When a supersaturated drug solution splits in two: liquid–liquid phase separation at the amorphous solubility

Background and motivation

Supersaturating formulations, such as amorphous solid dispersions (ASDs), aim to deliver a poorly water-soluble drug at a concentration above its crystal solubility so that more drug is available for absorption. Highly supersaturated aqueous drug solutions are also made routinely during drug testing, for example when a stock solution in an organic solvent is diluted into an assay buffer. The authors open with the observation that the phase behaviour of such solutions "appears complex and poorly understood", and that drug aggregates and colloids are often reported (p.2). C1

Most of that literature comes from high-throughput screening. There, drug aggregates bind enzymes non-specifically and produce false positives, a behaviour called promiscuous inhibition (Coan and Shoichet 2008, ref 1; Coan et al. 2009, ref 2; Feng et al. 2007, ref 3; Seidler et al. 2003, ref 6). In a screen of nearly 300 randomly chosen compounds, close to 20% behaved this way (Feng et al. 2005, ref 7). The aggregates usually appear when an organic stock is diluted into water and are 50 nm to more than 1000 nm in size, often growing with time (refs 4–6). They are not always a nuisance: Frenkel et al. (2005, ref 4) found that non-nucleoside reverse transcriptase inhibitors with good absorption formed aggregates with hydrodynamic radii below 100 nm, and suggested that these "may" be taken up directly into the lymphatic system. Colloids also form from dyes (ref 8) and from amorphous blends of a poorly soluble compound with a water-soluble polymer (refs 9, 10). C7

Two observations from the screening work set up this paper. Aggregation starts once a certain monomer concentration is reached, and adding more compound beyond it adds aggregates but does not raise the free (monomer) concentration (refs 1, 2). That implies an upper limit to the free drug concentration, which matters for dose–response curves and for any attempt to maximize exposure. Yet this limit could not be predicted, because the thermodynamics of drug aggregation had not been worked out (p.3–4). C8 The authors then argue that the known features of drug aggregation (a reproducible onset at a well-defined concentration, more aggregate at constant free monomer as compound is added, and reversal by dilution) "suggest" liquid–liquid phase separation (LLPS), a process familiar from polymer blends, protein solutions and organic crystallization, where it gives a solute-rich and a solvent-rich phase (refs 11–15). C9 LLPS had not been widely studied in aqueous solutions of lipophilic drugs, whose concentrations are typically below 50 µM (p.4). C10

The paper therefore sets out to: (1) measure the ritonavir–water phase diagram as a function of temperature, with the crystal solubility, the liquid–liquid co-existence curve (binodal) and the spinodal; (2) show and explain that LLPS of hydrophobic, high-melting drugs occurs in a solution that is still supersaturated with respect to the crystal, so that LLPS comes before crystallization; (3) show for several drugs that the concentration at which phase separation occurs can be predicted from the thermodynamic properties of the crystal and the supercooled liquid and from solution activity coefficients; and (4) confirm the liquid-like, hydrophobic character of the drug-rich phase with an environment-sensitive fluorescent probe (p.4). C4·C3·C19 The results section adds two formulation tests: whether the same LLPS appears when an ASD of ritonavir and poly(vinyl pyrrolidone) (PVP) dissolves, and how a solubilizing surfactant changes the LLPS concentration (p.20–22). C52·C53

Background concepts

Liquid–liquid phase separation and its boundaries. When a solute and a solvent are only partly miscible, a solution above a certain concentration splits into two liquids: here a water-rich continuous phase and a drug-rich dispersed phase. The paper uses two ways to locate the boundary. At a fixed temperature, the concentration at which the second phase appears is called the C_L-L boundary, the liquid–liquid phase transition concentration, the co-existence concentration or simply the LLPS concentration. At a fixed concentration, the temperature at which the solution clouds or clears is the T_L-L boundary; plotted against concentration, these points form the binodal. Inside the binodal lies the spinodal. Between the two curves, a new liquid phase must nucleate, so separation is an activated process; beyond the spinodal, the solution is unstable and separates spontaneously, by spinodal decomposition (p.17). C32 The spinodal temperature at a concentration $c$ was found by measuring the intensity $I_{{90}^{\circ }}$ of light scattered at 90° as the temperature changed, and extrapolating its reciprocal linearly to the temperature at which

In plain terms: scattering grows without limit as the solution approaches the spinodal, so the reciprocal intensity falls to zero there; the authors follow the method of Lafferrère et al. (2004, ref 12) and Pozharskaya et al. (1984, ref 28) (p.12). E13

