Why polymers move into drug-rich droplets: the thermodynamics of polymer partitioning and its effect on the supersaturation ceiling of ibuprofen

Background and motivation

Supersaturating formulations, among them amorphous solid dispersions (ASDs), raise the dissolved concentration of a poorly soluble drug above its crystalline solubility, and the extra concentration in water is what drives absorption. Polymers such as cellulose ethers and vinylpyrrolidone polymers are added to slow crystallization and keep the solution supersaturated. There is, however, a ceiling. When the dissolved drug reaches its amorphous solubility, the drug separates into a second, drug-rich phase by liquid–liquid phase separation (LLPS), or glass–liquid phase separation (GLPS) for drugs whose separated phase is glassy. From then on, adding more drug only feeds the drug-rich phase; the thermodynamic activity of the drug in water, which is what the membrane sees, cannot rise further (Ilevbare and Taylor 2013; Mosquera-Giraldo and Taylor 2015; Almeida e Sousa et al. 2015, refs 25–27). C1

The ceiling is not fixed. Anything that dissolves in the drug-rich phase dilutes the drug there and lowers its chemical potential, so less drug is needed in water to be in equilibrium with it. A second drug, a surfactant, lipids and polymers have all been shown to mix into drug-rich phases and lower the maximum drug activity in water (Trasi and Taylor 2015, ref 28; Ueda and Taylor 2021, ref 29; Lindfors et al. 2006, ref 30; refs 31–33); for polymers this has been linked to lower membrane transport (refs 32, 34). C2 In the discussion the authors add that, for polymers that inhibit crystallization well, the effect on the maximum solute activity has recently become a second criterion of polymer choice, because that activity sets the transport rate of high-permeability drugs (refs 36, 80, 81). C33

This paper continues a direct predecessor from the same groups (Ueda et al. 2021, ref 36). There, quantitative NMR showed that PVP, PVP−VA and HPMC distribute into the ibuprofen (IBP)-rich phase and markedly lower the amorphous solubility of IBP; HPMC or PVP−VA reduced the maximum solute activity of IBP to around half of its value without polymer; PVP−VA and HPMC partitioned more than PVP, and PVP−VA interacted more strongly with IBP than HPMC did. C3·R27 The authors regard the distribution of polymer into the drug-rich phase as the underlying cause of the lower maximum activity, but note that its thermodynamics was not understood. C34

Ibuprofen makes such a study possible by NMR. Its glass transition temperature is about −45 °C (Baird et al. 2010, ref 59), far below any measurement temperature, so the IBP-rich droplets are a mobile supercooled liquid that gives sharp solution-state NMR peaks, separate from those of IBP dissolved in water (Ueda et al. 2019, ref 31; Ueda and Taylor 2020, ref 33). M1·C4 Changing the temperature then turns a single measurement of where the polymer sits into a thermodynamic measurement of why it sits there.

The paper sets out to do three things: measure by variable-temperature solution NMR how the partitioning of the three polymers into the IBP-rich phase, and the resulting IBP amorphous solubility, change between 15 and 60 °C; measure by solid-state NMR how IBP interacts with each polymer and how those interactions change with temperature; and derive the free energy, enthalpy and entropy of polymer transfer between the water phase and the drug-rich phase. A1·A2·A3·A4

Background concepts

Amorphous solubility and the drug-rich phase. The amorphous solubility is the concentration of dissolved drug in equilibrium with a water-saturated, drug-rich liquid. The authors use the operational definition: whenever a drug-rich phase is present, the dissolved drug concentration in the water phase is the amorphous solubility in that solution, written $S_a^0$ in buffer and $S_a$ in a polymer solution. C15 The ratio of amorphous to crystalline solubility in buffer can be estimated from two quantities (eq 1, from Almeida e Sousa et al. 2015, ref 27): E1

Here $S_c^0$ is the crystalline solubility, $\Delta G_{c\to a}$ the free energy difference between the crystal and the amorphous form, $e^{-I(a_2)}$ the activity of the amorphous drug once it is saturated with water, $R$ the gas constant and $T$ the temperature. In plain terms: the amorphous form is more soluble than the crystal by the Boltzmann factor of its excess free energy, reduced somewhat because the amorphous drug takes up water, which lowers its own activity. E1

Why a dissolved additive lowers the ceiling. If a second component mixes ideally into the drug-rich phase, the drug in that phase is diluted and its activity falls in proportion to its mole fraction. To a first approximation (refs 28, 30–33) this gives eq 2: E2·C39

