times by UV absorbance, UV extinction and fluorescence for danazol with HPMC at 15 µg/mL were 172 ± 4, 111 ± 14 and 195 ± 21 min, and the first SHG crystals at 20 µg/mL appeared at 5 min, before the pyrene ratio rose at 10–15 min jackson2014 R17.h, R25, X5. For strong inhibitors the extinction rose above the baseline line before the fitted onset (efavirenz with CAB Adp 0.81 from about 25 min against a fitted 31.5 min; ritonavir with CAB Adp 0.81 from about 180 min against 260 min) ilevbare2013c R6.d, R6.f, X14. For danazol the authors warn that droplet size changes distort both the absorbance and the extinction signal, so orthogonal methods are needed jackson2014 C54, C55. In the rotating-disc runs the single no-polymer profile fell from about 4.0 to about 1.7 µg/mL in 50 min, and the slope window, the pH of that curve and the standard deviation of the ratio are not stated, so the comparison between two pH values assumes that the rate without polymer does not depend on pH schram2015 R1, X3, X11. For acetaminophen the fitted growth times were 7.8 s (PAA), 40.4 s (none), 350.1 s (HPMC) and 928 s (HPMCAS) against 95% crystallization times of 11 to 1043 min, so the growth part of the induction time is 0.2–3% of it even for HPMCAS (synthesis: 928 s = 15.5 min of 470 min), but the authors point out that turbidity appears only after significant nucleation, so the induction time is the time to the onset of massive nucleation trasi2015 R3, R1, C32. Crystal counts from the 4 mL vessel and induction times from the 1.2 mL vials gave different pictures for PVP and PVPVA (few vials nucleated in 48 h, all three counting runs nucleated within 570–9700 s), which the paper does not explain trasi2015 X6. For the danazol onset the time of reading mattered: the pyrene ratio read 15 s after each addition detected the drug-rich phase at 10–14 µg/mL, read after 1 or 5 min at about 8 µg/mL, and the polymer-free ultracentrifugation onset could not be measured because the drug crystallized during the 30 min spin jackson2016 R13, C56. For telaprevir above its glass–liquid phase separation (150 µg/mL) the apparent concentration drops twice; the induction time was taken from the second drop in the 270 nm signal, the first being assigned to the drug-rich aggregates, and below it (80 µg/mL) from the rise of the 370 nm extinction with the fall at 270 nm; a diffusion cell with 5 or 50 µg/mL HPMC showed the same mass flow (receiver 1.74 and 1.65 µg/mL after 60 min), so the first drop is not crystallization (see F25) mosqueragiraldo2016 R3, R10, R11, C11, C12. Lu and co-workers (2017) combined the seeded rate ratio and the unseeded induction time in the relative nucleation rate J/J_0 = (R_0/R)^3(t_{u,0}/t_u)^4 for telaprevir with bile salts; with a buffer time of about 30 min and a bile salt time capped at 960 min the induction times alone contribute about 10⁶ to E_J, so the estimate is a bound and rests on two bile salts at one supersaturation in one paper and on assumed rate ratios of 100 for STCDC and SGCDC in the other (see F32 and F33) lu2017 R10, X2; lu2017a P8, E4, E5, X13.

The SHG rates are counts and detected sizes per field without a per-volume normalization and are comparable only within the paper; the posaconazole nucleation rate ran from about 48 counts/min in FaSSIF-V1 to about 0.06 in pooled human fluid (see F42) elkhabaz2021 R14, X13. The nucleation-theory fits rest on 3–9 points per medium with R² 0.84–0.97, the way J was derived from the induction time is not stated, and the pre-exponential factor equals e raised to the fitted intercept, so its size and unit depend on that unstated step (see F34) duong2022b R15, X10, X11. None of the induction-time papers of 2018–2025 identified the scattering particles at the induction time as crystals by a solid-state method, except the atazanavir precipitates of the human-fluid paper (PXRD of a different crystal form from the supplied drug) indulkar2018 X14; enright2020 X15; elkhabaz2021 R20.

Figure

The amount of celecoxib in 50 mL falls from about 488 to 348 µg in 2 min without polymer and from about 485 to 460 µg with polymer; the fitted slopes (69.80 and 11.88 µg min⁻¹) give E_g of about 5.9 ilevbare2013b R8.

Why

Alonzo and co-workers chose felodipine for the seeded design because its solubility of about 0.5 µg/mL means that solutions up to S 12 contain only a few µg/mL, so too little drug crystallizes to change seed size and the seed surface area can be treated as constant; the same assumption for the face areas is called "likely to be small" in error alonzo2012 M1, C5, C6. Ilevbare and co-workers state that the induction time is the sum of the time to form nuclei and the time to grow them to a detectable size, and that if growth is fast the induction time is inversely proportional to the nucleation rate given by classical nucleation theory (t_{ind} = t_n + t_g; t_{ind} \propto J^{-1}) ilevbare2013c E2, E3, E4, C14. (synthesis: the second relation holds only if t_n \gg t_g, which was not tested; a polymer that slows early growth would also lengthen the induction time, so the unseeded values are nucleation plus early growth, not nucleation alone.)

Conditions and limits

Seed mass, volume and methanol fraction are not given in the 2012 ritonavir papers, and the solubility for S was measured without methanol; absolute rates therefore cannot be compared across studies ilevbare2012c X16; ilevbare2012b X12; ilevbare2013c X16. At concentrations near the amorphous solubility the 2-min slope may include secondary nucleation or formation of a drug-rich phase, and no measurement separated them ilevbare2012b X18. In 2013 the buffer molarity of the main series is not stated ilevbare2013b X10. The felodipine analysis assumes Langmuir-type coverage and a constant seed area, argued for S up to 10 although S 12 is also used alonzo2012 C21, X4. All values are for UV detection of the dissolved drug; light-scattering or fluorescence detection gives different lag times for the same system jackson2014 R17, R25. In the acetaminophen fits the printed sample volume (0.0012 m³) and the sign of the exponent are misprints, the absolute J holds only for V = 1.2 mL, and the printed confidence intervals of J are implausibly narrow trasi2015 X1, X2, X13. In the telaprevir screen the bars labelled ">500" and ">700" are lower bounds with unstated run length and averaging, and the traces of HPMC at 150 µg/mL (concentration falling from about 210 and 300 min) differ from the mean bars (243 and 233 min) mosqueragiraldo2016 X4, X19. In the telaprevir bile-salt studies the seeded growth method is not described in the supersaturation paper (seed form, amount, volume, temperature, stirring and replicates are missing), and the seeds of the growth paper were grown in situ for 6 h with their mass inferred from the return to the crystalline solubility lu2017 X3; lu2017a P1, C5.