Activity and equilibrium. The thermodynamic argument of the paper rests on one rule: at equilibrium, each component has the same activity in every phase (appendix eq 7), and activity is mole fraction times activity coefficient, $a_i=x_i{\gamma }_i$ (eq 8). E6·E7 For two coexisting liquids, a water-rich phase $L_1$ and a drug-rich phase $L_2$, this gives (eq 13):

In plain terms: the drug's activity in the water around the droplets equals its activity inside the droplets. Here $x$ is the drug mole fraction and $\gamma$ its activity coefficient in each phase. E12

Crystal solubility and amorphous solubility. The crystal is in equilibrium with a solution whose drug mole fraction $x_{C,L_1}$ follows (appendix eq printed as "(1)" but referred to as Equation 3):

Here $\Delta G_{a\to c}$ is the free-energy difference between the amorphous (supercooled liquid) and crystalline forms at temperature $T$, $R$ is the gas constant and ${\gamma }_{L_1}$ is the activity coefficient of the drug in water. In plain terms: crystal solubility is set by how much more stable the crystal is than the liquid drug and by how much the water dislikes the drug. E3·X4 An amorphous solid has no lattice to break, so its free-energy term is zero, and if the activity coefficient is the same at the crystal and the amorphous solubility (a "reasonable assumption" for these dilute solutions), the two solubilities are linked by (eq 5):

In plain terms: the amorphous (supercooled liquid, SL) solubility is the crystal solubility multiplied by $\exp (\Delta G_{a\to c}/RT)$. E5·C55·C58 The free-energy difference is estimated from the heat of fusion $\Delta H_f$ and the melting temperature $T_m$ with the Hoffman equation (eq 2, reprinted as eq 6):

In plain terms: the free-energy gap between liquid and crystal is zero at the melting point and grows as the temperature falls below it; the Hoffman form assumes a constant heat-capacity difference between liquid and crystal (p.25), and earlier work found it a good estimate (Marsac et al. 2006, ref 22). E2·C58

The water correction. The Hoffman estimate treats the amorphous drug as dry. In contact with water, however, the amorphous drug absorbs water, which lowers its activity below 1; the paper calls this the activity of the amorphous solute saturated with water, written $\exp (-I(a_2))$ and obtained, following Murdande et al. (2009, 2010, refs 19, 20), by applying the Gibbs–Duhem equation to the water sorption isotherm of the amorphous drug (p.6–7, p.25–26). C59·P2 With this correction the amorphous solubility becomes (eq 12):

In plain terms: the last term is the logarithm of the activity of the water-saturated amorphous drug, which is negative and so lowers the predicted solubility. E11 The main-text version used for the calculations, in concentration units, is (eq 1):

Here $C_{\mathrm{e}\mathrm{q}}$ is the measured crystal (equilibrium) solubility and $C_{\mathrm{a}\mathrm{m}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{h}\mathrm{o}\mathrm{u}\mathrm{s}}$ the predicted amorphous solubility, both in µg/mL. E1 The appendix states that "Equation 2" of the main text is equivalent to eq 12; the equation that carries the $-I(a_2)$ term and is equivalent to eq 12 is in fact Eq. 1, so the cross-reference is a numbering slip. X4

Why the LLPS concentration should equal the amorphous solubility. The key step of the appendix is to compare eq 13 with the equation for an amorphous solid equilibrated with water (eq 10, $x_{SL,L_1}{\gamma }_{SL,L_1}=x_{SL,L_2}{\gamma }_{SL,L_2}$). The two have the same left-hand side: the drug in water is in equilibrium either with a wet amorphous solid or with wet drug-rich droplets, and both are the same water-saturated supercooled liquid. The amorphous solubility is therefore the drug concentration in the continuous phase at LLPS, and it can be reached either by equilibrating an amorphous solid with water (the approach of Murdande et al.) or by supersaturating a solution until a drug-rich phase separates, the approach of this paper (p.27). C61·E9·E12

Other terms. The pyrene I₁/I₃ ratio is the intensity ratio of the first (373 nm) and third (383 nm) emission peaks of pyrene; it falls when pyrene moves from water into a less polar environment, and is widely used to detect micelles (refs 26, 27; p.10). C14 A slow crystallizer is a compound that, in the classification of Baird et al. (2010, ref 23), does not crystallize readily from its undercooled melt; all eight drugs here belong to this class (p.16). C27 The critical aggregation concentration (CAC) is the screening literature's name for the onset of aggregation (p.16). C29

Methods in detail

The study combines four kinds of work: detecting and characterizing the second phase for ritonavir, predicting the onset for eight drugs from thermodynamics, mapping the ritonavir phase diagram against temperature, and testing what the onset means when the medium changes, when additives are present and when an ASD dissolves. The flow below shows how they connect.

