When a dissolved weak base meets a higher pH: crystal or amorphous precipitate, and how long the solution stays supersaturated

Background and motivation

A drug has to dissolve before it can cross the gut wall, and most new drug candidates dissolve poorly: the paper cites solubilities typically above 20 µg/ml for compounds discovered in the 1980s against values below 1 µg/ml that are now common (Li et al. 2005). For an ionizable drug the solubility depends strongly on pH, because the ionized form is nearly always more soluble than the neutral one. The gastrointestinal (GI) tract makes this matter. The stomach runs at about pH 1.5 to 3.5 and the duodenum at pH 5 to 7, so a weak base with a pKa between 5 and 8 can dissolve fully in the stomach and then find itself far above the solubility of its neutral form once it reaches the intestine (Hillery et al. 2001; Figure 1a). C1

What happens next decides how much drug is absorbed. Classical nucleation theory says that a solution sufficiently supersaturated with respect to the crystal will nucleate spontaneously, after which the crystals grow until the solution is back at the crystal solubility (Mullin 2001). C3 On the other hand, "it is widely accepted" that a prolonged period of supersaturation can significantly improve the bioavailability of poorly soluble drugs, and many formulation approaches (supersaturating self-emulsifying systems, amorphous dispersions, polymers added to delay precipitation; Vandecruys et al. 2007, Gao et al. 2003, Miller et al. 2008, Curatolo et al. 2009) are built on that idea. Yet, as Brouwers et al. (2009) put it, precipitation itself is still poorly understood. C2

A practical tool for studying precipitation of ionizable drugs already existed. The chasing-equilibrium or CheqSol method (Stuart and Box 2005; Box et al. 2006) dissolves the compound fully ionized at low pH, then adds base to create the neutral species until a UV/Vis probe sees turbidity. The concentration of the neutral species at that moment is the "kinetic solubility". Small additions of acid and base then push the system slightly below or above saturation, and the point at which the pH stops drifting gives the intrinsic (equilibrium) solubility. C6 Using this method, Box and colleagues had seen two kinds of compound. "Chasers" (type 1) reached a kinetic solubility well above their equilibrium solubility and kept dissolving and precipitating as the pH was cycled. "Non-chasers" (type 2) precipitated rapidly, did not appear to supersaturate at all and responded instantaneously to changes in pH. C4 Nobody had asked what kind of solid each group produced.

The Taylor group had at the same time classified many drugs by their crystallization tendency: how readily they crystallize when an undercooled melt is cooled (Baird et al. 2010) and when a solution is evaporated rapidly by spin-coating (Van Eerdenbrugh et al. 2010). The authors reasoned that "intuitively" the ability to supersaturate should be related to this solid-state tendency. C5 The paper therefore sets out to measure the extent and duration of supersaturation that a pH rise creates for a set of weak bases, to characterize the solid that precipitates, to relate the two, and to discuss what the difference means for drug products. A1

Background concepts

Supersaturation, kinetic solubility and intrinsic solubility

Supersaturation is a non-equilibrium state in which the solution concentration (more strictly, the chemical potential) exceeds that of a solution saturated with the crystal. The paper uses the degree of supersaturation, printed in Figure 1a as

In plain terms: $S$ is the concentration $C$ divided by the intrinsic solubility $C_0$ of the crystalline neutral form; $S=1$ at saturation. E9 In practice the paper computes $S$ in two ways. For the type 1 compounds it is the peak (kinetic) concentration divided by the equilibrium solubility found in the titration; for the type 2 compounds it is the supernatant concentration after precipitation divided by the crystal solubility measured by HPLC. E9·R5·R10 The two definitions are not the same quantity, a point that matters when comparing the groups. X3

To combine how high and how long the supersaturation lasts, the paper borrows the supersaturation factor of Bevernage et al. (2010):

In plain terms: $A+B$ is the area under the whole concentration–time profile and $A$ the area under the equilibrium-solubility line over the same time (Figure 2b); $SF=1$ means no supersaturation at all, and larger values mean more drug kept in solution for longer. E10

