How a dissolved polymer lowers the highest free drug concentration: ibuprofen, PVP, PVP-VA and HPMC seen by solution NMR

Background and motivation

An amorphous solid dispersion (ASD) raises the concentration of a poorly water-soluble drug in solution above its crystalline solubility, and the polymer in the ASD helps keep it there by slowing crystallization. The authors start from a ceiling on this gain. The free drug concentration that can be reached depends on the chemical potential of the amorphous drug, which sets the amorphous solubility. Above that concentration the drug separates into a drug-rich phase, at first colloidal, by liquid–liquid phase separation (LLPS) or, for a glassy drug, glass–liquid phase separation (GLPS) (Ilevbare and Taylor 2013; Mosquera-Giraldo and Taylor 2015; Almeida e Sousa et al. 2015). The drug-rich phase is useful as a reservoir: it keeps the solution at the amorphous solubility while drug crosses a membrane (Indulkar et al. 2016). But the droplets themselves do not cross the membrane, so adding more drug above the amorphous solubility adds no flux (Raina et al. 2014). Knowing the amorphous solubility in a given medium is therefore central to predicting what an ASD can do for absorption. C1

The ceiling is not fixed. Anything that mixes into the drug-rich phase lowers the drug's chemical potential there and with it the amorphous solubility. Water absorbed into the amorphous drug does this and is routinely included in predictions (Murdande et al. 2010). A second drug does it too (Trasi and Taylor 2015), and Lindfors and co-workers used a miscible, poorly soluble additive to slow Ostwald ripening of drug nanodroplets for the same reason. More recently, the polymer used as the ASD carrier was found to lower the amorphous solubility by mixing into the drug-rich phase, and so to lower membrane transport (Mosquera-Giraldo et al. 2018; Ueda et al. 2019; Ueda and Taylor 2020; Huang et al. 2016; Ueda et al. 2020). The authors conclude that the effect of the polymer on the composition of the drug-rich phase, and on the free drug concentration, needs to be worked out before polymers can be chosen to maximise supersaturation. C2

Measuring that effect is the problem. The usual way to find the amorphous solubility is the solvent shift: a concentrated solution of the drug in an organic solvent is added stepwise to water, and the onset of a drug-rich phase is detected by UV/vis extinction, fluorescence or light scattering. The onset depends on mixing and on the detection limit, and the method says nothing about the free drug concentration once the drug-rich phase exists, which is exactly where a polymer might change it. Diffusion across a membrane measures the free drug directly, but the flux can be confounded by concentration gradients in the unstirred water layer next to the membrane (Elkhabaz et al. 2019). The authors therefore want a direct measurement of the drug concentration in the bulk water phase. C3

Solution NMR offers one. Drug dissolved in water and drug inside the drug-rich phase sit in different chemical environments, so their peaks appear separately and the dissolved amount can be read from its own peak area. For a drug with a low glass transition temperature ($T_g$), the drug-rich phase is a mobile supercooled liquid at the measuring temperature and also gives a solution spectrum, which reports how a polymer changes the drug's surroundings in that phase (Ueda et al. 2019; Ueda and Taylor 2020). C4 The authors chose ibuprofen (IBP), a low-$T_g$ drug, and six polymers: three grades of polyvinylpyrrolidone (PVP K12, K25, K90) and two of hypromellose (HPMC 603, 615) to vary the molecular weight (MW), and polyvinylpyrrolidone/vinyl acetate (PVP-VA) to compare with PVP. They varied the drug and polymer concentrations and measured the free IBP concentration in the aqueous phase by NMR. A1·A2·A3

Background concepts

Amorphous solubility and how to estimate it. The amorphous solubility is higher than the crystalline solubility because the amorphous form has a higher free energy. The paper uses an estimate from earlier work by the group (Almeida e Sousa et al. 2015):

In plain terms: the theoretical amorphous solubility $C_{\mathrm{a}\mathrm{m}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{h}\mathrm{o}\mathrm{u}\mathrm{s}}$ is the measured crystalline solubility $C_{\mathrm{e}\mathrm{q}}$ multiplied by the free-energy advantage of the amorphous form, $e^{\Delta G_{c\to a}/RT}$, and corrected by $e^{-I(a_2)}$, the activity of the amorphous solute when it is saturated with water. $\Delta G_{c\to a}$ is the free energy difference between the crystalline and amorphous forms, $R$ the gas constant and $T$ the temperature. The paper takes $\Delta G_{c\to a}$ and the activity term for IBP from the earlier study without printing them, and with the measured crystalline solubility of 43.1 µg/mL obtains 151 µg/mL (Equation 1). E1·R2·R6