Contribution 1: Showing that the cloudiness is a drug-rich liquid

Problem. Turbidity alone shows that a second phase exists but not what it is. To call it LLPS, the authors needed to show that the new phase is a liquid rather than crystals, that it is rich in drug, and where it starts.

What they did. The onset was measured by the solvent-shift titration: ritonavir dissolved in methanol at 4 mg/mL was pumped by a syringe pump into 10 mL of medium at a fixed temperature, stirred at 300 rpm, while a fibre-optic UV/Vis dip probe (path 5 mm) followed the extinction at non-absorbing wavelengths, 280–450 nm; the onset is the concentration at which extinction starts to rise. The pH of the ritonavir–water runs stayed above 7.0, where ritonavir (pKa 1.8 and 2.6) is un-ionized (p.8). P5·C13·C14 For ritonavir in water at 37 °C, the extinction and the DLS count rate (Malvern Nano-ZS, backscatter at 173°, flow cell pumped at 1 mL/min, a reading about every 7 min) were recorded at the same time (p.10). P11 In a separate titration, pyrene (0.5 µg/mL, from a DMSO stock) was added to 1 mL of water, ritonavir stock was added in 5 µL steps, and the I₁/I₃ ratio was read after each step (excitation 334 nm) (p.10). P10 To isolate the new phase, 0.5 mL of a 60 mg/mL methanol solution of ritonavir was added to 20 mL of double-distilled water at 10, 37 or 50 °C; the cloudy dispersion was examined under cross-polarized light, and the dispersed phase was spun down at 274,356 × g for 15 min. The pellet's water content was taken as its weight loss on drying at room temperature and below 5% RH in a gravimetric analyzer, and its glass transition was measured by DSC (cooled, then heated at 20 °C/min between −25 and 150 °C); the supernatant was analysed by UV (p.8–9). P7·P8·P9·C15

Why it works. Each read-out answers a different question. Extinction and DLS count rate respond to any scattering particle, so they locate the onset. Polarized light separates birefringent crystals from isotropic droplets. Pyrene partitions into a hydrophobic liquid but cannot enter a crystal lattice, so a falling I₁/I₃ indicates a liquid, drug-rich environment (p.13–14). C19 The DSC glass transition of the pellet shows whether it is a supercooled liquid at the working temperature, and its water content links the pellet to the water sorption of amorphous ritonavir, measured separately at 37 °C (Figure 6). P15

Contribution 2: Predicting the onset from crystal properties

Problem. If the drug-rich phase is water-saturated amorphous drug, its onset should equal the amorphous solubility. Measuring the amorphous solubility directly is awkward: powdered amorphous ritonavir agglomerates on contact with the medium and then dissolves very slowly (p.7). C12

What they did. Crystal solubility was measured by the shake-flask method for ritonavir and efavirenz (excess solid in 100 mM sodium phosphate buffer pH 6.8 at 37 °C for 48 h, ultracentrifugation and HPLC; ritonavir also in water at 25 and 50 °C, in 200 mM buffer, and with PVP or Tween 80); the other six solubilities were taken from earlier Taylor-group papers (refs 16–18) (p.5–6). P1 Melting point and heat of fusion came from Baird et al. (ref 23) or, for clozapine and efavirenz, were measured by the same methods (Table 2). M1·M2·M6·X3 The water-saturated amorphous activity, $\exp (-I(a_2))$, came from water sorption isotherms by the Gibbs–Duhem treatment of Murdande et al.; Table 2 lists values from 0.27 (ritonavir) to 0.85 (felodipine). P2·M1·M9 These went into Eq. 1 at 37 °C. As an independent check, the amorphous solubility of ritonavir was also measured directly: a spin-coated amorphous film (30 mg ritonavir in 0.5 mL methanol, 18 mm glass slide, dried under vacuum about 24 h, confirmed amorphous by PXRD and polarized light) was dissolved on a stir bar at 300 rpm and 37 °C, and the concentration was followed by second-derivative UV spectra every 45 s to suppress scattering (p.7). P3·P4·C11