Why precipitation moves the pH, and the Bjerrum plot

A weak base B in water is in equilibrium with its protonated form, $\mathrm{B}{\mathrm{H}}^{+}\rightleftharpoons B+{\mathrm{H}}^{+}$. When the neutral form precipitates, the equilibrium shifts to replace it, protons are released, and the pH falls; when the solid dissolves, protons are consumed and the pH rises (Figure 1b). C6 A titrator can therefore read precipitation and dissolution directly from the pH: a negative pH gradient after an addition of base means the solution is supersaturated and precipitating, a positive gradient after an addition of acid means it is subsaturated and dissolving, and a zero gradient means neither, so that the neutral concentration at that point is the solubility of whatever solid is present. C6

The Bjerrum plot shows the average number of protons bound per molecule, $Bj$, against pH. While all the compound is dissolved it follows the ionization curve (Eq. 1):

In plain terms: $[H^{+}]$ is the hydrogen-ion concentration from the pH reading and $K_a$ the ionization constant; $Bj$ falls from 1 to 0 around pH = pKa. E1 Once a solid phase is present, the curve changes to Eq. 2:

In plain terms: $S_0$ is the solubility of the solid that is present (the intrinsic solubility for a crystalline precipitate) and $X_{Total}$ the total sample concentration; the higher the solubility of the solid, the further to the right on the pH axis the curve lies. E2 Comparing the titration data with Eq. 2 for different values of $S_0$ thus tells which solubility the solid in the vessel has. For two solids of different solubility the two curves are shifted along the pH axis by ${\log }_{10}$ of the solubility ratio; for loratadine's 11.3 and 1.6 µg/ml this is 0.85 pH units, which matches the offset of about 0.85 read from Figure 4b. E2·R9

Amorphous solubility and how the paper estimates it

An amorphous solid has a higher free energy than its crystal and therefore a higher solubility. A solution in equilibrium with the amorphous form is supersaturated with respect to the crystal, but it can persist for a long time if crystallization is slow. The paper estimates the free energy difference with the Hoffman equation (Eq. 3) and converts it into a solubility ratio (Eq. 4):

In plain terms: $\Delta G_c$ is the free energy difference between amorphous and crystalline forms, estimated from the heat of fusion $\Delta H_f$ and melting temperature $T_m$ of the crystal at temperature $T$; its exponential, with $R$ the gas constant, gives how many times more soluble the amorphous form should be. Multiplying that ratio by the measured crystal solubility gives the predicted amorphous solubility. E3·E4·P13

Amorphous solids take up water, which lowers the activity of the drug in the solid and so its solubility advantage. The method of Murdande et al. (2009, 2010) corrects for this from a water sorption isotherm of the amorphous solid, using the Gibbs–Duhem equation (Eq. 5) and the corrected ratio of Eq. 6:

In plain terms: $n_1$ and $n_2$ are moles of water and of drug in the amorphous solid, $a_1$ the water activity, ${\overline{a}}_1^H$ the water activity at the limit of Henry's law and ${\overline{a}}_1^S$ the water activity in the solid in equilibrium with dilute solution; the integral sums up how much the sorbed water lowers the drug's activity, and the factor $\exp [-I(a_2)]$ shrinks the predicted solubility ratio accordingly. E5·E6 The paper measured the sorption isotherms by dynamic vapour sorption at 37 °C but does not show them, nor does it print the heats of fusion, so neither estimate can be recomputed from the article. P8·X14

Crystallization tendency classes

The group's earlier work sorts compounds into three classes by how they behave when solidified fast: class I are fast, class II intermediate and class III slow crystallizers. Two tests exist, cooling of the melt (Baird et al. 2010) and rapid solvent evaporation by spin-coating (Van Eerdenbrugh et al. 2010), and a compound can fall into different classes in the two tests. P7·M1–M10

Liquid–liquid phase separation

A highly supersaturated solution does not have to form crystals first. It can split into two liquid phases, a dilute aqueous phase and a concentrated drug-rich phase. Above the melting point this is called "oiling out". Below the melting point the drug-rich phase can be a supercooled liquid or, if its glass transition is above the temperature, a glassy solid; the paper uses "liquid–liquid phase separation" for all these cases. C34 From the literature the authors note that this separation has a very small metastable zone, so that it happens with little overshoot, and that crystals can form later from either liquid phase (Lai et al. 2007; Maeda et al. 2001; Groen and Roberts 2001). C35

Methods in detail

The study has one central experiment, the precipitation titration, and three supporting lines of work that interpret it: solid-state analysis of the precipitate, solubility measurements and estimates, and absorption modelling. Ten weak bases were chosen: bifonazole, carvedilol, clotrimazole, clozapine, dipyridamole, droperidol, ketoconazole, loratadine, papaverine and pyrimethamine. Papaverine free base was made from its HCl salt; the others were bought as supplied. M1–M10