Here $x_{\mathrm{d}\mathrm{r}\mathrm{u}\mathrm{g}}$ is the mole fraction of drug in the drug-rich phase when the additive is present. In plain terms: the fraction of the original ceiling that remains equals the fraction of drug molecules in the droplets. The equation assumes no specific interactions between drug and additive and only combinatorial entropy of mixing; the authors use it to argue qualitatively that more polymer in the droplets should mean a lower $S_a/S_a^0$. C39·C41 Note by the AI writer (not discussed in the paper): the paper does not say whether polymer molecules or their repeat units are counted in $x_{\mathrm{d}\mathrm{r}\mathrm{u}\mathrm{g}}$; counted per chain, polymers of 13,000–70,000 g/mol at the measured weight ratios would leave $x_{\mathrm{d}\mathrm{r}\mathrm{u}\mathrm{g}}$ near 1, far above the measured $S_a/S_a^0$, so eq 2 serves here as an argument, not a prediction. X3

Partition coefficient and the van't Hoff analysis. The distribution of a solute between two phases is set, the authors write, by its relative chemical affinity for each phase and by the entropy of mixing and distribution. C46 The partition coefficient of the solute between phases p and q is the ratio of its equilibrium concentrations (eq 3), and it fixes the free energy of moving the solute from q to p (eq 4): E3·E4

In plain terms: if the polymer is more concentrated in the drug-rich phase than in water ($K>1$), moving it into the drug-rich phase is downhill ($\Delta G<0$). Splitting the free energy into enthalpy and entropy gives the van't Hoff equation (eq 5): E5·E12

In plain terms: if $\Delta H$ and $\Delta S$ do not change with temperature, $\ln K$ is a straight line against $1/T$; the slope gives $\Delta H$ and the intercept gives $\Delta S$. A positive $\Delta H$ (endothermic transfer) makes $K$ rise with temperature. When the line curves, $\Delta H$ and $\Delta S$ depend on temperature, and the authors fit a quadratic in $1/T$ instead (eq 6, ref 89), from which $\Delta H$ and $\Delta S$ follow at each temperature (eqs 7 and 8): E6·E7·E8·C47

Here $A$, $B$ and $C$ are fitted constants. In plain terms: the curvature term $C$ lets the enthalpy and entropy of transfer drift with temperature; at any temperature, $\Delta H$ is minus $R$ times the local slope of $\ln K$ against $1/T$. Note by the AI writer: because $\Delta H$ and $\Delta S$ are derivatives of a fitted curve, their temperature trends depend on the fit form more than their mid-range values do. X8

Reading solution NMR of a two-phase sample. In the 1H NMR spectrum, IBP dissolved in water and IBP in the drug-rich droplets resonate at different chemical shifts, because the droplet interior is less polar. R4·C8 The area of each peak, against an internal standard (TSP) and with long enough delays between scans, gives the amount of IBP in each environment. P4 A peak moves "down-field" (to higher ppm) or "up-field" (to lower ppm) when the electronic environment changes, for example when another molecule mixes into the droplet. Two further effects broaden peaks: slow molecular motion, and exchange of molecules between two environments, which broadens a peak more as the exchange rate approaches the shift difference between the environments (refs 47, 48). C14 Large polymer chains inside the droplets move too slowly to give a solution-state signal at all; their presence is seen only as polymer missing from the water phase. R7·R8·C10

Solid-state NMR of hydrogen bonds. In the solid-state spectra of dry ASDs, the proton of a carboxylic acid that is hydrogen-bonded in an acid dimer appears at about 12–13 ppm, a free carboxylic proton at about 8 ppm (refs 63, 64). R28 Breaking a hydrogen bond moves the proton up-field. When molecules switch between bonding states faster than the NMR time scale, a single, population-averaged peak appears (fast exchange). C25 The temperature coefficient of a proton's chemical shift, $\mathrm{T}\mathrm{C}=\Delta (\mathrm{c}\mathrm{h}\mathrm{e}\mathrm{m}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{s}\mathrm{h}\mathrm{i}\mathrm{f}\mathrm{t})/\Delta T$, reflects how easily its hydrogen bond loosens on heating (refs 73–79). E9·C32 Two 13C methods are used: cross-polarization (CP) favours rigid components, while pulse saturation transfer (PST) favours mobile ones, which is why supercooled IBP gives no CP spectrum but a strong PST spectrum. P7·C27

The hydrophobic effect and the LCST. Water forms more ordered, "iceberg-like" structures around apolar groups. Removing such a solute releases that water, which costs enthalpy and gains entropy (Frank and Evans 1945, Tanford 1980, refs 90, 91). C50 HPMC solutions show a lower critical solution temperature (LCST): on heating, the water hydrogen-bonded to HPMC hydroxyls and the structured water around its methyl groups are lost, the chains associate and the solution gels (ref 99); PVP and PVP−VA show no LCST at ambient pressure (ref 100). R29·C57·C58

Methods in detail

The work has three parts. Quantitative solution NMR measures, at ten temperatures, how much IBP stays dissolved and how much polymer has gone into the IBP-rich phase. A van't Hoff analysis of the polymer partition coefficient turns those measurements into the free energy, enthalpy and entropy of transfer. Solid-state NMR of dry ASDs then probes the IBP–polymer interactions that the authors use to explain the differences between polymers. The figure below shows the workflow.