Why it works and how it differs. Murdande et al. had computed amorphous solubility advantages from first principles; this paper turns the calculation around and asks whether a measured onset of phase separation equals that amorphous solubility, for eight drugs in media where each is un-ionized (Table 3). C3 The onset itself is also tested for artefacts: the stock solvent (methanol, ethanol, THF), the rate of addition (0.01 to 0.125 mL/min) and an all-aqueous route in which the drug was dissolved in 0.1 M HCl at pH 1.0 and pumped into pH 6.8 buffer (Tables 4 and 5) (p.16). P6·R9·R10·C28

Contribution 3: The ritonavir phase diagram against temperature

Problem. A single onset concentration at 37 °C does not show where LLPS sits relative to crystallization, or how far a solution can be pushed before it separates spontaneously.

What they did. Following Lafferrère et al. (ref 12), the binodal was measured from cloud and clear points: a ritonavir solution of known concentration in a 100 mL jacketed vessel was cooled at 0.5 °C/min until the 90° scattering of a 474 nm LED rose (T_cloud), and a cloudy solution was heated until it cleared (T_clarify); T_L-L is their mean. The spinodal came from the extrapolation of the reciprocal 90° intensity to zero. The LLPS onset was measured by titration between 10 and 65 °C, in water and in 100 mM buffer, and the crystal solubility at 25, 37 and 50 °C (p.8, p.11–12, Figure 7). P12·E13·P5·P1 Efavirenz was titrated between 10 and 50 °C for comparison (Figure 9). R15

Note by the AI writer (not discussed in the paper). The method text says the binodal solutions were made up in buffer at pH 6.8 and that clouding was sought on cooling. The plotted binodal points, however, coincide with the onset values in water, not with the much lower buffer values, and they lie on the low-temperature branch of the diagram, where the onset concentration falls as temperature rises; on that branch a solution of fixed concentration would cloud on heating. The paper does not explain how the protocol was applied there, so the binodal points are best taken as plotted. X6·X7

Contribution 4: What the onset means for formulations

Problem. If the LLPS concentration is the highest concentration of free drug in a single-phase solution, it should also cap what a supersaturating formulation can reach, and an additive should be able to move it only by changing the reference activities (p.20). C48·C49

What they did. Two tests. First, PVP K29/32 at 25 µg/mL was dissolved in 100 mM buffer pH 6.8, and both the crystal solubility and the LLPS onset of ritonavir were measured; then an ASD of ritonavir and PVP at 1:9 by weight, made by rotary evaporation from methanol (bath 65 °C, vacuum 24 h), was added to 50 mL of the same buffer at 37 °C in portions of about 3 mg every 10 min, each portion worth 6.0 µg/mL ritonavir, while a UV probe followed concentration and extinction (p.12, p.21; Figure 10). P13·P14·M10 Second, Tween 80 at 500 µg/mL, above its critical micelle concentration of 23.6 µg/mL (0.018 mM), was used to raise the crystal solubility, and the LLPS onset was measured again (Table 7). M11·R16 PVP was chosen as the matrix because its high aqueous solubility makes the dispersion dissolve fast (p.21). C50

Experimental analysis

The second phase is wet, liquid ritonavir

Adding a concentrated ritonavir stock to water gave a cloudy dispersion with a slight bluish colour, and under cross-polarized light it contained small, spherical, non-birefringent droplets (Figure 1). The authors read this as a second dispersed phase with a liquid-like structure, "suggesting" LLPS (p.13). R1·C16 In water at 37 °C, extinction at 280 nm stayed below about 0.02 up to about 37 µg/mL and then rose steeply to about 0.14 at about 56 µg/mL; the DLS count rate, recorded at the same time, stayed below about 200 kcps up to about 41 µg/mL and then climbed to about 2050 kcps at about 55 µg/mL (Figure 2, read approximately). The printed onsets are 37.2 ± 0.9 µg/mL by UV and 39.8 ± 0.3 µg/mL by DLS, and below the onset DLS could not give a meaningful particle size. R2·R8.b·C17 The pyrene I₁/I₃ ratio stayed at about 1.67 to 1.69 up to 40 µg/mL and then fell steadily to about 1.39 at 120 µg/mL (Figure 4); the text puts the break at 39.0 µg/mL. Pyrene had moved into a less polar, drug-rich liquid, and the authors conclude that a second, liquid phase of ritonavir forms above "~40.0 µg/mL" in water at 37 °C. R4·C19·C20 The droplets grew from about 345 nm one minute after mixing to about 842 nm after about an hour (Figure 3), "consistent with coalescence of the droplets, commonly observed in LLPS" (p.13). R3·C18