Contribution 1: reading supersaturation from a pH titration

The problem. Following a supersaturated solution over time usually needs repeated sampling, filtration or centrifugation, and each of these can trigger crystallization. A potentiometric titration follows the same process without touching the solution, because the pH itself reports precipitation and dissolution. C32·C6

What they did. First the pKa values were measured at 37 °C in 0.15 M KCl under nitrogen with a Sirius GLpKa titrator and a UV dip probe: in water for seven compounds (19–100 µM, titrated from pH 1.8–2.0 with 0.5 M KOH, at least five runs each), in 8–52 wt% methanol–water for bifonazole and clotrimazole (UV detection, 26–200 µM, at least five mixtures) and in 8–39 wt% methanol–water for carvedilol (pH-metric, because its ionizable group is remote from the UV chromophore; 0.3–0.8 mM, at least eight mixtures). Cosolvent values were extrapolated to water by the Yasuda–Shedlovsky procedure. P1·P2·P3 The resulting pKa values are listed in Table I, for example 5.26 for loratadine, 6.08 for dipyridamole and 7.75 for carvedilol. M1–M10

The precipitation titration then followed the CheqSol protocol in the same instrument at 37 °C. Each compound was dissolved at low pH, where it is fully ionized, and titrated with 0.5 N KOH. When the UV probe detected turbidity, the instrument switched to a "chasing" sequence: it added small aliquots of 0.5 N HCl or KOH to make the solution slightly subsaturated or supersaturated, recorded the pH after each, and calculated the concentration of the neutral species from mass and charge balance equations as a function of time and pH. The neutral concentration at precipitation gives the kinetic solubility; the concentration where the pH gradient crosses zero gives the equilibrium solubility of the solid present. P4 The paper refers to earlier publications for the details and does not print the amount of drug per titration or the number of replicate runs. The scale-up factors of Table II suggest about 7.5–57 mg in 10–15 ml per titration, but this is the AI writer's arithmetic, not a stated condition. X13

What it delivers. For every compound: a concentration–time profile of the neutral species, a degree of supersaturation, a duration and a supersaturation factor (type 1), the kinetic and equilibrium solubilities, the pH response after each aliquot, and a Bjerrum plot. R2·R3·R4·R5·R6·R7·R8·R9·R10

Contribution 2: identifying the solid that precipitates

What they did. The slurry left by each titration was examined under a polarized light microscope for birefringence. The precipitate was separated by ultracentrifugation at 40,000 RPM (274,356 × g), dried under vacuum for 24 h and heated in a DSC from −50 °C to 10 °C above the melting point at 5 °C/min, looking for a glass transition, crystallization and melting. P5·P6 For powder X-ray diffraction the titration had to be scaled up 6- to 40-fold: the drug was dissolved in water with 0.5 N HCl in jars at 37 °C, precipitated by rapid addition of 0.5 N KOH (amounts in Table II), and collected by spatula (clozapine floated), by filtration through tissue (bifonazole, dipyridamole and pyrimethamine formed large agglomerates) or by centrifugation (the rest). The wet solid was blotted and measured within an hour of precipitation (within 30 min when no centrifugation was needed). For bifonazole the scale-up started from a quench-cooled amorphous film, because the crystal dissolved too slowly. P9·P10·M1

Why it matters. The word "precipitate" only says that a second, light-scattering phase has appeared. The authors argue that the structure of that phase, crystalline or disordered, should theoretically set the concentration the solution can keep, and that this link had not been studied. C48

Contribution 3: solubilities, measured and estimated

What they did. Crystal (equilibrium) solubility was measured by stirring excess solid for 72 h at 37 °C in buffer at least two pH units above the pKa, so that the neutral form dominates, followed by ultracentrifugation and HPLC. The same treatment applied to titration precipitates gave the "supernatant concentration" after precipitation. The HPLC method used a SymmetryShield RP8 column, acetonitrile with pH 2.5 phosphate buffer (20–40% acetonitrile depending on the compound) and UV detection between 230 and 288 nm. P11·P12 For the five compounds that precipitated as amorphous solids, the amorphous solubility was estimated with Eqs. 3 and 4 from the melting data of the crystal, and a second time with the water-sorption correction of Eqs. 5 and 6, using sorption isotherms of the amorphous drugs measured at 37 °C from 5 to 95% relative humidity (three samples each). P13·P8 The crystallization tendency class of each compound was determined on the original material by the group's two earlier methods; pyrimethamine could not be classed because it degrades on melting and is too poorly soluble in dichloromethane and methanol for spin-coating. P7·M10