Counterexamples and conflicts

The volume balance agrees only within a factor of 2.3, and the size axes of the distributions are in pixels with different ranges before and after growth ilevbare2012a X10. For efavirenz the growth with polymers could be tested at S 1.2 only, because of secondary nucleation ilevbare2013b R5, X12. None found in the library of a seeded slope that was proved to include nucleation for celecoxib or ritonavir. The count slope used by the acetaminophen study as a nucleation rate also contains growth to detectable size and agglomeration, and secondary nucleation was not separated from primary nucleation trasi2015 X7, C9.

Transfer check

Use the same fixed seed mass and stirring in a seeded run, and record the first 2–5 min; run an unseeded control at the same supersaturation for at least 4× the longest growth run; check turbidity at a wavelength where the drug does not absorb; and report the methanol fraction ilevbare2013b P10, P11; ilevbare2012a R9. If the unseeded control loses drug within the growth run, the slope is not pure growth. For induction times, state the detection method, because crystals appear in SHG minutes before they appear in a probe ratio or an extinction trace jackson2014 R25.

History

Alonzo and co-workers (2012) first paired seeded growth with unseeded induction times to estimate a nucleation-rate ratio (after Verdoes 1992, outside the library) alonzo2012 C11. Ilevbare and co-workers turned the seeded slope into the effectiveness ratio E_g (2012), added seed-area normalization and a turbidity check (2013) and used the induction-time decomposition for polymer screening (2013) ilevbare2012c E5; ilevbare2013b E6, R5; ilevbare2013c E2. Jackson and co-workers (2014) compared three read-outs with SHG imaging jackson2014 R13, R17. Elkhabaz and co-workers (2021) brought SHG nucleation and growth rates into biorelevant and human fluids, and Duong, Ni and Taylor (2022) the first fit of classical nucleation theory to induction times across media in the chapter elkhabaz2021 E5, E6; duong2022b E7.

How it was shown

Alonzo and co-workers (2012) ran seeded (growth) and unseeded (nucleation) experiments at S 10 with 1 µg/mL predissolved HPMC in pH 6.8 buffer at 25 °C and combined them in J/J_0 = (t_s/t_{s,0})^{3}(t_{u,0}/t_u)^{4} with the growth-rate ratio standing in for the seeded induction-time ratio alonzo2012 P4, P5, P10, E9, E10. Ilevbare and co-workers ranked polymers twice on the same drugs at 37 °C and pH 6.8 with 5 µg/mL polymer: by seeded growth at 10 µg/mL drug (S 7.6 for ritonavir; most of the ritonavir values from the 2012 papers) and by unseeded induction time at the calculated amorphous solubility (S about 15.4) ilevbare2013b P10, X15; ilevbare2013c P9.

What the data show

For felodipine the unseeded solution without HPMC lost drug from about 10–15 min and the induction time was 15.3 min; with 1 µg/mL HPMC the concentration stayed near 5.4 µg/mL for about an hour and the induction time was 136.5 min (a factor of 8.9; synthesis: 136.5/15.3); the growth-rate ratio at S 10 was 0.607, so J/J_0 = 7.05 × 10⁻⁴ (synthesis: 1/7.05 × 10⁻⁴ = 1,418) alonzo2012 R15, R16, R5, R17. For ritonavir the polymers that lengthened the induction time most were synthesized esters; Pn-IPAAmd, "a highly effective" growth inhibitor, did not change it ilevbare2013c R9.k, R19. The pairs below place the growth ratio (5 µg/mL polymer, 10 µg/mL ritonavir) beside the induction time (20 µg/mL ritonavir): For acetaminophen at S 1.5 the effect of the polymers on nucleation was much larger than on growth: J fell 18- and 36-fold with HPMCAS and HPMC (10 µg/mL), while seeded desupersaturation at 20 µg/mL left 14.5 and 16.1 mg/mL against 13.0 mg/mL without polymer at 24 h; HPMC and PVP led both rankings by image analysis, PAA raised J 2.6-fold (synthesis: 3820/1465) and did not slow growth, and PVPVA delayed the first crystals, after which the count rose at 5.4 nuclei/s (see F27) trasi2015 R3, R11, R10, C17, C18. Telaprevir with bile salts shows the separation at its largest. At 1.86 mM, STC, SGC, STDC and SGDC slowed seeded growth 1.2- to 3.2-fold at δ 2.4 while the estimated nucleation rate fell by about 360- to 300,000-fold; STCDC and SGCDC are the reverse: growth was stopped (no desupersaturation with STCDC; SGCDC judged from the residual only), and the authors say that their long induction times "can be due" to blocked growth of nuclei that may have formed (see F33) lu2017a R7, R10, R12, R14, C36, C37.

ilevbare2013b R9; ilevbare2012c R9.o; ilevbare2013c R9.a–r. CA 320S Sub 0.63 and 0.90 were the best growth inhibitors for ritonavir (10.8 and 12.6) but gave an induction time of about 139 min, against about 244 min for CAB Adp 0.81 ilevbare2013b R9.g, R9.h; ilevbare2013c R9.l, R9.r. For efavirenz the induction-time leaders were the same esters (CAB Adp 0.81 28.0 min, CAP Adp 0.85 24.9, CA 320S Seb 24.1, CAP Adp 0.33 21.6) while the growth leaders were PVPVA and CA 320S Sub 0.90 (about 4.9), and PVPVA left the induction time at 4.5 min against 5.1 ilevbare2013b R9; ilevbare2013c R9. For celecoxib the induction-time leaders were HPMC (12.6 min), CA 320S Adp (11.2), Pn-IPAAmd (10.9) and HPMCAS (10.5), and the growth leaders were HPMC (10.2), HPMCAS (8.5), PVPVA (7.4) and CA 320S Sub 0.90 (7.2) ilevbare2013c R9; ilevbare2013b R9. The growth paper itself cites the induction-time study for the result that the strongest nucleation inhibitors for ritonavir and efavirenz were CAB Adp 0.81, CAP Adp 0.33 and CAP Adp 0.85, and for celecoxib HPMC ilevbare2013b R16.

Figure

Without HPMC (black) the concentration falls from about 10–15 min; with 1 µg/mL HPMC (red) it stays near 5.4 µg/mL for more than an hour, which gives the induction times 15.3 and 136.5 min alonzo2012 R15, R16.