Why something dissolved in the drug-rich phase lowers the ceiling. If a second component mixes ideally into the drug-rich phase, the drug in that phase is diluted and its chemical potential falls. The paper writes this as Equation 2:

In plain terms: the amorphous solubility with the additive, $S_a$, is the additive-free amorphous solubility $S_a^0$ times the mole fraction of drug in the drug-rich phase, $x_{\mathrm{d}\mathrm{r}\mathrm{u}\mathrm{g}}$. The authors state its assumptions: ideal mixing between components of similar molar volume, with interactions between unlike molecules the same as between like ones, and no change in the water content of the drug-rich phase. They point out at once that a polymer breaks these assumptions: its molar volume is far larger than the drug's, and it can interact specifically with the drug. E2·C27·C28

Flory–Huggins mixing with a polymer. For a polymer the natural composition variable is the volume fraction, and the authors use the Flory–Huggins model. Assuming no specific interactions (ideal mixing with respect to interactions), the amorphous solubility of IBP becomes Equation 4:

In plain terms: $S_{a,\mathrm{I}\mathrm{B}\mathrm{P}}^0$ is the amorphous solubility of IBP without polymer, ${\Phi }_{\mathrm{I}\mathrm{B}\mathrm{P}}$ and ${\Phi }_{\mathrm{p}\mathrm{o}\mathrm{l}\mathrm{y}\mathrm{m}\mathrm{e}\mathrm{r}}$ are the volume fractions of IBP and polymer in the IBP-rich phase, and $x$ is the ratio of the molar volume of the polymer to that of IBP. The factor ${\Phi }_{\mathrm{I}\mathrm{B}\mathrm{P}}$ is the dilution; the exponential is the entropic correction for mixing molecules of very different size, which partly offsets the dilution. Adding an interaction term gives Equation 5:

In plain terms: $\chi$ is the Flory–Huggins interaction parameter between IBP and polymer. A net attraction gives a negative $\chi$, which lowers the predicted amorphous solubility further; a net repulsion gives a positive $\chi$, which raises it. E4·E5

What the NMR spectrum shows. Three features carry the paper's argument. The chemical shift is the position of a peak in ppm; a shift to higher ppm is called downfield, to lower ppm upfield. Because the IBP inside the drug-rich phase sits in a different environment from dissolved IBP, its aromatic protons H4 and H5 (labelled in Figure 1) give a second pair of peaks, H4* and H5*, upfield of the dissolved ones. A polymer that enters the drug-rich phase changes the environment of IBP there and moves H4* and H5*. Line broadening means wider peaks; for the drug-rich phase the authors read it as slower IBP motion, and for dissolved IBP as the effect of IBP exchanging between the water and the droplets. Finally, polymer chains inside the drug-rich phase reorient too slowly to give a solution-state signal: they are NMR-invisible. The loss of polymer signal when droplets form therefore measures how much polymer has entered the drug-rich phase. C6·C7·C9

Partitioning and molecular weight. To rationalise why longer chains partition more, the authors cite an empirical model proposed by Brønsted (Equation 3):

In plain terms: the partition coefficient $K$ of a substance between two phases grows exponentially with its molecular weight $M$, with $\lambda$ a constant. Flory–Huggins-based models of protein partitioning between two aqueous polymer phases make the same point: the larger the molecule, the more uneven its distribution between the phases (Baskir et al. 1989). E3·C29

Methods in detail

The paper has three parts that build on each other: a quantitative NMR measurement of both phases in the same tube, three series of experiments that vary the polymer and the drug concentration, and a thermodynamic analysis that tests whether simple mixing theory explains the results. A water-sorption experiment then tests one of the explanations.

Contribution 1: reading dissolved drug and dissolved polymer in one NMR tube

The problem. To see how a polymer changes the free drug concentration once a drug-rich phase exists, one needs the dissolved drug concentration in the presence of droplets, and ideally also how much polymer has left the solution for the droplets.