Contribution 4: what the difference could mean in vivo

What they did. One compound of each type was taken into an absorption model. For dipyridamole (type 1), a GastroPlus compartmental model of the fasted beagle was built and refined against dog data: oral dosing of 50 mg (5 mg/kg) as a suspension in a capsule after pentagastrin pretreatment (0.006 mg/kg IM) to keep the stomach acidic, plus intravenous data at 1 mg/kg. The inputs were a permeability of 1.5 × 10⁻⁴ cm/s, pKa values 0.8 and 6.08, and a reference solubility of 0.005 mg/mL at pH 8.62 (Table III). The amount absorbed was then computed for doses from 50 to 550 mg and mean precipitation times from about 100 to 1000 s. P14 For loratadine (type 2), with no in vivo data available, the authors used a proprietary Eli Lilly model based on a microscopic mass balance approach (MiMBA; Oh et al. 1993) to predict the dose absorbed in humans with either the HPLC crystal solubility or the solubility from the titration. P15

Experimental analysis

Two behaviours across ten compounds

The titrations split the ten bases into two groups of five. Bifonazole, dipyridamole, droperidol, papaverine and pyrimethamine supersaturated before precipitating, the supersaturation then fell quickly, and the precipitate was crystalline: type 1. Carvedilol, clotrimazole, clozapine, ketoconazole and loratadine precipitated rapidly, gave amorphous solids that persisted for extended periods, and responded immediately to small pH changes: type 2. C7·R1 Table A collects the solid-state results with the compound properties.

Table A. Compound and precipitate properties, rearranged from Table I of the paper with type 1 compounds first. Melting point and classes were measured on the original material; Tg was recorded only where the dried precipitate showed a glass transition. M1–M10·R1

The correspondence is complete within this set: every compound that supersaturated briefly gave a birefringent, crystalline precipitate, and every compound that precipitated at once gave a non-birefringent, X-ray amorphous precipitate with a glass transition between 28 and 56 °C. R1·C20 The abstract calls this a "significant correlation"; no statistical test is reported, and the word describes a ten-out-of-ten match. C47·X18

Type 1: a burst of supersaturation, then crystals (dipyridamole)

Figure 2a shows the neutral dipyridamole concentration during a titration. It stays near zero until about 18 min, climbs through about 20 µg/ml at 22 min to a peak of 71.3 µg/ml at about 24–25 min, where turbidity is detected, and then collapses: about 31 µg/ml at about 25 min, about 9 µg/ml at 29 min and about 5–6.5 µg/ml from 38 min to the end of the run at 78 min. R2 The peak is 12.5 times the titration equilibrium solubility of 5.7 µg/ml; Figure 2b plots it at about 12.9, a small difference from the text and Table IV. R3·R5·X4 The supersaturation lasted about 15 min (14.7 min in Table IV) and the supersaturation factor was 4.6. R2·R3·R5 The paper does not define in words when the "duration" starts and ends; Figure 2a draws it between two dotted lines at about 21 and 37 min. X5

The Bjerrum plot (Figure 2c) tells the same story in protons. The data follow the ionization curve up to pH about 5.1, leave it when precipitation begins (bound protons drop to about 0.41 at pH about 5.5), and during the chasing phase move back to lower pH until they meet, near pH 4.0, the curve calculated from Eq. 2 with the crystal solubility. The authors call this "consistent with" a precipitate that has the intrinsic free-base solubility. R4·C10

Table B gives the five type 1 compounds.