Why

Alonzo and co-workers attribute the small growth effect to the limit of an adsorbed polymer on a growing crystal (F9, F10) and call the nucleation effect "much more pronounced" than the growth effect, a factor of 1,000 against 2 alonzo2012 C46, C41. Ilevbare and co-workers propose that nucleation inhibition needs a polymer with greater affinity for the solute than for water or itself, so that it joins solute clusters and disrupts their reorganization into a crystal nucleus, whereas growth inhibition needs adsorption on a crystal face; they conclude "Clearly" that the polymer properties that matter differ for the two ilevbare2013c C4, C5, C40. The cluster mechanism, like adsorption, was not measured ilevbare2013c C5, X14. (synthesis: Pn-IPAAmd's growth effect was ascribed to hydrogen bonding to the fast-growing faces of the crystal (F8); a flexible chain that binds an existing crystal face need not interact with a solute cluster, which fits its null effect on nucleation.)

Conditions and limits

The growth and nucleation values for ritonavir come from different supersaturations (S 7.6 and about 15.4), polymer grades are named differently (CA 320S Sub appears as 0.63 and 0.90 in the growth paper, without a degree of substitution in the nucleation paper), and most ritonavir growth values were reported before ilevbare2013b X15; ilevbare2013c X15. The felodipine value is one polymer level at one supersaturation, and the induction times enter J/J_0 to the fourth power alonzo2012 X7. The Table 5 colour classes of the nucleation paper do not follow its own thresholds, so rankings should be taken from the bar values ilevbare2013c X1.

Counterexamples and conflicts

Celecoxib is the exception: HPMC led both tests ilevbare2013b R16. Konno and co-workers found that HPMCAS and HPMC reduced the felodipine dissolution slope 66- and 32-fold relative to buffer (synthesis: 0.1399/0.0021 and 0.1399/0.0044) at 150 µg/mL polymer, in a test that mixes both processes konno2008a R16. For acetaminophen the best polymers coincide: HPMC and PVP led both the image-analysis nucleation rank and the growth rank, so the separation seen for felodipine, ritonavir and efavirenz is not general; the nucleation and growth levels differ twofold (10 and 20 µg/mL) trasi2015 C36, X10, X11. For bile salts the pairs differ in kind as well as size: STC and SGC are strong nucleation and weak growth inhibitors, STCDC and SGCDC stop growth, and the nucleation estimates behind the first group come from two bile salts in one paper and from induction times capped at 960 min lu2017 R10, X2; lu2017a R14, X14.

Transfer check

Rank candidate polymers twice, by a seeded growth ratio and by an unseeded induction time, at the supersaturation the formulation will reach, and do not use one test for the other ilevbare2013c C40, P9. A polymer that tops the growth ranking but not the induction-time ranking is effective in a solution that already contains crystals, not in one that is crystal-free alonzo2012 C44, C45.

History

Alonzo and co-workers (2012) first separated the two for one drug and polymer alonzo2012 C46. Ilevbare and co-workers (2013) repeated the comparison across three drugs and 16–21 polymers and concluded that the properties differ ilevbare2013b C41; ilevbare2013c C40. Konno and co-workers (2008, in the ASD dissolution chapter) had measured felodipine dissolution profiles with the same polymer types before the growth/nucleation split was made konno2008a C36. Trasi and co-workers (2015) measured nucleation and growth for acetaminophen in solution, found HPMC and PVP best at both by image analysis and a different order in the melt, and described growth effects as much lower than nucleation effects trasi2015 C18, C24, C25.

How it was shown

Trasi and co-workers (2015) dissolved acetaminophen (APAP) in 10 mM sodium phosphate buffer, pH 6.8, at about 70 °C, with or without 10 µg/mL of one polymer (PVP K-12, Mw 2,000–3,000; PVPVA Kollidon VA64; HPMC 2910; HPMCAS of unstated grade, Mw 17,000–18,000; PAA, Mw 450,000), filtered the solution (0.2 µm) and cooled it to 20 °C at S 1.5 (crystalline solubility 13.2 mg/mL; start about 19.5–19.8 mg/mL) trasi2015 P1, P2, M1–M6. In the Crystal 16, 1.2 mL vials were stirred at 700 rpm, the induction time was the time from reaching 20 °C to the first drop in laser transmission, and each sample was reheated and cooled about 80 times; the cumulative probability was fitted with the Poisson model P(t) = 1 - \exp[-J V (t - t_g)] (Jiang and ter Horst method, gPROMS) to give a nucleation rate J and a growth time t_g trasi2015 P3, E5. In the Crystalline Particle Viewer, 4 mL of the same solutions were cycled in triplicate at 700 rpm, an image was taken every second, ImageJ counted the crystals, the slope of the count curve right after onset was taken as proportional to the nucleation rate and the first detection as the induction time trasi2015 P4, C10. For growth, 10 mL solutions at S 1.5 with 20 µg/mL polymer were seeded with 1 mg of APAP crystals (below 75 µm; d50 43.5 µm), shaken at 20 °C, and aliquots were filtered, diluted 40-fold and read by UV over 24 h; crystals harvested at the end were photographed (40×) and compared with a Bravais–Friedel–Donnay–Harker (BFDH) habit predicted in Mercury trasi2015 P5, P6, P7, M8. The authors take the polymer level of the Particle Viewer to be the same 10 µg/mL, which the card infers but the paper does not state trasi2015 X11.