What they did. All solutions were made in 50 mM phosphate buffer at pH 2.0 in deuterium oxide (D2O), containing trimethylsilyl propionate (TSP, 200 µg/mL) as the internal reference for both chemical shift and quantification; each polymer was dissolved in this buffer. M8·M10·M11 For saturated solutions, crystalline IBP was stirred for 24 h at 37 °C in buffer or in a 1000 µg/mL polymer solution and filtered through a 0.45 µm membrane. P1 For supersaturated solutions, a stock of IBP in methanol-d4 was added to the buffer or polymer solution to give a final methanol-d4 content of 2% (v/v); the samples were kept at 37 °C during preparation and transferred to 5 mm NMR tubes. P2 Spectra were recorded at 37 °C on an 800 MHz spectrometer with a cryoprobe, with a repetition delay of 15 s, five times the longest spin–lattice relaxation time $T_1$ of the samples, so that peak areas are quantitative. P3

The IBP peaks of the aqueous phase and of the IBP-rich phase overlap partly once polymer broadens them, so the authors decomposed them by Lorentzian curve fitting (the blue and red dashed fits in Figure 3). The dissolved IBP concentration came from the area of the aqueous-phase H4 and H5 peaks normalised by TSP, through a calibration line (Figure S3a). The dissolved polymer concentration came from the polymer peak near 2.0 ppm (PVP, PVP-VA) or near 3.1 ppm (HPMC), again normalised by TSP and calibrated (Figures S3b–g). All calibrations were linear, with $R^2$ between 0.9996 and 0.9999. In buffer, the total IBP signal of both phases at 200, 400 and 600 µg/mL fell on the same calibration line as the single-phase standards, so IBP in the drug-rich phase is fully counted there. Each condition was measured in triplicate (mean ± standard deviation). P3·R16

Why it works. Polymer chains that enter the IBP-rich phase lose their solution-state signal because they reorient slowly. The difference between the polymer added and the polymer still seen in solution is therefore the polymer in the drug-rich phase, and the difference between the IBP added and the dissolved IBP is the IBP in the drug-rich phase. From these the authors calculate the polymer weight ratio to IBP in the IBP-rich phase (the formula itself is not printed). P4·C7

Note by the AI writer (not discussed in the paper). This measure counts all polymer that becomes NMR-invisible. Polymer bound at the droplet surface, rather than dissolved inside the droplets, would be counted the same way; the paper does not separate the two, so the "weight ratio in the IBP-rich phase" is best read as NMR-invisible polymer per phase-separated IBP. X4

Contribution 2: three experimental series

The authors varied one factor at a time. (1) Polymer species and grade: buffer and six polymers, each at 1000 µg/mL, with 400 µg/mL IBP. (2) Polymer concentration: PVP K25, PVP-VA and HPMC 603 at 25, 50, 200, 500 and 1000 µg/mL, with 400 µg/mL IBP. (3) Drug concentration: total IBP of 50, 100, 200, 400 and 600 µg/mL in buffer or in 500 µg/mL of the same three polymers. All at 37 °C. A1·A2·A3 The polymers were chosen so that MW varies within a family, from PVP K12 (MW 2000−3000) through K25 (28 000−34 000) to K90 (1 000 000−1 500 000), and from HPMC 603 (average MW 13 000) to HPMC 615 (65 000), while chemistry varies between families: PVP-VA (Kollidon VA 64, MW 45 000−70 000) is a copolymer of 60 wt% vinylpyrrolidone and 40 wt% vinyl acetate. M2–M7

Contribution 3: testing mixing theory against the measurements

The authors first checked the polymer-free value: the theoretical amorphous solubility from Equation 1 against the measured dissolved IBP in buffer. E1·R6 They then asked whether the polymer content of the drug-rich phase, measured in Contribution 1, explains the drop in free IBP. Because the polymer's molar volume is so much larger than that of IBP, they used volume fractions and the Flory–Huggins forms (Equations 4 and 5). The volume fractions and the molar volume ratio $x$ were calculated from the true densities and MWs in Table S1: 1.18 g/cm³ for PVP-VA and 1.25 g/cm³ for HPMC 603, both measured by helium pycnometry (mean of five), and 1.11 g/cm³ for IBP, the reported value for crystalline IBP; with averaged MWs of 57 500 and 13 000 g/mol and 206 g/mol for IBP, the molar volumes are 48 729, 10 400 and 186 cm³/mol. M1·M5·M6·P5·P8 Equation 4 was evaluated for PVP-VA and HPMC 603, and Equation 5 for PVP-VA with $\chi$ from −1 to 1. P8

