Do polymers that stop acetaminophen crystallizing in the solid also stop it in solution? Nucleation and growth measured two ways

Background and motivation

An amorphous drug dissolves to a higher concentration than its crystal because the amorphous form has a higher free energy. That advantage is transient. The solution it creates is supersaturated with respect to the crystal, and crystallization from it is thermodynamically favoured (Kawakami 2012, ref 1; Alonzo et al. 2010, ref 2). To use an amorphous formulation, the formulator therefore has to delay crystal nucleation in the supersaturated solution that forms when the dosage form dissolves. C1

Additives can slow crystallization from supersaturated solutions. They come in two kinds: tailor-made small molecules and polymers (refs 3–6). An additive can act on nucleation, on growth, or on both (Alonzo et al. 2012, ref 7). Small-molecule inhibitors usually resemble the crystallizing molecule, so they can sit on the nucleus or on the growing face (Hendriksen and Grant 1995, ref 8). For polymers, the authors say the mechanism is not well understood, especially for nucleation; for growth, adsorption of the polymer on the growing face and its conformation there are "certainly of primary importance" (Ilevbare et al. 2012, ref 9; Patel and Anderson 2014, ref 10). C2·C3

In an amorphous formulation the polymer has two jobs. It must keep the solid amorphous during storage, and it must keep the solution supersaturated during dissolution. How well it does either depends strongly on how it interacts with the particular drug. Supersaturated transdermal systems face the same problem and also rely on polymers (Leichtnam et al. 2007, ref 11). C4

The starting point of this paper is the group's own earlier study of acetaminophen (APAP) crystallizing from its supercooled melt (Trasi and Taylor 2012, ref 12). There, the five polymers used here were ranked separately for slowing nucleation and slowing growth. HPMCAS was the best at slowing nucleation but not very effective against growth, while poly(acrylic acid) (PAA) increased the nucleation rate but was the best growth inhibitor. R14

The paper sets two aims. First, to find out whether the polymer effects in the solid state correlate with those in aqueous supersaturated solution. Second, to explore how well small, instrumented crystallization vessels can measure nucleation in solution: one that times the first crystals in many small vials, and one that counts crystals in images over time. A1·A2·A3

Background concepts

Nucleation and growth. A supersaturated solution crystallizes in two steps. Nuclei, the smallest stable crystals, must first form (nucleation), and these then grow by adding molecules (growth). An inhibitor can slow either step. The paper defines the nucleation rate $J$ as the number of nuclei formed per unit time and unit volume, and gives the classical expression (Mullin, ref 15): E6

Here $A$ is a pre-exponential factor, $\gamma$ the interfacial tension between nucleus and solution, $v$ the molecular volume, $k$ the Boltzmann constant, $T$ the temperature and $S$ the supersaturation, the ratio of the dissolved concentration to the crystal solubility. In plain terms: nucleation speeds up very steeply as supersaturation rises and slows steeply as the interfacial tension rises, so anything that changes $\gamma$, $T$ or $S$ changes $J$ by large factors. The authors use the equation to point out that they studied only one temperature and one supersaturation. E6·C20

Induction time. The induction time is the delay between bringing a solution to the test conditions and detecting crystals. It depends on supersaturation, stirring, impurities, viscosity and other factors, and it includes the time to form a stable nucleus and the time for that nucleus to grow to a detectable size (Söhnel and Mullin, ref 21). The authors stress that in their experiments a change in turbidity is the signal, and by then significant nucleation has already occurred, so their "induction time" is the time to the onset of massive nucleation. C32

Why induction times scatter, and how a rate is extracted from them. Nucleation is a random event, so identical vials nucleate at different times. Following Jiang and ter Horst (ref 13), the authors assume that the number of nuclei $m$ forming in a given time follows a Poisson distribution: E1

Here $P_m$ is the probability that exactly $m$ nuclei form and $N$ the average number forming in the time interval. In plain terms: if nuclei appear independently at a constant average rate, the chance of seeing 0, 1, 2 … of them follows this law. The probability that at least one nucleus has formed is then E2