Table B. Type 1 solubility and supersaturation data (Table IV of the paper). Degree of supersaturation = kinetic / titration equilibrium solubility. Droperidol degraded during 72 h of stirring at 37 °C, so its HPLC value is a literature value at 30 °C. R5·X15

Three things stand out. First, the titration equilibrium solubilities agree with the independently measured crystal solubilities ("good agreement"), which supports the reading that the precipitate is the crystal. C11·C21 Second, extent and duration "varied considerably": the degree of supersaturation runs from 1.4 for pyrimethamine to 26.7 for droperidol, the duration from 3.1 to 14.7 min, and the supersaturation factor from 2.8 to 12.9. C22·R5 Third, extent and duration do not move together: droperidol reaches the highest peak but stays supersaturated for only 6.4 min, while dipyridamole's lower peak lasts 14.7 min. R5 Some printed degrees of supersaturation differ slightly from the quotient of the printed solubilities (bifonazole 0.8/0.3 gives 2.7, printed 2.8; droperidol 82.0/3.1 gives 26.5, printed 26.7); the differences are within the rounding of the low-precision solubilities. X19

Type 2: precipitation at once, then a plateau (loratadine)

Loratadine behaves quite differently (Figure 4a). Its neutral concentration rises from about 0.7 µg/ml at 14 min to 10.7 µg/ml at about 19 min, where turbidity appears, and then stays between about 9.6 and 10.3 µg/ml up to about 91 min and at about 9 µg/ml to the end at 100 min. The crystal solubility measured by HPLC is 1.6 µg/ml. R8 In the Bjerrum plot (Figure 4b) the data leave the ionization curve at about pH 3.2 and fall directly, "without any transition period", onto the precipitation curve of Eq. 2 calculated with a solubility of 11.3 µg/ml, the HPLC concentration of the supernatant; the curve for the crystal solubility lies about 0.85 pH units further left. More drug is in solution than the crystal allows, and the system reaches this state at once. R9·C13 The figure legend calls the fitted curve the one "by predicted amorphous solubility" (11.0 µg/mL) while the text says 11.3 µg/ml was used; the two curves would differ by only about 0.01 pH unit. X6 The other four type 2 compounds showed the same pattern: "whatever concentration was achieved" after the pH increase "was maintained for extended periods". C12

Table C. Type 2 data (Table V of the paper), in µg/ml. Degree of supersaturation = supernatant / crystal solubility, both by HPLC; values in brackets are the amorphous / crystalline solubility ratios of the two estimates. R10

Two features of Table C separate type 2 from type 1. The titration kinetic and equilibrium values lie close together for every type 2 compound (for loratadine 10.7 and 9.9 µg/ml; for clozapine 180 and 170 µg/ml), whereas for type 1 the kinetic value can be many times the equilibrium value (dipyridamole 71.3 against 5.7). And the sustained concentration is 7.2 to 20.7 times the crystal solubility. R10·R5 The authors stress that the amorphous precipitate therefore also gives a supersaturation and a solubility advantage, but of a different kind from type 1. C8 Note that the degree of supersaturation in Table C is computed from HPLC values and that of Table B from titration values, and that one is a transient peak and the other a sustained level, so the two columns should not be ranked against each other. X3

The response to a small pH step

Figure 3a shows the pH after one small addition of KOH near equilibrium. For dipyridamole, 2.1 µL raised the pH from 4.14 to about 4.33; the pH then fell to about 4.25 after 50 s, 4.21 after 100 s and 4.19 after 150 s, still decreasing, as the drug precipitated and released protons. For loratadine, 8.3 µL raised the pH from 3.75 to about 3.86, where it stayed flat for 300 s. R6 Over the whole chasing experiment (Figure 3b), dipyridamole's pH gradient started at about −0.36 when precipitation began, returned to zero by about 30 min, and then swung to between about −0.03 and −0.04 after each aliquot; loratadine's stayed between about −0.002 and +0.013 throughout. R7 The authors conclude that loratadine's precipitation is instantaneous, "suggesting a very different precipitation mechanism", and that its dissolution and precipitation are "much faster" than dipyridamole's. C14·C15 This is exactly the "non-chaser" behaviour described by Box et al. (2006). C4

The solid behind each behaviour

Figure 5 gives the full solid-state picture for the two worked examples. The dipyridamole precipitate consists of birefringent needles; its DSC trace shows a single melting endotherm with an onset of 165.92 °C and 53.72 J/g (peak 167.66 °C), and its PXRD pattern shows the strongest peaks of the crystalline reference (about 8.2, 9, 10 and 21 °2θ) above a raised diffuse background, which the authors attribute ("likely") to water in the wet precipitate. R11·C16·C17 Table I lists 164 °C as the melting point of the original material. M5