Finally, to test whether water carried into the drug-rich phase by the polymer could explain part of the result, they measured water uptake by dynamic vapor sorption (DVS). IBP/polymer ASDs were made by heating physical mixtures of IBP with PVP-VA or HPMC 603 (4/1 and 1/1 w/w) at 85 °C for 30 min. Ten milligrams were dried for 60 min at 37 °C and then held at 99% relative humidity (RH) and 37 °C for 200 min. P6

Experimental analysis

Polymers leave dissolved ibuprofen alone

The first control asks whether the polymers act on IBP in solution at all. In IBP-saturated solutions containing 1000 µg/mL of any of the six polymers, every IBP peak (H2 to H8) stayed at its position in buffer and none was broadened (Figure 2). The TSP-normalised IBP peak area was also the same in all solutions, so the crystalline solubility, 43.1 µg/mL at 37 °C, was unchanged: at this concentration the polymers neither solubilise IBP nor change the environment of molecularly dissolved IBP. R1·R2·C5 This matters for everything that follows: any drop in dissolved IBP in the supersaturated solutions cannot come from complexation in water and must come from the drug-rich phase.

Every polymer enters the drug-rich phase and lowers the free drug

At 400 µg/mL total IBP all samples turned turbid (Figure S1): an IBP-rich phase had formed by LLPS. R15 The spectra then show two pairs of aromatic IBP peaks (Figure 3): the dissolved H4 and H5 at about 7.29 and 7.25 ppm, unchanged in every solution, and the drug-rich H4* and H5* further upfield. R3 With polymer present, H4* and H5* moved downfield and broadened. The shift grew with MW within PVP and HPMC and was larger for PVP-VA and HPMC than for PVP (Table A). At the same time the polymer peaks lost intensity when IBP-rich droplets were present, for all six polymers (Figure S2). R3·R4 The authors read these changes together: polymer distributes into the drug-rich phase, changes the chemical environment of IBP there and suppresses its mobility ("These changes arise from" both). C6·C7·C8

The dissolved-IBP peaks did not move, but they did broaden in the polymer solutions, most with HPMC and PVP-VA. Since the same polymers caused no broadening in saturated solutions, solution viscosity cannot explain it. The authors attribute it to IBP exchanging between the water and the drug-rich phase: the polymer-induced downfield shift reduces the frequency difference $\Delta \omega$ between the two sites, which promotes exchange broadening as the exchange rate approaches $\Delta \omega$, and slower IBP motion in the drug-rich phase adds lifetime broadening. They first call the exchange explanation "likely"; later, when the broadening appears only once an IBP-rich phase forms in the IBP-concentration series, they say the result "confirms" that exchange is the main source. C9

Table A. Six polymers at 1000 µg/mL with 400 µg/mL total IBP, pH 2.0, 37 °C. H4* read from Figure 3 (approximate, about ±0.01 ppm); dissolved IBP and weight ratio read from Figure 4 (approximate; n = 3), except the buffer value of 154 µg/mL, which is stated in the text. R3·R5

Dissolved IBP in buffer was 154 µg/mL, close to the 151 µg/mL predicted by Equation 1, and the authors take it as the amorphous solubility. R5·R6·C10 Every polymer lowered it (Figure 4). Within a family the higher-MW grades lowered it more: PVP K25 and K90 more than K12, HPMC 615 more than 603; across chemistries the order was PVP > HPMC > PVP-VA. C12 The weight ratio of polymer to IBP in the drug-rich phase followed the same ranking within families: higher for K25 and K90 than for K12, and for HPMC 615 than for 603. The authors connect this to the larger downfield shifts of these grades: more polymer in the drug-rich phase means a larger change in the surroundings of IBP and stronger mobility suppression. C13 PVP-VA and HPMC entered the drug-rich phase more than any PVP grade. But the ranking of shift and amount is not the same across chemistries: HPMC 603 had more polymer in the drug-rich phase than PVP-VA (ratio about 0.95 against 0.87), while PVP-VA moved H4* further (about 7.11 against 7.08 ppm). The authors conclude that the molecular state of IBP in the drug-rich phase depends both on the polymer's structure and on how much of it is there. C14

Note by the AI writer (not discussed in the paper). Two details limit the MW reading. PVP K25 and K90 gave the same weight ratio (about 0.52) and similar dissolved IBP (about 121 and 118 µg/mL), although K90 has a 30–50 times higher MW, so within PVP the effect levels off above K25. And the HPMC 603 versus PVP-VA difference in weight ratio at 1000 µg/mL lies within the HPMC 603 error bar (about 0.84–1.06 in Figure 6b). X7·X8