Table A. The ritonavir phase boundary in water at 37 °C by eight routes, from Tables 1, 3, 5 and 6 and the text on p.14. R4·R6·R8·R10·R13

The isolated drug-rich phase contained 95.97, 95.13 and 94.85% ritonavir and 4.03 ± 0.53, 4.87 ± 1.20 and 5.15 ± 2.12% water when formed at 10, 37 and 50 °C (Table 1). R6 Its DSC trace (Figure 5) shows a glass transition with onset −2.74 °C, midpoint 0.42 °C and end 4.29 °C, and according to the text no exothermic or melting peaks; dry amorphous ritonavir has a Tg of 50.4 °C (refs 32, 33). R5·M1 The authors explain the depression by water: amorphous ritonavir sorbs about 4.98% water at 95% RH, and a straight line through the high-humidity part of its isotherm (slope 0.075, intercept −2.290) gives 5.21% at 100% RH, close to the water in the drug-rich phase; the 50 °C drop also fits the rule of thumb of about 10 °C per 1% of water (refs 22, 34). R7·E14·E15·C23 Because 37 °C is far below the 121 °C melting point and the Tg of the wet phase is below every working temperature, the authors conclude that the dispersed phase is a supercooled liquid, "most likely" containing some water. C22 The water-rich phase held 36.0 µg/mL ritonavir at 37 °C, close to the titration onset, which the authors take as "suggesting" that the two phases equilibrate quickly during continuous addition. R6.b·C24

Note by the AI writer (not discussed in the paper): Figure 5 shows only −15 to 20 °C, so the absence of a melting peak near 121 °C is stated in the text but not shown, and the formation temperature of the analysed pellet is not given. X8

The onset sits at the predicted amorphous solubility for eight drugs

Table B. Crystal solubility, predicted amorphous solubility and LLPS onset at 37 °C (from Table 3; n = 3, mean ± SD). Buffered media are 100 mM phosphate; crystal solubilities of the last six drugs are cited from refs 16–18. R8

Across eight drugs whose LLPS onsets span 5.2 µg/mL (clotrimazole) to 135.8 µg/mL (clozapine), the measured onsets sit close to the predicted amorphous solubility (Table B). UV and DLS agree within 2.6 µg/mL for every drug. R8 The largest relative gap is clotrimazole (5.2 measured against 4.0 predicted) and the largest absolute gap indomethacin (30.4 against 26.7 µg/mL); measured values lie below the prediction for ritonavir, efavirenz and ketoconazole and above it for loratadine, indomethacin, felodipine, clotrimazole and clozapine. R8 The authors call the agreement "good" and "excellent" and draw two conclusions: the LLPS concentration differs between drugs as Eq. 1 expects, because Tm, ΔHf and crystal solubility differ, and the onset is "an alternative way to experimentally determine the amorphous 'solubility'" of compounds that phase-separate before crystallizing, without making a reference amorphous solid (p.15–16). C3·C26·C6 They add that all eight drugs are slow crystallizers in the classification of ref 23, which "may explain" why they phase-separate instead of crystallizing. C27

The onset did not depend on how the drug was brought into solution. Dissolving ritonavir, efavirenz and loratadine in 0.1 M HCl and pumping them into pH 6.8 buffer gave 18.8 ± 0.8, 16.9 ± 0.9 and 7.6 ± 0.2 µg/mL (Table 4), against 18.8, 18.4 and 7.6 µg/mL from methanol stocks; ethanol and THF stocks at several rates gave 34.0 to 37.5 µg/mL for ritonavir in water (Table 5). The authors conclude that methanol did not promote the LLPS and that solvent and rate have "minimal impact" (p.16). R9·R10·R8·C28 They also note that their data show all four features reported for drug "aggregates": no second phase below a threshold, a non-crystalline second phase, a constant free-drug concentration above the threshold, and a reproducible threshold in a given buffer. C29