In plain terms: a vial counts as nucleated as soon as one nucleus has formed, and this happens with probability one minus the chance of none. The average number of nuclei is the rate times the volume times the time available for nucleation, E3

where $V$ is the sample volume and $t_j$ the induction time. Detection comes later than the birth of the first nucleus, because the nucleus must still grow; this growth time $t_g$ is subtracted from the measured detection time $t$: E4

Putting these together gives the cumulative fraction of vials that have nucleated by time $t$: E5

In plain terms: the fraction of nucleated vials rises from zero after the growth delay $t_g$ and approaches one, the faster the higher $J$. Fitting this curve to about 80 measured induction times gives $J$ and $t_g$ for each solution. E5·P3 The paper prints Eq. 5 without the minus sign in the exponent; the sign follows from Eqs. 2–4, and without it $P(t)$ would be negative. X2

Primary and secondary nucleation. Primary nucleation is the formation of crystals from a clear solution. Secondary nucleation is the formation of new crystals induced by crystals that are already present, for example by fragments or by contact. The paper assigns the first crystals to primary nucleation and the rapid multiplication that follows to secondary nucleation. C21·C22

Desupersaturation and seeded growth. If crystals of the drug are added to a supersaturated solution, they grow and the dissolved concentration falls toward the solubility. The rate of this fall (desupersaturation) reflects the growth rate, provided no new crystals form. Polymers can slow the fall by adsorbing on the growing faces. C3·C16·C33

Crystal habit and BFDH. The habit is the outward shape of a crystal. The Bravais–Friedel–Donnay–Harker (BFDH) model predicts a habit from the crystal lattice alone, assuming that faces with large interplanar spacing grow slowly and therefore dominate. A habit that differs from the BFDH prediction, or that changes with an additive, shows that some faces grow faster or slower than the lattice alone implies. R13·P7

Methods in detail

The study has three experimental parts and one comparison. The same supersaturated solutions were used for two nucleation read-outs; a seeded test then looked at growth, and the resulting ranks were set against the melt ranks of the earlier study.

Materials and solutions

APAP came from Sigma-Aldrich. The polymers were PVP K-12 (Mw 2000–3000 g/mol) and PVPVA (Kollidon VA64, Mw 45 000–47 000 g/mol) from BASF; HPMC (Hypromellose USP, substitution type 2910) and HPMCAS (given as "Type AS-MF/LF/HF", Mw 17 000–18 000 g/mol) from Shin-Etsu; and PAA (Mw 450 000 g/mol) from Sigma-Aldrich (Figure 1 shows the structures). M1·M2·M3·M4·M5·M6 The paper does not say which of the three HPMCAS grades, or whether a blend, was used. X14 The crystalline solubility of APAP in pH 6.8 phosphate buffer, measured by UV at 248 nm after 24 h of equilibration, was 13.2 mg/mL at 20 °C. M1·P1

Supersaturated solutions were made by dissolving a known excess of APAP in 10 mM pH 6.8 sodium phosphate buffer at about 70 °C with stirring; for polymer samples, 10 µg/mL polymer had been added to the buffer first. After complete dissolution the solution was filtered (0.2 µm) and its concentration checked by UV to give a supersaturation ratio of 1.5. P2 At the measured solubility this corresponds to about 20 mg/mL, consistent with the starting concentrations of about 19.5–19.8 mg/mL in the growth test (Figure 4). M1·R11 (The product 1.5 × 13.2 = 19.8 mg/mL is the AI writer's arithmetic; the paper does not print the concentration.)

Contribution 1: induction-time statistics in a parallel crystallizer

Problem. A single induction time says little, because nucleation is random; a rate needs a distribution of many induction times measured under the same conditions.