More polymer, less free drug, until the drug-rich phase stops taking polymer

With 400 µg/mL IBP and increasing polymer, the drug-rich phase first showed two environments. At 25 µg/mL of each polymer, H4* and H5* each appeared as two doublets: a smaller one at the buffer position and a larger one downfield (Figure 5). The authors take this to mean ("This suggests") two kinds of drug-rich phase, one with little polymer and one with more ("it can be assumed"), and conclude that 25 and 50 µg/mL were not enough to form a homogeneous IBP-rich phase during the solvent shift. From 200 µg/mL a single downfield peak remained. R7·C15 As polymer increased, H4* moved further downfield and broadened. The shift stopped above 200 µg/mL for PVP K25 (H4* about 7.05 ppm from 200 to 1000 µg/mL) and above 500 µg/mL for PVP-VA (about 7.10 to 7.11 ppm), but continued for HPMC 603 up to 1000 µg/mL (about 6.97 ppm at 25 µg/mL to about 7.08 ppm at 1000 µg/mL). R7·C16

Table B. Dissolved IBP (µg/mL) and polymer:IBP weight ratio in the IBP-rich phase against total polymer concentration, 400 µg/mL total IBP. Read from Figure 6 (approximate; n = 3). No PVP K25 marker is distinguishable at 25 µg/mL in Figures 6 and 9, although a spectrum is shown in Figure 5a. R8

The quantitative data follow the spectra (Table B, Figure 6). Dissolved IBP fell with polymer concentration, more steeply with PVP-VA than with PVP K25. It levelled off above 200 µg/mL for PVP K25 (about 120 µg/mL) and above 500 µg/mL for PVP-VA (about 90 µg/mL), but kept falling for HPMC 603, which at 25–200 µg/mL left more IBP dissolved than PVP K25 and at 500 µg/mL and above left less. R8·C18 The weight ratio in the drug-rich phase mirrored this: it stopped rising above 200 µg/mL for PVP K25 and 500 µg/mL for PVP-VA, and rose continuously for HPMC 603. R8·C19 The authors "hypothesize" that the continued uptake of HPMC reflects its heterogeneity: methyl and hydroxypropyl groups are introduced at random, so HPMC is a mixture of chains with different substitution and hydrophilicity, and the less hydrophilic chains enter the drug-rich phase first ("likely explains" the missing plateau). C31

More drug: a fixed ceiling with PVP K25 and PVP-VA, a moving one with HPMC 603

The third series kept the polymer at 500 µg/mL and raised the IBP (Figures 7 and 8). In buffer, dissolved IBP followed the dose up to 100 µg/mL, reached about 150 µg/mL at 200 µg/mL total and stayed essentially constant, about 154–157 µg/mL, up to 600 µg/mL: the maximum free drug concentration did not depend on how much drug-rich phase had formed, and the IBP-rich peaks kept their shape and position as they grew. R9·R10·C20·C23 In the PVP K25 solution, as in buffer, no IBP-rich peaks were seen at 100 µg/mL. In the PVP-VA and HPMC 603 solutions, low-intensity IBP-rich signals appeared already at 100 µg/mL in the enlarged spectra, and dissolved IBP was only about 81 and 88 µg/mL; the authors conclude that the drug-rich phase forms at much lower IBP concentration in these two solutions ("Hence"). R9·R10·C21

Table C. Dissolved IBP (µg/mL) and polymer:IBP weight ratio in the IBP-rich phase against total IBP, buffer or 500 µg/mL polymer. Read from Figure 8 (approximate; n = 3). The condition 400 µg/mL IBP with 500 µg/mL polymer carries the same values here and in Table B. R10

Once the drug-rich phase had formed, dissolved IBP held at about 120 µg/mL with PVP K25 and about 90 µg/mL with PVP-VA. With HPMC 603 it kept rising, from about 88 µg/mL at 100 µg/mL total to about 123 µg/mL at 600 µg/mL. "This indicated", in the authors' words, that with HPMC 603 the maximum free IBP concentration can change with the amount of IBP-rich phase. R10·C24 The weight ratio explains why: as more IBP went into the drug-rich phase, each unit of IBP carried less polymer, and the drop was steepest for HPMC 603 (about 2.14 to 0.59) against PVP-VA (about 1.19 to 0.68) and PVP K25 (about 0.60 to 0.40). The HPMC 603 IBP-rich peaks moved back upfield as the phase grew (H4* about 7.08 ppm at 200 µg/mL to about 7.04 ppm at 600 µg/mL), which the authors read as a smaller change of the IBP environment by polymer mixing ("indicating"); the shifts changed little with PVP K25 and PVP-VA. R9·R10·C22·C25