Note by the AI writer (not discussed in the paper): the predicted values in Table B cannot all be recomputed from the inputs printed in Table 2. With the Hoffman equation at 37 °C and the printed melting points, heats of fusion and water-saturated activities, Eq. 1 reproduces ketoconazole, clotrimazole, felodipine and clozapine within about 5%, but gives about 32.9 instead of 39.2 µg/mL for ritonavir in water, about 10.3 instead of 19.8 for efavirenz, about 5.9 instead of 6.8 for loratadine and about 42.9 instead of 26.7 for indomethacin. The paper does not say which inputs were used, so the agreement for these four drugs rests on numbers that cannot be checked from the paper alone. Three smaller inconsistencies point the same way: Table 2 gives ritonavir a Log P of 5.6 while the text gives 5.98; the provenance of several properties differs between the methods text and the table footnotes; and the felodipine solubility carries a footnote "s" that does not exist. X1·X2·X3 For loratadine, the pH-shift runs ended at pH ~4.0 to 6.0, which brackets its pKa of 5.0, so it may not have been fully un-ionized as the text assumes. X9

For ritonavir, LLPS lies deep in the region where only crystals are stable

Figure 7 places three kinds of data on one temperature–concentration plane. The crystal solubility of ritonavir is about 1.2, 2.5 and 6.4 µg/mL at 25, 37 and 50 °C, while the LLPS onset lies between about 37 and 58 µg/mL over 10 to 65 °C (read from Figure 7). R11 At 37 °C in water the onset is 37.2 µg/mL against a crystal solubility of 2.4 µg/mL, and since the metastable Form I is only about 5 times more soluble than Form II (refs 31, 32), a solution at the LLPS concentration is supersaturated with respect to every crystal form (p.14). R8.b·M1·C21 The binodal points (about 11 °C at 58 µg/mL, 16 °C at 50, 20 °C at 46.5 and 25 °C at 42.7 µg/mL) coincide with the titration onsets, and the spinodal points lie only a few degrees beyond them (about 17.6, 23.4, 25.2 and 29.2 °C at the same concentrations). R11 From this the authors conclude that continuous addition "appears to give a reasonable estimate" of the co-existence concentration, with little overshoot before the second phase appears, "consistent with a low energy barrier to LLPS", and that the metastable zone for LLPS is small (p.17–18). C30·C31·C34

They then divide the diagram into regions. In region I, between the crystal solubility and the binodal, the solution is supersaturated only with respect to the crystal, so crystals may nucleate and grow. Above the binodal (region IIa) it is supersaturated with respect to both the crystal and the liquid phase, and LLPS "will only occur if the kinetics of crystal nucleation is slow relative to the LLPS process"; beyond the spinodal (region IIb) liquid demixing is spontaneous. C32 For ritonavir at 37 °C, crystal nucleation from a 34 µg/mL aqueous solution takes more than 2 hours, so LLPS wins at high supersaturation. R12·C33 The authors' summary, borrowing a phrase from Bonnett et al. (2003, ref 30), is that ritonavir has "a submerged liquid-liquid phase within the metastable zone for crystal nucleation": highly supersaturated solutions undergo LLPS into a water-saturated, viscous supercooled liquid, and this precedes crystallization (p.18). C35·C4

The flow below summarizes the authors' chain of reasoning from the phase diagram, with the two outcomes that matter for a formulation.

Note by the AI writer (not discussed in the paper): the binodal and spinodal were measured at only four concentrations, between about 11 and 29 °C; at 37 °C and on the rising high-temperature branch, only titration onsets exist. The induction time of more than 2 hours is given without a method or reference. X17·X11

Salt and temperature move the limit

Table C. Ritonavir in sodium phosphate buffers of increasing strength, pH 6.8 (from Table 6; n = 3, mean ± SD). R13

Salt lowered every quantity. The ritonavir LLPS onset fell from 37.2 µg/mL in water to 18.8, 14.3 and 4.7 µg/mL in 100, 200 and 500 mM phosphate buffer, and the amorphous solubility measured by dissolving a film followed it (34.2, 21.8, 13.8 and 5.2 µg/mL); the crystal solubility fell from 2.4 to 1.3 and 0.95 µg/mL (Table C). R13 The authors note that the measured amorphous solubility "corresponds well" to the LLPS onset at each ionic strength, and that the theoretical value does too when it is calculated from the crystal solubility in the same medium. C42 Across 10 to 65 °C, the onset in water stayed about twice that in 100 mM buffer (Figure 8). R14·C40 Increasing ionic strength was expected to promote aggregation through hydrophobic interactions (refs 38, 39), and the authors write that the change "may be attributed to the 'salting-out' effect": salt makes the solvent more polar, so drug molecules associate to reduce their contact with it, and both crystal solubility and co-existence concentration fall. C38·C41 Their practical conclusion is that the medium changes both quantities, "hence the need for consistency when performing experiments" (p.19). C43 They frame the whole series with the view that, for compounds with Log P values of 2.24 to 5.98, "It is therefore intuitive" that the LLPS is driven by hydrophobic interactions. C37