What they did. In the Crystal 16 Parallel Crystallizer (Avantium), 1.2 mL portions of each solution were sealed in 2 mL HPLC vials with stirrer bars, stirred at 700 rpm and cooled to 20 °C. Time zero was the moment the vial reached 20 °C, and the induction time was the moment the laser transmission through the vial first dropped. The vials were then heated until clear (transmission 100%) and cooled again, and the cycle was repeated until about 80 induction times had been collected per sample. P3 The cumulative distribution was fitted with Eq. 5 in gPROMS ModelBuilder, using an algorithm from the authors' earlier conference work (ref 14), to give $J$ and $t_g$. P3·R3

A problem with the printed volume. The paper states that $V$ in Eq. 5 was 0.0012 m³, which is 1.2 litres; the vials held 1.2 mL, or 1.2 × 10⁻⁶ m³. The fitted rates in Table 1 reproduce the stated times by which 95% of vials had nucleated only with the 1.2 mL volume; with 0.0012 m³ those times would be seconds. The printed value is most likely a unit slip (0.0012 L). X1·E5

Contribution 2: counting crystals by image analysis

Problem. Induction times give a rate only at the starting supersaturation, at the moment the first crystals appear. They say nothing about how fast crystals keep forming as the solution desupersaturates.

What they did. In the Crystalline Particle Viewer (Avantium), 4 mL of each solution, prepared in the same way, went through the same heating and cooling at 700 rpm, in triplicate. A camera took an image every second during precipitation. ImageJ thresholding separated crystals from the background and counted them in each frame, giving a count-versus-time trace (Figure 3). P4 The authors assumed that the rate of change of the count is proportional to the nucleation rate and took the slope of the rising part right after onset as its measure; the time of the first detected particles served as the induction time (Table 2). C10·R10 The polymer level in these runs is not stated explicitly; "the same method" as for the Crystal 16 implies 10 µg/mL. X11

How it differs from Contribution 1. The authors argue that the Crystal 16 needs many experiments and captures only primary nucleation, whereas the larger sample in the Particle Viewer gives information from far fewer runs and captures both primary and secondary nucleation. C21

Contribution 3: seeded growth and crystal habit

Problem. Whether a supersaturated solution survives depends not only on nucleation but also on how fast any nuclei that do form grow. Growth rates are hard to measure from desupersaturation after seeding, because new crystals can nucleate during the test. C15

What they did. Solutions of 10 mL at S = 1.5, with or without polymer, were cooled from 70 to 20 °C. Here the polymer level was doubled to 20 µg/mL to suppress primary and secondary nucleation during the test. At 20 °C, 1 mg of APAP seed crystals below 75 µm (d(50) = 43.5 µm, d(90) = 65.2 µm) was added, and the samples were kept in a shaker bath. Aliquots were filtered, diluted 40-fold and measured by UV with a 2 cm dip probe; Figure 4 shows samples at 2, 6, 12 and 24 h. P5·M8 The number of replicates is not stated. X9 The authors assume that growth of the added seeds is largely responsible for the fall in concentration. C16 At the end, the crystals were harvested and photographed under an optical microscope (Figure 5), and the BFDH habit of APAP was computed in Mercury 3.3 (Figure 6). P6·P7 Which crystal structure was used, and the solid form of the harvested crystals, are not stated. X12

Experimental analysis

Nucleation timed by turbidity (Figure 2, Table 1)

Without polymer, APAP crystallized "rather quickly": 95% of the vials had nucleated within 26 min. PAA made nucleation faster still, with 95% of the vials nucleated within 11 min, which the authors call notable because polymers more typically slow nucleation. HPMCAS and HPMC had an intermediate effect, with 95% of the vials nucleated by 470 and 1043 min. PVP and PVPVA slowed nucleation so much that only few vials had nucleated after 2 days, so no distribution could be fitted for them; the authors write that these two "appeared" to be the most effective. R1·C5·C6·C7

Table A. Induction-time results. J, t_g and their 95% confidence intervals from Table 1; 95% times from the text. The last column is the AI writer's recomputation of the 95% time from Eq. 5 with the sign of Eqs. 2–4 and V = 1.2 mL; it does not appear in the paper. R3·R1·E5·X1

The fitted nucleation rates span two orders of magnitude, from 40.68 # m⁻³ s⁻¹ with HPMC to 3820 # m⁻³ s⁻¹ with PAA, and the growth time ranged from 7.8 s with PAA to 928 s with HPMCAS. R3 Note by the AI writer (not discussed in the paper): the recomputed 95% times agree with the stated ones within about 12%, which supports the fits once the 1.2 mL volume is used E5·X1; but the stated 1043 min for HPMC lies beyond the last measured point of Figure 2 (about 59 000 s), so it must come from the fitted curve, and the paper does not say how the very narrow confidence intervals of J (0.02 and 0.11 # m⁻³ s⁻¹ for HPMCAS and HPMC) were obtained from about 80 random induction times. X5·X13