The loratadine precipitate shows no birefringence and consists of poorly defined particles. Its DSC trace has a Tg-like step from 24.28 to 32.51 °C (midpoint 29.25 °C), then a crystallization exotherm peaking at about 93 °C and a melting endotherm peaking at about 128 °C, and its PXRD pattern has no peaks, only a halo. R12 The authors take this as confirmation of an amorphous precipitate and put the recrystallization during heating down "most likely" to a little nucleation during drying or to residual moisture. C18·C19 Two details deserve mention. Dry amorphous loratadine has a reported Tg of 37 °C (Baird et al. 2010), so the precipitate's 29 °C, measured after vacuum drying without a stated water content, may still contain water. M8·X20 And the text says the endotherm lies at the temperature of the crystalline reference, but the peak read from Figure 5d (about 128 °C) is below the 136 °C listed in Table I. X8

For the other eight compounds the paper reports only the summary in Table I. The claim that the type 1 precipitates are "of the same phase as the starting material" is therefore demonstrated only for dipyridamole. C21·X7

Is the type 2 plateau the amorphous solubility?

The authors offer two pieces of evidence that the sustained concentration of the type 2 compounds is their amorphous solubility: the solid in contact with the solution is amorphous, and the measured supernatant "corresponds well" with the estimated amorphous solubility. C30 Table C allows a closer look. Clozapine's supernatant (157 µg/ml) lies between the uncorrected (179.5) and water-corrected (147) estimates. Clotrimazole (5.09 against 5.0 and 4.00) and loratadine (11.3 against 11.0 and 6.8) match the uncorrected estimate. Ketoconazole's 76.5 µg/ml lies between an uncorrected estimate 2.6 times higher (202) and a corrected estimate 0.74 times as high (56.6). R10·X2 Carvedilol is the exception the authors name: its supernatant (8.68 µg/ml) lies below both estimates (24.4 and 13.53), while its titration values (19.4 and 21.8) lie between them. They suggest the low value "may be attributed" to conversion to a less soluble form during ultracentrifugation, "possibly a liquid crystalline form given the lack of diffraction peaks", and that the titration catches the transient state before this happens. C31

On this basis the authors propose the titration as "a new avenue for the experimental determination of amorphous solubility" for type 2 compounds, with two practical advantages: no amorphous reference solid has to be prepared, and no filtration or centrifugation, which can trigger crystallization, is needed. C32 This matters because amorphous solubility is "notoriously difficult" to measure: the amorphous solid or the supersaturated solution it creates tends to crystallize during the experiment (Alonzo et al. 2010). C33

Crystallization tendency

Table A also lists the crystallization tendency classes. All five type 2 compounds are class III (slow crystallizers) by the melt test, and four of the five also by solvent evaporation (loratadine is II/III). M1–M10 The type 1 compounds are spread out: bifonazole II/II, dipyridamole I/III, droperidol II/III, papaverine III/II, and pyrimethamine unclassified. M1–M10 The authors write that the supersaturation behaviour "appears also to be highly correlated" with crystallization tendency, that the type 2 compounds "tend to fall" into the slow class, and that type 1 behaviour is "more variable and dependent on the evaluation method"; they conclude that crystallization during pH-induced precipitation "generally correlates to some extent" with crystallization from the melt or on solvent evaporation. C42 They add that in water, molecular mobility promoted by water should also play a part. C43

What the absorption models show

For dipyridamole, the GastroPlus model was reported to give "an excellent fit" to the dog plasma data, but neither the data nor the fit are shown in the paper. C26·X9 The sensitivity analysis (Figure 6a) predicts that at the clinically relevant 50 mg dose a precipitation time between 100 and 1000 s has no effect on absorption, while at 550 mg the amount absorbed increases significantly as the precipitation time rises from 100 to 1000 s. R14·C27 The authors add that "there is no in vivo data to support this model": the example shows the "theoretical importance" of the precipitation rate, that is, of the duration of supersaturation, for type 1 molecules. C28 The caption speaks of a "mean precipitation rate" while the axis reads mean precipitation time in seconds. X12

For loratadine, the MiMBA model (Figure 6b) predicts a dose absorbed of about 37.5 mg at a 100 mg dose, rising to a plateau of about 56 mg from about 700 mg upward, when the titration solubility is used, against about 8 mg rising to about 8.7 mg with the HPLC crystal solubility. R15 The authors read this as a significantly higher maximum absorbable dose with the titration value. C40 Which titration value was used (9.9, 10.7 or 11.3 µg/ml) is not stated; the ratio of the two plateaus, about 6.5, is in the range expected from these values divided by 1.6. X11