Note by the AI writer (not discussed in the paper). Three details deserve care. First, the text says that the IBP-rich peaks in buffer appeared "above 200 μg/mL", but Figure 7a already shows small H4* and H5* doublets at 200 µg/mL, and Figure 8a gives about 150 µg/mL dissolved at 200 µg/mL total; the onset lies between 100 and 200 µg/mL. X2 Second, at 100 µg/mL total IBP only about 12 µg/mL (HPMC 603) and 19 µg/mL (PVP-VA) of IBP is phase-separated (total minus dissolved), so the weight ratios there rest on small differences; the HPMC 603 point has the largest error bar of the data set (about 1.80–2.48). X3 Third, in Figure 7d the enlarged 100 µg/mL HPMC 603 trace shows a broad sloping signal without resolved maxima, whereas the PVP-VA trace in Figure 7c shows two broad maxima near the H4* and H5* positions. X12

The same polymer content does not mean the same effect

Equation 2 implies that the amorphous solubility should follow the amount of polymer in the drug-rich phase. The data at 1000 µg/mL contradict this across chemistries: dissolved IBP was lower with PVP-VA (about 89 µg/mL) than with HPMC 603 (about 106 µg/mL), although HPMC 603 had the higher polymer ratio. C32 To show the trend over the whole range, the authors plotted dissolved IBP against the polymer weight ratio for all measurements of the two series (Figure 9). At comparable ratios the PVP-VA points lie well below the HPMC 603 points (Table D). For chemically different polymers, the authors conclude, "the maximum free drug concentration cannot be explained only by the amount of polymer that mixes with the drug-rich phase". R11·C32

Table D. Dissolved IBP (µg/mL) at comparable polymer weight ratios in the IBP-rich phase, and the predictions of Equations 4 and 5. Measured values and Equation 4 curves read from Figure 9, Equation 5 from Figure 10 (all approximate). The Figure 9 points pool both concentration series; which point comes from which series is not stated and is inferred here by matching values. R11·R12·R13·X11

The ideal Flory–Huggins prediction (Equation 4) lies far above the data for both polymers: it falls from 154 µg/mL to about 129 µg/mL (PVP-VA) and 127 µg/mL (HPMC 603) at a ratio of 1.0, and to about 93 and 91 µg/mL at 2.5, while every measured point lies on or below these curves (Figure 9). The authors take this as "suggesting that additional factors" must be considered. R12·C33

Note by the AI writer (not discussed in the paper). The PVP-VA curve of Equation 4 can be recomputed from the printed inputs: at a weight ratio of 1.0, with $S^0=154$ µg/mL, a polymer volume fraction of 0.485 from the densities and $x=48729/186=262$, it gives 128.6 µg/mL, matching the plotted value of about 129. The HPMC 603 curve does not reproduce with the Table S1 density of 1.25 g/cm³ (104.0 µg/mL at a ratio of 2.0 against about 101 plotted); with 1.18 g/cm³, the PVP-VA value, it does (101.6). With the printed density the HPMC 603 curve would lie slightly above the PVP-VA curve rather than below it. The two curves differ by only a few µg/mL either way, so the conclusion that Equation 4 over-predicts both polymers stands. E4·X1

The authors then looked for the missing factors. The first candidate was water. Equation 4 assumes the drug-rich phase holds the same water with and without polymer, which for IBP alone is negligible (Almeida e Sousa et al. 2015), but hydrophilic polymers raise the water content of an ASD. Since PVP-VA has been reported to absorb more water than HPMC (Xie and Taylor 2017; Saboo et al. 2020), and PVP-VA deviated more from Equation 4, "a likely explanation" seemed to be more water in the PVP-VA drug-rich phase. C34·R18·R20 The DVS test pointed the other way (Figure S4). Water uptake rose with polymer content as expected, but at the same ratio the IBP/HPMC 603 ASDs took up more water than the IBP/PVP-VA ASDs: about 13.9% against 13.0% at 1/1 and about 6.5% against 4.2% at 4/1 after 200 min. This agrees with an earlier celecoxib study in which a PVP-VA ASD sorbed less water than neat PVP-VA would suggest, similar to an HPMC ASD. The authors conclude that "it seems unlikely" that the greater effect of PVP-VA comes from more water, while "it is clear" that extra water in the polymer-containing drug-rich phase still contributes to the gap from Equation 4. R17·C35·C36