The text also says that "solutions containing HPMC nucleated slightly faster than those with HPMCAS". C7 This holds only for the first part of Figure 2: below about 3000 s the HPMC points lie above the HPMCAS points, consistent with the shorter fitted growth time of HPMC (350.1 versus 928 s). Beyond that, HPMCAS reaches a nucleated fraction of 0.5 at about 8000 s and HPMC only at about 17 000 s, and the authors' own rank order puts HPMC ahead of HPMCAS. R2·R3·X3·C24

Nucleation followed by crystal counting (Figure 3, Table 2)

Without polymer, the three Particle Viewer runs nucleated at different times (180, 400 and 800 s in the text; 150, 415 and 785 s in Table 2), which the authors read as "reflecting the stochastic nature of nucleation". R4·R10·C8·X4 In each run the count rose steeply, peaked at about 640–890 crystals per image and then fell quickly to about 100–150 (Figure 3a). The authors attribute the fall to agglomeration, which reduces the number of free particles. R4·C9 PAA behaved "very similar to pure APAP", with peaks of about 540–900 and a similar collapse (Figure 3c). R6·C12

The cellulosic polymers changed the shape of the curve. With HPMCAS the first crystals appeared about as early as without polymer (100–290 s), but the count rose more slowly and levelled off at about 350–400 crystals per image in two runs and about 150–200 in the third, with no collapse up to 1000 s (Figure 3b). The authors write that the polymer "retards agglomeration of the crystals". HPMC behaved similarly, with onsets at 700–1300 s (Figure 3f). R5·R9·C11·C12

PVP delayed onset to 570, 1550 and 8000 s, and afterwards the count rose slowly; the authors call PVP "clearly the best polymer for decreasing nucleation kinetics" (Figure 3d). R7·R10·C13 PVPVA delayed onset the longest (1070, 1925 and 9700 s), but each run started with a sharp spike of about 500–630 crystals per image, dropped to about 100–150 and then rose steadily (Figure 3e). R8·R10

Table B. Crystal-count results, ordered by slope. Slopes and detection times from Table 2; curve shapes described from Figure 3 and the text. R10·R4·R5·R6·R7·R8·R9

The ranking by slope differs from the induction-time ranking in one place. In the Crystal 16, PVPVA looked as good as PVP and better than the cellulosics; in the count, its slope (5.4 nuclei s⁻¹) was about 28 times that of PVP and about 6 and 10 times those of HPMCAS and HPMC. R1·R10·C14 The authors give the two rank orders explicitly: for primary nucleation only (Crystal 16), PVP, PVPVA > HPMC > HPMCAS > PAA; for primary plus secondary nucleation (image analysis), PVP > HPMC > HPMCAS > PVPVA > PAA. C24

Growth after seeding (Figure 4)

Table C. Dissolved APAP (mg/mL) after adding 1 mg of seeds at 20 °C; all values about, read from Figure 4 (approximate). All samples start at about 19.5–19.8 mg/mL; the crystalline solubility is 13.2 mg/mL. R11·M1

Without polymer the concentration fell to about 13.9 mg/mL within 6 h and reached about 13.0 mg/mL at 24 h, close to the measured solubility. R11·M1 PAA barely changed this course. HPMC and PVP held the concentration highest, at about 18.7 and 18.4 mg/mL after 6 h and about 16.1 and 15.8 mg/mL after 24 h, with PVPVA and HPMCAS in between. R11 The authors conclude that PAA had very little effect on growth, that HPMC and PVP were the most effective, and that "the apparent effect of the polymers on growth rate is much lower than their effect on nucleation". C17·C18·C25 Note by the AI writer (not discussed in the paper): no growth rate was computed, the replicate number is not stated, and PVPVA and HPMCAS end within about 0.2 mg/mL of each other, inside the reading error of the plot; the separation of the extremes (HPMC and PVP against PAA and no polymer) is clear. X9

Crystal habit (Figures 5 and 6)