Discussion

The authors' picture: two ways out of supersaturation

The authors connect the findings in a chain. Raising the pH converts the dissolved salt into the neutral base, and its concentration climbs above the crystal solubility. C1·C6 For a compound that crystallizes readily, crystal nucleation needs a certain supersaturation because forming a new surface costs free energy, as classical nucleation theory states:

In plain terms: the nucleation rate $J$ depends exponentially on the free energy barrier $\Delta G^{*}$ relative to thermal energy ($k_B$ is Boltzmann's constant, $T$ the temperature), and the barrier falls steeply as the supersaturation $S$ rises; at low supersaturation nucleation is too slow to see, and above a critical level it becomes spontaneous. E7·E8·C3 The critical level depends on the compound and the conditions. Once nuclei form, crystals grow until the solution is back at the crystal solubility, which is the type 1 profile. C3·C21

For a compound that resists crystallization, the authors "believe" that the solution instead undergoes liquid–liquid phase separation: a drug-rich, liquid-like phase separates, and because the temperature is below the crystal melting point this phase is a supercooled liquid or a glass, seen as an amorphous precipitate. C34 They give three reasons. Turbidity in the type 2 titrations appeared at a concentration very close to the final one, so there was little or no overshoot beyond the separation point, "consistent with" the very small metastable zone known for liquid–liquid separation. R13·C36·C35 The system answered small pH changes instantly, "consistent with a very low energy barrier for the mass transfer between the two phases". C37 And weak bases whose free base is an oil at room temperature (amitriptyline, chlorpromazine, desipramine, fluoxetine, pramoxine) were already known to behave as type 2, which "supports our supposition" that the amorphous precipitates are the below-melting-point version of the same process. R17·C38 Because all ten free bases here melt above 110 °C (117–242 °C), the separated phase is metastable and can later crystallize. C38·M1–M10 The solution then sits in metastable equilibrium with the amorphous phase, at a concentration close to the amorphous solubility, and remains supersaturated with respect to the crystal for a long time. C29

The authors' summary sentence states the general idea with a hedge: "it seems apparent that highly supersaturated solutions of a crystallizing compound can either directly crystallize or undergo liquid-liquid phase separation", after which crystallization can still occur from the two-phase supersaturated solution. C45

Pharmaceutical relevance as the authors see it

For type 1 compounds, which crystallize after short-lived supersaturation, the authors expect that bioavailability is "likely" predictable from equilibrium values in absorption models. They add that the extent of supersaturation "often can" be influenced by dose, that polymers and additives can modify the precipitation rate, and that these compounds "may" show large variation between and within patients if food or other in vivo factors change crystallization. C23 Dipyridamole illustrates the point: its absorption is known to be variable and pH-dependent in humans and dogs, elderly or achlorhydric patients and those on proton pump inhibitors get lower exposure, and pretreatment with glutamic HCl raised exposure in achlorhydric subjects (Russell et al. 1994; Zhou et al. 2005). C24 With today's tools, the authors write, this risk "would have" been predicted, and the "most likely" formulation answer would be a solid dispersion or a formulation with a microenvironmental pH modifier; whether the drug then stays in solution in the small intestine is the question their precipitation-time model addresses. C25·C27

For type 2 compounds the authors expect a bioavailability "likely" to be higher than expected, because the amorphous precipitate is more soluble and slow to crystallize. Models that use the shake-flask crystal solubility underpredict the maximum absorbable dose, and the amorphous particles are "likely" to be dispersed during GI transit and absorbed on further dilution, which no current absorption model includes. C39·C40·C41 They go further and suggest that type 2 behaviour "may" correlate with the ability to make stable amorphous formulations with a long shelf life that give long-lived supersaturated solutions on dissolution, and "may" even predict whether a compound will form a crystalline free form at all. C44 The conclusion lists four areas where amorphous precipitation has "important implications": absorption prediction by modelling, risk assessment for solid dispersions (whether the drug stays in solution after dissolution), design of oral formulations that minimize variability, and "potentially" parenteral solubilization. C46

Note by the AI writer (not discussed in the paper)