Contribution 1: quantitative NMR of both phases at ten temperatures

① Problem. To obtain thermodynamics, the amorphous solubility and the polymer content of the drug-rich phase must be measured at many temperatures in the same sample type, without separating the colloidal droplets from the water, which would disturb the equilibrium.

② How. All solutions used 50 mM phosphate buffer at pH 2.0 made in D2O; each polymer was dissolved in it at 1000 µg/mL: PVP K25 (Kollidon 25, 28,000–34,000 g/mol), PVP−VA (Kollidon VA 64, 45,000–70,000 g/mol, 60 wt % vinylpyrrolidone and 40 wt % vinyl acetate) and HPMC 603 (Pharmacoat 603, average 13,000 g/mol). M2·M3·M4·M7 Supersaturated solutions were made by adding a stock of IBP (20 mg/mL in CD3OD) to give an IBP dose of 400 µg/mL and 2% (v/v) CD3OD, with 200 µg/mL TSP as internal reference; the sample was kept at the measurement temperature throughout preparation. P3 Because 400 µg/mL exceeds the amorphous solubility at every temperature, every sample contained an IBP-rich colloidal phase. R4 Spectra were recorded on a 600 MHz (14.1 T) spectrometer from 15 to 60 °C in 5 °C steps, with a 15 s repetition delay, five times the longest 1H T1, so that peak areas are quantitative. P4 The aromatic IBP peaks were decomposed by Lorentzian fitting into the aqueous-phase set (H5, H6) and the IBP-rich set (H5*, H6*), and concentrations were taken from peak areas against TSP; dissolved polymer was quantified from its peak near 2.0 ppm (PVP, PVP−VA) or 3.1 ppm (HPMC). P4·R8 The polymer:IBP weight ratio in the IBP-rich phase follows from the polymer and IBP that are missing from the aqueous phase. P4·R10 Each value is the mean of three samples. R9·R10 HPMC solutions were measured only up to 55 °C: with an IBP-rich phase present they formed gel-like aggregates at 60 °C (Figure S2), which HPMC alone did not, and the authors take this as IBP appearing "to promote" HPMC gelation. R3·C7

Crystalline solubility, needed for the amorphous-to-crystalline ratio, was measured by shaking excess crystalline IBP in buffer at 25–60 °C, and in the polymer solutions at 25, 40 and 55 °C, at 200 rpm for 48 h, filtering through 0.45 µm PTFE and assaying by HPLC at 260 nm (n = 3). P1·P2

③ Why it works. The droplet interior is a liquid well above its Tg, so IBP inside it gives a sharp, separate peak set; the integral of each set measures the amount of IBP in each phase without physical separation. C4·R4 Polymer in the droplets is invisible, but its loss from the water signal is measurable (Figure S3). R7·R8 Temperature was controlled from preparation onward, so each temperature is its own equilibrium sample.

④ Difference from earlier work. The predecessor study measured the same systems at 37 °C only (ref 36). R27 Extending the measurement to 15–60 °C is what gives access to enthalpy and entropy.

Contribution 2: from the partition coefficient to the thermodynamics of transfer

① Problem. A single partition coefficient says that polymer prefers the drug-rich phase, not why: whether the transfer is driven by favourable interactions (enthalpy) or by disorder (entropy).

② How. The polymer partition coefficient $K_{\mathrm{I}\mathrm{B}\mathrm{P}\text{-}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{h}/\mathrm{a}\mathrm{q}\mathrm{u}\mathrm{e}\mathrm{o}\mathrm{u}\mathrm{s}}$ was calculated from the polymer concentrations in the two phases, with the polymer concentration in the IBP-rich phase computed using 0.99 g/cm³, the density of amorphous IBP from molecular dynamics simulations (ref 88). P12·E3·M1 Plotted against $1/T$, $\ln K$ fitted a straight line reasonably for HPMC and PVP−VA ($R^2$ 0.962 and 0.961) but poorly for PVP ($R^2$ = 0.817) (Figure S4), so the authors used the quadratic form of eq 6, which fitted all three ($R^2$ 0.996, 0.994 and 0.971; Figure 12). R20·R21·C47 $\Delta H$ and $\Delta S$ at each temperature then followed from eqs 7 and 8, and $\Delta G$ from $\Delta H$ and $\Delta S$ (Figure 13). E7·E8·E12·R22·R23 Table A lists the printed fits.