Even at 20 µg/mL the polymers changed the shape of the crystals. Without polymer APAP grew thin, flat, elongated crystals, "quite unlike" the compact polyhedron predicted by BFDH. HPMCAS gave long rods; PAA gave large, prismatic, polyhedral crystals, closest to the prediction; PVPVA gave large parallelepipeds; PVP gave crystals of the same shape as without polymer but distinctly smaller; and HPMC, the strongest growth inhibitor, gave very small crystals of poorly defined shape. R12·R13·C19 The authors take these changes to mean that the polymers are "most certainly" adsorbed preferentially on specific faces, depending on the direction of the strongest hydrogen bonds (Wen et al., ref 22), and that attachment to the fastest-growing faces can lower desupersaturation rates. Adsorption itself was not measured. C33

Solution ranks against melt ranks

Table D. Rank orders, 1 = most effective; ties as stated by the authors. Solution ranks from the Discussion (p.1247); melt ranks cited from Trasi and Taylor 2012 (ref 12), not re-measured here. C24·C25·R14

The clearest reversal is PAA: an excellent growth inhibitor in the supercooled liquid but "largely ineffective" in solution, where it also sped up nucleation. HPMCAS moved from the best nucleation inhibitor in the melt to third in solution, and from the weakest growth inhibitor to a middle place. C26·R14·R10·R11 PVP, by contrast, ranked high in both states. R14·C24·C25

Discussion

How the authors read the results

The authors connect the findings through what each polymer does to the start of nucleation, to the multiplication of crystals afterwards, and to growth. The chain below follows their Discussion; the hedges are theirs.

Why PVPVA behaves differently in the two instruments. The authors argue that PVPVA takes a long time to let nucleation start, but once it occurs, the number of particles increases quickly. They conclude that "it seems that PVPVA may be good at inhibiting primary nucleation, but does not appear to be very effective at preventing or decreasing the rate of secondary nucleation", and that image analysis therefore provides more information than induction times alone. C22·C23 Note by the AI writer (not discussed in the paper): secondary nucleation was not measured separately; the count slope after onset also contains the growth of nuclei to a detectable size and, judging from the curves without polymer, agglomeration. Moreover, the two instruments differ in more than the read-out. With PVP and PVPVA only few Crystal 16 vials (1.2 mL) nucleated within 48 h, yet all three Particle Viewer runs (4 mL) of each polymer nucleated within about 2.7 h (570–9700 s). A 3.3-fold larger volume alone would not obviously close that gap, and the paper does not discuss it. X7·X6·R1·R10

Why PAA fails in solution. PAA had been an excellent growth inhibitor in the supercooled melt, where hydrogen bonding between drug and polymer had been shown to matter for growth inhibition (refs 12, 16). The authors suggest that "this could be due to the ionization of PAA at pH 6.8 and thus its inability to form hydrogen bonds". The ionization state of PAA and any drug–polymer hydrogen bonding in solution were not measured. C27·C26

What a polymer needs to inhibit nucleation. A small-molecule additive can be built into a pre-nucleus and disrupt its bonding network (Hendriksen et al., ref 20). A polymer is too large to be incorporated, so the authors argue that intermolecular interactions between drug and polymer "are presumably required", and that interactions able to compete with the solvent–drug interactions "are likely to be important". C31 They add that most explanations of nucleation inhibition by additives are the same as those for growth, such as adsorption and incorporation, because forming a critical nucleus resembles growth (ref 8). Since the efficacy orders for nucleation and growth are "similar but not the same", growth-type mechanisms "could have a role" in nucleation inhibition, but "there must be additional factors that also play a role". C34

Solid state versus solution. The authors conclude that "the crystallization inhibitory ability of a given polymer for the amorphous drug in the solid state may be quite different from its effect in solution", and in the Conclusions that the different order of efficacy indicates "different factors at play in an aqueous environment". C28 They also note that the effectiveness of PVP for APAP "does not necessarily translate to other compounds": PVP was much more effective than HPMC for estradiol (Megrab et al., ref 17), while cellulosic polymers worked better for danazol and ritonavir (refs 18, 19). C30·R15