Read today, the paper is an early, compact statement of an idea that later became central to supersaturating formulations: the concentration a weak base can hold after a pH shift is capped by the amorphous (liquid–liquid separation) limit, and whether it reaches that cap or falls to the crystal solubility depends on how readily it crystallizes. For a formulation scientist the practical reading is that a single precipitation titration on a few milligrams of drug can sort a weak base into one of two development problems. A type 1 base loses its supersaturation within minutes (3.1–14.7 min here), much faster than intestinal transit, so a formulation that relies on gastric dissolution needs an inhibitor that acts in that window. A type 2 base holds a plateau, and that plateau is the most any supersaturating formulation can keep dissolved; adding more drug produces more separated phase rather than a higher concentration. R5·R10 The size of the moisture correction is also instructive: for ketoconazole it changes the predicted amorphous solubility 3.6-fold, from 202 to 56.6 µg/ml, so a measured amorphous solubility is worth more than a calculated one. R10

Limitations

Limits stated by the authors

The authors state that "there is no in vivo data to support" the dipyridamole precipitation-time model; it shows only the theoretical importance of the precipitation rate. C28 They describe the correlation with crystallization tendency as holding "to some extent", with type 1 behaviour "more variable and dependent on the evaluation method", and they expect water-promoted mobility to affect crystallization during aqueous precipitation beyond what the dry tests capture. C42·C43 They flag carvedilol as an exception to the match with amorphous solubility, with a hedged explanation ("may be attributed", "possibly"). C31 The liquid–liquid mechanism is presented as their belief and supposition, not as a demonstrated fact. C34·C38

The AI writer's own judgement

What holds. The central observation is clean. All ten compounds fall into two groups by solution behaviour, and the precipitate form agrees in every case by three independent tests (birefringence, PXRD, glass transition). R1 The worked examples contrast in every readout: concentration profile, Bjerrum plot, pH response and solid state. R2·R4·R6·R7·R8·R9·R11·R12 For the type 1 compounds the titration solubilities agree with HPLC crystal solubilities measured independently, which supports the titration method itself. R5

What weakens it.

• The match between the type 2 plateau and the amorphous solubility depends on which estimate is used: the uncorrected value fits clotrimazole and loratadine, the corrected value clozapine, and neither fits ketoconazole closely; no amorphous solubility was measured independently, for example from a prepared amorphous solid. X2
• The estimates cannot be checked from the paper: the heats of fusion, the sorption isotherms and the preparation of the amorphous samples are not given. X14
• Liquid–liquid phase separation is inferred from kinetics and analogy; the early precipitate was neither imaged nor sized, and its water content was not measured. C34·X20
• The crystallization tendency class does not separate the two types in this set: class III also covers papaverine (melt) and dipyridamole and droperidol (solvent evaporation), all type 1. Class III is shared by all type 2 compounds but does not by itself predict type 2. X1
• Full solid-state data are shown for two of the ten precipitates, and polymorph identity is shown only for dipyridamole. X7
• Methodological details are thin: the titration drug amounts and replicate numbers are not printed, the duration of supersaturation has no stated criterion, and the degree of supersaturation is defined differently for the two types. X13·X5·X3
• The supernatant concentrations are single measurements after ultracentrifugation at an unstated time, and the authors themselves suspect a form change for carvedilol. X17
• The absorption models are illustrations: the dog fit is not shown, the 3D surface cannot be read numerically, and the MiMBA solubility input and other inputs are not given. X9·X11
• All titrations ran in 0.15 M KCl without polymers, surfactants or bile components, so the behaviour in biorelevant media or in a formulation is not addressed.

Conclusion

The paper turns a known curiosity of potentiometric solubility titrations, the difference between "chasers" and "non-chasers", into a statement about solid form. Weak bases that precipitate as crystals after a pH rise show a short burst of supersaturation, 3.1 to 14.7 minutes for the five studied, that ends at the crystal solubility; weak bases that precipitate as amorphous solids hold a concentration 7.2 to 20.7 times the crystal solubility, close to the estimated amorphous solubility in four of five cases. R5·R10·C20·C30 The authors explain the second behaviour by liquid–liquid phase separation and link both to crystallization tendency, two interpretations they hedge ("we believe"; "to some extent"). C34·C42 For formulation work the paper's lasting contribution is practical: one titration tells whether a weak base will lose its supersaturation within minutes or hold it at its amorphous solubility, and in the second case it also measures that solubility without preparing an amorphous solid. C32·C47