Table A. Fits of ln K against 1/T (T in K) printed in Figure 12 (quadratic, used for ΔH and ΔS) and Figure S4 (linear). R20·R21

③ Why it works, and a check. The printed constants reproduce the plotted values: for HPMC at 15 °C (288.15 K) the quadratic gives $\ln K$ = 5.13 against about 5.14 plotted, $\Delta H$ = 58.5 kJ/mol against about 58 in Figure 13b, $-T\Delta S$ = −70.8 kJ/mol against about −71, and $\Delta G=-RT\ln K$ = −12.3 kJ/mol against about −12.2 in Figure 13a. E4·E6·E7·E8 Note by the AI writer (not stated in the paper): the paper does not write out how the polymer concentration in the IBP-rich phase was computed; the plotted $\ln K$ values are reproduced when that phase is treated as IBP plus polymer only, with the polymer mass fraction $r/(1+r)$ ($r$ the polymer:IBP weight ratio) times 0.99 g/cm³, divided by the polymer left in water. On that basis the water in the water-saturated droplets is ignored and the phase density is held at that of amorphous IBP at every polymer content, so $K$ is comparable within this paper rather than an absolute partition coefficient. X2 The slopes of the linear fits correspond to temperature-independent $\Delta H$ of about 35 (HPMC), 15 (PVP−VA) and 12 kJ/mol (PVP), close to the quadratic values near 35 °C; the sign and the ranking of $\Delta H$ therefore do not depend on the fit form, while its temperature trend does. X8

④ Difference from earlier work. Van't Hoff analysis of partition coefficients is a standard way to obtain the thermodynamics of drug transfer between octanol or liposomes and buffer (refs 85–87). Here the solute is a polymer and the receiving phase is the drug's own colloidal phase, measured without separation. E3·E4·E5

Contribution 3: solid-state NMR of IBP–polymer interactions and their temperature dependence

① Problem. The enthalpy of transfer depends on what the polymer finds in the drug-rich phase: which IBP–IBP interactions it must break and which IBP–polymer interactions it can form. The droplets themselves are too dilute and too mobile for detailed interaction analysis, so the authors studied dry ASDs as a model of IBP mixed with polymer.

② How. IBP alone and IBP/polymer mixtures with a polymer weight ratio of 40% were placed in 4.0 mm zirconia rotors, vacuum-dried for 24 h in a glovebox, sealed under dry nitrogen, melted at 150 °C for 20 min and cooled to room temperature. P5 1H MAS spectra (single pulse) and 13C PST/MAS spectra were recorded at 25, 40 and 55 °C at 10 kHz spinning on a 400 MHz (9.4 T) spectrometer; crystalline IBP was recorded by 13C CP/MAS at 40 °C. P6·P7 DSC of in situ melt-quenched mixtures at 0–100% polymer showed a single glass transition for every composition (Figure S1), so IBP appears well mixed with each polymer on the 10–50 nm scale. P8·R26·C66 The measured Tg values were compared with the Gordon–Taylor equation (SI eq 1) with its constant estimated from glass transition temperatures and true densities (SI eq 2): E10·E11

Here $w_1$, $w_2$ are mass fractions, $T_{g1}$, $T_{g2}$ the glass transition temperatures of the two components and ${\rho }_1$, ${\rho }_2$ their true densities (polymer densities by helium pycnometry; amorphous IBP 0.99 g/cm³ from simulation). P9·P10 In plain terms: the Tg of an ideally mixed blend is a weighted average of the two Tgs, with weights set by mass fraction and, through $K$, by density; the SI reads a measured Tg below this line (a negative deviation) as possibly reflecting less favourable drug–polymer interactions ("may reflect"). E10·E11·C67 The polymer densities and the resulting $K$ values are not printed, so the dashed lines in Figure S1 cannot be recomputed. E11

③ Why it works. With a Tg of about −45 °C, amorphous IBP is a supercooled liquid at 25–55 °C, and its rapid motion averages the strong proton–proton couplings even at 10 kHz spinning, giving solution-like 1H peaks. C20·M1 The carboxylic acid proton is then a direct reporter of hydrogen bonding: its position tells whether IBP is in acid dimers or bonded to the polymer, and its temperature coefficient tells how easily that bond loosens. R28·E9·C32

④ Difference from earlier work. The predecessor study ranked interaction strength from solution-state shifts at one temperature. R27·C11 Here the interaction is examined in the solid mixtures and as a function of temperature, which is what the enthalpy argument needs. Note by the AI writer: the dry ASDs contain 40% polymer and no water, while the drug-rich droplets are water-saturated and their polymer content varies with temperature from about 17 to 59 wt% on a water-free basis; the transfer of the interaction ranking from one to the other is an assumption. X7