What it suggests for formulation

The authors' own recommendation is cautious: because one polymer may not cover both states, "a combination of polymers may be a useful approach to prevent crystallization both in the solid amorphous formulation and from the supersaturated solution created upon dissolution". No combination was tested. C29

Note by the AI writer (not discussed in the paper): three practical points follow from the data. First, a polymer chosen because it stabilizes the amorphous solid needs to be tested again in the dissolution medium; PAA is a clear case where the solid-state advantage did not carry over at pH 6.8. Second, an induction-time screen alone can rank a polymer high that lets crystals multiply quickly once the first ones appear, as with PVPVA here; for a dissolving formulation, where some crystals are likely, the multiplication rate after onset may matter as much as the delay. Third, all effects were measured at 10–20 µg/mL polymer, far below the polymer concentrations a dissolving dispersion releases, so the ranking at formulation-relevant concentrations remains open. R14·R10·R11·P2·P5

Limitations

Stated by the authors. They examined the polymers "at one temperature and at one supersaturation", although Eq. 6 shows that temperature, supersaturation and interfacial tension control the nucleation rate. C20 They note that growth rates are difficult to determine accurately from seeded desupersaturation because secondary nucleation can occur, which the higher polymer concentration reduces only "to some extent". C15 They also caution that their induction time marks the onset of massive nucleation rather than the birth of the first nucleus. C32

The AI writer's own judgement.

• Misprints in the fitting equations. The volume in Eqs. 3–5 is printed as 0.0012 m³ instead of 1.2 mL, and Eq. 5 lacks the minus sign in the exponent. The fitted rates are consistent with the correct volume and sign, so the conclusions are unaffected, but the absolute J values should be read as per cubic metre of a 1.2 mL sample. X1·X2
• Uncertainty of J. The printed 95% confidence intervals of J (0.02 and 0.11 # m⁻³ s⁻¹ for HPMCAS and HPMC, 106.6 and 31.5 for PAA and no polymer) are far narrower than counting statistics allow for about 80 random induction times, and how they were computed is not stated. X13
• An internal contradiction. The statement that HPMC solutions nucleated slightly faster than HPMCAS solutions conflicts with Table 1, the 95% times and the authors' own rank order; it holds only in the first about 3000 s of Figure 2. X3
• Primary versus secondary nucleation. The split is inferred from comparing two instruments that also differ in volume and number of runs; secondary nucleation was not measured on its own. X7·X6
• Method-dependent ranks. The abstract's statement that PVP and "the cellulosic polymers" were the most effective nucleation inhibitors, and the Conclusions' statement that the best nucleation inhibitors were also the best growth inhibitors, hold for the image-analysis rank, not for the induction-time rank. X8·X10
• Different polymer levels and small samples. Nucleation was tested at 10 µg/mL and growth at 20 µg/mL; the counting used three runs per polymer and the growth test an unstated number; the growth ranking rests on plot readings without computed rates. X11·X9
• Unidentified materials. The HPMCAS grade and the crystal form of the seeds, of the harvested crystals and of the BFDH model are not stated. X14·X12
• Cited comparison. The solid-state ranks come from the earlier melt study and were not re-measured with the same polymer lots. R14

Conclusion

For acetaminophen at a supersaturation of 1.5 in pH 6.8 buffer at 20 °C, five polymers at low concentration changed crystallization in solution in an order that did not follow their order in the amorphous solid. C35·C28 PVP and HPMC slowed both nucleation and growth most; HPMCAS, an excellent nucleation inhibitor in the melt, was intermediate; PAA, the best growth inhibitor in the melt, sped nucleation up and hardly slowed growth. C24·C25·C26·R14 Timing the first crystals and counting crystals over time agreed for most polymers but split on PVPVA, which delayed the first crystals as long as PVP yet let crystals multiply quickly afterwards; the authors read this as PVPVA inhibiting primary but not secondary nucleation and conclude that image analysis gives "a more accurate picture of nucleation kinetics". C22·C23 The paper is short and rests on one drug, one supersaturation and low polymer levels, and its fitting equations contain misprints, but its central point is direct: a polymer's performance in the solid state does not predict its performance in the solution the formulation creates. C20·X1·X2·C28