The second candidate was a specific interaction. IBP carries a carboxylic acid, a strong hydrogen-bond donor, and Equation 5 adds the interaction parameter $\chi$. Lowering $\chi$ lowers the predicted solubility: at a PVP-VA ratio of 2.5 the curves of Figure 10 run from about 152 µg/mL for $\chi =1$ through about 93 for $\chi =0$ to below 60 for $\chi =-1$. R13·C38 IBP has been reported to hydrogen-bond with PVP-VA in ASDs, the pyrrolidone carbonyl acting as acceptor for the carboxylic acid, with $\chi$ estimated at about −1 for a 1/1 blend (Xiang and Anderson 2019). With that value, Equation 5 gives about 100 µg/mL at a 1/1 ratio, against about 90 µg/mL measured, so Equation 5 "appears to provide an improved estimation", with the caveat that the drug–polymer $\chi$ "may be altered in the presence of water". R14·C39 HPMC 603 has only weak acceptor groups (hydroxyl and ether oxygens), and a molecular dynamics study found IBP–PVP-VA interactions much stronger than IBP–HPMC interactions (Yani et al. 2017). The larger downfield shift with PVP-VA, despite less polymer in the drug-rich phase than with HPMC 603, fits a stronger interaction, which "would, in turn, be consistent with" the larger drop in dissolved IBP. R19·C40 Note that the abstract states this more firmly, saying the larger reduction is "as a result of" more extensive drug–polymer interactions; no interaction was measured in the hydrated drug-rich phase itself. X5

Discussion

The authors' chain of reasoning. The paper's argument can be laid out as one chain with three parallel routes at the end. The routes are not better or worse outcomes; they are three ways in which polymer in the drug-rich phase lowers the drug's chemical potential, and the authors hold that all three act together.

In the authors' summary, "there are three factors that are responsible for the observed decrease in the dissolved IBP concentration": the dilution of the drug by polymer incorporated into the drug-rich phase, the increased water content that accompanies polymer incorporation, and favourable drug–polymer specific interactions in the drug-rich phase; they refer to Huang et al. (2016) for a fuller treatment of these factors in ASDs. They add that the water in the drug-rich phase "is expected" to change the IBP–polymer interaction, so that an accurate model would need water–drug and water–polymer interactions as well as drug–polymer ones. C41·C42

What sets the size of the drop. Within one polymer, the measured quantity that tracks the free drug is how much polymer the drug-rich phase holds. That amount depends on MW and on the polymer's hydrophobicity: the authors name the hydrophobic acetate groups as "the likely reason" PVP-VA partitions more than PVP, because water ordered around apolar groups makes their hydration entropically unfavourable, in line with earlier findings that more acetate-substituted HPMC derivatives partition more into drug-rich phases. It also depends on the polymer:drug ratio in solution, which is why, with HPMC 603, the free drug concentration moved with the amount of drug-rich phase. Between chemically different polymers, the paper's data show that the amount is not enough: at the same polymer content, PVP-VA lowers free IBP more than HPMC 603, and the authors attribute this to stronger drug–polymer interaction. C30·C24·C32·C40

A trade-off for polymer selection. The authors place the result in formulation terms. A high polymer loading in an ASD gives polymer-controlled drug release with high supersaturation and colloidal drug; higher-MW polymers have been found to improve the physical stability of ASDs; and amphiphilic polymers typically inhibit crystallization from supersaturated solution more strongly than hydrophilic ones. Polymer in the drug-rich phase also helps by suppressing molecular mobility and reducing supersaturation, and it slows coarsening of the drug-rich phase (all from cited work). "As noted in the present study", the same properties raise the distribution of polymer into the drug-rich phase and lower the dissolved drug concentration. Since the extent of supersaturation is directly related to the membrane transport rate, "ASD polymers should be selected considering the trade-offs between improved stability derived from polymer distribution into the drug-rich phase, versus a decreased maximum extent of supersaturation". For drugs that do not crystallise rapidly, they argue, the maximum solute thermodynamic activity matters, and the polymer's potential to lower it "must be considered". C26·C43·C44·C45

Note by the AI writer (not discussed in the paper). Read as numbers, the cost is not small. At 1000 µg/mL polymer and 400 µg/mL IBP the free drug fell by about 15% with PVP K12 and about 42% with PVP-VA, relative to the polymer-free 154 µg/mL. If membrane flux follows the free concentration, as the authors assume from cited work, that fraction of the driving force for absorption is lost before any crystallization is considered. The HPMC 603 behaviour adds a dose dependence: there the ceiling rose from about 88 to 123 µg/mL as more drug-rich phase formed, so the polymer:drug ratio delivered by a dissolving ASD would set the ceiling. Whether the same ranking holds for other drugs, for ionised drugs at intestinal pH, or in media with bile salts and surfactants is not addressed by this paper.