Experimental analysis

Crystalline and amorphous solubility in buffer

The crystalline solubility of IBP in the pH 2.0 buffer rose from about 23.5 µg/mL at 25 °C to about 49.5 µg/mL at 40 °C and about 116 µg/mL at 60 °C (Figure 2a), which the authors relate to entropy-driven dissolution of IBP in water (ref 37). R1·C6 At 25, 40 and 55 °C the crystalline solubility was the same within error with or without 1000 µg/mL polymer (about 22–23, 46.5–49 and 94–98 µg/mL), so the polymers do not solubilize dissolved IBP at this concentration. R2·C5 This control matters: it means that any loss of amorphous solubility with polymer comes from the drug-rich phase, not from the water phase.

In buffer, the amorphous solubility (dissolved IBP with a drug-rich phase present) rose from about 127 µg/mL at 15–20 °C to about 284 µg/mL at 60 °C (Figure 5a), which the authors read as a shrinking miscibility gap between water and liquid IBP, as is typical for such gaps (ref 50). R9·C16 Throughout, the chemical shift of the IBP-rich peak stayed at about 6.77 ppm, so the droplet environment hardly changed with temperature in buffer. R6·C9 The amorphous-to-crystalline solubility ratio fell from about 5.8 at 25 °C to about 3.6 at 40 °C and 2.5 at 60 °C (Figure 10). R16 It followed the same trend as the prediction from eq 1 but lay above it (prediction about 3.7, 2.5 and 1.5 at the same temperatures); the authors name the use of D2O, while the activity term of the prediction was determined in H2O, as "one possible reason". R16·C36·C37

Polymer partitioning and the loss of amorphous solubility

Every polymer lowered the dissolved IBP concentration at every temperature (Figure 5a), and the polymer content of the IBP-rich phase rose with temperature for every polymer (Figure 5b). R9·R10·C17·C19 Table B gives the values at selected temperatures.

Table B. Dissolved IBP (µg/mL; the amorphous solubility) and polymer:IBP weight ratio in the IBP-rich phase, IBP dose 400 µg/mL, polymer 1000 µg/mL, pH 2.0 D2O buffer, n = 3; read from Figure 5 (approximate). R9·R10

Three patterns stand out. First, PVP partitioned least: its ratio rose from about 0.24 to about 0.62, with a plateau of about 0.47–0.55 between 30 and 50 °C. R10 Second, PVP−VA partitioned most at low temperature and rose almost linearly, from about 0.46 to about 1.32. R10 Third, HPMC started lowest (about 0.20 at 15 °C) and rose most steeply, to about 1.46 at 55 °C; it passed PVP−VA between 35 and 40 °C. R10·R19 The amorphous solubility mirrored this. In PVP and PVP−VA solutions it rose with temperature like buffer, but in HPMC solution it stayed between about 102 and 129 µg/mL from 15 to 55 °C, which the authors call "almost constant". R9·C18 Note by the AI writer: that is still a rise of about a quarter, small only compared with buffer (127 to 250 µg/mL over the same range). X4 As a result the ranking reversed: at 15 °C HPMC (about 109 µg/mL) > PVP (102) > PVP−VA (84); at 55 °C PVP (185) > PVP−VA (143) > HPMC (129). R9·C59

The solution spectra tell the same story at the molecular level (Figures 3 and 4). In polymer solutions the IBP-rich peaks were broader and shifted down-field relative to buffer, and the polymer signal in the water phase fell when IBP was present (Figure S3), both read as polymer mixing into the droplets. R4·R5·R8·C10 At 40 °C the down-field shift of H6* ranked PVP (about 6.856 ppm) < HPMC (6.905) < PVP−VA (6.917), the order found earlier at 37 °C. R6.f·C11 On heating the shifts grew with every polymer, most with HPMC (about 6.835 to 6.933 ppm from 15 to 55 °C), which the authors read as "likely indicating" more partitioning, with a temperature dependence that "appears" stronger for HPMC than for PVP or PVP−VA. R6·C12 The IBP-rich peaks sharpened on heating in PVP and PVP−VA but much less in HPMC; the authors assume ("it can be assumed") that the extra HPMC entering the droplets offsets the gain in IBP mobility. R5·C13 The aqueous IBP peaks did not shift with polymer but broadened, more with PVP−VA and HPMC than with PVP, which the authors explain by exchange of IBP between the two phases. R5·R6·C14