What the data show

Induction times and fitted rates. Without polymer 95% of vials crystallized within 26 min; with PAA within 11 min, with HPMCAS within 470 min and with HPMC within 1043 min; with PVP and PVPVA only a few vials nucleated in 2 days (48 h for PVPVA), so no distribution was fitted trasi2015 R1, R2. The fits gave J = 3820, 1465, 81.86 and 40.68 # m⁻³ s⁻¹ and t_g = 7.8, 40.4, 928 and 350.1 s for PAA, no polymer, HPMCAS and HPMC, that is, PAA raised J 2.6-fold, HPMCAS lowered it 18-fold and HPMC 36-fold (synthesis: 3820/1465, 1465/81.86, 1465/40.68) trasi2015 R3. The fitted rates reproduce the stated 95% times (11.0, 29.1, 524 and 1029 min against 11, 26, 470 and 1043) only with V = 1.2 mL, not the printed 0.0012 m³, and the printed exponent lacks its minus sign; the 95% intervals of J (0.02 and 0.11 for HPMCAS and HPMC) are implausibly narrow, and the HPMC 95% time lies beyond the last data point of the figure trasi2015 X1, X2, X5, X13. The text says HPMC solutions nucleated slightly faster than HPMCAS ones, which holds only in the first about 3000 s of the plot trasi2015 X3. Crystal counts. First detection (s, three runs) was 150, 415, 785 without polymer; 100, 240, 620 with PAA; 100, 125, 290 with HPMCAS; 700, 750, 1300 with HPMC; 570, 1550, 8000 with PVP; and 1070, 1925, 9700 with PVPVA; the count slopes were 13.2, 11.3, 0.93, 0.56, 0.19 and 5.4 nuclei/s for none, PAA, HPMCAS, HPMC, PVP and PVPVA trasi2015 R10. Without polymer and with PAA the count rose to peaks of about 540–900 per image and fell to about 50–200 within minutes, which the authors put down to agglomeration; with HPMCAS and HPMC it rose to plateaus of about 150–400; with PVPVA each run began with a narrow spike of about 500–630 crystals per image, dropped to about 100–150 and then kept rising to about 350–450; with PVP the count rose slowly over hours in two runs and steeply in one trasi2015 R4–R9, C9, C11. In the text the pure-APAP induction times are 180, 400 and 800 s, in Table 2 150, 415 and 785 s trasi2015 X4. Growth. Concentrations at 2, 6, 12 and 24 h were about 16.3, 13.9, 13.4 and 13.0 mg/mL without polymer; 16.6, 14.5, 13.9 and 13.4 with PAA; 17.9, 16.1, 15.1 and 14.5 with HPMCAS; 18.3, 17.4, 16.0 and 14.7 with PVPVA; 18.8, 18.4, 17.2 and 15.8 with PVP; and 19.4, 18.7, 17.9 and 16.1 with HPMC (plot readings; no rate computed, replicates not stated) trasi2015 R11, X9. Habit. Without polymer thin, flat, elongated crystals unlike the compact BFDH shape; HPMCAS long rods; PAA large prisms nearest the prediction; PVPVA large parallelepipeds; PVP smaller crystals of the same shape; HPMC very small, ill-defined crystals trasi2015 R12, R13. Melt ranking (cited). From the supercooled melt the nucleation order was HPMCAS > PVP > HPMC > PVPVA > PAA and the growth order PAA > PVP > PVPVA > HPMC > HPMCAS, PAA raising nucleation but being the best growth inhibitor trasi2015 R14.

Figure

Peak-and-fall counts without polymer and with PAA, plateaus with the cellulosics, and late narrow spikes with PVPVA trasi2015 R4–R9.

HPMC and PVP hold the highest concentration at 6 h; PAA lies on the no-polymer curve trasi2015 R11.

Why

The authors argue that for nucleation the polymer must interact with the drug while embryos form and disrupt their assembly; unlike a small-molecule analogue it cannot be built into the nucleus, so drug–polymer interactions that compete with solvent–drug interactions are "presumably required" ("likely to be important") trasi2015 C31. Because the nucleation and growth ranks are "similar but not the same", growth-type mechanisms "could have a role" in nucleation inhibition, but "there must be additional factors" trasi2015 C34, C36. They think the failure of PAA in solution "could be due to" its ionization at pH 6.8 and the consequent inability to form the hydrogen bonds that matter in the solid trasi2015 C27. The late-start, fast-rise behaviour of PVPVA is read as "may be good at inhibiting primary nucleation" but "does not appear" to stop secondary nucleation, and the habit changes as adsorption "most certainly" on specific faces; secondary nucleation, adsorption and PAA ionization were not measured, and the count slope also contains growth to detectable size and agglomeration trasi2015 C22, C33, X7. They conclude that crystal counting gives "a more accurate picture" than induction times alone, which was not tested against an independent measure trasi2015 C23. (synthesis: an induction time records the first detectable crystals, and a slope records how fast the count rises after them; a polymer can lengthen the first and leave the second large, as PVPVA did, so a screen by induction time alone can rank it with PVP; this is the same distinction as between the growth and the nucleation rankings of F6, seen here within the nucleation side.)

Conditions and limits

One drug, S 1.5, 20 °C, pH 6.8, one low polymer level per test (10 µg/mL for nucleation, 20 µg/mL for growth, so the two ranks come from polymer levels differing twofold), far below the polymer concentrations a dissolving dispersion releases trasi2015 C20, X11. The Crystal 16 (1.2 mL, about 80 cycles) and the Particle Viewer (4 mL, three runs) differ in volume and number of runs: with PVP and PVPVA few Crystal 16 vials nucleated in 48 h, while all three Particle Viewer runs nucleated within 570–9700 s, which the paper does not explain, so PVP and PVPVA can be compared only within one method trasi2015 X6. The HPMCAS grade, the crystal form of APAP and the seeds, the Mw of HPMC and the buffer composition are not stated trasi2015 X12, X14. The growth ranking rests on plot readings without growth rates or replicate numbers, secondary nucleation during the growth test was not excluded, and PVPVA and HPMCAS (about 0.2 mg/mL apart at 24 h) are not separated trasi2015 C15, X9. The melt ranks are cited from an earlier paper, not re-measured trasi2015 R14.

Counterexamples and conflicts

The statement that the two polymers with the largest nucleation effect were also the strongest growth inhibitors holds for the image-analysis rank (PVP, HPMC) but not for the Crystal 16 rank, where PVPVA ties with PVP trasi2015 X10, C24. The abstract's "PVP and the cellulosic polymers" as the best nucleation inhibitors matches the counting method only trasi2015 X8. Polymer rank is drug-dependent: PVP was much more effective than HPMC against estradiol precipitation, and the cellulosics were more effective for danazol and ritonavir trasi2015 R15, C30. PAA, the best growth inhibitor in the melt, did not slow solution growth and raised J 2.6-fold (synthesis: 3820/1465) trasi2015 R3, R11, R14.

Transfer check

Measure nucleation with two read-outs, the time to the first detectable crystals (many small vials, many cycles) and the rate at which the count then rises (images of a larger vessel, in triplicate), at the supersaturation and polymer level of the product; a polymer that gives a long first-crystal time but a count slope above the cellulosics' (PVPVA here) is effective in an unseeded solution only until the first crystals appear trasi2015 P3, P4, R10. Test an acidic polymer such as PAA at the pH where the drug dissolves before relying on a melt or solid-state ranking trasi2015 C27, R14.