Temperature behaved differently for ritonavir and the other drugs. Efavirenz's onset in water rose steadily, from about 19 µg/mL at 10 °C to about 45 µg/mL at 50 °C (Figure 9), as expected for partially miscible liquids, whose miscibility usually increases with temperature (ref 12). R15·C44 The authors state that all compounds except ritonavir behaved this way, but show temperature data only for ritonavir and efavirenz. C45·X10 Ritonavir's onset in water fell from about 58 µg/mL at 10 °C to a minimum of about 37 µg/mL near 35 °C and rose again to about 53 µg/mL at 65 °C, a U-shaped profile; in 100 mM buffer the curve was flatter, about 27 µg/mL at 10 °C and about 18 µg/mL from 35 to 55 °C (Figure 8). R14·C46 The critical micelle concentration of many surfactants shows a similar U-shape with a minimum between 20 and 40 °C (refs 40–44), and the authors "surmise that the U-shaped profile ... may have its origin in a similar phenomenon" (p.20). C47

A dissolving dispersion stops at the limit, and a surfactant moves it only in proportion

Table D. Additives and dispersion dissolution (from Table 7 and the Figure 10 caption; n = 3 for Table 7). R16·R17

The PVP dispersion. At 25 µg/mL, PVP left the crystal solubility (1.3 µg/mL) and the LLPS onset (18.3 against 18.8 µg/mL) essentially unchanged, which the authors read as "suggesting that PVP is not incorporated into the ritonavir-rich phase". R16.a·C51 When the 1:9 dispersion was added in 3 mg portions, the dissolved ritonavir followed the amount added for three portions (6.4, 11.8 and 18.3 µg/mL against 6.0, 12.0 and 18.0) and then stayed at 18.0 µg/mL although 24.0 µg/mL had been added (Figure 10). Extinction stayed near zero for the first 20 minutes, rose to about 0.04 after the third portion and to about 0.12 after the fourth, and DLS showed colloids of about 325 nm. R17·R18 The authors conclude that LLPS can be generated by dissolving a solid dispersion, at "the same" concentration as the LLPS onset in that medium, and that PVP affects neither the solid–liquid nor the liquid–liquid equilibrium (p.21). C52 In the abstract this becomes the general statement that "there is an upper limit to the extent of supersaturation achievable by a supersaturating dosage form", dictated by the LLPS concentration. C5

The surfactant. With 500 µg/mL Tween 80, well above its critical micelle concentration of 23.6 µg/mL, the crystal solubility rose from 1.3 to 3.5 µg/mL and the LLPS onset from 18.8 to 46.1 µg/mL (Table 7); the text calls both rises "~3 times". R16.b·M11·C53 The authors explain why the two must move together. The solution saturated with crystal has the same drug activity with or without the additive, because the solid is the same; the drug-rich liquid also keeps its activity, as long as the additive does not enter it; and with a constant activity coefficient in the dilute bulk solution, the ratio of LLPS concentration to crystal solubility "must therefore be the same". Hence "the maximum extent of supersaturation achievable in the presence of a solubilizing additive is not increased", even though more drug is in solution (p.22). C54·C55·C49

Note by the AI writer (not discussed in the paper): the printed LLPS ratio of 2.6 does not match the table values (46.1/18.8 = 2.45), and the ratio of LLPS concentration to crystal solubility is 14.5 without and 13.2 with Tween 80, so "constant" holds within about 10%. In the dispersion test the extinction already rose after the third portion, when the solution held 18.3 µg/mL, slightly below the 18.8 µg/mL onset without PVP and equal to the 18.3 µg/mL with PVP; the UV probe measures total dissolved drug, and free drug was not measured. Only one dispersion composition, one PVP level and one surfactant level were tested. X5·X15

Discussion

What the paper establishes. For ritonavir, the identity of the "colloid" is well supported: several independent read-outs place the onset in water at 37 °C between 34 and 40 µg/mL, the separated phase is about 95% drug with 4 to 5% water, and its Tg of 0.4 °C makes it a supercooled liquid at every working temperature. R2·R4·R6·R5·X14 Across eight chemically different drugs, the onset lies near the water-corrected amorphous solubility, and the salt series moves onset, measured amorphous solubility and calculated amorphous solubility together. R8·R13 Together with the activity argument of the appendix, this makes the LLPS concentration a practical stand-in for the amorphous solubility, measurable by a simple titration. C6·C61