Expressed relative to buffer at the same temperature, $S_a/S_a^0$ fell "as an overall trend" with temperature (Figure 11a). PVP had a small effect with little temperature dependence (about 0.80–0.85 at 15–20 °C, 0.73 at 60 °C); PVP−VA had the largest effect at low temperature (about 0.66–0.69 at 15–25 °C, 0.54 at 60 °C); HPMC moved from the smallest effect at 15 °C (about 0.86) to the largest at 50–55 °C (about 0.54 and 0.52). R17·C38 Plotting $S_a/S_a^0$ against the polymer content of the droplets (Figure 11b) collapses most of these data onto one falling trend, from about 0.86 at a ratio of about 0.20 to about 0.52 at about 1.46; the authors conclude that PVP's small effect "clearly arises" from its low partitioning and that the amount of polymer in the drug-rich phase is "clearly" a critical factor. R18·C44·C45 With eq 2 in mind, the larger PVP−VA content correlates with its larger solubility loss compared with PVP, and the rising polymer content contributes to the fall of $S_a/S_a^0$ with temperature. C39·C40

The polymer content does not explain everything. $S_a/S_a^0$ of PVP−VA and HPMC crossed at 45–50 °C, but their polymer contents crossed at 35–40 °C. R19·C41 At 40–45 °C, PVP−VA gave a slightly lower $S_a/S_a^0$ than HPMC (about 0.62 against 0.64 and 0.59 against 0.60) with less polymer in the droplets (about 0.95 against 1.06 and 1.06 against 1.21). R17·R10 The authors attribute this to the stronger hydrogen bonding of IBP with PVP−VA, whose pyrrolidone carbonyl is a good hydrogen-bond acceptor, seen in their own solid-state data and in molecular dynamics studies (refs 82, 84): it "likely leads" to the lower $S_a/S_a^0$. C42·C43 Note by the AI writer: the 40–45 °C differences are within the error bars (about ±0.04–0.05); the stronger support is Figure 11b, where across ratios of about 0.45–1.3 the PVP−VA points lie below the HPMC points at equal polymer content. X10·R18

Thermodynamics of polymer transfer

The partition coefficients rose with temperature for all polymers (Figure 12): $\ln K$ from about 5.31 to 6.07 (PVP), 5.89 to 6.72 (PVP−VA) and 5.14 to 6.88 (HPMC). R21 Table C gives the derived quantities at three temperatures.

Table C. Free energy, enthalpy and entropy term of polymer transfer from water to the IBP-rich phase (kJ/mol), from the quadratic van't Hoff fits; read from Figure 13 (approximate); no uncertainty is given. R22·R23

$\Delta G$ was negative at every temperature, as a spontaneous transfer requires, and fell with temperature for every polymer, from about −12.2 kJ/mol (HPMC, 15 °C) to about −18.8 kJ/mol (HPMC, 55 °C). R22·C48·C56 $\Delta H$ was positive for HPMC and PVP−VA over the whole range and for PVP up to 50 °C, and $-T\Delta S$ was always larger in magnitude, so the authors conclude that transfer is endothermic, enthalpically unfavourable and driven by the entropy gain ("This analysis indicates"; abstract: positive "for most of the measured temperature range"). R23·C48 Note by the AI writer: the PVP enthalpy is about 1 kJ/mol at 50 °C and turns slightly negative at 55 and 60 °C (about −3 and −7 kJ/mol), so the unqualified "endothermic" of the results text and conclusions holds for most, not all, of the PVP range. X1 Because the transfer is endothermic, $\Delta G$ falls and partitioning grows with temperature. C56

Between polymers, HPMC had by far the largest $\Delta H$ at low temperature (about 58 kJ/mol against 25–30 at 15 °C), with the difference shrinking on heating; PVP and PVP−VA had similar values up to about 30 °C, after which PVP−VA had the larger $\Delta H$ and $\Delta S$. R23 PVP had the least negative $\Delta G$ at every temperature, which the authors say accounts for its low partitioning and small solubility loss. R22·C55 The faster fall of HPMC's $\Delta H$ and $\Delta S$ makes its $\Delta G$ cross that of PVP at 20–25 °C and that of PVP−VA at 35–40 °C, which, in the authors' words, "explains" the steep rise of HPMC partitioning and the reversed solubility ranking. R24·C59 The temperature change of $\Delta G$ was much smaller than those of $\Delta H$ and $\Delta S$, an entropy–enthalpy compensation (ref 98). C56 Polymer partitioning from water into octanol was minimal (data not shown). R25

IBP–polymer interactions in the dry ASDs

Table D. Carboxylic proton and carbonyl carbon of IBP: positions read from Figures 6 and 7 (approximate); shifts on heating printed in Figures 8 and 9 (all up-field); TC from the text. R11·R12·R13·R14·R15