History

Trasi and Taylor (2012, in the library) had ranked the same five polymers for APAP in the supercooled melt; Trasi and co-workers (2015) measured them in aqueous solution and found the order different, with PAA reversed trasi2015 R14, C26, C28. They add a Poisson fit to induction-time distributions and a crystal-count method to the induction-time approach of the polymer screens in F13 and F14, for a compound whose supersaturation (S 1.5) is far below that of the ritonavir, efavirenz and celecoxib screens. Xie and co-workers (2015, in the ASD dissolution chapter) cite this paper for the same polymer failing as a solution inhibitor (listed in the evidence index of this subcategory as a citing paper).

How it was shown

No paper of the library set out to compare controls; the comparison collects the polymer-free runs of the inhibitor papers of 2013–2025 for the drugs studied by more than one team (synthesis). For atazanavir: 60 µg/mL from a methanol stock into 47 mL of 100 mM phosphate pH 6.8 at 37 °C and 300 rpm, absorbance at 280 and 450 nm, n = 3, against a cited LLPS concentration of 66 µg/mL mosqueragiraldo2018a P4, M2; the amorphous solubility of the medium (65 µg/mL) from a methanol stock into 20 mL of pH 6.5 phosphate buffer (about 270 mOsmol), 300 rpm, extinction read every minute, replicate number not stated indulkar2018 P9, R8, X8; 70 µg/mL into 20 mL of 50 mM phosphate pH 6.8 with about 4.5% v/v methanol indulkar2019b P4, R1; 74.9 µg/mL from a methanol stock into 15 mL of FaSSIF phosphate buffer pH 6.5, 300 rpm, scattering at 350 nm, n = 3 enright2020 P14, R1; and the amorphous solubility from a DMSO stock into 4 mL of the phosphate (V1) or maleic acid (V2) buffer of FaSSIF at pH 6.5, 300 rpm, absorbance at 280 nm or scattering at 400 nm, n = 3 elkhabaz2021 P7. For posaconazole: methanol stock into 4 mL of the two buffers elkhabaz2021 P7; DMSO stock into 50 mL of PBS pH 6.5 at about 0.14 M ionic strength duong2022b P7, P2; methanol stock to 10 µg/mL in FaSSIF-V2 buffer, extinction at 400 nm over 4 h, three samples shah2025 P4. For ritonavir: at the calculated amorphous solubility in 100 mM phosphate pH 6.8 ilevbare2013c R8, R9.a; 20 µg/mL in 100 mM phosphate pH 6.8 mosqueragiraldo2018a P4; 30 µg/mL (the amorphous solubility in that buffer) in pH 6.5 phosphate indulkar2018 R8, R19.

What the data show

For atazanavir the controls run from about 40 min (mosqueragiraldo2018a, the only run below the stated LLPS concentration, at 60 against 66 µg/mL) through about 92 and 102 min (the two FaSSIF blank buffers), 170 min and about 200 min to 253 ± 65 min (synthesis: 253/40 ≈ 6.3) mosqueragiraldo2018a R1.b, M2; elkhabaz2021 R6.a, R6.c; indulkar2018 R19; indulkar2019b R3.a; enright2020 R2. For posaconazole they run from about 5 and 8 min (maleic and phosphate blank buffers, 4 mL) and 8.4 min (PBS, 50 mL) to 29 ± 5 min (maleate buffer, 10 µg/mL), about 3.5- to 6-fold apart (synthesis: 29/8.4 and 29/5) elkhabaz2021 R7.a, R7.c; duong2022b R10; shah2025 R3. For ritonavir they run from 66 ± 18 min through about 120 min, both in 100 mM phosphate pH 6.8 at about 20 µg/mL, to 320 ± 150 min in pH 6.5 buffer at 30 µg/mL mosqueragiraldo2018a R1.a; ilevbare2013c R9.a; indulkar2018 R19. Within papers the replicate spread was smaller: ±65 of 253 min for atazanavir, ±18 of 66 min for ritonavir, and below 15% in the 2013 induction-time screen (synthesis: 65/253 = 0.26; 18/66 = 0.27) enright2020 R2; mosqueragiraldo2018a R1.a; ilevbare2013c R17. Where the same protocol was repeated, the controls agreed: telaprevir at δ 11.5 in 50 mM phosphate pH 6.5 took about 30 min in 2017 and about 27–30 min in three figures of 2018, and telaprevir at 150 µg/mL in 100 mM phosphate pH 6.8 about 14–15 min in 2016 and about 15–16 min in 2018; celecoxib at 22 µg/mL took about 2.4 min in 2013 and about 4 min in 2018 lu2017 R3.a; lu2018 R3.a, R4.a, R6.a; mosqueragiraldo2016 R4.a; mosqueragiraldo2018a R1.c, R1.g, R2.c; ilevbare2013c R9.a.

Figure

No card figure sets the controls of different papers side by side.

Why

None of the papers discusses the spread. (synthesis: possible contributors differ between the runs: buffer species and strength, which in the chapter on amorphous solubility and LLPS move the LLPS concentration of ritonavir several-fold (37.2 µg/mL in water, 18.8 in 100 mM and 4.7 in 500 mM phosphate) and so the supersaturation at a fixed concentration ilevbare2013a R13; the cosolvent (methanol, DMSO, up to about 4.5%); the volume, since nucleation is stochastic and the fitted Poisson form P(t) = 1 - \exp[-JV(t - t_g)] makes the mean waiting time fall as volume rises trasi2015 E5; the detection limit of the probe and wavelength; and the starting concentration relative to the amorphous solubility, since the 40 min atazanavir run was below it and the others at it. The values do not follow volume alone (4 mL about 100 min, 15 mL 253, 20 mL 170–200, 47 mL 40 min) or buffer alone, so no single variable orders them.) The repeat pairs that agree used one laboratory protocol, which points to protocol details rather than to the drug lu2017 R3.a; lu2018 R6.a; mosqueragiraldo2016 R4.a; mosqueragiraldo2018a R1.c.

Conditions and limits

Three drugs have controls from three or more papers; the ritonavir and atazanavir values span 2013–2021 and different drug lots, which no card compares ilevbare2013c M1; mosqueragiraldo2018a M1, M2; indulkar2018 M1, M2. Several papers do not state replicate numbers, and the scattering particles were identified as crystals by a solid-state method in one of them only indulkar2018 X8; indulkar2019b X9; elkhabaz2021 R20. The ritonavir value of 2013 is at a calculated, not a measured, amorphous solubility ilevbare2013c R2.