Where it applies. The framework assumes that the drug is un-ionized, that it crystallizes slowly enough for LLPS to occur first, that the drug-rich phase is a water-saturated supercooled liquid, and that any additive stays out of both the crystal and the drug-rich phase. C13·C32·C27·C22·C49 All eight drugs are slow crystallizers, and the phase diagram, the salt series, the additive tests and the dispersion test were all done with ritonavir. C27·R11·R13·R16·R17 The temperature behaviour is drug-specific: ritonavir's U-shaped profile is unexplained beyond the authors' tentative micelle analogy. C47

What it suggests for formulation (AI writer's reading, not stated in the paper). The LLPS concentration in the actual medium is the useful target for an ASD: dissolving more drug than this adds a colloidal drug-rich phase rather than more free drug. A surfactant that raises total dissolved drug does not, by the authors' argument, raise the maximum supersaturation, so a higher total concentration in a surfactant-containing dissolution test is not a higher driving force. Buffer strength matters: ritonavir's limit roughly halves from water to 100 mM phosphate, so tests in water overstate it. The paper itself establishes where the droplets appear, not what they do for absorption.

Limitations

Limitations stated by the authors. The authors treat several steps as assumptions: the activity coefficient of the drug in the dilute bulk phase is taken as constant between the crystal and the amorphous solubility ("a reasonable assumption"); the Hoffman equation assumes a constant heat-capacity difference and, on its own, neglects water absorption by the amorphous drug, which is why the Murdande correction is applied; and the additive argument holds only "for the case where the solubilizing additive is not incorporated into either the crystal or the liquid phases" (p.20, p.22, p.24–26). C55·C58·C59·C49 LLPS can only be observed when crystal nucleation is slower than LLPS, which ties the method to slow crystallizers. C32·C27 Several interpretations are hedged: coalescence ("consistent with"), fast equilibration ("suggesting"), PVP exclusion from the drug-rich phase ("suggesting"), salting-out ("may be attributed") and the micelle analogy ("We surmise"). C18·C24·C51·C41·C47

The AI writer's own judgement (1): the prediction. The central quantitative claim is the match between onset and predicted amorphous solubility. Half of the predictions cannot be recomputed from the printed inputs, and the gaps are not small (efavirenz 10.3 against 19.8 µg/mL; indomethacin 42.9 against 26.7 µg/mL), so for these drugs the agreement cannot be verified from the paper. X1 Property sources and equation numbering are inconsistent in places (ritonavir Log P 5.6 or 5.98, missing table footnote, appendix eq "(1)" called Equation 3, "Equation 2" said to be equivalent to eq 12). X2·X3·X4 Media differ between drugs (pH 2.0, 6.8 and 10.0, water for one ritonavir row), so the eight onsets are not directly comparable with each other, only with their own predictions. X16

The AI writer's own judgement (2): the ceiling. The claim that the LLPS concentration is the upper limit of free drug is a sound thermodynamic argument, but the paper does not measure free drug or activity above the limit; the dispersion test reads total dissolved drug by UV, and the turbidity started slightly below the onset measured without PVP. C36·X15 The binodal and spinodal cover only four concentrations below about 30 °C, the binodal medium and scan direction are unclear, and the nucleation induction time that justifies "LLPS first" has no stated source. X17·X6·X7·X11 The DSC trace shown does not cover the melting region. X8 None of these undermines the qualitative picture, but they limit how far the numbers can be carried to other drugs, polymers and media.

Conclusion

The paper reframes drug "aggregation" in supersaturated aqueous solution as liquid–liquid phase separation into a water-saturated supercooled liquid of the drug. For ritonavir the drug-rich phase is about 95% drug with 4 to 5% water and a Tg of 0.4 °C, it appears at 37 to 40 µg/mL in water at 37 °C, far above the crystal solubility of 2.4 µg/mL, and it forms in the metastable zone before crystals nucleate. R6·R5·R8.b·C35 For eight drugs the onset matches the amorphous solubility calculated from crystal solubility, melting data and water uptake, which turns a simple titration into a measure of amorphous solubility. C3·C6 The same concentration caps what a dissolving ritonavir–PVP dispersion reaches, and a surfactant raises it only in step with crystal solubility, leaving the maximum supersaturation unchanged; salt lowers it, and temperature reshapes it. C5·C52·C53·C54·C39·C46 In the authors' words, the insights have "important implications for drug delivery" where absorption depends on "the extent and duration of supersaturation" (p.23). C57