Limitations

Limits the authors state. They note that Equation 2 assumes ideal mixing, similar molar volumes and an unchanged water content, none of which holds for a polymer ("it is clear that the molar volume of a polymer is much larger than that of the drug"). They point out that Equation 4 assumes the same water content with and without polymer and no specific interactions, and that the $\chi$ value used in Equation 5 "may be altered in the presence of water". They describe their explanation for HPMC's continuing partitioning as a hypothesis ("We hypothesize"), and they say an accurate prediction model needs the full set of water–drug, water–polymer and drug–polymer interactions. C28·C33·C37·C39·C41·C31

The AI writer's own judgement. The measurement at the core of the paper is direct and internally consistent: dissolved drug and dissolved polymer are read in the same sample against linear calibrations, in triplicate; the buffer value matches the theoretical amorphous solubility; and the condition shared by the two concentration series (400 µg/mL IBP with 500 µg/mL polymer) carries the same values in both. The PVP-VA versus HPMC 603 difference per unit polymer holds over many points of Figure 9, not one pair. The weaker parts are the explanations. P3·R16·R6·R8·R10·R11

• Interaction and water were not measured in the wet drug-rich phase. The interaction argument rests on a chemical-shift difference, a cited molecular dynamics study and a cited $\chi$ for a 1/1 blend; the water argument rests on DVS of melt-prepared solid ASDs at 99% RH for 200 min, in which the 4/1 HPMC 603 curve had not levelled off, and whose amorphous state is not reported. X5·X6
• What "polymer in the drug-rich phase" measures. All polymer that loses its solution signal is counted; polymer bound at droplet surfaces would be counted too. X4
• The MW and hydrophobicity trends are narrower than stated. PVP K25 and K90 behave alike, and polymer hydrophobicity was not measured; the HPMC 603 versus PVP-VA order of partitioning reverses with polymer concentration. X7·X8
• Low-drug points are the least certain. At 100 µg/mL total IBP the polymer ratios rest on about 12–19 µg/mL of phase-separated IBP, and the HPMC 603 drug-rich signal there is not resolved. X3·X12
• Small source inconsistencies. The HPMC 603 Equation 4 curve fits the PVP-VA density rather than its own; the LLPS onset in buffer is stated as "above 200 μg/mL" but seen at 200 µg/mL. Neither changes the conclusions. X1·X2
• Conditions. One drug, pH 2.0 phosphate buffer in D2O, 2% methanol-d4 from the stock in the supersaturated samples but not in the saturated ones, 37 °C, and an unstated time between mixing and measurement; all values except a few in the text are read from plots. X10·X9
• The trade-off is half shown. Partitioning and free drug were measured; stability, crystallization inhibition and membrane transport were not, so the other side of the trade-off rests on cited work. X13

Conclusion

The paper shows directly, by quantitative solution NMR, that polymers dissolved alongside a supersaturated drug do not stay in the water: PVP, PVP-VA and HPMC enter the ibuprofen-rich phase formed by liquid–liquid phase separation, more so for higher-MW grades and for PVP-VA than PVP, and the free ibuprofen in the water falls below the polymer-free amorphous solubility of 154 µg/mL, to about 89–131 µg/mL at 1000 µg/mL polymer. Within a polymer the drop tracks how much polymer the drug-rich phase holds, with plateaus for PVP K25 and PVP-VA and a ceiling that moves with the amount of drug-rich phase for HPMC 603. Across polymers it does not: PVP-VA lowers the free drug more than HPMC 603 at the same polymer content, beyond what ideal Flory–Huggins mixing predicts, which the authors attribute to stronger drug–polymer interaction rather than to water. In the authors' conclusion, "Highly water-soluble polymers show a surprisingly great extent of partitioning into the drug-rich phase", and the polymer's effect on attainable supersaturation is a factor to weigh alongside stability when choosing an ASD polymer. R5·R8·R10·R11·R12·C40·C45·C46