Counterexamples and conflicts

Celecoxib at 22 µg/mL in 100 mM phosphate pH 6.8 gave nearly the same control in two papers (about 2.4 and 4 min), and telaprevir controls agreed within the same protocol, so the spread is not universal ilevbare2013c R9.a; mosqueragiraldo2018a R1.g; lu2017 R3.a; lu2018 R6.a. For celecoxib with polymer, however, two laboratories differed by a factor of about 40–90 at the same nominal conditions (see F13) xie2015 R1; ilevbare2013c R9.j.

Transfer check

Run the polymer-free control in the same session, vessel, volume, buffer, cosolvent level and detection as the inhibitor runs, and report the inhibitor effect as the ratio to that control; before comparing with another paper's inhibitor, compare the two controls, and treat a difference above about twofold as a protocol difference, not a drug property (synthesis). Express the starting concentration as a fraction of the amorphous solubility measured in the same medium indulkar2018 C7; enright2020 C10.

History

The three-drug comparison of 2013 compared drugs within one protocol (see F3) ilevbare2013c R8. From 2018, atazanavir, ritonavir and posaconazole were studied by several teams of the group with different protocols, and the controls diverged mosqueragiraldo2018a R1; indulkar2018 R19; indulkar2019b R3; enright2020 R2; elkhabaz2021 R6, R7; duong2022b R10; shah2025 R3. A Bioperformance study found that induction times did not rank enzalutamide formulations by exposure in rats (see Bioperformance F25).

How it was shown

Ilevbare and co-workers (2012) screened 34 polymers (15 synthetic and 5 cellulose-based commercial polymers, and 14 new cellulose ω-carboxyalkanoate esters) on ritonavir Form II needle seeds at pH 6.8 and 37 °C, with 5 µg/mL polymer predissolved and ritonavir raised to 10 µg/mL (S 7.6) in methanol; a fibre-optic UV probe gave the slope over the first 2 min, in triplicate ilevbare2012c P12, R9. A solubility control dissolved crystalline ritonavir for 48 h at 37 °C with eight of the polymers at 5 µg/mL ilevbare2012c P1, R1. Ilevbare and co-workers (2013) ran 16 of the polymers on celecoxib (S 6.6), efavirenz (S 1.2) and ritonavir (S 7.6) with the same seed mass of 0.010 g in 50 mL ilevbare2013b P10, R9. Alonzo and co-workers (2012) varied HPMC from 0.2 to 3.5 µg/mL on felodipine seeds at S 3–12 alonzo2012 A1, A2.

What the data show

For ritonavir the commercial cellulose derivatives gave about 2.54 (HPMCAS), 2.19 (HPMC), 2.12 (CAPh), 1.63 (CMCAB) and 1.32 (HPC); the new esters spanned 0.83 (CAB Sub) to 2.98 (CAP Adp 0.85); PVP and PAA gave about 1.20, PVPVA about 1.42 ilevbare2012c R9. Without polymer the dissolved ritonavir fell from about 10.0 to 6.9 µg/mL in 2 min; with CAP Adp 0.85 it fell to about 9.25 ilevbare2012c R7. The 2013 series gave: celecoxib HPMC 10.2, HPMCAS 8.5, PVPVA 7.4, CA 320S Sub 0.90 7.2, CA 320S Sub 0.63 6.1; efavirenz PVPVA and CA 320S Sub 0.90 about 4.9, CA 320S Sub 0.63 3.8, HPMCAS 2.9; ritonavir CA 320S Sub 0.90 12.6, CA 320S Sub 0.63 10.8, CA 320S Seb 5.7 ilevbare2013b R9. The authors count 12, 13 and 10 of 16 polymers as effective for celecoxib, efavirenz and ritonavir, a count that matches a cut-off near E_g 1.2 rather than the stated E_g above 1 ilevbare2013b C19, X3. For felodipine at S 8–10, HPMC at 0.3–0.7 µg/mL gave a growth ratio of about 0.55 (1.8-fold slower) and 50 and 100 µg/mL gave 0.45–0.61, so the effect plateaus at about 1 µg/mL alonzo2012 R8, R10. PVPVA and CA 320S Sub, which worked for celecoxib and efavirenz, differed for ritonavir: PVP and PVPVA gave about 1.0 and 1.2 ilevbare2013b R9.a, R9.c. The seeded dissolution slopes of felodipine at 150 µg/mL polymer were about 0.1399 µg mL⁻¹ min⁻¹ in buffer, 0.0398 with PVP, 0.0044 with HPMC and 0.0021 with HPMCAS konno2008a R16. Bile salts act in the same range as the polymers on growth: the authors call the E_G of 1.4–3.2 for monomeric STC, SGC and SGDC comparable with values reported for commercial polymers; STCDC alone stopped growth (see F33) lu2017a C15, R7.

Figure

White bars are synthetic polymers, blue commercial cellulose-based polymers and red the new cellulose esters; a ratio above 1 means slower growth, and the bar labelled "CAB Adp 0.85" is CAB Adp 0.81 ilevbare2012c R9, X5.

Why

Ilevbare and co-workers take the effect to be kinetic: the polymers left the solubility unchanged, and they assume the dilute polymer solutions have the viscosity of water, so the differences are not due to supersaturation or mass transport ilevbare2012c C16, C33. They attribute inhibition to adsorption of the polymer on the crystal surface, which "is likely" to depend on hydrophobicity, rigidity and amphiphilicity (F8); adsorption on ritonavir crystals was not measured in these two papers ilevbare2012c C35, C50; ilevbare2013b X14. Alonzo and co-workers read the plateau of the felodipine inhibition near 1 µg/mL as support for an adsorption mechanism because the fitted coverage reaches about 0.98 there (F10) alonzo2012 C30, R7. (synthesis: the ranking shifts between drugs and, as F8 shows, with the polymer's hydrophobicity relative to the drug, so a polymer ranking made on one drug does not transfer; the largest effects (10–13-fold) occur at moderate supersaturation, S 6.6–7.6, and shrink at higher S (F9).)

Conditions and limits

One polymer concentration (5 µg/mL), 37 °C, pH 6.8, the first 2 min, three drugs; efavirenz only at S 1.2 because of secondary nucleation ilevbare2013b R5, X12. Most ritonavir values in 2013 were reported before and the new bars are not identified ilevbare2013b X15. The "effective" cut-off is applied loosely: PVPVA (about 1.42) and HPC (about 1.32) lie above 1 yet are not counted ilevbare2012c X7. Seed mass, volume and methanol fraction are not printed in 2012, so absolute rates do not transfer ilevbare2012c X16.