Crystalline IBP, in which molecules form carboxylic acid dimers, gave broad 1H peaks with its carboxylic proton near 12.5 ppm; amorphous IBP gave sharp peaks with the carboxylic proton slightly up-field, at about 12.2 ppm, which the authors read as dimers weakened but "largely retained" ("it can be assumed"). R11·R28·C21 In the ASDs the IBP peaks broadened, the aliphatic and aromatic peaks moved slightly down-field (a more polar environment), and the carboxylic proton moved far up-field to a single peak at 9–10 ppm. R11·C22 The authors read this as dimer disruption by all three polymers ("likely"), with drug–polymer hydrogen bonds formed instead in PVP and PVP−VA ("likely contributed"), since a free carboxylic proton would lie near 8 ppm; the single peak means fast exchange between free and bound states. C23·C24·C25 The IBP/HPMC carboxylic proton lay most up-field, so the interaction through it "might be stronger" with PVP and PVP−VA. C26 In the 13C spectra the carbonyl moved further up-field in IBP/PVP and IBP/PVP−VA than in IBP/HPMC; the authors read the first as loss of hydrogen bonding through the IBP C=O and the second as HPMC hydroxyls bonding to the IBP C=O ("it can be assumed"). R12·C29·C30 They summarize: polymer mixing disrupts IBP–IBP hydrogen bonds; the IBP carboxylic proton binds PVP and PVP−VA strongly and HPMC weakly, and HPMC binds the IBP C=O. C31

On heating from 25 to 55 °C the carboxylic proton moved up-field in every ASD, by 0.279 ppm (PVP), 0.271 ppm (PVP−VA) and 0.717 ppm (HPMC), and the HPMC carbonyl moved most as well (0.219 ppm against 0.049 and 0.073). R13·R14 The resulting TC of about −9 × 10⁻³ ppm/K "indicates" intermolecular hydrogen bonding of the IBP carboxylic proton with PVP and PVP−VA; the TC of −24 × 10⁻³ ppm/K for HPMC implies a bond "disrupted more easily" by heat. R15·C32 DSC supports a weaker IBP–HPMC interaction from another angle: at 40% polymer the ASD Tg was about −10 (PVP), −18 (PVP−VA) and −30 °C (HPMC), and HPMC ASDs fell furthest below the Gordon–Taylor line. R26·C66·C67 Note by the AI writer: the SI calls the PVP and PVP−VA ASDs "reasonably close" to the prediction, but at 40% polymer they also lie about 17–18 °C below it, against about 33 °C for HPMC. X11

Discussion

The authors assemble the results into a two-step picture of polymer transfer, shown below. C49

Leaving water. When the polymer leaves the aqueous phase, water rearranges into the space it vacates, hydrogen bonds between water and the polymer break, and the iceberg-like water around apolar groups (the methyls of HPMC, the alkyl backbone of PVP and PVP−VA) is released. C49·C50 Both cost enthalpy and gain entropy; the authors add that PVP and HPMC have negative enthalpies of solution in water (refs 92, 93), "consistent with" an endothermic transfer out of water. C50·R29

Entering the droplet. The polymer needs a cavity in the IBP-rich phase, which costs enthalpy because IBP–IBP interactions such as carboxylic acid dimers must be broken. The new IBP–polymer interactions are weaker than the IBP–IBP ones, "as inferred from solid-state NMR analysis", which is again consistent with an endothermic transfer, while mixing a second component in and breaking dimers adds entropy. C51 Drug–polymer interactions "do appear important" to offset the enthalpy cost: in earlier work polymers partitioned much less into the drug-rich phase of a drug unable to bind them than into those of acidic drugs such as IBP and ketoprofen, and here the polymers barely partitioned into octanol. C52·R25·R29

Why the polymers differ. HPMC's larger transfer enthalpy is, in the authors' words, at least partly explained by its weaker new interaction with IBP, which leaves a larger net cost for breaking IBP–IBP contacts ("enabling at least partial rationalization"). C53 Its strong temperature dependence is linked to its LCST behaviour: at low temperature HPMC holds hydrogen-bonded water and structured water around its methyls, so leaving water costs much enthalpy; on heating it dehydrates, the enthalpy penalty and the entropy gain both shrink, and $\Delta G$ falls fastest (abstract: "likely reflecting the temperature-induced dehydration of HPMC in the aqueous phase"). C57 PVP and PVP−VA, without an LCST and less hydrophobic, show the same effect more weakly ("suggesting a lower contribution of the hydrophobic effect"). C58 At higher temperatures, where the hydrophobic effect is larger, the 40 wt % vinyl acetate of PVP−VA "likely" adds a hydrophobic contribution that raises its $\Delta H$ and $\Delta S$ above those of PVP. C54·M3

What it means for formulation, as stated by the authors. Polymer in the drug-rich phase lowers the benefit of supersaturation, but a more polymer-rich drug-rich phase "will facilitate" crystallization inhibition by suppressing drug mobility and slows coarsening of the drug-rich colloids (refs 31, 33, 95, 101); the ASD polymer "should be selected based on balancing these favorable and unfavorable effects". C60 The thermodynamics of partitioning depends on the polymer; the molecular state of the dissolved polymer and the drug–polymer compatibility in the drug-rich phase both matter. C61 Because a surfactant changed polymer partitioning before (ref 29), ionic strength, pH and other components of the gastrointestinal tract "can be assumed" to change it too. C63 The driving forces of polymer distribution are, the authors conclude, "a factor that should be considered for polymer selection for ASD formulation to maximize the attainable drug supersaturation". C65

Note by the AI writer (not discussed in the paper). The temperature reversal has a practical edge. Amorphous solubility screens are often run at room temperature; in this system HPMC looked like the most benign polymer at 15–25 °C and the most damaging at 50–55 °C, and at 35–40 °C it carried about as much polymer into the droplets as PVP−VA. A ranking of polymers by their effect on the supersaturation ceiling therefore needs to be made at body temperature. R9·R10·R17 The same polymers that lower the ceiling most also make the most polymer-rich droplets, which by the authors' own argument favours crystallization inhibition; the two goals of a formulation pull in opposite directions, and this paper measures only one of them. C60

Limitations

Limits the authors state. The measurements were made in D2O; partitioning "can change" in H2O because of isotope effects on intermolecular interactions, although the temperature trends "are expected to be similar". C62 D2O is also named as one possible reason why the measured amorphous-to-crystalline solubility ratio lies above the prediction. C37 Ionic strength, pH, surfactants and other gastrointestinal components may change partitioning and were not studied. C63 Eq 2 assumes ideal mixing, and the polymer content alone "does not completely explain" the solubility trends. C41 The interaction-based explanation of HPMC's enthalpy is offered as "at least partial rationalization". C53

The AI writer's own judgement (1): what the thermodynamic numbers rest on. The enthalpy and entropy values are derivatives of a three-constant fit to nine or ten mean points, reported without uncertainty; the mid-range values agree with simple straight-line fits, but the strong temperature trends, such as HPMC's fall from about 58 to about 12 kJ/mol, rest on the curvature term. X8 The partition coefficient uses a basis that is not written out and that, judging from the plotted values, treats the drug-rich phase as water-free IBP plus polymer at 0.99 g/cm³. X2 The transfer energies are per mole of polymer molecules whose molar masses differ several-fold (13,000 to 70,000 g/mol) at equal mass dose, so comparing their sizes between polymers mixes chemistry with chain size. X9 Finally, the "endothermic" conclusion does not hold for PVP above 50 °C. X1

The AI writer's own judgement (2): what the molecular explanation rests on. The interaction ranking that carries the explanation of HPMC's larger enthalpy comes from dry, melt-quenched ASDs with 40% polymer, while the droplets are water-saturated and hold different amounts of polymer at each temperature; neither the interactions in the wet droplets nor the water content of the droplets were measured, and HPMC dehydration on heating was not measured in these solutions either. X7·C45·C57 The 40–45 °C comparison offered for the interaction effect lies within the error bars; the equal-ratio comparison in Figure 11b supports it better. X10 Eq 2 cannot reproduce the size of the solubility loss if polymer chains are counted as molecules, so it is an argument, not a model. X3 The data cover one drug, one pH (2.0) and one polymer dose. X6 Small textual slips (the SI calls Figure S1 "Figure 5", the main text writes "ln ln K", the Figure 11 caption labels "(a)" twice) do not affect the results. X5

Conclusion

The paper turns a known observation, that ASD polymers dissolve in the drug-rich phase and lower the supersaturation ceiling, into a thermodynamic one. For ibuprofen at pH 2.0, the transfer of PVP, PVP−VA and HPMC from water into the drug-rich droplets is spontaneous, endothermic over most of 15–60 °C and driven by entropy, so more polymer enters the droplets and the amorphous solubility falls further as the temperature rises. C64·R22·R23 The polymer content of the droplets is the main determinant of the solubility loss, with stronger drug–polymer interaction adding to it. C45·C43 HPMC is the most temperature-sensitive: its transfer is the most endothermic at low temperature and becomes favourable fastest on heating, which reverses the polymer ranking between 15 and 55 °C. R10·R17·R24·C59 The molecular reasons offered for this, weaker IBP–HPMC hydrogen bonding and HPMC dehydration, are supported by dry-ASD spectra and literature rather than by measurements in the droplets. C53·C57·X7