Counterexamples and conflicts

The solubility is not always unchanged: in the nucleation study CAP Adp 0.85 and Pn-IPAAmd raised the celecoxib solubility from 1.5 to 2.1 and 2.3 µg/mL (F19) ilevbare2013c R1.e, R1.g. Konno and co-workers' dissolution slopes rank HPMCAS above HPMC above PVP for felodipine, the same order as the cellulose polymers in the ritonavir screen, but at 30–150 times the polymer concentration and in a test in which dissolution and growth both contribute konno2008a R16, C36.

Transfer check

Test the candidate polymers at the same low concentration (about 5 µg/mL) with seeds of the drug in the medium of interest, at a moderate supersaturation, in triplicate, and with a solubility control with polymer; a polymer ratio of about 1.2 or below is inside the "ineffective" group of this evidence, about 2–3 inside the "good" group, and above 5 the exceptional cases (CA 320S Sub on ritonavir, HPMC on celecoxib) ilevbare2012c R1, R9; ilevbare2013b R9, X3.

History

Alonzo and co-workers (2012) quantified HPMC on felodipine growth alonzo2012 C46. Ilevbare and co-workers (2012) extended the seeded method to 34 polymers on ritonavir and (2013) to three drugs with second-generation esters designed from the first screen ilevbare2012c C22; ilevbare2013b C7, C20. The conclusion that the ranking is drug-dependent first appears in the 2013 paper ilevbare2013b C21, C44. Schram, Beaudoin and Taylor (2015) added a second felodipine polymer (HPMCAS-LF at 5 µg/mL, S 8) on rotating-disc seeds schram2015 R4. Schram, Beaudoin and Taylor (2016) showed that the seed origin changes the ratio for the same polymer and level, from 2.7 to 12 for HPMCAS on felodipine (see F24) schram2016 R2.

How it was shown

The solubility parameter \delta = \sqrt{\sum_i \Delta e_i / \sum_i \Delta v_i} = \sqrt{\Delta E_v / V} was calculated by the Fedors group-contribution method from the structural formula, with a molar-volume correction for glassy polymers; lower \delta means more hydrophobic, water is 49.01 MPa^1/2 ilevbare2012c E1, E2, E3; ilevbare2013c P1. The 14 new esters (cellulose acetate, propionate, acetate propionate and acetate butyrate carrying adipate, suberate or sebacate groups with a free carboxyl) span \delta 19.62–23.28 and degree of substitution of the carboxylated group, DS (CO2H), 0.19–0.85, with Mn 3,850–61,000 g/mol and Tg 74–134 °C ilevbare2012c M23–M36, X1. Growth effectiveness was measured by seeded growth (F7). An OPLS-DA of 19 cellulose-based polymers in two classes used seven descriptors (SP, DP, Mn, monomer Mw, hydrogen-bond acceptors and donors, Tg) ilevbare2012c P14, R12. In 2013 the 16 polymers were run on three drugs with different SP and Log P ilevbare2013b R9, M1–M3. Hsieh, Box and Taylor (2014) used nine polymers on glyburide, warfarin, papaverine and dipyridamole and discussed hydrogen bonding and hydrophobicity without measuring either hsieh2014 C35–C39.

What the data show

Ordered from least to most hydrophobic the new esters gave: CP Adp 1.68 (SP 23.28), CA 320S Adp 1.83 (22.95), CAP Adp 0.85 2.98 (21.27), CA 398-30 Adp 0.95 (20.91), CAB Adp 0.81 2.70 (20.86), CAP Adp 0.33 1.64 (20.56), then CAP Seb 0.67 0.85 (20.41), CAP 482-20 Adp 1.01, CAP Sub 0.94, CAB 381-20 Adp 0.85, CAB Adp 0.25 0.99, CAP Seb 0.24 0.93, CAB Sub 0.83 and CAB Seb 0.84 (19.62) ilevbare2012c R10, R9. By DS (CO2H), esters with 0.33–0.85 gave 1.64–2.98 except CAP Seb 0.67 (0.85, SP 20.41), and those with 0.19–0.26 gave 0.83–1.01; CA 398-30 Adp, with a suitable SP (20.91) but DS (CO2H) 0.21, failed ilevbare2012c R11, X3. Within each series a higher DS (CO2H) gives a higher SP (CAP Adp 0.85 21.27 against CAP Adp 0.33 20.56; CAB Adp 0.81 20.86 against CAB Adp 0.25 20.05), so the two factors are confounded and only two single polymers (CA 398-30 Adp and CAP Seb 0.67) separate them ilevbare2012c X10. The OPLS-DA loadings were about 0.70 (SP), 0.46 (hydrogen-bond donors), 0.39 (Tg), 0.29 (monomer Mw), 0.01 (Mn), −0.17 (DP) and −0.19 (acceptors) ilevbare2012c R14. Of the synthetic polymers only Pn-IPAAmd (3.25) was a strong inhibitor; PVP, PVPVA, PAA, Pnn-DMAAmd, EUD L100 and PAlAmn gave about 0.9–1.4 on ritonavir ilevbare2012c R9. Across three drugs the effective cellulose polymers lay at SP 20.56–23.28 for drugs of SP 20.03–23.38; the best cellulose polymer shifted with the drug (CA 320S Sub and Seb for ritonavir and efavirenz, HPMC for celecoxib), CAP Seb, CAB Seb and CAB Adp 0.25 gave about 0.85–1.3, and PVPVA was more effective than PVP for celecoxib (about 7.4 against 2.7) and efavirenz (about 4.9 against 2.5) ilevbare2013b R9, C43, C44, C52. For the acidic drugs of the pH-shift study, PVP, PVPVA, HPMC, both HPMCAS grades and Eudragit E100 kept the precipitates amorphous, the very hydrophilic PAA and moderately hydrophilic CMCAB failed for warfarin, and the most hydrophobic CAP-adipate failed for both acids (F16) hsieh2014 R4. In the dihydropyridine study at 4.5 mg/mL polymer, PVPVA, HPMC and HPMCAS kept four of six precipitates amorphous beyond 24 h, PVP was weaker, the very hydrophilic PAA and the hydrophobic P2VP changed nothing, and CMCAB and CAPAdp, at 1/45 of the dose, matched the best polymers only for cilnidipine (see F26) raina2015b R9, X8. For telaprevir the solubility parameter no longer ordered the polymers when the chemistry differed: the effective ω-carboxyalkanoates lay at SP 22.46–23.18 MPa^1/2, CAP-Seb-024 at 23.04 failed (acid DS 0.24), the branched short-spacer acid A5a (25.54) worked and its long-spacer twin A5b (24.29) did not, and pectin, PAA and EUD L100, which carry acids, gave only 11–21 min against 14–15 without polymer (see F25) mosqueragiraldo2016 C25, M12–M14, M24, M25, R4, R5, R6.

Figure

The six esters at the left (SP 23.28–20.56) inhibit growth, except the yellow CA 398-30 Adp; the esters at the right, more hydrophobic, give ratios of 0.83–1.01 ilevbare2012c R10.

Why

Ilevbare and co-workers argue that adsorption on the crystal surface is required and that hydrophobicity "is likely" to set its extent: a very hydrophilic polymer has a greater affinity for water and stays in solution, a very hydrophobic one has a greater affinity for its own monomer units and forms a condensed globule that "may not adsorb"; semirigid cellulose backbones lie flat in trains with more contact than flexible chains, which form loops; and the adipate carboxyls (pKa about 4.43), nearly fully ionized at pH 6.8, make the polymers amphiphilic and "may influence" the adsorbed conformation ilevbare2012c C35, C36, C39, C40, R15, R16. The flexible synthetic chains "most likely" failed for this reason even when their SP matched; Pn-IPAAmd's amide "can potentially" hydrogen-bond to the carbonyl oxygens and thiazole nitrogens exposed on the four fast-growing faces (see F12) ("It is speculated") ilevbare2012c C38, C44, C45, C47. In 2013 the salt test supports a hydrophobic contribution for the cellulose polymers and the N–H band shifts a hydrogen-bond contribution for PVPVA (F11), and the authors conclude that moderate hydrophobicity relative to the drug "and/or" groups for specific interactions promote adsorption ilevbare2013b C60, C4, C48, C51. Hsieh, Box and Taylor say hydrogen bonds between drug and polymer, which water can compete for, and hydrophobicity "may" explain why the same polymers were effective for the acids and not for the bases hsieh2014 C35–C39. (synthesis: the window depends on the drug SP, so the same polymer can be mid-range for one drug and too hydrophobic or hydrophilic for another; HPMC is the best for celecoxib and mid-range for ritonavir, and CA 320S Sub, with a lower SP, is best for the more hydrophobic ritonavir.) Raina and co-workers also call PVPVA, HPMC and HPMCAS moderately hydrophobic and attribute the failure of the more hydrophilic PAA and PVP and the more hydrophobic P2VP, CMCAB and CAPAdp to a much greater affinity for one phase; they say this agrees with the earlier growth and nucleation work and that hydrogen bonding "may also play a role", without measuring hydrophobicity raina2015b C41, C42, C44, C45, X9. Mosquera-Giraldo and co-workers (2016) explain the telaprevir result by ionized carboxylates on side chains short enough to stay extended, which make the polymer amphiphilic, and find the calculated solubility parameter "insufficient" to describe amphiphilicity across complex structures; the earlier SP window was derived on polymers of one chemistry mosqueragiraldo2016 C27, C26, C56, C4.

Conditions and limits

One polymer concentration, one protocol, 37 °C and pH 6.8 ilevbare2013b P10. SP is calculated from the repeat-unit structure, and the SP values of the commercial and synthetic polymers are not printed in the 2012 paper, so the 20.56–25.98 range and the "similar hydrophobicity" of synthetic polymers cannot be checked there ilevbare2012c X11. The OPLS-DA used 19 polymers, seven descriptors and four components; Tg, donors and monomer Mw also load clearly, against the statement that Mn, monomer Mw, DP, acceptors and Tg are not significantly correlated, and the classes are described loosely ilevbare2012c X8, X9. In the 2013 text the failing range is printed as SP "greater than 20.56", the reverse of the stated convention, and efavirenz with CAB Adp 0.25 (SP 20.05) reached about 1.3, so the cut is not sharp ilevbare2013b X2.

Counterexamples and conflicts

PVPVA and PVP, hydrophilic synthetic polymers with SP 25.77 and 28.39, were among the best inhibitors for celecoxib and efavirenz and useless for ritonavir ilevbare2013b R9.a, R9.c. Pn-IPAAmd (SP 22.64 in the 2013 nucleation paper) was the best single ritonavir growth inhibitor but its activity is attributed to a specific interaction, not to hydrophobicity alone ilevbare2012c C44, C47; ilevbare2013c M7. PAA, with many ionized carboxyl groups, failed for all three drugs, which the authors take as support for the "conjecture" that a balance of features is needed ilevbare2012c C41; ilevbare2013b R9.b. Across telaprevir polymers of different chemistry the calculated SP gave "only a weak correlation" with effectiveness (no statistic shown) and the pair A5a/A5b differ by 1.25 MPa^1/2, more than the 0.72 spread of the effective acids mosqueragiraldo2016 C25, X7, X8. CP-Tod-202, without a carboxylic acid, gave about 61 min, as long as two polymers listed as effective mosqueragiraldo2016 X5.

Transfer check

Calculate the Fedors solubility parameter of the drug and of each candidate polymer; polymers within roughly 20.5–23.3 MPa^1/2 for drugs with SP 20–23.4 are inside the evidence, polymers more hydrophobic than that or with few ionizable groups are outside it ilevbare2012c R10, R11; ilevbare2013b R9. Then confirm with the seeded growth test (F7); for a drug that can donate hydrogen bonds (N–H), test PVPVA as well ilevbare2013b R12.

History

Hasegawa and co-workers (1988, outside the library) had named adsorption of carboxymethylethyl cellulose on nifedipine as the key factor ilevbare2012c R19. Ilevbare and co-workers (2012) were the first in the library to link growth inhibition to the polymer's hydrophobicity, for ritonavir, and (2013) extended it to celecoxib and efavirenz, adding specific interactions for PVPVA ilevbare2012c C34, C25; ilevbare2013b C60. Hsieh, Box and Taylor (2014) used the same reasoning for pH-shift precipitation hsieh2014 C39. Raina and co-workers (2015) carried the moderate-hydrophobicity reading to the lifetime of amorphous precipitates of six dihydropyridines raina2015b C44, C47. Mosquera-Giraldo and co-workers (2016) tested the SP and carboxyl-content rules of the ritonavir work on a chemically wide set against telaprevir and found that they hold within one chemistry only mosqueragiraldo2016 C4, C5.